question
stringlengths 37
38.8k
| group_id
int64 0
74.5k
| sentence_embeddings
sequencelengths 1.02k
1.02k
|
|---|---|---|
<p>I'm trying to set up the problem of deriving the thermodynamics of hadronic matter. I know how to proceed in the case of an effective description such as mean field (<a href="http://arxiv.org/abs/nucl-th/9701058" rel="nofollow">Walecka/linear sigma model</a>) but I'm trying to start from QCD. I do not wish to actually obtain the partition function, but I want to at least set up the complete problem.</p>
<p>In the mean field approximation, we usually write baryon and meson fields and baryon/meson couplings as the interactions, meaning that we also bypass the problem of describing the hadrons as QCD bound states. On the extreme oposite, I know how to proceed in the case of pure quark matter (it's just the "QCD Lagrangian").</p>
<p>How do I write the full Lagrangian? How do I represent the hadrons and the hadron-hadron strong (well, and EM) interaction without shifting to an effective approximation? Can it be done with quarks and gluons as the basic degrees of freedom?</p>
<p>I don't have any compromise with the "practical usefulness" of the result and I'm not particularly interested on the peculiarities of the dynamics of the bound states.</p> | 2,813 | [
0.015485952608287334,
-0.005819651763886213,
-0.00422756839543581,
0.0024321002420037985,
0.016273697838187218,
0.05611215904355049,
-0.02668001502752304,
-0.0016429369570687413,
-0.02412254922091961,
-0.03281335160136223,
0.027410075068473816,
-0.001394599094055593,
0.05561840161681175,
0.006696805357933044,
0.021726248785853386,
-0.03453444689512253,
-0.008643458597362041,
0.003266823012381792,
0.011911141686141491,
-0.03635026142001152,
0.029278943315148354,
0.022087667137384415,
-0.006993837188929319,
0.012433229014277458,
-0.033912576735019684,
0.01068132184445858,
-0.0021001880522817373,
0.01960085704922676,
0.0036915536038577557,
0.06519165635108948,
-0.00888968538492918,
-0.058367788791656494,
0.0436590202152729,
0.019074339419603348,
0.03599156439304352,
0.04553009569644928,
-0.04968728870153427,
-0.0031390755902975798,
-0.017024854198098183,
0.015509990975260735,
-0.09647364169359207,
-0.02871822752058506,
-0.015180069953203201,
0.016776368021965027,
-0.003618305316194892,
0.017410432919859886,
0.02802046574652195,
-0.010756516829133034,
0.05800778791308403,
-0.0710081085562706,
0.030611427500844002,
0.05573070049285889,
0.040543220937252045,
0.006846199277788401,
-0.02358441986143589,
-0.055721208453178406,
0.048788487911224365,
0.058573246002197266,
0.03373127430677414,
-0.059618301689624786,
-0.015705542638897896,
0.004750492516905069,
-0.001646153861656785,
-0.0038327521178871393,
-0.011598081327974796,
-0.014901009388267994,
0.013778407126665115,
0.00558107253164053,
0.01673373579978943,
-0.004441835451871157,
0.01503997202962637,
0.010009822435677052,
0.05854814499616623,
-0.011792860925197601,
0.03982515633106232,
0.010757473297417164,
0.015277210623025894,
-0.0021841831039637327,
0.00218280334956944,
0.029932668432593346,
-0.02132347971200943,
0.04855726286768913,
0.025399742648005486,
0.017548715695738792,
-0.004835027270019054,
-0.03322255238890648,
0.05667111277580261,
-0.01666993461549282,
-0.03113851696252823,
0.0497402660548687,
-0.013681620359420776,
-0.0036572557874023914,
0.05752655863761902,
0.01045762188732624,
-0.03737371787428856,
-0.0008769217529334128,
0.027671242132782936,
0.05391034111380577,
-0.022211506962776184,
-0.015336317010223866,
-0.025584183633327484,
-0.03156644478440285,
-0.016212983056902885,
0.08750846982002258,
-0.0022572209127247334,
-0.006980243604630232,
-0.041371554136276245,
0.004865502007305622,
0.017116667702794075,
-0.027356915175914764,
-0.01931886002421379,
-0.007349601946771145,
-0.00664858240634203,
-0.036595042794942856,
-0.021679712459445,
-0.04022304341197014,
-0.020250098779797554,
-0.049570612609386444,
0.04471215978264809,
0.08439488708972931,
0.05620955303311348,
-0.005752548109740019,
0.02737795189023018,
-0.04816516116261482,
-0.04294637590646744,
-0.011984016746282578,
0.012251638807356358,
-0.03298511356115341,
-0.004401413258165121,
0.01733805239200592,
0.010278928093612194,
-0.014219067059457302,
0.00642675394192338,
0.019681621342897415,
0.025874000042676926,
-0.05085831135511398,
-0.08453342318534851,
-0.02829235978424549,
0.028705349192023277,
-0.025178514420986176,
-0.04989391937851906,
-0.05039018765091896,
0.006916367914527655,
0.04136640578508377,
0.06489136070013046,
-0.005632455926388502,
-0.005632129032164812,
-0.019110653549432755,
0.05181969329714775,
0.01739053800702095,
-0.02820540964603424,
-0.023404560983181,
-0.010135087184607983,
-0.036305222660303116,
-0.0283134113997221,
-0.04675974324345589,
0.05030696466565132,
0.03457630053162575,
-0.012431862764060497,
0.0035560126416385174,
0.07388737797737122,
-0.01586802862584591,
-0.007247004192322493,
0.007116562221199274,
0.010143909603357315,
-0.007582442369312048,
0.06886965036392212,
-0.0031091542914509773,
0.028254374861717224,
0.0025329652708023787,
-0.0056657446548342705,
0.015864623710513115,
0.003233437892049551,
0.026217903941869736,
0.06085410341620445,
-0.025377126410603523,
-0.02787935920059681,
-0.003534400137141347,
-0.029312722384929657,
-0.011816676706075668,
-0.01429623644798994,
-0.03502491116523743,
-0.013826880604028702,
0.002829307923093438,
-0.03246317803859711,
0.014599140733480453,
0.013089231215417385,
-0.012860434129834175,
0.01593189686536789,
-0.07244838774204254,
-0.04005378857254982,
-0.08018684387207031,
0.0015922320308163762,
-0.017781531438231468,
-0.0052232262678444386,
0.042585521936416626,
0.014477492310106754,
0.01780644990503788,
0.01052639726549387,
-0.06127401441335678,
0.011316530406475067,
0.03236735239624977,
-0.008002450689673424,
0.02186296321451664,
0.015759048983454704,
0.04944460093975067,
0.061269573867321014,
-0.011964620091021061,
0.03376537561416626,
-0.042382996529340744,
-0.06541143357753754,
-0.004211188293993473,
-0.033332403749227524,
0.03677105903625488,
-0.0007562888786196709,
0.005570694804191589,
-0.032021377235651016,
-0.014179745689034462,
0.01885272189974785,
0.017722660675644875,
-0.019661081954836845,
0.08977735787630081,
0.03688156232237816,
0.004415991250425577,
-0.013591253198683262,
0.06870554387569427,
-0.00843607448041439,
0.00048166821943596005,
0.0008331549470312893,
-0.03442106023430824,
-0.03178732097148895,
-0.005317837465554476,
0.03809739276766777,
0.057157304137945175,
-0.03650073707103729,
0.005521913059055805,
0.03098185360431671,
0.013055904768407345,
0.030261265113949776,
-0.0009746295982040465,
-0.03236251696944237,
-0.019966352730989456,
0.04928934946656227,
-0.0017739174654707313,
-0.041238781064748764,
-0.024928787723183632,
0.0022358593996614218,
0.0027486977633088827,
-0.00801339652389288,
0.031230410560965538,
-0.05471047759056091,
0.0607304610311985,
-0.004496058914810419,
-0.011668099090456963,
-0.01513147447258234,
-0.05106958746910095,
0.0390031673014164,
-0.032322295010089874,
0.03580951690673828,
0.013940948061645031,
-0.017382074147462845,
0.011818144470453262,
0.000055633357987971976,
-0.01572307199239731,
-0.00431266101077199,
0.008551571518182755,
-0.0128974923864007,
0.01640244945883751,
0.018089475110173225,
-0.0423925407230854,
0.027145544067025185,
0.004062836058437824,
0.007013932801783085,
-0.02007104642689228,
0.006371987517923117,
0.01893722638487816,
0.011309296824038029,
-0.010752403177320957,
-0.017596280202269554,
-0.025024481117725372,
0.026949038729071617,
-0.0034252966288477182,
0.0012785103172063828,
0.0760878473520279,
-0.04161226376891136,
-0.01823221892118454,
-0.08182162791490555,
-0.01963292993605137,
-0.013922587968409061,
-0.02681482955813408,
0.011464069597423077,
-0.0031196139752864838,
-0.007626327686011791,
-0.04657183960080147,
-0.015009980648756027,
-0.0006438691634684801,
-0.016336670145392418,
-0.03477758914232254,
0.028290290385484695,
0.0454988107085228,
0.034530993551015854,
-0.04355741664767265,
-0.005570169538259506,
-0.03020004741847515,
-0.015818119049072266,
-0.0256979800760746,
0.004210140556097031,
-0.0002062429120996967,
-0.039468757808208466,
0.04982048273086548,
0.06295560300350189,
-0.037315431982278824,
0.0075301663018763065,
-0.05823000147938728,
-0.005183187313377857,
0.026407061144709587,
0.0233652051538229,
0.018188143149018288,
0.01081231888383627,
-0.029409335926175117,
0.0824594795703888,
0.018802450969815254,
-0.03198494389653206,
-0.005356464069336653,
-0.01836724579334259,
0.0002912934869527817,
-0.008043370209634304,
0.044499583542346954,
0.01596955396234989,
-0.043440353125333786,
0.025718510150909424,
0.007962518371641636,
0.015102677047252655,
0.008728054352104664,
0.02272074855864048,
-0.011742323637008667,
0.015455017797648907,
0.01145813800394535,
0.0025450109969824553,
0.052030958235263824,
-0.018426449969410896,
-0.01577782817184925,
0.03240872919559479,
0.009607444517314434,
0.016962457448244095,
0.03276602923870087,
-0.057565443217754364,
0.056780897080898285,
0.026288097724318504,
-0.015436695888638496,
-0.043766364455223083,
0.05242709442973137,
-0.025230348110198975,
-0.055475663393735886,
0.03163442388176918,
0.0015230041462928057,
-0.006517235655337572,
0.00490739569067955,
-0.0007002780912443995,
0.022986337542533875,
0.05210251361131668,
-0.023936305195093155,
-0.04295571520924568,
-0.03519781306385994,
-0.026322580873966217,
0.005684110336005688,
-0.021616626530885696,
0.015968021005392075,
0.03187248483300209,
0.0325288325548172,
0.018594173714518547,
-0.02440144307911396,
-0.03296426311135292,
-0.0005145347095094621,
-0.08420227468013763,
-0.00353909726254642,
0.007608948741108179,
0.05324999615550041,
0.014052631333470345,
0.05435767024755478,
0.009758947417140007,
0.007718282286077738,
0.019498860463500023,
0.005257523152977228,
-0.07508336007595062,
0.005543145351111889,
-0.01641853153705597,
0.01289245393127203,
-0.02369876019656658,
-0.007428223732858896,
0.012815630994737148,
-0.010641101747751236,
-0.045130655169487,
-0.03147570416331291,
-0.010185666382312775,
-0.023833923041820526,
-0.005119833163917065,
-0.06800252199172974,
-0.04559028521180153,
-0.029317384585738182,
0.042618829756975174,
0.058726005256175995,
-0.02437073364853859,
0.015716196969151497,
0.010883999988436699,
-0.061569694429636,
-0.03448307514190674,
-0.00416894257068634,
0.02764754369854927,
0.010374076664447784,
0.06154850125312805,
0.011729166842997074,
0.022374439984560013,
-0.028139479458332062,
0.0009053645189851522,
0.062296636402606964,
0.05822844058275223,
-0.00009762522677192464,
-0.0040649003349244595,
0.03273281082510948,
-0.04111188277602196,
-0.015869181603193283,
0.02203178033232689,
0.027379773557186127,
0.0017561479471623898,
0.004186216741800308,
0.039720382541418076,
0.008590835146605968,
-0.04112950712442398,
0.03196444734930992,
0.050377555191516876,
0.014667547307908535,
-0.010320067405700684,
-0.041942719370126724,
-0.00801401399075985,
-0.00686412351205945,
0.008161624893546104,
-0.01571883074939251,
-0.017188958823680878,
0.005738349165767431,
0.026615090668201447,
-0.008560586720705032,
0.01632564514875412,
-0.033826470375061035,
-0.029685797169804573,
0.006445732433348894,
0.04573426395654678,
-0.009845336899161339,
0.01822006329894066,
0.02047806605696678,
0.07062046974897385,
0.01699710823595524,
0.008587482385337353,
0.02928886003792286,
-0.0446498766541481,
-0.026275549083948135,
0.04183081537485123,
0.0624457523226738,
0.04569382220506668,
0.007293956819921732,
-0.05922932177782059,
0.0026328261010348797,
0.063422292470932,
-0.01708322763442993,
0.017748046666383743,
0.004054277669638395,
-0.01162010245025158,
0.012696437537670135,
-0.030660998076200485,
-0.030507486313581467,
0.03175908327102661,
-0.012739140540361404,
0.00963334459811449,
-0.04167807474732399,
-0.025777118280529976,
-0.02726755663752556,
0.027802275493741035,
0.004392860922962427,
0.05020966753363609,
0.015491869300603867,
0.024061627686023712,
0.0213079322129488,
0.012791399843990803,
-0.017820915207266808,
-0.0866798609495163,
-0.020172446966171265,
-0.007467691786587238,
0.04048740491271019,
0.03585394471883774,
-0.039291609078645706,
-0.032255787402391434,
-0.0023607234470546246,
-0.001402714871801436,
-0.015595359727740288,
-0.010420229285955429,
-0.05113232135772705,
0.07485338300466537,
0.022737884894013405,
-0.005810149013996124,
0.0542253702878952,
0.024233659729361534,
-0.0008741905330680311,
0.0026080249808728695,
-0.03155328333377838,
0.019331324845552444,
-0.011995828710496426,
0.014080017805099487,
-0.06110742315649986,
-0.007104218006134033,
-0.022118162363767624,
0.027570415288209915,
-0.05231516435742378,
0.02460809424519539,
0.0011980743147432804,
-0.050644244998693466,
-0.03622599318623543,
0.011184371076524258,
0.011030944064259529,
-0.017213482409715652,
0.015647435560822487,
0.02730570174753666,
0.016388103365898132,
-0.003572845831513405,
0.00370990508235991,
-0.015128846280276775,
0.0020066688302904367,
0.0042812032625079155,
-0.04049147292971611,
0.024291478097438812,
-0.005373350810259581,
-0.016604430973529816,
0.0032488834112882614,
-0.03439603000879288,
0.03822793811559677,
-0.039264366030693054,
0.009434843435883522,
0.03493010252714157,
-0.047396332025527954,
-0.01773674786090851,
-0.0006361967534758151,
-0.026164183393120766,
0.024510474875569344,
-0.022132981568574905,
0.0071611786261200905,
-0.00815264880657196,
0.0037909261882305145,
-0.10245921462774277,
-0.04597270488739014,
-0.009832155890762806,
-0.013758250512182713,
-0.04343256726861,
-0.038348741829395294,
0.009728495962917805,
-0.023176196962594986,
-0.01938582770526409,
0.0031993063166737556,
0.04261383041739464,
-0.041110653430223465,
0.0032003039959818125,
-0.000343511434039101,
0.044562000781297684,
0.0448179729282856,
-0.010040228255093098,
-0.012943259440362453,
0.005945251323282719,
-0.0002475946384947747,
0.01174517534673214,
0.01920272968709469,
0.02207144722342491,
-0.011398506350815296,
-0.016873281449079514,
-0.0006483573233708739,
0.01938256248831749,
0.01801876723766327,
0.0035855602473020554,
-0.007452886551618576,
0.03294527158141136,
0.029125692322850227,
0.009287334978580475,
-0.015986254438757896,
-0.004619439598172903,
0.0013716832036152482,
0.019402550533413887,
-0.024173876270651817,
-0.0075490036979317665,
-0.010862997733056545,
-0.03141248598694801,
0.05504989996552467,
-0.02145281434059143,
0.01394970715045929,
-0.001206090091727674,
0.041978683322668076,
0.017813468351960182,
-0.02426648698747158,
0.04515177384018898,
-0.006914640311151743,
0.0023756730370223522,
-0.0045908731408417225,
0.007221255451440811,
0.013921824283897877,
0.004996157716959715,
-0.02944227308034897,
-0.02949918806552887,
-0.04207144305109978,
0.0018624162767082453,
0.039938122034072876,
0.020612796768546104,
0.00745630357414484,
-0.012062841095030308,
0.0011498206295073032,
0.010757862590253353,
-0.008850064128637314,
-0.04664810001850128,
0.010172919370234013,
0.003870135173201561,
0.03820573538541794,
-0.013332990929484367,
0.005238699726760387,
0.014521506614983082,
0.04718698561191559,
-0.06999243050813675,
0.020669255405664444,
0.046755868941545486,
-0.012058259919285774,
0.024067718535661697,
-0.009856327436864376,
-0.029709195718169212,
0.03017806075513363,
-0.037220992147922516,
0.02678050473332405,
-0.011008201166987419,
-0.012400617823004723,
0.02822251431643963,
0.004309597425162792,
0.05596205219626427,
-0.021649962291121483,
-0.028999287635087967,
-0.004076017532497644,
0.03472820669412613,
0.044545769691467285,
0.01739773526787758,
0.05788043513894081,
0.005709491204470396,
0.056634098291397095,
0.00907195545732975,
-0.00995883159339428,
0.032904140651226044,
-0.03722047060728073,
-0.021948209032416344,
-0.024675000458955765,
-0.06703442335128784,
0.03877457231283188,
-0.03652568906545639,
-0.03337651118636131,
0.027004361152648926,
-0.009425880387425423,
-0.007799259852617979,
-0.0039045291487127542,
0.017575765028595924,
-0.008757106028497219,
0.07368098944425583,
-0.011450903490185738,
0.025639671832323074,
-0.02055368386209011,
0.0035346047952771187,
0.1121661365032196,
0.04102613404393196,
0.03275877982378006,
-0.07662956416606903,
0.03607315570116043,
-0.0020494344644248486,
0.02620837837457657,
-0.026261601597070694,
0.02704893797636032,
0.0009372399654239416,
-0.012534840032458305,
0.010462933219969273,
0.06690720468759537,
-0.007559579331427813,
0.005809593014419079,
0.03715311735868454,
-0.028705323114991188,
-0.04445603862404823,
0.007593856193125248,
0.0004974004696123302,
-0.029452383518218994,
-0.005698338150978088,
-0.029079409316182137,
0.00544712133705616,
0.016473885625600815,
0.02764793671667576,
-0.024522405117750168,
-0.06105761602520943,
0.012381295673549175,
-0.01804744265973568,
-0.033890459686517715,
0.00613566255196929,
-0.009145714342594147,
0.007536680903285742,
-0.020434826612472534,
-0.01240737084299326,
0.018208416178822517,
-0.02985091134905815,
0.025510553270578384,
0.019161811098456383,
-0.012899925000965595,
-0.006374060176312923,
0.006077897734940052,
-0.0018190272385254502,
-0.014933072961866856,
-0.03602080047130585,
-0.017763400450348854,
0.08341836929321289,
-0.02762998268008232,
-0.035226769745349884,
0.04594551399350166,
0.004409487824887037,
0.038952961564064026,
-0.018956242129206657,
0.029441891238093376,
-0.008558220230042934,
0.027719607576727867,
-0.028493965044617653,
-0.0012546528596431017,
0.006966766435652971,
0.05364815890789032,
-0.0353928841650486,
-0.002805739641189575,
-0.003003645921126008,
0.01568344049155712,
-0.0043168459087610245,
-0.018579013645648956,
0.029975762590765953,
0.01567002199590206,
-0.017830293625593185,
-0.02439671754837036,
0.012140619568526745,
-0.05659719929099083,
-0.02360413782298565,
0.01114505436271429,
-0.005442117340862751,
0.03704114258289337,
0.012482923455536366,
0.0030651597771793604,
-0.03658388555049896,
-0.08433502912521362,
0.03464718908071518,
-0.04812128469347954,
-0.0376025028526783,
-0.031900689005851746,
-0.019053904339671135,
0.015458513982594013,
0.08496591448783875,
0.011115184053778648,
-0.015058135613799095,
0.0017492222832515836,
0.0601450577378273,
0.018480680882930756,
-0.030118606984615326,
-0.015967965126037598,
-0.0029085574205964804,
-0.05197115242481232,
-0.0005373349413275719,
0.00048115383833646774,
0.03912603110074997,
0.02471937984228134,
0.024764714762568474,
0.011304945684969425,
0.014988569542765617,
0.004647641908377409,
0.013372257351875305,
0.009689722210168839,
-0.017763981595635414,
-0.0048091295175254345,
0.001714838668704033,
-0.0010228116298094392,
-0.02242058701813221,
-0.031857408583164215,
-0.027778854593634605,
-0.016134845092892647,
-0.010602976195514202,
-0.008002102375030518,
-0.01736099272966385,
0.026489516720175743,
-0.008029631339013577,
-0.0067945984192192554,
-0.02245132252573967,
0.0006021966109983623,
-0.04775300994515419,
0.010951208882033825,
-0.02439716085791588,
0.009092239663004875,
-0.035274192690849304,
0.014185142703354359,
-0.024052541702985764,
-0.013004877604544163,
0.030613353475928307,
0.020113300532102585,
-0.032264262437820435,
-0.013639316894114017,
0.0059171696193516254,
0.00950630009174347,
0.03727974742650986,
-0.009512001648545265,
-0.02904427796602249,
0.02913854457437992,
-0.04237489402294159,
-0.06420530378818512,
0.009062252007424831,
0.016927426680922508,
0.025720633566379547,
0.042300913482904434,
-0.004923608154058456,
-0.03752262145280838,
0.042284563183784485,
0.0034922179765999317,
0.00008622060704510659,
-0.014437967911362648,
-0.04567395895719528,
0.008458273485302925,
-0.012793883681297302,
0.028774775564670563,
0.019325269386172295,
-0.0028690285980701447,
0.011458130553364754,
0.022138189524412155,
-0.001860098447650671,
0.021593259647488594,
-0.01897892914712429,
-0.00475495308637619,
0.03999301418662071,
0.011948664672672749,
0.02288210764527321,
-0.007760710082948208,
0.03292051702737808,
-0.021858399733901024,
0.0037052880506962538,
0.005662539508193731,
0.040363796055316925,
-0.09833594411611557,
-0.004728745669126511,
-0.00284011522307992,
-0.011137777008116245,
0.07787308841943741,
-0.06648764759302139,
0.01369098387658596,
0.017362311482429504,
-0.02530130371451378,
0.020689310505986214,
-0.020135929808020592,
0.0005861753015778959,
-0.017658349126577377,
0.002650930779054761,
-0.04209180921316147,
0.0712473914027214,
0.03613419458270073,
0.03651408478617668,
0.02267380803823471,
0.021730858832597733,
-0.0016631577163934708,
-0.017094185575842857,
0.002305590780451894,
0.0055371602065861225,
0.02496608905494213,
-0.009538701735436916,
0.10365691035985947,
-0.00866915937513113,
-0.06256481260061264,
0.01567183807492256,
-0.012120276689529419,
-0.017192022874951363,
-0.02748916856944561,
-0.0005158176063559949,
-0.03240589052438736,
0.04331538453698158,
0.027874570339918137,
-0.001646338845603168,
0.03403543680906296,
0.0029873428866267204,
0.013421068899333477,
0.019009295850992203,
-0.04113680496811867,
0.014252416789531708,
0.028900103643536568,
-0.016750585287809372,
-0.05412207543849945,
0.06290090084075928,
-0.00007220662519102916,
-0.0014251492684707046,
-0.0047546979039907455,
-0.014517021365463734,
0.017752207815647125,
-0.013048761524260044,
0.0011297367746010423,
-0.025674909353256226,
0.03582523390650749,
0.04611499607563019,
0.035158947110176086,
-0.026608962565660477,
0.05223986133933067,
0.012767676264047623,
0.002739636693149805,
-0.014647585339844227,
0.002252648351714015,
-0.02451164647936821,
-0.026093553751707077,
-0.02517620101571083,
-0.006544400472193956,
0.023998260498046875,
-0.04169917479157448,
-0.045427773147821426,
-0.04199536144733429,
0.0009927774081006646,
-0.002900918712839484,
0.05044591426849365,
-0.02851526066660881,
-0.03861770033836365,
0.01612917333841324,
-0.04307357221841812,
0.008999982848763466,
0.011385483667254448,
0.02884802781045437,
0.0020493960473686457,
-0.0064450898207724094,
0.00047251262003555894,
0.0007901937351562083,
0.038615964353084564,
0.002866350347176194,
-0.030504873022437096,
0.013772236183285713,
-0.01063873153179884,
0.010534554719924927,
0.012167409993708134,
-0.02724205143749714,
-0.04651660844683647,
0.0037965443916618824,
0.002080286154523492,
-0.006707257125526667,
-0.03314264863729477,
0.017571095377206802,
0.02851393260061741,
-0.009818349033594131,
-0.02071339264512062,
0.01448400691151619,
-0.07573651522397995,
0.08170530945062637,
0.0018743538530543447,
-0.0055745444260537624,
0.06356081366539001,
-0.02205522544682026,
0.01662602834403515,
0.06002020835876465,
-0.06092086434364319,
-0.030095327645540237,
0.010694622993469238,
-0.03269454091787338,
-0.023424217477440834,
-0.012931757606565952,
-0.008016189560294151,
0.014333309605717659,
-0.06655675172805786,
0.024445228278636932,
0.047521356493234634,
-0.016274891793727875,
-0.02048364281654358,
0.04137125983834267,
0.042893603444099426,
0.047783300280570984,
0.019974341616034508,
-0.0006844465970061719,
0.007426918484270573,
0.011453102342784405,
0.017043370753526688,
0.04509623721241951,
0.048929356038570404,
0.04542330279946327,
0.022593803703784943,
0.03482350707054138,
-0.03168025612831116,
0.0014759076293557882,
0.013970529660582542,
0.02281199023127556,
-0.03949228301644325,
-0.0044152685441076756,
0.038262464106082916,
-0.02433646284043789,
0.027295280247926712,
0.008603227324783802,
-0.041225649416446686,
0.10357335209846497,
-0.06258543580770493,
-0.009106120094656944,
-0.05007699877023697,
-0.009139010682702065,
-0.015611507929861546,
0.01937946304678917,
0.00627706665545702,
0.06735651940107346,
-0.013555456884205341,
0.010554006323218346,
-0.0035147699527442455,
0.00007956346962600946,
0.025765832513570786,
-0.023648446425795555,
-0.027313167229294777,
-0.006079436745494604,
0.0037411849480122328,
-0.026657024398446083,
-0.013895508833229542,
-0.0072756120935082436,
-0.0027855245862156153,
0.02728131227195263,
0.0560990646481514,
0.017309069633483887,
0.01006426103413105,
-0.013175238855183125,
-0.026999641209840775,
0.054367344826459885,
-0.03645884618163109,
-0.016784632578492165,
-0.04520276561379433,
0.0052038333378732204,
-0.03534513711929321,
-0.007322235498577356
] |
<blockquote>
<p><strong>Question:</strong>
A police boat is chasing a boat with criminals along a straight river
by moving against the stream. The speed of the river stream is 3 miles
per hour, the speed of the boat with criminals relative to the river
is 30 miles per hour, and the police boat is 4 miles per hour faster
than the boat with criminals. </p>
<p>Currently the criminals are ahead of the police, and horizontally
throw a stone at the police boat at a speed 16 miles per hour relative
to their boat (i.e. relative to the boat of criminals).</p>
<p>What is the horizontal velocity of the stone relative to the police
boat and to the river bank? You need to state what the origin and the
positive direction of motion are.</p>
</blockquote>
<p>Choose the direction of the river stream to be the positive direction and choose the origin to be in front of criminals' boat.</p>
<p>Denote the velocity of the river stream by $\dot{x}_R$
Denote the velocity of the police boat by $\dot{x}_P$
Denote the velocity of the criminal boat by $\dot{x}_C$.
Denote the velocity of the stone thrown by $\dot{x}_S$.</p>
<p>From the question we have that $\dot{x}_R = 3$, and we also have that the velocity of the criminal boat relative to the river stream is
\begin{align*}
\dot{x}_C - \dot{x}_R &= -30 \\
\implies \dot{x}_C - 3 &= -30 \\
\implies \dot{x}_C &= -27
\end{align*}
Note that the minus 30 is because from the point of view of the river, the criminal boat is travelling in the negative direction.</p>
<p>Now from $\dot{x}_C$ I can calculate $\dot{x}_P$, since
\begin{align*}
\dot{x}_P &= \dot{x}_C + (-4) \\
&= -27 - 4 \\
&= -31
\end{align*}</p>
<p>Note that the minus 4 is because the police boat is 4 mph faster, but in the negative direction.</p>
<p>Also from $\dot{x}_C$ I can calculate $\dot{x}_S$. From the question we have that
\begin{align*}
\dot{x}_S - \dot{x}_C &= 16 \\
\implies \dot{x}_S - (-27) &= 16 \\
\implies \dot{x}_S &= -11
\end{align*}</p>
<p>I was wondering if my solution was right, even though $\dot{x}_S = -11$ is negative, even though it moves in the positive direction.</p> | 2,814 | [
-0.044714249670505524,
0.008463907986879349,
-0.006221947725862265,
0.0027809967286884785,
0.0733453556895256,
-0.03537754714488983,
-0.011776918545365334,
0.015617571771144867,
0.004619827028363943,
0.046938128769397736,
-0.0011927917366847396,
0.06790215522050858,
0.02745491825044155,
0.0305426474660635,
0.06298646330833435,
0.0366959385573864,
0.013843484222888947,
-0.012602536007761955,
0.03493886440992355,
0.0031852112151682377,
-0.0057431855238974094,
-0.024928689002990723,
0.0349731408059597,
0.014545444399118423,
0.0235112514346838,
-0.02308472990989685,
0.03309321776032448,
-0.029927222058176994,
-0.03197396546602249,
0.05733528733253479,
0.03974740952253342,
-0.018008975312113762,
0.01372393686324358,
0.006356794852763414,
0.01403947826474905,
0.0925588309764862,
-0.019807778298854828,
-0.02793099358677864,
-0.016057882457971573,
0.0371960811316967,
-0.01849670708179474,
-0.010666338726878166,
0.022215835750102997,
0.055470097810029984,
-0.03861350193619728,
0.0309213325381279,
0.007040028925985098,
-0.013710311613976955,
0.015257309190928936,
-0.006589410826563835,
0.07658891379833221,
-0.03595036268234253,
0.013182612136006355,
-0.030960502102971077,
-0.023361215367913246,
-0.033114850521087646,
0.055407918989658356,
0.06692132353782654,
0.004189800005406141,
-0.017637666314840317,
0.03275970742106438,
-0.020477786660194397,
-0.01730039156973362,
-0.041717611253261566,
-0.04601157829165459,
-0.03071442060172558,
0.009596777148544788,
-0.023447226732969284,
0.022883707657456398,
-0.012082605622708797,
-0.006009889766573906,
-0.00723806768655777,
-0.01419072411954403,
0.0032583712600171566,
0.012181048281490803,
-0.058723244816064835,
0.003536612493917346,
0.053967785090208054,
-0.011433308012783527,
0.01860514096915722,
-0.01361802313476801,
-0.007214375305920839,
0.012856046669185162,
0.04362741485238075,
0.026765478774905205,
-0.02205812744796276,
0.05449632182717323,
0.0318632498383522,
0.026629434898495674,
-0.00005819084617542103,
0.036181218922138214,
-0.006774059496819973,
-0.013696671463549137,
-0.0029099546372890472,
0.010806502774357796,
0.019671669229865074,
-0.02347797155380249,
-0.0013878113823011518,
0.05816497653722763,
-0.013069113716483116,
-0.03889818117022514,
-0.046220291405916214,
0.021627439185976982,
0.06460727006196976,
0.022404061630368233,
0.00037803768645972013,
0.00011070226173615083,
0.017251765355467796,
-0.028167972341179848,
-0.03526589274406433,
-0.02623351290822029,
0.03423494100570679,
0.0074701146222651005,
0.00990399532020092,
-0.03498225286602974,
-0.0006465616170316935,
0.01838529296219349,
-0.002232759492471814,
0.043755870312452316,
-0.00037749295006506145,
0.04380802810192108,
-0.037127330899238586,
-0.0146099254488945,
-0.05051537603139877,
-0.04384971037507057,
0.02074744924902916,
-0.005784998647868633,
-0.029980510473251343,
0.015830885618925095,
0.04123907536268234,
0.025504907593131065,
0.00014437759818974882,
-0.04153112322092056,
0.041825756430625916,
0.0074490951374173164,
-0.005419569090008736,
-0.12010331451892853,
-0.06704604625701904,
0.05833938717842102,
0.03464239090681076,
0.02474561147391796,
-0.07661424577236176,
-0.020118853077292442,
0.007828600704669952,
0.06030585616827011,
-0.017446009442210197,
-0.03295464068651199,
0.05181821808218956,
0.01445789448916912,
-0.02268623746931553,
0.011792425997555256,
0.0296956617385149,
-0.02879892662167549,
-0.014241108670830727,
-0.0034092660062015057,
-0.052123598754405975,
-0.02253500372171402,
-0.005557124502956867,
0.0022526427637785673,
-0.035785477608442307,
0.03477119281888008,
-0.006927143782377243,
0.0014570566127076745,
0.02032032236456871,
-0.020638931542634964,
-0.02254357747733593,
0.05044052377343178,
0.030172158032655716,
-0.06073217839002609,
-0.02764734998345375,
0.012666593305766582,
0.015462754294276237,
-0.016816480085253716,
0.003260079538449645,
0.07731086015701294,
-0.03755654767155647,
0.0028394979890435934,
0.012964013032615185,
-0.014400254935026169,
0.0021360141690820456,
-0.03844103217124939,
-0.03821152448654175,
-0.027909869328141212,
-0.020613742992281914,
0.047420889139175415,
0.0520225390791893,
-0.01628636009991169,
0.047573089599609375,
-0.0009065798949450254,
-0.04638630896806717,
0.04456276446580887,
-0.04779858887195587,
0.054666806012392044,
0.03077215701341629,
-0.02156933769583702,
0.008984400890767574,
-0.01464188564568758,
0.0025398489087820053,
-0.015497352927923203,
-0.014714383520185947,
0.017208853736519814,
0.026379380375146866,
0.02087724581360817,
-0.004718281328678131,
0.02947590872645378,
0.026448003947734833,
0.030603645369410515,
-0.00564388046041131,
0.005326880142092705,
0.002386074047535658,
0.015269160270690918,
0.01927967555820942,
0.003044363111257553,
0.007016403134912252,
0.005357665941119194,
0.011891912668943405,
0.005103593226522207,
0.02074461616575718,
0.010960213840007782,
-0.011075181886553764,
-0.04918926954269409,
0.041963450610637665,
0.0521165169775486,
-0.002318969462066889,
-0.01091186422854662,
0.013117197901010513,
-0.007061236537992954,
0.050489094108343124,
0.03236410766839981,
-0.020511170849204063,
-0.03650236874818802,
-0.009422087110579014,
-0.030485685914754868,
0.01928805373609066,
-0.054714687168598175,
0.028863981366157532,
0.03252117708325386,
0.016201427206397057,
-0.00031938671600073576,
0.03593416139483452,
-0.012166745960712433,
-0.03405778482556343,
0.03549770638346672,
0.03900416940450668,
-0.019409026950597763,
-0.013494705781340599,
0.01758686453104019,
0.010611646808683872,
-0.029936568811535835,
-0.00034103720099665225,
-0.04739050567150116,
0.01976470835506916,
0.018765978515148163,
0.017935944721102715,
-0.02176876738667488,
-0.02589239366352558,
0.03386814147233963,
0.0065277693793177605,
-0.004782756790518761,
0.04846368357539177,
-0.019212087616324425,
0.05908699333667755,
-0.004218604415655136,
0.0230158232152462,
-0.017587486654520035,
0.03543979302048683,
0.0005921059055253863,
0.02148832380771637,
0.029001595452427864,
-0.0382080115377903,
-0.006293861195445061,
-0.046665459871292114,
-0.03718561679124832,
-0.033566780388355255,
-0.013721373863518238,
0.043950051069259644,
0.03661210089921951,
0.013214625418186188,
-0.003783419029787183,
0.0418679416179657,
-0.0130662452429533,
0.01673530600965023,
-0.008643576875329018,
0.04717271775007248,
-0.030973881483078003,
0.026089124381542206,
-0.0322023443877697,
-0.056906502693891525,
0.017834952101111412,
0.029978662729263306,
-0.03803432732820511,
0.03746243193745613,
0.0063678063452243805,
-0.015629764646291733,
0.010858063586056232,
-0.031124766916036606,
0.0009847069159150124,
-0.06769882142543793,
0.0050224680453538895,
0.027680937200784683,
0.024999191984534264,
-0.012813813053071499,
0.0028140342328697443,
-0.032400619238615036,
-0.0429324246942997,
-0.0095567237585783,
-0.004279773682355881,
-0.003890560008585453,
0.009928334504365921,
0.006429324392229319,
-0.015869418159127235,
0.0034441000316292048,
-0.009878590703010559,
-0.07451597601175308,
-0.023514792323112488,
-0.00022006992367096245,
0.021070456132292747,
0.06168803200125694,
-0.01686510071158409,
-0.01434291061013937,
0.05712278187274933,
0.034615132957696915,
-0.021065834909677505,
-0.009616201743483543,
-0.014283622615039349,
-0.050722185522317886,
-0.044115081429481506,
0.0032579998951405287,
0.07036476582288742,
-0.016039464622735977,
0.004303047899156809,
-0.022781474515795708,
0.08050765842199326,
0.051207855343818665,
-0.034524306654930115,
0.02868572622537613,
0.03224809095263481,
-0.017820239067077637,
0.014605099335312843,
0.050555530935525894,
0.029453033581376076,
-0.036913417279720306,
-0.0004090198199264705,
-0.0015420261770486832,
0.059911202639341354,
0.010961498133838177,
-0.03251604363322258,
0.02989761345088482,
0.004995031747967005,
-0.0018412955105304718,
0.007879230193793774,
0.046673670411109924,
0.012027527205646038,
-0.02004489302635193,
-0.015847528353333473,
-0.015334642492234707,
0.026883810758590698,
-0.003150251228362322,
0.02205011062324047,
0.01733238250017166,
0.061567533761262894,
-0.010788966901600361,
-0.05261102691292763,
-0.00793915893882513,
-0.02988576889038086,
0.05153965950012207,
-0.0056212907657027245,
0.02412925846874714,
0.011153891682624817,
0.030177030712366104,
-0.025006646290421486,
0.010643844492733479,
0.004222480114549398,
0.0013196902582421899,
-0.07662981003522873,
0.0170363187789917,
-0.006678872741758823,
0.017588403075933456,
0.013064644299447536,
0.027186190709471703,
0.010391819290816784,
0.009273681789636612,
-0.014746488071978092,
0.026479138061404228,
-0.05854886397719383,
0.009076026268303394,
-0.010708281770348549,
-0.0016086235409602523,
-0.018450580537319183,
-0.04491038993000984,
0.030709048733115196,
-0.05187153071165085,
-0.000812297745142132,
0.012142300605773926,
-0.06217731535434723,
-0.0476720817387104,
0.04522576928138733,
0.005775816738605499,
-0.028918985277414322,
0.006931881885975599,
-0.001873064087703824,
0.036284033209085464,
-0.04182421416044235,
0.07773587852716446,
0.023927802219986916,
-0.002244585892185569,
0.009344353340566158,
-0.03436262160539627,
-0.00024133488477673382,
0.05920207127928734,
0.020270919427275658,
-0.008988473564386368,
0.015132193453609943,
-0.0006248141871765256,
-0.0007272627553902566,
-0.01975812017917633,
0.019835224375128746,
-0.004835634957998991,
-0.02428685873746872,
-0.010071942582726479,
-0.026537654921412468,
0.028640707954764366,
-0.001602361211553216,
0.03168787807226181,
-0.006165195722132921,
0.002109319670125842,
0.04750371724367142,
0.015415736474096775,
-0.000005357748705137055,
0.05564966797828674,
0.030294641852378845,
0.03323453664779663,
0.023478448390960693,
-0.03889041021466255,
0.008358788676559925,
-0.011333095841109753,
-0.0283989105373621,
0.015053114853799343,
-0.029937557876110077,
0.0007568923756480217,
-0.013357254676520824,
0.0649789497256279,
0.03439635783433914,
-0.043249160051345825,
0.05128389969468117,
-0.03416761755943298,
0.01279893983155489,
-0.02975803054869175,
0.013179512694478035,
-0.012776256538927555,
0.030913466587662697,
0.009351525455713272,
-0.0283285453915596,
-0.04035084694623947,
-0.042715176939964294,
-0.020906776189804077,
-0.008563099429011345,
0.058256957679986954,
-0.02782229706645012,
-0.03129191696643829,
-0.053334254771471024,
-0.00862973928451538,
0.005870030261576176,
-0.0023230346851050854,
0.026808833703398705,
-0.016577837988734245,
-0.032164618372917175,
-0.017762813717126846,
-0.07484869658946991,
-0.06614600121974945,
-0.012610591016709805,
-0.033911678940057755,
0.007467573508620262,
-0.02086205966770649,
0.010254012420773506,
-0.00004188893944956362,
0.02702677994966507,
0.08106540143489838,
0.015098747797310352,
-0.028472311794757843,
-0.008218759670853615,
-0.013960110954940319,
0.04796440526843071,
-0.01763893850147724,
-0.07552890479564667,
0.052613258361816406,
0.01088382862508297,
-0.007609076797962189,
0.006966658867895603,
-0.03554137423634529,
-0.02291678451001644,
0.02659209445118904,
-0.0269792340695858,
-0.03842306137084961,
0.019948778674006462,
-0.06416253745555878,
-0.0068748267367482185,
0.009551373310387135,
-0.03020336665213108,
0.03190087527036667,
0.03858565166592598,
-0.051807910203933716,
-0.03846539184451103,
-0.008655702695250511,
-0.034382645040750504,
-0.026288695633411407,
-0.04284689202904701,
-0.043583665043115616,
0.00011654346599243581,
-0.006303074769675732,
0.0186812374740839,
-0.016510862857103348,
0.02247844822704792,
-0.02146272547543049,
-0.008659938350319862,
-0.009677376598119736,
-0.006331937853246927,
-0.0070476168766617775,
0.031552620232105255,
-0.013435523957014084,
-0.037820879369974136,
0.018348755314946175,
-0.015594509430229664,
0.0016327365301549435,
-0.02684493362903595,
0.05816929414868355,
0.02666633576154709,
-0.008872773498296738,
-0.008409619331359863,
-0.04027017205953598,
-0.011048729531466961,
-0.021451767534017563,
-0.06035332754254341,
0.04568777233362198,
0.021623117849230766,
-0.021009182557463646,
0.020037095993757248,
-0.01252980437129736,
-0.030807361006736755,
0.013731974177062511,
0.04897340387105942,
-0.02423640340566635,
-0.04846369847655296,
0.019557639956474304,
0.042950645089149475,
0.02448950707912445,
-0.04314226657152176,
-0.04677863046526909,
0.010691612958908081,
-0.012370758689939976,
-0.03139949589967728,
0.00808249693363905,
0.001503969426266849,
0.017643965780735016,
-0.030733628198504448,
-0.010578624904155731,
0.036825843155384064,
-0.01028530765324831,
-0.021997572854161263,
-0.0006751636974513531,
-0.006049875169992447,
0.04095611348748207,
-0.015637923032045364,
0.012339078821241856,
0.038881126791238785,
-0.029417576268315315,
-0.022349508479237556,
-0.020661458373069763,
0.05052100867033005,
-0.0006612076540477574,
-0.012915759347379208,
0.012137336656451225,
0.013680579140782356,
0.010197820141911507,
-0.006031234283000231,
0.002432586858049035,
-0.03521539270877838,
0.009869839064776897,
-0.039867617189884186,
0.0012895403197035193,
-0.014083590358495712,
0.03258005529642105,
0.01171545498073101,
-0.0011812536977231503,
0.01288643665611744,
-0.05877634510397911,
-0.054625362157821655,
-0.0032753238920122385,
-0.034873805940151215,
-0.0400509238243103,
-0.017244460061192513,
0.057508595287799835,
-0.009052690118551254,
0.007368429098278284,
0.013154190964996815,
0.036078330129384995,
0.040891557931900024,
-0.014232070185244083,
-0.0005782717489637434,
0.015722334384918213,
0.029445717111229897,
0.027660537511110306,
-0.022040070965886116,
-0.06539655476808548,
0.06402713060379028,
0.07502599060535431,
0.008286652155220509,
0.08657699078321457,
0.020060405135154724,
0.01666564680635929,
0.0029984444845467806,
-0.011992362327873707,
-0.025222184136509895,
-0.00848222803324461,
-0.0007923360681161284,
0.061780400574207306,
-0.05836400017142296,
0.0023746853694319725,
0.036174461245536804,
0.019711051136255264,
-0.005151469726115465,
-0.028764041140675545,
0.03304804861545563,
-0.031079215928912163,
-0.0050041857175529,
-0.02293197065591812,
-0.026645801961421967,
0.002412826521322131,
-0.03683726117014885,
0.03764701634645462,
0.015791073441505432,
-0.037418462336063385,
0.03535770624876022,
0.04187196493148804,
-0.025621764361858368,
-0.051738839596509933,
-0.0056220050901174545,
-0.030042489990592003,
-0.011100202798843384,
-0.011535411700606346,
0.006199070252478123,
-0.03720825910568237,
0.012637367472052574,
0.037196893244981766,
-0.014873032458126545,
0.06190819293260574,
-0.038088757544755936,
-0.058273833245038986,
0.00768679566681385,
-0.03194556385278702,
-0.021872974932193756,
0.03661829233169556,
0.02199503406882286,
0.007697184570133686,
0.017550654709339142,
-0.01574578508734703,
0.039274416863918304,
0.020127855241298676,
0.011274630203843117,
-0.023588355630636215,
0.09111163020133972,
-0.038612037897109985,
0.035931363701820374,
-0.015602678060531616,
-0.01915845088660717,
0.13720719516277313,
0.008593728765845299,
0.004764843266457319,
-0.033401407301425934,
0.018640870228409767,
-0.014303342439234257,
0.022978119552135468,
-0.004669151734560728,
0.004537749569863081,
0.04171371087431908,
0.0010875072330236435,
-0.03522069379687309,
0.027795618399977684,
-0.012637932784855366,
-0.029351934790611267,
0.030490264296531677,
-0.06420654058456421,
-0.04976809769868851,
-0.005897365976125002,
0.02486623451113701,
-0.004104305524379015,
0.01778736151754856,
0.013081202283501625,
0.019500786438584328,
-0.04418376833200455,
0.004251526203006506,
-0.04631772264838219,
-0.016445869579911232,
0.028834151104092598,
-0.014977785758674145,
-0.04554162546992302,
0.004813229665160179,
-0.0004837981250602752,
-0.04998372867703438,
-0.048145592212677,
0.01609158329665661,
0.016278380528092384,
-0.038796111941337585,
0.001968623837456107,
0.04261419549584389,
-0.010828877799212933,
0.03906533122062683,
0.0014356347965076566,
0.009311417117714882,
-0.04953949153423309,
-0.004994615446776152,
-0.08201397955417633,
0.018842484802007675,
-0.01394098810851574,
0.022926637902855873,
-0.036858052015304565,
0.035189807415008545,
0.011509747244417667,
-0.07950196415185928,
0.007987753488123417,
-0.0037415677215903997,
0.050873737782239914,
0.00967862643301487,
-0.03769637644290924,
-0.015138545073568821,
0.01144168246537447,
0.06468439847230911,
-0.05634203180670738,
0.01676374115049839,
0.007711525075137615,
-0.023791203275322914,
-0.005576473195105791,
0.035977695137262344,
0.006492308806627989,
-0.013088393025100231,
-0.01981738954782486,
0.010716898366808891,
-0.003976140171289444,
-0.0004941530060023069,
-0.009203569032251835,
0.037398532032966614,
-0.0037400671280920506,
0.0385766364634037,
-0.011760633438825607,
-0.009396901354193687,
-0.05557689815759659,
0.0012932552490383387,
-0.03997768089175224,
-0.01527076680213213,
-0.01599416695535183,
-0.03260505571961403,
-0.018199797719717026,
0.05246904119849205,
0.012482019141316414,
0.00855314452201128,
0.008150050416588783,
0.08122246712446213,
0.00460759736597538,
-0.006375051103532314,
-0.012247429229319096,
-0.013853336684405804,
-0.021602408960461617,
0.007173693738877773,
-0.006283702794462442,
0.024155065417289734,
0.049504898488521576,
0.002162233227863908,
-0.025428958237171173,
0.03048625960946083,
0.014574985019862652,
-0.01980847865343094,
0.0655350461602211,
-0.019428439438343048,
0.0008504076395183802,
0.06996670365333557,
0.03058108314871788,
-0.04631638899445534,
0.0171959325671196,
-0.018017465248703957,
-0.02005459927022457,
0.011586692184209824,
-0.02228442206978798,
-0.03390893340110779,
-0.01655603013932705,
-0.08078887313604355,
0.05494396761059761,
-0.0395495742559433,
0.008794457651674747,
-0.009256824851036072,
-0.001388912321999669,
-0.01522788405418396,
-0.033427733927965164,
-0.05930861830711365,
0.05323021113872528,
-0.007239771541208029,
0.01545354351401329,
0.015673814341425896,
0.005678264424204826,
0.01901710219681263,
-0.02920875884592533,
0.032414551824331284,
0.010037081316113472,
0.04128129035234451,
0.012383011169731617,
-0.00045792112359777093,
0.05182372406125069,
-0.040645599365234375,
0.011695110239088535,
0.02445835992693901,
0.024097686633467674,
0.03542919084429741,
-0.023803239688277245,
0.029940905049443245,
0.0038910938892513514,
0.04117129370570183,
-0.016195252537727356,
-0.008085100911557674,
0.005034163594245911,
-0.034957047551870346,
-0.0009128317469730973,
-0.03680077940225601,
0.03471565619111061,
0.0017803477821871638,
-0.016239849850535393,
0.004594225436449051,
0.03707956522703171,
-0.057730451226234436,
0.05112791433930397,
0.02176249772310257,
-0.005542879458516836,
-0.026671897619962692,
-0.007771224249154329,
0.001268405350856483,
0.0046441988088190556,
0.0016203958075493574,
-0.0024454877711832523,
-0.007236178033053875,
0.015232601203024387,
0.007915027439594269,
-0.11784318834543228,
0.03292587026953697,
0.0486275739967823,
0.0021923722233623266,
0.05426390469074249,
-0.06260651350021362,
-0.0061334166675806046,
0.05780618637800217,
-0.05265986546874046,
-0.0028891563415527344,
-0.03993812948465347,
0.021943869069218636,
-0.02313380502164364,
-0.00415248004719615,
0.0033221228513866663,
0.03684163838624954,
0.006765588652342558,
0.020386572927236557,
0.03181269019842148,
0.053380999714136124,
-0.024031823500990868,
-0.008996857330203056,
-0.0023825117386877537,
0.03280632942914963,
0.03172736242413521,
0.05542510747909546,
0.03942006081342697,
-0.06627355515956879,
0.05236243084073067,
0.02864149957895279,
-0.005196054466068745,
0.008707970380783081,
-0.0021913039963692427,
0.04395291954278946,
-0.015158910304307938,
0.020741287618875504,
0.04401051253080368,
0.0322665274143219,
0.006529585458338261,
0.0066839479841291904,
0.014550454914569855,
0.05292448028922081,
-0.010266125202178955,
-0.010683964006602764,
0.009294592775404453,
-0.0628947839140892,
-0.02620350383222103,
0.011871693655848503,
-0.02811155468225479,
0.01937871426343918,
0.021552234888076782,
0.004909849260002375,
-0.026428161188960075,
0.0007827356457710266,
-0.016719583421945572,
-0.0051100244745612144,
-0.02935045398771763,
0.020941954106092453,
-0.013722296804189682,
-0.016245907172560692,
0.01448581088334322,
-0.008519990369677544,
-0.04579451307654381,
-0.03864448890089989,
-0.03780209645628929,
-0.005636611487716436,
-0.012511366978287697,
-0.020669391378760338,
0.01524503342807293,
0.00994840543717146,
-0.04332883656024933,
-0.007286841049790382,
-0.025582153350114822,
0.029812868684530258,
0.003972433973103762,
0.013554194942116737,
-0.03208599239587784,
0.02374887280166149,
-0.016505179926753044,
-0.03293474391102791,
0.019227284938097,
0.04033719748258591,
-0.026580408215522766,
-0.05366014316678047,
-0.02108491025865078,
0.009475117549300194,
0.00243968004360795,
0.038998376578092575,
-0.04537525773048401,
-0.01028651837259531,
0.022233350202441216,
0.015399754978716373,
-0.02037806250154972,
-0.015319516882300377,
-0.0018150671385228634,
-0.01985304057598114,
-0.01036091335117817,
0.02672087587416172,
0.021253563463687897,
-0.017095422372221947,
0.0033415842335671186,
-0.0022106089163571596,
0.015341416001319885,
-0.05469902977347374,
-0.006200113333761692,
-0.027580104768276215,
0.024823924526572227,
0.005522300489246845,
-0.00773265864700079,
0.05312688276171684,
0.04063938930630684,
-0.0005786684341728687,
0.012567926198244095,
-0.037673916667699814,
-0.022245461121201515,
0.012094107456505299,
-0.006352516356855631,
-0.026795480400323868,
0.03498171269893646,
-0.014063222333788872,
0.015134541317820549,
-0.04915255308151245,
0.0075803049840033054,
0.0574500672519207,
-0.008031687699258327,
-0.015033531002700329,
0.03626127913594246,
0.014282232150435448,
0.030307944864034653,
-0.015070298686623573,
0.022376470267772675,
0.0001942689996212721,
-0.0032724374905228615,
-0.00316583551466465,
0.007895107381045818,
0.015744056552648544,
-0.009396743029356003,
-0.03763659670948982,
0.04631645977497101,
0.012206453830003738,
0.02288936637341976,
0.046993426978588104,
0.05003465712070465,
0.00146882061380893,
0.01726028323173523,
0.018569685518741608,
0.000949261651840061,
0.0010410278337076306,
0.034285496920347214,
-0.005051439628005028,
0.04248718544840813,
0.031817298382520676,
0.006221465766429901,
-0.002823021961376071,
0.03580520302057266,
-0.026079077273607254,
0.02273891121149063,
-0.0507209375500679,
-0.018470399081707,
-0.016464190557599068,
-0.04536763206124306,
0.0051508015021681786,
0.02308201976120472,
0.002833153586834669,
-0.016885943710803986,
-0.005092313978821039,
0.0305623896420002,
0.010271859355270863,
-0.073285773396492,
-0.0161733515560627,
0.0038358925376087427,
-0.0266807209700346,
0.02154538966715336,
0.03112001344561577,
-0.016808314248919487,
-0.024408698081970215,
-0.0199999138712883,
-0.029363436624407768,
0.0455545037984848,
-0.057740192860364914,
-0.03178497776389122,
-0.03397129103541374,
0.01819152943789959,
0.012796181254088879,
-0.015281079337000847
] |
<p>If I have a long solenoid, e.g. length $l$ and radius $r$ with $l = kr$, where k >> 1, with a nonpermeable (e.g. air) core, how much of the magnetic energy is stored outside as compared to inside?</p>
<p>If I go by the Wikipedia article on <a href="http://en.wikipedia.org/wiki/Solenoid" rel="nofollow">solenoids</a>, $B = \frac{\mu Ni}{l} \to H = \frac{Ni}{l}$ inside the coil, so the energy density should be $\frac{1}{2}\mu H^2$, and therefore the total energy inside the coil is $\frac{\mu N^2i^2}{2l^2}l\pi r^2 = \frac{\mu N^2 i^2}{2l}\pi r^2$.</p>
<p>The inductance is supposed to be $L = \frac{\mu N^2 A}{l} = \frac{\mu N^2 \pi r^2}{l}$, and if you compute energy $\frac{1}{2} Li^2$ you get $\frac{\mu N^2 i^2 \pi r^2}{2l}$ which is the same answer as the energy inside the coil calculated above, which relies on approximations, so we can't subtract these and figure out the energy stored outside.</p>
<p>Are there practical rules of thumb?</p> | 2,815 | [
-0.039347223937511444,
-0.005345521029084921,
-0.007230187300592661,
-0.010329680517315865,
0.046083465218544006,
0.02295447699725628,
-0.05507146194577217,
-0.05539765581488609,
-0.011317897588014603,
-0.003122437745332718,
0.01422499306499958,
0.0503317154943943,
0.0496373176574707,
0.023824498057365417,
0.012962166219949722,
-0.027185825631022453,
-0.002977491356432438,
-0.011539289727807045,
0.02372456155717373,
-0.027836132794618607,
0.0017181419534608722,
0.011497212573885918,
-0.0017796591855585575,
0.0017692075343802571,
-0.017767252400517464,
0.032236095517873764,
0.021610386669635773,
-0.04580802470445633,
0.009544172324240208,
0.05525429546833038,
0.000023549102479591966,
-0.030984779819846153,
0.007616308517754078,
0.006277017295360565,
0.03244449943304062,
-0.006936120335012674,
-0.046116750687360764,
-0.038082413375377655,
-0.004275518003851175,
0.058935876935720444,
-0.036596301943063736,
-0.015668094158172607,
-0.0008510271436534822,
0.04399381950497627,
-0.0020271006505936384,
-0.004279045388102531,
0.008398603647947311,
-0.0241412166506052,
0.019549723714590073,
-0.0630681961774826,
0.05080461502075195,
-0.0009075854904949665,
0.04533121734857559,
0.015598123893141747,
-0.02327095903456211,
-0.009377832524478436,
0.0686478465795517,
0.05672613903880119,
-0.0002889875031542033,
-0.044602617621421814,
-0.002234136685729027,
0.001245515770278871,
-0.017964696511626244,
-0.03104592300951481,
0.007265452295541763,
0.01325357984751463,
-0.026804931461811066,
-0.011867714114487171,
0.045306459069252014,
-0.012617339380085468,
0.0330563522875309,
0.007883727550506592,
-0.009658466093242168,
-0.02068185806274414,
0.04986489564180374,
0.011990632861852646,
0.01032678410410881,
0.01165362261235714,
0.05343344435095787,
0.04662174731492996,
-0.05023070052266121,
-0.021048065274953842,
0.060848698019981384,
0.07739698141813278,
0.018312349915504456,
0.008003152906894684,
0.027605853974819183,
0.03254261240363121,
0.0382121279835701,
-0.007912697270512581,
0.05439858138561249,
0.03694592043757439,
0.028180480003356934,
-0.01349387876689434,
0.003949406091123819,
0.04528898000717163,
-0.011458412744104862,
0.06074113771319389,
-0.00943748839199543,
-0.04439585655927658,
0.020300863310694695,
0.015217836014926434,
0.030665645375847816,
0.06844214349985123,
0.03462588042020798,
-0.055968619883060455,
-0.007148148026317358,
0.011340601369738579,
0.008760719560086727,
-0.006177330855280161,
-0.04271988943219185,
0.03559490293264389,
0.0028169844299554825,
-0.014810420572757721,
-0.0038745212368667126,
-0.04786915332078934,
0.010416988283395767,
-0.018133949488401413,
-0.004650859162211418,
0.04193800687789917,
0.0020177066326141357,
-0.001324235345236957,
0.01572018675506115,
-0.036380209028720856,
-0.0819283053278923,
0.02242765948176384,
0.030863555148243904,
0.016014939174056053,
-0.06996762752532959,
0.024282285943627357,
-0.0014493982307612896,
0.0005739687476307154,
-0.007183761801570654,
-0.014303195290267467,
0.04067804664373398,
0.01007088553160429,
-0.08111760765314102,
-0.045996688306331635,
0.028794050216674805,
-0.030524952337145805,
0.02254769206047058,
-0.09133674204349518,
-0.006489226594567299,
0.02651049941778183,
0.10336827486753464,
-0.009511185809969902,
-0.035354133695364,
-0.009756178595125675,
0.031821586191654205,
-0.029928745701909065,
-0.023545771837234497,
-0.007359797600656748,
-0.021212521940469742,
-0.031159862875938416,
0.01084841601550579,
-0.03048805333673954,
0.03064635396003723,
0.018803352490067482,
0.009041252546012402,
-0.0023622126318514347,
0.06026986241340637,
-0.0057352823205292225,
-0.01361532136797905,
0.00882189255207777,
-0.029233509674668312,
-0.02590015158057213,
0.08951679617166519,
0.01085885614156723,
0.05316466838121414,
0.03497932478785515,
0.013230010867118835,
-0.011659408919513226,
-0.013596837408840656,
-0.011217668652534485,
0.09730257093906403,
-0.0585545152425766,
-0.017287448048591614,
-0.04205736517906189,
0.059014029800891876,
0.030029579997062683,
-0.050276581197977066,
-0.05304122343659401,
0.010295112617313862,
0.003412520047277212,
0.043001189827919006,
0.02717004530131817,
-0.009323162026703358,
-0.037785787135362625,
-0.00012025408068438992,
-0.01929108425974846,
-0.0056318072602152824,
-0.02156376838684082,
0.04134935140609741,
-0.005978623870760202,
-0.04766184464097023,
0.02723800018429756,
0.0017121504060924053,
0.02014373056590557,
-0.031373243778944016,
-0.0479460284113884,
-0.008979100733995438,
0.022286882624030113,
0.003173538949340582,
-0.007405465003103018,
0.01899295300245285,
0.0453178696334362,
0.005927382502704859,
0.010707098990678787,
0.03512198477983475,
-0.017150769010186195,
-0.04672187566757202,
-0.02775019221007824,
-0.05728672817349434,
-0.002870676340535283,
0.026775972917675972,
-0.03448900580406189,
0.02744903601706028,
-0.015192391350865364,
0.022636840119957924,
0.018393436446785927,
0.014861248433589935,
0.08700399100780487,
0.033563803881406784,
0.0363708920776844,
0.018396127969026566,
0.02478364296257496,
-0.007160743232816458,
0.03135526925325394,
-0.02800201065838337,
-0.015921752899885178,
-0.0651135966181755,
-0.001859202398918569,
0.060487452894449234,
0.004726467654109001,
-0.05304335057735443,
0.004677038639783859,
0.02570057287812233,
0.016199495643377304,
0.034975484013557434,
-0.008559510111808777,
-0.051134511828422546,
-0.05421675369143486,
0.0006097532459534705,
0.06931482255458832,
-0.04380987584590912,
0.005566251464188099,
0.010226648300886154,
0.028196653351187706,
0.028843820095062256,
0.014670487493276596,
0.02573896199464798,
0.046796321868896484,
0.004984408151358366,
0.008497202768921852,
-0.0004495787725318223,
-0.009204057976603508,
0.04210657626390457,
-0.04303693398833275,
0.04117980971932411,
-0.011736796237528324,
-0.03388286754488945,
0.013702492229640484,
-0.018617501482367516,
0.0029919627122581005,
-0.006584321614354849,
-0.010371910408139229,
-0.015930261462926865,
-0.00214568804949522,
0.01271951012313366,
-0.028013594448566437,
0.0073759970255196095,
-0.030826475471258163,
0.011118780821561813,
-0.025188565254211426,
0.0016293616499751806,
0.015098674222826958,
-0.03531753271818161,
0.006759037729352713,
-0.03965800255537033,
-0.009501391090452671,
-0.02119552344083786,
-0.024707555770874023,
0.006512764375656843,
0.020645905286073685,
-0.02798989973962307,
0.007299971766769886,
-0.03204226866364479,
-0.006900475360453129,
0.041278015822172165,
0.028852498158812523,
-0.014952395111322403,
0.005484714172780514,
0.0009158606990240514,
-0.09995565563440323,
0.003201613435521722,
0.010628512129187584,
-0.0023884333204478025,
0.0009982914198189974,
-0.010336348786950111,
0.07758307456970215,
-0.015063473023474216,
-0.005767831578850746,
0.021824821829795837,
-0.015732891857624054,
-0.009603392332792282,
0.005198921542614698,
-0.00862001534551382,
0.02961193211376667,
-0.014901015907526016,
0.02348962239921093,
0.020794272422790527,
-0.04428404942154884,
-0.016511378809809685,
-0.04012228921055794,
-0.03831777349114418,
-0.003826077561825514,
-0.028181280940771103,
0.04008537903428078,
-0.0023746334481984377,
-0.04201309755444527,
0.053416844457387924,
0.0005521347047761083,
-0.04161638393998146,
0.00850367546081543,
-0.012069270946085453,
0.01383866649121046,
-0.03446383401751518,
-0.04397046938538551,
0.037126947194337845,
-0.02161862514913082,
-0.017177579924464226,
0.0032950679305940866,
0.028577473014593124,
0.01863284409046173,
0.03971884027123451,
0.0012642950750887394,
0.05043371021747589,
0.029466599225997925,
-0.013621623627841473,
0.106467105448246,
-0.009280411526560783,
-0.009302565827965736,
0.021481290459632874,
-0.015623010694980621,
0.01270812377333641,
0.029531871899962425,
-0.03344523161649704,
0.04719587415456772,
-0.024730732664465904,
0.013530355878174305,
-0.046922724694013596,
0.035585302859544754,
0.003788093803450465,
0.020179804414510727,
0.004260723013430834,
0.05288945510983467,
0.0386682003736496,
-0.00800283718854189,
0.0017093843780457973,
-0.018629178404808044,
0.04298413172364235,
-0.009458551183342934,
-0.03362593427300453,
-0.006261519622057676,
-0.010055698454380035,
-0.006928689312189817,
-0.010145272128283978,
-0.035522375255823135,
0.027205726131796837,
0.061404917389154434,
0.05058721452951431,
-0.007424845360219479,
-0.0006565923104062676,
0.008330783806741238,
-0.07873745262622833,
-0.031454090029001236,
-0.039309389889240265,
0.048891305923461914,
0.013576382771134377,
-0.007513679098337889,
0.02174057625234127,
0.0058570909313857555,
0.017592204734683037,
0.011752648279070854,
-0.0863608792424202,
0.02445334568619728,
-0.028178216889500618,
-0.007886468432843685,
0.006787480786442757,
-0.008327960968017578,
0.012621145695447922,
-0.02537498250603676,
0.003163855755701661,
0.010727006010711193,
0.004421137738972902,
-0.03037363477051258,
0.014940130524337292,
-0.0028643764089792967,
-0.014599657617509365,
-0.026987656950950623,
0.05625531077384949,
0.004552742466330528,
-0.05361660197377205,
0.011485240422189236,
0.02349472977221012,
-0.024676037952303886,
0.00937234703451395,
-0.0037552309222519398,
-0.00020223947649355978,
-0.0234129186719656,
0.013617459684610367,
0.025804344564676285,
-0.009265817701816559,
-0.017108337953686714,
0.005637661553919315,
0.030582750216126442,
0.02632337249815464,
0.01675613597035408,
-0.02487301081418991,
-0.04406985267996788,
-0.030898338183760643,
-0.0327410027384758,
0.01119227521121502,
0.047988783568143845,
0.00494025181978941,
0.03231820836663246,
0.007334109395742416,
-0.006827070843428373,
0.012373114936053753,
0.020220475271344185,
0.027481257915496826,
0.003169701434671879,
-0.030470140278339386,
-0.060310546308755875,
-0.014124646782875061,
-0.03530934080481529,
-0.009289181791245937,
-0.002164913108572364,
-0.03609650954604149,
-0.026846012100577354,
-0.01397572923451662,
0.009626729413866997,
0.01636088639497757,
0.013864884153008461,
0.02525206282734871,
0.02389984205365181,
0.0348999947309494,
0.006327351555228233,
-0.005414888262748718,
0.024255184456706047,
0.0002465661964379251,
0.0687679797410965,
0.023446787148714066,
0.005818441975861788,
-0.09958399832248688,
-0.03236740827560425,
0.027420412749052048,
0.018305620178580284,
0.003030451014637947,
-0.018138272687792778,
-0.04821467027068138,
0.00031286757439374924,
0.04575613886117935,
-0.027535680681467056,
0.08569012582302094,
-0.002435816917568445,
-0.0036665606312453747,
-0.034913916140794754,
-0.04149157926440239,
-0.01631363295018673,
0.028716914355754852,
-0.0033647846430540085,
0.06864707171916962,
-0.06063556671142578,
-0.01360416691750288,
-0.0000055973664530029055,
0.008947791531682014,
0.030715156346559525,
0.04875835031270981,
-0.01781267672777176,
0.005887409672141075,
-0.01588534377515316,
0.032449960708618164,
0.008579014800488949,
-0.07016511261463165,
-0.0030626414809376,
-0.02789994329214096,
-0.007003480568528175,
0.028538675978779793,
-0.014640373177826405,
-0.06264603137969971,
0.03746967017650604,
0.0327792689204216,
0.006449751555919647,
-0.01607140712440014,
-0.03438149765133858,
0.0661252811551094,
0.011487618088722229,
0.015633082017302513,
0.05165684595704079,
0.01133508700877428,
0.005418739281594753,
0.027147112414240837,
-0.03097563050687313,
0.007028414402157068,
-0.011641191318631172,
0.012526152655482292,
-0.01293926127254963,
0.021594548597931862,
-0.012922033667564392,
0.07066623121500015,
-0.01208803802728653,
0.0064544170163571835,
-0.02187962271273136,
-0.023201342672109604,
0.008351444266736507,
0.015294534154236317,
-0.018474819138646126,
-0.011555220000445843,
0.0036856026854366064,
0.027731336653232574,
0.013837438076734543,
-0.02142859622836113,
0.022350450977683067,
-0.024471992626786232,
0.03158747777342796,
0.03376602381467819,
-0.024210656061768532,
-0.00792789738625288,
-0.05436096712946892,
0.00782206654548645,
0.025157874450087547,
-0.03412749618291855,
0.05721132084727287,
-0.025060489773750305,
-0.010283302515745163,
-0.024437876418232918,
-0.03694978728890419,
-0.002458174480125308,
-0.030510617420077324,
0.015922369435429573,
0.009497812949120998,
-0.028569035232067108,
-0.007798869628459215,
0.011948970146477222,
-0.00903621967881918,
-0.03867942467331886,
-0.008208307437598705,
0.0013395496644079685,
0.03136271610856056,
0.018839770928025246,
-0.01582045666873455,
-0.006643509026616812,
-0.010692253708839417,
-0.04633740335702896,
0.017778480425477028,
0.005710574332624674,
-0.03807717561721802,
0.020983166992664337,
-0.00668036425486207,
0.022494450211524963,
0.06916753947734833,
0.0011508880415931344,
0.009438605979084969,
0.028601203113794327,
-0.006379094906151295,
-0.007361989933997393,
-0.01913926564157009,
0.04828174039721489,
-0.03692829608917236,
-0.012759449891746044,
0.018824705854058266,
-0.003845673520117998,
0.06616073846817017,
-0.0016480970662087202,
-0.052539754658937454,
0.050994958728551865,
-0.008112111128866673,
-0.011882667429745197,
-0.00008479527605231851,
0.027267033234238625,
-0.001069743768312037,
0.04020150005817413,
-0.004000765271484852,
-0.01750749908387661,
-0.060181837528944016,
-0.012278863228857517,
-0.0027684932574629784,
0.011659677140414715,
0.02286623977124691,
-0.030412286520004272,
0.07611744850873947,
-0.02914014644920826,
-0.011556185781955719,
0.005303252022713423,
-0.021392246708273888,
-0.0010198233649134636,
0.0009171713027171791,
-0.00397805729880929,
0.022417230531573296,
0.015292744152247906,
-0.02845642901957035,
-0.054252926260232925,
-0.044540684670209885,
0.010185792110860348,
0.038030002266168594,
-0.009807360358536243,
0.03188056871294975,
0.00014348198601510376,
-0.01753324456512928,
0.0005048427847214043,
-0.02642415277659893,
-0.02859809249639511,
0.0066877976059913635,
-0.01251134742051363,
0.058949049562215805,
-0.019631220027804375,
-0.031582899391651154,
0.03583522513508797,
0.03572216257452965,
-0.014750715345144272,
0.0028525153174996376,
0.0286298468708992,
0.061691924929618835,
0.001081710448488593,
-0.012796150520443916,
-0.03211279585957527,
0.01649593934416771,
-0.021683748811483383,
0.028952226042747498,
0.010513396933674812,
0.003084201132878661,
0.052930328994989395,
0.01881917007267475,
0.03132930397987366,
-0.01155050378292799,
0.009580533020198345,
-0.02651842124760151,
0.02027221769094467,
0.025993233546614647,
0.00251020141877234,
-0.022998381406068802,
0.03375400975346565,
0.019131474196910858,
-0.011283555999398232,
0.015253987163305283,
0.0021995531860738993,
-0.05525057390332222,
-0.004784821532666683,
0.006124719511717558,
-0.07242436707019806,
0.02835143357515335,
-0.0054628001525998116,
-0.03517121449112892,
0.05103444308042526,
-0.011176874861121178,
0.028343776240944862,
0.0348009318113327,
0.027050316333770752,
0.005337301641702652,
0.06992629170417786,
-0.039335548877716064,
-0.012515983544290066,
-0.04752478748559952,
0.028163693845272064,
0.11615800857543945,
0.04049073904752731,
0.006710708606988192,
-0.07516072690486908,
0.018040243536233902,
-0.054420821368694305,
0.008470532484352589,
-0.0669415071606636,
0.01837562583386898,
-0.03442183509469032,
-0.02394847758114338,
0.028339950367808342,
0.02584218606352806,
-0.036516621708869934,
-0.002566270064562559,
0.0296799223870039,
-0.017572537064552307,
0.009497812949120998,
0.019210273399949074,
0.03575018048286438,
-0.006859385408461094,
-0.02330406941473484,
-0.02644950896501541,
0.01792776770889759,
-0.021332861855626106,
-0.01951775513589382,
-0.0293184295296669,
-0.03784928470849991,
0.032320186495780945,
-0.04026518017053604,
-0.060903992503881454,
0.020415540784597397,
-0.034711651504039764,
0.012149776332080364,
0.0032678982242941856,
0.017561472952365875,
0.05130011960864067,
0.01920641027390957,
-0.018383510410785675,
0.017905984073877335,
0.03669627755880356,
0.002616076497361064,
0.02534627728164196,
0.04771711304783821,
-0.045601822435855865,
-0.009043354541063309,
-0.039076704531908035,
0.0282243974506855,
0.01757645420730114,
-0.004508849699050188,
0.016409069299697876,
0.023270653560757637,
0.023542048409581184,
-0.026780419051647186,
-0.021367670968174934,
0.02019606903195381,
0.028933115303516388,
-0.017598673701286316,
-0.015655353665351868,
-0.014702939428389072,
0.02410120703279972,
0.011225337162613869,
0.008047627285122871,
-0.003133821999654174,
-0.009555915370583534,
0.034982260316610336,
0.024495236575603485,
0.03476256877183914,
-0.007010253146290779,
-0.0009794165380299091,
-0.02877943590283394,
-0.009817440994083881,
-0.03709151968359947,
-0.004970867652446032,
-0.012118224985897541,
-0.004952145740389824,
0.045875079929828644,
-0.023350104689598083,
-0.016188936308026314,
-0.00463438406586647,
-0.03850904479622841,
0.027811629697680473,
0.03321881964802742,
0.0030730559956282377,
-0.029439100995659828,
-0.01811523362994194,
-0.012706143781542778,
0.03708463907241821,
-0.018960008397698402,
0.0008087389869615436,
0.00864946935325861,
0.0312366783618927,
-0.017603881657123566,
-0.0003507223736960441,
-0.04364807531237602,
-0.03226996585726738,
-0.07338975369930267,
0.015312792733311653,
-0.0014145590830594301,
-0.005860866978764534,
0.0014669304946437478,
0.04775556921958923,
0.008827609941363335,
0.05077838897705078,
-0.007018436212092638,
-0.029549449682235718,
-0.009828358888626099,
-0.036420367658138275,
0.008860896341502666,
-0.031054243445396423,
0.009498167783021927,
0.0004542595415841788,
-0.017565451562404633,
-0.008583463728427887,
-0.03127967566251755,
0.021147361025214195,
0.025368716567754745,
-0.023124830797314644,
-0.009217899292707443,
-0.050500791519880295,
0.0011770151322707534,
-0.026158878579735756,
0.018115581944584846,
0.0013361043529585004,
-0.022469412535429,
0.030136873945593834,
0.0024884995073080063,
0.0069828936830163,
0.030233634635806084,
-0.029702594503760338,
-0.013346177525818348,
0.04329471290111542,
-0.013611533679068089,
-0.00839180313050747,
0.013738441281020641,
-0.00588397029787302,
0.02841968648135662,
0.021720170974731445,
-0.018532251939177513,
-0.04324820637702942,
0.050817083567380905,
-0.0010245490120723844,
-0.032738637179136276,
0.0055479127913713455,
0.006034517660737038,
-0.022041335701942444,
0.04671960696578026,
-0.028207940980792046,
-0.019235583022236824,
0.0500732958316803,
-0.033996377140283585,
-0.00798467081040144,
0.0048424480482935905,
-0.005056746304035187,
0.021045885980129242,
-0.034388039261102676,
0.01892666332423687,
-0.02276182547211647,
0.007046769373118877,
0.01794506050646305,
0.009758805856108665,
0.010105687193572521,
-0.013479949906468391,
0.021044647321105003,
0.03688402101397514,
-0.019465742632746696,
0.0030010994523763657,
0.013896712101995945,
0.01082304585725069,
0.044968027621507645,
-0.011811373755335808,
0.005277080927044153,
-0.008871937170624733,
-0.005940018687397242,
-0.08273562043905258,
-0.022731950506567955,
-0.01711495965719223,
-0.0026938728988170624,
0.007094805594533682,
-0.046624213457107544,
0.015244039706885815,
0.011525317095220089,
-0.07358041405677795,
-0.026058964431285858,
-0.03873218223452568,
-0.02565254457294941,
-0.02030758373439312,
-0.020928028970956802,
-0.047156695276498795,
0.015637831762433052,
0.025210238993167877,
0.033729251474142075,
-0.002256894949823618,
-0.018861528486013412,
-0.03379223123192787,
-0.022143295034766197,
-0.01854485273361206,
0.03869493305683136,
-0.002680024364963174,
-0.01877390593290329,
0.0436609610915184,
-0.019365863874554634,
0.0005198774160817266,
0.01292918249964714,
-0.05395432561635971,
0.037382129579782486,
0.0037194632459431887,
0.020381372421979904,
-0.02843116596341133,
0.04166983440518379,
0.032740525901317596,
-0.0055420855060219765,
-0.00003653549720183946,
0.035149626433849335,
0.02608952485024929,
0.006386122200638056,
-0.03694058582186699,
0.010282467119395733,
0.05433596298098564,
0.0036881088744848967,
-0.010620299726724625,
0.04168445244431496,
-0.06273406744003296,
0.005915993824601173,
0.0362800657749176,
-0.018845761194825172,
0.023137860000133514,
-0.03782806172966957,
0.022889748215675354,
-0.018387695774435997,
-0.03956332057714462,
0.019451526924967766,
-0.014792360365390778,
-0.01372028049081564,
-0.005140327848494053,
0.008783658966422081,
-0.030808892101049423,
0.03423325717449188,
0.002102202270179987,
-0.01864013634622097,
-0.05432487279176712,
0.007852839305996895,
0.005137429106980562,
-0.021107204258441925,
0.006148966960608959,
-0.057502441108226776,
-0.04234040901064873,
0.043876539915800095,
0.04900819808244705,
0.02668686956167221,
0.03938501700758934,
-0.025259384885430336,
-0.04849035292863846,
-0.07326165586709976,
0.022478623315691948,
-0.04515351355075836,
-0.024508533999323845,
-0.04943573474884033,
-0.06124201789498329,
-0.0008410706650465727,
0.021563105285167694,
0.0921575203537941,
0.01806441880762577,
-0.02575656957924366,
0.030718710273504257,
0.011431618593633175,
0.01944860629737377,
-0.04914815351366997,
0.026800021529197693,
0.028164353221654892,
0.009162796661257744,
0.024470707401633263,
-0.011755390092730522,
-0.022799571976065636,
0.017211779952049255,
0.036290112882852554,
0.0283938217908144,
0.010929715819656849,
-0.017540713772177696,
0.01590832881629467,
0.036164820194244385,
-0.04401201009750366,
0.011936667375266552,
0.07738927751779556,
0.016783051192760468,
0.015546861104667187,
0.0010266234166920185,
-0.0022878306917846203,
-0.05260363593697548,
0.01924486830830574,
-0.03669288754463196,
-0.013722285628318787,
-0.04277585446834564,
-0.027797779068350792,
0.07670348882675171,
-0.02621486224234104,
-0.009584381245076656,
0.03415592014789581,
-0.04205966368317604,
-0.012848990969359875,
0.027056869119405746,
0.01697217859327793,
0.01580902189016342,
-0.02654646523296833,
0.03960143402218819,
0.035992756485939026,
0.02372162789106369,
-0.03216420114040375,
0.03024948760867119,
0.05271568521857262,
-0.0038802502676844597,
-0.012526391074061394,
0.06119774281978607,
-0.029292382299900055,
0.005723100621253252,
-0.010695614852011204,
0.013971986249089241,
-0.03765720874071121,
-0.06064461171627045,
0.02345680072903633,
-0.006501618307083845,
-0.02105873078107834,
0.032511841505765915,
-0.03739131987094879,
0.07639940828084946,
-0.005795890465378761,
0.00968953873962164,
-0.03370213881134987,
0.00012420787243172526,
0.005022660829126835,
0.034102849662303925,
0.01874358020722866,
0.03743482008576393,
0.00787463877350092,
0.014223871752619743,
-0.02307337149977684,
-0.027030613273382187,
0.05592501908540726,
-0.03871573135256767,
0.033312007784843445,
-0.004977126140147448,
-0.0001685825700405985,
-0.05765874311327934,
-0.03558752313256264,
-0.028625497594475746,
-0.051992811262607574,
0.0224353838711977,
0.03183377534151077,
0.010421167127788067,
0.0199732668697834,
-0.01602293737232685,
-0.0038584726862609386,
0.08855527639389038,
-0.07662531733512878,
0.0008668830851092935,
-0.047400474548339844,
0.013096575625240803,
0.014479858800768852,
-0.007509982213377953
] |
<p>suppose there is a scale able to measure weight with an uncertainty of $10^{-9}kg$ . On the scale, an airtight plastic chamber is placed. Initially, a fly of mass $10^{-5}kg$ is sitting at the bottom of the chamber, which sits on the scale. At a later point in time the fly is flying around the chamber. Will there be a difference in the observed weight as measured by the scale when the fly is sitting at the bottom of the chamber compared to when it is flying around the chamber at some point in time? If so, what does the value of this difference depend on (I am most concerned with the case where the fly has not touched any surface of the container in enough time for the scale to reach some equilibrium value (or do the pressure variations induced from the flies wings cause constant fluctuations in the scale)?</p> | 792 | [
-0.019399315118789673,
-0.04136504977941513,
-0.0315033458173275,
-0.008435893803834915,
0.01620510406792164,
0.0185040682554245,
-0.023572061210870743,
0.009275670163333416,
0.01154546532779932,
-0.014620009809732437,
0.03236997500061989,
0.05016569048166275,
0.0729140043258667,
-0.025783784687519073,
0.004987557418644428,
0.01215593796223402,
-0.04713434353470802,
0.012006478384137154,
-0.013426505960524082,
-0.024604247882962227,
0.0065199206583201885,
0.0184777844697237,
0.019383609294891357,
-0.03989611566066742,
-0.026642370969057083,
0.006758182775229216,
0.04615320265293121,
-0.006734145805239677,
-0.012915775179862976,
0.07590358704328537,
-0.04022737964987755,
0.02751929499208927,
0.0026192914228886366,
0.04114004969596863,
0.03066791035234928,
-0.020473020151257515,
-0.03243196755647659,
-0.036817923188209534,
-0.004454133100807667,
0.020803948864340782,
-0.07266741991043091,
-0.02039976790547371,
0.019466334953904152,
-0.005262318067252636,
0.021881643682718277,
-0.00467877509072423,
-0.008441446349024773,
0.017655977979302406,
0.07145920395851135,
-0.06823354959487915,
0.039995044469833374,
-0.010982322506606579,
0.021837936714291573,
0.046337276697158813,
0.003621591255068779,
-0.015319551341235638,
0.04992301017045975,
0.06385639309883118,
-0.019913816824555397,
-0.0685226246714592,
-0.021692806854844093,
-0.029108738526701927,
0.009889636188745499,
-0.025412963703274727,
-0.018847620114684105,
0.006354005541652441,
-0.03077828139066696,
0.00798136368393898,
0.03757411986589432,
-0.008090409450232983,
0.0013797266874462366,
0.039133600890636444,
0.027323555201292038,
0.0018111604731529951,
0.033045411109924316,
-0.04460763931274414,
0.04466231167316437,
0.04293442144989967,
0.031181659549474716,
0.05134526267647743,
-0.015774864703416824,
0.010867316275835037,
0.0430760532617569,
0.02655436284840107,
0.028900455683469772,
-0.052857011556625366,
0.06546085327863693,
-0.035005323588848114,
0.005651912651956081,
0.053985606878995895,
-0.0048320237547159195,
0.02064722217619419,
0.00863130297511816,
-0.02994566597044468,
0.027400707826018333,
0.041386011987924576,
-0.010117126628756523,
0.03358493745326996,
-0.024158714339137077,
-0.04535793513059616,
0.005744948051869869,
-0.05376676470041275,
0.040657658129930496,
0.07918064296245575,
-0.028961000964045525,
-0.020039867609739304,
-0.006147598382085562,
-0.0004227767640259117,
-0.008831318467855453,
-0.008855772204697132,
-0.004440088290721178,
-0.016566263511776924,
-0.017129290848970413,
-0.02394426427781582,
0.04475589841604233,
-0.014339747838675976,
0.014449943788349628,
-0.016513654962182045,
0.04735745117068291,
0.0029533691704273224,
0.04895901307463646,
-0.04550982639193535,
-0.013846379704773426,
-0.0017866580747067928,
-0.026817046105861664,
0.008662565611302853,
0.057525135576725006,
-0.04550155997276306,
-0.03910217061638832,
0.02074248716235161,
-0.0037200774531811476,
-0.006620145868510008,
0.073271743953228,
-0.003224070882424712,
0.019683532416820526,
0.012373531237244606,
-0.09220646321773529,
-0.06385720521211624,
0.051353927701711655,
-0.039332352578639984,
-0.016729891300201416,
-0.04225422441959381,
0.0005875678034499288,
0.0339316762983799,
0.05179483816027641,
0.021130619570612907,
0.01578763872385025,
-0.0277706291526556,
0.04516477882862091,
0.009816071949899197,
0.013101089745759964,
-0.003145056776702404,
0.04964767023921013,
-0.03305276483297348,
-0.000886008667293936,
-0.054233796894550323,
0.015990382060408592,
0.05134500935673714,
-0.015702301636338234,
-0.038605161011219025,
0.022417832165956497,
-0.020463699474930763,
-0.0014534288784489036,
-0.025393933057785034,
0.013148926198482513,
-0.024510420858860016,
0.03452039137482643,
0.0019016256555914879,
0.007827289402484894,
-0.02008940279483795,
0.029423169791698456,
0.04609309136867523,
-0.02251572720706463,
-0.004613965749740601,
0.07494230568408966,
0.01848651096224785,
-0.013982380740344524,
-0.03535020351409912,
0.028189320117235184,
0.016748210415244102,
-0.009034319780766964,
-0.023609327152371407,
-0.047817062586545944,
-0.016658980399370193,
0.00010459088662173599,
0.0021722500678151846,
-0.019179118797183037,
0.006419805809855461,
0.013434919528663158,
-0.04620771482586861,
-0.0448303148150444,
-0.07199625670909882,
0.018243305385112762,
-0.004716627765446901,
-0.01091612596064806,
0.05572841316461563,
0.012026661075651646,
0.008196455426514149,
0.013904016464948654,
-0.009121658280491829,
-0.027727842330932617,
0.01806691288948059,
0.024994300678372383,
-0.040406957268714905,
0.013991550542414188,
0.018622010946273804,
0.07770034670829773,
0.008104605600237846,
0.02641613595187664,
-0.009961530566215515,
-0.02737143449485302,
-0.016745872795581818,
-0.04246635362505913,
-0.025540724396705627,
0.016790935769677162,
-0.02131774090230465,
0.03708282858133316,
-0.012850468046963215,
-0.012919601984322071,
0.015334103256464005,
-0.003045342629775405,
0.06093995273113251,
0.09579198062419891,
-0.014460716396570206,
0.025486180558800697,
0.027398258447647095,
0.04297298192977905,
0.022786952555179596,
-0.03257772698998451,
-0.069478839635849,
-0.0643521100282669,
-0.018103623762726784,
-0.024948803707957268,
0.03260650485754013,
-0.021304285153746605,
0.017428230494260788,
0.03477269038558006,
0.026246938854455948,
0.03840414434671402,
0.01372506283223629,
-0.021789181977510452,
-0.05838702991604805,
0.037094734609127045,
0.03227168694138527,
0.03074718452990055,
-0.019808989018201828,
0.05352708324790001,
0.014210336841642857,
0.03945576772093773,
-0.011279195547103882,
0.030990079045295715,
-0.027020789682865143,
-0.008363569155335426,
0.026909055188298225,
-0.029789434745907784,
-0.018674984574317932,
0.055711567401885986,
-0.01846909150481224,
0.03017524816095829,
0.013413028791546822,
-0.020684435963630676,
0.016986170783638954,
-0.015841422602534294,
-0.02025972492992878,
0.00785435177385807,
0.02164599671959877,
-0.002448155079036951,
-0.015651481226086617,
0.015414485707879066,
-0.005637382157146931,
0.015321007929742336,
-0.02921523153781891,
-0.003338915528729558,
-0.026817090809345245,
-0.022925332188606262,
0.04919244721531868,
0.01747914031147957,
0.037137892097234726,
-0.029828425496816635,
-0.04948505014181137,
-0.021257393062114716,
-0.0381382592022419,
-0.01801539584994316,
0.01679747737944126,
-0.042415160685777664,
0.027994293719530106,
-0.020935537293553352,
-0.025983722880482674,
0.028878863900899887,
-0.0006523770862258971,
0.019616760313510895,
0.012540644034743309,
-0.00048597785644233227,
-0.028809107840061188,
0.0014144066954031587,
0.0006665230030193925,
-0.060544416308403015,
-0.015209101140499115,
0.004173048306256533,
0.02594802714884281,
0.0018123759655281901,
-0.0036916749086230993,
0.05608176440000534,
-0.07433880120515823,
-0.03172904625535011,
-0.06518390774726868,
0.01584990695118904,
-0.000820913992356509,
-0.04265788197517395,
-0.001793837291188538,
-0.000045413238694891334,
-0.02300274930894375,
-0.03813471645116806,
-0.012916290201246738,
-0.06039043888449669,
0.031883567571640015,
-0.01563166081905365,
0.03361630439758301,
-0.02080562897026539,
0.0003593479632399976,
0.10631053149700165,
0.013642354868352413,
-0.007154383696615696,
-0.011388316750526428,
-0.004148788284510374,
-0.024099595844745636,
-0.03828601911664009,
-0.022610120475292206,
0.011802378110587597,
0.004070999100804329,
0.024119608104228973,
0.08893732726573944,
0.015618449077010155,
-0.022470779716968536,
0.038148432970047,
-0.00688028521835804,
0.019419755786657333,
0.019307704642415047,
0.02869468368589878,
0.03072352707386017,
-0.005467054899781942,
-0.011554311029613018,
-0.01620648056268692,
-0.006975466851145029,
0.03216340020298958,
0.012295762076973915,
-0.07648391276597977,
0.0716770738363266,
0.026064593344926834,
0.00628045154735446,
-0.03717995062470436,
0.019953176379203796,
-0.0037882959004491568,
0.013402068987488747,
-0.012729153037071228,
0.0026939704548567533,
0.038796961307525635,
-0.028399528935551643,
-0.025709113106131554,
0.06022975593805313,
0.06270444393157959,
-0.01456670556217432,
-0.05608711019158363,
-0.010466608218848705,
-0.01586279645562172,
0.06372097879648209,
-0.027136214077472687,
-0.03175291419029236,
0.03361664339900017,
0.05886441841721535,
0.040809907019138336,
-0.00021487311460077763,
-0.021031923592090607,
0.000828687974717468,
-0.04121272265911102,
-0.04306786134839058,
0.033967308700084686,
0.037347130477428436,
-0.02113182656466961,
0.026888824999332428,
0.047388385981321335,
0.0024615006987005472,
0.03964447230100632,
-0.005613396409898996,
-0.09295997023582458,
0.05222411826252937,
-0.00697327870875597,
-0.017117217183113098,
0.011743848212063313,
0.028458362445235252,
0.0027697139885276556,
-0.05709509924054146,
0.01909721828997135,
-0.025839053094387054,
0.026590621098876,
-0.05067360773682594,
0.005882828496396542,
-0.0094694122672081,
-0.04794519022107124,
-0.03274471312761307,
0.03881065547466278,
0.03602445870637894,
-0.02912149764597416,
0.07301278412342072,
0.006200522184371948,
-0.009221509099006653,
0.007726538460701704,
-0.024985743686556816,
-0.004022082779556513,
-0.0002093842049362138,
0.04585375264286995,
0.03473317250609398,
0.022064197808504105,
-0.02133810892701149,
0.040367405861616135,
0.021898746490478516,
0.049975745379924774,
-0.008280492387712002,
0.013401338830590248,
-0.03930162265896797,
-0.05100991204380989,
-0.034197431057691574,
-0.005819801241159439,
0.01050912868231535,
0.027618519961833954,
0.009092798456549644,
0.0347428023815155,
-0.005430134013295174,
-0.030207158997654915,
0.022549064829945564,
0.04420560225844383,
-0.007910222746431828,
-0.0010772701352834702,
-0.04658746346831322,
0.010352421551942825,
-0.061268456280231476,
-0.012334456667304039,
0.007007848471403122,
0.02977052330970764,
0.0072510321624577045,
0.020851651206612587,
0.02600843273103237,
0.026278117671608925,
0.0033823903650045395,
-0.019342167302966118,
0.0052183098159730434,
0.014526340179145336,
-0.023468032479286194,
-0.015933562070131302,
0.05324668809771538,
0.03045813739299774,
0.007723568938672543,
0.016369681805372238,
-0.0060744076035916805,
-0.07760414481163025,
-0.03929236903786659,
0.02719171904027462,
0.02632390707731247,
-0.04416342079639435,
0.004542042966932058,
-0.03219868615269661,
-0.03203195333480835,
0.05742946267127991,
-0.02471339888870716,
0.030620843172073364,
-0.03856692835688591,
-0.01436232402920723,
0.011885808780789375,
0.011454802006483078,
-0.02924433909356594,
0.03713231161236763,
-0.020078109577298164,
0.01632995530962944,
-0.02501661702990532,
-0.022583220154047012,
0.007327262777835131,
0.009355820715427399,
0.020926684141159058,
0.0628785640001297,
-0.007833624258637428,
0.0073445262387394905,
-0.03689325600862503,
-0.024609819054603577,
-0.026400677859783173,
-0.03167138993740082,
0.01764797605574131,
-0.01900585927069187,
0.02242155931890011,
0.01283323485404253,
-0.0004425199585966766,
-0.060015399008989334,
0.017325904220342636,
-0.0003095240972470492,
-0.014282655902206898,
-0.017499690875411034,
0.006068060640245676,
0.05428767576813698,
0.050468605011701584,
-0.028246082365512848,
0.010555342771112919,
0.03378959000110626,
-0.0029809754341840744,
0.0014478976372629404,
0.00690762884914875,
0.04619879275560379,
-0.017681868746876717,
0.012341366149485111,
-0.029301537200808525,
0.0027122071478515863,
-0.02473818138241768,
0.07903006672859192,
0.02770499885082245,
0.0330236479640007,
-0.009385683573782444,
-0.012172318994998932,
-0.01614602841436863,
0.03619040176272392,
0.038368966430425644,
0.0053326962515711784,
0.0010658579412847757,
0.005739063490182161,
0.009731454774737358,
-0.043432749807834625,
-0.010490361601114273,
0.02482421137392521,
-0.0026383327785879374,
-0.02205643057823181,
-0.05198147892951965,
0.04710458964109421,
-0.05076310783624649,
0.005817301105707884,
0.0336703285574913,
-0.02779437229037285,
0.042742084711790085,
-0.011595779098570347,
-0.014048642478883266,
0.014369921758770943,
-0.052696261554956436,
-0.02324661985039711,
0.005224782973527908,
-0.018705066293478012,
0.009172379039227962,
-0.07147646695375443,
0.023808829486370087,
0.015872061252593994,
-0.004075201228260994,
-0.08038301020860672,
-0.021982017904520035,
0.023595955222845078,
0.017276791855692863,
0.0032101222313940525,
-0.00005278928074403666,
-0.0036003643181174994,
-0.012935475446283817,
-0.016259951516985893,
-0.042866773903369904,
0.00384109397418797,
-0.006638624239712954,
-0.007736177183687687,
-0.0015526787610724568,
-0.006430621258914471,
0.05353822931647301,
0.0005519420956261456,
0.005689394194632769,
-0.0015533295227214694,
-0.012710834853351116,
-0.0334772989153862,
0.020121952518820763,
0.015628544613718987,
-0.020261190831661224,
-0.01706751063466072,
0.019002404063940048,
-0.012919016182422638,
0.03564786911010742,
-0.02541145123541355,
-0.004577208776026964,
0.005727017764002085,
-0.019515467807650566,
0.029218852519989014,
0.024533221498131752,
0.01952410489320755,
-0.03840819373726845,
0.0335875079035759,
-0.022748148068785667,
-0.030998125672340393,
-0.012427621521055698,
-0.022647719830274582,
0.03035736456513405,
0.016010403633117676,
-0.03915529325604439,
0.018115779384970665,
0.07144619524478912,
-0.006867467425763607,
-0.04074598476290703,
-0.0031371242366731167,
-0.05915627256035805,
-0.013011975213885307,
-0.02593258209526539,
-0.01636216603219509,
0.04922240227460861,
0.022262470796704292,
-0.04369942471385002,
-0.016672102734446526,
-0.04319577291607857,
-0.011129665188491344,
0.07422668486833572,
0.034825943410396576,
0.06690888106822968,
0.0026148506440222263,
-0.012174495495855808,
0.0041923318058252335,
-0.026578165590763092,
-0.007785733789205551,
0.00562268914654851,
0.00924986507743597,
0.024881409481167793,
-0.032624516636133194,
0.0028064073994755745,
0.005623271688818932,
0.021035343408584595,
0.003640478476881981,
0.003216629847884178,
0.041559651494026184,
0.04105259105563164,
0.0036982044111937284,
-0.0005733889993280172,
-0.039629604667425156,
0.028384458273649216,
-0.010477821342647076,
0.025085726752877235,
-0.04000371694564819,
-0.018844369798898697,
0.0056058261543512344,
0.036816686391830444,
-0.01182978693395853,
-0.04505530372262001,
-0.012556477449834347,
-0.04917359724640846,
0.01863691583275795,
-0.0265105701982975,
0.023044902831315994,
0.027969511225819588,
0.012411088682711124,
0.05180194973945618,
0.023001044988632202,
0.015538294799625874,
-0.02536461129784584,
-0.027644475921988487,
-0.021002745255827904,
-0.01454446092247963,
-0.03954044356942177,
0.03256835415959358,
-0.014635290019214153,
-0.005049802362918854,
0.024923717603087425,
-0.03224797174334526,
0.03014145977795124,
0.034705448895692825,
0.00411212258040905,
-0.02144136093556881,
0.06498736143112183,
-0.012704189866781235,
-0.00220221234485507,
-0.03639481961727142,
0.013016832992434502,
0.10453782230615616,
0.010173100978136063,
0.008258293382823467,
-0.01417140755802393,
-0.003929350525140762,
0.032772742211818695,
0.016674108803272247,
-0.0032865223474800587,
0.01331717986613512,
0.03312973305583,
-0.010363223031163216,
-0.0004048277041874826,
0.05044429004192352,
-0.025214554741978645,
-0.02508525550365448,
0.036319613456726074,
-0.023288492113351822,
-0.013291009701788425,
-0.03970059007406235,
-0.008271708153188229,
-0.002259894972667098,
0.01233077235519886,
0.00856813695281744,
0.03303398936986923,
-0.017915358766913414,
-0.0061910683289170265,
-0.027043865993618965,
-0.023775044828653336,
-0.02458990179002285,
0.013713222928345203,
-0.05207774415612221,
0.02934528887271881,
-0.0017704112688079476,
-0.011368253268301487,
-0.09793906658887863,
-0.004265574272722006,
-0.012637870386242867,
0.011395852081477642,
0.03409679979085922,
0.03299442306160927,
0.00015761890972498804,
-0.016534453257918358,
0.00998631026595831,
0.02333061583340168,
-0.0630083754658699,
-0.04493002966046333,
-0.02916630730032921,
0.04639388248324394,
-0.014624474570155144,
-0.003004431491717696,
0.009190608747303486,
-0.020327415317296982,
-0.005017207004129887,
-0.041668493300676346,
-0.026286719366908073,
0.008279153145849705,
0.016563311219215393,
-0.023543452844023705,
-0.017911385744810104,
-0.005960808601230383,
0.01525207795202732,
-0.011603272520005703,
0.004784456919878721,
0.01956287771463394,
0.007467942778021097,
-0.025824762880802155,
0.015241054818034172,
0.06134506314992905,
-0.023687545210123062,
-0.010496608912944794,
0.002554146805778146,
0.00815760437399149,
-0.043814752250909805,
0.019528817385435104,
0.015393344685435295,
0.01209027599543333,
0.022231917828321457,
0.007472103461623192,
-0.016240978613495827,
-0.002234390703961253,
-0.035683996975421906,
0.004140270408242941,
-0.03595335781574249,
-0.018877673894166946,
-0.024678103625774384,
-0.020743530243635178,
0.00016522254736628383,
0.01904333010315895,
-0.016721446067094803,
0.009705600328743458,
-0.014215893112123013,
0.03416253626346588,
0.023305581882596016,
-0.043979451060295105,
0.014896685257554054,
0.021380463615059853,
-0.02915733866393566,
0.022000836208462715,
-0.006251978222280741,
0.012415972538292408,
0.018678192049264908,
0.014623327180743217,
-0.026799149811267853,
0.012758923694491386,
-0.00688020559027791,
0.014205348677933216,
0.01159582193940878,
-0.035097941756248474,
0.014984391629695892,
0.0038821985945105553,
0.02691553346812725,
-0.046492092311382294,
-0.05157214775681496,
-0.05605239421129227,
-0.02244892716407776,
-0.024184558540582657,
0.016971221193671227,
0.006476979237049818,
0.03884351998567581,
-0.012511883862316608,
0.0019508481491357088,
-0.04649117961525917,
0.010019121691584587,
-0.0637110024690628,
0.0013841375475749373,
0.04474432393908501,
0.03317629173398018,
0.03042248822748661,
0.024556854739785194,
-0.05225054547190666,
-0.0239116158336401,
0.016683312132954597,
0.014247833751142025,
0.02950921654701233,
-0.0052285646088421345,
0.024383746087551117,
0.032067518681287766,
0.05507083237171173,
-0.007749914191663265,
-0.03116874396800995,
0.05812748894095421,
-0.03928965702652931,
-0.04128516837954521,
0.0664544478058815,
0.032747309654951096,
0.028223350644111633,
0.03341269865632057,
-0.030391085892915726,
0.0009132042177952826,
0.02861982397735119,
-0.02226434275507927,
-0.0018918449059128761,
-0.023936690762639046,
-0.03682064637541771,
-0.04088634252548218,
-0.0006343113491311669,
0.030840931460261345,
0.002445630496367812,
0.0046998197212815285,
0.04482079669833183,
0.035725291818380356,
-0.002155634807422757,
-0.02983125112950802,
0.017933031544089317,
-0.02436358481645584,
0.03449910879135132,
0.009882241487503052,
-0.018221573904156685,
0.016556784510612488,
0.07081010937690735,
-0.0381181500852108,
0.03126544505357742,
-0.003890357678756118,
-0.021578477695584297,
-0.10389848053455353,
-0.017838405445218086,
0.019861841574311256,
0.013462389819324017,
0.02938513085246086,
-0.05830981954932213,
0.002818524371832609,
0.012943328358232975,
-0.048310697078704834,
-0.002970646834000945,
-0.06562700867652893,
-0.022561801597476006,
-0.010722924955189228,
-0.020509017631411552,
-0.025917846709489822,
0.03849146142601967,
0.028701722621917725,
0.023562539368867874,
0.016887737438082695,
0.004939742852002382,
0.009543403051793575,
-0.059334252029657364,
0.011310892179608345,
0.034023262560367584,
0.019234517589211464,
-0.02038545161485672,
0.051124367862939835,
-0.03191302716732025,
0.013614035211503506,
0.03794035688042641,
-0.014410401694476604,
0.03004060685634613,
-0.03353070840239525,
0.031206341460347176,
-0.024659596383571625,
0.039018381386995316,
0.017400037497282028,
0.0020774449221789837,
0.005516152363270521,
0.04955307021737099,
0.006024142261594534,
0.007390831131488085,
-0.005770434159785509,
-0.007819830439984798,
-0.004064470063894987,
-0.012929798103868961,
-0.005283892620354891,
0.03978646174073219,
-0.01587267778813839,
-0.022640788927674294,
0.026500191539525986,
0.0014684486668556929,
-0.021612374112010002,
-0.018267013132572174,
0.0021923910826444626,
-0.07837256044149399,
-0.011540270410478115,
0.010736241936683655,
0.04162873700261116,
-0.03061477281153202,
0.010309488512575626,
-0.0030034342780709267,
-0.02707698568701744,
0.021257491782307625,
0.011733430437743664,
-0.030911525711417198,
-0.02939591184258461,
-0.02789025567471981,
-0.02044432796537876,
0.002288895659148693,
0.005413391627371311,
-0.025173788890242577,
-0.032667260617017746,
0.012545510195195675,
-0.0325014553964138,
-0.025227844715118408,
-0.030211102217435837,
-0.05976944416761398,
-0.012432411313056946,
-0.0833592489361763,
0.055025387555360794,
0.015516187995672226,
0.003212389536201954,
-0.05042139068245888,
-0.017775559797883034,
-0.0017885681008920074,
0.018313148990273476,
0.0432622954249382,
0.0009106618817895651,
-0.034386951476335526,
0.03541994094848633,
0.004523911513388157,
0.011878647841513157,
-0.02310866303741932,
0.009781064465641975,
-0.033451326191425323,
-0.00033505199826322496,
0.0247281976044178,
0.015503959730267525,
0.01874667964875698,
0.03620219975709915,
0.000648178334813565,
-0.04085402190685272,
-0.010107128880918026,
-0.012101118452847004,
-0.046314507722854614,
0.07499362528324127,
0.021115612238645554,
0.03681875392794609,
0.05933959409594536,
0.0057016839273273945,
0.03954276069998741,
0.0072700041346251965,
0.002743722638115287,
-0.024513740092515945,
0.05363195016980171,
-0.040325090289115906,
0.008945259265601635,
-0.01595441624522209,
0.04086045175790787,
-0.015468526631593704,
-0.048484381288290024,
-0.027440523728728294,
-0.0014975148951634765,
-0.010261619463562965,
-0.002474412554875016,
0.04330955445766449,
0.02560361474752426,
0.03678785264492035,
0.05070994421839714,
-0.010388103313744068,
0.034738436341285706,
0.020957259461283684,
0.011464237235486507,
0.06790447980165482,
0.04529125988483429,
0.02028682827949524,
0.002476497320458293,
0.0039763068780303,
-0.023614592850208282,
0.008849500678479671,
-0.0055057876743376255,
0.047319550067186356,
-0.0030062240548431873,
-0.04933828115463257,
0.007923522032797337,
0.040041327476501465,
-0.021729717031121254,
0.029819298535585403,
-0.02095859684050083,
0.02819836139678955,
-0.02088858373463154,
-0.008694852702319622,
-0.03188437968492508,
-0.0003844478342216462,
0.006339952349662781,
-0.018362732604146004,
-0.002136037452146411,
0.03760522976517677,
0.027438633143901825,
-0.00286077125929296,
-0.029879825189709663,
0.017689866945147514,
0.0023553865030407906,
-0.02369268611073494,
-0.005313079338520765,
0.00455672200769186,
0.021099703386425972,
-0.0338318832218647,
-0.05593140795826912,
-0.06446386873722076,
-0.024615902453660965,
0.030616609379649162,
0.04008827358484268,
0.07069198787212372,
0.009524607099592686,
-0.023929687216877937,
-0.024122782051563263,
0.07483703643083572,
-0.01809753105044365,
-0.033320944756269455,
-0.010356869548559189,
0.024582477286458015,
0.03273706138134003,
-0.019904060289263725
] |
<p>I believe in Neutron Scattering the neutrons after hitting a nucleus can bounce in any of 360*3 dimensions -> 1080 degrees?</p>
<p>Why is this so? Shouldn't it only bounce "off" the neutron in approximately the same "direction" that it came in such as when a particle bounces off a mirror -> because of the cross-section ...</p> | 2,816 | [
-0.013174633495509624,
-0.015965858474373817,
0.0096229063346982,
-0.05196395516395569,
0.05164314806461334,
0.03126312047243118,
-0.041521813720464706,
-0.0006516576977446675,
0.004635143093764782,
-0.030537597835063934,
0.05290728062391281,
0.01811312884092331,
0.052065107971429825,
0.02273489162325859,
0.032459285110235214,
0.03822515532374382,
-0.011601443402469158,
0.011896294541656971,
0.0007424617069773376,
-0.07159366458654404,
0.042001958936452866,
0.0008584671304561198,
-0.015118485316634178,
-0.014801312237977982,
-0.01661691628396511,
0.03850176930427551,
0.00379636837169528,
0.002178363734856248,
0.06668595969676971,
0.025864651426672935,
0.02227744646370411,
-0.010507631115615368,
0.02594010904431343,
0.04880110174417496,
0.004999950993806124,
-0.029342254623770714,
-0.03327393904328346,
-0.0038354203570634127,
-0.011185452342033386,
0.031322453171014786,
0.004245701711624861,
-0.0010338649153709412,
-0.0218887347728014,
0.06476090848445892,
-0.031583208590745926,
0.04708433151245117,
-0.018079834058880806,
-0.012292895466089249,
0.05609877407550812,
-0.040095388889312744,
0.0618111714720726,
-0.03819987177848816,
0.008752178400754929,
0.0026349197141826153,
0.027613580226898193,
-0.03684370219707489,
0.0835411474108696,
0.06297023594379425,
-0.009876735508441925,
-0.023367522284388542,
-0.011560999788343906,
-0.015183478593826294,
-0.030837129801511765,
0.029646093025803566,
0.0025050914846360683,
0.008707101456820965,
-0.00451383413746953,
-0.04119737446308136,
0.012281537055969238,
-0.008474095724523067,
-0.006558052729815245,
0.029269615188241005,
0.013517316430807114,
0.0033796760253608227,
0.00040802586590871215,
0.0014320274349302053,
0.07097682356834412,
-0.014592102728784084,
0.02417522482573986,
0.016102513298392296,
-0.02652069739997387,
0.011765732429921627,
0.016548387706279755,
-0.001498128636740148,
0.009438619948923588,
-0.017467955127358437,
0.06435979902744293,
-0.008025282993912697,
-0.00721909711137414,
0.06024983897805214,
0.033554740250110626,
-0.0017879949882626534,
0.044455450028181076,
0.027317848056554794,
-0.017240356653928757,
0.016404256224632263,
0.02699495665729046,
0.07196329534053802,
0.008477656170725822,
-0.010078811086714268,
-0.025271659716963768,
-0.03063952922821045,
0.006226705387234688,
0.0598982572555542,
0.004686928819864988,
0.012656769715249538,
-0.03929877281188965,
0.03391212597489357,
-0.022328071296215057,
-0.00020998950640205294,
-0.035887379199266434,
0.007823023945093155,
-0.0011790578719228506,
-0.007745032198727131,
0.03390832990407944,
-0.049027614295482635,
-0.0012815470108762383,
-0.006622061133384705,
0.026695387437939644,
0.05385715514421463,
0.01091073453426361,
0.008191630244255066,
0.006351321469992399,
-0.05938874930143356,
-0.08324068784713745,
0.014792308211326599,
0.05014243349432945,
0.026890652254223824,
-0.019175725057721138,
0.03688769415020943,
0.008208246901631355,
-0.007378941401839256,
0.030016647651791573,
-0.03199930861592293,
0.026996608823537827,
0.01124813687056303,
-0.12073272466659546,
-0.03301427140831947,
0.04551538825035095,
0.015415414236485958,
-0.04502695053815842,
-0.07967743277549744,
0.003363657044246793,
0.041765112429857254,
0.07048235088586807,
-0.029410451650619507,
0.014165983535349369,
0.034127019345760345,
0.037560295313596725,
-0.010237173177301884,
-0.0031279893592000008,
-0.024818744510412216,
-0.019604066386818886,
-0.042139191180467606,
0.003552913898602128,
-0.02878333441913128,
0.05014987662434578,
0.011741148307919502,
0.004488970618695021,
-0.028194453567266464,
0.02892223931849003,
-0.03571653738617897,
0.0071572838351130486,
-0.014212488196790218,
-0.002805075841024518,
-0.007746278773993254,
0.08857491612434387,
0.039084553718566895,
-0.01590157486498356,
0.009533323347568512,
-0.040282152593135834,
0.003066473873332143,
-0.01812196709215641,
0.04132412374019623,
0.028215333819389343,
-0.027508117258548737,
-0.01869804784655571,
-0.012730797752737999,
0.015394525602459908,
-0.029985377565026283,
-0.035469185560941696,
-0.01596478559076786,
-0.00316028343513608,
0.02165192738175392,
-0.003456387436017394,
0.016419755294919014,
0.0037876321002840996,
-0.008247816935181618,
-0.0008739843615330756,
-0.025300022214651108,
-0.036691006273031235,
-0.020313410088419914,
0.016110312193632126,
-0.028448188677430153,
-0.04267655685544014,
-0.0010070749558508396,
0.03991745784878731,
0.00315167848020792,
-0.020883839577436447,
-0.050747331231832504,
-0.02457425743341446,
0.010267894715070724,
0.0360456183552742,
0.005368412006646395,
0.0010801804019138217,
0.03965841233730316,
0.005491601303219795,
-0.018303945660591125,
0.022215498611330986,
0.012068170122802258,
0.01836460269987583,
-0.022774342447519302,
-0.019175712019205093,
-0.00654135225340724,
0.01176623534411192,
-0.030880415812134743,
0.01670778915286064,
0.01317973155528307,
-0.02345801144838333,
0.018062837421894073,
-0.013283617794513702,
0.08693600445985794,
0.018377846106886864,
0.002876829355955124,
-0.018758604303002357,
0.016599925234913826,
0.009104509837925434,
0.005758135579526424,
0.017657825723290443,
-0.03960058093070984,
-0.057934410870075226,
-0.03897641599178314,
-0.0030888919718563557,
0.011125000193715096,
-0.04671398177742958,
0.014300436712801456,
0.0229325070977211,
0.04524923861026764,
0.005414030980318785,
0.043774064630270004,
-0.02613406628370285,
-0.07436259090900421,
0.02437487058341503,
-0.02023160457611084,
-0.002161797136068344,
-0.01521480455994606,
0.0058992658741772175,
0.01521299034357071,
0.007725123316049576,
-0.05541478469967842,
-0.03763727471232414,
0.005315844900906086,
-0.029724083840847015,
-0.028827441856265068,
0.010639256797730923,
-0.06515969336032867,
0.041532810777425766,
0.014048631303012371,
0.012337474152445793,
0.00695636123418808,
-0.0011769053526222706,
0.0013297497062012553,
-0.05852735415101051,
0.008843062445521355,
0.024300415068864822,
0.03385592997074127,
-0.002246146323159337,
-0.04987572506070137,
0.03255138173699379,
-0.028132719919085503,
-0.022657619789242744,
-0.009499659761786461,
0.0034397230483591557,
-0.004811339545994997,
0.00788554921746254,
0.05236022546887398,
0.03693362697958946,
0.017169060185551643,
-0.00809508003294468,
-0.04987061023712158,
0.013135455548763275,
-0.024315010756254196,
0.0010411252733319998,
0.0013975488254800439,
-0.04254467785358429,
0.04394202306866646,
-0.032414212822914124,
0.013220112770795822,
0.04507959261536598,
-0.007943728007376194,
0.004020204301923513,
0.026124954223632812,
-0.02335887961089611,
-0.0567178912460804,
-0.00788139272481203,
0.010548369027674198,
0.03757772967219353,
-0.021542033180594444,
0.005638774950057268,
0.07183320075273514,
0.007215536665171385,
-0.026201916858553886,
0.012262900359928608,
-0.010810326784849167,
-0.0316445454955101,
-0.009863005951046944,
-0.013019705191254616,
0.0250471830368042,
-0.011454529128968716,
0.006682923994958401,
0.06963612139225006,
-0.03450397402048111,
-0.02194809913635254,
-0.03839004039764404,
-0.021549664437770844,
0.020545106381177902,
-0.01805519498884678,
0.04255853593349457,
-0.003730427473783493,
-0.02295614592730999,
0.07148788124322891,
0.039813436567783356,
-0.061860743910074234,
0.009399604052305222,
0.0062565584667027,
-0.01841357909142971,
-0.03379364684224129,
0.043406713753938675,
0.005495067685842514,
-0.009230834431946278,
0.026086587458848953,
-0.02111186645925045,
0.06058968976140022,
0.024973716586828232,
-0.014602080918848515,
-0.01464826613664627,
-0.019318293780088425,
0.01300077885389328,
-0.0026745880022644997,
-0.01673170179128647,
0.0015021746512502432,
-0.03740273416042328,
-0.0022004160564392805,
0.021603485569357872,
0.021951382979750633,
0.006916315760463476,
-0.07809630036354065,
0.07148709893226624,
0.0009169095428660512,
0.02600880339741707,
-0.033147603273391724,
0.019992506131529808,
-0.028833752498030663,
-0.016002271324396133,
0.012462040409445763,
0.02475908026099205,
0.058967214077711105,
-0.00597275048494339,
0.012887803837656975,
-0.004974398761987686,
0.021312136203050613,
0.02332565374672413,
-0.011946508660912514,
-0.03098682500422001,
0.009296735748648643,
0.01818697340786457,
0.019369807094335556,
-0.004533922299742699,
0.03561169281601906,
0.009111795574426651,
0.033584970980882645,
-0.002698092022910714,
-0.0265318863093853,
0.0027150718960911036,
-0.06192079186439514,
-0.0001281620643567294,
-0.01691485568881035,
0.037882499396800995,
0.026766829192638397,
0.05505329370498657,
0.04061354696750641,
0.009915055707097054,
-0.027931109070777893,
-0.014818173833191395,
-0.05295420438051224,
-0.022939085960388184,
-0.03946765139698982,
0.013155232183635235,
-0.018830304965376854,
-0.023310311138629913,
-0.023756135255098343,
0.020815454423427582,
-0.04661307856440544,
0.00869917031377554,
-0.013287214562296867,
-0.0528545156121254,
0.02009532041847706,
-0.02860429510474205,
-0.04068379104137421,
-0.014483986422419548,
0.08117447793483734,
0.0391463004052639,
-0.010496086440980434,
0.03754930570721626,
0.03337721899151802,
-0.03421318158507347,
-0.006870925426483154,
-0.007414842955768108,
0.06183331087231636,
-0.005024587735533714,
0.06714703142642975,
-0.006641062907874584,
0.02558344602584839,
0.001961942994967103,
0.013974708504974842,
-0.011220920830965042,
-0.010198771022260189,
0.0028008322697132826,
-0.04217315837740898,
-0.02879149094223976,
-0.06341125071048737,
-0.0034754283260554075,
-0.0009851729264482856,
0.02863662876188755,
-0.004196076653897762,
0.012622605077922344,
0.02599618397653103,
0.010718402452766895,
-0.0393969789147377,
0.025355691090226173,
0.052119091153144836,
0.018909774720668793,
-0.018879607319831848,
-0.07355822622776031,
-0.023264653980731964,
-0.01211603358387947,
-0.022426344454288483,
0.02122255228459835,
-0.02945472113788128,
-0.02424858696758747,
0.016127632930874825,
0.01040349155664444,
-0.0218600332736969,
-0.017443403601646423,
0.01931190676987171,
-0.013430697843432426,
-0.009178798645734787,
-0.04383619874715805,
-0.0029533624183386564,
0.0072989254258573055,
0.035372864454984665,
0.03916625306010246,
0.01913372427225113,
-0.005154082551598549,
-0.04999459534883499,
-0.008284199051558971,
0.03854172304272652,
0.06073944270610809,
-0.044007327407598495,
-0.002947515808045864,
-0.050953324884176254,
-0.02947036735713482,
0.07896561920642853,
-0.02529994770884514,
0.018476011231541634,
-0.03318065032362938,
-0.010660400614142418,
-0.016796737909317017,
-0.01654701493680477,
-0.008152414113283157,
0.011030610650777817,
0.014662479981780052,
0.0016223762650042772,
-0.047552917152643204,
-0.03157602623105049,
0.013466755859553814,
0.007428074721246958,
0.037719596177339554,
0.017965389415621758,
0.03815599903464317,
0.028274565935134888,
0.008788594976067543,
0.023218216374516487,
-0.02661212906241417,
-0.08261473476886749,
0.031399816274642944,
0.013390148989856243,
0.025947850197553635,
0.024967273697257042,
-0.03806120902299881,
-0.06523680686950684,
-0.01024309266358614,
0.011953127570450306,
0.008989745751023293,
-0.022380635142326355,
-0.02257230505347252,
0.035252559930086136,
0.01092454046010971,
-0.030836939811706543,
0.029342977330088615,
0.015374376438558102,
0.016311874613165855,
-0.01757618971168995,
-0.026148149743676186,
0.05287981405854225,
-0.013858212158083916,
0.011269367299973965,
-0.037014350295066833,
0.0076490240171551704,
-0.004168686922639608,
0.014876258559525013,
-0.004422884434461594,
-0.0057640885934233665,
0.026739010587334633,
-0.032422732561826706,
-0.03269488736987114,
0.02690509520471096,
-0.0035663405433297157,
-0.012174755334854126,
0.007594732102006674,
0.00011377476766938344,
0.017267299816012383,
-0.043130531907081604,
0.01168557908385992,
0.01730182394385338,
0.021434281021356583,
0.013983377255499363,
0.0033439474646002054,
-0.01872161217033863,
-0.03457694873213768,
-0.016667215153574944,
0.00811841432005167,
-0.03799891099333763,
0.04748686030507088,
-0.0051653883419930935,
0.008057789877057076,
0.04850957170128822,
-0.051645517349243164,
0.0010222012642771006,
-0.0026189216878265142,
-0.03664655238389969,
0.03210500255227089,
-0.05096253380179405,
0.006458653602749109,
0.000005954719654255314,
0.028155185282230377,
-0.09341082721948624,
-0.026258321478962898,
0.022389821708202362,
-0.004133995622396469,
-0.013288910500705242,
-0.032297469675540924,
-0.015884768217802048,
-0.01950927823781967,
-0.01080644503235817,
0.006807658355683088,
-0.011130446568131447,
-0.0014058378292247653,
-0.0113800298422575,
0.04993747919797897,
0.023168059065937996,
0.06472484022378922,
-0.011946402490139008,
-0.0053499056957662106,
0.009183704853057861,
-0.02603749744594097,
0.001029080944135785,
0.0026146085001528263,
0.04792896658182144,
-0.03223221376538277,
-0.0424979105591774,
0.00395236536860466,
-0.009310397319495678,
0.02545217238366604,
-0.01987142115831375,
0.0065988884307444096,
-0.01718803495168686,
-0.03178483620285988,
0.027041001245379448,
-0.003007156541571021,
0.013095582835376263,
-0.005191539879888296,
0.0003058438596781343,
-0.041335687041282654,
-0.007581453770399094,
-0.0242215096950531,
-0.030254922807216644,
0.03740917146205902,
-0.01225641556084156,
0.02886160835623741,
0.01941191777586937,
0.032108571380376816,
-0.002423276659101248,
-0.03518042340874672,
-0.00008923991117626429,
-0.026417382061481476,
-0.0028213688638061285,
-0.03710871934890747,
-0.020238591358065605,
0.020712394267320633,
0.008619975298643112,
-0.015013101510703564,
-0.04262268543243408,
-0.039662811905145645,
0.04574008285999298,
0.03150920197367668,
-0.05423003435134888,
0.04347094148397446,
0.0008936791564337909,
0.005561626050621271,
-0.04307962954044342,
-0.024343227967619896,
-0.020810769870877266,
-0.005478703882545233,
0.017527494579553604,
0.07666507363319397,
-0.010020396672189236,
-0.017207615077495575,
-0.006039389409124851,
0.03593624755740166,
-0.005236227996647358,
0.041183892637491226,
0.0014891152968630195,
0.005993432831019163,
0.03536136448383331,
-0.005847156513482332,
-0.023102737963199615,
0.04039818048477173,
-0.01745324395596981,
0.0221781637519598,
0.03292449191212654,
0.000021982477846904658,
0.03642462193965912,
-0.024398671463131905,
0.0276144091039896,
-0.036619801074266434,
-0.008059914223849773,
-0.030013611540198326,
-0.014391190372407436,
0.06447184830904007,
0.02376069501042366,
-0.02229602262377739,
0.01657678931951523,
0.03493545576930046,
0.008970853872597218,
-0.00022198009537532926,
0.017467334866523743,
-0.04019847512245178,
-0.04236812889575958,
-0.03264198079705238,
-0.045474324375391006,
0.042207472026348114,
-0.02281852997839451,
-0.008567027747631073,
-0.018280236050486565,
-0.025968775153160095,
0.03441522642970085,
0.0342380665242672,
0.0422351136803627,
-0.011223286390304565,
0.04229145124554634,
0.01893884316086769,
0.0005977137479931116,
-0.02702806517481804,
-0.020892277359962463,
0.11412686854600906,
0.03881789743900299,
-0.006674653384834528,
-0.05931321531534195,
-0.0024382027331739664,
-0.01717366836965084,
0.01348416693508625,
-0.0074388934299349785,
-0.02355165220797062,
-0.014133176766335964,
0.0071570673026144505,
0.009504597634077072,
0.05826069414615631,
0.01970587857067585,
0.0013594517949968576,
0.016855550929903984,
-0.008447125554084778,
-0.05983036383986473,
-0.0036586897913366556,
-0.005115803796797991,
-0.007377633824944496,
0.0022771742660552263,
-0.05390201881527901,
0.037831973284482956,
-0.001604224438779056,
-0.017079820856451988,
-0.016000263392925262,
-0.017513291910290718,
0.009177585132420063,
0.03241144120693207,
-0.021384330466389656,
-0.009157909080386162,
-0.0012908759526908398,
-0.01655399799346924,
-0.018705375492572784,
0.027136193588376045,
0.009150347672402859,
-0.057961639016866684,
0.029640328139066696,
0.038759585469961166,
-0.0055261035449802876,
0.005248041823506355,
0.021673403680324554,
0.005708446726202965,
-0.05004904046654701,
-0.037660665810108185,
-0.0005307704559527338,
0.019284281879663467,
-0.011800459586083889,
-0.008660647086799145,
-0.03243968263268471,
0.024075228720903397,
0.04822772368788719,
-0.05068036913871765,
-0.004005596041679382,
0.003868001513183117,
0.020919425413012505,
-0.022552872076630592,
-0.011176097206771374,
0.00796916801482439,
0.011264042928814888,
-0.008835929445922375,
0.04658693075180054,
-0.005813921336084604,
-0.002724753925576806,
0.0018392392667010427,
0.012004561722278595,
0.0361606627702713,
0.008233873173594475,
-0.0015461213188245893,
-0.055084653198719025,
0.03750446438789368,
-0.051665887236595154,
0.006691725458949804,
0.014481171034276485,
0.04966404661536217,
0.004027476999908686,
0.008832781575620174,
-0.013749639503657818,
0.008675799705088139,
-0.006277257576584816,
0.037220824509859085,
-0.047880642116069794,
-0.01264541782438755,
-0.03346455842256546,
0.009826362133026123,
-0.0051375990733504295,
0.03130976855754852,
-0.03517037257552147,
-0.002412065165117383,
-0.02058013714849949,
-0.015820175409317017,
0.034623075276613235,
-0.024518895894289017,
0.003053450956940651,
0.059258174151182175,
-0.04643672704696655,
0.017984000965952873,
0.01507027167826891,
0.05188152194023132,
0.04135899245738983,
-0.026896821334958076,
0.028746169060468674,
0.036184463649988174,
-0.018298033624887466,
-0.048061057925224304,
-0.010651362128555775,
-0.03859519213438034,
0.006200507748872042,
-0.020205626264214516,
-0.02361840195953846,
-0.047618426382541656,
-0.02199525013566017,
-0.014582906849682331,
0.0013672967907041311,
0.018243417143821716,
0.03735342249274254,
-0.013504290021955967,
0.0010988465510308743,
-0.043746668845415115,
0.02528628520667553,
0.005899148061871529,
0.008110767230391502,
-0.02721942774951458,
-0.0011756991734728217,
-0.001465519773773849,
0.018841449171304703,
-0.020236950367689133,
0.021024443209171295,
-0.027768798172473907,
-0.02575943060219288,
0.013987760059535503,
0.014871670864522457,
-0.0014081280678510666,
0.0013131978921592236,
0.034294772893190384,
0.024105986580252647,
0.04284712299704552,
-0.004513260908424854,
-0.007905354723334312,
0.057220593094825745,
-0.05618136003613472,
-0.0659748837351799,
0.027007238939404488,
-0.023238444700837135,
0.020087046548724174,
0.03686346858739853,
0.0036918441765010357,
-0.011876273900270462,
0.06846972554922104,
0.000986400875262916,
0.004359711892902851,
0.01750580593943596,
-0.003673228435218334,
0.021421542391180992,
-0.005015830509364605,
0.01826106570661068,
-0.0335627906024456,
-0.006089760456234217,
0.03979974985122681,
-0.00926505122333765,
0.017307646572589874,
0.01453677099198103,
-0.05495094507932663,
-0.00640871562063694,
0.006490495055913925,
0.01788158155977726,
0.005323872435837984,
-0.03672230988740921,
0.046213746070861816,
-0.041474759578704834,
0.05505672097206116,
0.02248506247997284,
0.01025515515357256,
-0.08953355997800827,
0.018372638151049614,
0.007621421478688717,
-0.004423499573022127,
0.013252422213554382,
-0.07702741771936417,
0.025431497022509575,
0.02258913591504097,
-0.11019710451364517,
0.05459868907928467,
-0.04084828868508339,
-0.027600079774856567,
-0.03213677182793617,
-0.010590394027531147,
-0.0019044032087549567,
0.05194981023669243,
0.05101677030324936,
0.04526769742369652,
0.01047271117568016,
-0.012802192009985447,
-0.04883287847042084,
0.00266973371617496,
-0.025036878883838654,
0.030755260959267616,
-0.02319006249308586,
0.008538752794265747,
0.06280579417943954,
-0.002847939496859908,
-0.04776367172598839,
0.030835090205073357,
-0.011725371703505516,
0.03430265560746193,
-0.032537754625082016,
-0.01007890421897173,
0.02303849346935749,
0.00829134602099657,
-0.0026806227397173643,
0.006241421680897474,
0.024272821843624115,
0.024711446836590767,
0.036113109439611435,
0.02487468533217907,
0.0005108954501338303,
-0.01510584820061922,
-0.02031158097088337,
-0.03594231233000755,
-0.018166514113545418,
0.04753638431429863,
-0.0031456532888114452,
-0.007037147413939238,
-0.04429185763001442,
-0.0142815625295043,
0.05808167904615402,
-0.04242471233010292,
0.0041810814291238785,
-0.050201013684272766,
-0.016665512695908546,
-0.002661692211404443,
0.007038790266960859,
-0.0037517498712986708,
0.06906460225582123,
-0.003358484711498022,
-0.05741375684738159,
0.0015622786013409495,
-0.004668066743761301,
-0.020007790997624397,
-0.03556498885154724,
-0.028201419860124588,
0.03350992500782013,
0.017846165224909782,
0.013880853541195393,
-0.002340154256671667,
-0.05494140088558197,
0.028096362948417664,
0.03158324956893921,
0.07472696155309677,
0.026972519233822823,
-0.060243621468544006,
-0.0570048913359642,
-0.0904923528432846,
0.03414001315832138,
0.009106844663619995,
-0.02126266062259674,
-0.0538422130048275,
-0.011943196877837181,
-0.009594053030014038,
0.03033287078142166,
0.04333087429404259,
0.01717815361917019,
-0.0027429761830717325,
-0.030504949390888214,
-0.01946478709578514,
0.0060886722058057785,
-0.03484334424138069,
-0.019924355670809746,
-0.00470866821706295,
-0.027513179928064346,
-0.016460243612527847,
0.010121108964085579,
-0.043478935956954956,
0.022385170683264732,
-0.022930974140763283,
-0.003920635208487511,
0.008621079847216606,
0.005934754386544228,
-0.03966245427727699,
0.057300176471471786,
-0.0030796395149081945,
-0.00006940931780263782,
0.06539837270975113,
-0.00037114243605174124,
0.0009777311934158206,
0.006738006602972746,
-0.05063207820057869,
-0.014900547452270985,
-0.001442922162823379,
-0.011314031668007374,
-0.008411159738898277,
-0.033249709755182266,
-0.00038700096774846315,
0.04889710247516632,
0.006296015344560146,
0.01170192938297987,
0.037964701652526855,
-0.0223248228430748,
-0.005555912386626005,
0.05417599529027939,
0.017310388386249542,
0.03625663369894028,
0.005174599122256041,
0.0033392927143722773,
0.0446477048099041,
-0.011239754036068916,
0.022679530084133148,
0.07517562061548233,
0.038643088191747665,
0.005383843090385199,
0.00886573176831007,
0.02229267545044422,
0.004679641220718622,
0.014978200197219849,
0.04611387848854065,
0.08820150047540665,
-0.0276016928255558,
0.0005411485908553004,
0.035535745322704315,
-0.012995077297091484,
-0.02212594635784626,
0.012245220132172108,
-0.052277494221925735,
0.08295188844203949,
-0.012489981018006802,
0.02782740443944931,
0.0019852614495903254,
-0.016832511872053146,
0.019357148557901382,
0.004776555113494396,
0.019177116453647614,
0.04068965092301369,
-0.03884781524538994,
-0.03199774771928787,
0.010532446205615997,
0.022864483296871185,
0.043786246329545975,
-0.025782646611332893,
0.0032613438088446856,
-0.03767329826951027,
0.017684031277894974,
0.007393775507807732,
-0.005318030249327421,
-0.006958484183996916,
-0.00664923619478941,
0.05186481773853302,
0.031053369864821434,
0.015906618908047676,
0.028603266924619675,
0.011140957474708557,
-0.02877829037606716,
0.10117792338132858,
-0.06573912501335144,
-0.017860135063529015,
-0.07278116047382355,
0.07555048912763596,
-0.03951789811253548,
0.0213734470307827
] |
<p>I would like to ask what are the experimental evidences that led to the conclusion that QCD is the right theory to describe strong interactions. I know that some of the key point are the decay of $\pi_{0}$ and the measurement of Jets but I'd love to see a full answer to this question. Is there a still a chance to <a href="http://en.wikipedia.org/wiki/Regge_theory">Regge theory</a> nowadays?</p> | 2,817 | [
-0.005599647294729948,
-0.009652357548475266,
-0.009852832183241844,
-0.05651763081550598,
0.03682536259293556,
0.05286300927400589,
0.01669389195740223,
-0.03256012871861458,
0.03299296274781227,
-0.04362524300813675,
0.019545864313840866,
0.00894737895578146,
0.03937724232673645,
0.01876061223447323,
-0.007392730098217726,
0.032305777072906494,
0.005460248328745365,
-0.023701254278421402,
0.002285861875861883,
0.0018299523508176208,
-0.024594895541667938,
0.02397635020315647,
-0.027163811028003693,
0.03600585460662842,
-0.030615299940109253,
-0.0036728479899466038,
0.006890992633998394,
0.04416019096970558,
-0.003440701635554433,
0.048933036625385284,
-0.011132600717246532,
-0.02627803012728691,
-0.005973206367343664,
0.014370771124958992,
0.01832636259496212,
-0.000009465204129810445,
0.03913791477680206,
-0.04363144934177399,
-0.006109785754233599,
0.02477843686938286,
-0.021953023970127106,
-0.04968184977769852,
0.006220400799065828,
0.02052786760032177,
-0.03373170271515846,
-0.011742859147489071,
-0.011877150274813175,
-0.050215888768434525,
0.0873352512717247,
-0.06432925164699554,
0.03567195683717728,
0.0032950094901025295,
0.03849082440137863,
0.01529000699520111,
-0.020547671243548393,
-0.04412645101547241,
0.056376852095127106,
0.04128550365567207,
-0.01140622328966856,
-0.06803677976131439,
-0.03749940171837807,
-0.026465458795428276,
0.01703176088631153,
0.005177555605769157,
-0.047544870525598526,
0.026493532583117485,
-0.013960082083940506,
-0.0022883897181600332,
0.031172407791018486,
-0.014091193675994873,
0.011284400708973408,
-0.0008204837795346975,
0.04107131436467171,
0.04123541712760925,
0.016721472144126892,
0.021056316792964935,
-0.00118786352686584,
0.01195178646594286,
0.027567589655518532,
0.02202812395989895,
-0.038533736020326614,
-0.009420114569365978,
0.027391254901885986,
0.016446173191070557,
0.0010423957137390971,
0.0032189281191676855,
0.07289866358041763,
-0.030896976590156555,
-0.05201290547847748,
0.040129244327545166,
-0.024248722940683365,
-0.016549812629818916,
0.020536843687295914,
0.01155943050980568,
-0.011087644845247269,
0.003723990870639682,
0.013567613437771797,
0.049175020307302475,
0.0020187264308333397,
-0.0031884789932519197,
0.025791360065340996,
-0.00944644957780838,
-0.01078388188034296,
0.07473144680261612,
-0.023812782019376755,
-0.0015231233555823565,
-0.012528856284916401,
-0.00044696382246911526,
-0.04829908162355423,
-0.017983390018343925,
-0.028980711475014687,
0.025720087811350822,
0.003582906210795045,
0.008897818624973297,
-0.014867120422422886,
-0.017771560698747635,
0.0031518563628196716,
-0.02562306635081768,
0.1154935359954834,
0.06324896216392517,
0.0462883859872818,
-0.049294743686914444,
-0.014149322174489498,
-0.03505469113588333,
-0.029830515384674072,
0.00035238207783550024,
0.059998974204063416,
-0.017268585041165352,
-0.024789420887827873,
0.05239452049136162,
0.0004745119658764452,
0.0068252207711339,
-0.041176192462444305,
0.008658873848617077,
0.053937312215566635,
-0.0399920828640461,
-0.09828778356313705,
-0.048115625977516174,
0.04541495069861412,
-0.011882902123034,
-0.031086871400475502,
-0.07888250052928925,
0.0002705705410335213,
0.020501887425780296,
0.08304096013307571,
-0.039375293999910355,
0.018555641174316406,
-0.01725236140191555,
0.01812131702899933,
-0.006577657535672188,
-0.020381109789013863,
-0.022910630330443382,
0.049143169075250626,
-0.016547320410609245,
-0.039555955678224564,
-0.06355126202106476,
-0.023057499900460243,
0.008873299695551395,
-0.022521382197737694,
-0.02334410883486271,
0.0665348544716835,
-0.02246297523379326,
0.000789664511103183,
0.022247817367315292,
-0.00942507479339838,
-0.004323568660765886,
0.09409024566411972,
0.045867592096328735,
-0.007432478945702314,
0.03762954846024513,
-0.004870974458754063,
0.02668331004679203,
0.055176857858896255,
-0.005846390035003424,
0.017229624092578888,
-0.024914581328630447,
-0.042955026030540466,
0.005235069431364536,
-0.010023459792137146,
-0.033014148473739624,
-0.022713754326105118,
0.012084887363016605,
-0.017289603129029274,
-0.005035203415900469,
-0.013765999116003513,
0.04979391023516655,
-0.023338712751865387,
-0.02369452826678753,
0.04686012119054794,
-0.043298933655023575,
-0.03328987583518028,
-0.057930607348680496,
-0.0004949307185597718,
-0.009453612379729748,
-0.013718059286475182,
0.003634802531450987,
-0.018709948286414146,
-0.006780993193387985,
-0.01334192045032978,
-0.0240824893116951,
-0.006631406024098396,
0.030285056680440903,
0.002956882817670703,
0.021900128573179245,
0.0033602104522287846,
0.027315933257341385,
0.016852589324116707,
-0.05162695422768593,
0.018255412578582764,
-0.01083758007735014,
-0.020915526896715164,
0.009691596031188965,
-0.026526881381869316,
-0.004376489669084549,
0.005199150647968054,
0.013655257411301136,
0.027078019455075264,
-0.014594594947993755,
-0.0035170679911971092,
0.03807733580470085,
0.0021192296408116817,
0.06400591135025024,
-0.005920793861150742,
0.009682313539087772,
-0.019279317930340767,
0.04493109881877899,
-0.019709769636392593,
0.012592418119311333,
-0.0008346072281710804,
-0.024469848722219467,
-0.05433354899287224,
-0.00829954631626606,
0.04649315029382706,
0.04266703873872757,
-0.04542387276887894,
0.037081457674503326,
0.01987234130501747,
0.016052864491939545,
0.0018629399128258228,
0.03225858882069588,
-0.03460412472486496,
-0.05140937119722366,
0.008216395042836666,
0.04896976053714752,
-0.03427993506193161,
0.009329010732471943,
-0.007075684145092964,
0.02247329242527485,
-0.0011058623204007745,
0.03327511250972748,
-0.0243714340031147,
0.028916196897625923,
-0.019603820517659187,
0.0027925092726945877,
0.008387334644794464,
-0.057430658489465714,
0.0355415865778923,
-0.023447060957551003,
0.04503975063562393,
-0.019401932135224342,
-0.002746687037870288,
0.01980695314705372,
-0.023475216701626778,
-0.030628981068730354,
0.029834751039743423,
0.004967586603015661,
-0.009640459902584553,
-0.018412889912724495,
0.026521766558289528,
-0.04379798844456673,
0.013052568770945072,
-0.037412721663713455,
-0.032655563205480576,
-0.03982314467430115,
0.0011378532508388162,
0.030252451077103615,
0.00494467094540596,
-0.004196694120764732,
-0.019612988457083702,
-0.02611854486167431,
0.023704223334789276,
-0.06724807620048523,
0.0363846980035305,
0.04366999492049217,
-0.017345236614346504,
-0.0019645781721919775,
-0.09959228336811066,
0.018724845722317696,
0.015507037751376629,
-0.03225268796086311,
0.02018864080309868,
0.025115331634879112,
-0.01138316746801138,
-0.05439089611172676,
-0.0018714835168793797,
-0.04462716355919838,
0.0301068052649498,
0.0005878480151295662,
0.01128513552248478,
0.02779129520058632,
0.014113136567175388,
-0.042157452553510666,
0.026279866695404053,
-0.01245927531272173,
-0.005984371528029442,
0.01041566301137209,
0.011573076248168945,
0.014599964022636414,
-0.03309421241283417,
0.0532640777528286,
0.03985212370753288,
-0.03023456037044525,
-0.016813160851597786,
-0.033079467713832855,
-0.033195119351148605,
0.03241587430238724,
0.014887714758515358,
0.015751823782920837,
-0.0106742512434721,
-0.0077117024920880795,
0.060848258435726166,
0.032847464084625244,
-0.05725982412695885,
-0.015331482514739037,
0.015796741470694542,
-0.0049081663601100445,
-0.03715413063764572,
0.018606463447213173,
0.009431015700101852,
-0.003790308255702257,
0.03855948895215988,
-0.013686166144907475,
0.04066561535000801,
-0.024393631145358086,
0.04025963321328163,
-0.031078753992915154,
0.02630472742021084,
0.006357396952807903,
-0.0013677366077899933,
0.04129011556506157,
0.01980028860270977,
-0.07444138824939728,
-0.03713122010231018,
0.00873315054923296,
0.025674480944871902,
0.02489543706178665,
-0.04431205615401268,
0.08940183371305466,
0.0055166310630738735,
0.019481515511870384,
-0.009895543567836285,
-0.01019294373691082,
-0.015497052110731602,
-0.03386347368359566,
0.05520154535770416,
0.01185322180390358,
-0.004852563142776489,
0.011469482444226742,
0.007672532461583614,
0.02037840709090233,
0.03788609057664871,
-0.030711546540260315,
-0.03311266377568245,
-0.06301902234554291,
-0.017564289271831512,
0.015022133477032185,
0.011336216703057289,
-0.01627216301858425,
0.016418922692537308,
0.014871207065880299,
0.02315245009958744,
-0.019505832344293594,
-0.03466607630252838,
-0.004217902664095163,
-0.05178362503647804,
0.010809274390339851,
-0.023863591253757477,
0.06179032847285271,
0.0045152525417506695,
0.036647360771894455,
0.03395994007587433,
-0.017194034531712532,
-0.0014949861215427518,
-0.010495351627469063,
-0.10464867949485779,
0.03173957020044327,
-0.04775528237223625,
-0.011334619484841824,
-0.029349086806178093,
-0.030274853110313416,
-0.014767981134355068,
-0.005342274438589811,
-0.035493023693561554,
-0.0359872505068779,
-0.020197974517941475,
-0.05967021360993385,
-0.01255879644304514,
-0.04404657706618309,
-0.03479215130209923,
-0.023091133683919907,
0.03427814319729805,
0.050426777452230453,
-0.024422915652394295,
-0.015097304247319698,
-0.004037295933812857,
-0.04063800722360611,
-0.039592064917087555,
-0.0037442375905811787,
0.0327763706445694,
-0.020639872178435326,
0.030780130997300148,
0.05296091362833977,
0.03099704161286354,
-0.0326700285077095,
0.019711120054125786,
0.041965268552303314,
0.06336433440446854,
0.022624759003520012,
-0.01416357234120369,
-0.010022744536399841,
-0.05275701358914375,
0.014636562205851078,
0.022240133956074715,
0.05043879151344299,
0.0339663028717041,
-0.021868538111448288,
0.021413316950201988,
0.015536917373538017,
-0.048056937754154205,
0.0467178151011467,
0.0318981297314167,
-0.004480455536395311,
-0.03089287504553795,
-0.03094259835779667,
-0.034552305936813354,
0.018567876890301704,
-0.024604566395282745,
-0.004370870999991894,
0.00038346467772498727,
-0.006646635010838509,
0.01376072596758604,
0.035175081342458725,
0.04875508323311806,
-0.07098522782325745,
-0.002902303822338581,
-0.014919585548341274,
0.0048325988464057446,
-0.005102761089801788,
0.009146700613200665,
-0.01167868822813034,
0.03971713036298752,
0.059647656977176666,
0.03113866224884987,
0.002612423850223422,
-0.040478721261024475,
0.010363852605223656,
0.045236192643642426,
0.053184423595666885,
-0.034900862723588943,
0.009715081192553043,
-0.025208240374922752,
-0.015800602734088898,
0.05277400091290474,
-0.039064694195985794,
0.010329646058380604,
-0.04638129472732544,
-0.003377887886017561,
-0.028590312227606773,
-0.010063579306006432,
0.001023722579702735,
0.019605116918683052,
0.03535909205675125,
0.004866487812250853,
-0.03155149891972542,
-0.024642271921038628,
-0.01126385759562254,
0.03728754445910454,
0.02341308444738388,
0.04714779555797577,
0.021697998046875,
0.04085114970803261,
-0.003172942204400897,
0.01787768490612507,
-0.026923969388008118,
-0.07432597875595093,
0.023535722866654396,
0.007623674347996712,
-0.016439829021692276,
0.06627335399389267,
-0.029695186764001846,
-0.06137225776910782,
-0.012293037958443165,
0.009400896728038788,
-0.01096772775053978,
0.011754203587770462,
-0.06526606529951096,
0.009575690142810345,
0.025891339406371117,
-0.0006987520027905703,
0.052832890301942825,
0.05259041488170624,
-0.034176304936409,
-0.014096146449446678,
0.004808458033949137,
0.033462103456258774,
-0.03113924153149128,
-0.00013100718206260353,
-0.02239440195262432,
0.004432248417288065,
-0.03275489807128906,
0.04378862679004669,
-0.029623715206980705,
0.034258365631103516,
-0.004786735866218805,
-0.03926008939743042,
-0.020339976996183395,
0.02886558137834072,
0.00915287435054779,
-0.021978899836540222,
-0.0004642148269340396,
0.031025778502225876,
0.02626236155629158,
-0.01677083410322666,
0.0011699985479936004,
-0.0014474239433184266,
-0.0210415031760931,
-0.004011990502476692,
-0.0004583690024446696,
0.016650371253490448,
0.00045999520807527006,
-0.0036498168483376503,
-0.01548809465020895,
-0.008217261172831059,
0.05995143949985504,
-0.030072197318077087,
-0.01119934767484665,
-0.012679699808359146,
-0.05504155531525612,
-0.01835755445063114,
0.006617951672524214,
-0.0009118249290622771,
0.035180311650037766,
-0.02847480960190296,
0.024361271411180496,
-0.0156273003667593,
0.0022349986247718334,
-0.07678921520709991,
-0.040608689188957214,
0.004222084768116474,
0.02690931409597397,
-0.03612194582819939,
0.00025348496274091303,
-0.019815806299448013,
-0.027056144550442696,
-0.023966263979673386,
-0.025055330246686935,
0.02880854718387127,
-0.0435025580227375,
-0.005819373298436403,
0.039729733020067215,
0.018324092030525208,
0.025912601500749588,
-0.00040983755025081336,
-0.022975804284214973,
0.0007556596538051963,
-0.00508017698302865,
0.009934132918715477,
0.0053934622555971146,
0.029620936140418053,
-0.0024555257987231016,
-0.018174007534980774,
-0.00960855558514595,
0.010730370879173279,
0.016309920698404312,
-0.017482483759522438,
0.007090508472174406,
0.0631483718752861,
-0.006574355065822601,
0.021528009325265884,
-0.020987436175346375,
0.0028386549092829227,
-0.01439464371651411,
0.024125704541802406,
-0.00410048384219408,
0.015166708268225193,
-0.02839558757841587,
-0.02442759834229946,
0.06904694437980652,
-0.021271895617246628,
0.027394616976380348,
0.0297445859760046,
-0.011049509979784489,
0.040301159024238586,
-0.04574021324515343,
0.006286153104156256,
-0.03313853591680527,
0.008932818658649921,
-0.006586151197552681,
0.04921592399477959,
-0.015928877517580986,
0.02188103459775448,
-0.019314317032694817,
-0.04413653165102005,
0.005656362045556307,
-0.01820920966565609,
0.08020111173391342,
0.022149687632918358,
0.03340259566903114,
0.00266169267706573,
-0.018548985943198204,
-0.03743875399231911,
-0.014877541922032833,
-0.009213254787027836,
0.012306737713515759,
0.03470935672521591,
0.014354407787322998,
-0.010638566687703133,
0.008858874440193176,
0.01772550493478775,
0.03391626104712486,
-0.006432836875319481,
-0.0047182319685816765,
0.02384004555642605,
0.003626415738835931,
0.044412385672330856,
-0.01340015884488821,
-0.01646237075328827,
0.04312412813305855,
-0.04624836891889572,
0.01564430445432663,
-0.005638718605041504,
0.010784555226564407,
0.0060335141606628895,
-0.0022161409724503756,
0.007685542106628418,
-0.0044998363591730595,
0.005201240535825491,
-0.06410033255815506,
0.00472654914483428,
0.0062388405203819275,
0.01488742046058178,
0.012103988789021969,
0.017564093694090843,
0.0013894445728510618,
0.0155188525095582,
0.023612694814801216,
0.009709746576845646,
-0.09443662315607071,
-0.012969134375452995,
-0.004255214706063271,
-0.002659530844539404,
0.06060127913951874,
-0.024247637018561363,
-0.030321864411234856,
-0.013359745033085346,
-0.019320247694849968,
-0.0037979306653141975,
-0.0059030489064753056,
0.011386019177734852,
-0.02064458467066288,
0.027298124507069588,
-0.021138353273272514,
0.02453109435737133,
0.003920586314052343,
0.010439084842801094,
0.11019571870565414,
0.06286197900772095,
0.0018142650369554758,
-0.07707158476114273,
0.014788277447223663,
0.0039646378718316555,
0.006423021666705608,
-0.03084455616772175,
0.049143947660923004,
0.0323215052485466,
0.013834547251462936,
0.005907972808927298,
0.058183010667562485,
0.027523821219801903,
0.02159244939684868,
0.039320915937423706,
-0.011547571048140526,
-0.0845617726445198,
0.006112963426858187,
0.03632649779319763,
-0.023783870041370392,
-0.004773659631609917,
-0.008981484919786453,
0.019381798803806305,
-0.0018057192210108042,
-0.021645158529281616,
0.026933159679174423,
-0.015505420975387096,
-0.002224545693024993,
-0.01359145250171423,
-0.02848987653851509,
0.013383856043219566,
0.007261869963258505,
0.02153811603784561,
-0.06960264593362808,
0.012656135484576225,
-0.01694345287978649,
0.02589958719909191,
-0.0017969028558582067,
0.030771926045417786,
0.020755521953105927,
-0.03701181709766388,
0.0038042820524424314,
0.0069024027325212955,
-0.03175712749361992,
-0.0578683577477932,
-0.007701332215219736,
0.040806978940963745,
-0.012208139523863792,
-0.017825139686465263,
0.02049153670668602,
0.0012077840510755777,
-0.0016706293681636453,
-0.016110742464661598,
-0.00967276468873024,
0.03288057819008827,
0.05712660402059555,
-0.06694423407316208,
-0.017719369381666183,
-0.0013458032626658678,
0.066482312977314,
-0.07461992651224136,
0.02952948957681656,
0.015538308769464493,
-0.02501077391207218,
-0.012964545749127865,
-0.03702833876013756,
0.025719447061419487,
0.030435753986239433,
-0.0019315618555992842,
-0.005550048779696226,
0.008835950866341591,
-0.03172636032104492,
-0.013547640293836594,
0.0105279590934515,
0.03310211002826691,
0.04476187005639076,
0.02232307195663452,
0.007866776548326015,
-0.031321197748184204,
-0.06737235188484192,
0.07663648575544357,
-0.04023408517241478,
-0.03075781837105751,
-0.02561059407889843,
-0.002929832087829709,
0.030023666098713875,
0.05852759629487991,
0.0035920992959290743,
-0.019251879304647446,
-0.034394051879644394,
0.014424221590161324,
0.0028415073174983263,
-0.04105598106980324,
-0.035020846873521805,
0.010817119851708412,
-0.049534667283296585,
-0.016484564170241356,
-0.00852043554186821,
0.04420200735330582,
0.020647326484322548,
0.006182130891829729,
0.037176307290792465,
0.0025705702137202024,
-0.027625124901533127,
-0.00044965778943151236,
0.04101180657744408,
-0.03672296553850174,
0.01371048390865326,
-0.027420926839113235,
0.01197226531803608,
-0.025078052654862404,
-0.04832866042852402,
-0.047325100749731064,
0.02345377951860428,
0.02466662973165512,
-0.0069482154212892056,
-0.0007313763489946723,
0.04623693972826004,
-0.002717903582379222,
0.02372206561267376,
-0.03128804266452789,
-0.007661346346139908,
-0.04115547612309456,
0.0009518717415630817,
-0.029788222163915634,
-0.029887348413467407,
-0.006989059969782829,
0.011670613661408424,
0.02600296027958393,
-0.05642973631620407,
0.008552495390176773,
0.02468363381922245,
-0.05575769767165184,
-0.0288231298327446,
-0.005253567826002836,
0.006222532596439123,
0.04656107351183891,
-0.017835859209299088,
-0.010650870390236378,
0.033580780029296875,
-0.05175783112645149,
-0.05270397290587425,
0.018634503707289696,
-0.02160485088825226,
-0.016169298440217972,
0.011388372629880905,
0.01283207256346941,
0.00919984932988882,
0.0392848402261734,
0.0034366666804999113,
-0.011533617042005062,
0.009623605757951736,
-0.010711105540394783,
0.017033228650689125,
0.019709348678588867,
0.04030513018369675,
0.005380815360695124,
0.004330586642026901,
0.0382469967007637,
-0.0031094071455299854,
-0.013355559669435024,
0.010487676598131657,
0.014443175867199898,
-0.01942659541964531,
0.08135400712490082,
0.019767217338085175,
0.020478488877415657,
0.010398332960903645,
0.056840185075998306,
-0.038364361971616745,
0.03058844618499279,
-0.0183323435485363,
-0.020760588347911835,
-0.08677130937576294,
-0.018338775262236595,
-0.0017352921422570944,
-0.008853808976709843,
0.024029942229390144,
-0.06814336031675339,
0.054042913019657135,
0.04442603141069412,
-0.05466039478778839,
0.030539190396666527,
-0.03459160402417183,
0.001276151044294238,
-0.03040430322289467,
-0.005351253319531679,
0.002082191174849868,
0.04744789004325867,
0.043799739331007004,
0.055949050933122635,
0.020991308614611626,
0.003169034840539098,
0.020310048013925552,
0.026889018714427948,
-0.03444930911064148,
-0.012432863004505634,
0.015017157420516014,
-0.010987565852701664,
0.07796591520309448,
-0.024702906608581543,
-0.02978728711605072,
0.02724403701722622,
0.03317468613386154,
0.019083451479673386,
-0.003629278391599655,
-0.012406398542225361,
-0.009592081420123577,
0.04881693795323372,
0.034271709620952606,
-0.03781691566109657,
0.004923342727124691,
0.0035219162236899137,
-0.003663690062239766,
0.04357878118753433,
-0.006466661114245653,
0.02180333249270916,
-0.016921373084187508,
-0.04408099129796028,
-0.013934615068137646,
0.023377515375614166,
0.006511426065117121,
-0.01619654707610607,
0.03048809804022312,
-0.00555217731744051,
0.02774161659181118,
0.006982407066971064,
-0.012044359929859638,
-0.02544911950826645,
0.000438209914136678,
0.03767789527773857,
0.047495074570178986,
0.014242008328437805,
0.030743608251214027,
-0.03144991397857666,
-0.007939856499433517,
0.012427635490894318,
0.006220515817403793,
-0.004649676848202944,
-0.04390603303909302,
-0.025784941390156746,
-0.0037342202849686146,
0.04771209508180618,
-0.0015321128303185105,
-0.03168874606490135,
-0.04456418380141258,
0.005721366964280605,
-0.000903598906006664,
0.04520079120993614,
-0.0012870426289737225,
-0.0480809360742569,
0.00989135354757309,
-0.03234020620584488,
0.05253845080733299,
0.03573991358280182,
0.01715797558426857,
-0.025066746398806572,
-0.007376309018582106,
0.0106206638738513,
-0.005257831420749426,
0.03519990295171738,
-0.010925806127488613,
-0.03317945823073387,
0.03374835476279259,
0.0023604976013302803,
-0.015609147027134895,
-0.02379290573298931,
-0.012774982489645481,
-0.024718552827835083,
0.005657522939145565,
-0.025525065138936043,
-0.01693635806441307,
0.0032472056336700916,
0.04584609717130661,
0.0304450374096632,
0.0019343853928148746,
0.02976895309984684,
-0.011887505650520325,
-0.05891890078783035,
0.0826394259929657,
0.014819900505244732,
0.016028394922614098,
0.06502454727888107,
-0.012928342446684837,
0.027566922828555107,
0.003558490192517638,
-0.02105148881673813,
-0.010758894495666027,
0.05010291188955307,
-0.036826618015766144,
-0.017286619171500206,
-0.008869828656315804,
-0.013458821922540665,
0.008284050039947033,
-0.044817011803388596,
0.021259939298033714,
0.04562588781118393,
-0.02109649032354355,
-0.001934207626618445,
0.047792948782444,
0.03664085268974304,
0.015482334420084953,
0.0069908685982227325,
0.008200989104807377,
0.0331135168671608,
0.024970699101686478,
0.008628764189779758,
0.058934058994054794,
0.05356309190392494,
0.031002137809991837,
0.01109969150274992,
0.01292320154607296,
0.013304190710186958,
0.0001288578350795433,
-0.0033874129876494408,
0.04791106656193733,
-0.026645300909876823,
-0.003343819174915552,
0.007028570398688316,
-0.041508741676807404,
-0.010082287713885307,
0.02928711287677288,
-0.05550938844680786,
0.07341571152210236,
-0.059471338987350464,
-0.0062492843717336655,
-0.008505170233547688,
-0.03260570764541626,
0.006600039545446634,
0.017482493072748184,
0.0238482728600502,
0.056885749101638794,
-0.009871022775769234,
0.03126436844468117,
0.012598474510014057,
-0.01450349111109972,
0.020289696753025055,
-0.007200722116976976,
0.00019953155424445868,
0.014533051289618015,
-0.025407349690794945,
-0.03851831704378128,
-0.0027755885384976864,
-0.023353541269898415,
-0.028105318546295166,
0.013141253031790257,
0.05933898687362671,
0.013853251002728939,
-0.014843753539025784,
-0.021571505814790726,
-0.03958683833479881,
0.05565584823489189,
-0.03486305847764015,
0.02994648739695549,
-0.036991704255342484,
0.0036950204521417618,
-0.025183172896504402,
-0.0034705360885709524
] |
<p>I have been wondering recently how useful programming is to a physicist. It seems fairly useful (simulations are a lot cheaper than the actual thing in many cases) in some areas (say space programs), but in other areas (for example at CERN) it seems pointless. So is it useful and perhaps how do you use it?</p> | 2,818 | [
0.03053727187216282,
-0.005298523232340813,
-0.040448445826768875,
-0.07673399895429611,
0.054734524339437485,
0.0445043183863163,
0.0023555289953947067,
-0.0511457733809948,
-0.014619071036577225,
-0.007357994094491005,
0.007024816237390041,
0.028957044705748558,
0.011314932256937027,
-0.014237256720662117,
0.03883655369281769,
0.007760791573673487,
0.01205116230994463,
-0.02800821326673031,
0.0029602274298667908,
0.001285624341107905,
0.006167026236653328,
0.005249685142189264,
-0.0013717610854655504,
-0.018368206918239594,
0.004851787816733122,
0.04086122661828995,
-0.011691330932080746,
-0.03405407816171646,
0.002480350434780121,
0.03462481498718262,
-0.010641513392329216,
-0.02843196503818035,
0.019986392930150032,
0.03140795975923538,
0.02031649276614189,
0.01724451407790184,
-0.022199617698788643,
-0.04273996874690056,
0.011259513907134533,
0.010274595580995083,
-0.029310090467333794,
-0.014432133175432682,
-0.017438890412449837,
0.039661429822444916,
0.024943772703409195,
0.03580048680305481,
-0.04122148081660271,
0.0017482195980846882,
0.04833052307367325,
-0.05509021878242493,
0.042101457715034485,
0.01501565333455801,
0.03326595574617386,
-0.0001461143110645935,
-0.00961531512439251,
0.0049207438714802265,
0.06422485411167145,
0.05473584309220314,
0.003999270964413881,
-0.05449877306818962,
0.0019565769471228123,
-0.0186822060495615,
-0.010987510904669762,
0.0032494417391717434,
0.016918031498789787,
0.026912925764918327,
-0.03715791180729866,
-0.0074946824461221695,
0.00011595435353228822,
0.012399289757013321,
0.0013644843129441142,
0.02363668382167816,
0.006474328693002462,
0.00012420890561770648,
0.023300843313336372,
-0.02406328357756138,
0.021211152896285057,
-0.01182371936738491,
0.006122690625488758,
0.012921251356601715,
-0.03399898111820221,
0.0018583314958959818,
0.013699308037757874,
0.04258567467331886,
0.0013368040090426803,
-0.005109207704663277,
0.06645242124795914,
-0.05583956092596054,
-0.00042813789332285523,
0.0027647153474390507,
-0.044678445905447006,
0.006701814942061901,
0.04698990285396576,
0.02769622392952442,
-0.033857688307762146,
0.018345534801483154,
0.007165307179093361,
0.057879261672496796,
0.03561842814087868,
-0.0038194237276911736,
-0.0014329062541946769,
-0.004517625086009502,
0.007664854172617197,
0.065887950360775,
0.011661900207400322,
-0.018233608454465866,
0.007464298978447914,
-0.010741189122200012,
0.010301727801561356,
-0.023364664986729622,
-0.06059839203953743,
-0.01079341396689415,
-0.0011271913535892963,
0.032732464373111725,
0.051118917763233185,
-0.04952113702893257,
-0.01569698378443718,
0.012131128460168839,
0.024622002616524696,
0.06452187895774841,
0.04037422314286232,
-0.02878551557660103,
0.03405487537384033,
-0.010774307884275913,
-0.09426719695329666,
-0.017131920903921127,
0.019521482288837433,
-0.04751671850681305,
-0.06049750745296478,
0.020459050312638283,
-0.031599175184965134,
-0.013690491206943989,
0.011557132937014103,
0.003440418979153037,
0.02595675364136696,
-0.0015025930479168892,
-0.10692134499549866,
-0.06693152338266373,
0.02845383621752262,
0.020129581913352013,
0.0017386536346748471,
-0.05622035264968872,
0.0016220372635871172,
0.03708583861589432,
0.0676708072423935,
0.0058963787741959095,
-0.003235362935811281,
-0.028064511716365814,
0.04869586229324341,
-0.00625332398340106,
-0.035495907068252563,
0.005260644014924765,
-0.00048008575686253607,
-0.035473477095365524,
0.023521441966295242,
-0.07783135026693344,
-0.012645602226257324,
0.04309092089533806,
-0.005802281200885773,
-0.01435016468167305,
0.06368186324834824,
-0.010763099417090416,
0.005677776411175728,
0.01511258166283369,
-0.03158187493681908,
-0.015288121066987514,
0.05549502745270729,
-0.002963160164654255,
0.023663334548473358,
0.03586899861693382,
0.004571680910885334,
-0.0008345088572241366,
0.01603134535253048,
0.0004402323975227773,
0.06461433321237564,
-0.027850715443491936,
-0.019018661230802536,
0.033960890024900436,
-0.01142826210707426,
-0.048693712800741196,
-0.03621644899249077,
-0.0496322438120842,
0.02540159784257412,
-0.018981071189045906,
-0.007801240310072899,
0.04516349360346794,
0.02381731942296028,
0.008016754873096943,
0.03209519386291504,
-0.01944359391927719,
-0.056350912898778915,
-0.07057080417871475,
0.0009752957266755402,
-0.025471743196249008,
0.03919661417603493,
0.0015439267735928297,
0.036149583756923676,
-0.0029392093420028687,
0.007282761391252279,
-0.056942958384752274,
-0.024926409125328064,
0.04866121709346771,
-0.0006969719543121755,
-0.016500530764460564,
-0.006924106739461422,
0.029773999005556107,
-0.004672047682106495,
-0.012144668027758598,
0.022909553721547127,
-0.008539021946489811,
-0.03970718756318092,
-0.040237292647361755,
-0.029238441959023476,
-0.02349238656461239,
0.011514886282384396,
-0.028215456753969193,
0.005785053595900536,
-0.02579735592007637,
-0.02753274329006672,
0.027648236602544785,
-0.002475227927789092,
0.08269476145505905,
0.01770869456231594,
0.015991786494851112,
0.013483342714607716,
0.017751075327396393,
-0.0015216112369671464,
-0.0010420925682410598,
0.037652093917131424,
-0.004994878079742193,
-0.0419180765748024,
-0.0007865249644964933,
0.038766372948884964,
0.08006510883569717,
-0.03392713516950607,
0.024309717118740082,
0.016894403845071793,
0.011264106258749962,
0.019031325355172157,
0.020647594705224037,
-0.06639039516448975,
0.010478365235030651,
0.04226536303758621,
-0.004844638053327799,
0.014347837306559086,
0.042117711156606674,
-0.0008549999911338091,
0.04347870126366615,
-0.003512742230668664,
0.004538658075034618,
-0.03936553746461868,
0.04817812144756317,
-0.013474904000759125,
-0.006045132409781218,
0.028901534155011177,
-0.059210386127233505,
0.023668337613344193,
-0.05151965096592903,
0.004025973379611969,
-0.015064683742821217,
-0.0015950048109516501,
0.020010367035865784,
-0.025669990107417107,
-0.026362938806414604,
0.01774303987622261,
-0.0033790760207921267,
0.0028337067924439907,
-0.00238149450160563,
0.03599739074707031,
-0.029999462887644768,
0.024186449125409126,
-0.015364009886980057,
-0.0048691569827497005,
-0.05595274642109871,
0.021941490471363068,
0.00993641559034586,
0.014542149379849434,
0.027782874181866646,
-0.026790747418999672,
-0.020924421027302742,
-0.002354241209104657,
-0.05233309045433998,
0.00027747199055738747,
0.037235938012599945,
-0.04517653211951256,
0.021656665951013565,
-0.03495744988322258,
-0.057199861854314804,
0.01053766068071127,
-0.04785763844847679,
0.016031036153435707,
0.020585831254720688,
-0.03399481624364853,
-0.03608144447207451,
-0.023892080411314964,
-0.005881933495402336,
-0.02385685034096241,
-0.01423304807394743,
-0.002350762952119112,
0.013417022302746773,
-0.020958170294761658,
-0.010389932431280613,
0.010419328697025776,
-0.03874746337532997,
-0.0663667693734169,
-0.033709652721881866,
0.008935542777180672,
0.02059243805706501,
-0.03667422756552696,
0.004092087969183922,
0.04802080988883972,
-0.07396406680345535,
0.015801535919308662,
-0.02895326353609562,
-0.05116686597466469,
-0.014551728963851929,
-0.00988637376576662,
0.013467427343130112,
-0.018206723034381866,
-0.03015202470123768,
0.09033746272325516,
0.03029218129813671,
-0.04337744042277336,
0.0004887940012849867,
-0.017354197800159454,
-0.004808519035577774,
-0.007365937810391188,
0.027343252673745155,
0.02174663171172142,
-0.027145741507411003,
-0.02143576741218567,
0.013082573190331459,
0.04331468045711517,
0.01678265631198883,
0.020826248452067375,
-0.0015732130268588662,
-0.01855050027370453,
0.007803461514413357,
0.00420305086299777,
-0.00009019790013553575,
-0.0038628072943538427,
-0.05679783597588539,
0.03308939188718796,
-0.0003311578475404531,
0.008293930441141129,
0.03575927019119263,
0.008106162771582603,
0.06895032525062561,
0.008127976208925247,
0.03560124710202217,
-0.008216886781156063,
0.03889032453298569,
-0.02263069525361061,
0.00971193891018629,
0.011010314337909222,
0.025512998923659325,
0.022071391344070435,
-0.005453635472804308,
-0.010902407579123974,
0.03688672557473183,
0.06667023152112961,
-0.03489533066749573,
-0.03408818319439888,
0.016091488301753998,
-0.025240058079361916,
0.016987944021821022,
-0.021909328177571297,
-0.03254556655883789,
0.07413385063409805,
0.05405852943658829,
0.032180238515138626,
0.009834603406488895,
-0.036748092621564865,
-0.011326869949698448,
-0.06978676468133926,
0.01113169640302658,
-0.038268495351076126,
0.06692399829626083,
0.025919044390320778,
0.05839702486991882,
-0.017188461497426033,
0.0005477305385284126,
0.010213618166744709,
-0.01794351451098919,
-0.08149950951337814,
0.020833110436797142,
-0.040748123079538345,
0.012411917559802532,
-0.026465903967618942,
-0.007866921834647655,
0.039250366389751434,
-0.015327257104218006,
-0.017809607088565826,
-0.022576063871383667,
0.026326945051550865,
-0.040109921246767044,
0.009403526782989502,
-0.037717804312705994,
-0.019814172759652138,
-0.043953895568847656,
-0.003395926207304001,
0.032491717487573624,
-0.0060077207162976265,
0.01422503124922514,
0.06561247259378433,
-0.053915467113256454,
-0.044887442141771317,
0.019890667870640755,
0.014049327932298183,
0.0034921434707939625,
0.027665287256240845,
0.03507155925035477,
0.040055155754089355,
-0.07392285764217377,
-0.0036630937829613686,
-0.00544704357162118,
0.06727499514818192,
0.009915119037032127,
-0.023594839498400688,
0.03129754215478897,
-0.04766659811139107,
-0.01857263781130314,
0.006105744279921055,
0.02713736891746521,
-0.0040383897721767426,
0.018016012385487556,
0.051641277968883514,
0.0033836462534964085,
-0.04175983741879463,
0.03036697581410408,
0.08030872792005539,
-0.0065967789851129055,
-0.020590726286172867,
-0.01683029904961586,
-0.020186958834528923,
-0.035872310400009155,
-0.0026210572104901075,
0.020402228459715843,
0.022926226258277893,
-0.0350017249584198,
0.04069116711616516,
-0.0040082563646137714,
-0.007549791596829891,
-0.018252084031701088,
0.01676962710916996,
0.017862576991319656,
0.034097056835889816,
0.024040888994932175,
0.018975304439663887,
0.02436811476945877,
0.05233136937022209,
-0.011698215268552303,
0.02498103678226471,
-0.0032652791123837233,
-0.09034545719623566,
0.020262842997908592,
0.062204599380493164,
0.05995528772473335,
-0.04265701770782471,
-0.05290579795837402,
-0.03600313141942024,
-0.006100138649344444,
0.07422091066837311,
-0.04570634663105011,
0.04571200907230377,
-0.01904420554637909,
-0.009675415232777596,
-0.04064187407493591,
0.0020739384926855564,
-0.002956197364255786,
0.05875873938202858,
-0.032625485211610794,
0.06298906356096268,
-0.049364123493433,
-0.026741888374090195,
-0.03675701841711998,
0.04456983134150505,
0.023957666009664536,
0.05033397674560547,
0.0042268321849405766,
-0.0036657159216701984,
-0.0008508806931786239,
-0.0005463103880174458,
-0.012166977860033512,
-0.06994618475437164,
-0.018243351951241493,
0.04148305952548981,
-0.023091504350304604,
0.02569693513214588,
-0.011445132084190845,
-0.058148760348558426,
0.0000013823896551912185,
-0.02295798808336258,
0.0031178612262010574,
-0.024998057633638382,
-0.023376120254397392,
0.02470684051513672,
0.021523242816329002,
-0.01698661968111992,
0.03620999678969383,
0.028417648747563362,
-0.04659070447087288,
0.015335436910390854,
0.010473697446286678,
0.0033867396414279938,
0.005147912073880434,
0.024447938427329063,
-0.015367012470960617,
-0.019758470356464386,
-0.02435692399740219,
0.021237507462501526,
-0.0068405927158892155,
0.02332671545445919,
-0.006648091599345207,
-0.01573874242603779,
-0.04338815063238144,
0.025806652382016182,
-0.024115577340126038,
-0.05207090452313423,
-0.026894638314843178,
-0.044034216552972794,
-0.0017561273416504264,
-0.04297570884227753,
-0.000021173937057028525,
0.011350130662322044,
-0.01230713166296482,
0.020169150084257126,
-0.028926793485879898,
-0.0017101961420848966,
-0.021435247734189034,
0.007328410632908344,
0.03454069793224335,
-0.05183335393667221,
0.00835480634123087,
-0.006487717851996422,
-0.021553056314587593,
0.010946073569357395,
-0.07583174109458923,
-0.032942771911621094,
-0.006594178732484579,
0.0036316565237939358,
0.01253417506814003,
-0.04153359308838844,
0.035755034536123276,
-0.040508463978767395,
0.02121664397418499,
-0.027304906398057938,
-0.04421268031001091,
0.01153500098735094,
-0.02299376204609871,
-0.006837562192231417,
-0.028076713904738426,
-0.012222645804286003,
0.003370566526427865,
-0.017809856683015823,
0.0011592344380915165,
0.03464591130614281,
-0.03698029741644859,
0.0018169439863413572,
0.010620838962495327,
-0.016350157558918,
0.0741918534040451,
0.0064750900492072105,
-0.009843059815466404,
0.027010232210159302,
0.0440550334751606,
0.0059828683733940125,
-0.017090467736124992,
0.04110551252961159,
-0.023486902937293053,
0.00035299788578413427,
0.006874059326946735,
0.004069553688168526,
0.02048569917678833,
-0.0008552591316401958,
0.02179035358130932,
0.06371455639600754,
0.02932804822921753,
0.013107136823236942,
-0.010620339773595333,
0.005396232008934021,
-0.03034747764468193,
0.023003827780485153,
-0.000034605629480211064,
0.02453542873263359,
0.007644242607057095,
-0.019999807700514793,
0.01120564341545105,
-0.022308599203824997,
-0.0018455939134582877,
0.049601249396800995,
-0.010040801018476486,
0.013159574009478092,
-0.01806386560201645,
0.005578623618930578,
-0.019933046773076057,
-0.014970656484365463,
0.007068322505801916,
0.030958324670791626,
0.03173621743917465,
0.06408774107694626,
-0.025120288133621216,
-0.04418119415640831,
-0.024117227643728256,
-0.040642086416482925,
0.08483748883008957,
-0.02758302539587021,
0.06335870921611786,
0.05185678228735924,
0.014783178456127644,
-0.03151592239737511,
-0.010835444554686546,
-0.022156400606036186,
-0.019187912344932556,
0.009712261147797108,
0.02110627479851246,
-0.0009306134306825697,
-0.025461461395025253,
0.03350740671157837,
0.026838423684239388,
-0.027250373736023903,
0.020357124507427216,
-0.00855046883225441,
0.04173159599304199,
-0.016008034348487854,
-0.05227014422416687,
-0.05329735577106476,
0.030056552961468697,
-0.03770933300256729,
0.03472127765417099,
-0.018116792663931847,
-0.025998681783676147,
0.024425603449344635,
-0.013393530622124672,
0.0112412478774786,
-0.03011583723127842,
0.020438402891159058,
-0.031056858599185944,
0.0074422829784452915,
0.03653310611844063,
-0.01628251001238823,
0.014405176043510437,
0.016152486205101013,
0.016372891142964363,
0.039785511791706085,
0.015872560441493988,
-0.01538301631808281,
-0.08319024741649628,
-0.02849446050822735,
-0.036811430007219315,
-0.025022629648447037,
0.056638527661561966,
0.050303876399993896,
-0.010014917701482773,
0.005130788777023554,
-0.0022831701207906008,
0.06667659431695938,
0.011051569133996964,
0.03437214344739914,
-0.03608321398496628,
0.06859512627124786,
-0.050967998802661896,
0.00362196983769536,
-0.04350937157869339,
0.020014885812997818,
0.10105850547552109,
0.018633205443620682,
0.010534697212278843,
-0.04150984063744545,
0.01994672790169716,
-0.03119645267724991,
0.04323509335517883,
-0.015672456473112106,
0.016682354733347893,
0.021969463676214218,
0.016851747408509254,
0.012287735939025879,
0.03688943013548851,
0.03559273108839989,
0.043530941009521484,
0.08766715228557587,
-0.04349365457892418,
-0.0480039119720459,
-0.008920170366764069,
0.01151979435235262,
-0.0006758536328561604,
0.008094226941466331,
-0.036185186356306076,
-0.013246938586235046,
-0.035591211169958115,
-0.008794436231255531,
-0.015785474330186844,
0.0010842226911336184,
0.009951399639248848,
-0.007411416154354811,
-0.03459448739886284,
0.01775616593658924,
-0.014725476503372192,
-0.01049740519374609,
-0.04812140017747879,
0.03390256687998772,
0.014039922505617142,
-0.01021940540522337,
0.00007783174078213051,
0.03356004133820534,
0.012474285438656807,
-0.00003674940307973884,
-0.04420625790953636,
0.009801041334867477,
-0.0333741195499897,
0.003057717112824321,
-0.0291310902684927,
0.044458989053964615,
-0.01899454928934574,
-0.007357421796768904,
-0.02098914422094822,
0.016559403389692307,
0.0006327188457362354,
0.0016620405949652195,
-0.006315268110483885,
0.0037517244927585125,
0.031776994466781616,
-0.030760152265429497,
0.03310135751962662,
-0.0007165285060182214,
0.04009811952710152,
-0.03541703522205353,
0.017574038356542587,
0.01089512649923563,
-0.021433040499687195,
0.01442593801766634,
0.010883842594921589,
0.00849279947578907,
-0.056028932332992554,
-0.0435325987637043,
-0.0370497889816761,
0.012327187694609165,
-0.037432070821523666,
-0.022726455703377724,
0.02782164141535759,
0.02405432052910328,
-0.005163234658539295,
-0.024037959054112434,
-0.00938537809997797,
-0.009282366372644901,
-0.04436039552092552,
0.03291100636124611,
-0.019533304497599602,
-0.006646017078310251,
0.0024270727299153805,
-0.007322392892092466,
0.045320767909288406,
0.01473931409418583,
0.004783866461366415,
-0.0035303307231515646,
-0.026735831052064896,
0.0003136489540338516,
0.011359131895005703,
-0.020752020180225372,
-0.01458741445094347,
-0.009832925163209438,
-0.03666093572974205,
0.039437755942344666,
-0.05139664560556412,
-0.0038614526856690645,
0.02125566080212593,
-0.017574314028024673,
-0.020937766879796982,
0.042791977524757385,
-0.04704620689153671,
0.023988334462046623,
0.01000747736543417,
-0.03847239539027214,
-0.017011163756251335,
0.002132343826815486,
0.036496520042419434,
-0.06170685961842537,
0.005320527590811253,
-0.03134920820593834,
-0.011392892338335514,
0.01371648721396923,
0.02382986806333065,
-0.0024285046383738518,
0.013022179715335369,
0.000049374652007827535,
0.02303258702158928,
-0.034661974757909775,
0.026082931086421013,
-0.047606851905584335,
0.0047991229221224785,
-0.014919509179890156,
-0.04365260899066925,
-0.011140548624098301,
-0.010700056329369545,
-0.005347989033907652,
-0.009913916699588299,
0.017453812062740326,
0.04443611204624176,
0.021327562630176544,
0.0038972394540905952,
0.04740089178085327,
-0.0038939700461924076,
0.022679835557937622,
-0.02758162096142769,
-0.0324459969997406,
0.04278252273797989,
-0.01233654748648405,
-0.07787725329399109,
0.05280103161931038,
-0.01778755709528923,
0.02408476732671261,
0.044941749423742294,
0.003125348361209035,
-0.03261435776948929,
0.05709299072623253,
-0.006270589306950569,
-0.005098469089716673,
0.025841124355793,
-0.00890333391726017,
0.003572214627638459,
-0.0015817132079973817,
0.030361318960785866,
-0.014116542413830757,
-0.013868470676243305,
0.023646852001547813,
0.009298533201217651,
-0.006007781717926264,
0.033543407917022705,
-0.0036020888946950436,
0.030133135616779327,
0.010406133718788624,
0.04281861335039139,
-0.03233054280281067,
-0.0024296212941408157,
0.044752877205610275,
0.006261053495109081,
0.03193879872560501,
0.034810107201337814,
0.012924177572131157,
-0.0838426873087883,
-0.00032396448659710586,
0.01454504206776619,
-0.013864290900528431,
0.04873424768447876,
-0.015095553360879421,
0.05212755873799324,
0.01951676607131958,
-0.04140164703130722,
0.026453858241438866,
-0.03652716055512428,
-0.039478905498981476,
-0.01698763482272625,
-0.008455873467028141,
-0.03325878456234932,
0.03916381672024727,
0.030307866632938385,
0.020124344155192375,
0.027165822684764862,
-0.002663089195266366,
0.03810952976346016,
0.0015612072311341763,
-0.033475082367658615,
0.03873004764318466,
-0.014673941768705845,
-0.006820984650403261,
0.048079438507556915,
-0.009387193247675896,
-0.023020800203084946,
0.022490430623292923,
-0.0034250111784785986,
0.013924280181527138,
-0.03588130697607994,
0.04333674907684326,
-0.008345366455614567,
0.08123641461133957,
0.029500801116228104,
-0.029401741921901703,
-0.022490233182907104,
0.016938960179686546,
0.03103427216410637,
-0.006614893674850464,
0.017100412398576736,
0.05498908460140228,
-0.0028407627250999212,
-0.012834676541388035,
-0.012308700941503048,
0.014271593652665615,
0.02242264151573181,
0.003940646070986986,
-0.003440123051404953,
0.0053247446194291115,
0.032914891839027405,
0.0042508128099143505,
-0.0068320780992507935,
-0.052370671182870865,
0.024617362767457962,
0.008357158862054348,
0.0202854722738266,
0.021322550252079964,
-0.006215590983629227,
-0.021943118423223495,
-0.013876558281481266,
0.020899998024106026,
0.028153780847787857,
-0.022749101743102074,
-0.035631127655506134,
-0.005156543105840683,
0.02854114957153797,
0.045874081552028656,
0.017641214653849602,
-0.04539449140429497,
-0.0017585072200745344,
0.03709754720330238,
0.0008753041620366275,
0.04137839004397392,
-0.013358278200030327,
-0.044698309153318405,
0.004089522175490856,
-0.06988924741744995,
0.08131323009729385,
-0.01614028587937355,
0.03904799371957779,
-0.03244257718324661,
0.0026371090207248926,
-0.0135112963616848,
0.023926574736833572,
0.045761220157146454,
-0.021897632628679276,
0.019926607608795166,
0.011558206751942635,
-0.01076806802302599,
-0.010318205691874027,
-0.039877891540527344,
-0.00642964756116271,
-0.021312247961759567,
-0.04063770920038223,
-0.022469496354460716,
-0.04184028506278992,
-0.03323996812105179,
0.025364411994814873,
0.051886238157749176,
0.02888684719800949,
0.011003831401467323,
-0.03876698762178421,
-0.030918577685952187,
0.058713074773550034,
0.024012211710214615,
-0.019771644845604897,
0.044571660459041595,
-0.02494509331882,
0.015055207535624504,
0.01859496533870697,
-0.013134785927832127,
0.0003471922827884555,
0.027019813656806946,
-0.04315304011106491,
-0.00034237693762406707,
-0.03690735623240471,
-0.019205335527658463,
0.0013908159453421831,
-0.06933275610208511,
0.0015456238761544228,
0.02908952906727791,
-0.013018066063523293,
-0.023224664852023125,
0.04186997562646866,
0.006617740727961063,
-0.004091937094926834,
0.0324607752263546,
0.03508581593632698,
0.025107000023126602,
0.012228199280798435,
-0.024462301284074783,
0.03142876178026199,
0.04458766430616379,
-0.012765297666192055,
0.010039291344583035,
0.04954535514116287,
0.009228508919477463,
-0.0036234899889677763,
0.0413353256881237,
0.025923125445842743,
-0.011319587007164955,
-0.019954873248934746,
0.03178093209862709,
-0.016864551231265068,
0.0028083231300115585,
0.052180562168359756,
-0.0439019501209259,
0.09452398121356964,
-0.01834055595099926,
-0.028841322287917137,
-0.013169546611607075,
-0.03237297013401985,
0.0049843695014715195,
-0.016513988375663757,
-0.007879301905632019,
0.055217936635017395,
-0.014138997532427311,
-0.004675647709518671,
-0.006922811269760132,
0.03406975790858269,
0.06343341618776321,
-0.04065965116024017,
0.023906460031867027,
0.008287250064313412,
-0.011037999764084816,
-0.021509312093257904,
0.011725261807441711,
-0.06286422163248062,
-0.021334128454327583,
0.05609271302819252,
0.03557022660970688,
-0.002296152524650097,
0.005101680755615234,
-0.02761705406010151,
0.00032462889794260263,
0.023377420380711555,
-0.0347876138985157,
-0.009237832389771938,
-0.02177847921848297,
0.018237970769405365,
-0.025574566796422005,
0.015267930924892426
] |
<p>For me, the gradient of a scalar field (say, in three dimensions) is simply (formally)</p>
<p>$\nabla f = \left(\frac{\partial f}{\partial x}, \frac{\partial f}{\partial y},\frac{\partial f}{\partial z} \right)$.</p>
<p>In which way do we need a metric?</p>
<p>But some people did tell me only on a Riemann manifold (with a metric) can we define the gradient. </p> | 2,819 | [
-0.028026970103383064,
0.0038592852652072906,
-0.009468047879636288,
-0.04399951919913292,
0.028271256014704704,
0.03327618166804314,
-0.042650703340768814,
-0.010766022838652134,
-0.009815595112740993,
-0.018900083377957344,
0.008805257268249989,
-0.003092421917244792,
0.07556536048650742,
0.016682792454957962,
0.02531626634299755,
0.0043351841159164906,
-0.01730981282889843,
0.004452642053365707,
-0.015333343297243118,
-0.03160121291875839,
0.022074759006500244,
0.01597977988421917,
0.016961336135864258,
0.007358989212661982,
-0.02325274795293808,
0.006668635178357363,
0.03082508035004139,
0.017511988058686256,
0.00039234693394973874,
0.022533418610692024,
-0.018297474831342697,
-0.046644311398267746,
0.005775978788733482,
0.03468615189194679,
0.050998322665691376,
-0.0001412130513926968,
-0.06139279901981354,
-0.018641706556081772,
-0.02636425942182541,
-0.01020922139286995,
-0.04275363311171532,
-0.031680941581726074,
0.020575951784849167,
0.032645631581544876,
-0.05806952714920044,
0.01656796969473362,
0.00595969008281827,
-0.015104063786566257,
0.019960306584835052,
-0.05985394865274429,
0.05815348029136658,
0.010673967190086842,
0.04062572866678238,
0.03194725513458252,
-0.028059402480721474,
0.012069566175341606,
0.061523839831352234,
0.06295345723628998,
-0.0035670583602041006,
-0.04738670587539673,
-0.03067738376557827,
0.008519579656422138,
-0.02054433897137642,
-0.04091868922114372,
-0.015166661702096462,
0.04209902510046959,
-0.007561621721833944,
-0.0025350756477564573,
0.05119331181049347,
-0.023157093673944473,
-0.0064635127782821655,
0.005514298100024462,
-0.001068806741386652,
-0.02498370036482811,
-0.01217737141996622,
-0.010461101308465004,
0.014506920240819454,
-0.025385448709130287,
0.07237879186868668,
-0.016577649861574173,
0.020250441506505013,
-0.01881536841392517,
0.039594147354364395,
0.050234608352184296,
0.018884973600506783,
0.007481907960027456,
0.1043911725282669,
-0.025561537593603134,
0.016674842685461044,
0.025060057640075684,
0.03127191215753555,
0.007278909906744957,
0.009103425778448582,
-0.028635798022150993,
-0.03674973547458649,
0.044168420135974884,
-0.022916657850146294,
0.02466409280896187,
-0.001791776274330914,
0.00263811438344419,
-0.021638942882418633,
-0.03292962536215782,
-0.02226068824529648,
0.0483364537358284,
-0.0030165251810103655,
0.023766979575157166,
-0.035812269896268845,
0.0037145584356039762,
-0.02463305927813053,
0.00796510186046362,
-0.035247307270765305,
0.027743102982640266,
-0.01765616610646248,
-0.005046256817877293,
0.01369335688650608,
-0.03640921041369438,
0.016533637419342995,
-0.026945896446704865,
0.03132568672299385,
0.08126755058765411,
0.05979492515325546,
-0.027989039197564125,
-0.005886176135390997,
0.005101634189486504,
-0.08027005940675735,
0.02952255681157112,
0.030511343851685524,
-0.004711287561804056,
-0.023454321548342705,
-0.01495386566966772,
-0.004366901237517595,
-0.00231574522331357,
0.0024432640057057142,
0.030475810170173645,
0.03822324797511101,
-0.02554219588637352,
-0.10744055360555649,
-0.03987107425928116,
0.030046259984374046,
0.021180272102355957,
0.021996399387717247,
-0.052914202213287354,
-0.0008716682787053287,
0.019427211955189705,
0.03579564392566681,
0.01865345798432827,
0.02831651270389557,
0.01855648122727871,
0.020823277533054352,
-0.015240177512168884,
-0.022336287423968315,
-0.03184056282043457,
-0.011974867433309555,
-0.03681856393814087,
0.0023755047004669905,
-0.027558114379644394,
-0.007317588198930025,
0.003892058739438653,
0.0015254702884703875,
-0.012673530727624893,
0.06398763507604599,
-0.023918889462947845,
0.018064625561237335,
0.02217627689242363,
-0.016170620918273926,
-0.014290564693510532,
0.06600729376077652,
0.013122474774718285,
0.035896219313144684,
0.02068639174103737,
-0.0074460250325500965,
0.004333290737122297,
0.008778149262070656,
0.03015039674937725,
0.059931155294179916,
-0.046977732330560684,
-0.046922728419303894,
-0.0018967019859701395,
-0.0028944690711796284,
0.01410756353288889,
-0.05144654959440231,
-0.07295364886522293,
-0.014844301156699657,
0.01572244055569172,
0.005839611403644085,
0.024369481950998306,
0.031199390068650246,
-0.0035712504759430885,
0.006561966147273779,
-0.042047563940286636,
0.01809176802635193,
-0.06590396165847778,
0.0008016061037778854,
-0.005483665969222784,
-0.0374089814722538,
0.025205761194229126,
-0.0063352459110319614,
-0.020810604095458984,
-0.045558858662843704,
-0.06259175390005112,
0.0027662180364131927,
0.04967304691672325,
0.014236005954444408,
-0.02192295715212822,
-0.0010625483701005578,
0.056724872440099716,
0.011663496494293213,
0.02155231311917305,
0.040651626884937286,
-0.0078051271848380566,
-0.014401265420019627,
0.024922415614128113,
-0.002555291634052992,
-0.00013836458674632013,
0.004397375043481588,
0.008065586909651756,
-0.010709023103117943,
0.0048047821037471294,
-0.04186032712459564,
0.03190528601408005,
-0.08042588829994202,
0.0847555622458458,
0.037529878318309784,
0.027549870312213898,
0.00887567363679409,
0.018623827025294304,
-0.018815500661730766,
0.027204230427742004,
0.006653571501374245,
-0.020749196410179138,
-0.04650518670678139,
0.00952815916389227,
0.08195193111896515,
0.027756111696362495,
-0.039818618446588516,
0.0011363161029294133,
0.042834844440221786,
0.020984388887882233,
0.0017590004717931151,
0.006235731765627861,
-0.016805827617645264,
-0.04895307496190071,
0.013877240009605885,
-0.00027081125881522894,
0.027044333517551422,
0.042951550334692,
0.01892290823161602,
-0.020586181432008743,
0.04310931637883186,
-0.027205374091863632,
0.007966081611812115,
0.052593693137168884,
-0.008328506723046303,
-0.0009641976212151349,
0.033224914222955704,
0.013159021735191345,
0.048005759716033936,
-0.01869947463274002,
0.0293305404484272,
0.042828742414712906,
-0.008216829039156437,
-0.01279410719871521,
0.00605274923145771,
-0.0245403740555048,
0.009045633487403393,
0.03361441567540169,
-0.027034174650907516,
0.004532196093350649,
0.021814949810504913,
-0.04244912043213844,
-0.018590010702610016,
-0.001437596743926406,
-0.013486006297171116,
-0.02814927138388157,
-0.03361598402261734,
0.011562659405171871,
-0.016204578801989555,
0.002825693925842643,
-0.015349170193076134,
-0.015721576288342476,
0.030738437548279762,
-0.03653421625494957,
0.007842419669032097,
-0.009806770831346512,
-0.01945345290005207,
0.042270876467227936,
-0.03601941093802452,
-0.006697875447571278,
0.01877949759364128,
-0.01345653273165226,
0.045573730021715164,
-0.0015494105173274875,
-0.013198199681937695,
-0.046040572226047516,
-0.02262561023235321,
-0.023835314437747,
0.04847382754087448,
0.013943042606115341,
0.01583453081548214,
0.06761659681797028,
-0.022885819897055626,
-0.06896109879016876,
-0.013874990865588188,
-0.004631259012967348,
-0.05841132998466492,
-0.05352994054555893,
0.022551268339157104,
0.012506273575127125,
-0.028567152097821236,
0.01610076241195202,
0.06592081487178802,
-0.042772404849529266,
-0.017316117882728577,
-0.03017524443566799,
-0.053710490465164185,
0.036927856504917145,
-0.003229656955227256,
-0.004086967092007399,
0.002035086276009679,
-0.047564081847667694,
0.08685990422964096,
0.028633246198296547,
-0.035590220242738724,
-0.034178365021944046,
0.051729779690504074,
-0.0002927831083070487,
-0.047222621738910675,
0.004954048432409763,
0.0039662811905145645,
-0.0005490570329129696,
0.015214239247143269,
0.011211133562028408,
0.06273194402456284,
0.019559258595108986,
0.0060067023150622845,
-0.032712217420339584,
-0.004620259627699852,
0.00660750875249505,
-0.0020745592191815376,
0.06055331975221634,
0.040565382689237595,
-0.059335917234420776,
0.0030636582523584366,
-0.003006071550771594,
0.03598950430750847,
0.013805546797811985,
-0.022299878299236298,
0.032240528613328934,
0.009130861610174179,
0.003268724074587226,
-0.035292670130729675,
0.02103520557284355,
0.009915061295032501,
-0.0015435098903253675,
0.04006786644458771,
0.017367392778396606,
0.00559261254966259,
-0.007768417242914438,
-0.018572011962532997,
0.018570169806480408,
0.020608197897672653,
-0.07848086953163147,
0.025081997737288475,
-0.027879221364855766,
0.015480581670999527,
0.012071737088263035,
-0.0073334998451173306,
-0.005283901002258062,
0.03054407611489296,
0.03046335279941559,
-0.006999658886343241,
-0.004152878187596798,
-0.042027547955513,
0.0026598689146339893,
-0.08287695795297623,
0.01867496967315674,
0.020640205591917038,
0.05833236500620842,
0.011077332310378551,
0.07058980315923691,
-0.018228821456432343,
0.013432287611067295,
0.036188896745443344,
-0.006884456146508455,
-0.07864925265312195,
0.011219276115298271,
-0.04315238445997238,
-0.026940330862998962,
-0.02901829220354557,
-0.047632623463869095,
-0.00402142433449626,
-0.05208619683980942,
-0.01812252588570118,
-0.019640492275357246,
0.012479593977332115,
-0.0673089250922203,
0.024038175120949745,
-0.03574386239051819,
-0.04858119785785675,
-0.016455264762043953,
0.018782977014780045,
0.07401677966117859,
-0.01962263137102127,
0.021405978128314018,
0.023513631895184517,
0.016099872067570686,
-0.028163326904177666,
-0.002209150930866599,
-0.023602832108736038,
0.03583519905805588,
0.02568148449063301,
-0.033445555716753006,
0.01871553063392639,
0.014022250659763813,
0.030106903985142708,
0.02265767566859722,
0.034888461232185364,
0.0006844647577963769,
-0.013013776391744614,
-0.013569892384111881,
-0.079692542552948,
0.0028115876484662294,
-0.007985785603523254,
0.07507685571908951,
0.005376680754125118,
-0.026937374845147133,
-0.004260970279574394,
0.009843320585787296,
-0.02195052057504654,
-0.01818048022687435,
0.03417820483446121,
-0.02173323929309845,
-0.0419127494096756,
-0.05455712601542473,
-0.004987343680113554,
-0.02144884690642357,
-0.020859597250819206,
0.01278782356530428,
-0.007318899966776371,
-0.024393253028392792,
0.017802221700549126,
0.005525173153728247,
-0.01374782994389534,
-0.0026116524823009968,
-0.0020179564598947763,
0.013525938615202904,
0.026817485690116882,
-0.01994796097278595,
-0.008900536224246025,
0.0071962871588766575,
0.08868588507175446,
0.07574682682752609,
0.014227145351469517,
-0.03065640479326248,
-0.07002374529838562,
0.019206453114748,
0.0007404357311315835,
0.012774307280778885,
-0.012848448008298874,
-0.004671374335885048,
-0.02903762087225914,
-0.017338352277874947,
0.07185833156108856,
-0.01073623076081276,
0.023664025589823723,
-0.000811873294878751,
-0.005119639448821545,
-0.0125783896073699,
-0.03361494839191437,
-0.00894904788583517,
0.036183178424835205,
0.009969769045710564,
-0.009294870309531689,
0.00567279290407896,
0.030550606548786163,
-0.03329799324274063,
0.02985529415309429,
-0.021600835025310516,
0.05568435788154602,
0.00815981812775135,
0.0028306839521974325,
0.010102363303303719,
0.00481102941557765,
-0.005244026426225901,
-0.08480667322874069,
0.001169200404547155,
0.027938775718212128,
-0.035744067281484604,
0.001428786781616509,
0.0009683678508736193,
-0.05919766426086426,
0.042806901037693024,
0.024895966053009033,
-0.017043301835656166,
0.057543881237506866,
-0.03850862756371498,
0.0525909960269928,
0.06858354061841965,
0.042387429624795914,
0.05319253355264664,
0.03413683548569679,
-0.020490698516368866,
-0.017370756715536118,
-0.025100206956267357,
0.01138779241591692,
-0.01333491038531065,
-0.013361799530684948,
-0.01690373383462429,
-0.025719033554196358,
-0.0519116148352623,
0.03445902094244957,
-0.027391768991947174,
-0.004869911354035139,
-0.021188050508499146,
-0.040983691811561584,
-0.05272648483514786,
0.0048208292573690414,
0.0017280346946790814,
-0.018453719094395638,
0.0029845654498785734,
0.01430337131023407,
0.0006102147162891924,
-0.006494700908660889,
-0.0017453934997320175,
-0.009090065956115723,
-0.03173603489995003,
0.047862764447927475,
-0.007219346705824137,
0.012523004785180092,
0.002691427245736122,
0.010263354517519474,
0.02791220135986805,
-0.054302554577589035,
0.044612906873226166,
-0.013343793340027332,
-0.016372350975871086,
-0.014211061410605907,
-0.03073163330554962,
-0.020614389330148697,
-0.01010195817798376,
-0.024093033745884895,
0.016988513991236687,
-0.02982930652797222,
0.014691960997879505,
0.013043458573520184,
0.015171135775744915,
-0.07910651713609695,
-0.03040679171681404,
0.032599009573459625,
-0.02684149332344532,
-0.036195240914821625,
-0.010166729800403118,
0.020361900329589844,
-0.029005298390984535,
-0.04942803084850311,
0.014911653473973274,
0.06530003249645233,
-0.03938978537917137,
-0.028623707592487335,
-0.020509619265794754,
0.01919807307422161,
0.01622781902551651,
0.006107985973358154,
-0.008323658257722855,
0.013840590603649616,
0.020827729254961014,
0.01203744113445282,
0.007387076038867235,
0.0419064536690712,
-0.015151545405387878,
0.015325209125876427,
-0.03681042790412903,
-0.011910992674529552,
0.018066592514514923,
-0.001643234514631331,
0.012153463438153267,
0.009132114239037037,
0.013920447789132595,
-0.02884957194328308,
-0.048888739198446274,
0.0282662995159626,
-0.025666283443570137,
0.02323363907635212,
-0.05122480168938637,
0.02440830133855343,
0.018591001629829407,
-0.04077541083097458,
0.05988162010908127,
0.027310751378536224,
0.04567284882068634,
-0.028263701125979424,
0.021224375814199448,
-0.029315367341041565,
-0.0206063911318779,
0.00032371521228924394,
-0.005074637476354837,
-0.0014030621387064457,
-0.018776683136820793,
0.0400874949991703,
-0.007816659286618233,
0.0009693250758573413,
-0.032642994076013565,
-0.0019020640756934881,
-0.004050247371196747,
0.0006346719455905259,
0.07688159495592117,
-0.0038902286905795336,
0.04549460485577583,
0.03918737545609474,
-0.028775056824088097,
0.016759932041168213,
-0.006091480143368244,
-0.02416182868182659,
-0.00645619397982955,
-0.006577604915946722,
0.07419472932815552,
-0.0031434292905032635,
0.013260582461953163,
0.03785929083824158,
0.03273192048072815,
-0.03634815290570259,
0.04083776846528053,
-0.007183834444731474,
0.04373723641037941,
0.00645786989480257,
-0.020704375579953194,
-0.0689547136425972,
0.06071383133530617,
-0.003913493361324072,
0.028300222009420395,
0.012371073476970196,
-0.03967973217368126,
0.05131028592586517,
-0.003792776260524988,
0.009926381520926952,
-0.029531149193644524,
-0.008361204527318478,
-0.03579442575573921,
-0.00505517004057765,
0.015259689651429653,
0.027245821431279182,
-0.018913963809609413,
0.00047075471957214177,
0.03305993974208832,
-0.004011866170912981,
0.011241478845477104,
0.030334079638123512,
-0.04983866587281227,
-0.014310721307992935,
-0.06258421391248703,
-0.04365742951631546,
0.050554268062114716,
0.027680005878210068,
-0.05740611255168915,
-0.022776970639824867,
-0.0143673000857234,
0.005974431987851858,
0.002093943767249584,
0.018188219517469406,
-0.02729543298482895,
0.054076652973890305,
0.028489617630839348,
0.03178766742348671,
-0.00007157722575357184,
0.0013632365735247731,
0.1298394799232483,
0.0696905329823494,
0.011046274565160275,
-0.035660725086927414,
0.04478023946285248,
-0.05286704748868942,
-0.012648279778659344,
-0.032905805855989456,
0.06832418590784073,
-0.024159403517842293,
0.03410280868411064,
0.02339542657136917,
0.04016736149787903,
-0.00930908415466547,
-0.028841862455010414,
0.05246012285351753,
-0.05819109082221985,
-0.02818899229168892,
0.020035549998283386,
0.020120352506637573,
-0.01453856285661459,
0.02175300009548664,
0.004218009300529957,
0.029607921838760376,
0.008142273873090744,
0.009516080841422081,
-0.01936550810933113,
-0.030243083834648132,
0.012900123372673988,
0.00017693302652332932,
-0.05141986533999443,
-0.011291944421827793,
0.031562693417072296,
-0.02135653793811798,
-0.03844970092177391,
-0.010155829600989819,
0.03081844560801983,
-0.02230961062014103,
-0.0006497986614704132,
0.008411149494349957,
-0.0019316718680784106,
0.03462496027350426,
-0.022798828780651093,
-0.0013162244576960802,
-0.0047999233938753605,
-0.02155456505715847,
-0.04712309315800667,
0.04040165990591049,
-0.00477511016651988,
0.030107369646430016,
0.0009629904525354505,
0.02056841365993023,
0.01747928187251091,
-0.05415569990873337,
0.008754328824579716,
-0.018230050802230835,
0.02921489253640175,
0.003991305828094482,
-0.005085248965770006,
0.008059512823820114,
0.04886215925216675,
0.011965315788984299,
0.0012671543518081307,
0.0026929499581456184,
-0.031106455251574516,
0.028360024094581604,
-0.025187985971570015,
0.03351130336523056,
-0.017766177654266357,
-0.010288956575095654,
-0.02972985804080963,
-0.01252831146121025,
-0.05559388920664787,
-0.004681497346609831,
0.0066318451426923275,
-0.003229723544791341,
0.04038108140230179,
0.007308003026992083,
0.011197615414857864,
0.013891265727579594,
-0.05101466923952103,
0.046519115567207336,
0.005619490053504705,
-0.002150123007595539,
-0.02217217907309532,
0.010985228233039379,
0.02186686359345913,
0.04612612724304199,
0.026082772761583328,
-0.007280304562300444,
-0.012121188454329967,
-0.004376463126391172,
0.018783094361424446,
0.0007468074909411371,
-0.0010718429693952203,
0.020017288625240326,
-0.03673907741904259,
0.003262036247178912,
-0.01546009723097086,
0.0037252302281558514,
0.05544570833444595,
0.023411590605974197,
-0.007174408994615078,
0.034072477370500565,
-0.015731042250990868,
0.03947394713759422,
0.04336676746606827,
-0.02462059259414673,
0.0195310041308403,
0.01642194762825966,
0.0018629918340593576,
-0.05514588579535484,
-0.0344076044857502,
-0.03556982800364494,
0.02562822215259075,
0.00022473435092251748,
0.01348836813122034,
-0.02539907954633236,
-0.019318189471960068,
-0.024303508922457695,
0.02729286625981331,
-0.06669051200151443,
-0.0027530482038855553,
-0.03620989993214607,
0.04338579997420311,
0.011464661918580532,
-0.004124967847019434,
-0.008789809420704842,
-0.0014954882208257914,
-0.0383230485022068,
-0.021024765446782112,
0.022298838943243027,
0.00452331081032753,
-0.008494706824421883,
0.03249669820070267,
0.01257488876581192,
0.0047384873032569885,
0.017367323860526085,
-0.0019426678773015738,
-0.0355846993625164,
0.017944499850273132,
-0.04937213286757469,
-0.061480917036533356,
-0.00857538916170597,
0.018855592235922813,
-0.005343867931514978,
0.03396778926253319,
-0.0020506782457232475,
-0.04233696684241295,
0.0055799963884055614,
0.03188229724764824,
-0.0018061654409393668,
-0.012950773350894451,
-0.05439413711428642,
0.001565215177834034,
-0.0511341318488121,
0.04760022461414337,
-0.016406193375587463,
-0.0022514835000038147,
0.001794510055333376,
-0.018538862466812134,
-0.034579746425151825,
-0.018239561468362808,
0.027305997908115387,
-0.0013023194624111056,
0.019265053793787956,
0.026289094239473343,
-0.020890621468424797,
0.06033308431506157,
0.023642709478735924,
-0.04065287858247757,
0.012398946098983288,
0.021564984694123268,
0.014650726690888405,
-0.09266242384910583,
-0.007870197296142578,
0.03615529462695122,
-0.0010226125596091151,
0.019706083461642265,
-0.0867210105061531,
0.013554316945374012,
-0.0033376351930201054,
-0.09163825213909149,
0.030426757410168648,
-0.009371377527713776,
-0.02412552572786808,
-0.0023448802530765533,
0.030533866956830025,
0.016732003539800644,
0.04400067403912544,
0.019685208797454834,
0.03298025205731392,
-0.020915111526846886,
0.00660935090854764,
0.013939633965492249,
0.009809865616261959,
-0.033227354288101196,
0.032454412430524826,
-0.007056261412799358,
-0.008172565139830112,
0.07073104381561279,
-0.00013251362543087453,
-0.008287088945508003,
0.012403382919728756,
0.024985533207654953,
-0.0060647097416222095,
0.024641280993819237,
0.00028718251269310713,
0.0005771549185737967,
0.014008356258273125,
0.03486832231283188,
0.007683043368160725,
-0.023605836555361748,
0.03242836892604828,
0.0067024617455899715,
0.02315390855073929,
0.0013732211664319038,
0.005919894203543663,
0.030889805406332016,
-0.02997725084424019,
-0.031201966106891632,
0.04880756512284279,
-0.050702668726444244,
-0.051587384194135666,
0.009545360691845417,
-0.005485534202307463,
0.006555780302733183,
-0.0047915722243487835,
-0.0017692119581624866,
-0.005750836804509163,
-0.007281066849827766,
0.027220342308282852,
-0.013795743696391582,
-0.028942925855517387,
0.00403287960216403,
-0.020819129422307014,
-0.017992433160543442,
0.01859733834862709,
-0.022181928157806396,
0.014707649126648903,
-0.06291379779577255,
0.002106964122503996,
0.010793433524668217,
-0.03026495687663555,
-0.006954762618988752,
0.003627191064879298,
0.014955873601138592,
0.035103123635053635,
0.043260298669338226,
0.0010725711472332478,
-0.007929166778922081,
-0.03911886364221573,
-0.012247774749994278,
-0.09505495429039001,
0.022791991010308266,
0.023039918392896652,
-0.0034116231836378574,
-0.018914639949798584,
-0.011286645196378231,
-0.013299968093633652,
-0.007026113569736481,
0.06579433381557465,
-0.012232312932610512,
-0.008225172758102417,
0.02316279336810112,
0.02971988543868065,
0.03900715336203575,
-0.04671400040388107,
-0.001987655647099018,
-0.014435556717216969,
-0.01164350938051939,
-0.023017071187496185,
-0.0076014455407857895,
-0.014359238557517529,
0.01836659386754036,
0.03648166358470917,
0.012112085707485676,
0.031454190611839294,
-0.0076749371364712715,
-0.030124522745609283,
0.055518925189971924,
0.019263196736574173,
-0.0629059448838234,
0.03782973438501358,
-0.006174668204039335,
-0.0001646741438889876,
0.04511788487434387,
-0.03082425706088543,
0.005809977650642395,
0.005507206078618765,
-0.0325150266289711,
-0.015314231626689434,
-0.010599302127957344,
-0.0350634902715683,
0.023587191477417946,
-0.02511999011039734,
-0.018208501860499382,
0.040526024997234344,
-0.0729643777012825,
-0.01901751197874546,
0.04824323579668999,
0.011562476865947247,
0.026185154914855957,
0.005682765506207943,
0.0060997395776212215,
-0.000799771340098232,
0.0022945418022572994,
0.0008411231101490557,
0.034496575593948364,
0.031138146296143532,
0.00948921125382185,
-0.007359351962804794,
0.04396802932024002,
-0.038556911051273346,
-0.0002475568326190114,
0.015026096254587173,
0.03537110239267349,
-0.04021492227911949,
0.002839519875124097,
0.012489568442106247,
0.0002616757119540125,
0.015343671664595604,
0.04411516711115837,
-0.027847109362483025,
0.09696068614721298,
-0.010140595957636833,
-0.007265166379511356,
-0.03914971277117729,
0.022538533434271812,
-0.03150505572557449,
0.040263060480356216,
0.010916478000581264,
0.05298827961087227,
0.021581009030342102,
0.014466216787695885,
-0.012765299528837204,
-0.0024986793287098408,
0.020004771649837494,
-0.03652546927332878,
0.03817804157733917,
0.013084412552416325,
-0.004704388789832592,
-0.019028594717383385,
0.0199134461581707,
-0.042249392718076706,
0.014868607744574547,
0.05101051181554794,
0.015747103840112686,
0.04375658929347992,
0.023101836442947388,
0.004453718662261963,
-0.04092959687113762,
0.03450945019721985,
-0.08663894236087799,
-0.010548274032771587,
-0.023243658244609833,
-0.004497712943702936,
0.0012196751777082682,
-0.012102510780096054
] |
<blockquote>
<p>The ball of mass $m$ is given a speed of $v_a = \sqrt{3gr}$ at position $A$. When it reaches $B$, the cord hits the small peg $P$ after which the ball describes a smaller circular path. Determine the position $x$ of $P$ so that the ball will be able to reach point $C$.</p>
</blockquote>
<p><img src="http://i.stack.imgur.com/58MPI.png" alt="enter image description here"></p>
<p><strong>My Work</strong></p>
<p>Let $T$ represent kinetic energy and $V$ potential energy. Let $O$ be the datum for gravitational potential energy.</p>
<p>$T_1 + V_1 = T_2 + V_2$</p>
<p>$1/2m(3gr) - mgr = mg(r-x)$</p>
<p>$3/2r - r = r-x$</p>
<p>$x = r-3/2r + r$</p>
<p>$x = 1/2r$</p>
<p>However the correct answer is $x = 2/3r$. What's my mistake? Thanks a lot.</p> | 2,820 | [
-0.03789941221475601,
0.0020586622413247824,
-0.03411514684557915,
-0.012797648087143898,
-0.011014670133590698,
-0.007498483173549175,
-0.030522067099809647,
-0.015428947284817696,
0.02392454259097576,
0.036871153861284256,
0.050264082849025726,
0.0548846460878849,
0.06664742529392242,
0.013768079690635204,
0.04418157413601875,
0.0007779125589877367,
0.003969711251556873,
0.004878214094787836,
0.01708013191819191,
-0.05857621505856514,
-0.00785622838884592,
-0.01726496033370495,
0.004441442899405956,
-0.0075373961590230465,
0.016569212079048157,
0.013020525686442852,
0.05961015820503235,
-0.02051883190870285,
-0.010602646507322788,
0.05048583820462227,
-0.02012448199093342,
0.00014680426102131605,
0.01410717237740755,
-0.002502007642760873,
0.020958371460437775,
0.049510709941387177,
-0.05971020460128784,
-0.021908318623900414,
-0.014728249981999397,
0.03011140786111355,
-0.02900470234453678,
-0.02828248217701912,
-0.023842820897698402,
0.05918673425912857,
-0.0021470405627042055,
0.020771898329257965,
0.0077501279301941395,
-0.023368312045931816,
0.07814813405275345,
-0.02677149325609207,
0.0855686143040657,
0.021375339478254318,
0.021752702072262764,
-0.014504645951092243,
-0.01932775042951107,
-0.01812843233346939,
0.0649539977312088,
0.08933095633983612,
-0.0038482227828353643,
-0.026655085384845734,
-0.008117715828120708,
-0.04114850237965584,
-0.015357215888798237,
-0.04115892946720123,
0.00657365657389164,
0.01130334846675396,
0.0001613005151739344,
0.0415976420044899,
0.028566457331180573,
-0.030414998531341553,
0.010289764031767845,
0.013762203976511955,
0.013453595340251923,
-0.01104176789522171,
0.007766807917505503,
0.006438992451876402,
0.008027671836316586,
0.009593253955245018,
0.019528396427631378,
0.03638581931591034,
-0.016212008893489838,
0.010248854756355286,
0.08232443779706955,
0.05140804499387741,
-0.00017839373322203755,
0.0031677093356847763,
0.04557604715228081,
0.008995515294373035,
-0.0034248470328748226,
0.011950918473303318,
0.01956767402589321,
-0.011136525310575962,
0.003564795246347785,
-0.023104729130864143,
0.018776752054691315,
0.06308037042617798,
-0.010951235890388489,
0.03826790302991867,
0.004259197507053614,
-0.009008698165416718,
-0.020775923505425453,
-0.04452388361096382,
0.028021950274705887,
0.07835961878299713,
-0.006665145047008991,
-0.03154176473617554,
-0.019497128203511238,
-0.009484038688242435,
0.0017350948182865977,
-0.01899663172662258,
-0.03985319286584854,
0.01929403282701969,
-0.021238448098301888,
-0.008315891958773136,
-0.004291309509426355,
-0.02758863754570484,
-0.001916482113301754,
-0.023203136399388313,
0.05924515053629875,
-0.02660452574491501,
0.04194720461964607,
0.0002955633099190891,
0.0530175045132637,
-0.035717979073524475,
-0.04240822419524193,
0.02444426529109478,
0.04837775230407715,
-0.022033771499991417,
-0.021059146150946617,
-0.00037944185896776617,
0.024145595729351044,
-0.011539522558450699,
-0.005369381047785282,
0.0111643485724926,
0.018299227580428123,
-0.03787080571055412,
-0.11743486672639847,
-0.03765338659286499,
0.03798892721533775,
0.015273033641278744,
0.0026293566916137934,
-0.05342869833111763,
-0.016537455841898918,
0.024722665548324585,
0.07693260163068771,
-0.000034802320442395285,
-0.0033132086973637342,
0.023781221359968185,
0.015015033073723316,
-0.0004249048070050776,
-0.007729763630777597,
-0.019034627825021744,
-0.0016579481307417154,
-0.03187129646539688,
0.0063340808264911175,
-0.03236791864037514,
0.03576093167066574,
0.03711371123790741,
0.00759144639596343,
-0.03688916936516762,
0.06161198392510414,
-0.005986577831208706,
0.01987634412944317,
0.015351147390902042,
-0.01899663545191288,
0.019212491810321808,
0.04817147180438042,
0.007716139778494835,
-0.021542267873883247,
0.040364790707826614,
-0.0074775321409106255,
0.03471893444657326,
0.012880801223218441,
0.003836883930489421,
0.0614674910902977,
-0.05750309303402901,
0.008217993192374706,
-0.0003949918318539858,
-0.010244821198284626,
-0.01104870717972517,
-0.029848119243979454,
-0.060701336711645126,
0.015491635538637638,
-0.015590623952448368,
-0.00976620428264141,
0.05008363723754883,
0.019142618402838707,
0.00006991170812398195,
-0.025741182267665863,
-0.0010665201116353273,
-0.00006652150477748364,
-0.05912505090236664,
0.02617228589951992,
0.0038970750756561756,
-0.02839977853000164,
-0.015244759619235992,
-0.008832882158458233,
0.012616319581866264,
-0.017560983076691628,
0.03163880109786987,
0.0477045401930809,
0.053116872906684875,
-0.025552822276949883,
0.013357282616198063,
0.006089326925575733,
0.0518302284181118,
0.0432165265083313,
0.013968996703624725,
-0.020589906722307205,
-0.008077817037701607,
0.018261423334479332,
0.010961265303194523,
-0.017480572685599327,
0.03393521159887314,
-0.026768194511532784,
-0.0006323003326542675,
0.013281001709401608,
0.006036650855094194,
-0.01208056416362524,
0.050830382853746414,
-0.03582746163010597,
0.0692104622721672,
0.05260111391544342,
-0.004380176775157452,
-0.022565500810742378,
0.026735978201031685,
-0.005663611460477114,
0.03214910626411438,
-0.014383682981133461,
-0.03187542036175728,
-0.038169510662555695,
-0.028849836438894272,
0.0010480796918272972,
0.032155632972717285,
-0.02877603843808174,
-0.004322639666497707,
0.050095923244953156,
-0.00961881410330534,
0.017556801438331604,
0.036948271095752716,
-0.00863629300147295,
-0.04734482243657112,
0.028943322598934174,
0.030959738418459892,
-0.02962273545563221,
0.008527087979018688,
-0.002448758576065302,
0.031855009496212006,
0.02403181977570057,
-0.021395506337285042,
-0.011477972380816936,
0.03027712181210518,
-0.01934431865811348,
0.016520235687494278,
0.02122529223561287,
0.01031135581433773,
0.0629810243844986,
-0.03629899397492409,
0.023668736219406128,
0.03906083479523659,
0.010588831268250942,
0.007906584069132805,
-0.016202785074710846,
-0.0035824300721287727,
-0.004011702258139849,
0.03322663903236389,
-0.02755296416580677,
0.002027693670243025,
0.020931662991642952,
-0.025794554501771927,
-0.002944067819043994,
-0.04474223405122757,
-0.0007943713571876287,
-0.03905535116791725,
-0.0030703663360327482,
-0.005007039289921522,
0.003773561678826809,
0.02824178710579872,
-0.030962709337472916,
-0.010324355214834213,
-0.02137126214802265,
-0.019740084186196327,
-0.012303070165216923,
-0.006850929465144873,
-0.03007476031780243,
0.01779092289507389,
-0.004389455541968346,
0.0010215630754828453,
0.039642974734306335,
0.012686314061284065,
-0.0005070199258625507,
0.010502665303647518,
0.014575213193893433,
-0.035106759518384933,
-0.02660517953336239,
-0.011651108972728252,
0.025720015168190002,
-0.05252886191010475,
-0.006264982279390097,
0.040104564279317856,
0.0443335585296154,
-0.006553922314196825,
0.04277169704437256,
-0.06454753875732422,
-0.03872699290513992,
-0.005974165163934231,
0.0167835783213377,
0.017645403742790222,
-0.013019619509577751,
0.02951231226325035,
-0.004026398994028568,
0.02646194025874138,
0.0004399773315526545,
-0.09501243382692337,
-0.010761842131614685,
0.013864338397979736,
0.009216196835041046,
0.04175572097301483,
-0.01568463444709778,
-0.01840062253177166,
0.10539775341749191,
0.02931591123342514,
-0.003383389674127102,
-0.017217513173818588,
-0.008980817161500454,
-0.0026717346627265215,
-0.05228792876005173,
0.01172872819006443,
0.03537626191973686,
-0.023464536294341087,
-0.011996709741652012,
0.021877897903323174,
0.03804803267121315,
0.05594058707356453,
-0.000561910739634186,
0.023990444839000702,
-0.0022859431337565184,
0.009087443351745605,
-0.04710239917039871,
0.05168762430548668,
-0.009520153515040874,
0.008077503181993961,
0.004071076400578022,
-0.016387872397899628,
0.008330426178872585,
-0.020452646538615227,
-0.05076959729194641,
0.05299974977970123,
-0.04420062527060509,
0.01630117930471897,
0.014620528556406498,
0.031923435628414154,
0.0581243671476841,
-0.042732030153274536,
0.006663985084742308,
0.02428441122174263,
0.054508015513420105,
-0.008994515053927898,
0.016941694542765617,
0.06091729924082756,
0.011158709414303303,
-0.035171423107385635,
-0.03765684738755226,
-0.0072007207199931145,
0.011833537369966507,
0.059262715280056,
0.01037953607738018,
-0.027817150577902794,
0.035986799746751785,
0.03443722799420357,
0.0013423473574221134,
-0.006357170641422272,
-0.028180060908198357,
-0.0024978939909487963,
-0.040292780846357346,
-0.021814553067088127,
-0.028608787804841995,
0.03591962158679962,
-0.012398134917020798,
0.04624555632472038,
0.025149282068014145,
0.01890668272972107,
0.01613152027130127,
0.038097407668828964,
-0.07460957020521164,
0.029187915846705437,
-0.044405125081539154,
-0.034776680171489716,
0.0032635109964758158,
-0.006987189408391714,
-0.02766469120979309,
-0.002474593697115779,
-0.00626101391389966,
0.019798289984464645,
-0.010786863043904305,
-0.03977691009640694,
0.00909365899860859,
-0.036171793937683105,
-0.031319428235292435,
0.003141609951853752,
0.0051796515472233295,
0.026791175827383995,
-0.021325483918190002,
0.055458154529333115,
0.047994039952754974,
-0.0456584170460701,
-0.022847777232527733,
-0.03448015823960304,
-0.01840105652809143,
0.016283221542835236,
0.047843437641859055,
-0.008215583860874176,
0.015598433092236519,
0.010216008871793747,
-0.007650191430002451,
0.006987079046666622,
0.04473536089062691,
0.011688710190355778,
-0.015287881717085838,
-0.047529131174087524,
-0.06485462933778763,
-0.029958494007587433,
-0.0009183161309920251,
0.051287610083818436,
-0.03634674847126007,
-0.005401902366429567,
0.035055506974458694,
0.0186934731900692,
0.03407227620482445,
0.017997201532125473,
0.07362356781959534,
0.0028890506364405155,
-0.03857596591114998,
-0.05076921358704567,
-0.02451263926923275,
-0.03203096240758896,
-0.026420926675200462,
-0.00428494717925787,
-0.025862688198685646,
-0.0409354604780674,
-0.025646410882472992,
0.06196724250912666,
0.0778358057141304,
-0.002342804102227092,
0.02638113498687744,
0.0034924992360174656,
0.024234319105744362,
-0.024699224159121513,
-0.033755116164684296,
0.022483201697468758,
-0.016445353627204895,
0.01981702819466591,
-0.03371109068393707,
-0.035365160554647446,
-0.05536802113056183,
-0.04322533681988716,
0.03932522237300873,
0.058267343789339066,
-0.008727873675525188,
-0.027119126170873642,
-0.0640457272529602,
-0.011103525757789612,
0.050001367926597595,
-0.030736617743968964,
0.040356166660785675,
-0.03089299611747265,
0.04126135632395744,
-0.013807929120957851,
-0.054562538862228394,
-0.06537260115146637,
0.003066018223762512,
-0.018857376649975777,
0.00016851609689183533,
-0.01190497912466526,
0.0044200425036251545,
0.00700249383226037,
0.006845965515822172,
0.054197732359170914,
0.06367183476686478,
0.0046693491749465466,
-0.01861562207341194,
0.006940246094018221,
0.007554375100880861,
-0.006902052089571953,
-0.07850392162799835,
0.0007304329774342477,
-0.02672295644879341,
-0.026774778962135315,
0.013859245926141739,
-0.00948812160640955,
-0.0574382059276104,
0.0678061693906784,
-0.0031285297591239214,
0.04310473054647446,
0.026447277516126633,
-0.030385753139853477,
0.0183852706104517,
0.05702989175915718,
-0.023584431037306786,
0.03662092238664627,
0.015541860833764076,
-0.019764410331845284,
-0.0003979823086410761,
-0.012412888929247856,
0.009037505835294724,
-0.016179274767637253,
-0.024396222084760666,
-0.013722146861255169,
-0.011498023755848408,
-0.02033473178744316,
0.03647376969456673,
0.03264932706952095,
0.0031848466023802757,
-0.053620271384716034,
-0.03888643905520439,
0.0012052792590111494,
0.00926307775080204,
0.0401482991874218,
0.027411354705691338,
-0.0014480201061815023,
-0.011639819480478764,
0.017087535932660103,
-0.010075853206217289,
0.013271697796881199,
-0.008975841104984283,
-0.0010533854365348816,
0.0465640090405941,
0.009541772305965424,
-0.014513387344777584,
-0.029518112540245056,
-0.024508560076355934,
-0.015208299271762371,
-0.07110609114170074,
0.07075885683298111,
-0.003962123300880194,
-0.015479043126106262,
0.03278585150837898,
-0.028462016955018044,
-0.06960354745388031,
-0.009133507497608662,
0.01136404275894165,
-0.01737060211598873,
-0.035033099353313446,
-0.0007241371786221862,
-0.005223650019615889,
0.036114513874053955,
-0.04455937072634697,
-0.035501234233379364,
-0.002094124909490347,
0.004290140699595213,
-0.008026396855711937,
0.03584377095103264,
0.012420626357197762,
-0.01016644760966301,
-0.003913890104740858,
0.014236259274184704,
0.027352841570973396,
-0.0396815724670887,
0.0035551870241761208,
0.00537693640217185,
0.046430252492427826,
0.030047442764043808,
0.02851654775440693,
-0.004380525089800358,
-0.004459317773580551,
-0.022797878831624985,
-0.03061148338019848,
-0.0026962836273014545,
0.07495211064815521,
-0.03959806635975838,
-0.044361282140016556,
-0.008362038992345333,
-0.010749812237918377,
0.038318004459142685,
-0.027958087623119354,
-0.02716822549700737,
0.038450125604867935,
0.02843981795012951,
-0.01163111999630928,
0.0027138683944940567,
0.029728742316365242,
0.013841923326253891,
-0.021615736186504364,
-0.013075125403702259,
0.0100610526278615,
-0.03931521996855736,
-0.028986023738980293,
0.04593467712402344,
0.01062832586467266,
-0.0327649787068367,
-0.01251209806650877,
0.07943177968263626,
-0.04426135495305061,
0.00969831645488739,
0.01254202425479889,
0.004878052044659853,
0.04050299897789955,
-0.03131517767906189,
-0.03456945717334747,
0.012603833340108395,
0.000572061340790242,
-0.012891042046248913,
-0.041105739772319794,
-0.01992187090218067,
0.033383164554834366,
0.06980934739112854,
0.0010365970665588975,
0.07888833433389664,
-0.021509429439902306,
-0.005540652200579643,
0.00012614009028766304,
-0.0012923061149194837,
-0.02192998304963112,
-0.03454253450036049,
0.008564027026295662,
0.013233521953225136,
-0.047906309366226196,
0.014895179308950901,
0.020180577412247658,
0.004504332318902016,
-0.010236335918307304,
0.011861707083880901,
0.02935541607439518,
-0.007101007737219334,
-0.00005791692456114106,
-0.012602834962308407,
-0.001906482968479395,
-0.0019526275573298335,
0.018180925399065018,
0.06949416548013687,
-0.006269349716603756,
-0.042402103543281555,
0.06452947109937668,
0.010684390552341938,
-0.02832486294209957,
-0.02819402515888214,
0.017286134883761406,
-0.04798956215381622,
-0.03961968049407005,
0.030343713238835335,
-0.02951093390583992,
0.012966149486601353,
0.012173361144959927,
0.034505028277635574,
-0.0041453163139522076,
0.055555056780576706,
-0.05316872149705887,
-0.05355414003133774,
-0.025432337075471878,
-0.03958481177687645,
-0.056530117988586426,
0.019035743549466133,
0.02739354968070984,
-0.03723018988966942,
0.06481487303972244,
-0.019287360832095146,
-0.012555869296193123,
0.030754927545785904,
0.029414163902401924,
-0.03923357278108597,
0.10103780776262283,
-0.009800366126000881,
0.026438824832439423,
-0.01374649628996849,
-0.0031806807965040207,
0.12812182307243347,
0.03950350359082222,
-0.0028719932306557894,
-0.015100411139428616,
0.0363166518509388,
-0.00022894059657119215,
0.011671519838273525,
-0.028371324762701988,
-0.018901672214269638,
-0.008230775594711304,
-0.010942557826638222,
0.008207366801798344,
0.04110100492835045,
-0.035667095333337784,
-0.00509707722812891,
0.045430976897478104,
-0.0004096769553143531,
-0.06437648087739944,
0.007800615858286619,
-0.007905538193881512,
0.011212754063308239,
0.010741396807134151,
0.03279540687799454,
0.050985075533390045,
-0.062465835362672806,
-0.006431734189391136,
-0.019966252148151398,
-0.04379967600107193,
0.056951530277729034,
-0.01223969180136919,
-0.0464484766125679,
0.007746734656393528,
-0.005131544545292854,
-0.0307418555021286,
0.002401039469987154,
0.03514210507273674,
0.027416512370109558,
-0.04824541136622429,
0.02083328738808632,
0.0319303460419178,
-0.0038440206553786993,
0.017736701294779778,
0.008783940225839615,
0.0074866036884486675,
-0.08849243819713593,
-0.01558589655905962,
-0.04139867052435875,
0.016438396647572517,
-0.006265850272029638,
0.003115122439339757,
-0.0053839972242712975,
-0.02265007235109806,
-0.010151542723178864,
-0.035359855741262436,
0.0056893606670200825,
0.010619379580020905,
-0.026973478496074677,
-0.005670452956110239,
0.005508575588464737,
-0.04889276623725891,
-0.026438796892762184,
0.024196509271860123,
-0.02316240407526493,
-0.0356435626745224,
-0.0014574889792129397,
0.01739298738539219,
-0.0049499706365168095,
0.056673239916563034,
-0.013637484982609749,
-0.007705997675657272,
0.013512631878256798,
-0.023089921101927757,
-0.009063320234417915,
-0.020072586834430695,
-0.02386663854122162,
0.030618326738476753,
0.0005972682847641408,
0.0223111379891634,
0.024569936096668243,
-0.0018485983600839972,
-0.07157944142818451,
0.008516001515090466,
-0.010824344120919704,
-0.0012246592668816447,
-0.06627592444419861,
-0.0013291975483298302,
0.004536155611276627,
0.01871250569820404,
0.033778849989175797,
0.004744048696011305,
-0.01108414214104414,
0.07060020416975021,
0.001380081637762487,
-0.012532046996057034,
-0.028577398508787155,
-0.00937329139560461,
-0.021308492869138718,
0.03238591551780701,
-0.014685814268887043,
0.051568202674388885,
0.01906631700694561,
0.03238549456000328,
-0.017819233238697052,
-0.0029634288512170315,
0.001269070548005402,
0.01602291315793991,
0.008561705239117146,
0.0004568926524370909,
0.0036048409529030323,
0.036060381680727005,
0.0025507269892841578,
-0.028136562556028366,
0.018300972878932953,
-0.0017572769429534674,
-0.009937691502273083,
-0.0008161859586834908,
-0.023772548884153366,
-0.030874568969011307,
0.02080613747239113,
-0.032861821353435516,
0.00855859462171793,
-0.0421316958963871,
0.006018771789968014,
-0.004781664349138737,
-0.02875652350485325,
-0.009400309063494205,
-0.012552187778055668,
-0.03718414157629013,
0.04972299188375473,
-0.02156219817698002,
0.016078727319836617,
-0.034855231642723083,
0.006784355267882347,
-0.016200095415115356,
-0.0038057516794651747,
0.03281209617853165,
0.0016580763040110469,
0.055711064487695694,
-0.014732729643583298,
-0.05540657415986061,
0.02470458671450615,
-0.023319389671087265,
-0.037348370999097824,
0.016396252438426018,
0.026667054742574692,
0.07005291432142258,
-0.00706813670694828,
-0.062087006866931915,
0.015076255425810814,
0.06586166471242905,
-0.022877661511301994,
0.010177498683333397,
-0.0036135695409029722,
-0.04922294616699219,
0.03268624469637871,
-0.014121376909315586,
-0.013968930579721928,
-0.05789165943861008,
-0.017727091908454895,
0.0441383495926857,
0.008345686830580235,
-0.032542455941438675,
0.01967802457511425,
0.004525719676166773,
0.028193224221467972,
-0.021895956248044968,
0.012361655943095684,
0.02661980502307415,
0.04152463749051094,
0.020534491166472435,
-0.01677756942808628,
0.0250568650662899,
0.036946412175893784,
-0.007206372916698456,
-0.08841356635093689,
-0.03320833668112755,
-0.024801235646009445,
0.005234288051724434,
0.0599491111934185,
-0.05998218432068825,
-0.007541776169091463,
0.030051838606595993,
-0.039248812943696976,
-0.0030539454892277718,
-0.012716436758637428,
-0.00035049516009166837,
0.0133965527638793,
-0.05039336159825325,
-0.010768775828182697,
0.02608201839029789,
0.031054319813847542,
0.02698359079658985,
0.013091766275465488,
0.023096026852726936,
-0.030580610036849976,
-0.0418127104640007,
0.018145054578781128,
0.03870317339897156,
-0.04594957083463669,
-0.0007228858303278685,
0.05639318749308586,
-0.032679714262485504,
0.024274297058582306,
0.02591692842543125,
-0.04649842157959938,
0.004767639096826315,
0.018240496516227722,
-0.011175638064742088,
-0.020923815667629242,
0.05611507594585419,
0.021240824833512306,
0.0170249342918396,
-0.009503312408924103,
0.001891102408990264,
0.016273122280836105,
0.013024288229644299,
-0.02698943205177784,
-0.006659267470240593,
0.01317480020225048,
-0.03480711206793785,
-0.049077101051807404,
-0.007137051783502102,
-0.042924173176288605,
0.00103320914786309,
-0.0010228988248854876,
0.016903601586818695,
-0.024456949904561043,
-0.06241845339536667,
-0.016355661675333977,
-0.009919057600200176,
0.005440260283648968,
0.0471973679959774,
-0.03386883810162544,
-0.007630509324371815,
0.012426304630935192,
0.008850297890603542,
-0.0012075281701982021,
0.0037125851958990097,
0.008561666123569012,
-0.012331340461969376,
-0.030586721375584602,
0.030167030170559883,
0.0034844791516661644,
0.01690305583178997,
-0.008768127299845219,
-0.038184259086847305,
-0.010766793042421341,
0.028208693489432335,
0.015000788494944572,
0.008573858998715878,
0.05030413717031479,
0.03778069093823433,
-0.02538883499801159,
-0.09564902633428574,
0.029875202104449272,
0.024796968325972557,
-0.06711289286613464,
-0.022349262610077858,
-0.03725545108318329,
-0.009762786328792572,
-0.00976394210010767,
0.04347153753042221,
-0.03861844539642334,
-0.008184473030269146,
0.03200815990567207,
0.01862567663192749,
0.01549114752560854,
-0.03798927366733551,
-0.0012605745578184724,
-0.001304842997342348,
0.03126242011785507,
0.010768604464828968,
0.012622559443116188,
-0.011555449105799198,
0.007615050300955772,
-0.03310886025428772,
0.012795290909707546,
0.01670229807496071,
0.012269116006791592,
0.00878132227808237,
0.01140332967042923,
-0.003842515405267477,
-0.0002620203304104507,
0.06890857219696045,
-0.005726231262087822,
-0.0010526946280151606,
0.01989663764834404,
-0.04506292566657066,
-0.0227842815220356,
0.03172231838107109,
-0.03313668444752693,
-0.023691466078162193,
-0.011318131349980831,
-0.03935021907091141,
0.02487165294587612,
-0.07654351741075516,
-0.0384187251329422,
0.018731944262981415,
-0.019833389669656754,
-0.021141214296221733,
0.03236839175224304,
0.025214601308107376,
0.03137046843767166,
-0.02275095321238041,
0.03752272203564644,
0.03638848289847374,
-0.02996065840125084,
0.00962620135396719,
-0.02038489654660225,
0.026043124496936798,
0.0010366338538005948,
-0.014326613396406174,
0.047563329339027405,
-0.030800126492977142,
0.026730066165328026,
0.005707748234272003,
0.03747594356536865,
-0.018675751984119415,
0.0064567639492452145,
0.008797284215688705,
-0.01979614794254303,
-0.004328418988734484,
0.016718000173568726,
-0.035296451300382614,
0.046320680528879166,
-0.0019064496736973524,
-0.020543623715639114,
0.02116311527788639,
0.017862774431705475,
0.004078001715242863,
0.027123263105750084,
-0.014160440303385258,
-0.02005249261856079,
0.008567984215915203,
-0.026702728122472763,
0.0031887819059193134,
0.0098867267370224,
0.028236916288733482,
0.021073415875434875,
0.017273250967264175,
0.00946024153381586,
0.010799254290759563,
-0.02903108485043049,
-0.04183639585971832,
-0.0004711408109869808,
-0.008503280580043793,
0.06013841927051544,
0.03672410175204277,
0.01424480602145195,
-0.048607852309942245,
0.012710443697869778,
-0.026983382180333138,
0.05866708979010582,
-0.07005346566438675,
-0.03521023318171501,
-0.022378113120794296,
0.008200815878808498,
0.040054868906736374,
-0.014509066008031368
] |
<p>Maybe this is a silly question, but why does, say, a gasoline-powered AC generator have to use more gas depending on the load?</p>
<p>Let's say I have a 120VAC generator and either a 1A or a 10A load, and assume it can handle 1200W without issue. For 10A, the generator uses more gas and works harder compared to 1A. </p>
<p>Is this because the 10A is passively causing a magnetic field that makes the generator shaft physically more difficult to spin? If so, why does the magnetic field oppose the generators movement if the current is flowing in the direction the generator is trying to make it go to begin with? (Sorry, I know that is probably silly but I have a very limited understanding of electricity and magnetism.)</p>
<p>Or is it because the circuitry in the generator is actively sensing voltage drop due to higher load, and increasing the throttle to maintain a constant output voltage? Sort of like I'd imagine a water pump would have to work harder to maintain a constant pressure in a system with a leak in it or with flow. (Related: If so, is this type of sensing <em>necessary</em> for a generator to limit the voltage to low loads, or is it just a bonus feature to increase efficiency by not running at full throttle all the time?)</p>
<p>Or is it some combination of both? Or are both of those somehow the same thing? (It seems like it must be a little bit of the former; because the generator stalls under too high loads, which I guess means something is resisting the spin - unless the generator just actively shuts itself down?)</p>
<p>What is the process from "higher load" => "higher fuel usage"? </p> | 2,821 | [
-0.04425555840134621,
0.009179545566439629,
-0.004850619472563267,
-0.025804612785577774,
0.030193056911230087,
-0.03199617564678192,
-0.0418202243745327,
-0.004350463394075632,
0.008084075525403023,
-0.006295446772128344,
0.032050784677267075,
0.05361929535865784,
0.047512948513031006,
0.0019687004387378693,
0.017260992899537086,
-0.042282283306121826,
0.015006407164037228,
-0.017089493572711945,
0.012277597561478615,
-0.036912817507982254,
-0.02358223684132099,
-0.002514088759198785,
0.04077988117933273,
0.010511323809623718,
-0.0374416820704937,
0.013319556601345539,
0.03713088855147362,
0.016087515279650688,
-0.005352517124265432,
0.022354373708367348,
-0.014788935892283916,
-0.009339931420981884,
-0.010562832467257977,
0.021556084975600243,
0.022725636139512062,
-0.015545660629868507,
-0.004225174430757761,
-0.0456387922167778,
-0.016672445461153984,
0.047932352870702744,
-0.06917808949947357,
0.03999421000480652,
-0.03943166509270668,
0.009308811277151108,
0.0036024332512170076,
0.03787863627076149,
-0.041489288210868835,
0.007730874698609114,
0.053435567766427994,
-0.10531312227249146,
0.03545193374156952,
-0.008301365189254284,
-0.001897305017337203,
0.031207889318466187,
0.012058669701218605,
0.009813393466174603,
0.09228043258190155,
0.09178194403648376,
-0.006070925388485193,
-0.060801275074481964,
-0.004897323437035084,
-0.00009040837903739884,
-0.04831152781844139,
-0.03527569770812988,
-0.022304145619273186,
0.022509915754199028,
0.0353364571928978,
-0.03654651716351509,
0.04406574368476868,
-0.02779236249625683,
0.039984870702028275,
-0.022185606881976128,
-0.005750235635787249,
0.017522133886814117,
-0.00010854651191039011,
-0.019331328570842743,
0.011622912250459194,
0.02348346821963787,
0.04785209149122238,
0.021463438868522644,
-0.032967183738946915,
0.015026859939098358,
0.031090022996068,
0.04435472562909126,
-0.003979612607508898,
0.011347618885338306,
0.06694753468036652,
0.01490179356187582,
0.06359971314668655,
0.021650107577443123,
0.0032947033178061247,
0.002027754904702306,
0.04164934530854225,
-0.05942733585834503,
-0.03358020633459091,
0.03228306397795677,
-0.018007958307862282,
0.018622586503624916,
0.024624519050121307,
-0.01861533336341381,
-0.010656256228685379,
-0.017323840409517288,
0.041012052446603775,
0.0596567802131176,
0.0000551825032744091,
-0.024496447294950485,
-0.03878038004040718,
-0.010179789736866951,
-0.030784640461206436,
-0.000019961802536272444,
-0.05925757437944412,
0.01591409370303154,
-0.0018310616724193096,
0.00759838568046689,
-0.028195347636938095,
-0.0002514760126359761,
0.03591914847493172,
-0.02294335700571537,
0.02620072476565838,
0.05057255178689957,
0.02326171286404133,
-0.007808993570506573,
0.01757187396287918,
-0.0050578671507537365,
-0.021880410611629486,
0.0057907309383153915,
0.02258751355111599,
-0.01982833258807659,
-0.06555027514696121,
0.029294710606336594,
-0.0093922084197402,
-0.01280150841921568,
0.034938033670186996,
-0.011145798489451408,
0.04763417690992355,
-0.02270602062344551,
-0.0580466128885746,
-0.06210344657301903,
0.014770873822271824,
-0.006762372329831123,
0.01232173852622509,
-0.060518912971019745,
0.010609360411763191,
0.0391557514667511,
0.08988764882087708,
-0.02928783744573593,
0.0006872758385725319,
0.0014102546265348792,
0.021078340709209442,
-0.019725225865840912,
0.005586836952716112,
-0.014566035009920597,
0.00021660274069290608,
-0.009698797017335892,
-0.037630293518304825,
-0.0483175553381443,
0.0689731314778328,
0.031566184014081955,
-0.00070565304486081,
-0.01752401702105999,
0.022703828290104866,
0.0024311989545822144,
-0.01798720844089985,
0.006542202550917864,
-0.003455461235716939,
-0.007884475402534008,
0.07102278620004654,
-0.011120819486677647,
0.04471413046121597,
0.019092092290520668,
0.018518976867198944,
0.02937907539308071,
0.043487053364515305,
0.02897121012210846,
0.06374669820070267,
-0.017391983419656754,
-0.022951750084757805,
-0.037385061383247375,
0.006353807635605335,
0.006998227909207344,
0.005081141833215952,
-0.021570459008216858,
-0.046976327896118164,
0.016449861228466034,
0.004825036972761154,
0.01392192579805851,
-0.016779165714979172,
0.013777637854218483,
0.006946843583136797,
-0.027531061321496964,
-0.03810941055417061,
-0.05370568111538887,
-0.0036341825034469366,
-0.03831445053219795,
0.011902404949069023,
0.030502326786518097,
-0.0031357721891254187,
0.00001927725134009961,
-0.0062617151997983456,
-0.027895871549844742,
0.024329688400030136,
0.040628645569086075,
0.0007802395848557353,
0.0006448912899941206,
-0.026692353188991547,
0.017168518155813217,
-0.00914817675948143,
-0.017963968217372894,
0.027898069471120834,
-0.012790548615157604,
-0.02989274077117443,
0.019090261310338974,
-0.017808102071285248,
0.00368487648665905,
0.0414397232234478,
0.011584438383579254,
0.022297052666544914,
0.0005521169514395297,
-0.019725754857063293,
0.017924195155501366,
-0.006135407369583845,
0.035092540085315704,
0.08214417099952698,
-0.0195999126881361,
-0.009412462823092937,
0.04663087800145149,
-0.01507560070604086,
-0.006909787654876709,
-0.022392097860574722,
0.006132872309535742,
-0.040851492434740067,
0.008238292299211025,
0.04669790714979172,
0.019980700686573982,
-0.01660200022161007,
0.03480162099003792,
0.06763903051614761,
0.012576146051287651,
0.02117323875427246,
0.012394336983561516,
-0.027064789086580276,
-0.019246526062488556,
0.012934492900967598,
0.03761550039052963,
0.0074121481738984585,
-0.004344095475971699,
0.07122480124235153,
0.024167466908693314,
0.035668279975652695,
0.011401643976569176,
-0.019572902470827103,
0.05340713635087013,
0.0018331515602767467,
0.036290910094976425,
0.011066410690546036,
0.011707966215908527,
0.047403063625097275,
-0.025804022327065468,
0.014999083243310452,
-0.011875282041728497,
0.0023458709474653006,
0.03263704851269722,
0.013955920934677124,
-0.03393273055553436,
-0.004648130387067795,
-0.0283673033118248,
0.016333654522895813,
-0.02333664335310459,
0.029489673674106598,
-0.01964922808110714,
0.025263652205467224,
-0.03613061457872391,
0.009789957664906979,
-0.03545236214995384,
0.014090504497289658,
0.015837576240301132,
-0.013459336943924427,
0.04187818989157677,
-0.02293652482330799,
-0.029398441314697266,
0.00873475894331932,
-0.0543334074318409,
0.032136429101228714,
0.03761669248342514,
-0.03057137131690979,
-0.0027989568188786507,
-0.014610528014600277,
-0.016965176910161972,
0.049070388078689575,
0.03582027181982994,
0.004065333865582943,
-0.014311293140053749,
0.021050048992037773,
-0.0790005475282669,
0.007516815792769194,
-0.0068928818218410015,
0.02008679509162903,
-0.01899614743888378,
-0.05581890791654587,
0.09931933134794235,
0.0022686931770294905,
-0.04252472147345543,
0.011220286600291729,
-0.049094658344984055,
0.01776309497654438,
0.012154333293437958,
-0.013863961212337017,
0.017212528735399246,
-0.02748757414519787,
0.00021133653353899717,
0.03548652306199074,
-0.037665992975234985,
-0.03351547569036484,
-0.034990858286619186,
-0.0392155721783638,
-0.0344250425696373,
-0.012768091633915901,
0.08774366974830627,
0.019800754263997078,
-0.01921846531331539,
0.052681226283311844,
0.04132379591464996,
0.009474409744143486,
-0.012976028956472874,
-0.02524389512836933,
-0.007056184578686953,
-0.06809459626674652,
-0.023678934201598167,
0.06365133821964264,
-0.0029666158370673656,
0.006127606611698866,
0.028936466202139854,
0.05847878381609917,
0.00975513644516468,
0.0011396214831620455,
-0.01687881164252758,
0.02838234044611454,
-0.013667082414031029,
-0.013209287077188492,
0.04081068933010101,
-0.008942927233874798,
0.02203061804175377,
0.017360907047986984,
-0.01960255205631256,
0.025915276259183884,
-0.002703239908441901,
-0.03934679925441742,
0.02985515631735325,
-0.012156401760876179,
0.03351901099085808,
-0.04610007628798485,
0.022444279864430428,
0.012776847928762436,
-0.01927950233221054,
0.01623566448688507,
0.0715513601899147,
0.08449233323335648,
-0.04935004189610481,
-0.02798859216272831,
0.016913937404751778,
0.019740134477615356,
-0.03262726962566376,
-0.036676984280347824,
-0.00832191202789545,
-0.032428257167339325,
0.04275854304432869,
-0.004289682023227215,
-0.00850727129727602,
0.07383954524993896,
-0.01380530558526516,
0.03949035704135895,
0.013235471211373806,
-0.018640931695699692,
0.06903976947069168,
-0.0871974527835846,
0.013014858588576317,
-0.029565511271357536,
0.03995776176452637,
0.021337516605854034,
0.029359208419919014,
0.021005956456065178,
-0.005889466032385826,
-0.008167773485183716,
-0.006344748195260763,
-0.10149452090263367,
0.0012939699226990342,
-0.028090253472328186,
-0.019037563353776932,
0.011490155011415482,
-0.009074672125279903,
0.0035239718854427338,
-0.011978761292994022,
-0.015107769519090652,
-0.04977615550160408,
-0.0046249376609921455,
-0.07058598846197128,
0.03708858788013458,
-0.01657765358686447,
-0.03708232194185257,
-0.03704940900206566,
0.01118046697229147,
0.0061636618338525295,
-0.037706516683101654,
0.035230062901973724,
0.00797652080655098,
-0.04198630154132843,
0.00849431287497282,
-0.001797492615878582,
0.019370628520846367,
-0.021354567259550095,
0.04135368764400482,
0.04475143179297447,
-0.015317586250603199,
-0.007821042090654373,
-0.05291158705949783,
0.003331974847242236,
0.03917120397090912,
0.010442886501550674,
-0.0013523189118131995,
-0.05264992639422417,
0.008089848794043064,
-0.046097345650196075,
-0.00611523725092411,
0.044504281133413315,
-0.011168748140335083,
0.014589027501642704,
-0.02812994085252285,
-0.028972655534744263,
-0.018194111064076424,
0.02224033884704113,
0.009707478806376457,
-0.00971346627920866,
-0.03356853500008583,
-0.044189393520355225,
-0.01902545802295208,
0.005219539161771536,
0.03652248904109001,
-0.0032892918679863214,
0.0018067776691168547,
-0.03212541714310646,
-0.02539915218949318,
0.07369574904441833,
-0.005318004637956619,
-0.04200965538620949,
0.03498178720474243,
0.03397126495838165,
0.0011735082371160388,
0.022007478401064873,
0.013405945152044296,
0.04408741742372513,
0.007022706791758537,
0.04225347191095352,
0.02230515331029892,
-0.01785963773727417,
-0.10737437754869461,
-0.04225308820605278,
0.03644309192895889,
0.0069739301688969135,
0.01774163544178009,
-0.03644132614135742,
-0.04275178909301758,
-0.023874256759881973,
0.020831454545259476,
-0.057454515248537064,
0.058872681111097336,
-0.020793292671442032,
-0.002218959154561162,
-0.02491530030965805,
-0.056741971522569656,
-0.013335230760276318,
0.02100468799471855,
-0.018439242616295815,
0.05093373730778694,
0.02507081814110279,
-0.030894283205270767,
-0.015633631497621536,
-0.00834399089217186,
0.004470018669962883,
0.020966384559869766,
-0.019181065261363983,
-0.009327736683189869,
-0.01823713630437851,
0.07565198838710785,
-0.014431384392082691,
-0.06948848813772202,
0.011534050107002258,
-0.04137679934501648,
-0.03233616426587105,
0.03096800111234188,
-0.012743741273880005,
-0.03556182608008385,
0.011767154559493065,
-0.01696660928428173,
-0.028921635821461678,
-0.05102003738284111,
-0.047858282923698425,
0.055885035544633865,
0.03642817959189415,
0.012858349829912186,
0.028295151889324188,
0.06847991794347763,
-0.05815758928656578,
0.01645163632929325,
0.024899687618017197,
0.03759327903389931,
-0.008689498528838158,
-0.014992119744420052,
-0.020007260143756866,
0.031175415962934494,
-0.032878294587135315,
0.05417020246386528,
-0.022951386868953705,
0.023629214614629745,
-0.007127294782549143,
-0.033805184066295624,
0.018294889479875565,
0.004180488642305136,
-0.0006569465040229261,
-0.045861952006816864,
-0.028423842042684555,
0.025682998821139336,
-0.031115779653191566,
0.007694686762988567,
0.027639444917440414,
-0.01758887991309166,
-0.015047818422317505,
0.049071889370679855,
-0.02234039083123207,
0.011457723565399647,
-0.04654805362224579,
0.01548613328486681,
0.020808685570955276,
-0.022877205163240433,
0.06754988431930542,
-0.017577817663550377,
-0.0015331361209973693,
-0.0076835365034639835,
-0.002754689659923315,
-0.032521795481443405,
0.043093111366033554,
0.0034292424097657204,
0.028146134689450264,
-0.009087230078876019,
0.027409270405769348,
-0.022086920216679573,
-0.01751197688281536,
-0.012875070795416832,
-0.024697275832295418,
0.020824439823627472,
0.04323370382189751,
-0.012983768247067928,
-0.02599385380744934,
-0.033305153250694275,
0.012076124548912048,
-0.020824888721108437,
0.018052294850349426,
0.005762279964983463,
-0.047955673187971115,
0.005028454586863518,
0.03582135960459709,
0.0043247416615486145,
0.046804796904325485,
-0.013385274447500706,
-0.038406722247600555,
0.01826152391731739,
-0.03149999678134918,
-0.017162028700113297,
-0.009055289439857006,
0.01180423703044653,
-0.04201994091272354,
0.0025480976328253746,
0.018020465970039368,
-0.0052792285569012165,
0.050397150218486786,
-0.016060950234532356,
0.01596236601471901,
0.032530397176742554,
0.0023119058459997177,
0.026238324120640755,
0.014357750304043293,
-0.00720506114885211,
-0.01173968892544508,
0.014871669001877308,
0.011535868979990482,
-0.01190917193889618,
-0.027652477845549583,
-0.027013303712010384,
0.004905888345092535,
0.04796411097049713,
-0.01209003385156393,
0.02412373572587967,
0.05507773533463478,
0.0018573921406641603,
0.031892016530036926,
0.011159772984683514,
-0.00020423489331733435,
0.02207578346133232,
-0.018704501911997795,
0.028057659044861794,
0.010397996753454208,
-0.015235049650073051,
-0.012543883174657822,
-0.036213118582963943,
0.001734345336444676,
-0.01419760286808014,
0.018697986379265785,
0.011068488471210003,
0.05600506439805031,
-0.02984854206442833,
-0.0340023972094059,
-0.027685366570949554,
-0.056227441877126694,
-0.020270725712180138,
-0.029365306720137596,
-0.003148260060697794,
0.0022572684101760387,
0.03349358215928078,
-0.007059237454086542,
0.04725649207830429,
0.014261918142437935,
0.019627269357442856,
-0.026855774223804474,
0.0667465329170227,
0.016655530780553818,
0.023473279550671577,
-0.01151229441165924,
-0.04719797149300575,
0.02420155704021454,
-0.022288290783762932,
0.04588882625102997,
-0.00994215626269579,
0.03692331537604332,
0.04195548593997955,
0.006584363989531994,
-0.0022169710136950016,
-0.08976966142654419,
0.00004301019725971855,
-0.0702928826212883,
-0.002069332869723439,
0.031237410381436348,
-0.024104973301291466,
0.029808498919010162,
0.01285217609256506,
0.018958095461130142,
-0.01665591076016426,
0.006679065525531769,
-0.024775806814432144,
-0.020708639174699783,
-0.009015344083309174,
-0.004402597434818745,
-0.058501310646533966,
0.010344166308641434,
0.004678685218095779,
-0.031664952635765076,
0.009294004179537296,
-0.007459606509655714,
0.027233939617872238,
-0.037248801440000534,
0.026537779718637466,
0.019319970160722733,
0.08702176064252853,
0.002399589167907834,
0.01704159565269947,
-0.023313699290156364,
-0.0240736436098814,
0.14471322298049927,
-0.004328704904764891,
0.013101482763886452,
-0.04821915924549103,
-0.01576296053826809,
-0.0136897386983037,
0.020762454718351364,
-0.0009981178445741534,
-0.009403328411281109,
0.01092903595417738,
0.008294453844428062,
0.03702747821807861,
0.004505499731749296,
0.014904942363500595,
0.02781127206981182,
0.056444622576236725,
-0.015129613690078259,
0.009793248027563095,
0.008818856440484524,
0.07363247871398926,
0.00010943087545456365,
0.017962489277124405,
-0.011284544132649899,
0.011735956184566021,
-0.009933361783623695,
0.0040700677782297134,
-0.028441648930311203,
-0.06364087760448456,
0.021766435354948044,
-0.024625595659017563,
-0.020011454820632935,
0.01819394715130329,
0.00036684711812995374,
0.004824828822165728,
-0.010697493329644203,
0.0306082796305418,
-0.0008241134928539395,
0.018432248383760452,
-0.023183347657322884,
0.0411577932536602,
0.0019066175445914268,
0.023101113736629486,
-0.020792648196220398,
0.003927171695977449,
-0.04644513130187988,
-0.007328112609684467,
-0.03385790064930916,
0.002715139416977763,
0.008615088649094105,
0.02945026196539402,
0.013828656636178493,
-0.0019715765956789255,
0.05888569355010986,
-0.019029617309570312,
-0.05523381754755974,
-0.01675133779644966,
0.008893621154129505,
-0.043839920312166214,
-0.033556487411260605,
-0.04860730096697807,
0.012569560669362545,
0.006997023243457079,
0.02467951364815235,
-0.02629864774644375,
-0.01381551381200552,
0.030568962916731834,
-0.0038674480747431517,
0.03631474822759628,
-0.012837977148592472,
-0.039795707911252975,
-0.0027028536424040794,
0.008623057045042515,
-0.016965975984930992,
-0.010729358531534672,
0.03766750916838646,
0.030461179092526436,
0.0031843571923673153,
0.00027757699717767537,
0.01030551828444004,
0.007755330763757229,
-0.05693313851952553,
0.006454037502408028,
-0.018632352352142334,
-0.003790243761613965,
-0.0014082600828260183,
-0.0007904554367996752,
-0.019478846341371536,
0.0357062891125679,
-0.012271953746676445,
-0.0012452852679416537,
-0.01305247750133276,
0.0382835753262043,
0.013561229221522808,
-0.004162915516644716,
-0.03656606748700142,
0.040814854204654694,
-0.06605406850576401,
0.020630083978176117,
0.06046158820390701,
0.0667877271771431,
0.02468877099454403,
-0.008181077428162098,
-0.018467558547854424,
-0.013334140181541443,
0.002600790001451969,
-0.0002675443247426301,
0.042740996927022934,
0.0020605078898370266,
-0.015572252683341503,
-0.017317073419690132,
-0.010726140812039375,
-0.009062371216714382,
-0.0360976867377758,
-0.024375593289732933,
-0.018646905198693275,
-0.003986109513789415,
0.008873717859387398,
0.00720399571582675,
0.008621813729405403,
-0.03777192160487175,
0.040256425738334656,
-0.03889365494251251,
0.006916112266480923,
-0.03742463141679764,
-0.0018244798993691802,
0.043390918523073196,
0.005847353488206863,
0.02789544127881527,
0.011721484363079071,
-0.02539703994989395,
0.02223469316959381,
-0.01439620740711689,
-0.03212660178542137,
-0.039836861193180084,
-0.010844985954463482,
-0.0011386532569304109,
0.033717960119247437,
0.05514855682849884,
-0.03651313856244087,
-0.024243861436843872,
0.060017891228199005,
0.0036040800623595715,
0.007303719408810139,
0.02882697433233261,
-0.017686855047941208,
0.008511088788509369,
0.02445385977625847,
-0.024515382945537567,
0.0021688223350793123,
0.03614456206560135,
-0.007501556072384119,
-0.01335580088198185,
-0.03348919749259949,
0.010106047615408897,
0.02754419669508934,
0.026897309347987175,
0.01053277775645256,
-0.025546491146087646,
0.041734885424375534,
0.014436658471822739,
0.025915421545505524,
-0.03595783933997154,
-0.045080073177814484,
-0.019688855856657028,
0.017372896894812584,
0.02995314449071884,
0.02100813016295433,
0.023349566385149956,
0.0216718427836895,
-0.008896230719983578,
-0.031263045966625214,
0.005753755569458008,
-0.008876804262399673,
0.0168156661093235,
-0.0421823188662529,
-0.0108752166852355,
0.014700016006827354,
-0.00669118482619524,
-0.009812748990952969,
-0.007286761421710253,
-0.019726146012544632,
-0.003389531746506691,
-0.0901583582162857,
-0.027175426483154297,
-0.0027885539457201958,
-0.011861762031912804,
-0.07235679775476456,
0.009358159266412258,
0.0027792672626674175,
-0.0018734830664470792,
-0.004281813744455576,
0.007317268755286932,
0.02041536010801792,
-0.014748039655387402,
-0.025988783687353134,
-0.04453565925359726,
0.029144875705242157,
0.035975199192762375,
0.00030418651294894516,
-0.015892447903752327,
0.05540614202618599,
-0.07686489075422287,
-0.009197458624839783,
0.052999284118413925,
-0.021405695006251335,
0.015638306736946106,
-0.014212487265467644,
-0.0051690503023564816,
-0.015516314655542374,
0.02473902516067028,
0.03606497496366501,
0.009604346938431263,
-0.031151091679930687,
0.05516669526696205,
0.039190083742141724,
0.02947315387427807,
-0.0013830073876306415,
0.05427150800824165,
0.0060496763326227665,
0.00014327518874779344,
0.043231356889009476,
0.023616747930645943,
-0.045095738023519516,
-0.036568693816661835,
0.027842994779348373,
0.021502012386918068,
-0.009019182994961739,
-0.005679380148649216,
0.01863844506442547,
-0.002486474346369505,
-0.037431806325912476,
0.03746967017650604,
-0.03934761881828308,
0.019752006977796555,
0.006775541231036186,
-0.02678767777979374,
-0.0010315532563254237,
0.03578682616353035,
0.032158203423023224,
-0.021119603887200356,
-0.031621161848306656,
0.023604774847626686,
-0.023282354697585106,
0.003976463805884123,
-0.03173146769404411,
-0.014464249834418297,
-0.004128310829401016,
0.042240165174007416,
0.026454579085111618,
0.012029197067022324,
0.021710172295570374,
-0.05014689639210701,
-0.00975891761481762,
-0.04951494187116623,
0.020033691078424454,
-0.005068969912827015,
0.011346944607794285,
-0.025264309719204903,
-0.07093542814254761,
0.0044303168542683125,
-0.009951971471309662,
0.018991248682141304,
-0.011957141570746899,
-0.044722773134708405,
0.021957233548164368,
-0.003949368838220835,
0.008003899827599525,
-0.009044177830219269,
0.03894161432981491,
-0.006918688770383596,
-0.0507776215672493,
0.017111875116825104,
-0.017794163897633553,
-0.04060276597738266,
-0.0018837579991668463,
0.04623249173164368,
0.043394021689891815,
-0.003652882995083928,
-0.027271803468465805,
-0.01122811809182167,
0.02224579267203808,
0.010596570558845997,
0.02950030192732811,
0.06164039298892021,
-0.02651015669107437,
0.03425844386219978,
0.0025765644386410713,
0.03724903240799904,
-0.016139348968863487,
0.055655479431152344,
-0.044201694428920746,
0.032906223088502884,
-0.030039440840482712,
-0.009488631971180439,
0.06699376553297043,
-0.031574491411447525,
-0.005465051159262657,
-0.006063495296984911,
-0.021323662251234055,
-0.002957858145236969,
0.016065295785665512,
0.01855192892253399,
0.0008747918182052672,
-0.0432327575981617,
0.0074653723277151585,
-0.052126072347164154,
0.02292858622968197,
-0.048285502940416336,
0.04587244614958763,
0.027025284245610237,
-0.012875085696578026,
-0.03188895806670189,
0.06342688947916031,
-0.019686877727508545,
0.015070224180817604,
-0.008773944340646267,
0.04699035361409187,
-0.04210367798805237,
-0.06204644963145256,
0.03348500281572342,
-0.014827999286353588,
0.0015736427158117294,
0.045774754136800766,
-0.0008907957235351205,
0.056997328996658325,
0.00984228402376175,
-0.011058858595788479,
-0.03791983798146248,
-0.00537347374483943,
0.024318382143974304,
-0.015971655026078224,
-0.025634566321969032,
0.03283984214067459,
-0.0020737238228321075,
0.011666558682918549,
-0.014238594099879265,
-0.019861865788698196,
0.06345571577548981,
-0.034366313368082047,
0.03781667724251747,
-0.0068319677375257015,
-0.001952070859260857,
-0.006304577924311161,
-0.052670400589704514,
-0.03992670029401779,
-0.06465067714452744,
0.010905008763074875,
0.01513100415468216,
-0.0028945193625986576,
-0.03142959251999855,
-0.037688691169023514,
-0.0054729594849050045,
0.028732994571328163,
-0.05848521739244461,
-0.008687734603881836,
-0.0013259114930406213,
0.0038506374694406986,
0.035486556589603424,
-0.007445078808814287
] |
<p>Law of equipartition predicts the heat capacity of gases correctly. It assumes that inter-molecular attraction in gases is negligible (which is true). But for solids, inter-molecular attraction is not negligible, the, how come it still predicts the correct value for molar heat capacity?</p>
<p>How can we ignore the potential energy due to inter-molecular attraction in solids?</p>
<p>Each oscillator has two degree of freedom (kinetic and potential). Solid has oscillators in all the 3 dimension. So, total degree for freedom will be $6$. Using equipartition, the internal energy of one mole a solid will be $ U = 6 \times \frac{1}{2}RT = 3RT$. </p>
<p>Heat capacity, $C = \dfrac{dQ}{dT} = \dfrac{dU + PdV}{dT} = \dfrac{dU}{dT}$ $(\because V \text{ is constant})$</p>
<p>$\implies C = \dfrac{d}{dT}[3RT] = 3R \approx 25 J mol^{-1} K^{-1}$</p>
<p>Which is a very close approximation of the <a href="http://hyperphysics.phy-astr.gsu.edu/hbase/tables/sphtt.html" rel="nofollow">actual values</a>.</p>
<p>My question is why is this prediction in agreement with experimentally determined values, when we have ignored the potential energy due to inter-molecular attraction. Which is not negligible for solids? </p> | 2,822 | [
0.006649887189269066,
-0.006857186555862427,
-0.019857259467244148,
-0.006113262847065926,
0.018979361280798912,
-0.004630299750715494,
-0.03407314047217369,
-0.0021802301052957773,
0.0023905225098133087,
0.000028062917408533394,
0.02033250965178013,
0.007041465025395155,
0.028856193646788597,
-0.02593376860022545,
-0.01303904876112938,
-0.01546389888972044,
-0.0034589895512908697,
-0.046189069747924805,
0.01879274472594261,
-0.038423627614974976,
-0.020374028012156487,
0.0288076288998127,
0.0031092637218534946,
-0.01440668199211359,
-0.04108239710330963,
0.031027980148792267,
-0.016846632584929466,
0.004965461790561676,
0.03764189034700394,
0.02609000913798809,
0.013270719908177853,
-0.02227969467639923,
0.022261708974838257,
0.004874560050666332,
0.02864181436598301,
-0.0021162868943065405,
0.011861054226756096,
-0.025516869500279427,
-0.027815081179142,
0.04855030030012131,
-0.050899989902973175,
-0.004572262056171894,
-0.014969016425311565,
0.03673357516527176,
0.022531868889927864,
0.01251209806650877,
0.0034603786189109087,
-0.04108686372637749,
0.0370793454349041,
-0.06759718060493469,
0.041465334594249725,
-0.0008728110115043819,
0.026626596227288246,
0.037397727370262146,
0.0065195937640964985,
-0.04155667498707771,
0.06512008607387543,
0.09540349990129471,
-0.005893114488571882,
-0.044294748455286026,
-0.029047420248389244,
-0.03422689437866211,
0.0029063087422400713,
0.03031950816512108,
-0.012359410524368286,
0.03300091251730919,
-0.008571610786020756,
-0.017927590757608414,
0.03288143873214722,
0.004597438033670187,
0.025369681417942047,
0.03249907121062279,
0.06587045639753342,
0.01164644118398428,
0.05003974586725235,
0.00439525255933404,
0.002896994585171342,
0.03917548432946205,
0.04329200088977814,
0.029267283156514168,
-0.03586471453309059,
-0.004700511693954468,
0.05096901208162308,
0.019693413749337196,
0.013516047038137913,
-0.0367991179227829,
0.05166647583246231,
0.003665308700874448,
0.007820994593203068,
0.021794116124510765,
-0.007010906469076872,
0.03690693899989128,
0.03846851736307144,
0.025692138820886612,
-0.0019107051193714142,
0.026109224185347557,
0.017107490450143814,
0.029543090611696243,
-0.028181273490190506,
-0.024623429402709007,
-0.022520415484905243,
-0.01969883032143116,
0.04726439341902733,
0.07689006626605988,
-0.002069175010547042,
-0.081080861389637,
-0.03185928985476494,
0.011464306153357029,
0.01733081415295601,
-0.023222966119647026,
-0.01289775874465704,
0.0386933758854866,
-0.009833005256950855,
-0.03523068502545357,
-0.02806318923830986,
0.020316332578659058,
-0.009766661562025547,
-0.01928376406431198,
0.025838259607553482,
0.03904690593481064,
0.013944507576525211,
-0.00841054879128933,
0.0017315794248133898,
-0.038293953984975815,
-0.09340281784534454,
0.012331226840615273,
0.015429616905748844,
-0.0322229340672493,
-0.017639650031924248,
0.03447551652789116,
-0.013800635933876038,
-0.0034402518067508936,
-0.02655613422393799,
0.013501630164682865,
0.01354631595313549,
0.017554422840476036,
-0.08639243245124817,
-0.023121098056435585,
0.07014984637498856,
-0.044848740100860596,
-0.013635815121233463,
-0.08066576719284058,
-0.01458197645843029,
0.018809886649250984,
0.0730389729142189,
-0.020085809752345085,
0.02005838230252266,
-0.026622282341122627,
0.031595345586538315,
-0.007183845620602369,
-0.04728173837065697,
-0.05451720580458641,
0.0038370161782950163,
-0.03796105831861496,
0.002336119068786502,
-0.03668198361992836,
0.05718442425131798,
0.04706192761659622,
0.03980939835309982,
-0.0203965213149786,
-0.005220450460910797,
-0.032995086163282394,
-0.013347202911973,
-0.018167095258831978,
0.009545373730361462,
-0.034448299556970596,
0.05153525248169899,
-0.00189194455742836,
0.04586412385106087,
0.018032517284154892,
-0.015556173399090767,
0.020937839522957802,
-0.007982601411640644,
0.0373593270778656,
0.031578272581100464,
0.0007544392719864845,
-0.010920382104814053,
-0.038556382060050964,
-0.016693899407982826,
0.016179470345377922,
-0.04699435457587242,
-0.027229629456996918,
0.021336179226636887,
-0.005544390995055437,
-0.01841156929731369,
0.015298430807888508,
0.02344384230673313,
0.014375279657542706,
-0.0009854147210717201,
-0.05340373516082764,
-0.026393631473183632,
-0.06839372217655182,
0.03091488592326641,
0.010425737127661705,
-0.03224590793251991,
0.03499000892043114,
0.018626879900693893,
0.024745043367147446,
0.005411830730736256,
-0.013079124502837658,
-0.0038284093607217073,
0.009912839159369469,
-0.004892189055681229,
-0.028749192133545876,
0.05288691073656082,
0.0623517781496048,
0.05054576322436333,
-0.012004914693534374,
0.0171967800706625,
-0.014820702373981476,
-0.04712282493710518,
0.0037935543805360794,
-0.03996696323156357,
-0.012144229374825954,
-0.033284153789281845,
-0.03201877698302269,
0.013893220573663712,
0.0013247828464955091,
-0.028953783214092255,
0.05291888862848282,
-0.019459085538983345,
0.02208862453699112,
0.015654826536774635,
0.02763216570019722,
-0.013793843798339367,
0.053695205599069595,
-0.013691624626517296,
0.0459052249789238,
-0.0288511011749506,
-0.029722018167376518,
-0.04525909945368767,
-0.030196115374565125,
0.037056710571050644,
0.06135299801826477,
-0.06751546263694763,
-0.027756191790103912,
0.003204201813787222,
0.0018739355728030205,
0.025071876123547554,
0.01479065790772438,
-0.011681672185659409,
-0.032579731196165085,
0.048405010253190994,
-0.013286934234201908,
0.013142261654138565,
0.0023962901905179024,
-0.0010600382229313254,
0.06043060123920441,
0.02119954116642475,
-0.01665360853075981,
0.02969297394156456,
0.0233168825507164,
-0.025504572317004204,
0.012918193824589252,
0.008827912621200085,
-0.023979278281331062,
0.034015923738479614,
0.0067068724893033504,
0.0008118813275359571,
0.003149867756292224,
0.014025658369064331,
0.03892679885029793,
-0.03182102367281914,
-0.03702336922287941,
0.0057273791171610355,
0.0011246220674365759,
-0.01830011047422886,
-0.014114946126937866,
0.0002745020901784301,
-0.04885271191596985,
-0.011978375725448132,
-0.03735027834773064,
0.043606314808130264,
-0.0035049302969127893,
0.027191530913114548,
0.029525788500905037,
-0.0032012276351451874,
0.017613697797060013,
-0.05410090088844299,
-0.0017421254888176918,
-0.012493913993239403,
-0.019553234800696373,
-0.007917655631899834,
-0.004943700507283211,
-0.022535104304552078,
0.011250382289290428,
0.014330342411994934,
-0.026797780767083168,
0.030564071610569954,
-0.011682845652103424,
-0.020160755142569542,
-0.0019998610951006413,
-0.023715797811746597,
-0.06768718361854553,
-0.02889220602810383,
-0.008387653157114983,
-0.006667050067335367,
-0.04572713002562523,
-0.009429313242435455,
0.02427663840353489,
-0.029320361092686653,
-0.014016768895089626,
0.03794005513191223,
-0.0416402705013752,
-0.036153193563222885,
0.015458440408110619,
0.003720193635672331,
0.01591056026518345,
-0.025641346350312233,
0.016408704221248627,
0.06795117259025574,
-0.03196948021650314,
-0.03775705397129059,
-0.07640652358531952,
-0.04532518610358238,
0.024876119568943977,
-0.003336211433634162,
0.048542119562625885,
0.008138817735016346,
-0.028971444815397263,
0.03939634561538696,
0.007924181409180164,
-0.08024407178163528,
0.010502447374165058,
-0.028605487197637558,
-0.024479271844029427,
-0.021643340587615967,
0.007537458557635546,
0.05930056795477867,
0.008643162436783314,
0.012597096152603626,
0.001067638979293406,
0.006584669463336468,
0.0113756712526083,
-0.018459046259522438,
0.012235013768076897,
0.014895079657435417,
0.00015620834892615676,
-0.02108311839401722,
0.024753747507929802,
0.006930115167051554,
-0.02633851394057274,
0.014467810280621052,
-0.03449142724275589,
0.047098077833652496,
0.04780677706003189,
-0.0846276506781578,
0.030401581898331642,
0.00433717155829072,
0.04923893138766289,
-0.046328190714120865,
0.018842162564396858,
0.012741051614284515,
0.0011722708586603403,
0.030217096209526062,
0.029131656512618065,
0.03082267940044403,
0.02126060053706169,
0.01765032298862934,
0.019484572112560272,
0.020285766571760178,
0.014954427257180214,
-0.04297617822885513,
0.025362038984894753,
0.004935102537274361,
-0.010860370472073555,
0.02435547485947609,
0.0055254725739359856,
0.05702938139438629,
-0.013841433450579643,
0.04463929310441017,
-0.01977461390197277,
-0.0233907550573349,
0.015289835631847382,
-0.06449950486421585,
-0.021843859925866127,
-0.023534022271633148,
0.049532122910022736,
-0.005885151214897633,
0.0399695448577404,
0.035732071846723557,
0.009764369577169418,
0.009573676623404026,
0.0051228925585746765,
-0.08138877153396606,
0.032752860337495804,
0.0129769342020154,
-0.023900087922811508,
-0.009700252674520016,
0.002881207037717104,
-0.01115884818136692,
-0.022781280800700188,
0.005404546856880188,
-0.00038145887083373964,
-0.01463387068361044,
-0.0562928281724453,
-0.009553884156048298,
0.0020817271433770657,
0.021340597420930862,
-0.047417715191841125,
0.035965435206890106,
0.037819452583789825,
-0.04426548257470131,
-0.0022677299566566944,
0.050089094787836075,
-0.04359360784292221,
-0.018225783482193947,
-0.0718032717704773,
0.01282951608300209,
0.035928528755903244,
0.04258979484438896,
0.04363333433866501,
0.01738889515399933,
0.0139571912586689,
0.007742625195533037,
0.024043219164013863,
0.009551085531711578,
0.01083090715110302,
-0.025382163003087044,
-0.0469113327562809,
-0.048912134021520615,
-0.008638706058263779,
0.019912531599402428,
0.05161852017045021,
-0.03182607889175415,
0.0479748360812664,
-0.014924941584467888,
-0.003512780414894223,
0.02038612961769104,
0.025596680119633675,
0.015800364315509796,
0.017839178442955017,
-0.01873607560992241,
-0.06402061879634857,
-0.01861102506518364,
-0.031173529103398323,
-0.005022956524044275,
0.04594412446022034,
0.030393725261092186,
-0.02131034806370735,
-0.029421519488096237,
0.020971348509192467,
0.029712125658988953,
0.011496073566377163,
-0.00359130697324872,
-0.00037944832001812756,
0.05861683934926987,
-0.022706035524606705,
-0.02649509720504284,
-0.000463202508399263,
0.00759193254634738,
0.03447527810931206,
0.004649449605494738,
-0.019210711121559143,
-0.08414488285779953,
0.006434487644582987,
0.028682565316557884,
0.027222048491239548,
-0.02229134738445282,
-0.003706635208800435,
-0.04369717836380005,
0.008063090965151787,
0.02623075619339943,
-0.011209359392523766,
0.014684373512864113,
-0.006826257333159447,
0.030910009518265724,
-0.0121228052303195,
-0.041245803236961365,
-0.021826675161719322,
-0.009841687977313995,
0.040789294987916946,
0.033181082457304,
-0.04253755509853363,
-0.018818791955709457,
-0.00709121860563755,
0.008724769577383995,
0.04124656319618225,
0.061468105763196945,
-0.019555166363716125,
0.027208376675844193,
0.04031548649072647,
-0.007132205180823803,
-0.022122446447610855,
-0.0770568773150444,
0.008678842335939407,
-0.03924558684229851,
0.010826212354004383,
0.02220328524708748,
-0.0767756998538971,
-0.03987506777048111,
0.025260722264647484,
0.04111836850643158,
-0.054071251302957535,
-0.046046383678913116,
-0.02297239378094673,
0.046731915324926376,
-0.00824807956814766,
-0.03604399785399437,
0.07180999219417572,
0.04448654502630234,
-0.009158209897577763,
-0.023127365857362747,
-0.0395122654736042,
0.0207483172416687,
-0.01882483996450901,
0.007104890886694193,
-0.041395243257284164,
0.033586617559194565,
-0.020873168483376503,
0.03262532129883766,
-0.040253281593322754,
0.018696485087275505,
-0.009116562083363533,
-0.004215163178741932,
-0.011183390393853188,
0.007428203243762255,
0.018587376922369003,
0.04752844199538231,
0.0007591191097162664,
0.045218147337436676,
-0.004039898980408907,
-0.01219352800399065,
0.009297407232224941,
0.0022939867340028286,
-0.014161065220832825,
0.04933086782693863,
-0.00992642156779766,
0.02851836010813713,
-0.048496030271053314,
-0.009179141372442245,
-0.0040979813784360886,
-0.05297479033470154,
-0.000776828674133867,
-0.03333482891321182,
0.050757598131895065,
0.016527632251381874,
-0.022789396345615387,
0.01800471358001232,
-0.02411160059273243,
0.021061720326542854,
0.03851817548274994,
-0.011415230110287666,
0.011474382132291794,
-0.021907055750489235,
0.006110825575888157,
-0.04980851337313652,
-0.051672447472810745,
0.023070713505148888,
0.024502595886588097,
-0.04875157028436661,
-0.03918688744306564,
0.013242633081972599,
-0.023693440482020378,
-0.039108045399188995,
0.012375050224363804,
0.06245066225528717,
0.022260142490267754,
-0.016317324712872505,
0.030296633020043373,
0.05314687639474869,
0.047268521040678024,
0.013155676424503326,
-0.01011742651462555,
0.004032398108392954,
0.026825370267033577,
-0.02069794572889805,
0.010994949378073215,
0.03517141565680504,
-0.025883596390485764,
-0.029504844918847084,
0.013013877905905247,
-0.0179829690605402,
0.05240165442228317,
0.009310727007687092,
-0.03223947435617447,
0.018754396587610245,
-0.00010004291834775358,
-0.048405855894088745,
-0.022733241319656372,
0.026309195905923843,
0.014371568337082863,
0.028757156804203987,
-0.003486229106783867,
-0.0035773972049355507,
-0.05171743780374527,
-0.019290922209620476,
0.002249041572213173,
-0.006380814127624035,
-0.011394328437745571,
0.030413389205932617,
0.07826212793588638,
0.02262772060930729,
0.004487529397010803,
0.0024788903538137674,
-0.011517295613884926,
0.022861501201987267,
-0.022469814866781235,
0.023070506751537323,
-0.010988396592438221,
0.03732818365097046,
-0.03629228100180626,
-0.024706261232495308,
-0.060225725173950195,
0.06115465238690376,
0.030592435970902443,
-0.08639176934957504,
0.041453249752521515,
0.007982169277966022,
-0.024994447827339172,
-0.025533590465784073,
-0.01829284057021141,
-0.0109631959348917,
0.024506334215402603,
-0.012108983471989632,
0.030883193016052246,
-0.025455791503190994,
-0.0338108204305172,
0.03947724774479866,
0.025589166209101677,
-0.030104195699095726,
0.00144453055690974,
0.048121023923158646,
0.003595605492591858,
-0.005276050418615341,
-0.05154353007674217,
-0.018997451290488243,
0.06519167125225067,
-0.006802158895879984,
0.03500930219888687,
0.01825650967657566,
0.013318571262061596,
0.019150100648403168,
-0.009323236532509327,
-0.006379345897585154,
-0.04956195130944252,
-0.04610306769609451,
0.004362005274742842,
0.04797457531094551,
0.03459187224507332,
0.013791733421385288,
0.0214238204061985,
-0.006478231865912676,
0.00962083600461483,
0.04778477922081947,
0.007602841593325138,
0.016573289409279823,
-0.05059200897812843,
-0.001869629486463964,
0.009429000318050385,
-0.041153810918331146,
0.03412302955985069,
0.00755328219383955,
-0.05326642841100693,
0.02403371036052704,
0.004864708986133337,
0.05099485069513321,
0.026088396087288857,
-0.011087718419730663,
0.025256188586354256,
0.0713009238243103,
-0.007050212472677231,
0.009540090337395668,
-0.0009521730244159698,
0.04210842773318291,
0.13629958033561707,
0.03461923450231552,
-0.002219291403889656,
-0.04658159986138344,
-0.008657500147819519,
-0.004635939374566078,
-0.019672147929668427,
-0.04878140240907669,
0.01601913571357727,
0.01438367459923029,
0.03013329580426216,
0.011912943795323372,
0.060759834945201874,
0.021465126425027847,
-0.01117028295993805,
0.0024068288039416075,
-0.045809950679540634,
-0.03086341731250286,
0.00014354776067193598,
-0.004746186546981335,
0.024848200380802155,
-0.021419435739517212,
0.006119055673480034,
-0.04440532624721527,
0.01592162624001503,
0.0033919985871762037,
-0.02928602509200573,
-0.04834252595901489,
0.023556793108582497,
0.027671363204717636,
-0.035394493490457535,
0.004683576989918947,
0.01798313297331333,
0.0017831753939390182,
-0.01991370879113674,
-0.009695037268102169,
0.021479493007063866,
-0.025125468149781227,
-0.005170860327780247,
0.0048894924111664295,
-0.007500439882278442,
0.0075563108548521996,
0.017407501116394997,
0.049242109060287476,
-0.024901675060391426,
-0.021509982645511627,
-0.04593722149729729,
0.025354070588946342,
-0.043113838881254196,
-0.02855829894542694,
0.00337325525470078,
-0.0011074659414589405,
-0.00525533314794302,
-0.062085315585136414,
-0.03257271274924278,
0.00002053293246717658,
0.05667015537619591,
-0.03431907668709755,
-0.013452986255288124,
-0.041628699749708176,
-0.008333287201821804,
0.03703433647751808,
0.007594306021928787,
-0.016981802880764008,
0.006130704656243324,
0.00760458130389452,
-0.012316456064581871,
0.054021865129470825,
-0.025933196768164635,
0.015303132124245167,
-0.012502605095505714,
-0.00905980821698904,
-0.016030943021178246,
-0.043999455869197845,
0.0011026484426110983,
0.027774309739470482,
0.04077259078621864,
-0.01313871145248413,
-0.0008426833082921803,
-0.000693723326548934,
-0.06573262810707092,
0.0191323384642601,
-0.003236933145672083,
0.0016779613215476274,
-0.06589855253696442,
-0.018628833815455437,
0.02255197800695896,
0.04604031890630722,
-0.03447994589805603,
0.00664640823379159,
0.00889280904084444,
0.008982417173683643,
-0.00731025543063879,
-0.028493890538811684,
-0.0210674237459898,
0.012031663209199905,
-0.06387120485305786,
0.01459570974111557,
0.0494847409427166,
0.03773118928074837,
0.01005946658551693,
0.008614839054644108,
-0.006568026728928089,
0.04275518283247948,
-0.017173537984490395,
0.01718435436487198,
-0.01339000929147005,
0.017870543524622917,
-0.026713762432336807,
0.03309142589569092,
-0.03351351618766785,
-0.011109971441328526,
-0.052433133125305176,
-0.05091455206274986,
-0.020034564658999443,
0.013787548989057541,
0.006482250522822142,
-0.03466428071260452,
-0.0010454572038725019,
-0.021380454301834106,
0.015870865434408188,
-0.032266512513160706,
-0.013345467858016491,
-0.01789829507470131,
-0.014534613117575645,
-0.0003784352447837591,
0.00239987182430923,
-0.029681308194994926,
-0.019341934472322464,
-0.045985087752342224,
0.01541315671056509,
0.03297257423400879,
0.03137100487947464,
0.007114949636161327,
-0.06581151485443115,
0.006427380256354809,
-0.01955328695476055,
0.051018666476011276,
-0.050219547003507614,
-0.044373322278261185,
0.04715583100914955,
-0.044855747371912,
-0.08764577656984329,
0.016341183334589005,
-0.015955733135342598,
-0.024077201262116432,
0.041026562452316284,
0.008076842874288559,
-0.011265874840319157,
0.059183426201343536,
-0.017497917637228966,
0.015330157242715359,
0.02520432136952877,
0.00486379861831665,
0.007035179529339075,
-0.011047554202377796,
-0.0156704131513834,
-0.01771753467619419,
0.001510215806774795,
0.055802762508392334,
0.034504469484090805,
0.014882231131196022,
0.0010512715671211481,
0.013860438019037247,
-0.0084688076749444,
0.00242560519836843,
0.07111082226037979,
0.022427188232541084,
0.03477324917912483,
0.03833417221903801,
-0.015026110224425793,
0.01835767738521099,
0.04377978295087814,
0.025131475180387497,
-0.08981440961360931,
-0.014528577215969563,
-0.018775077536702156,
0.0074460068717598915,
0.010380213148891926,
-0.035429731011390686,
0.02074092999100685,
-0.014047510921955109,
-0.07011213898658752,
-0.006732778158038855,
-0.04232664778828621,
-0.016967102885246277,
-0.04224700108170509,
-0.015904735773801804,
-0.02817557193338871,
0.03938496857881546,
0.03188975155353546,
0.047523099929094315,
0.02387171983718872,
0.04664601758122444,
-0.02858886681497097,
0.012415303848683834,
0.018840612843632698,
0.04414664953947067,
-0.012972836382687092,
-0.03678092360496521,
0.05427251383662224,
-0.013067751191556454,
-0.03176698461174965,
0.0076581151224672794,
-0.04391058161854744,
-0.03791990131139755,
0.028000107035040855,
0.02094644494354725,
-0.03611103072762489,
0.04011759161949158,
0.039835136383771896,
-0.008795958012342453,
-0.006101673934608698,
0.04010790213942528,
-0.0025979734491556883,
0.027864357456564903,
-0.013429226353764534,
-0.01901264116168022,
0.024479582905769348,
-0.025435151532292366,
-0.011124893091619015,
0.05406944453716278,
-0.03170715272426605,
0.007761293090879917,
-0.006562722846865654,
0.004198144655674696,
0.0022963981609791517,
-0.02894393354654312,
-0.005523846950381994,
-0.03244631364941597,
0.02008502557873726,
0.04054034501314163,
0.03030826710164547,
0.003508808556944132,
-0.008864418603479862,
-0.013129564002156258,
-0.0016060592606663704,
0.02508426643908024,
0.02436101622879505,
-0.004709795583039522,
-0.01631961017847061,
-0.032347939908504486,
0.0325063057243824,
0.009105516597628593,
-0.035523779690265656,
-0.04394753649830818,
-0.06451398134231567,
0.04006306454539299,
0.04932759702205658,
0.027673888951539993,
0.02057015523314476,
-0.020938580855727196,
-0.010719441808760166,
-0.05779053643345833,
0.019415833055973053,
-0.029525937512516975,
-0.019260765984654427,
-0.025779426097869873,
-0.013968328945338726,
0.05713948234915733,
0.01161004789173603,
0.05476449802517891,
0.008568108081817627,
-0.021797167137265205,
0.006134888622909784,
0.0035261951852589846,
0.0009371956693939865,
-0.022317957133054733,
0.0017767491517588496,
0.0000561293272767216,
0.008263847790658474,
0.012314308434724808,
-0.006068682298064232,
-0.022361911833286285,
0.015946079045534134,
0.03160158917307854,
-0.03515135869383812,
0.02193455398082733,
-0.00833872426301241,
0.005648263730108738,
0.04000570997595787,
0.0032989911269396544,
-0.01118085253983736,
0.07371646910905838,
-0.007350468542426825,
0.017128175124526024,
0.03746890649199486,
-0.02812495268881321,
-0.034256305545568466,
0.021791551262140274,
-0.00019545912800822407,
-0.01515906397253275,
0.010328488424420357,
-0.013727745972573757,
0.052243296056985855,
-0.020755063742399216,
0.03981253504753113,
0.03571121394634247,
-0.03368333354592323,
0.008068766444921494,
0.016695477068424225,
0.02449391968548298,
0.03221896290779114,
-0.003616006812080741,
0.033353038132190704,
0.03207867592573166,
-0.007610742002725601,
0.006269427482038736,
0.05230916664004326,
0.0602228157222271,
-0.004363554064184427,
0.012301838956773281,
0.05758668854832649,
-0.005678602494299412,
-0.00423324853181839,
0.04572243615984917,
0.008644167333841324,
-0.023185627534985542,
-0.04848918318748474,
0.0137932812795043,
-0.019873924553394318,
0.024654323235154152,
-0.002299572341144085,
0.012820526026189327,
0.09794973582029343,
-0.014867063611745834,
-0.03508443012833595,
-0.032880932092666626,
0.0057799555361270905,
0.030866943299770355,
0.015080644749104977,
0.019794510677456856,
0.0035268410574644804,
0.015280813910067081,
-0.0015174157451838255,
-0.02365916036069393,
0.008524134755134583,
-0.014713829383254051,
-0.009769405238330364,
-0.021591730415821075,
-0.021365566179156303,
0.021199192851781845,
-0.045737847685813904,
-0.009252830408513546,
-0.006166635546833277,
0.018589837476611137,
0.06406684964895248,
0.02873663231730461,
0.031863242387771606,
-0.007154916413128376,
-0.010626710020005703,
0.0050201318226754665,
0.0754215270280838,
-0.0633825957775116,
-0.007488357834517956,
-0.0410856157541275,
-0.007369245868176222,
-0.005015579517930746,
-0.010211937129497528
] |
<p>As part of a hw problem for a class, we're supposed to be deriving the equivalence given in equation 2.3 of this paper <a href="http://arxiv.org/abs/1107.5563" rel="nofollow">http://arxiv.org/abs/1107.5563</a>. I was wondering if there is some special relation involving the Ricci Curvature in 5d's relationship to one in 4d. Since with a general metric like the one given in 2.1, calculating the Christoffel symbols would seem to be an enormous and not particularly smart idea.</p> | 2,823 | [
-0.02931308187544346,
0.0003767888993024826,
-0.015141851268708706,
0.002105661667883396,
0.01392387505620718,
0.05769631639122963,
-0.03235789015889168,
-0.0007031538407318294,
0.028100354596972466,
-0.030811097472906113,
-0.014904026873409748,
0.01822478137910366,
0.05705796554684639,
0.04791116341948509,
0.025987310335040092,
-0.023256028071045876,
-0.03323627635836601,
-0.016501694917678833,
-0.0007961527444422245,
-0.07790631055831909,
0.03832988440990448,
0.007619398180395365,
0.0007745163748040795,
-0.02576722577214241,
-0.018879514187574387,
0.044075921177864075,
0.00717719504609704,
0.00010535216279095039,
0.007495059631764889,
0.0426458977162838,
-0.0076673575676977634,
0.009633680805563927,
0.0017857610946521163,
0.025196311995387077,
0.02017875574529171,
-0.017988432198762894,
-0.05828667804598808,
-0.05823200196027756,
0.0063728331588208675,
0.024473614990711212,
-0.020162085071206093,
-0.027090903371572495,
-0.005627314560115337,
0.0683726817369461,
-0.015062629245221615,
-0.016284750774502754,
-0.010128946974873543,
0.004870719742029905,
0.03893997520208359,
-0.04543522745370865,
0.09455793350934982,
0.011364374309778214,
0.00730067677795887,
-0.020368501543998718,
-0.028987882658839226,
0.03548808768391609,
0.03394896164536476,
0.05643244460225105,
-0.009873786009848118,
-0.030841687694191933,
-0.04407486692070961,
-0.0052089025266468525,
-0.015747832134366035,
-0.04678192734718323,
-0.03697515279054642,
0.02505582384765148,
-0.03447084128856659,
-0.02006729133427143,
0.02295665815472603,
-0.02772163413465023,
0.008371230214834213,
0.007652892265468836,
0.08443033695220947,
-0.018981490284204483,
0.015154031105339527,
0.018783284351229668,
-0.007603236939758062,
0.02307070791721344,
0.04399019852280617,
0.0024458442348986864,
-0.008462503552436829,
0.0008449706947430968,
0.028826074674725533,
0.04211149737238884,
-0.03429631516337395,
0.009859447367489338,
0.019130675122141838,
0.016347458586096764,
0.020004579797387123,
0.042777929455041885,
0.025965027511119843,
-0.009078487753868103,
0.07982241362333298,
-0.0344715379178524,
-0.008302969858050346,
0.030268162488937378,
-0.018375037238001823,
0.06459809094667435,
0.01837833970785141,
-0.0044694882817566395,
-0.021854756399989128,
-0.04453325644135475,
-0.023258941248059273,
0.05469551309943199,
0.03302285075187683,
-0.011306864209473133,
-0.004774668253958225,
0.010263502597808838,
-0.005079788621515036,
-0.004745564889162779,
-0.03563830628991127,
-0.013688144274055958,
-0.010119039565324783,
-0.01373264193534851,
0.02649574913084507,
-0.04446641728281975,
0.029729122295975685,
-0.0046208640560507774,
0.03310483321547508,
0.04826204106211662,
0.023135002702474594,
-0.026370514184236526,
0.021245885640382767,
-0.012365249916911125,
-0.0157668124884367,
0.017567871138453484,
0.03341622278094292,
-0.05343814566731453,
-0.014644811861217022,
-0.01953982375562191,
0.0006465759943239391,
0.001002520089969039,
0.00214663939550519,
-0.005101693794131279,
0.02079806663095951,
-0.03370548412203789,
-0.08686749637126923,
-0.062256187200546265,
0.029325595125555992,
0.06281153112649918,
-0.03825103119015694,
-0.051626935601234436,
0.03908737748861313,
0.024191880598664284,
0.08886508643627167,
-0.036518972367048264,
0.03767310827970505,
0.039753276854753494,
0.05873722583055496,
0.015156791545450687,
-0.0052071805112063885,
-0.02704600617289543,
-0.023130537942051888,
-0.0427292101085186,
-0.045567333698272705,
-0.05863356590270996,
-0.035687386989593506,
0.006734798196703196,
-0.0002400884695816785,
-0.02401556260883808,
0.0683102160692215,
-0.010230553336441517,
-0.0030253136064857244,
0.022822413593530655,
0.007792017888277769,
-0.014858173206448555,
0.058925751596689224,
0.012966440990567207,
-0.006642336957156658,
0.009677411057054996,
-0.021305041387677193,
0.00661337748169899,
-0.0014448172878473997,
0.04363769665360451,
0.024190813302993774,
-0.045814987272024155,
-0.009374137967824936,
-0.0021780957467854023,
0.028491148725152016,
0.01774882897734642,
-0.026513345539569855,
-0.040539756417274475,
-0.004590882454067469,
-0.0017653837567195296,
-0.01508481614291668,
0.02078692428767681,
-0.006294600665569305,
0.019630271941423416,
0.015015737153589725,
-0.03494666516780853,
-0.0026458464562892914,
-0.03814214840531349,
-0.017914509400725365,
0.02799290418624878,
-0.04357925057411194,
0.029327059164643288,
0.016923345625400543,
0.031045392155647278,
-0.014673677273094654,
-0.0495108887553215,
-0.01886921562254429,
-0.01580602303147316,
0.03136857599020004,
-0.010642522014677525,
0.009415054693818092,
0.008472282439470291,
0.06474006175994873,
-0.010359463281929493,
0.027444174513220787,
-0.043914709240198135,
-0.022724615409970284,
0.008915485814213753,
0.0195762999355793,
0.03155821934342384,
0.010000473819673061,
0.03199752792716026,
0.010663565248250961,
0.00041156765655614436,
0.0029804883524775505,
0.027050433680415154,
-0.04258359223604202,
0.055080052465200424,
0.06593803316354752,
0.004956067074090242,
0.010659711435437202,
0.026768343523144722,
-0.0012190178968012333,
0.031686436384916306,
0.012048621661961079,
-0.028555188328027725,
-0.006101606879383326,
-0.04177205264568329,
0.020424770191311836,
0.028213096782565117,
-0.05319247394800186,
0.007412185426801443,
0.06276653707027435,
0.03692122921347618,
0.004881707951426506,
-0.01006077229976654,
0.014184631407260895,
-0.06795087456703186,
0.04164116084575653,
-0.020411238074302673,
0.014407824724912643,
0.010241112671792507,
0.007623628713190556,
-0.013499594293534756,
0.029079141095280647,
-0.024653617292642593,
-0.014495503157377243,
0.03378971666097641,
-0.011903380043804646,
0.019467242062091827,
-0.0028167252894490957,
-0.006012883502990007,
0.02279144711792469,
-0.023314563557505608,
0.006916206795722246,
0.07865644991397858,
0.004081516992300749,
-0.00898686796426773,
-0.006748745683580637,
-0.01603122614324093,
0.013593757525086403,
0.011989163234829903,
-0.01705361343920231,
-0.010046706534922123,
-0.010044343769550323,
-0.03823549300432205,
0.0095899049192667,
0.0033032263163477182,
-0.034524235874414444,
-0.002434945199638605,
0.0017369204433634877,
0.03448881208896637,
-0.017734337598085403,
0.020758984610438347,
-0.009734975174069405,
-0.02394862286746502,
0.05516235530376434,
-0.0038323088083416224,
0.0046975333243608475,
0.007424735464155674,
-0.05724262446165085,
0.004737728275358677,
-0.034022264182567596,
-0.027029328048229218,
0.02626892738044262,
0.01792009547352791,
0.023983053863048553,
0.022369127720594406,
-0.03029957227408886,
-0.010461384430527687,
-0.03453677147626877,
-0.010548466816544533,
0.034962814301252365,
-0.03331083804368973,
0.04601851850748062,
0.06836014986038208,
0.00018741075473371893,
-0.03549064323306084,
-0.025858217850327492,
-0.007252423092722893,
-0.06832288950681686,
-0.029226981103420258,
-0.001663649920374155,
0.0002801263763103634,
-0.021249160170555115,
0.018029920756816864,
0.04149496555328369,
-0.003955994267016649,
-0.020805103704333305,
-0.057241108268499374,
-0.07623396813869476,
0.08267948776483536,
0.006599659565836191,
0.019565248861908913,
0.013300049118697643,
-0.05671481415629387,
0.09071660786867142,
0.026914015412330627,
-0.032076675444841385,
-0.06153574213385582,
0.012177701108157635,
0.005392664112150669,
-0.017779266461730003,
-0.02144835703074932,
0.0334833525121212,
-0.023780426010489464,
0.012917838990688324,
0.0500866174697876,
0.01621788553893566,
0.048678770661354065,
-0.013874190859496593,
-0.0355590358376503,
-0.013287188485264778,
0.0404098778963089,
0.015604402869939804,
0.03820309415459633,
-0.01922464184463024,
-0.012831585481762886,
-0.007964649237692356,
0.04353334754705429,
0.006244808901101351,
0.015132781118154526,
-0.03674563765525818,
0.031899817287921906,
-0.014018062502145767,
0.001501288847066462,
-0.01094672828912735,
0.006030089687556028,
0.008393739350140095,
-0.027411969378590584,
0.029716363176703453,
0.03699740767478943,
0.041204165667295456,
-0.0321621410548687,
-0.009134921245276928,
0.027893831953406334,
-0.011201457120478153,
0.0123979477211833,
-0.012715121731162071,
-0.014011850580573082,
-0.006573348771780729,
0.023129167035222054,
-0.0386931411921978,
-0.0073501369915902615,
0.0315975584089756,
-0.0031343866139650345,
0.03779195621609688,
0.006970196031033993,
-0.08349684625864029,
0.03136683627963066,
-0.08210568875074387,
-0.022798268124461174,
-0.045748271048069,
0.025169065222144127,
0.004834064282476902,
0.027566827833652496,
-0.005759709049016237,
0.020963264629244804,
0.02390844002366066,
0.0030916898977011442,
-0.05892123654484749,
-0.00847709458321333,
-0.022201135754585266,
-0.01836586184799671,
-0.0011266489746049047,
-0.024150505661964417,
0.03395693004131317,
0.0016650358447805047,
-0.014971264638006687,
-0.0067943790927529335,
-0.021330244839191437,
-0.07408776134252548,
0.038455523550510406,
-0.013475673273205757,
-0.036338578909635544,
-0.008872621692717075,
0.016524888575077057,
0.04740438610315323,
-0.021880075335502625,
0.010443909093737602,
0.04228324070572853,
-0.015590451657772064,
0.03984212502837181,
-0.02795911207795143,
0.043115466833114624,
0.010534585453569889,
0.02636457234621048,
0.008378771133720875,
0.020505135878920555,
-0.008657134138047695,
0.01152467168867588,
-0.015460643917322159,
0.03924155607819557,
0.0042514074593782425,
-0.026467643678188324,
-0.01949051395058632,
-0.05377980321645737,
-0.025710484012961388,
-0.02997804433107376,
0.08010757714509964,
-0.016761118546128273,
0.0010471947025507689,
0.022953055799007416,
0.02439558133482933,
-0.01404179260134697,
-0.007946442812681198,
0.058803874999284744,
-0.012213259004056454,
-0.0527680441737175,
-0.0404217466711998,
-0.010191554203629494,
-0.014961276203393936,
-0.020037002861499786,
0.03349284827709198,
0.0030631939880549908,
-0.03643101081252098,
0.01680275984108448,
0.03817479684948921,
-0.013768586330115795,
-0.011024218052625656,
-0.018189553171396255,
-0.017361406236886978,
0.015112657099962234,
0.007293512113392353,
-0.007789291441440582,
0.00013903147191740572,
0.04160502180457115,
0.05759263038635254,
0.010567348450422287,
-0.0215210672467947,
-0.06904502958059311,
-0.015141082927584648,
0.00366954249329865,
0.036955609917640686,
-0.011556909419596195,
0.007124746218323708,
-0.05731581524014473,
-0.03104637749493122,
0.04955904185771942,
0.007066899910569191,
0.01962110958993435,
0.020116373896598816,
-0.004024314694106579,
0.006221788469702005,
0.0009455591789446771,
-0.03363252431154251,
0.03373013809323311,
0.0072945840656757355,
0.0004934555618092418,
-0.004430851433426142,
0.025287188589572906,
-0.02091217041015625,
0.03063294105231762,
0.015189584344625473,
0.025492381304502487,
0.011844776570796967,
-0.0002687904052436352,
0.016875840723514557,
0.03944879025220871,
-0.043642010539770126,
-0.05789969861507416,
0.009398083202540874,
0.03828403353691101,
-0.03526682034134865,
0.044948022812604904,
-0.03628406301140785,
0.0168705303221941,
0.038883138447999954,
-0.003949158824980259,
-0.011199306696653366,
0.026133347302675247,
-0.026043247431516647,
0.05186997726559639,
0.03531413897871971,
-0.000684598577208817,
0.03683187812566757,
0.034062180668115616,
0.043472856283187866,
-0.018626105040311813,
-0.00814870372414589,
0.03161489591002464,
-0.03322882205247879,
-0.007233516778796911,
-0.0035114092752337456,
0.009151278994977474,
-0.06372140347957611,
0.027579445391893387,
-0.04036018252372742,
0.015994178131222725,
0.004167525097727776,
-0.03961102291941643,
-0.004159926902502775,
0.004096758086234331,
-0.002636690391227603,
0.004502210766077042,
0.0012902442831546068,
0.005056528374552727,
0.04858889803290367,
-0.041920263320207596,
0.016698040068149567,
-0.020784154534339905,
-0.03164590522646904,
0.04404546692967415,
0.018842332065105438,
0.0229563619941473,
-0.030866554006934166,
-0.006069278344511986,
0.027357086539268494,
-0.0467437282204628,
0.02259044535458088,
-0.02346719242632389,
-0.00127004727255553,
-0.007832716219127178,
-0.011127984151244164,
0.016095725819468498,
-0.0013499610358849168,
-0.03428316116333008,
-0.013375409878790379,
-0.013725011609494686,
0.018996167927980423,
0.018822040408849716,
-0.01421173196285963,
-0.09836990386247635,
-0.02243843302130699,
0.0408366322517395,
0.02481694146990776,
-0.027499722316861153,
-0.04660523682832718,
-0.02680017054080963,
-0.04230779781937599,
-0.04727509245276451,
0.013355136848986149,
0.07972579449415207,
-0.036609798669815063,
-0.036778151988983154,
0.006447347812354565,
0.020316269248723984,
0.06881269067525864,
-0.021990761160850525,
0.004392672795802355,
0.008298814296722412,
-0.007553459145128727,
-0.0173577181994915,
0.01895485818386078,
0.04681852087378502,
-0.006800469476729631,
-0.019605934619903564,
-0.03151286765933037,
-0.011026295833289623,
0.021914629265666008,
-0.027727177366614342,
0.023785380646586418,
0.020844455808401108,
0.020270954817533493,
-0.0003059686569031328,
-0.04779042676091194,
-0.0029939301311969757,
-0.03275451809167862,
0.002350756898522377,
-0.013554644770920277,
0.007934809662401676,
0.00329483300447464,
-0.04007025063037872,
0.04911557957530022,
-0.02699517086148262,
-0.003909521270543337,
-0.02667032554745674,
0.07304130494594574,
-0.00863711442798376,
-0.05453396961092949,
0.013007375411689281,
-0.03573158010840416,
-0.013740143738687038,
-0.002786353463307023,
0.0026827307883650064,
-0.0008644767804071307,
0.03516427055001259,
-0.03051059879362583,
-0.03524646908044815,
-0.030971631407737732,
0.022679142653942108,
0.05042280629277229,
-0.011620288714766502,
0.06099625304341316,
0.037807196378707886,
-0.03773338720202446,
0.03202611953020096,
-0.006710634101182222,
-0.005850824993103743,
0.012016569264233112,
0.0020179934799671173,
0.0755680650472641,
-0.026335233822464943,
-0.0209206510335207,
0.03213975578546524,
0.03197347745299339,
-0.04073157534003258,
0.013787700794637203,
0.008408723399043083,
0.012976237572729588,
0.017970457673072815,
-0.015965290367603302,
-0.03976184502243996,
0.04896746948361397,
0.005326396785676479,
0.031944192945957184,
-0.022379640489816666,
-0.03483535721898079,
0.05284198001027107,
0.028291210532188416,
0.035783980041742325,
-0.008149011060595512,
-0.04103393852710724,
-0.03789527341723442,
-0.003047403646633029,
0.04952085018157959,
0.017561525106430054,
-0.00671140942722559,
0.025270361453294754,
0.04158826172351837,
0.0003668084682431072,
0.05386098101735115,
-0.006353253498673439,
-0.04944740980863571,
-0.019044896587729454,
-0.03764830902218819,
-0.01449253223836422,
0.03212312236428261,
0.014196604490280151,
0.008166497573256493,
-0.018724173307418823,
-0.04391580447554588,
0.013817094266414642,
0.028250936418771744,
0.07436353713274002,
0.0283849835395813,
0.04199279472231865,
-0.03663460537791252,
0.02440524846315384,
-0.013072599656879902,
-0.008643100969493389,
0.11439507454633713,
0.05095667392015457,
0.0021053000818938017,
-0.04577220603823662,
0.05318347364664078,
0.0010133686009794474,
0.03595217317342758,
-0.0344415046274662,
0.07166647166013718,
-0.02739395759999752,
-0.008446075953543186,
0.024079471826553345,
0.0715305283665657,
-0.013866136781871319,
-0.020666349679231644,
0.03279951587319374,
-0.025606971234083176,
-0.0005946285091340542,
0.008893540129065514,
0.003301673335954547,
0.008008143864572048,
-0.0073192487470805645,
-0.037910476326942444,
0.03653288632631302,
-0.018416233360767365,
0.013515531085431576,
-0.04612463340163231,
-0.010321049019694328,
-0.011586609296500683,
-0.014700251631438732,
-0.019718891009688377,
0.011699995957314968,
-0.011859401129186153,
-0.02787940204143524,
-0.016259171068668365,
0.014608875848352909,
0.018298251554369926,
0.011384700424969196,
0.009538012556731701,
0.04535054415464401,
-0.0030252651777118444,
0.02787070907652378,
0.02534662000834942,
0.03471852466464043,
-0.035462088882923126,
0.011643169447779655,
-0.02420785464346409,
0.029456298798322678,
-0.01952512376010418,
0.00005262247213977389,
0.01681482419371605,
0.005397527012974024,
0.008185360580682755,
-0.08261150866746902,
0.001940092770382762,
-0.03891151025891304,
0.024095049127936363,
0.0018254040041938424,
0.007862946949899197,
-0.005993118975311518,
0.03796246275305748,
0.03589041531085968,
0.017890004441142082,
-0.0363825298845768,
-0.0206424742937088,
0.012313557788729668,
-0.03027784265577793,
0.03822137042880058,
-0.03181583434343338,
-0.04344708472490311,
-0.021070463582873344,
-0.000055160180636448786,
-0.031081782653927803,
0.002236063126474619,
-0.0343281552195549,
0.028225118294358253,
0.027910316362977028,
0.01688378117978573,
-0.021610435098409653,
0.03247372433543205,
-0.045847099274396896,
-0.0018657901091501117,
-0.01733323745429516,
-0.0046134875155985355,
-0.03277111425995827,
0.005232516676187515,
0.06074666604399681,
0.04264991730451584,
-0.0075059132650494576,
-0.012512771412730217,
-0.0227567870169878,
0.00175786844920367,
-0.023342905566096306,
-0.022565258666872978,
0.01901692897081375,
0.013656609691679478,
-0.039064403623342514,
-0.0004206765443086624,
-0.010808260180056095,
-0.004324509296566248,
0.05098620057106018,
0.0068181524984538555,
0.008690038695931435,
0.04074671119451523,
-0.00999522302299738,
0.007497570477426052,
-0.023045044392347336,
-0.058797743171453476,
0.011737757362425327,
-0.005196176934987307,
0.023754773661494255,
-0.03994711488485336,
-0.007260165177285671,
-0.06117917224764824,
-0.0058263204991817474,
-0.024462612345814705,
0.008985275402665138,
-0.03241755813360214,
-0.02099766582250595,
-0.07114732265472412,
0.0073580071330070496,
-0.0881754606962204,
0.005078683607280254,
-0.02561100572347641,
0.03653120994567871,
-0.0022540781646966934,
-0.004011670593172312,
0.019091229885816574,
0.03330247849225998,
-0.020829565823078156,
-0.01846059411764145,
0.017861127853393555,
0.01839921995997429,
-0.04051966965198517,
0.023144876584410667,
0.02523459494113922,
0.00010769470100058243,
0.03145761787891388,
-0.011968659237027168,
-0.04178686439990997,
0.01817334070801735,
-0.07590628415346146,
-0.06940066814422607,
0.032008230686187744,
-0.020780406892299652,
0.022469311952590942,
0.010550482198596,
-0.034419603645801544,
-0.03428114950656891,
0.053560156375169754,
-0.040131352841854095,
-0.0007047126418910921,
0.02364238165318966,
-0.02013409696519375,
0.017809683457016945,
0.002602452877908945,
0.02159983292222023,
0.014481442980468273,
0.015194951556622982,
0.010931669734418392,
-0.011706935241818428,
-0.01408094260841608,
-0.0008874802151694894,
0.02347070537507534,
-0.06850191950798035,
0.02050304040312767,
-0.008021016605198383,
0.01656991057097912,
0.05816682428121567,
0.04898575693368912,
-0.036297548562288284,
0.006631255149841309,
0.047548480331897736,
0.04208696261048317,
-0.1001749038696289,
0.0022975176107138395,
0.0247033704072237,
0.05458051711320877,
0.0378350205719471,
-0.06289058178663254,
0.05829687416553497,
0.017995839938521385,
-0.058797143399715424,
0.0657983049750328,
-0.03813670575618744,
-0.019655674695968628,
-0.054876040667295456,
-0.005422650836408138,
-0.02483576536178589,
0.03680896759033203,
0.056283529847860336,
0.017638832330703735,
-0.009286765940487385,
0.012429041787981987,
-0.03006638027727604,
-0.012082399800419807,
-0.02159518003463745,
-0.010922144167125225,
0.0023503105621784925,
-0.034338340163230896,
0.05765915289521217,
0.018075795844197273,
-0.0320650190114975,
0.003432514378800988,
-0.004708652850240469,
0.013725030235946178,
0.01074827928096056,
0.011954051442444324,
0.02781863324344158,
0.01274267677217722,
0.026262478902935982,
-0.023341257125139236,
-0.012025902979075909,
-0.012822057120501995,
0.004643002524971962,
0.018621237948536873,
-0.0139425378292799,
0.01992471143603325,
0.010834714397788048,
-0.021440912038087845,
-0.03368781879544258,
0.038993142545223236,
-0.01795458234846592,
-0.043358754366636276,
-0.0593332014977932,
-0.05979336425662041,
0.004231948405504227,
0.0031207273714244366,
0.013533820398151875,
-0.05797160789370537,
-0.014238911680877209,
0.05635838955640793,
-0.013286937028169632,
0.010003688745200634,
0.027302531525492668,
-0.012308728881180286,
-0.018509086221456528,
0.02724967896938324,
0.0016626253491267562,
0.0008722377824597061,
-0.0325140506029129,
0.025804582983255386,
-0.0071859220042824745,
-0.00929020531475544,
-0.01248394139111042,
-0.06295298784971237,
0.0065744612365961075,
0.009625140577554703,
0.015590021386742592,
-0.0018936749547719955,
0.008335404098033905,
-0.024759378284215927,
-0.04687344282865524,
-0.06597945839166641,
0.011051708832383156,
0.027051476761698723,
-0.021695174276828766,
0.014045153744518757,
0.034993257373571396,
-0.01238503959029913,
0.022612689062952995,
0.05793040245771408,
-0.004836904816329479,
-0.02323000878095627,
0.013553181663155556,
0.01914672553539276,
0.0031451378017663956,
-0.04262033849954605,
-0.015446698293089867,
0.004297507926821709,
-0.02829359658062458,
-0.0081099271774292,
0.023859042674303055,
-0.0038681700825691223,
0.01191414799541235,
0.01601099781692028,
0.015161436051130295,
0.03599604591727257,
0.01183172408491373,
-0.026782559230923653,
0.03334815055131912,
0.032330822199583054,
-0.023291099816560745,
0.08455133438110352,
0.02048405632376671,
-0.0038701884914189577,
0.05341193079948425,
-0.009228038601577282,
-0.023589011281728745,
0.025699129328131676,
-0.011496023274958134,
-0.06486596912145615,
-0.007436175365000963,
0.00033323277602903545,
-0.00962062831968069,
-0.04587468132376671,
0.012063913978636265,
0.05537359043955803,
-0.05328774452209473,
-0.03579840064048767,
0.04183001071214676,
0.024257317185401917,
0.03652830794453621,
0.011125890538096428,
0.015771200880408287,
0.02324674464762211,
-0.0032068591099232435,
0.020894214510917664,
0.024411071091890335,
0.018453722819685936,
0.01803935132920742,
-0.03792225196957588,
0.0027952739037573338,
-0.003347002435475588,
0.009063279256224632,
-0.011468740180134773,
0.03545572608709335,
-0.033128928393125534,
-0.015223185531795025,
0.007774779573082924,
-0.021453484892845154,
0.00034899695310741663,
0.032639939337968826,
-0.0358688123524189,
0.054848551750183105,
-0.023704607039690018,
0.011464403010904789,
-0.04154735803604126,
0.0016001310432329774,
-0.04054282233119011,
0.0546751394867897,
0.009267146699130535,
0.03460019454360008,
0.00304856663569808,
0.021239137277007103,
0.009307502768933773,
-0.037513166666030884,
0.0045996676199138165,
-0.05274350568652153,
0.017490675672888756,
0.009635529480874538,
0.026817424222826958,
-0.008754434064030647,
-0.018135087564587593,
-0.027628498151898384,
0.01929198019206524,
0.014874937944114208,
0.051740728318691254,
0.02975543402135372,
-0.01196512021124363,
-0.024934889748692513,
0.0004697420517913997,
0.04889757186174393,
-0.07749778777360916,
-0.029183458536863327,
0.02025497518479824,
0.021266905590891838,
0.008131046779453754,
-0.02191312611103058
] |
<p>I am doing a (mostly qualitative) course on Particle Physics, and am confused about the concept of <a href="http://en.wikipedia.org/wiki/Asymptotic_freedom" rel="nofollow">asymptotic freedom</a>. The lecture notes basically say that a quark may experience no force/be "unbound" temporarily as a result of a collision. (due to properties of the strong force) Is there all there is to it?</p>
<p>Later, it mentioned that asymptotic freedom is important in electron-positron annihilation into hadrons. Were there no asymptotic freedom, the cross section of the process would be different. I can't see how this follows on from what was said above.</p>
<p>So I am seeking an qualitative explanation of this concept, and perhaps something about its consequences as well.</p> | 2,824 | [
0.016009485349059105,
-0.0012955727288499475,
0.02524387277662754,
-0.024453185498714447,
0.024045059457421303,
0.015177875757217407,
-0.03456931188702583,
-0.002679385244846344,
-0.014953913167119026,
-0.03183365240693092,
0.010182964615523815,
0.009323368780314922,
0.04663156345486641,
0.002821743255481124,
0.039551302790641785,
0.01920843869447708,
0.0019531946163624525,
-0.030711308121681213,
0.021845057606697083,
-0.024441540241241455,
-0.008942641317844391,
0.012803108431398869,
0.0012357848463580012,
0.0158847626298666,
-0.023193849250674248,
0.020640544593334198,
0.020009616389870644,
0.0156639963388443,
0.057436805218458176,
0.05677104741334915,
0.008574487641453743,
-0.02281787060201168,
-0.007129470352083445,
-0.002433196408674121,
0.04399646073579788,
0.021162953227758408,
-0.014631050638854504,
-0.026506764814257622,
-0.005405973177403212,
0.008965442888438702,
-0.044291961938142776,
-0.009234749712049961,
-0.02668818272650242,
0.06341081857681274,
-0.03534522280097008,
0.04699821025133133,
0.017737112939357758,
-0.005742619279772043,
0.0785815566778183,
-0.02826334536075592,
0.022067444398999214,
0.019168641418218613,
0.037976719439029694,
0.022289369255304337,
0.0008511972264386714,
-0.024536514654755592,
0.09267126023769379,
0.06503366678953171,
-0.03082321211695671,
-0.034256890416145325,
-0.029246609658002853,
-0.05732966214418411,
-0.006923094857484102,
-0.00913485512137413,
-0.02448146976530552,
0.042724475264549255,
-0.02696210891008377,
-0.019396066665649414,
0.01714608259499073,
-0.0019291471689939499,
0.018809974193572998,
0.03252297267317772,
0.02127230539917946,
0.011621843092143536,
0.006446377374231815,
-0.015840301290154457,
0.04191474989056587,
0.01299190428107977,
0.011658917181193829,
0.06218104809522629,
-0.01825103349983692,
0.028058430179953575,
0.018706578761339188,
0.01180456392467022,
0.023036623373627663,
-0.01733417436480522,
0.050658218562603,
-0.004665568936616182,
-0.011427957564592361,
0.058801762759685516,
-0.021092751994729042,
-0.005850789602845907,
0.01845506578683853,
-0.002724133664742112,
-0.03482862934470177,
0.023442406207323074,
0.016093824058771133,
0.0575316846370697,
0.04555855318903923,
-0.02619730494916439,
-0.0013488918775692582,
-0.029373183846473694,
-0.004317251965403557,
0.0384255051612854,
0.00442978972569108,
-0.016022395342588425,
-0.011348970234394073,
0.021199343726038933,
0.004678152035921812,
-0.015409489162266254,
-0.009537728503346443,
-0.007881837897002697,
-0.0010834778659045696,
-0.027298377826809883,
-0.005881038028746843,
-0.029474956914782524,
-0.014986541122198105,
0.024432580918073654,
0.06866831332445145,
0.08820292353630066,
0.07128942757844925,
-0.02729814127087593,
-0.008396117016673088,
-0.021475398913025856,
-0.02905949391424656,
0.0013353795511648059,
0.019750433042645454,
-0.006026498042047024,
-0.033076271414756775,
0.043093059211969376,
-0.02134099416434765,
-0.014684158377349377,
-0.002615066710859537,
-0.005215953569859266,
0.03679915517568588,
-0.04868963360786438,
-0.08857353776693344,
-0.04793965816497803,
0.055085569620132446,
-0.009732993319630623,
-0.03940927982330322,
-0.08593374490737915,
-0.0033815365750342607,
0.005487797781825066,
0.08107765763998032,
-0.014232151210308075,
-0.028745705261826515,
-0.021790901198983192,
0.021189674735069275,
0.009423228912055492,
-0.023539403453469276,
0.012559705413877964,
0.012420878745615482,
-0.025736255571246147,
0.004655526950955391,
-0.07900959998369217,
0.03138125315308571,
0.03286660090088844,
0.004764742683619261,
0.0032296949066221714,
0.07030931115150452,
-0.04381971061229706,
-0.015440443530678749,
-0.020701438188552856,
0.0024562699254602194,
-0.0061050886288285255,
0.08069495856761932,
0.00811087153851986,
-0.018475469201803207,
0.019342543557286263,
0.010762534104287624,
0.03793690353631973,
-0.009233152493834496,
0.02579820714890957,
0.025154052302241325,
-0.033626239746809006,
-0.016015874221920967,
-0.02760852500796318,
-0.02000129409134388,
-0.04858330264687538,
-0.02560422569513321,
-0.026810316368937492,
-0.04595787450671196,
0.012321840040385723,
-0.011383164674043655,
0.033567171543836594,
-0.02534610964357853,
0.003540631616488099,
-0.002853332320228219,
-0.03695681318640709,
-0.05815541371703148,
-0.09882210195064545,
0.028159990906715393,
-0.019843989983201027,
-0.031533610075712204,
0.02597573585808277,
0.00994960218667984,
0.015966257080435753,
-0.021529776975512505,
-0.050502028316259384,
-0.005767069756984711,
0.010108983144164085,
-0.010012688115239143,
-0.020314982160925865,
0.03077057935297489,
0.050983354449272156,
0.03642923757433891,
0.016014156863093376,
0.0372852087020874,
-0.009355315938591957,
-0.036260273307561874,
0.008432511240243912,
-0.02037421427667141,
0.00199693301692605,
0.012307674624025822,
0.014326649717986584,
0.00001745315057632979,
-0.03686613589525223,
0.005804324056953192,
0.022193733602762222,
0.012832248583436012,
0.10118171572685242,
0.02822979725897312,
0.005823591724038124,
-0.02832515724003315,
0.052031710743904114,
0.017405154183506966,
-0.006725229788571596,
-0.04266500845551491,
-0.023921795189380646,
-0.02002176083624363,
0.009316998533904552,
0.01944900117814541,
0.050494227558374405,
-0.016614163294434547,
0.00946437194943428,
-0.011532921344041824,
-0.003738072933629155,
0.045271649956703186,
0.03154652565717697,
-0.04206111654639244,
-0.07048270106315613,
-0.000060516638768604025,
0.03219233453273773,
-0.03230888769030571,
-0.013551689684391022,
0.023832326754927635,
-0.010478653945028782,
0.016835926100611687,
0.021733678877353668,
-0.03806660696864128,
0.03589317575097084,
-0.021901488304138184,
-0.014880014583468437,
-0.015259435400366783,
-0.04557531327009201,
0.01741201803088188,
-0.04360382631421089,
0.053190428763628006,
0.002650274196639657,
-0.038684990257024765,
0.03271034359931946,
-0.03855815529823303,
0.005274681374430656,
0.010585831478238106,
-0.034761860966682434,
-0.006338073406368494,
-0.0044839889742434025,
0.024853508919477463,
-0.036921802908182144,
-0.01289459690451622,
-0.011785865761339664,
-0.059081777930259705,
0.003274640766903758,
-0.00985855795443058,
0.05276837944984436,
0.012677574530243874,
0.029998553916811943,
-0.037892360240221024,
-0.033560607582330704,
0.008429969660937786,
-0.035678740590810776,
0.00014399077917914838,
0.023731878027319908,
-0.003867464605718851,
0.029164766892790794,
-0.06540556997060776,
-0.020183265209197998,
0.048683036118745804,
-0.04713898524641991,
0.034544892609119415,
0.04238219931721687,
-0.01963723637163639,
-0.04231666401028633,
0.007147094700485468,
-0.023638151586055756,
0.0034013523254543543,
-0.02492655999958515,
0.02902604639530182,
0.0504300594329834,
-0.019253358244895935,
-0.0177997387945652,
-0.0021887156181037426,
-0.08399328589439392,
-0.02939726412296295,
-0.0005633476539514959,
0.017474621534347534,
0.053544990718364716,
-0.01225068885833025,
0.032875992357730865,
0.04041143134236336,
-0.06046421080827713,
-0.004601655062288046,
-0.012792712077498436,
-0.021348224952816963,
0.019720949232578278,
-0.0004286111507099122,
0.02457408420741558,
-0.002198802074417472,
-0.06048709526658058,
0.08335606008768082,
0.02924486994743347,
-0.039089322090148926,
-0.024024683982133865,
-0.01092485524713993,
-0.020270243287086487,
-0.009760599583387375,
0.031641025096178055,
0.01166337076574564,
-0.03189889341592789,
-0.0031488302629441023,
0.002839508466422558,
0.056488264352083206,
-0.0012375105870887637,
-0.006344896275550127,
0.00046925523201934993,
-0.011750433593988419,
0.010579783469438553,
-0.01092708669602871,
0.012136477045714855,
0.016574785113334656,
-0.035658061504364014,
-0.00950998067855835,
0.002847151132300496,
0.061860840767621994,
0.0005718969623558223,
-0.04187477007508278,
0.08779440820217133,
0.0428769513964653,
-0.014147438108921051,
-0.015417682006955147,
0.03950764611363411,
-0.061378881335258484,
-0.018843526020646095,
0.035394761711359024,
0.00586792454123497,
0.008188232779502869,
-0.032609108835458755,
0.013300186954438686,
0.01667456328868866,
0.045143626630306244,
-0.05945645272731781,
-0.03163650259375572,
-0.025520408526062965,
-0.018766840919852257,
0.019543062895536423,
0.041268303990364075,
-0.028211822733283043,
0.031384289264678955,
0.033080607652664185,
0.02596319280564785,
0.0050878520123660564,
-0.05496359243988991,
-0.003085074480623007,
-0.037447065114974976,
0.0036870837211608887,
0.017374316230416298,
0.0550890751183033,
0.027007145807147026,
0.07244230806827545,
-0.00877700001001358,
0.020093748345971107,
-0.009963948279619217,
0.0036776980850845575,
-0.10391268134117126,
0.03804099187254906,
-0.04071050509810448,
-0.03549579903483391,
-0.02192380093038082,
0.0017974033253267407,
0.01598248817026615,
-0.012113139033317566,
-0.03683555871248245,
-0.024836190044879913,
0.026565074920654297,
-0.03458281606435776,
0.006214651744812727,
-0.04313015192747116,
-0.016730790957808495,
-0.03668671101331711,
0.024799447506666183,
0.0405915267765522,
-0.04346545785665512,
0.019734151661396027,
0.0373091846704483,
-0.0574529655277729,
-0.01873685047030449,
-0.015113071538507938,
-0.022594120353460312,
0.01338438130915165,
0.021048953756690025,
0.04529714211821556,
0.02659318409860134,
-0.03509409353137016,
0.012032190337777138,
0.04946761578321457,
0.06186791509389877,
-0.011688563972711563,
0.012362472712993622,
-0.002012028358876705,
-0.05758770555257797,
-0.038696058094501495,
-0.004396506119519472,
0.029445955529808998,
-0.017699062824249268,
0.01416756585240364,
0.04114261642098427,
0.023733465000987053,
-0.03912140801548958,
0.048071615397930145,
0.05755244195461273,
0.025509055703878403,
0.012971300631761551,
-0.04459775239229202,
0.03171173483133316,
-0.004106058739125729,
-0.006577466148883104,
-0.010187983512878418,
-0.020223623141646385,
-0.009784824214875698,
0.009533396922051907,
0.009066978469491005,
0.031165150925517082,
-0.06058615446090698,
0.01332708727568388,
-0.017405463382601738,
-0.02022583596408367,
0.005717084743082523,
-0.011805699206888676,
0.0334547683596611,
0.03411293402314186,
0.030087942257523537,
0.02453368529677391,
0.02459140121936798,
-0.03407367691397667,
-0.004426812753081322,
0.04103202372789383,
0.06962943822145462,
-0.0027844796422868967,
0.0031711221672594547,
-0.05003597214818001,
0.00448313495144248,
0.05727500841021538,
-0.009821549989283085,
0.027175620198249817,
-0.006092009134590626,
-0.004281159490346909,
0.006214775610715151,
-0.04591257870197296,
-0.038117870688438416,
0.005134015344083309,
-0.028415247797966003,
-0.014496578834950924,
-0.035238876938819885,
-0.01867649517953396,
0.0030679344199597836,
-0.005284574348479509,
-0.013360283337533474,
0.06058427691459656,
-0.00677526043727994,
0.020935481414198875,
-0.0067572444677352905,
0.005372233688831329,
0.006389142479747534,
-0.10600147396326065,
0.0019936379976570606,
-0.010761106386780739,
-0.005781844723969698,
0.07432671636343002,
-0.05317312479019165,
-0.06502221524715424,
-0.017413020133972168,
0.0018536971183493733,
-0.03268665075302124,
-0.023800931870937347,
-0.04000033065676689,
0.03519560024142265,
0.01391830574721098,
-0.01141768041998148,
0.029502859339118004,
0.03922375664114952,
-0.005884382873773575,
-0.006080355029553175,
-0.014435787685215473,
0.07143527269363403,
-0.03283005952835083,
0.012712562456727028,
-0.06121582165360451,
-0.019225649535655975,
-0.027575254440307617,
0.041953280568122864,
-0.0005443393019959331,
-0.007189554627984762,
-0.01282417494803667,
-0.053583063185214996,
-0.00836881808936596,
0.0281684510409832,
0.002183422213420272,
-0.006426852196455002,
-0.008388031274080276,
0.004221298731863499,
-0.035456132143735886,
-0.02624833956360817,
0.0049043865874409676,
0.01906917802989483,
0.014920488931238651,
0.020154306665062904,
-0.02618277817964554,
-0.007120889145880938,
-0.0019306716276332736,
-0.0625205934047699,
0.02305317297577858,
-0.03081129863858223,
0.024727461859583855,
-0.028324972838163376,
0.005679461173713207,
0.023334626108407974,
-0.08524062484502792,
-0.05580286309123039,
0.014339200221002102,
-0.023627890273928642,
0.024434298276901245,
-0.03443946689367294,
0.04399442672729492,
-0.0006504363846033812,
0.017129983752965927,
-0.0878015086054802,
-0.03582373633980751,
0.01601293310523033,
0.01061468105763197,
-0.03929365426301956,
0.01241654809564352,
-0.04074682667851448,
-0.03643720969557762,
-0.032689034938812256,
0.005832776427268982,
0.04074757173657417,
0.0007805709028616548,
-0.01229989342391491,
0.01712931878864765,
0.0030343839898705482,
-0.0019901578780263662,
0.006465359125286341,
-0.005956163164228201,
-0.007193947210907936,
-0.0074579245410859585,
0.019553693011403084,
0.01698944717645645,
0.05405016243457794,
0.0066480254754424095,
-0.05292370542883873,
-0.0046251071617007256,
-0.005090863909572363,
0.0008522894931957126,
-0.02458902820944786,
0.003874752903357148,
0.023263603448867798,
0.022447990253567696,
0.020739799365401268,
-0.003410883015021682,
0.013995502144098282,
0.01053015235811472,
0.044778645038604736,
0.03249466419219971,
-0.020154008641839027,
-0.006051013711839914,
-0.06517498940229416,
0.023577984422445297,
0.0035657393746078014,
0.04501216113567352,
0.014600440859794617,
0.002702586352825165,
-0.014836815185844898,
-0.018076056614518166,
-0.006946733687072992,
-0.00012870221689809114,
0.03193667158484459,
-0.0037837917916476727,
0.012569146230816841,
0.009732114151120186,
-0.021563200280070305,
-0.009891880676150322,
-0.04193549230694771,
-0.03070329874753952,
0.04045768454670906,
0.05547155439853668,
-0.053891491144895554,
0.05267353728413582,
0.02607819065451622,
0.019363030791282654,
-0.01793007366359234,
-0.002238618675619364,
-0.01808101497590542,
-0.016072388738393784,
0.012882011942565441,
0.03921035677194595,
-0.036088697612285614,
-0.014297539368271828,
0.01919272541999817,
0.04930410161614418,
-0.0358571819961071,
0.010759122669696808,
0.04352961480617523,
0.0295901820063591,
0.02956429310142994,
0.023996641859412193,
-0.031166112050414085,
0.006098087411373854,
-0.017291489988565445,
0.022911312058568,
0.009041390381753445,
-0.033102720975875854,
0.012877058237791061,
-0.00015568765229545534,
0.04179079458117485,
-0.007113644853234291,
-0.018304722383618355,
-0.05247630923986435,
0.04796114191412926,
0.030372988432645798,
0.02296885848045349,
0.005804229062050581,
0.008620478212833405,
0.030606510117650032,
0.011149472557008266,
0.006068581715226173,
0.019121810793876648,
-0.061579979956150055,
-0.04657397419214249,
-0.043893225491046906,
-0.003070360515266657,
0.020369043573737144,
-0.03833340108394623,
-0.023511458188295364,
0.002981174737215042,
-0.007847950793802738,
0.001082690549083054,
0.02538531832396984,
0.029410824179649353,
-0.011541338637471199,
0.05490080639719963,
-0.004123648628592491,
0.021970273926854134,
-0.0393768735229969,
0.047346241772174835,
0.10678549855947495,
0.051051415503025055,
0.015266607515513897,
-0.024287549778819084,
-0.0021987638901919127,
-0.00995143037289381,
0.01382429338991642,
-0.029456624761223793,
0.03224355727434158,
0.034504279494285583,
-0.004222270101308823,
0.03397367149591446,
0.05255075916647911,
0.02280692756175995,
-0.008788828738033772,
0.061823710799217224,
-0.058624498546123505,
-0.03465462848544121,
-0.00668466417118907,
0.007235480472445488,
-0.026879582554101944,
0.012448525056242943,
-0.04061643406748772,
0.03052898310124874,
0.024505924433469772,
0.0004451113345567137,
-0.01323805470019579,
-0.004766686819493771,
-0.0017573527293279767,
-0.001805245061405003,
-0.017265427857637405,
0.013188718818128109,
0.0003517149016261101,
0.015227345749735832,
-0.03798506036400795,
0.027110032737255096,
0.02888251468539238,
-0.057540230453014374,
0.009110674262046814,
0.03795480355620384,
0.02247547172009945,
-0.024916060268878937,
0.00517802219837904,
0.02005665935575962,
-0.03422169387340546,
-0.03987724706530571,
0.02087327465415001,
0.06516513973474503,
-0.012878342531621456,
0.017590545117855072,
0.011024437844753265,
0.02575886994600296,
0.027569549158215523,
-0.006631472613662481,
0.008286491967737675,
-0.021015658974647522,
-0.006489843130111694,
-0.015123957768082619,
0.0009310552850365639,
-0.01888912171125412,
0.01035290490835905,
-0.015883339568972588,
0.0008679449674673378,
-0.00694485055282712,
0.019670242443680763,
0.0031836198177188635,
0.013670491054654121,
0.006384697277098894,
-0.007602845784276724,
-0.02800591103732586,
-0.0026335986331105232,
0.024780962616205215,
-0.04847123846411705,
-0.010351709090173244,
0.037679463624954224,
0.016103269532322884,
0.04879583790898323,
0.009226162917912006,
-0.011971422471106052,
-0.02498355507850647,
-0.05557158961892128,
0.06857720017433167,
-0.020715788006782532,
-0.034359630197286606,
0.004716896917670965,
-0.0049204411916434765,
0.0077175600454211235,
0.04082723334431648,
-0.01953253336250782,
-0.023655615746974945,
-0.009701184928417206,
0.022946882992982864,
-0.011459742672741413,
-0.019383301958441734,
0.011361864395439625,
0.01742258109152317,
-0.029845666140317917,
-0.010474460199475288,
0.0011840204242616892,
0.03130068629980087,
0.045296959578990936,
0.008960383012890816,
-0.007836162112653255,
0.0072571574710309505,
0.0008357311598956585,
0.013394176959991455,
0.055500056594610214,
-0.00799492560327053,
0.015981381759047508,
0.03442855924367905,
0.019902706146240234,
-0.027758240699768066,
-0.005548511631786823,
-0.020653150975704193,
-0.0013497404288500547,
-0.020671991631388664,
0.02628081478178501,
-0.012139622122049332,
0.03726356849074364,
0.0020621302537620068,
0.03761743754148483,
0.005677690729498863,
0.00931592844426632,
-0.05386059358716011,
-0.005719843786209822,
-0.009402040392160416,
-0.021301519125699997,
0.00810896698385477,
0.027484241873025894,
0.015361662022769451,
-0.05062176287174225,
-0.000387220352422446,
0.03657245263457298,
-0.037863247096538544,
-0.028965432196855545,
0.021923914551734924,
-0.01265737321227789,
0.05413719639182091,
0.005281722638756037,
-0.004849504213780165,
0.039591170847415924,
-0.06712053716182709,
-0.07518148422241211,
0.013950717635452747,
-0.02257572114467621,
0.03496215492486954,
0.03799596056342125,
-0.0036034437362104654,
-0.03871448338031769,
0.06250081211328506,
0.006833289284259081,
0.0025287603493779898,
-0.01009172573685646,
-0.05336056649684906,
-0.013851459138095379,
-0.014597387984395027,
0.001541154459118843,
-0.0022364400792866945,
-0.01084253191947937,
0.03110714629292488,
0.06498605012893677,
0.007858694531023502,
-0.0005356665351428092,
-0.00774085009470582,
0.027644885703921318,
0.008959328755736351,
0.007363276090472937,
0.009372823871672153,
-0.005171329714357853,
0.062160614877939224,
-0.009307486936450005,
0.01194479875266552,
-0.0285822544246912,
0.03383843973278999,
-0.11957486718893051,
-0.040047284215688705,
-0.026243500411510468,
0.0015876030083745718,
0.04745269566774368,
-0.06972403824329376,
0.007353396620601416,
0.040115613490343094,
-0.06593597680330276,
-0.007338179275393486,
-0.03581253066658974,
-0.02592840977013111,
-0.01508610974997282,
-0.01743542030453682,
-0.011382590979337692,
0.07710564881563187,
0.017136527225375175,
0.03505895659327507,
0.017277108505368233,
0.02488434500992298,
-0.007936332374811172,
-0.014676342718303204,
-0.06252780556678772,
0.01074138842523098,
-0.016124309971928596,
-0.01326291635632515,
0.07414858788251877,
-0.017955578863620758,
-0.014100190252065659,
0.06591309607028961,
-0.02579207345843315,
-0.022781290113925934,
-0.015446298755705357,
0.011510063894093037,
0.006794121116399765,
-0.006181843113154173,
-0.0028222983237355947,
-0.0058588325046002865,
0.0193216223269701,
0.010600464418530464,
0.011053789407014847,
0.0031299288384616375,
0.013981033116579056,
0.018979186192154884,
0.02624078467488289,
-0.018533118069171906,
-0.05915198102593422,
0.031735051423311234,
-0.0011436330387368798,
0.00010260356066282839,
0.016809556633234024,
-0.005973475985229015,
-0.007433334365487099,
-0.008513597771525383,
0.016352809965610504,
-0.038282617926597595,
-0.0295391958206892,
0.014626812189817429,
0.029128750786185265,
-0.0012937724823132157,
0.035457443445920944,
-0.022081734612584114,
0.00736828101798892,
0.013197566382586956,
0.006183671299368143,
-0.008046437054872513,
-0.006242008414119482,
-0.029434993863105774,
-0.004371109418570995,
0.009044053964316845,
0.00928215216845274,
-0.02363009750843048,
-0.03484584391117096,
0.013555670157074928,
-0.0014846747508272529,
0.03863897919654846,
-0.041427627205848694,
-0.015706954523921013,
-0.010710225440561771,
-0.057141777127981186,
0.03554856777191162,
-0.016013557091355324,
0.041995394974946976,
-0.054141074419021606,
-0.0171089805662632,
0.022690484300255775,
0.010272358544170856,
0.04188057780265808,
0.005770096555352211,
0.004345150664448738,
0.021607540547847748,
0.006602656561881304,
-0.021682117134332657,
-0.005415146704763174,
-0.03386304900050163,
-0.01480928622186184,
0.02104966528713703,
-0.02444649301469326,
-0.03179854899644852,
-0.0069150300696492195,
0.030971014872193336,
0.014287116937339306,
-0.001436204998753965,
0.01809660904109478,
0.007186840288341045,
-0.0635424554347992,
0.05557797849178314,
0.011034875176846981,
0.018628275021910667,
0.06305813044309616,
0.000842174980789423,
0.014305171556770802,
0.02228594198822975,
-0.04802398011088371,
-0.02773427590727806,
0.015626035630702972,
-0.036158837378025055,
-0.012682792730629444,
-0.010311828926205635,
-0.016839422285556793,
0.004820098634809256,
-0.03411714360117912,
0.00982089713215828,
0.03451633080840111,
-0.05903034284710884,
-0.025552434846758842,
0.04049069434404373,
0.045165035873651505,
0.051129139959812164,
-0.01030393224209547,
-0.04126952961087227,
-0.004000084474682808,
-0.003977682441473007,
0.00767924590036273,
0.0410262756049633,
0.019409649074077606,
0.03846871480345726,
0.02274477481842041,
-0.002404486760497093,
0.0014665877679362893,
-0.0002507733879610896,
0.032707296311855316,
0.03618437051773071,
-0.021811751648783684,
-0.019133081659674644,
0.019156843423843384,
-0.002834898419678211,
0.02511836774647236,
0.022954195737838745,
-0.03207742050290108,
0.06158432364463806,
-0.021214788779616356,
0.0421387180685997,
0.01340643409639597,
0.02013249136507511,
-0.02849632501602173,
0.026763860136270523,
0.018000656738877296,
0.07027511298656464,
-0.04161425679922104,
-0.01894170604646206,
-0.0013646922307088971,
-0.004692088346928358,
0.03029738925397396,
-0.0015540745807811618,
0.01899697445333004,
0.021375365555286407,
-0.0053864470683038235,
-0.051349710673093796,
-0.006566531024873257,
0.0034273460041731596,
-0.019148992374539375,
0.018077965825796127,
0.03745618090033531,
0.006672809831798077,
0.0004227302852086723,
-0.011014502495527267,
-0.022351089864969254,
0.04701129347085953,
-0.0573413223028183,
0.01920185051858425,
-0.029094068333506584,
0.02340056002140045,
-0.0696871355175972,
0.03069782629609108
] |
<p>I'm trying to find the potential energy of multiple geometric shapes made entirely out of point charges.
This particular shape is a cube made out of two different point charges, A and B, each separated by a constant distance.</p>
<p>I'm not entirely sure how to go about this problem but I'm pretty sure that the equations V=Ed and E=kQ/r^2. I'm pretty sure you just add up the charges but I have no idea how to do this in a cube form..</p> | 2,825 | [
-0.02989177219569683,
0.018615055829286575,
0.002822550944983959,
-0.028318220749497414,
0.008455251343548298,
0.004840027075260878,
-0.01335888635367155,
-0.025108840316534042,
0.017113832756876945,
-0.03589046001434326,
0.04051096364855766,
0.020146507769823074,
0.054083481431007385,
0.035204511135816574,
-0.017204511910676956,
-0.020812256261706352,
0.025679273530840874,
-0.008885383605957031,
0.02285023219883442,
-0.06466910988092422,
0.007180286105722189,
0.003630607156082988,
0.018956119194626808,
0.0033796923235058784,
-0.002717353869229555,
0.0764133632183075,
0.06228566914796829,
-0.06730402261018753,
0.010713313706219196,
0.08909618109464645,
-0.0358797125518322,
-0.05660172179341316,
0.027368120849132538,
0.019107922911643982,
0.01921948231756687,
-0.006576955318450928,
-0.027481168508529663,
-0.029222438111901283,
-0.0309810359030962,
0.028446950018405914,
-0.0038403933867812157,
-0.02050228789448738,
-0.008253775537014008,
0.04632670804858208,
-0.0037739991676062346,
-0.0063401092775166035,
0.0009396979585289955,
-0.027767593041062355,
0.04072900116443634,
-0.06270912289619446,
0.09026139974594116,
0.01886737160384655,
0.046404629945755005,
0.04701535776257515,
-0.026951778680086136,
0.003071579849347472,
0.05008948966860771,
0.07591040432453156,
0.012793176807463169,
-0.06237737834453583,
-0.0054495022632181644,
0.008860254660248756,
-0.00810278207063675,
-0.03878365829586983,
-0.021746337413787842,
0.014942392706871033,
-0.024702128022909164,
0.005517041776329279,
0.026651786640286446,
-0.036794669926166534,
0.036414746195077896,
0.04822613671422005,
0.01656503602862358,
-0.057237569242715836,
-0.0012185509549453855,
0.0011021398240700364,
0.007136859931051731,
0.015483170747756958,
0.05194227769970894,
0.014303237199783325,
-0.0429760105907917,
0.004218159709125757,
0.049678247421979904,
0.05649413540959358,
-0.0009964426280930638,
-0.009430011734366417,
0.0435878150165081,
-0.023036330938339233,
-0.02086509019136429,
-0.0032729478552937508,
0.003260519355535507,
-0.0038356201257556677,
0.0740177109837532,
0.0015139301540330052,
-0.03284473717212677,
0.023195065557956696,
0.002543531358242035,
0.07975096255540848,
0.0005457224324345589,
-0.031214173883199692,
0.028525030240416527,
-0.024959152564406395,
-0.004312257282435894,
0.06825278699398041,
0.0025428603403270245,
-0.0023814465384930372,
-0.02319297380745411,
0.027059173211455345,
0.023015527054667473,
-0.008182183839380741,
0.0012420864077284932,
0.03422282263636589,
-0.017356378957629204,
-0.021805807948112488,
-0.017085615545511246,
-0.028028463944792747,
-0.011990313418209553,
-0.021587980911135674,
0.013574290089309216,
-0.002421160228550434,
0.013520878739655018,
-0.048021264374256134,
0.02516593411564827,
-0.04034509137272835,
-0.08767712116241455,
-0.017895366996526718,
0.023751698434352875,
0.0038001155480742455,
-0.04574017599225044,
0.027225712314248085,
0.011911445297300816,
-0.034707147628068924,
-0.01386173814535141,
-0.015455284155905247,
0.03101425990462303,
-0.009742663241922855,
-0.0713331401348114,
-0.05961150303483009,
0.011620558798313141,
0.0050545562990009785,
-0.018395710736513138,
-0.052458520978689194,
-0.039105143398046494,
0.02441088669002056,
0.06229536980390549,
-0.0061171515844762325,
-0.021982558071613312,
0.015123178251087666,
0.04143268242478371,
0.017427226528525352,
-0.017877064645290375,
-0.03508390858769417,
-0.01784239523112774,
-0.021970009431242943,
0.03736655414104462,
-0.06056749448180199,
-0.012640257366001606,
0.0019923739600926638,
-0.013002302497625351,
0.016763826832175255,
0.02922181971371174,
0.010485374368727207,
-0.02716991864144802,
0.019334876909852028,
-0.0012599385809153318,
-0.008792945183813572,
0.07283515483140945,
0.008187801577150822,
0.004265576601028442,
0.03672993183135986,
-0.010416940785944462,
0.0243260208517313,
0.04171452298760414,
0.03172826021909714,
0.07033179700374603,
-0.014250857755541801,
0.01864537037909031,
-0.036001965403556824,
0.045145370066165924,
0.013827558606863022,
-0.07136203348636627,
-0.06629499793052673,
0.017901021987199783,
-0.008397811092436314,
0.015683773905038834,
0.03968405723571777,
-0.020875396206974983,
-0.04514972120523453,
-0.03582284599542618,
-0.006359861232340336,
-0.017837634310126305,
-0.0877191498875618,
0.052513692528009415,
0.011540473438799381,
-0.009725868701934814,
-0.005351074039936066,
0.01978013478219509,
0.01809152401983738,
-0.031311191618442535,
-0.035981204360723495,
-0.01149993110448122,
0.048099175095558167,
0.0010988053400069475,
-0.025658585131168365,
0.005402177106589079,
0.01919274963438511,
0.08080751448869705,
-0.0085805868729949,
0.035563644021749496,
0.006776341702789068,
0.03044804558157921,
-0.008687002584338188,
-0.03934183344244957,
0.010998656041920185,
-0.0029995450749993324,
-0.009793811477720737,
-0.019537726417183876,
0.030073750764131546,
0.0005166555638425052,
0.05333869531750679,
-0.019866645336151123,
0.06289482861757278,
0.04546308144927025,
0.026926914229989052,
-0.0118466941639781,
0.054703276604413986,
0.025807002559304237,
0.05636347457766533,
0.013363813981413841,
-0.044553328305482864,
-0.04219239950180054,
0.008004212751984596,
0.03827730566263199,
0.01369319949299097,
-0.06849010288715363,
0.016034219413995743,
0.03489474579691887,
0.03272673860192299,
0.0017432644963264465,
0.025023190304636955,
-0.01859135739505291,
0.023517154157161713,
0.015677867457270622,
0.02040151320397854,
0.009207070805132389,
0.009012715891003609,
0.034363195300102234,
0.030138565227389336,
-0.0031781212892383337,
-0.0550130270421505,
-0.014243783429265022,
0.026025332510471344,
-0.010410037823021412,
0.028932997956871986,
0.015547189861536026,
-0.03100728429853916,
0.05348650738596916,
-0.02275916188955307,
0.04205456003546715,
0.02109629102051258,
0.008844302967190742,
-0.016597097739577293,
-0.03957872837781906,
-0.007510351482778788,
0.010288662277162075,
0.025167247280478477,
0.008331257849931717,
-0.0059105027467012405,
0.016485940665006638,
0.003305288963019848,
0.005147974938154221,
0.006239744368940592,
-0.03717916086316109,
-0.014149482361972332,
0.003377361688762903,
0.008987030014395714,
-0.0011617712443694472,
0.022826531901955605,
-0.041278041899204254,
-0.03246455267071724,
-0.0063560898415744305,
-0.02174312248826027,
0.01101215835660696,
-0.0020392993465065956,
-0.05938443914055824,
-0.0014830859145149589,
-0.0449402891099453,
0.002152948873117566,
0.042733028531074524,
-0.013729368336498737,
-0.034965451806783676,
0.0843290388584137,
0.011686383746564388,
-0.012031729333102703,
0.005752601660788059,
0.008306736126542091,
0.04911206290125847,
-0.051462750881910324,
0.00804340559989214,
0.01979760266840458,
0.023597922176122665,
-0.040164604783058167,
0.04725339636206627,
-0.018248599022626877,
-0.015406766906380653,
-0.016308216378092766,
-0.012052142061293125,
0.0030174902640283108,
-0.026905471459031105,
0.02406187914311886,
0.014539448544383049,
-0.03270046412944794,
0.008609174750745296,
-0.06993904709815979,
-0.04214537516236305,
0.007160784211009741,
0.00009169572149403393,
0.04412081465125084,
-0.030201202258467674,
-0.04531335458159447,
0.07247930765151978,
-0.019476452842354774,
-0.03420737013220787,
-0.0011853910982608795,
-0.018900854513049126,
-0.003144076094031334,
0.020787812769412994,
0.032954514026641846,
0.010537548922002316,
-0.04420040175318718,
-0.04345833882689476,
-0.011024203151464462,
0.03846117481589317,
0.04076804965734482,
-0.0323496088385582,
-0.01705038547515869,
0.014946351759135723,
0.03600069880485535,
-0.01567409746348858,
0.041545722633600235,
0.014768862165510654,
-0.042793579399585724,
0.0005877532530575991,
0.011441300623118877,
0.0134386345744133,
0.04128589481115341,
-0.034828197211027145,
0.017424389719963074,
-0.036213360726833344,
0.013518020510673523,
-0.026210054755210876,
0.019891079515218735,
0.02241450548171997,
-0.045857422053813934,
-0.0005467218579724431,
0.026741234585642815,
0.05758708715438843,
-0.02516111545264721,
-0.03188120573759079,
0.016831308603286743,
0.07203297317028046,
-0.03189396113157272,
-0.06435077637434006,
0.00593401025980711,
0.022834431380033493,
0.021571528166532516,
0.022887179628014565,
-0.03154262155294418,
0.03761754930019379,
0.02256971411406994,
0.03929620981216431,
0.019319817423820496,
-0.02196795865893364,
-0.000008946932211983949,
-0.09425874799489975,
0.007616665214300156,
0.0067421854473650455,
0.06214481219649315,
-0.007368133403360844,
0.05815917253494263,
-0.00005996114123263396,
-0.01634405553340912,
0.02279246225953102,
0.022816743701696396,
-0.05262221023440361,
0.02439439855515957,
-0.038300156593322754,
0.005181267391890287,
-0.0024255116004496813,
-0.01416787225753069,
-0.023532617837190628,
-0.042840976268053055,
-0.038210608065128326,
0.012961048632860184,
-0.015126264654099941,
-0.04497957602143288,
0.02359243482351303,
-0.04835564270615578,
-0.015483305789530277,
-0.0015985640930011868,
0.037966806441545486,
0.016085276380181313,
-0.06456775963306427,
0.011742028407752514,
0.043394118547439575,
-0.03548313304781914,
-0.00035216103424318135,
0.011393166147172451,
-0.007297901902347803,
0.01132426131516695,
0.03409084305167198,
-0.03719884902238846,
0.01842327229678631,
0.026959512382745743,
-0.01874438114464283,
-0.01633945293724537,
0.06948255002498627,
-0.004986873362213373,
-0.0379684679210186,
-0.019757768139243126,
-0.04823419824242592,
-0.012995567172765732,
-0.036994896829128265,
0.042908817529678345,
-0.03088298998773098,
0.04372146353125572,
-0.006237013265490532,
0.03695635497570038,
-0.023964133113622665,
0.03670946881175041,
0.0894789844751358,
0.012661718763411045,
-0.07922617346048355,
-0.03725172579288483,
-0.011151558719575405,
-0.02383040077984333,
-0.0016644668066874146,
0.01253849733620882,
-0.03234722837805748,
-0.03157999739050865,
-0.005377005320042372,
0.01913406513631344,
-0.01175149716436863,
-0.022730667144060135,
-0.023114502429962158,
0.011474509723484516,
0.0008551611099392176,
-0.05815798044204712,
-0.008476403541862965,
0.026590460911393166,
0.007987807504832745,
0.04287056252360344,
-0.0056463670916855335,
-0.003077275352552533,
-0.07302581518888474,
-0.00025501506752334535,
0.0671430304646492,
0.022798970341682434,
0.010488352738320827,
0.005498545244336128,
-0.061390962451696396,
0.015022492967545986,
0.06103599816560745,
-0.024397872388362885,
-0.0105671351775527,
0.01676040329039097,
0.010504907928407192,
-0.011203397996723652,
0.0018803654238581657,
-0.030072974041104317,
0.0031386520713567734,
-0.016177602112293243,
0.03967534750699997,
-0.011062603443861008,
0.022292641922831535,
0.049476198852062225,
0.05992152541875839,
0.07642140239477158,
0.08549679070711136,
0.016344141215085983,
-0.015136797912418842,
0.019171997904777527,
-0.012240654788911343,
-0.031016841530799866,
-0.06636802852153778,
0.022441759705543518,
-0.029999809339642525,
-0.025443745777010918,
0.05651506781578064,
-0.024962356314063072,
-0.03305942192673683,
0.043377842754125595,
-0.03172525763511658,
0.013221106491982937,
-0.01980835199356079,
-0.041015900671482086,
0.04031629487872124,
0.06362216174602509,
-0.0027527878992259502,
0.024816231802105904,
0.026150573045015335,
-0.06537065654993057,
0.002768487436696887,
-0.043510839343070984,
0.02283308282494545,
0.029881006106734276,
-0.009993267245590687,
-0.020501738414168358,
0.008294160477817059,
-0.024042759090662003,
-0.020552197471261024,
-0.0472119115293026,
0.007701305206865072,
-0.035955220460891724,
-0.005528272595256567,
-0.010615007020533085,
0.024127885699272156,
0.010163683444261551,
0.028077198192477226,
0.029865248128771782,
0.024911431595683098,
0.0512864887714386,
-0.03997665271162987,
-0.0023010317236185074,
-0.009294191375374794,
-0.0020398551132529974,
0.007456100545823574,
-0.028778716921806335,
-0.011726051568984985,
-0.010320845991373062,
-0.010738197714090347,
0.01149690244346857,
-0.041416898369789124,
0.06932839751243591,
-0.03456611558794975,
0.005116560030728579,
0.025475740432739258,
-0.06972021609544754,
-0.02211485058069229,
0.0018171700648963451,
0.01455602701753378,
0.04538332670927048,
-0.01840154267847538,
0.0699353739619255,
-0.023191215470433235,
0.015144218690693378,
-0.0701647400856018,
-0.013406369835138321,
0.029435716569423676,
0.025693543255329132,
-0.012719416990876198,
-0.03989197313785553,
0.004347673617303371,
-0.011576264165341854,
0.005869654007256031,
0.0011714998399838805,
0.039289772510528564,
-0.035163480788469315,
-0.012025435455143452,
0.02685256488621235,
0.04234186187386513,
0.017958305776119232,
0.02024131454527378,
0.015271739102900028,
0.03466152027249336,
-0.03028557449579239,
-0.005095562431961298,
0.02414354868233204,
0.033541906625032425,
-0.014997309073805809,
-0.05342361703515053,
0.0015607330715283751,
0.015581074170768261,
0.055086687207221985,
-0.0628744587302208,
0.013959991745650768,
0.018846895545721054,
0.021345864981412888,
-0.01965370774269104,
-0.006753836292773485,
0.026648780331015587,
0.00037532654823735356,
0.018913205713033676,
-0.02928033284842968,
0.022477123886346817,
-0.06123028323054314,
-0.015068667940795422,
0.016052991151809692,
-0.006227691657841206,
0.022269530221819878,
0.0001826198713388294,
0.0720764771103859,
-0.019642183557152748,
-0.03501201793551445,
-0.0027982359752058983,
-0.015055312775075436,
0.029457705095410347,
-0.008692636154592037,
-0.022285373881459236,
0.021085165441036224,
0.011416432447731495,
-0.01616169698536396,
0.005159545224159956,
-0.010803603567183018,
0.009587645530700684,
0.08285529166460037,
0.008915104903280735,
0.03753489628434181,
0.03535144776105881,
0.014624634757637978,
0.012307701632380486,
-0.015090184286236763,
-0.03784376010298729,
0.006339083891361952,
0.015359889715909958,
0.04798431321978569,
-0.028723306953907013,
0.01020850520581007,
0.025665687397122383,
0.030021486803889275,
-0.029856914654374123,
0.02891710214316845,
0.01391666755080223,
0.01685241051018238,
-0.004766055382788181,
-0.01726880855858326,
-0.041533567011356354,
0.0402679406106472,
-0.01458899024873972,
-0.001090395380742848,
-0.013129375874996185,
-0.011446014977991581,
0.03097411058843136,
0.025454359129071236,
-0.02215411700308323,
0.0029111953917890787,
-0.025000987574458122,
-0.026072535663843155,
0.038808681070804596,
0.0319158211350441,
0.015975818037986755,
-0.0404592864215374,
0.026152353733778,
0.01292392984032631,
-0.011246216483414173,
-0.008289411664009094,
-0.02251363731920719,
-0.054138682782649994,
-0.020841021090745926,
-0.0281321220099926,
-0.049956779927015305,
0.01719146966934204,
0.016981376335024834,
0.006474066525697708,
0.011254769749939442,
0.01418896671384573,
0.011251017451286316,
0.0189951341599226,
0.020647607743740082,
-0.014053184539079666,
0.06923284381628036,
-0.01007762923836708,
0.021014923229813576,
-0.031981535255908966,
0.005056449677795172,
0.09676121920347214,
0.016052434220910072,
0.008653043769299984,
-0.06442129611968994,
0.0157901793718338,
-0.038733672350645065,
-0.008517070673406124,
-0.043365783989429474,
0.0017034854972735047,
-0.035068329423666,
-0.0008795351022854447,
-0.0027822062838822603,
0.020034966990351677,
0.01912839338183403,
-0.009862031787633896,
0.049616485834121704,
-0.006865895818918943,
-0.06165232136845589,
0.01954326406121254,
0.025441084057092667,
-0.02142365276813507,
0.004600463900715113,
-0.03726278245449066,
0.041811924427747726,
-0.059616126120090485,
-0.02997674234211445,
-0.05191729590296745,
-0.021033335477113724,
0.035735320299863815,
0.05345211178064346,
-0.03075362928211689,
0.038302231580019,
0.012536313384771347,
0.008656056597828865,
-0.018451986834406853,
0.0404362827539444,
0.05459747090935707,
-0.027358433231711388,
0.0037017706781625748,
0.021593648940324783,
-0.008526835590600967,
0.0029090349562466145,
0.016801884397864342,
0.006844149902462959,
-0.0441746711730957,
-0.00040655655902810395,
-0.03213585168123245,
0.03142056241631508,
-0.01268102414906025,
-0.007109754253178835,
0.0020223374012857676,
0.004518373403698206,
-0.022460799664258957,
-0.03439200296998024,
-0.014945954084396362,
-0.05007035285234451,
-0.007047457620501518,
0.008724438957870007,
-0.009742526337504387,
-0.008783552795648575,
0.05744701623916626,
0.015699874609708786,
0.013653377071022987,
-0.00972826313227415,
0.002619039500132203,
0.018288254737854004,
-0.03523030877113342,
0.03605658933520317,
-0.003334927139803767,
-0.012906014919281006,
0.0046211970038712025,
-0.03549398109316826,
-0.015559395775198936,
-0.043861035257577896,
-0.009607586078345776,
0.07481462508440018,
0.022202251479029655,
-0.017510361969470978,
0.02648910880088806,
-0.007699425332248211,
-0.07808957993984222,
0.007554079405963421,
-0.04015339910984039,
-0.022738931700587273,
-0.03871835768222809,
0.028036633506417274,
0.059714797884225845,
0.03263988718390465,
0.0031181075610220432,
0.008705394342541695,
-0.006191815249621868,
0.011073106899857521,
-0.004023064859211445,
-0.017750229686498642,
-0.014315850101411343,
0.00005436352876131423,
-0.012635666877031326,
0.03869878500699997,
-0.028763646259903908,
0.007957548834383488,
-0.0019214843632653356,
0.012759702280163765,
0.0065727862529456615,
0.06062369421124458,
-0.0520559586584568,
0.014082521200180054,
-0.010722682811319828,
-0.01950322650372982,
-0.003114855382591486,
-0.0030365786515176296,
-0.009696811437606812,
-0.020172815769910812,
0.012491997331380844,
-0.02913188561797142,
-0.0014317177701741457,
0.009952460415661335,
0.003317389404401183,
-0.03634684532880783,
-0.02823772095143795,
0.006124204024672508,
-0.000653698923997581,
-0.009622277691960335,
0.019176729023456573,
-0.03585352003574371,
-0.0034683027770370245,
0.005595261696726084,
0.014230160973966122,
-0.014800389297306538,
0.007127046585083008,
-0.03675997629761696,
0.027414744719862938,
0.026744795963168144,
0.001459481311030686,
0.027899928390979767,
-0.04131985455751419,
0.02147037535905838,
-0.01096345204859972,
0.06404225528240204,
0.020871607586741447,
-0.03510414808988571,
-0.007684409152716398,
-0.01440402865409851,
-0.0022322554141283035,
-0.01624426245689392,
-0.008253871463239193,
0.03575814142823219,
0.011910024099051952,
-0.02426416240632534,
-0.026384014636278152,
0.05844241753220558,
-0.0025283608119934797,
-0.01042086724191904,
0.014542050659656525,
-0.04447538033127785,
-0.016073260456323624,
-0.004702436272054911,
0.010743393562734127,
-0.015151333063840866,
-0.013502964749932289,
0.03379851207137108,
-0.008443858474493027,
-0.014213885180652142,
-0.02181103080511093,
-0.013110344298183918,
-0.01241816021502018,
0.0039644790813326836,
0.029423577710986137,
0.009932084009051323,
0.024364208802580833,
0.019706036895513535,
-0.010593918152153492,
0.021903419867157936,
0.003201431827619672,
-0.0041001709178090096,
-0.05437636375427246,
-0.02772204764187336,
-0.02531643770635128,
0.013063596561551094,
0.06306461244821548,
-0.06766483187675476,
0.02319537103176117,
0.024093884974718094,
-0.05600866302847862,
0.018424497917294502,
-0.004430905915796757,
0.000029350312615861185,
0.004683093633502722,
0.022517118602991104,
0.010458897799253464,
0.0033529477659612894,
0.02251778170466423,
0.07194281369447708,
0.018979424610733986,
0.01348708663135767,
-0.018051011487841606,
-0.03525487333536148,
0.00399005226790905,
0.018346626311540604,
0.011090915650129318,
-0.02744852937757969,
0.0072347563691437244,
-0.030047260224819183,
0.012757745571434498,
0.016263211145997047,
-0.027512695640325546,
-0.002674797782674432,
0.0015862875152379274,
0.019411461427807808,
0.024153290316462517,
0.07963145524263382,
-0.007141596172004938,
-0.004114294424653053,
-0.022472301498055458,
-0.0317106656730175,
0.006874437909573317,
0.003756715916097164,
-0.0155811021104455,
0.01121655385941267,
-0.00004195162910036743,
-0.005089310463517904,
-0.05903397873044014,
0.05292988941073418,
-0.013302893377840519,
-0.017337746918201447,
-0.019607873633503914,
0.008156698197126389,
0.043603431433439255,
-0.021865077316761017,
-0.019412575289607048,
-0.06741460412740707,
0.02787075936794281,
0.04198875650763512,
-0.018742237240076065,
0.005068723578006029,
0.015239538624882698,
-0.005884098820388317,
-0.0121944984421134,
0.0024357351940125227,
-0.029302507638931274,
-0.03695536032319069,
-0.05874623358249664,
-0.007013404741883278,
0.00005897951268707402,
-0.02141903154551983,
0.0076475017704069614,
-0.04160667583346367,
-0.022545289248228073,
0.002472948981449008,
0.04103998467326164,
0.035911306738853455,
0.04123077169060707,
-0.012168417684733868,
-0.018291939049959183,
-0.05738956108689308,
0.03658409044146538,
-0.021227562800049782,
-0.06000108644366264,
-0.009109852835536003,
-0.016473017632961273,
0.015257312916219234,
-0.011052178218960762,
0.04704740643501282,
-0.02468152344226837,
-0.010466660372912884,
0.008488999679684639,
-0.026127327233552933,
0.024102531373500824,
-0.04853205755352974,
-0.000920417660381645,
0.04450756683945656,
-0.007666167337447405,
0.009673413820564747,
0.005684174597263336,
0.01222850102931261,
-0.005584161262959242,
0.011615252122282982,
-0.038705457001924515,
-0.005113521125167608,
-0.012299139983952045,
-0.03198160231113434,
0.006687623914331198,
0.00868940819054842,
-0.02477688528597355,
0.07972999662160873,
-0.0259254090487957,
0.021753709763288498,
0.015466629527509212,
-0.035038385540246964,
0.01585921086370945,
0.0211140438914299,
-0.03972315415740013,
-0.020986368879675865,
0.0034554307349026203,
-0.03880327194929123,
0.05693717300891876,
-0.04163408279418945,
-0.01658652536571026,
0.022602403536438942,
-0.05507037788629532,
-0.002193677006289363,
0.08344009518623352,
0.03889723867177963,
0.04012938216328621,
0.00014783855294808745,
0.0007248161709867418,
0.0016245173756033182,
-0.027569282799959183,
0.029961036518216133,
-0.021338991820812225,
0.040325384587049484,
0.024980584159493446,
-0.016182778403162956,
0.03867587447166443,
0.010406452231109142,
0.004162688739597797,
-0.020400675013661385,
-0.007991140708327293,
-0.014370647259056568,
-0.012857547029852867,
0.02958858571946621,
0.005724059883505106,
0.043642863631248474,
-0.02248038537800312,
-0.038508716970682144,
0.0906919464468956,
-0.029007529839873314,
-0.001613544998690486,
-0.0353180356323719,
-0.034212298691272736,
0.0006596921593882143,
0.025745939463377,
0.020163970068097115,
0.04429180547595024,
-0.015795232728123665,
0.015155757777392864,
-0.042355164885520935,
-0.012681294232606888,
0.024496842175722122,
0.0018734675832092762,
0.03706974908709526,
-0.009961769916117191,
-0.011469293385744095,
-0.021113377064466476,
0.013720960356295109,
0.01213080808520317,
-0.004826338030397892,
0.026946518570184708,
0.040865443646907806,
0.01045546866953373,
-0.012480434961616993,
0.033849239349365234,
-0.01724020019173622,
0.03699110820889473,
-0.028050269931554794,
-0.01922963745892048,
-0.04796372354030609,
0.020606854930520058,
0.006278846878558397,
-0.002015444217249751
] |
<p>I understand that the electromagnetic spectrum is made up of different frequencies of light waves, but is this true in all cases such as with longer wave frequencies? "such as with microwaves". sometimes I get the impression that with microwave ovens for example use waves of electrons, so my question is, is there some kind of threshold where somewhere between infrared to microwaves does the frequency makes the conversion from light to electrons? (and if so, how?) or is it always light and has some other correlation such as light influencing the electrons thru the air? </p> | 2,826 | [
-0.032457344233989716,
-0.023287799209356308,
0.01693270541727543,
-0.046512965112924576,
0.025920320302248,
0.01565304957330227,
-0.03519197180867195,
-0.03647194802761078,
0.004601410124450922,
-0.024476293474435806,
0.03346315398812294,
0.050081100314855576,
0.05243503674864769,
0.0056478832848370075,
0.026119686663150787,
0.04236544668674469,
-0.009998160414397717,
0.013556567020714283,
-0.031325578689575195,
-0.003356600645929575,
0.00321787316352129,
0.014384408481419086,
-0.002305937698110938,
0.001771646784618497,
-0.05680277943611145,
0.0064509217627346516,
0.04358448088169098,
0.019345572218298912,
0.06010299175977707,
0.015363464131951332,
0.003935869317501783,
-0.02049878053367138,
-0.009714833460748196,
0.05679216608405113,
0.03547610342502594,
-0.013009313493967056,
-0.04897080361843109,
-0.04238228127360344,
-0.006469067186117172,
0.023181838914752007,
0.015626508742570877,
0.0005843965918757021,
-0.014441541396081448,
0.013286015018820763,
-0.02671860158443451,
-0.013875679112970829,
-0.007810905110090971,
-0.042000748217105865,
0.05168064683675766,
-0.091192826628685,
0.07556017488241196,
-0.0459725596010685,
0.04455823823809624,
0.011852373369038105,
0.016086457297205925,
0.011190704070031643,
0.11205125600099564,
0.039321787655353546,
-0.0085816765204072,
-0.020733552053570747,
-0.012941623106598854,
-0.015248619951307774,
-0.017590045928955078,
-0.011128092184662819,
-0.0656958743929863,
0.03775076940655708,
-0.029725152999162674,
-0.02313440479338169,
0.04266927391290665,
0.03960055112838745,
0.008318835869431496,
0.013139585964381695,
0.038238704204559326,
0.004149295389652252,
0.0015190783888101578,
-0.03432442247867584,
0.03787638247013092,
-0.0044951243326067924,
0.022533375769853592,
0.036446478217840195,
-0.01157836988568306,
-0.005943685304373503,
-0.004110561218112707,
0.011131469160318375,
0.02323119342327118,
-0.01117930468171835,
0.0664336234331131,
-0.061821095645427704,
-0.010910509154200554,
0.008357097394764423,
-0.027424117550253868,
0.010377662256360054,
0.029015926644206047,
-0.0004821132170036435,
-0.03453265130519867,
0.035489603877067566,
-0.0030304458923637867,
0.0380278043448925,
0.017233984544873238,
-0.018232807517051697,
0.054281946271657944,
0.006395274773240089,
0.044204890727996826,
0.0641803964972496,
-0.012245310470461845,
-0.02587701380252838,
-0.02342868596315384,
0.00997965782880783,
-0.0077657876536250114,
-0.0191266480833292,
-0.02302226424217224,
0.0150077473372221,
0.011010734364390373,
0.022170377895236015,
0.012973308563232422,
0.009855557233095169,
0.037596192210912704,
-0.01850607804954052,
0.07286746799945831,
0.08873611688613892,
0.03455488756299019,
-0.05938439071178436,
0.01620475761592388,
-0.020271077752113342,
-0.06055538356304169,
0.022610191255807877,
-0.016000661998987198,
0.020470120012760162,
-0.051155801862478256,
0.015214570797979832,
-0.004530673380941153,
-0.03166332095861435,
0.025527913123369217,
-0.05238724872469902,
0.03385506942868233,
-0.028514618054032326,
-0.06594013422727585,
-0.0346209779381752,
0.005607530474662781,
-0.032720766961574554,
-0.03885035589337349,
-0.0671449676156044,
0.004504349082708359,
0.018050074577331543,
0.0589279942214489,
0.029829537495970726,
-0.004216532688587904,
-0.03337521478533745,
0.039984192699193954,
0.018359217792749405,
-0.013530587777495384,
-0.0017323661595582962,
0.008454468101263046,
-0.03262314572930336,
0.05025546997785568,
-0.03637125343084335,
0.027698596939444542,
0.03813141956925392,
0.010989873670041561,
-0.02893003821372986,
0.04984404891729355,
-0.020554477348923683,
-0.018231738358736038,
0.03574738651514053,
0.021887287497520447,
-0.03854869678616524,
0.07364172488451004,
0.003094131825491786,
0.011575049720704556,
0.030475184321403503,
-0.013103142380714417,
0.010778950527310371,
0.021577365696430206,
0.041956834495067596,
0.007033064961433411,
-0.00995735451579094,
-0.011134740896522999,
-0.023846719413995743,
0.05207246169447899,
-0.021694455295801163,
-0.03399238362908363,
-0.02047659084200859,
0.009413640014827251,
0.024753538891673088,
0.011216576211154461,
0.05712457373738289,
-0.0240633487701416,
-0.04832936078310013,
-0.021735595539212227,
-0.0931919515132904,
0.0077583943493664265,
-0.020373638719320297,
0.018578194081783295,
-0.028587637469172478,
-0.012704359367489815,
0.02530481293797493,
-0.0014011883176863194,
-0.00011127762991236523,
-0.04623561352491379,
-0.020567432045936584,
-0.019391778856515884,
0.01006900705397129,
0.016025785356760025,
-0.042210765182971954,
0.033563267439603806,
0.05659797042608261,
0.009037652984261513,
0.012090626172721386,
0.022055141627788544,
-0.01158755924552679,
-0.05644427239894867,
0.0012961548054590821,
-0.023314282298088074,
0.04075826704502106,
0.02100975066423416,
0.002391965128481388,
0.008139348588883877,
-0.031060468405485153,
-0.03757403418421745,
0.06305108219385147,
-0.022501016035676003,
0.05957776680588722,
0.040207166224718094,
-0.024208510294556618,
-0.007286922540515661,
0.04520892724394798,
0.04868027940392494,
0.00711045740172267,
0.008959890343248844,
-0.03543270379304886,
-0.06867441534996033,
-0.003460605861619115,
0.033787231892347336,
-0.007285715080797672,
-0.050687167793512344,
0.007707023527473211,
0.014139220118522644,
0.06142162159085274,
0.03719869256019592,
0.04427255690097809,
-0.03517184406518936,
-0.006252085790038109,
0.015055091120302677,
0.004617690574377775,
0.022805241867899895,
0.02979796566069126,
0.010782905854284763,
0.014143046922981739,
-0.0005217149155214429,
-0.002179004717618227,
-0.0001201709674205631,
0.045976344496011734,
-0.03127187117934227,
-0.0044527058489620686,
-0.016591161489486694,
-0.025248028337955475,
0.015586315654218197,
-0.06199149414896965,
0.00043693691259250045,
0.009097560308873653,
-0.013604751788079739,
-0.012651920318603516,
-0.01716519705951214,
-0.007725875359028578,
0.027663342654705048,
-0.03474297374486923,
-0.03771800920367241,
0.0027918771374970675,
0.03327168896794319,
-0.04153091087937355,
0.004468981642276049,
0.0028472114354372025,
-0.010159051977097988,
-0.016657156869769096,
-0.02246723137795925,
0.011175038293004036,
0.000566805771086365,
0.07151482254266739,
-0.05207738280296326,
-0.05263364315032959,
-0.009626908227801323,
-0.0741988867521286,
-0.01566486991941929,
-0.005442567635327578,
-0.018477406352758408,
0.023691192269325256,
-0.032057005912065506,
-0.05688672885298729,
0.051096782088279724,
-0.04634629935026169,
0.012924538925290108,
0.008929328992962837,
-0.025001075118780136,
-0.05464685708284378,
-0.023190122097730637,
0.0007116222404874861,
0.022246262058615685,
0.01775866001844406,
0.010021999478340149,
0.03547528013586998,
-0.004741768352687359,
-0.03509452939033508,
0.008751938119530678,
0.005510217044502497,
-0.06645026803016663,
-0.023214947432279587,
-0.028304969891905785,
0.026776041835546494,
-0.021012337878346443,
0.03482886776328087,
0.012090237811207771,
-0.05863668769598007,
0.022256605327129364,
-0.006784889847040176,
-0.04438887909054756,
0.035440441220998764,
-0.008486267179250717,
0.06894222646951675,
0.0031813476234674454,
-0.029398540034890175,
0.03868357092142105,
0.018161246553063393,
-0.014909964986145496,
-0.017926622182130814,
0.00198687007650733,
-0.0181431882083416,
-0.01944642886519432,
0.02303207665681839,
0.0462176613509655,
-0.023431921377778053,
0.03996620699763298,
0.026250043883919716,
0.01754686050117016,
0.017184024676680565,
0.0019169406732544303,
-0.004791778977960348,
0.02389875240623951,
-0.005447252653539181,
0.005647590383887291,
0.026716601103544235,
0.01559535600244999,
-0.03975258395075798,
0.05675777420401573,
0.019174542278051376,
0.026958581060171127,
0.03825465589761734,
-0.019031137228012085,
0.03246408328413963,
0.003252970753237605,
0.021622933447360992,
0.001597859780304134,
0.017107229679822922,
-0.0017679198645055294,
0.01917503960430622,
0.021017225459218025,
0.04988614097237587,
0.03021775186061859,
-0.027568822726607323,
0.00031835612026043236,
0.039579492062330246,
0.0492735393345356,
-0.025960611179471016,
-0.004414372146129608,
0.028637826442718506,
0.0066360123455524445,
0.009778134524822235,
-0.02323843725025654,
-0.03315235301852226,
0.065508633852005,
0.019884923473000526,
0.04596235975623131,
0.02686677686870098,
-0.01871117204427719,
-0.0013249843614175916,
-0.029063312336802483,
-0.0020785953383892775,
0.0202384814620018,
0.046136416494846344,
-0.00771570298820734,
0.06419201195240021,
0.030159227550029755,
0.02433524839580059,
0.028629878535866737,
-0.006835148204118013,
-0.0770203098654747,
-0.003312306944280863,
-0.031616248190402985,
-0.007205542176961899,
-0.05184788256883621,
-0.001381470006890595,
-0.03588344156742096,
-0.014065539464354515,
-0.03600502759218216,
-0.014107589609920979,
-0.023629173636436462,
-0.02413218468427658,
0.04850872606039047,
-0.028638677671551704,
-0.03012974001467228,
-0.0318642184138298,
0.0025856243446469307,
-0.004029309377074242,
0.006983394268900156,
-0.016966549679636955,
0.03322939574718475,
-0.03240752965211868,
0.024169282987713814,
-0.02081751823425293,
0.015274041332304478,
-0.004022130277007818,
0.04579777270555496,
0.06853371858596802,
-0.007873856462538242,
-0.03735450655221939,
0.04198522865772247,
0.01929163560271263,
0.04155559465289116,
-0.0019488483667373657,
-0.056287821382284164,
-0.05813857167959213,
-0.027367593720555305,
-0.027041098102927208,
-0.01885882206261158,
0.06701549887657166,
-0.004430410452187061,
-0.012141277082264423,
0.04192584753036499,
-0.018384570255875587,
-0.02824990078806877,
0.06558908522129059,
0.015885427594184875,
-0.02266146056354046,
-0.02887851931154728,
-0.04354644566774368,
-0.003507868153974414,
-0.031225254759192467,
0.009454324841499329,
0.022986801341176033,
-0.006904967129230499,
-0.01235427800565958,
-0.00841567199677229,
0.023562632501125336,
-0.0007705198950134218,
0.004446287639439106,
0.001398779102601111,
-0.0027315306942909956,
-0.008932339027523994,
-0.0076056537218391895,
-0.07409194111824036,
-0.02884243056178093,
0.042295586317777634,
0.016240408644080162,
-0.011409979313611984,
-0.0038457426708191633,
-0.09233641624450684,
0.020970994606614113,
0.044204436242580414,
0.030621398240327835,
-0.02251078374683857,
0.00806556548923254,
-0.04598523676395416,
0.0009827804751694202,
0.015724029392004013,
-0.005733904428780079,
0.01759456656873226,
-0.01831745356321335,
0.00894248392432928,
-0.010538537055253983,
-0.020255563780665398,
0.027598083019256592,
-0.009309469722211361,
0.04490552470088005,
0.0332636758685112,
-0.046361830085515976,
-0.012133021838963032,
0.003816134063526988,
0.016840524971485138,
0.06331125646829605,
0.032653890550136566,
0.003029097802937031,
-0.015136869624257088,
0.019782675430178642,
0.004046814050525427,
-0.005597368814051151,
-0.06675858795642853,
-0.010975106619298458,
0.030225995928049088,
0.005376601591706276,
0.0420086532831192,
-0.030688609927892685,
-0.024590659886598587,
0.009386884979903698,
0.03825520724058151,
0.016356974840164185,
-0.0029266176279634237,
-0.014224289916455746,
0.05114447697997093,
-0.002964581595733762,
-0.008947556838393211,
0.03429349139332771,
0.027262872084975243,
-0.03323966637253761,
-0.006595275364816189,
-0.004634336568415165,
0.07023661583662033,
-0.02190009132027626,
-0.029687730595469475,
0.006582451984286308,
-0.025120673701167107,
-0.005118814762681723,
0.07519745081663132,
0.006303032860159874,
0.007714495994150639,
0.0030207617674022913,
-0.04068319499492645,
-0.023949163034558296,
0.022723762318491936,
-0.02012345753610134,
-0.026841720566153526,
-0.011240861378610134,
0.015360407531261444,
-0.038171906024217606,
-0.016828984022140503,
0.0029882481321692467,
0.0022545154206454754,
0.016534296795725822,
0.0032867344561964273,
0.00014002701209392399,
0.024788854643702507,
-0.07783485949039459,
0.02055308222770691,
-0.0034196816850453615,
-0.04508873447775841,
0.045002881437540054,
0.012275338172912598,
0.008699989877641201,
-0.015529216267168522,
-0.08592229336500168,
-0.04858580604195595,
0.01559474878013134,
-0.005989480298012495,
0.027142247185111046,
-0.026200298219919205,
0.047653552144765854,
-0.010166226886212826,
0.007415149360895157,
-0.0652582123875618,
-0.047183942049741745,
-0.016370251774787903,
0.06663563847541809,
0.010609078221023083,
-0.018572602421045303,
0.02748773992061615,
-0.06719208508729935,
-0.02444879151880741,
0.011447915807366371,
0.034943100064992905,
-0.03447927162051201,
-0.012891029939055443,
0.002341062296181917,
-0.027887418866157532,
0.047594472765922546,
0.008433106355369091,
-0.05976191908121109,
0.009403185918927193,
-0.0004545396950561553,
0.015533615835011005,
-0.0039069317281246185,
0.04041863977909088,
-0.004422097001224756,
-0.04460892081260681,
0.0005422859103418887,
-0.0017003450775519013,
0.04776853695511818,
-0.05767729878425598,
-0.009297225624322891,
0.07571917027235031,
0.04393427446484566,
0.031192559748888016,
-0.01576206460595131,
0.034413568675518036,
-0.0052978526800870895,
0.00673712557181716,
0.03648494556546211,
-0.003261834615841508,
-0.05068254470825195,
-0.04200262576341629,
0.0094145517796278,
-0.01650359109044075,
0.04745424538850784,
0.015859872102737427,
0.05550446733832359,
-0.014115117490291595,
0.017921004444360733,
-0.024434147402644157,
-0.023156501352787018,
-0.009623191319406033,
-0.040121566504240036,
0.016199180856347084,
0.0007003700593486428,
0.019536670297384262,
0.011110560968518257,
-0.03457314893603325,
-0.01768951117992401,
-0.031797152012586594,
0.04739399999380112,
-0.020052673295140266,
0.020750755444169044,
0.02057286538183689,
-0.0026547096204012632,
-0.005776275414973497,
-0.022477995604276657,
0.008752997033298016,
0.02050514705479145,
-0.025600343942642212,
0.011117006652057171,
-0.019355224445462227,
-0.001510217203758657,
0.0024919607676565647,
0.025164561346173286,
0.0009461158188059926,
-0.00042925190064124763,
0.04855795204639435,
0.05411428213119507,
0.006614276207983494,
-0.005866291467100382,
-0.04554440453648567,
0.025979315862059593,
-0.04396107792854309,
0.03248566389083862,
0.009000849910080433,
-0.004907313268631697,
0.03488105162978172,
0.02864309586584568,
0.02506324090063572,
-0.001560225966386497,
-0.013362838886678219,
-0.01878322660923004,
0.041881263256073,
-0.023442227393388748,
-0.006106463726609945,
-0.015290604904294014,
-0.0014998494880273938,
0.04822849482297897,
0.012425846420228481,
0.010046401992440224,
0.0005370937287807465,
-0.048069264739751816,
-0.04154429957270622,
-0.049732986837625504,
-0.025622745975852013,
0.04160917550325394,
-0.02629849687218666,
-0.019856084138154984,
-0.010632279329001904,
-0.03354717418551445,
0.024584336206316948,
0.026802340522408485,
0.03099900297820568,
-0.023695560172200203,
0.02159401774406433,
0.005823977757245302,
0.031157679855823517,
0.021528447046875954,
0.011525457724928856,
0.1084408238530159,
0.04822961613535881,
-0.019902650266885757,
-0.0618659071624279,
0.014784866012632847,
-0.061238665133714676,
0.022326115518808365,
-0.02313542366027832,
-0.01709926500916481,
-0.023592274636030197,
0.02650505304336548,
-0.009186225943267345,
0.057200320065021515,
-0.004905661568045616,
0.018784793093800545,
0.036809295415878296,
-0.03645921126008034,
-0.009690862149000168,
0.035748645663261414,
0.015391938388347626,
-0.005383675917983055,
0.03410341590642929,
-0.05175168439745903,
-0.00748505350202322,
-0.08036269247531891,
-0.006415777839720249,
0.007281802594661713,
-0.00017201555601786822,
0.051723748445510864,
-0.044422589242458344,
-0.04452526569366455,
-0.016095038503408432,
-0.001976683037355542,
-0.02122066728770733,
-0.01705811731517315,
0.02460773102939129,
0.04036255553364754,
0.007954856380820274,
-0.011576137505471706,
0.0007217925740405917,
0.030778270214796066,
0.0018249514978379011,
0.011589985340833664,
0.007938572205603123,
-0.02717776410281658,
-0.00803268514573574,
-0.02637230046093464,
-0.004254975356161594,
-0.0008045481517910957,
0.021708767861127853,
0.014388833194971085,
0.029478317126631737,
-0.01588158868253231,
-0.04880068823695183,
-0.006803396623581648,
-0.01932065561413765,
0.03814736381173134,
-0.025643695145845413,
-0.02641161158680916,
-0.04433184117078781,
0.027229666709899902,
-0.010048327036201954,
0.042811840772628784,
0.00924430601298809,
-0.005810146685689688,
0.009443460032343864,
0.02984604984521866,
0.03615935146808624,
-0.0003670826554298401,
-0.03670404851436615,
0.007443432230502367,
-0.019739102572202682,
-0.03882153332233429,
-0.031197495758533478,
0.04814458638429642,
0.04109365865588188,
0.032239604741334915,
-0.02106272056698799,
-0.025965996086597443,
-0.004754610359668732,
-0.09590542316436768,
0.00874025747179985,
0.032557226717472076,
-0.04371941462159157,
0.023632459342479706,
-0.0028642816469073296,
0.016609977930784225,
0.017031606286764145,
-0.028430139645934105,
0.015042556449770927,
-0.020789623260498047,
-0.033328860998153687,
0.02269187569618225,
-0.05974969267845154,
-0.006917791906744242,
0.03259505704045296,
0.010199869982898235,
0.007330555003136396,
-0.023547779768705368,
0.06014455854892731,
0.021925559267401695,
0.010568560101091862,
0.004733039531856775,
0.02381986565887928,
-0.028573449701070786,
-0.014506216160953045,
0.0011898359516635537,
-0.0037665346171706915,
0.023101096972823143,
0.010801148600876331,
0.0002512955979909748,
-0.02737714909017086,
-0.05116349458694458,
-0.030068473890423775,
0.013987753540277481,
-0.005735587328672409,
0.022472722455859184,
0.008351026102900505,
0.027650846168398857,
-0.003699611173942685,
0.0039441525004804134,
-0.018022164702415466,
-0.029587095603346825,
-0.05233749374747276,
-0.005875132512301207,
0.02649131789803505,
-0.02603723667562008,
0.003396909451112151,
0.02103860303759575,
-0.0077329371124506,
-0.04240986332297325,
0.045731667429208755,
0.06192979961633682,
0.0036746524274349213,
0.005633399356156588,
0.015135853551328182,
-0.02959832176566124,
0.07552836090326309,
-0.041692908853292465,
-0.051048215478658676,
0.04274538531899452,
-0.04928622022271156,
-0.023565219715237617,
0.04056815430521965,
-0.02621101588010788,
0.012623662129044533,
0.05180973559617996,
-0.004822914954274893,
0.00935481395572424,
0.052063461393117905,
0.003506895387545228,
0.03293571621179581,
0.004308180417865515,
0.014790399931371212,
0.013325388543307781,
0.02429642342031002,
0.025901958346366882,
-0.018046721816062927,
-0.01297871582210064,
0.03638062626123428,
0.027341343462467194,
0.019735857844352722,
-0.008678941056132317,
-0.009007117711007595,
-0.033402781933546066,
0.028981033712625504,
0.04166975989937782,
0.013205645605921745,
0.02664109878242016,
0.03470981866121292,
-0.0117559302598238,
0.048838451504707336,
0.024555692449212074,
-0.005093473941087723,
-0.09141701459884644,
-0.027170490473508835,
0.008588992990553379,
0.011188114993274212,
0.014420806430280209,
-0.020440291613340378,
-0.002462876494973898,
0.017825620248913765,
-0.09490902721881866,
-0.018044399097561836,
-0.0015229550190269947,
0.004582949448376894,
-0.03454011306166649,
0.011830318719148636,
-0.04274329915642738,
0.005931668449193239,
0.019373083487153053,
0.05662288889288902,
0.004017780534923077,
0.0315542034804821,
-0.009130408987402916,
-0.029380664229393005,
-0.020402539521455765,
0.04645383358001709,
0.012578808702528477,
-0.02537248469889164,
0.04611748084425926,
-0.01943650282919407,
-0.01723807491362095,
0.0058315047062933445,
0.020443780347704887,
0.03651633486151695,
-0.026985423639416695,
-0.011041880585253239,
0.02080981805920601,
0.016296381130814552,
-0.0005893385387025774,
-0.0423424206674099,
-0.003284364938735962,
0.05238425359129906,
0.02418864704668522,
0.030303388833999634,
-0.015252460725605488,
-0.002859892789274454,
0.022690549492836,
-0.05099087953567505,
-0.030283529311418533,
0.004054024815559387,
-0.027295948937535286,
-0.024378441274166107,
0.017725002020597458,
0.02193833328783512,
0.020788175985217094,
-0.047320108860731125,
0.01803254894912243,
-0.09375087171792984,
-0.05478692054748535,
0.001439572311937809,
0.03352556377649307,
0.010148354806005955,
-0.012616542167961597,
-0.006540772970765829,
-0.031850721687078476,
0.01046355627477169,
0.01684119738638401,
-0.018383944407105446,
-0.010177566669881344,
0.02168692648410797,
0.025504155084490776,
-0.005552783142775297,
0.012046129442751408,
-0.027651431038975716,
-0.061229292303323746,
0.026577474549412727,
-0.020365960896015167,
0.02323526330292225,
-0.00747442152351141,
-0.04617445543408394,
-0.03132948279380798,
-0.03299209102988243,
0.024857478216290474,
-0.02037816308438778,
0.010818329639732838,
-0.06428516656160355,
-0.014885526150465012,
-0.023643581196665764,
0.03919410705566406,
0.05865287035703659,
0.004829176235944033,
-0.00609381590038538,
-0.0081724151968956,
-0.010899003595113754,
0.017507832497358322,
-0.04618115350604057,
0.00857901107519865,
-0.010095062665641308,
-0.03442719206213951,
-0.036020319908857346,
-0.020346196368336678,
-0.0558183416724205,
-0.00008916431397665292,
0.005766160320490599,
-0.004882988519966602,
0.03483319282531738,
-0.030802804976701736,
-0.0201107207685709,
0.06835154443979263,
0.036268386989831924,
-0.010126459412276745,
0.04163502901792526,
0.0008732231217436492,
0.0083541888743639,
0.046147823333740234,
-0.01601358875632286,
-0.03618783503770828,
0.018701642751693726,
0.0005335512687452137,
0.03332417085766792,
-0.005372758489102125,
0.015928467735648155,
0.028855178505182266,
-0.020143531262874603,
0.010011346079409122,
0.049141958355903625,
-0.011705352924764156,
0.012721510604023933,
0.05271482095122337,
-0.0030139563605189323,
-0.008619359694421291,
-0.018546458333730698,
-0.012139066122472286,
0.0006157825118862092,
0.008341210894286633,
-0.0031746127642691135,
0.04926548898220062,
0.02098425291478634,
-0.005370656028389931,
0.053614918142557144,
0.037919383496046066,
-0.017454832792282104,
-0.016040701419115067,
-0.011402180418372154,
0.02080964855849743,
-0.03065035678446293,
-0.022114548832178116,
0.025395074859261513,
0.0021105119958519936,
-0.009613068774342537,
0.03944045677781105,
-0.03580736741423607,
0.06630170345306396,
-0.02042558789253235,
0.0215282142162323,
-0.009226566180586815,
0.02548879198729992,
-0.005511549301445484,
0.017301790416240692,
-0.0020687435753643513,
0.03745182231068611,
-0.02184135653078556,
0.0016950048739090562,
-0.053787603974342346,
0.0007951021543703973,
0.05675981566309929,
-0.053657207638025284,
0.04386444389820099,
-0.007566463202238083,
-0.020014554262161255,
-0.03518666326999664,
0.016123954206705093,
-0.0032827723771333694,
-0.012405955232679844,
0.004649023991078138,
0.024117931723594666,
0.0011813519522547722,
-0.005665760021656752,
-0.013099814765155315,
-0.013086690567433834,
0.026919888332486153,
-0.05396924912929535,
-0.006540689151734114,
-0.01268234197050333,
0.02892342023551464,
-0.023963579908013344,
-0.005688737146556377
] |
<p>If I understand correctly, lightning is the discharge of electricity from the atmosphere into the planet. However, if I switch on a lamp, the wires are not causing thunder (or any audible sound).</p>
<p>I've also heard that the thunder comes from lightning breaking the sound barrier. This sounds weird to me since I would assume that lightning would be traveling at, well, light speed, so I'm not sure how the threshold could be crossed.</p>
<p>How does lightning cause thunder?</p> | 2,827 | [
-0.04921276494860649,
-0.03876194357872009,
0.00966452807188034,
-0.0342290885746479,
-0.003545433981344104,
0.004231841303408146,
-0.015570747666060925,
-0.03228731080889702,
0.01645328477025032,
0.032042477279901505,
0.03115125186741352,
0.056611862033605576,
0.03950047865509987,
0.03297809138894081,
0.017408082261681557,
-0.0013871659757569432,
0.004843304865062237,
-0.015128334052860737,
0.01647084951400757,
-0.050438739359378815,
-0.034573912620544434,
-0.0006527230143547058,
-0.01752587780356407,
0.036063723266124725,
-0.014504620805382729,
0.014828243292868137,
0.02198861353099346,
0.01600291207432747,
0.049920421093702316,
0.008836385793983936,
0.009629172272980213,
-0.03487415611743927,
0.00992813240736723,
0.011435565538704395,
0.041858892887830734,
0.010519666597247124,
-0.010759043507277966,
-0.0035229751374572515,
-0.013893453404307365,
-0.009599491022527218,
-0.001809702254831791,
0.003888984676450491,
0.020239371806383133,
0.03073427639901638,
-0.04407159239053726,
-0.013044179417192936,
0.02222367562353611,
-0.03390427678823471,
0.018468646332621574,
-0.1050272062420845,
0.026989100500941277,
-0.00904590729624033,
0.013376787304878235,
0.04002269729971886,
0.003589412895962596,
0.03780636563897133,
0.10045334696769714,
0.06909099966287613,
-0.016645221039652824,
-0.044369447976350784,
0.004801182541996241,
-0.004640947561711073,
-0.01811007782816887,
-0.026469845324754715,
-0.014242756180465221,
0.04097317159175873,
-0.007328466046601534,
-0.02400025725364685,
0.02943781390786171,
0.00537765771150589,
-0.0012156852753832936,
-0.0065439362078905106,
0.012078143656253815,
0.014255017042160034,
0.011168533004820347,
-0.020986542105674744,
0.02400652877986431,
-0.015141434967517853,
0.02274457737803459,
0.051566921174526215,
0.010957141406834126,
0.005490433890372515,
0.003887027967721224,
0.002371701877564192,
0.017221907153725624,
-0.020358415320515633,
0.09888959676027298,
-0.008961575105786324,
-0.0072797988541424274,
-0.0007472600555047393,
-0.016990702599287033,
-0.0044799200259149075,
-0.014427467249333858,
0.04037858918309212,
0.00013431783008854836,
0.030319716781377792,
0.0038940375670790672,
0.034262515604496,
0.02428755909204483,
-0.05049899220466614,
0.02383735217154026,
0.03354398533701897,
0.06445334851741791,
0.0462128221988678,
-0.01439839880913496,
-0.056618936359882355,
-0.026276057586073875,
0.006238258443772793,
-0.012298185378313065,
-0.0027066601905971766,
-0.04759996011853218,
0.02398502640426159,
0.017419904470443726,
-0.03164268285036087,
-0.010018045082688332,
-0.02619500830769539,
0.034314144402742386,
-0.014187171123921871,
0.024423891678452492,
0.03206859901547432,
0.0004956558695994318,
-0.018019184470176697,
0.04244138300418854,
-0.020277250558137894,
-0.03451915457844734,
0.022202573716640472,
0.008685985580086708,
-0.029651904478669167,
-0.0070206825621426105,
0.06076649948954582,
-0.018135128542780876,
-0.033464714884757996,
-0.00743625033646822,
-0.03783121705055237,
0.06603582948446274,
-0.033379048109054565,
-0.09461827576160431,
-0.028537692502141,
0.03261757269501686,
-0.006253944709897041,
-0.022461656481027603,
-0.07771700620651245,
0.023085668683052063,
0.00906833354383707,
0.03940996527671814,
-0.008411696180701256,
-0.0037137907929718494,
0.006758349947631359,
0.007480571046471596,
0.040952082723379135,
-0.01979934051632881,
-0.01788792572915554,
0.018080895766615868,
-0.0034771827049553394,
0.04567107558250427,
-0.05196613073348999,
0.02531619928777218,
0.014358415268361568,
0.008622018620371819,
-0.016424203291535378,
0.05650123208761215,
-0.012557648122310638,
-0.016979187726974487,
0.03149297088384628,
0.005595089867711067,
-0.00970548391342163,
0.08210185170173645,
0.0022847175132483244,
-0.0315697118639946,
0.06640937179327011,
0.02266145497560501,
0.02334599196910858,
0.01611790433526039,
0.02055767923593521,
0.01816258393228054,
-0.059595026075839996,
-0.025169093161821365,
-0.04477255418896675,
0.022401828318834305,
-0.02604285441339016,
-0.031116725876927376,
-0.012220400385558605,
0.03311089426279068,
-0.008184773847460747,
0.008656163699924946,
0.05311712622642517,
-0.03206105902791023,
-0.028561824932694435,
-0.00886475294828415,
-0.009523729793727398,
0.0028242396656423807,
-0.026893656700849533,
0.014318573288619518,
-0.04059884697198868,
0.004624823573976755,
0.006923163775354624,
-0.002730071544647217,
0.0569964163005352,
-0.043574873358011246,
0.007505276706069708,
-0.00263883825391531,
0.028934985399246216,
0.0026780113112181425,
-0.04172490909695625,
0.006744765676558018,
0.04079084098339081,
0.014763559214770794,
0.011023242026567459,
0.00966593436896801,
-0.00973975658416748,
-0.010099940933287144,
0.008787060156464577,
-0.012658828869462013,
0.02352299354970455,
-0.005083826836198568,
-0.022245138883590698,
0.03725174814462662,
-0.01785622537136078,
-0.0011849688598886132,
0.027511321008205414,
-0.001486895140260458,
0.047414809465408325,
0.023169120773673058,
-0.008773715235292912,
-0.008602486923336983,
0.042856913059949875,
-0.01824209839105606,
-0.021875157952308655,
0.003945401404052973,
0.0002749608247540891,
-0.07012985646724701,
0.007071599829941988,
0.07165608555078506,
-0.00855529960244894,
0.0021470217034220695,
0.03126257285475731,
0.01921769417822361,
0.03816133737564087,
0.026751628145575523,
0.04426565393805504,
-0.03290419653058052,
-0.009214554913341999,
0.012130306102335453,
0.03026764467358589,
0.010116195306181908,
0.024559207260608673,
0.06899574398994446,
0.0027311111334711313,
0.00502846809104085,
-0.046711575239896774,
-0.036020427942276,
0.06229155883193016,
-0.020743194967508316,
0.029975030571222305,
-0.004425390623509884,
-0.051157526671886444,
0.048525676131248474,
-0.031836364418268204,
0.015109462663531303,
-0.0004343213513493538,
0.027897590771317482,
0.04224715754389763,
-0.03698120266199112,
0.022097546607255936,
0.016752438619732857,
-0.016914835199713707,
-0.03507336229085922,
0.0028101566713303328,
0.044337399303913116,
-0.08675646036863327,
0.0275739636272192,
0.01288588996976614,
0.004837265238165855,
-0.043728284537792206,
-0.007987775839865208,
0.023557210341095924,
0.022149894386529922,
0.043781377375125885,
-0.02732933685183525,
-0.06539587676525116,
-0.009022599086165428,
-0.04382865130901337,
-0.015073651447892189,
-0.005327784921973944,
0.0010616652434691787,
0.03517458587884903,
-0.022949008271098137,
-0.011216746643185616,
0.06270356476306915,
-0.017944369465112686,
0.013017664663493633,
0.005095291417092085,
-0.006993889342993498,
-0.028815312311053276,
0.036417294293642044,
-0.055823639035224915,
0.019529065117239952,
-0.023679884150624275,
-0.0053380499593913555,
0.03369094803929329,
-0.0018701652297750115,
-0.012689181603491306,
-0.0038865082897245884,
-0.037639766931533813,
-0.02224937453866005,
-0.001577627845108509,
-0.021146008744835854,
0.033205293118953705,
-0.04051016643643379,
0.006421009544283152,
0.007856646552681923,
-0.07966785132884979,
0.02081848308444023,
-0.01381039246916771,
-0.03924589976668358,
0.030552202835679054,
0.020350294187664986,
0.06480700522661209,
-0.01993437297642231,
-0.07592043280601501,
0.015897544100880623,
0.023542609065771103,
-0.028636539354920387,
0.003870036918669939,
-0.02111392840743065,
-0.015314190648496151,
-0.029884520918130875,
-0.0028897495940327644,
0.07670724391937256,
-0.00664139399304986,
0.012106644921004772,
0.04662971571087837,
0.02126098796725273,
0.017792223021388054,
-0.0032746123615652323,
-0.005882437340915203,
-0.026706520467996597,
-0.010910571552813053,
0.021619699895381927,
0.016675900667905807,
0.009028727188706398,
-0.03927924484014511,
-0.00956723839044571,
-0.02880614437162876,
0.00015618212637491524,
0.020345531404018402,
-0.019965488463640213,
0.0314253568649292,
0.015369624830782413,
0.015254631638526917,
-0.04883904382586479,
0.012980138882994652,
-0.0025393806863576174,
-0.0017558425897732377,
-0.0031864813063293695,
0.01507436204701662,
0.02931046113371849,
-0.011602096259593964,
-0.014687523245811462,
0.005299402866512537,
0.04017415642738342,
-0.03815009817481041,
-0.05520984157919884,
0.018411725759506226,
-0.012023699469864368,
0.008654724806547165,
0.029189618304371834,
0.029180068522691727,
0.0369226299226284,
0.0004662988649215549,
0.01176222413778305,
0.014581596478819847,
-0.03865182399749756,
-0.006824788637459278,
-0.057610224932432175,
0.035309940576553345,
-0.012482082471251488,
0.013596558012068272,
-0.028289400041103363,
0.10479655861854553,
0.02986864373087883,
0.03552054986357689,
0.0396963506937027,
-0.01665591634809971,
-0.07487958669662476,
0.022620534524321556,
-0.056611962616443634,
-0.024535419419407845,
-0.021433701738715172,
-0.008551595732569695,
-0.060659073293209076,
0.00032511891913600266,
-0.032062020152807236,
-0.03777935728430748,
-0.025002675130963326,
-0.07398433238267899,
-0.005408354103565216,
-0.011513103730976582,
-0.017227618023753166,
-0.006163198500871658,
-0.008908986113965511,
0.0349251925945282,
0.012186404317617416,
0.013660760596394539,
0.046547550708055496,
0.009162714704871178,
-0.012411920353770256,
-0.02858257107436657,
-0.02411000058054924,
-0.0024988630320876837,
0.02420050837099552,
0.035066112875938416,
-0.03236585855484009,
-0.020776687189936638,
0.004368505906313658,
-0.008516823872923851,
0.040153611451387405,
0.03148115426301956,
0.014021115377545357,
-0.06006605550646782,
-0.007649953477084637,
-0.002760374452918768,
-0.0060394685715436935,
0.03621871396899223,
-0.02317633666098118,
-0.0017406746046617627,
0.017163900658488274,
-0.012833736836910248,
-0.00305929291062057,
0.03306243568658829,
0.01990881934762001,
-0.0024552049580961466,
-0.01937253586947918,
-0.05044829845428467,
-0.022102899849414825,
-0.05880718678236008,
-0.0214033592492342,
0.008232266642153263,
-0.021571725606918335,
-0.015622712671756744,
0.0037467656657099724,
0.039753884077072144,
-0.0007801434840075672,
0.01611553132534027,
-0.0017059346428140998,
0.02842390164732933,
0.016975248232483864,
-0.0006909294752404094,
0.01270932238548994,
0.0010990530718117952,
0.004186829552054405,
0.02295263111591339,
0.003017118899151683,
-0.031277697533369064,
-0.08393595367670059,
0.006600763648748398,
0.043172672390937805,
0.04766197130084038,
-0.04483940824866295,
-0.0032555903308093548,
-0.0620681568980217,
-0.0035298215225338936,
0.00404898589476943,
0.009026219137012959,
0.02070647105574608,
-0.00772658409550786,
0.02201007306575775,
-0.02986994758248329,
-0.017810935154557228,
0.016210168600082397,
0.02032739482820034,
0.019734542816877365,
0.021778881549835205,
-0.003383785020560026,
-0.035873789340257645,
-0.015284908935427666,
0.02651047706604004,
0.020841099321842194,
0.0642954558134079,
0.01243512611836195,
-0.01033621933311224,
-0.024356475099921227,
0.016046231612563133,
-0.008880509063601494,
-0.05472330003976822,
-0.019376438111066818,
-0.014868861064314842,
-0.03061317466199398,
0.04247665777802467,
-0.007107440382242203,
-0.02958488091826439,
0.023496653884649277,
0.022499751299619675,
-0.01155407726764679,
-0.014226526953279972,
-0.014427580870687962,
0.02378888800740242,
0.007243454456329346,
0.03139073774218559,
0.05847691744565964,
0.003574189031496644,
-0.045353520661592484,
0.0038563101552426815,
0.01817883737385273,
0.0713149905204773,
-0.011011849157512188,
0.011327831074595451,
0.012179830111563206,
0.02665460854768753,
-0.031459566205739975,
0.06335404515266418,
-0.018234891816973686,
0.012503542006015778,
-0.014646555297076702,
-0.015303525142371655,
-0.012336351908743382,
0.04030027240514755,
0.015949366614222527,
0.012205613777041435,
-0.03377900272607803,
0.045719437301158905,
-0.0137399323284626,
-0.011233014985918999,
-0.007083881180733442,
-0.0035060171503573656,
0.008674977347254753,
0.026869580149650574,
-0.008557246997952461,
0.018937967717647552,
-0.04516832157969475,
-0.01815519481897354,
0.04045132175087929,
-0.06242072209715843,
0.08722946047782898,
0.0030842553824186325,
-0.03299468383193016,
0.03753568232059479,
-0.06473034620285034,
-0.022538363933563232,
0.0032045478001236916,
-0.009404697455465794,
0.07338979840278625,
-0.07004798203706741,
0.013359775766730309,
-0.004108003806322813,
0.009329498745501041,
-0.06676219403743744,
-0.06824284046888351,
0.043805692344903946,
0.030416026711463928,
-0.031501252204179764,
-0.030904056504368782,
0.008874858729541302,
-0.039264045655727386,
-0.04369034990668297,
-0.0015375762013718486,
0.017878636717796326,
-0.02761220932006836,
0.02135786972939968,
0.03274106979370117,
-0.03749779611825943,
0.05757489427924156,
-0.00027370371390134096,
-0.026502154767513275,
-0.004189683590084314,
-0.04158435016870499,
0.002705934224650264,
-0.05208972096443176,
0.06042466685175896,
-0.014393535442650318,
-0.04218481108546257,
-0.011143799871206284,
-0.004013821016997099,
0.024903325363993645,
-0.060238081961870193,
0.026635708287358284,
0.015769848600029945,
0.03563178703188896,
-0.0012018646812066436,
-0.02554820105433464,
0.02952665276825428,
0.009042905643582344,
0.019423026591539383,
-0.013979654759168625,
-0.011962286196649075,
-0.05524208024144173,
-0.0322599932551384,
0.02150130830705166,
0.017029525712132454,
0.03506912663578987,
-0.01733781397342682,
0.07028960436582565,
0.0062830401584506035,
0.001232424285262823,
0.038839489221572876,
-0.048739392310380936,
0.04376323148608208,
-0.014219513162970543,
0.0013941606739535928,
0.01202574372291565,
-0.01364823617041111,
-0.012177160009741783,
-0.04450631141662598,
0.007953480817377567,
-0.013301239348948002,
0.056576624512672424,
-0.05851256102323532,
0.0531550869345665,
0.01778203807771206,
-0.009768407791852951,
0.006425816565752029,
-0.01744987443089485,
-0.02399279922246933,
0.015217486768960953,
-0.008416409604251385,
-0.004365206230431795,
-0.006941183470189571,
0.04573963209986687,
0.0013363789767026901,
0.018494615331292152,
0.008492005057632923,
0.018657024949789047,
0.04198659583926201,
0.04451419785618782,
0.012209247797727585,
0.021166197955608368,
-0.02403232268989086,
0.010526466183364391,
-0.040182843804359436,
0.017131173983216286,
0.03791365772485733,
0.013033779338002205,
0.06759459525346756,
-0.01795581541955471,
-0.0171456728130579,
-0.005470966920256615,
-0.0045648240484297276,
-0.010342040099203587,
0.00574073288589716,
0.026725977659225464,
0.02538030408322811,
0.010298948734998703,
0.04002595692873001,
-0.0004380774626042694,
0.0026243373285979033,
-0.0009416801040060818,
0.008197600953280926,
-0.06631655991077423,
-0.036454636603593826,
-0.008977781049907207,
-0.030805429443717003,
0.06994228065013885,
0.008676592260599136,
-0.04433576762676239,
0.040347982197999954,
-0.051293279975652695,
0.04435404762625694,
0.019328365102410316,
0.04462013021111488,
0.001984224421903491,
0.0702158510684967,
0.009939506649971008,
-0.004457309376448393,
0.000346078013535589,
0.011916105635464191,
0.10934381932020187,
0.024778887629508972,
0.016487201675772667,
-0.07081302255392075,
-0.01860123686492443,
-0.03659610450267792,
0.0038661507423967123,
-0.04211078956723213,
-0.01423448882997036,
-0.049368325620889664,
0.049193866550922394,
0.0457163080573082,
0.06695940345525742,
-0.0011758982436731458,
0.0116577735170722,
0.06917484849691391,
0.00032028532586991787,
-0.02070116624236107,
0.03265255317091942,
0.030151693150401115,
-0.019106155261397362,
0.02971227467060089,
-0.06755680590867996,
0.01703743450343609,
-0.04319770634174347,
-0.012427431531250477,
-0.029528629034757614,
-0.04030843451619148,
0.04807793349027634,
-0.019497286528348923,
-0.039075564593076706,
-0.008751433342695236,
0.039145056158304214,
-0.03709594905376434,
-0.03327212110161781,
0.022909073159098625,
0.043528515845537186,
-0.003783448599278927,
0.005438863765448332,
0.020024016499519348,
0.018257534131407738,
-0.031332649290561676,
-0.020788254216313362,
0.038364991545677185,
-0.035516638308763504,
-0.01009890902787447,
-0.0016117857303470373,
0.004747854545712471,
-0.0011509581236168742,
0.0332699753344059,
0.0019004449713975191,
0.027836928144097328,
-0.004510199185460806,
-0.021973103284835815,
-0.019997671246528625,
-0.00688827084377408,
0.01899496093392372,
-0.009070170111954212,
-0.04208755120635033,
-0.07112502306699753,
0.00755380280315876,
-0.01764359511435032,
0.020653950050473213,
-0.01638471893966198,
0.02268952690064907,
0.003382300026714802,
0.0015465016476809978,
-0.032189324498176575,
-0.026814520359039307,
-0.010752134956419468,
-0.0375254824757576,
0.009294391609728336,
-0.045298781245946884,
-0.030501991510391235,
0.03730551153421402,
0.03994122892618179,
0.031693827360868454,
0.0445476733148098,
-0.037315886467695236,
-0.002760171191766858,
-0.04546172916889191,
0.033984407782554626,
0.015695124864578247,
-0.03550667315721512,
-0.029856130480766296,
-0.0018294319743290544,
0.032550469040870667,
-0.024512961506843567,
0.01439598761498928,
0.03666451573371887,
-0.0029477032367140055,
0.032404880970716476,
0.012074706144630909,
-0.03845789283514023,
-0.01400106493383646,
0.01993539370596409,
0.02827952615916729,
0.014989089220762253,
0.018871458247303963,
0.03730449825525284,
0.016896173357963562,
0.003821905003860593,
0.022321591153740883,
0.02038935013115406,
-0.036804113537073135,
0.002765743527561426,
0.02572101727128029,
-0.015500119887292385,
-0.03528859093785286,
0.0061802370473742485,
0.02925235778093338,
0.007545303553342819,
-0.03862995281815529,
-0.01521600317209959,
0.004615408834069967,
-0.0014315602602437139,
0.0010890867561101913,
-0.05098821595311165,
0.022860877215862274,
0.014141231775283813,
-0.0008647020440548658,
-0.0313909649848938,
-0.007285189349204302,
-0.04415742680430412,
-0.0029604858718812466,
0.020361801609396935,
-0.007943634875118732,
-0.0025746244937181473,
0.029284922406077385,
-0.05198827013373375,
-0.003940148279070854,
0.049513861536979675,
0.018739473074674606,
0.007178383879363537,
0.02858561836183071,
0.008709645830094814,
-0.03560805693268776,
0.055211689323186874,
-0.027451081201434135,
-0.03529585525393486,
0.06543642282485962,
-0.028470739722251892,
-0.03125728666782379,
0.04492635279893875,
-0.008377906866371632,
0.026364143937826157,
0.05725445598363876,
-0.01860739290714264,
-0.011853925883769989,
0.09135068207979202,
-0.003777478588744998,
0.011886557564139366,
-0.03166988492012024,
0.0006907304050400853,
-0.00584933627396822,
0.04117962345480919,
-0.017124127596616745,
-0.05451032146811485,
-0.00816849060356617,
0.04635132849216461,
0.04054904356598854,
0.004488620441406965,
0.027260107919573784,
0.013032513670623302,
-0.039457231760025024,
0.000850897456984967,
0.032022178173065186,
0.02644585259258747,
0.01804736629128456,
0.03094184398651123,
-0.016073985025286674,
0.0405951552093029,
0.0022028700914233923,
-0.0238366536796093,
-0.10869148373603821,
-0.0036221847403794527,
-0.036068595945835114,
-0.026895834133028984,
0.01171521283686161,
-0.03468133881688118,
0.03762732446193695,
0.016931572929024696,
-0.055581968277692795,
-0.010325416922569275,
0.010288394056260586,
-0.04424963518977165,
-0.009504931047558784,
0.005377479363232851,
0.005190269555896521,
0.04235438257455826,
0.023424971848726273,
0.03223193436861038,
0.016499556601047516,
0.03569401055574417,
-0.020973486825823784,
-0.002035534242168069,
-0.005175051279366016,
0.051737818866968155,
0.01432863250374794,
0.003964101895689964,
0.06961420923471451,
-0.04325300082564354,
-0.02284855581820011,
0.033499278128147125,
0.005722277332097292,
0.014918304048478603,
0.004222892224788666,
0.002454184927046299,
-0.0015958731528371572,
0.0030174232088029385,
-0.004711268004029989,
-0.025089403614401817,
-0.007932804524898529,
0.06526300311088562,
0.020278971642255783,
0.020477311685681343,
-0.0441078320145607,
-0.05370572954416275,
0.004371455870568752,
-0.028699560090899467,
-0.05154822766780853,
0.02009936235845089,
-0.026161834597587585,
0.02417825162410736,
0.004131924826651812,
0.051195621490478516,
0.0055913617834448814,
-0.024034829810261726,
-0.03812281787395477,
-0.03820199519395828,
-0.010533732362091541,
0.024081621319055557,
0.015683535486459732,
-0.014194385148584843,
0.019849693402647972,
-0.006676247343420982,
-0.030394278466701508,
-0.013812138698995113,
0.0026019990909844637,
-0.030578738078475,
-0.07580488920211792,
-0.019673673436045647,
0.0035932031460106373,
0.0023068480659276247,
0.021997200325131416,
-0.002680625766515732,
-0.030882125720381737,
0.021849168464541435,
0.0026220118161290884,
0.029022637754678726,
0.020472317934036255,
-0.06853222846984863,
-0.017025303095579147,
-0.05016925185918808,
0.03360212221741676,
-0.021133391186594963,
-0.018214330077171326,
-0.0584738664329052,
-0.059561047703027725,
-0.014014537446200848,
0.04801993444561958,
0.06404642015695572,
-0.01896352507174015,
-0.013389400206506252,
0.019192447885870934,
-0.01370654720813036,
0.02697637863457203,
-0.05406661331653595,
-0.024798277765512466,
0.018377771601080894,
-0.0184917151927948,
-0.019132044166326523,
-0.03300384804606438,
-0.03885157033801079,
0.019959809258580208,
0.031873445957899094,
0.005831052083522081,
0.05962787941098213,
-0.04175097495317459,
-0.04733810946345329,
0.019199339672923088,
0.035531215369701385,
-0.007746283430606127,
0.05241885036230087,
-0.05645175650715828,
-0.006184256635606289,
0.019113443791866302,
-0.021535346284508705,
-0.04661552235484123,
0.057962022721767426,
-0.016328344121575356,
0.01186875905841589,
-0.0003570636617951095,
0.006838357076048851,
0.02193906344473362,
-0.023151854053139687,
0.011175998486578465,
0.012777091935276985,
0.002952389419078827,
0.007686000317335129,
0.05706220865249634,
-0.03574414178729057,
0.02133772522211075,
-0.020076248794794083,
0.01326395757496357,
-0.011213338002562523,
-0.002717574592679739,
-0.01637781597673893,
0.03939433768391609,
0.0124495979398489,
-0.0031670425087213516,
0.022695932537317276,
0.021525992080569267,
0.012965532019734383,
0.02218538522720337,
0.0009124874486587942,
0.025476720184087753,
-0.0409352146089077,
-0.038118090480566025,
0.011640354059636593,
-0.030448930338025093,
0.031096523627638817,
0.03938012942671776,
-0.010643435642123222,
0.07645706832408905,
-0.0021793763153254986,
0.02562263235449791,
0.0068268077448010445,
0.01309241633862257,
0.0031091165728867054,
-0.0010239181574434042,
-0.03432106971740723,
0.019004661589860916,
-0.029270894825458527,
0.006580589804798365,
-0.011016936041414738,
-0.01742221973836422,
0.041968561708927155,
-0.035800136625766754,
0.0065305414609611034,
-0.03467530757188797,
-0.016875850036740303,
-0.003419672604650259,
0.03240766003727913,
-0.019304461777210236,
-0.004418644122779369,
0.04055430367588997,
0.01247324701398611,
-0.019435780122876167,
-0.002908955793827772,
-0.008424730971455574,
-0.0324673168361187,
0.0128522589802742,
-0.06030016392469406,
0.008751055225729942,
-0.027709735557436943,
0.014642586931586266,
-0.037478458136320114,
-0.014275147579610348
] |
<p>The problem of the infinite resistor grid is very common. The solution for the resistance between any 2 nodes in an infinite resistor lattice is all over the internet.</p>
<p>My question is somewhat similar but more pragmatic.
If we had a grid that was very large but yet finite... Then what would be the average voltage drop across a given grid for a given current density?</p>
<p>For arguments sake, a grid in the region of say 4000 by 4000. Maybe it would be safe to assume an infinite grid(?)</p>
<p>Very interesting Q. Can anyone shed any light?</p> | 2,828 | [
0.006786809302866459,
0.004523925483226776,
0.007624661549925804,
-0.0155921196565032,
0.03720744699239731,
0.017122259363532066,
-0.02344856783747673,
-0.027402736246585846,
0.017033416777849197,
-0.01843138597905636,
0.0072200302965939045,
0.030816299840807915,
0.0628339946269989,
0.016813630238175392,
0.04183824732899666,
-0.01090232189744711,
-0.008537947200238705,
0.03340888023376465,
0.0059562865644693375,
-0.06787214428186417,
0.01791810616850853,
0.03538738191127777,
-0.002502435352653265,
-0.02624848298728466,
-0.03786926344037056,
0.01584363356232643,
0.0353449285030365,
-0.001966266194358468,
-0.00809311680495739,
0.04651501029729843,
0.00919403787702322,
-0.025697583332657814,
0.008932719938457012,
0.03234026953577995,
0.04659031331539154,
-0.02009953372180462,
-0.025115588679909706,
-0.061469681560993195,
0.0025046037044376135,
0.006729437503963709,
0.003823441918939352,
-0.011147565208375454,
-0.0031625162810087204,
0.04771718755364418,
-0.008794919587671757,
-0.001522555248811841,
0.002905686153098941,
-0.040296562016010284,
0.021142704412341118,
-0.08795354515314102,
0.044749047607183456,
0.0002636428689584136,
0.09325718879699707,
0.02695397660136223,
0.009726698510348797,
-0.0106043154373765,
0.050643663853406906,
0.06236308440566063,
-0.031807512044906616,
-0.02851937711238861,
-0.000032663981983205304,
0.0017908219015225768,
-0.010804636403918266,
-0.03081239014863968,
-0.020541297271847725,
0.027644863352179527,
-0.016599291935563087,
-0.04449500888586044,
0.0016300507122650743,
0.005763312801718712,
-0.011059856973588467,
0.023576956242322922,
0.000397950760088861,
0.004844477865844965,
0.023472171276807785,
0.028966441750526428,
0.018749643117189407,
-0.003699713386595249,
-0.00888355914503336,
0.02572840452194214,
-0.03428579121828079,
0.021243754774332047,
0.04535682126879692,
0.04295878857374191,
-0.020701047033071518,
-0.02557389810681343,
0.053839944303035736,
-0.020643530413508415,
0.0043503413908183575,
0.03591100126504898,
0.0001040199349517934,
0.02245664782822132,
0.014620835892856121,
0.0074534243904054165,
-0.04415039345622063,
0.022946797311306,
-0.012840396724641323,
0.07420564442873001,
0.012504232116043568,
-0.011504250578582287,
0.011979673989117146,
-0.028537234291434288,
-0.009595937095582485,
0.08739971369504929,
0.0038229443598538637,
-0.014085397124290466,
-0.010394641198217869,
0.010999755933880806,
-0.00796184316277504,
-0.022549564018845558,
-0.06366777420043945,
0.056236445903778076,
-0.029026150703430176,
0.022898316383361816,
0.03271971642971039,
-0.03038320504128933,
0.009605508297681808,
-0.03903403505682945,
0.01697660982608795,
0.04987189546227455,
0.014550527557730675,
-0.017838671803474426,
0.01895618624985218,
-0.012289635837078094,
-0.05284182354807854,
0.0557597391307354,
0.029494399204850197,
-0.014388306066393852,
-0.027086127549409866,
0.00965209398418665,
-0.020448632538318634,
0.005300541874021292,
-0.028017880395054817,
-0.0321236252784729,
0.058423466980457306,
-0.00944183673709631,
-0.04702247306704521,
-0.07718845456838608,
0.034585777670145035,
0.004709505941718817,
-0.03034396283328533,
-0.07204125076532364,
0.00576166994869709,
0.03260163962841034,
0.05340151861310005,
-0.01013240683823824,
-0.0010896027088165283,
0.00939431507140398,
0.0003636874898802489,
0.013760359957814217,
-0.026854554191231728,
-0.00850929319858551,
0.0004417858144734055,
-0.02756407856941223,
0.014192439615726471,
-0.0569101981818676,
0.034288786351680756,
0.035956382751464844,
0.015980659052729607,
0.0010459437035024166,
0.031169597059488297,
0.016229672357439995,
-0.02879294753074646,
0.010759426280856133,
-0.026073917746543884,
-0.022540461272001266,
0.078713558614254,
0.0003102943010162562,
0.03667096793651581,
0.003386715892702341,
-0.00040617864578962326,
0.01868378184735775,
0.00947925727814436,
0.0021824727300554514,
0.04681450501084328,
-0.012681449763476849,
-0.009424707852303982,
-0.015910759568214417,
0.005250365007668734,
0.00795526523143053,
-0.044481366872787476,
-0.0382777601480484,
0.00565379299223423,
-0.010934052057564259,
0.019760632887482643,
0.0440811812877655,
-0.024246077984571457,
-0.03256302326917648,
-0.033080872148275375,
-0.010155324824154377,
-0.031633660197257996,
-0.05255221202969551,
-0.009409905411303043,
-0.02487880177795887,
0.015088462270796299,
-0.007876293733716011,
-0.0024746363051235676,
0.009337155148386955,
-0.02591288834810257,
-0.016302913427352905,
-0.03675515949726105,
0.0007202135166153312,
0.014387333765625954,
-0.029145127162337303,
0.016153471544384956,
0.027154922485351562,
0.027357306331396103,
-0.014324788935482502,
0.039900586009025574,
-0.049637116491794586,
-0.05582946538925171,
-0.014611653052270412,
-0.038706712424755096,
0.04885602369904518,
0.01779896579682827,
-0.015329130925238132,
0.005963819567114115,
0.00028527717222459614,
-0.012863441370427608,
0.03817231208086014,
-0.03778199851512909,
0.06999802589416504,
0.044344712048769,
0.051149606704711914,
-0.04344074800610542,
0.02081996016204357,
-0.002278244821354747,
-0.04256093129515648,
-0.03277715668082237,
0.01176910474896431,
-0.07144905626773834,
0.03641567379236221,
0.06737206876277924,
0.005949326325207949,
-0.020838424563407898,
0.02308833971619606,
0.03971560671925545,
0.04817109555006027,
0.03722149133682251,
0.0045582931488752365,
-0.013016780838370323,
-0.0005467850132845342,
0.020467747002840042,
0.03297648951411247,
0.024359604343771935,
0.009925785474479198,
-0.013141498900949955,
0.0413951575756073,
-0.006314163561910391,
-0.011986036784946918,
-0.019559737294912338,
0.03131621330976486,
0.021366070955991745,
0.03769848868250847,
-0.010225596837699413,
-0.028010601177811623,
0.030085232108831406,
-0.015926135703921318,
-0.010341884568333626,
0.0010563748655840755,
-0.006593648344278336,
0.018277570605278015,
-0.014122093096375465,
-0.027833545580506325,
0.02813383936882019,
0.021318353712558746,
-0.04531775787472725,
-0.027303479611873627,
0.017309587448835373,
-0.019338402897119522,
0.03435157611966133,
-0.044223375618457794,
0.020793134346604347,
-0.027448482811450958,
-0.013623569160699844,
-0.0012318152002990246,
0.011436978355050087,
-0.004916433710604906,
-0.0324106439948082,
-0.035405233502388,
-0.00047357246512547135,
-0.024378901347517967,
0.014236323535442352,
0.01426148135215044,
-0.02336221933364868,
0.0026515971403568983,
-0.0027093039825558662,
-0.07854749262332916,
0.04541143402457237,
0.023071587085723877,
0.014582390896975994,
0.02014261670410633,
-0.004224709700793028,
-0.0652826577425003,
0.009283814579248428,
-0.01642744243144989,
0.03883048892021179,
-0.04482725262641907,
0.00015184597577899694,
0.05967685952782631,
-0.011507850140333176,
-0.05625725910067558,
0.014828513376414776,
-0.03707210347056389,
-0.073760487139225,
-0.02279561758041382,
-0.006505401339381933,
-0.0033660177141427994,
-0.028198054060339928,
0.03606127202510834,
0.022097047418355942,
-0.045187488198280334,
-0.04505521431565285,
-0.030796896666288376,
-0.05004868656396866,
0.01773468218743801,
-0.023210149258375168,
0.0627419501543045,
0.003874276066198945,
-0.03673289716243744,
0.10073205083608627,
0.021396879106760025,
-0.018184833228588104,
-0.004432980902493,
-0.05600685998797417,
0.021121950820088387,
0.005371957551687956,
0.031847644597291946,
0.04309704527258873,
-0.0193021297454834,
0.007575373165309429,
0.035414919257164,
0.022852173075079918,
0.022969579324126244,
0.00526050291955471,
0.010622299276292324,
0.017116820439696312,
0.014964836649596691,
-0.012014786712825298,
0.060317859053611755,
0.014053267426788807,
-0.016202423721551895,
-0.004022463224828243,
-0.00002118303564202506,
0.009162912145256996,
0.019813958555459976,
-0.06603681296110153,
0.022904831916093826,
-0.037713851779699326,
0.01397765427827835,
-0.022775806486606598,
0.018925651907920837,
0.0077154869213700294,
0.010166916996240616,
0.0010000203037634492,
0.05329088121652603,
0.053948547691106796,
-0.017626939341425896,
-0.009783545508980751,
-0.009075472131371498,
0.04979889094829559,
-0.02300122007727623,
-0.03820189833641052,
0.0011714689899235964,
-0.02476165071129799,
-0.005130311008542776,
-0.00028657971415668726,
-0.04272128641605377,
0.05168036371469498,
0.03552251309156418,
0.0011812070151790977,
0.035961706191301346,
-0.011907385662198067,
0.01851656474173069,
-0.07783082127571106,
-0.027110759168863297,
-0.01887674070894718,
0.04156448692083359,
0.02819547802209854,
0.02897985838353634,
-0.011337975971400738,
0.019821640104055405,
0.01758148893713951,
0.03921912610530853,
-0.07923464477062225,
-0.016150306910276413,
-0.05253588408231735,
-0.009304664097726345,
-0.029947170987725258,
-0.007037082687020302,
0.0029820397030562162,
0.03503089398145676,
-0.022950896993279457,
-0.016632987186312675,
-0.0020309025421738625,
-0.06963150948286057,
0.017778759822249413,
0.020466398447752,
0.007135814521461725,
-0.056916479021310806,
0.03239096328616142,
0.04107147827744484,
-0.021329645067453384,
0.033765554428100586,
-0.011633845046162605,
-0.019549954682588577,
-0.04901905730366707,
-0.025321776047348976,
0.015407744795084,
0.005007451865822077,
0.0009773512138053775,
0.04613661393523216,
0.021869011223316193,
-0.027906864881515503,
-0.005109178368002176,
-0.023595577105879784,
0.05446361377835274,
0.0025095241144299507,
-0.013004058040678501,
0.02192787267267704,
-0.06314649432897568,
0.007290444802492857,
0.01911589689552784,
0.03533380478620529,
-0.02212441712617874,
0.009891155175864697,
0.01980111002922058,
0.01867741346359253,
-0.026371022686362267,
0.02699776366353035,
0.03909255191683769,
0.01797657459974289,
-0.015485418029129505,
-0.02563702128827572,
-0.012609481811523438,
-0.012123788706958294,
0.031808461993932724,
0.05073893070220947,
0.0011500532273203135,
0.00569929089397192,
0.001568811247125268,
0.034804537892341614,
0.031446754932403564,
-0.01738382689654827,
0.034307848662137985,
0.005696085747331381,
0.02170712873339653,
-0.008249888196587563,
0.019135581329464912,
0.011050297878682613,
-0.011099609546363354,
0.0395866297185421,
0.009835563600063324,
-0.011192887090146542,
-0.0911685898900032,
-0.01861884631216526,
0.03351563215255737,
0.03837760537862778,
0.012015439569950104,
-0.018933508545160294,
-0.040962863713502884,
-0.02441055327653885,
0.08408892154693604,
-0.010718168690800667,
0.007938246242702007,
-0.010101995430886745,
-0.028780261054635048,
-0.011242569424211979,
-0.042238641530275345,
0.024504143744707108,
0.0025919002946466208,
0.03981173783540726,
0.03212231770157814,
-0.0032146903686225414,
-0.01369612105190754,
0.019478753209114075,
0.03981349989771843,
0.04319736361503601,
0.06929738819599152,
0.0396527424454689,
0.02859271690249443,
-0.0023013909813016653,
0.027792783454060555,
-0.007119143847376108,
-0.07900799065828323,
0.03932587057352066,
0.0010868208482861519,
0.013487056829035282,
0.05082396790385246,
-0.023234833031892776,
-0.041260797530412674,
0.03549030050635338,
0.01683906652033329,
-0.009506753645837307,
0.0046335384249687195,
-0.024621590971946716,
0.053266964852809906,
0.06195222958922386,
-0.011955082416534424,
0.06497148424386978,
0.026444215327501297,
-0.012794386595487595,
-0.010077903047204018,
-0.0014625117182731628,
0.009352297522127628,
-0.031138921156525612,
0.003947962541133165,
-0.01122696790844202,
-0.01248734537512064,
-0.011387782171368599,
0.03343479707837105,
-0.015160651877522469,
0.0401180274784565,
-0.01149639394134283,
-0.043017033487558365,
0.02443019114434719,
0.0014278815360739827,
0.005533793941140175,
0.007442480884492397,
-0.04179199039936066,
0.030003296211361885,
0.008844130672514439,
-0.047270819544792175,
0.004875941667705774,
-0.006523032207041979,
0.046907152980566025,
0.017604758962988853,
-0.011832166463136673,
-0.0011009296867996454,
-0.05101601779460907,
-0.002470801817253232,
0.0007903777295723557,
-0.011789755895733833,
0.10064834356307983,
-0.005892256274819374,
0.022116418927907944,
0.03045412339270115,
-0.04061316326260567,
-0.059020768851041794,
0.004094699863344431,
0.019806263968348503,
0.03354992717504501,
-0.05186723172664642,
0.03229285404086113,
-0.01290037389844656,
0.032190676778554916,
-0.08136767148971558,
-0.06317365914583206,
0.04614948853850365,
0.034114133566617966,
0.01728830672800541,
-0.01839805208146572,
-0.031249692663550377,
-0.021797113120555878,
-0.03911687061190605,
0.04874719679355621,
0.04933817312121391,
-0.014278411865234375,
-0.0008512004278600216,
0.0077384770847857,
0.021175852045416832,
0.05858300253748894,
0.009625423699617386,
-0.013542070053517818,
0.033597417175769806,
-0.06514063477516174,
-0.0026521545369178057,
-0.03732803836464882,
0.05841974914073944,
-0.04379627853631973,
-0.003976958338171244,
-0.0126102389767766,
-0.03198501840233803,
0.06504929065704346,
-0.03834424167871475,
-0.009260052815079689,
0.028700878843665123,
-0.01622186042368412,
0.01678859442472458,
0.0019347791094332933,
-0.0000730212705093436,
-0.01907842792570591,
0.010481994599103928,
0.020117735490202904,
-0.040136415511369705,
-0.027846243232488632,
-0.006851130165159702,
-0.0013378080911934376,
0.03647799789905548,
-0.006380115635693073,
-0.004069505725055933,
0.07360716164112091,
-0.036662373691797256,
-0.027724342420697212,
0.04466903582215309,
-0.023358812555670738,
0.010686060413718224,
-0.022401312366127968,
0.006053296849131584,
0.04605957120656967,
-0.009190290234982967,
-0.02951035276055336,
-0.07619648426771164,
-0.03720739483833313,
0.011189219541847706,
0.034740302711725235,
-0.028867661952972412,
0.004408237524330616,
-0.020068569108843803,
-0.010476827621459961,
-0.009450891055166721,
-0.00537830637767911,
0.0061106509529054165,
0.0357724130153656,
-0.015494242310523987,
0.05053844302892685,
-0.034779250621795654,
-0.011896217241883278,
0.027386261150240898,
0.000590417708735913,
-0.013398479670286179,
0.0347696989774704,
0.0008825548575259745,
0.0049257478676736355,
0.024439707398414612,
-0.010479222051799297,
-0.00531726935878396,
0.015733707696199417,
-0.05343632772564888,
0.013780368492007256,
-0.022726736962795258,
-0.01201676670461893,
0.056366272270679474,
-0.004182575270533562,
-0.012406596913933754,
-0.020680299028754234,
-0.01130579598248005,
-0.0022503335494548082,
-0.009248523972928524,
0.031137896701693535,
0.0134699996560812,
0.008332296274602413,
0.04428354278206825,
0.007923888973891735,
-0.0012503749458119273,
-0.003339051501825452,
-0.023624170571565628,
-0.060138314962387085,
0.0027731063310056925,
-0.014407244510948658,
-0.10363684594631195,
0.03201157599687576,
0.042541440576314926,
-0.026248665526509285,
0.008266945369541645,
-0.025370163843035698,
0.018951822072267532,
0.016043437644839287,
0.029700493440032005,
-0.04244010150432587,
0.08242764323949814,
0.0018752418691292405,
0.08414419740438461,
-0.00023504772980231792,
-0.002930204151198268,
0.09136827290058136,
0.04653586074709892,
0.013107439503073692,
-0.07143682986497879,
0.027986755594611168,
-0.0021585277281701565,
0.004633134696632624,
-0.0456484779715538,
-0.027446450665593147,
-0.01018027774989605,
-0.004860066343098879,
0.033340007066726685,
0.024986205622553825,
-0.010091880336403847,
-0.009894674643874168,
0.03164698928594589,
-0.022861944511532784,
-0.02146163024008274,
0.030226493254303932,
0.04647333547472954,
-0.0011566572356969118,
0.006329117342829704,
-0.06332317739725113,
0.03810052201151848,
-0.010127564892172813,
0.0008903604466468096,
-0.04335079714655876,
0.024099405854940414,
0.03259509056806564,
-0.015703575685620308,
-0.019484827294945717,
-0.006062647793442011,
0.031068366020917892,
-0.058902475982904434,
-0.01667683757841587,
0.0186521764844656,
0.011533180251717567,
0.009893802925944328,
0.01379361655563116,
0.03760945424437523,
-0.0005084304721094668,
-0.008395180106163025,
0.02665676362812519,
0.010486409068107605,
-0.018040556460618973,
-0.033967263996601105,
-0.02567264810204506,
0.027899177744984627,
-0.022332971915602684,
0.004593509249389172,
0.03569655492901802,
0.025341911241412163,
0.0007325963815674186,
-0.03906063362956047,
-0.03038439154624939,
-0.01289439294487238,
0.03795390948653221,
-0.019588269293308258,
-0.03146784380078316,
0.007821678183972836,
0.05355716496706009,
-0.03319671005010605,
0.007412311155349016,
-0.023347027599811554,
-0.021114524453878403,
-0.03306502103805542,
-0.0013820230960845947,
0.05727219581604004,
0.012757194228470325,
-0.05779305472970009,
-0.041144028306007385,
-0.00374599895440042,
-0.021290604025125504,
-0.03560682758688927,
-0.006303042639046907,
0.018059493973851204,
0.03557659313082695,
0.0021182552445679903,
-0.016972243785858154,
0.01805047132074833,
-0.057693369686603546,
0.021469417959451675,
0.00191014155279845,
0.010988048277795315,
-0.03970171883702278,
0.010387366637587547,
0.007977725006639957,
0.0211611520498991,
-0.0254739411175251,
-0.0026303683407604694,
0.009118893183767796,
0.03792042285203934,
0.03170115500688553,
-0.007695301435887814,
-0.001366327633149922,
-0.010904583148658276,
-0.057130083441734314,
0.028896192088723183,
0.011628411710262299,
0.04100430756807327,
-0.002713196910917759,
0.0013385628117248416,
0.011927297338843346,
0.02815442718565464,
-0.02718452736735344,
-0.0004261195717845112,
0.012127929367125034,
-0.04353442043066025,
0.022978244349360466,
0.01720069721341133,
0.00840636808425188,
0.0013354831608012319,
-0.005397325847297907,
-0.017946608364582062,
-0.013722100295126438,
0.0014453176409006119,
-0.0005988346529193223,
-0.034191545099020004,
-0.02275364100933075,
-0.052585359662771225,
-0.008496076799929142,
-0.00833179708570242,
-0.023298034444451332,
-0.0038393186405301094,
-0.045561566948890686,
-0.011596913449466228,
0.03089294582605362,
0.007347217295318842,
0.007424279116094112,
-0.016223469749093056,
-0.006718870718032122,
0.004012806806713343,
0.019574185833334923,
-0.03350146487355232,
-0.001672597834840417,
-0.030127424746751785,
0.02422354556620121,
-0.00021141523029655218,
-0.05759113281965256,
-0.045915983617305756,
0.09282296150922775,
-0.019081855192780495,
-0.0063937450759112835,
0.009469474665820599,
-0.029957685619592667,
0.042870670557022095,
0.012846343219280243,
-0.026538308709859848,
-0.04705940559506416,
0.058698251843452454,
-0.0017669695662334561,
-0.007348946761339903,
-0.014025688171386719,
-0.0257247481495142,
0.01427279133349657,
0.019387399777770042,
-0.019991083070635796,
-0.02092006802558899,
-0.00011096350499428809,
0.009038667194545269,
0.02296600677073002,
-0.039632368832826614,
0.008698410354554653,
0.03865779563784599,
0.0049628871493041515,
0.011433507315814495,
-0.009124158881604671,
0.014719812199473381,
-0.005073442589491606,
0.05176489055156708,
-0.03644376993179321,
0.009410005062818527,
-0.029075734317302704,
-0.023831572383642197,
-0.0757688581943512,
0.013421118259429932,
0.02787277102470398,
0.011696248315274715,
0.017724568024277687,
-0.052977290004491806,
-0.024926993995904922,
0.0247217807918787,
-0.09830022603273392,
-0.001734864548780024,
0.005566814448684454,
-0.021906765177845955,
-0.026203446090221405,
-0.05980115756392479,
-0.004416805692017078,
0.046068016439676285,
0.027764253318309784,
0.0450766496360302,
0.009472117759287357,
0.010884199291467667,
-0.0067134215496480465,
-0.0188902597874403,
0.001723085530102253,
0.024745242670178413,
-0.033345624804496765,
0.015905477106571198,
0.015131877735257149,
-0.03241622820496559,
0.004697894211858511,
0.016792843118309975,
-0.0036959515418857336,
0.013549442403018475,
0.015605985186994076,
0.020253224298357964,
-0.005410788115113974,
0.07242465019226074,
-0.010271569713950157,
-0.015779435634613037,
0.00455844821408391,
-0.0010782076278701425,
0.008391886949539185,
0.0031291390769183636,
-0.029619313776493073,
0.008890626952052116,
0.028915036469697952,
0.008378373458981514,
-0.02458888851106167,
0.021872907876968384,
-0.02276911400258541,
-0.02636478841304779,
-0.0007336590788327157,
-0.008192374370992184,
0.05963250994682312,
-0.00583544559776783,
-0.009830608032643795,
-0.018587008118629456,
-0.046186674386262894,
0.03374733403325081,
-0.010090160183608532,
0.03514811769127846,
0.04106391593813896,
-0.023868117481470108,
-0.038500748574733734,
0.023731844499707222,
-0.007285035215318203,
-0.015549132600426674,
-0.08275894820690155,
-0.02680947072803974,
-0.019269248470664024,
-0.00040749492472968996,
0.03905279189348221,
-0.024167004972696304,
-0.01848350465297699,
-0.006682666018605232,
0.02003072388470173,
0.02098591811954975,
-0.013525493443012238,
-0.002393664326518774,
0.0058777304366230965,
-0.048193175345659256,
0.04555237293243408,
-0.012191095389425755,
-0.002097571734338999,
-0.012129679322242737,
-0.04808236286044121,
-0.00873005110770464,
-0.00621360307559371,
0.062312327325344086,
0.010153013281524181,
-0.014756463468074799,
-0.008745215833187103,
0.0019681304693222046,
0.04020846635103226,
-0.06676735728979111,
0.00956764630973339,
-0.012053970247507095,
-0.023239005357027054,
-0.029643464833498,
-0.014033113606274128,
0.015853924676775932,
-0.006677558645606041,
0.010994070209562778,
0.009702743031084538,
-0.005178301595151424,
-0.032660942524671555,
0.0017338444013148546,
0.02657160349190235,
0.0032727743964642286,
-0.008973567746579647,
0.07726041227579117,
-0.038877345621585846,
0.02594856172800064,
-0.008765512146055698,
0.0124026695266366,
-0.028057971969246864,
0.02888679876923561,
-0.026850702241063118,
0.020258527249097824,
-0.0007204479188658297,
0.032032813876867294,
-0.003387204837054014,
-0.049095042049884796,
-0.025081409141421318,
0.02781043015420437,
-0.06124211102724075,
-0.012974288314580917,
0.0666794404387474,
-0.021389266476035118,
0.05767422169446945,
-0.014596926979720592,
-0.005750033538788557,
0.01714327372610569,
0.023774290457367897,
-0.006190444342792034,
-0.007928493432700634,
0.020796140655875206,
0.009614584967494011,
0.011101353913545609,
0.0656035989522934,
-0.030982833355665207,
0.03741050884127617,
0.0005188380600884557,
-0.00848802737891674,
-0.04463956132531166,
-0.0413789227604866,
0.013147451914846897,
-0.020845331251621246,
-0.008083065040409565,
0.021691223606467247,
-0.03157608583569527,
0.1058070957660675,
0.04725559055805206,
-0.003652432933449745,
-0.018514910712838173,
-0.01839219592511654,
-0.013420270755887032,
0.008359387516975403,
-0.0044194054789841175,
0.05213886499404907,
-0.03595392405986786,
-0.002926662564277649,
0.004894627258181572,
0.037725090980529785,
0.042014963924884796,
-0.06758613139390945,
0.0513024739921093,
-0.03698541224002838,
0.0059379213489592075,
-0.009869500994682312,
0.025159765034914017,
-0.03271430358290672,
-0.01470995880663395,
0.043235041201114655,
0.032951224595308304,
0.029790855944156647,
0.03618652746081352,
0.0015628139954060316,
0.016915353015065193,
0.0652209147810936,
-0.03687301278114319,
-0.006245875731110573,
-0.051157157868146896,
0.0023570749908685684,
0.04129983112215996,
0.008166790939867496
] |
<p>Question:
A bungee jumper jumps from a bridge. The length of the loose rope is 30 m. When the jumper reach the lowest point possible, the rope stretches 10 m. What is the final stretch of the rope, when the oscillation of the rope stops? Mechanical energy loss is null. Hook law applies for the elastic.</p>
<p>I think this problem is unsolvable, because we need mass or the coefficient of the rope?</p> | 2,829 | [
-0.056847650557756424,
0.0008592138765379786,
-0.040377046912908554,
-0.011562447994947433,
0.007260741665959358,
0.006669029127806425,
-0.046876437962055206,
-0.04352329671382904,
-0.002957957563921809,
-0.02397511526942253,
0.018720708787441254,
0.0211014524102211,
-0.0063689397647976875,
0.038475632667541504,
0.045580409467220306,
0.001122495625168085,
0.007293360773473978,
-0.020549459382891655,
0.012889754958450794,
-0.038186319172382355,
-0.02837991714477539,
-0.014120462350547314,
0.004148127976804972,
0.014435936696827412,
-0.005674510728567839,
-0.0025158259086310863,
0.05272549018263817,
-0.01789630763232708,
-0.011940845288336277,
0.054250750690698624,
0.02133672498166561,
-0.02315007895231247,
-0.02276667393743992,
0.016137413680553436,
0.02821521833539009,
0.03725723922252655,
-0.03705480694770813,
-0.036481041461229324,
-0.01828179694712162,
0.014798270538449287,
0.010402051731944084,
-0.016246579587459564,
-0.016007352620363235,
0.052405063062906265,
-0.04348199814558029,
0.03829261288046837,
-0.011432209983468056,
-0.01730004884302616,
0.051149915903806686,
-0.025564828887581825,
0.060371823608875275,
-0.00480326171964407,
0.013007300905883312,
-0.018732141703367233,
-0.01917836256325245,
-0.021313050761818886,
0.05569625645875931,
0.05057213827967644,
-0.026708681136369705,
-0.052545540034770966,
-0.039186686277389526,
-0.052936896681785583,
-0.05068344622850418,
-0.0026755707804113626,
-0.025177862495183945,
0.003126421244814992,
-0.04385588690638542,
0.008702846243977547,
0.03506634756922722,
-0.03124639019370079,
-0.035952821373939514,
-0.00903679896146059,
0.04223852604627609,
0.011874031275510788,
0.04160097986459732,
0.0018146809889003634,
0.01350286602973938,
0.0006086500943638384,
0.05757799372076988,
0.07362678647041321,
-0.019487960264086723,
-0.014366506598889828,
0.060137249529361725,
0.07446154206991196,
0.008593391627073288,
-0.04634828865528107,
0.0701574981212616,
0.008526798337697983,
0.0032224548049271107,
0.018276168033480644,
-0.005983147770166397,
-0.0036010018084198236,
-0.002092871116474271,
0.008294141851365566,
0.018913574516773224,
0.05139763653278351,
-0.0038172584027051926,
0.06564953923225403,
0.0308508463203907,
-0.030100181698799133,
0.012525212951004505,
-0.00984891876578331,
0.04152734950184822,
0.08368297666311264,
-0.016577882692217827,
0.011888047680258751,
-0.01210938859730959,
-0.013886808417737484,
-0.0038122953847050667,
-0.03633831441402435,
-0.027052422985434532,
-0.0021768517326563597,
0.0077317035757005215,
-0.03664444014430046,
-0.009475604631006718,
-0.0425051674246788,
0.03442544490098953,
0.007401883602142334,
0.027353154495358467,
0.023793501779437065,
0.021568376570940018,
-0.014977219514548779,
0.028145572170615196,
-0.009497850202023983,
-0.025338811799883842,
-0.0022946842946112156,
0.047606952488422394,
-0.03269067034125328,
-0.03147607669234276,
0.03799537569284439,
-0.012542390264570713,
0.011968745850026608,
-0.025504719465970993,
-0.01690886728465557,
0.045577120035886765,
-0.023778194561600685,
-0.08916934579610825,
-0.04976867884397507,
0.03941219300031662,
0.005411982070654631,
-0.012957083061337471,
-0.03472106158733368,
0.019441956654191017,
0.020695790648460388,
0.07226258516311646,
0.0040481737814843655,
0.015248492360115051,
0.010752315632998943,
0.01370334718376398,
-0.01567542739212513,
0.01840689592063427,
0.0016577222850173712,
-0.008328583091497421,
0.018828002735972404,
-0.017070947214961052,
-0.047154221683740616,
-0.030738169327378273,
0.027420761063694954,
-0.01087171770632267,
-0.025767631828784943,
0.03924145549535751,
-0.007560694590210915,
0.03303825110197067,
-0.0068651526235044,
-0.02785649336874485,
-0.048593632876873016,
0.11071034520864487,
0.005980753805488348,
0.002505136653780937,
0.017688602209091187,
0.034408021718263626,
0.006963400635868311,
0.001350244041532278,
0.006610515061765909,
0.029636507853865623,
-0.0724286288022995,
-0.005550290923565626,
-0.02227712981402874,
-0.007817842997610569,
0.012407838366925716,
-0.035703934729099274,
-0.039093125611543655,
-0.015227243304252625,
-0.032257746905088425,
-0.007506853435188532,
0.003134154248982668,
-0.0236190352588892,
0.03582194074988365,
0.020602157339453697,
-0.024149103090167046,
-0.0017188965575769544,
-0.05750191956758499,
0.03320774808526039,
0.024628669023513794,
0.03563627973198891,
0.019876569509506226,
0.008553923107683659,
0.0037208120338618755,
-0.05215071514248848,
-0.0034918643068522215,
0.000017260730601265095,
0.047116633504629135,
-0.009589703753590584,
0.0095179732888937,
0.017565451562404633,
0.0516352541744709,
0.05176983028650284,
0.020423756912350655,
0.017196666449308395,
-0.012515418231487274,
-0.016565442085266113,
0.031261030584573746,
-0.038120124489068985,
0.03219510614871979,
-0.008495381101965904,
0.04343174770474434,
0.0580931194126606,
-0.02047216147184372,
0.011400624178349972,
0.04519413039088249,
0.00034494404098950326,
0.06493318825960159,
0.055625781416893005,
0.036438990384340286,
0.019926585257053375,
0.011111675761640072,
-0.04410921037197113,
0.04571055248379707,
0.01591675356030464,
-0.04116937890648842,
-0.01473312359303236,
0.0012222161749377847,
-0.003434960963204503,
0.02800869755446911,
-0.030153688043355942,
-0.007585286628454924,
0.022509489208459854,
0.025093408301472664,
0.02102053537964821,
0.02687987871468067,
-0.017020942643284798,
-0.021488897502422333,
0.0029634430538862944,
0.009654131717979908,
-0.029215849936008453,
0.01276237890124321,
0.003275623545050621,
0.04802451282739639,
0.005797180812805891,
-0.03812083974480629,
-0.009367295540869236,
0.021390436217188835,
0.030488500371575356,
0.0058507840149104595,
0.013680199161171913,
-0.02515244483947754,
0.01689363829791546,
-0.056794896721839905,
0.030989525839686394,
0.046922650188207626,
-0.01035820972174406,
0.033273644745349884,
-0.012295049615204334,
-0.009788515977561474,
0.01968379132449627,
0.01454495545476675,
-0.007567005231976509,
-0.016020404174923897,
0.03185747563838959,
-0.04675440490245819,
-0.016043035313487053,
-0.026114683598279953,
-0.00785509217530489,
-0.017557624727487564,
0.004890374839305878,
0.033081915229558945,
-0.018794840201735497,
0.038145486265420914,
-0.04065430164337158,
-0.015528535470366478,
-0.006348173134028912,
-0.051139816641807556,
0.027817532420158386,
-0.013395430520176888,
-0.02125316485762596,
0.010020443238317966,
-0.010523272678256035,
-0.04833247885107994,
0.06962619721889496,
0.033958956599235535,
-0.007863570936024189,
0.0456172414124012,
0.013973116874694824,
0.013421637937426567,
-0.006432566791772842,
-0.0004725565086118877,
0.036478303372859955,
-0.02511170320212841,
0.006368726957589388,
0.04772128164768219,
0.03610756993293762,
-0.009811225347220898,
0.053123459219932556,
-0.0836675688624382,
-0.07371389120817184,
-0.024142013862729073,
0.019742373377084732,
0.04904097691178322,
-0.009201018139719963,
0.06382619589567184,
0.008019855245947838,
-0.0033953741658478975,
-0.011576028540730476,
-0.06635942310094833,
-0.08093221485614777,
0.00864333100616932,
-0.014767160639166832,
0.033910032361745834,
0.001962679671123624,
-0.019657766446471214,
0.07004684954881668,
0.015296095982193947,
-0.025178110226988792,
-0.036669254302978516,
-0.002598777413368225,
0.03389698266983032,
-0.007966138422489166,
0.0018525667255744338,
0.010280405171215534,
-0.010218612849712372,
0.010715773329138756,
0.0012542230542749166,
0.015968911349773407,
0.018056878820061684,
0.015644347295165062,
0.01690843142569065,
-0.0002275649458169937,
0.02160038612782955,
0.005102712195366621,
0.05016607046127319,
0.008160727098584175,
-0.021116338670253754,
0.03146577626466751,
-0.013636808842420578,
0.07579545676708221,
-0.0005440383101813495,
-0.07170276343822479,
0.05485769733786583,
0.0009042947203852236,
0.020059768110513687,
0.016608379781246185,
0.03025204688310623,
0.02046472579240799,
-0.061256349086761475,
0.024518609046936035,
0.040206119418144226,
0.02494787983596325,
-0.018346473574638367,
-0.008278125897049904,
0.03458250313997269,
0.04023651033639908,
-0.01723291352391243,
-0.061145246028900146,
-0.04125657305121422,
0.01901412568986416,
0.04899103567004204,
-0.017824172973632812,
-0.04842836409807205,
0.01831856183707714,
0.023563925176858902,
0.05561905354261398,
-0.01727866940200329,
-0.06190672516822815,
0.0070190648548305035,
-0.025952136144042015,
-0.032704807817935944,
0.018869802355766296,
0.03253469988703728,
-0.01903090626001358,
0.01677817478775978,
0.024368900805711746,
0.07425811141729355,
0.03811696916818619,
0.0521240197122097,
-0.09536154568195343,
0.03778566047549248,
-0.05611511319875717,
-0.008774979040026665,
0.03484004735946655,
0.020848209038376808,
0.034581344574689865,
0.005507812835276127,
0.025003599002957344,
0.0131112951785326,
0.027548765763640404,
-0.05652380734682083,
0.01104532741010189,
-0.02927306666970253,
-0.03361700475215912,
0.03271206095814705,
-0.03770430386066437,
0.03403390571475029,
-0.00310242990963161,
0.028181569650769234,
0.031420595943927765,
0.000032174339139601216,
-0.006978875491768122,
-0.02567472495138645,
-0.0025816094130277634,
-0.04176495969295502,
0.013184751383960247,
0.009051783941686153,
0.04087613523006439,
0.010116682387888432,
0.010374356061220169,
0.00519175361841917,
0.06500066071748734,
-0.014204838313162327,
-0.0022988426499068737,
-0.008117280900478363,
-0.08260153234004974,
-0.006538883782923222,
-0.01024963054805994,
0.04958603158593178,
0.001428077812306583,
-0.011697174981236458,
0.04356331378221512,
0.0036778440698981285,
-0.02725541591644287,
0.05640615150332451,
0.015290586277842522,
0.03971141576766968,
-0.010270897299051285,
0.009571302682161331,
-0.007326977327466011,
-0.057610660791397095,
-0.02375529333949089,
0.007096397690474987,
-0.014201379381120205,
-0.020818550139665604,
0.008857731707394123,
0.07309170812368393,
0.042797405272722244,
-0.02054818719625473,
-0.006071978714317083,
-0.02125074714422226,
0.039126019924879074,
-0.03153375908732414,
-0.024780042469501495,
0.01592494361102581,
-0.015345773659646511,
0.022561395540833473,
-0.010987128131091595,
-0.0007546894485130906,
-0.06507668644189835,
-0.020684026181697845,
0.014881299808621407,
0.03387437015771866,
-0.02291104942560196,
-0.026822393760085106,
-0.07687049359083176,
-0.019281763583421707,
-0.006618911866098642,
-0.037861306220293045,
0.020401496440172195,
-0.013468971475958824,
0.052510157227516174,
0.0036607393994927406,
-0.010799618437886238,
-0.002252915408462286,
-0.026914723217487335,
0.001889976323582232,
0.02064625173807144,
-0.020346809178590775,
0.005250096321105957,
0.009108534082770348,
0.034748468548059464,
0.008325998671352863,
0.06416331231594086,
0.011355064809322357,
-0.028513388708233833,
0.015653055161237717,
0.012299055233597755,
0.000325025524944067,
-0.09828464686870575,
-0.0068081459030508995,
0.025652606040239334,
-0.0313371866941452,
0.011014130897819996,
-0.018766332417726517,
-0.04351364076137543,
0.01401963084936142,
0.0035106309223920107,
-0.02009248547255993,
0.029417313635349274,
-0.019997840747237206,
0.012535578571259975,
0.011810985393822193,
-0.020260851830244064,
0.01910284347832203,
0.06870345026254654,
-0.029671069234609604,
0.001860502059571445,
-0.0021516031119972467,
0.03329257294535637,
-0.02070428803563118,
0.004521680995821953,
-0.030815478414297104,
0.020448753610253334,
-0.025599228218197823,
0.03064432553946972,
-0.02892884984612465,
0.006312445271760225,
-0.03809334710240364,
-0.03143566474318504,
0.040397342294454575,
0.029044903814792633,
0.013949437998235226,
0.01778295263648033,
0.03239106759428978,
-0.0022014507558196783,
-0.0023325332440435886,
-0.010248426347970963,
-0.02054533362388611,
0.01381758227944374,
-0.014429017901420593,
0.02340267412364483,
-0.020166128873825073,
0.000872545875608921,
-0.03516155108809471,
-0.01406661607325077,
0.049347128719091415,
-0.049786511808633804,
0.008396082557737827,
-0.003878171555697918,
-0.019336877390742302,
0.014715910889208317,
-0.0032409452833235264,
-0.0360659584403038,
-0.023234963417053223,
-0.011985001154243946,
0.03341377526521683,
-0.0012481437297537923,
0.00864620041102171,
0.01489955559372902,
0.007803773041814566,
-0.03703714907169342,
-0.04589046537876129,
0.03863351047039032,
0.025868134573101997,
-0.014525461941957474,
0.010586777701973915,
0.02286778949201107,
-0.03251476585865021,
-0.054433275014162064,
0.004036802798509598,
0.017420783638954163,
-0.03091784380376339,
0.01068205013871193,
0.0015355886425822973,
-0.036832522600889206,
0.04528532177209854,
0.04492247849702835,
0.01600605808198452,
0.00012371082266326994,
-0.010880214162170887,
-0.021917203441262245,
-0.0026494567282497883,
0.04460644721984863,
0.0033991136588156223,
-0.014695378951728344,
0.025911768898367882,
-0.013122382573783398,
0.04350215569138527,
-0.013727480545639992,
0.013918966054916382,
0.04474439471960068,
0.03421900421380997,
0.005007549654692411,
0.005476679187268019,
0.048133548349142075,
-0.009204587899148464,
0.04846302419900894,
0.00418790802359581,
-0.0038501014932990074,
-0.03466552495956421,
-0.040075454860925674,
-0.005356979556381702,
-0.0002788104466162622,
0.022287895902991295,
0.017801696434617043,
0.06139974668622017,
-0.011651302687823772,
-0.038096703588962555,
-0.009347759187221527,
0.018478447571396828,
0.010926047340035439,
-0.020327404141426086,
-0.017170535400509834,
0.03296886384487152,
0.030465727671980858,
-0.040653057396411896,
-0.06157610937952995,
-0.0369223952293396,
0.04104163870215416,
0.039048440754413605,
-0.04152919724583626,
0.04014326259493828,
-0.01552443578839302,
0.010989569127559662,
0.00016342943126801401,
-0.0006419594865292311,
0.009727888740599155,
0.0010796644492074847,
0.0475444421172142,
0.017455173656344414,
-0.022250447422266006,
0.011523337103426456,
0.044493451714515686,
0.009050212800502777,
-0.029634978622198105,
0.03903408348560333,
0.020061612129211426,
0.023241961374878883,
0.024188555777072906,
-0.021833036094903946,
-0.020666001364588737,
-0.02576359733939171,
-0.029334869235754013,
0.048672839999198914,
-0.0009875011164695024,
-0.022836124524474144,
0.020275171846151352,
0.02133500576019287,
0.02349155768752098,
-0.008887132629752159,
-0.004758289083838463,
-0.045360539108514786,
0.0017801617505028844,
-0.011240150779485703,
0.014218172989785671,
0.020178399980068207,
0.03184092789888382,
0.003998931031674147,
-0.01132291927933693,
0.04381102696061134,
-0.02280835062265396,
-0.04588989168405533,
-0.0402042530477047,
-0.00610287906602025,
-0.05383666604757309,
0.022220008075237274,
0.026238592341542244,
-0.003949945792555809,
0.04547332227230072,
-0.0290664192289114,
0.00870474148541689,
-0.0011110898340120912,
0.048934102058410645,
-0.011644596233963966,
0.08596469461917877,
-0.01871109940111637,
0.016772253438830376,
-0.01549909170717001,
0.010189147666096687,
0.11632311344146729,
0.05859203264117241,
-0.022437002509832382,
-0.009682034142315388,
-0.013270653784275055,
-0.005437181331217289,
-0.019154930487275124,
-0.015001549385488033,
0.005729075986891985,
0.022884903475642204,
-0.03333975747227669,
0.011959148570895195,
0.03394624590873718,
-0.036686334758996964,
-0.025488166138529778,
0.020716391503810883,
-0.046786677092313766,
-0.028469836339354515,
0.028196996077895164,
-0.027632270008325577,
-0.003048487240448594,
-0.003338101552799344,
0.0010792944813147187,
0.0688055083155632,
-0.010943024419248104,
-0.03063017502427101,
-0.059989336878061295,
-0.009556453675031662,
0.017125429585576057,
-0.018919307738542557,
-0.028642432764172554,
0.026090523228049278,
0.01446576789021492,
-0.027677835896611214,
-0.014564018696546555,
0.053086426109075546,
0.04205537587404251,
-0.003794683376327157,
-0.00660032220184803,
0.03885674476623535,
0.010196744464337826,
-0.0028951489366590977,
0.02936992235481739,
0.004002721048891544,
-0.029367202892899513,
-0.013266157358884811,
-0.012274377979338169,
0.025437170639634132,
0.012554051354527473,
0.0013405345380306244,
-0.009160477668046951,
0.0050324369221925735,
-0.0033528695348650217,
-0.07476051896810532,
-0.023583335801959038,
-0.02449926547706127,
0.032608095556497574,
-0.021674014627933502,
-0.05482977628707886,
-0.03276624158024788,
-0.021390380337834358,
0.03248075395822525,
-0.008321192115545273,
-0.023196205496788025,
0.004184321500360966,
-0.04557742550969124,
0.005843539722263813,
0.0739525854587555,
0.018688401207327843,
-0.0328250378370285,
-0.006060303654521704,
-0.06115974858403206,
-0.006533158477395773,
-0.016653086990118027,
0.0011412749299779534,
0.0353287011384964,
0.012412714771926403,
-0.00013981926895212382,
-0.03636712208390236,
-0.021449359133839607,
-0.02142922952771187,
0.03545749559998512,
0.02054229937493801,
0.014375795610249043,
-0.035002268850803375,
0.008786697871983051,
-0.01439765002578497,
0.07222722470760345,
0.020349867641925812,
-0.002397511387243867,
-0.006659572012722492,
0.030464541167020798,
0.00798084307461977,
-0.031102998182177544,
-0.0370800644159317,
0.014226674102246761,
-0.032086413353681564,
0.02058057300746441,
-0.013956060633063316,
0.045002829283475876,
0.012417270801961422,
0.029428770765662193,
-0.00919161643832922,
0.0023347120732069016,
-0.03144000470638275,
-0.02967061661183834,
0.01629193127155304,
-0.0015063651371747255,
-0.013238812796771526,
0.01529046893119812,
0.033278971910476685,
-0.034014418721199036,
-0.021753961220383644,
-0.03555255010724068,
-0.01914883404970169,
0.04380069300532341,
0.04019612446427345,
-0.029873620718717575,
0.006315463222563267,
-0.012639393098652363,
0.03290265053510666,
-0.021763892844319344,
-0.005376297514885664,
-0.02948998473584652,
-0.0018665470415726304,
-0.012515475042164326,
-0.038411013782024384,
-0.039208296686410904,
0.005555793177336454,
-0.03309709206223488,
-0.03341997414827347,
0.005748848430812359,
0.029547059908509254,
0.0003428168420214206,
-0.011381397023797035,
0.03241543844342232,
-0.025558171793818474,
0.045389674603939056,
0.001860908349044621,
-0.053292568773031235,
0.036834467202425,
-0.07854951918125153,
-0.024363571777939796,
0.043223053216934204,
-0.012187760323286057,
0.04900737851858139,
0.021042920649051666,
-0.003943502437323332,
-0.009957569651305676,
0.023105435073375702,
0.0019825506024062634,
-0.02229585312306881,
-0.019092729315161705,
-0.043473951518535614,
-0.024376915767788887,
0.01878461241722107,
-0.030901681631803513,
-0.032822418957948685,
-0.016124026849865913,
0.011350362561643124,
0.04697020351886749,
0.01019628718495369,
-0.013870006427168846,
0.030363699421286583,
0.015339875593781471,
-0.008728007785975933,
0.04845243692398071,
0.030654290691018105,
-0.03553534671664238,
0.07508580386638641,
-0.005186811089515686,
0.016028983518481255,
-0.021763866767287254,
-0.0009612964349798858,
-0.09887821972370148,
-0.029057754203677177,
-0.025549625977873802,
-0.0014656418934464455,
0.038628797978162766,
-0.013134277425706387,
-0.01649976521730423,
0.014645453542470932,
-0.06995274871587753,
0.05124104395508766,
-0.019954292103648186,
0.0023929488379508257,
0.02850351668894291,
-0.023354632779955864,
-0.030017578974366188,
0.03356611728668213,
-0.010404275730252266,
0.07791455835103989,
0.013293550349771976,
0.027274003252387047,
-0.0033952733501791954,
0.0004741241573356092,
-0.032623838633298874,
0.021406715735793114,
-0.018980996683239937,
0.009622368961572647,
0.09317900985479355,
-0.03947142884135246,
-0.013689250685274601,
0.043778516352176666,
-0.018236737698316574,
0.008560135960578918,
0.002208353253081441,
-0.012113017961382866,
-0.0308529119938612,
0.038183242082595825,
0.023256417363882065,
-0.013324244879186153,
0.0034183734096586704,
0.06145832687616348,
-0.03585337474942207,
-0.0017635785043239594,
-0.038588542491197586,
0.012931406497955322,
0.04086778312921524,
-0.07469283044338226,
-0.06410198658704758,
0.039708591997623444,
-0.00464389706030488,
0.011727339588105679,
-0.0018724924884736538,
-0.008392209187150002,
-0.00023639957362320274,
-0.03754004091024399,
-0.06575644016265869,
-0.023714721202850342,
-0.026089634746313095,
0.06484384089708328,
-0.009118274785578251,
-0.010106057859957218,
0.0024456442333757877,
-0.0352315828204155,
-0.004328371491283178,
-0.010766720399260521,
-0.012178492732346058,
-0.04345725104212761,
-0.03265608102083206,
-0.010702831670641899,
-0.021918250247836113,
0.010785170830786228,
-0.015074732713401318,
-0.023585358634591103,
-0.059280604124069214,
0.004037622362375259,
0.05235796421766281,
0.05119895935058594,
0.007410637103021145,
-0.04843325912952423,
-0.028976868838071823,
-0.10997061431407928,
-0.005259491503238678,
0.00883400347083807,
-0.01790032722055912,
-0.054231174290180206,
-0.056004635989665985,
0.019450360909104347,
0.03575241565704346,
0.05202852189540863,
-0.04873579740524292,
-0.033712971955537796,
0.018932782113552094,
0.012518391013145447,
-0.010162719525396824,
-0.00641896016895771,
-0.01193427573889494,
-0.02000911720097065,
-0.030144330114126205,
-0.0058256397023797035,
-0.022317586466670036,
-0.0051339236088097095,
-0.012721552513539791,
-0.00021616840967908502,
0.008594815619289875,
-0.011023888364434242,
-0.025110114365816116,
-0.005518604535609484,
0.010950826108455658,
0.0005682475166395307,
0.0038134134374558926,
0.04168733209371567,
-0.0006086084758862853,
-0.01048190612345934,
-0.0035297360736876726,
-0.02521541155874729,
-0.038955241441726685,
0.04155394434928894,
-0.017444757744669914,
0.005898847244679928,
-0.025343503803014755,
-0.015526683069765568,
0.02732793428003788,
-0.03460413217544556,
-0.007452983409166336,
0.07137060165405273,
-0.03958835452795029,
-0.02828134037554264,
0.02614891715347767,
-0.013776472769677639,
0.020426815375685692,
-0.009631729684770107,
0.004118951037526131,
0.03667718917131424,
-0.010478891432285309,
0.03350822627544403,
0.07534373551607132,
0.017850317060947418,
-0.04562385380268097,
-0.0035934054758399725,
0.005046810954809189,
-0.013232325203716755,
0.07226395606994629,
0.011549003422260284,
0.03899829089641571,
-0.01991037279367447,
-0.067633256316185,
0.002163539407774806,
-0.009648606181144714,
-0.004461887292563915,
0.017588594928383827,
-0.04266498237848282,
0.04904565587639809,
0.017403660342097282,
0.03729135915637016,
0.02474989928305149,
0.004871171433478594,
-0.04526032134890556,
0.016500620171427727,
0.006794623099267483,
0.025478310883045197,
0.00033403802081011236,
-0.017032548785209656,
-0.005964566022157669,
0.015835195779800415,
0.03996799886226654,
-0.007865190505981445,
-0.00042779697105288506,
-0.0049790069460868835,
-0.0002756339672487229,
-0.0005936042289249599,
-0.021927841007709503,
-0.02302367426455021,
-0.009653529152274132,
0.05316552147269249,
0.007853707298636436,
-0.011380480602383614,
-0.008270970545709133,
-0.009791458025574684,
-0.02110462449491024,
0.02310936339199543,
-0.012968248687684536,
-0.0033275079913437366,
-0.026066360995173454,
-0.007542148698121309,
-0.009147425182163715,
0.004958008881658316
] |
<p>A system might have internal energy and/or kinetic energy. Kinetic energy in classical mechanics is a form of energy the object has, only because of its relative movement to other objects. </p>
<p>If you have a system like an oscillator, then you have a system where the amount of internal energy (energy of the spring, say) and the kinetic energy oscillate periodically. The amount of energy that is flowing from "internal energy" to "kinetic energy" and back therefore also meassures how this system is different from a system with might have the same amount of energy in total, but all its energy only stored in form of internal energy. </p>
<p>Is there a reasonable meassure of this difference, that is the ''energy-form flow''? </p>
<p>Maybe such a meassure might also be related to the entropy, because if there is kinetic energy around, I expect the entropy to be higher than otherwise.</p>
<p>Then I was thinking mabye that something like $\frac{dE_{kin}}{dt}$ might therefore be relevant. But the only quantity which directly puts energy and time together is the action. However, I'm not sure if the action has an illustative meaning, which goes beyond its definition, anyway.</p> | 2,830 | [
-0.02468828484416008,
-0.007327849045395851,
-0.020983155816793442,
-0.015480716712772846,
0.021360918879508972,
0.018809134140610695,
-0.017051152884960175,
-0.011209397576749325,
-0.008970309980213642,
-0.007941951975226402,
-0.003921999596059322,
-0.0020874482579529285,
0.01919129304587841,
0.017980387434363365,
0.019171306863427162,
-0.02458379790186882,
-0.028559794649481773,
-0.045357368886470795,
-0.012258503586053848,
-0.047709424048662186,
0.01696397177875042,
-0.00019875711586792022,
-0.005094908643513918,
0.006643747445195913,
-0.03384479507803917,
0.05092061683535576,
0.0184783898293972,
-0.006987809203565121,
-0.00010732837108662352,
0.04756496474146843,
0.028065750375390053,
-0.03504124656319618,
-0.00408225879073143,
0.03414418548345566,
0.03897552564740181,
-0.008823164738714695,
-0.03725796192884445,
-0.04288910701870918,
-0.007150041870772839,
0.0323755256831646,
-0.08265359699726105,
0.005385206546634436,
-0.020076213404536247,
0.01161893643438816,
-0.03763303905725479,
0.01395387388765812,
0.024076838046312332,
-0.030841531231999397,
0.030639011412858963,
-0.04212797060608864,
0.06063319370150566,
-0.024905486032366753,
0.03348126634955406,
-0.019442474469542503,
-0.017371544614434242,
0.0004630390030797571,
0.07459057867527008,
0.08925139158964157,
-0.026766400784254074,
-0.06327952444553375,
-0.009119912981987,
-0.00452469801530242,
0.0005211234674789011,
-0.03703872486948967,
-0.0035933107137680054,
0.023282229900360107,
0.024853596463799477,
-0.029398905113339424,
0.051576606929302216,
-0.008628105744719505,
-0.010487379506230354,
0.015511831268668175,
0.07113412022590637,
-0.015037198550999165,
-0.008059092797338963,
-0.020916908979415894,
0.02824036404490471,
-0.004063989035785198,
0.02937006764113903,
0.04575888067483902,
-0.02311045490205288,
-0.04376989230513573,
-0.000039690476114628837,
0.054145243018865585,
0.01361139863729477,
-0.0160472821444273,
0.04432360827922821,
0.00039867855957709253,
0.0023771892301738262,
0.019351989030838013,
0.004371629096567631,
0.026711227372288704,
0.01958467811346054,
-0.03689788654446602,
-0.03356488049030304,
0.06090915575623512,
0.02377587929368019,
0.03392014279961586,
0.020700303837656975,
-0.004713592119514942,
0.012580360285937786,
-0.05188487097620964,
0.02667795680463314,
0.07442787289619446,
0.037073858082294464,
-0.006886233109980822,
-0.022199269384145737,
0.00014645076589658856,
-0.031219787895679474,
0.016771966591477394,
-0.06469236314296722,
-0.01559446845203638,
0.007736783474683762,
0.0360567644238472,
-0.01020289957523346,
0.004416949115693569,
-0.006479082629084587,
0.011975860223174095,
0.04033542796969414,
0.06941956281661987,
0.019764259457588196,
-0.036439575254917145,
0.023977380245923996,
-0.007439200766384602,
-0.057688456028699875,
0.004824081435799599,
0.0395362451672554,
-0.0018042627489194274,
-0.03926923871040344,
0.010869299992918968,
-0.027241038158535957,
-0.013113074004650116,
-0.010827668011188507,
-0.009253918193280697,
0.0395822748541832,
-0.002466263948008418,
-0.08013583719730377,
-0.05133715644478798,
0.0437830425798893,
0.00781475193798542,
-0.0365593396127224,
-0.07522797584533691,
-0.003832749091088772,
0.02119852788746357,
0.04749798774719238,
0.020855719223618507,
-0.013202783651649952,
0.0005004563136026263,
0.010220165364444256,
0.015643898397684097,
-0.009680042043328285,
-0.009280171245336533,
0.037876348942518234,
-0.025623131543397903,
0.003518927376717329,
-0.017627056688070297,
0.03151634708046913,
0.04785006120800972,
0.0010851874249055982,
0.014217901974916458,
0.03834504261612892,
-0.04193048179149628,
-0.007237735204398632,
0.02536645717918873,
0.01832585409283638,
-0.028292164206504822,
0.04036780074238777,
-0.020305998623371124,
0.03384936600923538,
-0.0012028854107484221,
0.062111321836709976,
0.00789258349686861,
0.000044396143493941054,
0.00822621863335371,
0.02860756777226925,
-0.019660456106066704,
-0.028433846309781075,
-0.0011667474173009396,
-0.03910757973790169,
0.004162404220551252,
-0.026677271351218224,
-0.045285291969776154,
-0.006666678003966808,
-0.020882058888673782,
-0.01853448711335659,
0.03118222951889038,
0.014479318633675575,
-0.0025670798495411873,
-0.00954575277864933,
-0.017915744334459305,
-0.0054107122123241425,
-0.053264498710632324,
0.04322619363665581,
-0.023414798080921173,
-0.006169263739138842,
0.03606231138110161,
0.03438326716423035,
0.0492335744202137,
-0.04687986522912979,
-0.0463746152818203,
-0.015494219027459621,
-0.006014615762978792,
-0.009988781996071339,
-0.02297326549887657,
0.04941771924495697,
0.03884776681661606,
0.014510725624859333,
-0.004541048780083656,
0.030028847977519035,
0.028184540569782257,
-0.08169444650411606,
0.009062155149877071,
-0.055416300892829895,
0.02857457846403122,
0.009758876636624336,
0.0027873076032847166,
0.023678800091147423,
-0.005699549801647663,
-0.0068897828459739685,
-0.011502820067107677,
-0.017328929156064987,
0.05620359256863594,
0.03493569418787956,
0.008526240475475788,
0.006480159237980843,
0.09251675009727478,
0.02642502263188362,
0.03398372232913971,
-0.01712190732359886,
-0.04100412130355835,
-0.03155919536948204,
-0.00019772499217651784,
0.04843468591570854,
0.04037763178348541,
-0.04665951058268547,
-0.0013365322956815362,
0.030633479356765747,
0.017817266285419464,
0.047035422176122665,
0.0022370002698153257,
-0.0047188205644488335,
-0.024630634114146233,
0.002691430039703846,
0.003860791912302375,
0.009585688821971416,
0.0036932139191776514,
0.02222919836640358,
-0.019559672102332115,
0.019020063802599907,
-0.006490504834800959,
0.02370603010058403,
0.03221308812499046,
-0.0004354752891231328,
0.034145135432481766,
0.018552761524915695,
-0.03834216669201851,
0.02567090466618538,
-0.006511143874377012,
0.03522801771759987,
0.026579363271594048,
-0.007039361167699099,
0.040650319308042526,
-0.02582896314561367,
-0.03575307875871658,
-0.02326657436788082,
0.02183861844241619,
-0.02613934688270092,
-0.029261114075779915,
0.028619645163416862,
-0.017436424270272255,
0.006377967540174723,
0.005578997079282999,
-0.006313877645879984,
-0.022417377680540085,
-0.043984781950712204,
0.005819082260131836,
-0.00487520219758153,
0.014848512597382069,
-0.030525512993335724,
-0.006354443728923798,
0.009179502725601196,
-0.029683630913496017,
-0.011365046724677086,
-0.0032730360981076956,
-0.027673950418829918,
0.0096039529889822,
-0.004029106814414263,
-0.03351208567619324,
0.029011454433202744,
-0.020685074850916862,
0.01819070614874363,
0.02582927979528904,
-0.013172326609492302,
-0.04629579558968544,
-0.024431301280856133,
-0.016723772510886192,
0.005962229333817959,
-0.027059966698288918,
0.003042919561266899,
0.06655614078044891,
-0.046136051416397095,
-0.04490106552839279,
-0.005594352260231972,
-0.03401812165975571,
-0.04198800399899483,
-0.026063092052936554,
-0.011700264178216457,
0.04325990751385689,
-0.0195932500064373,
0.011916594579815865,
0.05925259366631508,
-0.048537477850914,
-0.03411056846380234,
-0.056050270795822144,
-0.07553751021623611,
0.030675532296299934,
-0.00163229089230299,
0.05500262975692749,
0.0019866027869284153,
-0.030825812369585037,
0.08089122921228409,
0.04429350048303604,
-0.030260562896728516,
0.005484098102897406,
-0.01658349111676216,
-0.010742479003965855,
-0.019756531342864037,
-0.007002252619713545,
0.008978302590548992,
-0.002980902325361967,
0.032872043550014496,
0.027267204597592354,
0.01349687296897173,
0.0042021912522614,
-0.011295432224869728,
-0.016742251813411713,
0.04038138687610626,
0.013792669400572777,
0.016290614381432533,
0.03769519180059433,
0.03410352021455765,
-0.013063891790807247,
0.04105845093727112,
-0.02354622818529606,
0.05471973493695259,
0.036662086844444275,
-0.06692662835121155,
0.0461653433740139,
0.03783252090215683,
-0.006840900052338839,
-0.040451180189847946,
0.028519393876194954,
-0.009311428293585777,
0.03569605201482773,
-0.001354681677184999,
0.058712322264909744,
0.03342336043715477,
0.013990149833261967,
0.052305951714515686,
0.022107373923063278,
0.043309859931468964,
0.005116378888487816,
-0.03162151947617531,
-0.014928741380572319,
0.005289532244205475,
0.0051158699207007885,
-0.004390918184071779,
0.00824180617928505,
0.03661284223198891,
0.006779433693736792,
0.0298612080514431,
0.002543695969507098,
-0.0446581169962883,
-0.021918892860412598,
-0.09026411920785904,
-0.04030138999223709,
-0.03000243939459324,
0.028128724545240402,
0.018374204635620117,
0.07548654079437256,
-0.004793291445821524,
0.023626847192645073,
0.03785791993141174,
-0.033161647617816925,
-0.0721522867679596,
0.06599760800600052,
-0.029358137398958206,
-0.02914726547896862,
-0.00030508171766996384,
0.025902124121785164,
0.02485007420182228,
-0.04121130332350731,
-0.041352204978466034,
0.016035495325922966,
0.0030024072621017694,
-0.07399945706129074,
0.01208398025482893,
-0.037786055356264114,
-0.06685590744018555,
0.00020811417198274285,
0.03635186329483986,
0.05088390037417412,
-0.0412118136882782,
0.007686409633606672,
0.08306875079870224,
-0.020172294229269028,
0.007201127242296934,
-0.019471287727355957,
-0.02153821848332882,
0.02172665297985077,
-0.005579009186476469,
0.04314613342285156,
0.01639167033135891,
0.025604013353586197,
0.03959999978542328,
0.023176543414592743,
0.03323720395565033,
0.007259115111082792,
-0.027973361313343048,
-0.01651657558977604,
-0.05387791246175766,
-0.011099763214588165,
0.024497931823134422,
0.057136766612529755,
0.007988578639924526,
0.013436874374747276,
-0.0037837522104382515,
0.020399177446961403,
-0.01073555089533329,
0.05229175463318825,
0.013725917786359787,
0.0037254607304930687,
-0.047914057970047,
-0.01930590160191059,
-0.022751376032829285,
-0.013465648517012596,
-0.029557405039668083,
-0.033214062452316284,
0.004657365847378969,
0.007413941901177168,
0.02848060056567192,
-0.027386363595724106,
0.003947426099330187,
-0.007965883240103722,
-0.032041050493717194,
0.013756963424384594,
0.018093962222337723,
0.015600710175931454,
0.007245773449540138,
0.03636525198817253,
0.012173973023891449,
0.04182429239153862,
0.0172041617333889,
0.013300786726176739,
-0.09022937715053558,
-0.03543207421898842,
0.061729591339826584,
0.019255394116044044,
-0.006381079088896513,
-0.01100065279752016,
-0.0024992325343191624,
-0.0452192984521389,
0.04344115033745766,
-0.007916733622550964,
0.062435332685709,
0.0029605471063405275,
-0.020768003538250923,
-0.015124598518013954,
-0.07329325377941132,
-0.009771337732672691,
0.027566228061914444,
0.026588790118694305,
0.011951739899814129,
-0.00952463410794735,
-0.03249846026301384,
0.0023315560538321733,
0.026409383863210678,
0.019535904750227928,
0.023792443796992302,
-0.0007149598677642643,
-0.019593752920627594,
-0.014194083400070667,
0.021815244108438492,
-0.007298900745809078,
-0.09632190316915512,
-0.0012303253170102835,
0.03168471157550812,
-0.01581246219575405,
-0.015465366654098034,
-0.029266074299812317,
-0.01905769482254982,
0.0026863093953579664,
-0.009009936824440956,
-0.010994144715368748,
-0.0006928403745405376,
-0.040964409708976746,
0.07396193593740463,
0.025651494041085243,
0.0005203092587180436,
0.028987416997551918,
0.05866941437125206,
-0.022159647196531296,
-0.030349571257829666,
0.03312096744775772,
0.03969142585992813,
-0.03936577960848808,
0.01992608606815338,
-0.05909772962331772,
0.026999294757843018,
-0.05112480744719505,
0.03148961812257767,
-0.007898510433733463,
-0.012036945670843124,
-0.011360232718288898,
-0.021158551797270775,
-0.02562134899199009,
0.018981678411364555,
0.02896830253303051,
-0.012961551547050476,
-0.014870567247271538,
0.031943753361701965,
-0.006127309985458851,
0.01863214001059532,
0.01108589768409729,
0.016935434192419052,
-0.0244611706584692,
0.06737009435892105,
-0.007623791228979826,
0.01963791623711586,
-0.020506592467427254,
-0.03666956350207329,
0.015319752506911755,
0.0007608758169226348,
0.02739025093615055,
-0.018060531467199326,
-0.012181314639747143,
0.014450062066316605,
-0.010371819138526917,
-0.03827016055583954,
0.009819584898650646,
0.0004616582882590592,
0.0029327766969799995,
-0.02001599408686161,
0.012074540369212627,
-0.010129041969776154,
-0.015221836976706982,
-0.08579323440790176,
-0.042803917080163956,
0.040916506201028824,
-0.0020885691046714783,
-0.040310800075531006,
-0.012711581774055958,
0.0031716865487396717,
-0.03688281029462814,
0.008959398604929447,
0.02806011773645878,
0.02247164398431778,
-0.022416777908802032,
0.03211875632405281,
0.0043406435288488865,
0.04651821404695511,
0.014917338266968727,
0.010450121015310287,
-0.0005851386813446879,
0.02175264246761799,
0.02952439710497856,
-0.02194856107234955,
-0.01934814453125,
0.04069061204791069,
-0.021797075867652893,
0.017632396891713142,
0.013263381086289883,
0.0010839361930266023,
0.03254669904708862,
-0.0134725421667099,
-0.021169764921069145,
0.06458448618650436,
0.008302723988890648,
-0.0027026846073567867,
-0.01292863767594099,
0.05223270505666733,
0.0035947426222264767,
0.025660837069153786,
0.019553864374756813,
-0.012426522560417652,
-0.01843661069869995,
-0.051568590104579926,
0.0069042472168803215,
-0.003317572409287095,
-0.024743275716900826,
0.00042988950735889375,
0.05162106826901436,
-0.008067524060606956,
-0.012540415860712528,
0.016072941944003105,
0.00913712102919817,
0.034840334206819534,
-0.027127083390951157,
0.024635998532176018,
-0.010662445798516273,
-0.01494750939309597,
-0.0366181805729866,
-0.05101460963487625,
-0.037815432995557785,
-0.03167472407221794,
0.0380866713821888,
-0.04664306342601776,
0.06820202618837357,
0.0027678776532411575,
0.006388865411281586,
0.03739270940423012,
-0.002039911225438118,
0.027890630066394806,
0.021904591470956802,
0.01828600838780403,
0.04746821150183678,
-0.043410517275333405,
-0.032744601368904114,
0.047516610473394394,
0.038608305156230927,
-0.051449406892061234,
0.05548788607120514,
0.028189631178975105,
0.008593746460974216,
0.015202070586383343,
-0.03491688519716263,
-0.05878404527902603,
-0.0030704240780323744,
-0.030002690851688385,
0.04375411570072174,
0.003190708812326193,
-0.023435231298208237,
0.045258842408657074,
0.04319211095571518,
-0.010346474125981331,
-0.05882050096988678,
0.03111245483160019,
-0.04878796264529228,
0.013417181558907032,
-0.0005850945599377155,
0.02886122837662697,
0.0050263842567801476,
-0.01836969703435898,
0.06645424664020538,
0.010504179634153843,
-0.008853621780872345,
0.019239861518144608,
-0.04810748249292374,
0.012321563437581062,
-0.04629501327872276,
-0.08094589412212372,
0.045425575226545334,
-0.033725954592227936,
-0.01586245372891426,
0.0016531359869986773,
0.0019838151056319475,
0.03478609770536423,
0.01680968515574932,
0.021671650931239128,
-0.005817305762320757,
0.09147477895021439,
-0.007046917453408241,
0.034771908074617386,
-0.029041454195976257,
0.023203954100608826,
0.11658992618322372,
0.03900063782930374,
0.013452192768454552,
-0.01013491302728653,
-0.006485139951109886,
-0.0007739649154245853,
0.01838296838104725,
-0.000478042580652982,
0.01104070246219635,
0.02812529355287552,
-0.003562048776075244,
0.02348359115421772,
0.021909747272729874,
-0.01462369691580534,
-0.03757959231734276,
0.03855770826339722,
-0.06877639144659042,
0.005700855050235987,
0.02320205606520176,
0.015075907111167908,
0.010307020507752895,
0.020472131669521332,
-0.003930740524083376,
0.005067629273980856,
-0.01442119013518095,
0.03935109078884125,
-0.019007161259651184,
-0.05001924932003021,
0.014528848230838776,
-0.002993465168401599,
-0.034995898604393005,
0.01967208832502365,
-0.007342866621911526,
-0.018423005938529968,
-0.013327590189874172,
-0.027479324489831924,
0.011125916615128517,
0.02019873633980751,
0.011983986012637615,
0.0476544126868248,
0.02967425435781479,
0.0038993980269879103,
0.01662415638566017,
-0.008159120567142963,
-0.04078545421361923,
-0.023235859349370003,
-0.04153135418891907,
0.02466481737792492,
-0.02920767292380333,
0.028089724481105804,
-0.01989082805812359,
-0.013489029370248318,
0.003074455773457885,
-0.04408123716711998,
-0.021185753867030144,
-0.030799735337495804,
0.04856099188327789,
-0.01182250864803791,
-0.004220924340188503,
-0.03013869933784008,
0.006762044038623571,
0.024145232513546944,
0.021273285150527954,
-0.038273122161626816,
-0.008518120273947716,
0.04306701943278313,
0.01732165552675724,
0.0364687442779541,
-0.03361253812909126,
-0.011158674024045467,
-0.025571541860699654,
-0.02866346202790737,
-0.038861289620399475,
0.005680601578205824,
-0.008379494771361351,
0.014209899120032787,
0.01303519681096077,
0.028435437008738518,
-0.011240572668612003,
-0.027296407148241997,
-0.03253310173749924,
0.022887540981173515,
0.04437294602394104,
-0.005915191024541855,
0.007887902669608593,
0.014086777344346046,
0.03551492840051651,
0.048486579209566116,
-0.02285805530846119,
0.023695146664977074,
0.014592479914426804,
0.011964759789407253,
0.03595074638724327,
-0.01341521367430687,
-0.012280136346817017,
0.01927405223250389,
-0.027194686233997345,
0.007102455943822861,
0.0011449847370386124,
0.0013583203544840217,
0.01829013228416443,
0.015901705250144005,
0.002754231682047248,
0.0563354417681694,
-0.001467915833927691,
0.003855185816064477,
0.009632202796638012,
-0.020647823810577393,
-0.028838427737355232,
-0.007791496813297272,
0.015509803779423237,
-0.0017995437374338508,
-0.03087456524372101,
-0.017054719850420952,
0.009280135855078697,
-0.016335096210241318,
0.02413533627986908,
-0.03022732399404049,
0.021789249032735825,
-0.052255988121032715,
0.020112738013267517,
-0.04752570390701294,
0.01390168908983469,
-0.06173790246248245,
0.00015282946696970612,
0.029298901557922363,
-0.020299624651670456,
0.019066939130425453,
0.05431441217660904,
0.009357266128063202,
-0.03885747119784355,
0.018799304962158203,
0.0491744726896286,
-0.0030117963906377554,
-0.016459617763757706,
0.03631002455949783,
-0.011292691342532635,
0.032999441027641296,
-0.0324096754193306,
-0.04347602650523186,
0.04191896319389343,
-0.023105185478925705,
-0.019675903022289276,
0.028109822422266006,
-0.021976329386234283,
-0.01474090851843357,
0.01704172044992447,
-0.001202830346301198,
-0.014244568534195423,
0.014098447747528553,
-0.0016397504368796945,
0.003126707160845399,
-0.005251444410532713,
-0.05410764738917351,
-0.05209016427397728,
-0.04790647700428963,
0.027296066284179688,
0.0038636622484773397,
-0.01359711866825819,
0.009401862509548664,
0.04303835332393646,
0.012447741813957691,
-0.027861138805747032,
0.006976218428462744,
-0.029779793694615364,
0.005273331422358751,
0.03100925125181675,
-0.0052155074663460255,
0.031021438539028168,
0.04661340266466141,
-0.03190600126981735,
-0.0016787383938208222,
0.022502562031149864,
0.004009367898106575,
-0.07323984056711197,
0.008569280616939068,
-0.0034966145176440477,
0.01626204513013363,
0.012607265263795853,
-0.03131970018148422,
-0.008370410650968552,
-0.006522167008370161,
-0.05111416056752205,
0.03931901231408119,
-0.0401950366795063,
0.014232444576919079,
0.010580971837043762,
0.005307985004037619,
-0.05105218663811684,
0.01719621941447258,
0.04563690721988678,
0.0382501445710659,
0.01649596355855465,
0.03655402362346649,
0.011009175330400467,
-0.02872190810739994,
-0.010299925692379475,
0.016013020649552345,
-0.0033711513970047235,
-0.0008782148943282664,
0.06844811141490936,
-0.029172373935580254,
-0.05105706304311752,
0.005121814087033272,
-0.04060026630759239,
0.0037052766419947147,
-0.018258828669786453,
0.01841883733868599,
-0.0034236495848745108,
0.05180840566754341,
0.020907411351799965,
-0.03508399799466133,
-0.008680377155542374,
0.003623037599027157,
0.009376517497003078,
0.01409243606030941,
-0.03192509710788727,
-0.011969571001827717,
0.02643420733511448,
-0.032628439366817474,
-0.03801456838846207,
0.03866683319211006,
-0.025568760931491852,
-0.016457151621580124,
0.0183122456073761,
0.00015733302279841155,
0.018084336072206497,
0.0077006621286273,
-0.004139546770602465,
-0.020364457741379738,
-0.0038772395346313715,
0.015997711569070816,
0.0026032321620732546,
-0.013309495523571968,
-0.012667660601437092,
0.003702664515003562,
-0.022341497242450714,
0.03108745813369751,
0.01182839460670948,
-0.007032456807792187,
-0.07163943350315094,
-0.013461440801620483,
-0.036462198942899704,
-0.01823543570935726,
-0.04906374588608742,
-0.04431323707103729,
-0.05136226862668991,
0.037804193794727325,
0.04241269454360008,
0.03740635886788368,
-0.007274337578564882,
-0.04242062568664551,
-0.02816350758075714,
-0.06954317539930344,
0.006403220351785421,
0.0014679188607260585,
0.03448314219713211,
-0.05423985794186592,
-0.020558767020702362,
-0.00685886712744832,
0.0025823411997407675,
0.06400402635335922,
-0.0018541982863098383,
-0.05488483980298042,
0.05753481015563011,
0.007313822396099567,
0.03776615485548973,
-0.026493074372410774,
0.005706335883587599,
-0.07651630789041519,
-0.011997058987617493,
0.0208758357912302,
-0.021566737443208694,
-0.04143809899687767,
0.012770423665642738,
0.05323538929224014,
-0.028233662247657776,
-0.006754790432751179,
-0.02532319724559784,
-0.013799911364912987,
0.0737294852733612,
0.0027185636572539806,
-0.012611180543899536,
0.04566625878214836,
0.021952355280518532,
0.015159647911787033,
0.03452097252011299,
-0.029245581477880478,
-0.04878666624426842,
0.029419101774692535,
-0.011765910312533379,
-0.02624034881591797,
-0.010122661478817463,
-0.043215811252593994,
0.02914203703403473,
-0.027338944375514984,
-0.021261494606733322,
0.06265125423669815,
-0.055455923080444336,
-0.012248476967215538,
0.020492803305387497,
0.0011788028059527278,
0.04463512450456619,
-0.007452939637005329,
0.034941233694553375,
0.03526151180267334,
0.02778969705104828,
-0.018605900928378105,
0.05485501512885094,
0.057742372155189514,
-0.04316999763250351,
-0.03189302608370781,
0.004267056938260794,
-0.013563386164605618,
0.017597615718841553,
0.003744270885363221,
0.00869289692491293,
-0.06205148249864578,
-0.029835877940058708,
0.0267129335552454,
0.0013083508238196373,
0.0074428776279091835,
0.03850390017032623,
-0.02691289223730564,
0.041645001620054245,
0.02252689190208912,
-0.013186334632337093,
-0.061311401426792145,
0.0008764413651078939,
-0.030635211616754532,
-0.015524915419518948,
0.03049299120903015,
0.003084915690124035,
-0.02337835542857647,
0.022742370143532753,
-0.025590727105736732,
0.004625700879842043,
0.005776610691100359,
-0.06938175857067108,
0.0014107917668297887,
0.01782938465476036,
0.008789743296802044,
0.010679054073989391,
-0.01145881600677967,
-0.05154360085725784,
-0.04421938583254814,
0.02974318526685238,
0.04064878076314926,
0.06339545547962189,
0.014723509550094604,
-0.0031894613057374954,
-0.012662786990404129,
0.07591666281223297,
-0.06241961568593979,
0.011366099119186401,
-0.03791482001543045,
0.030649341642856598,
0.03428035229444504,
-0.03208417445421219
] |
<p>so one uses equations of motion to describe liquids (e.g. Navier–Stokes equations). These are equations for $\vec{v}(\vec{r},t)$ with boundary conditions on the surface $S$ of the liquid (e.g. $\vec{v}(\vec{r}\in S,t) = \vec{0}$).</p>
<p>How should one incorporate surface tension $\sigma$ in these equations/boundary conditions? It seems, only boundary conditions must change, and $\Delta p = \sigma (1/R_1 + 1/R_2)$ is the first thing that comes to mind, but how to get $1/R$ from $\vec{v}(\vec{r},t)$?</p> | 2,831 | [
0.03564745932817459,
-0.005705767776817083,
-0.03809969872236252,
0.0050776125863194466,
-0.01586582139134407,
0.005024151876568794,
-0.03167141228914261,
-0.010787914507091045,
0.012082100845873356,
-0.002101563150063157,
0.02630285546183586,
0.014445798471570015,
0.05040675401687622,
-0.013603631407022476,
0.03278034180402756,
-0.0018197903409600258,
0.004114703740924597,
-0.0219787135720253,
-0.011677908711135387,
-0.020498210564255714,
0.00007919083145679906,
0.027301855385303497,
0.041209615767002106,
-0.010161921381950378,
-0.020874112844467163,
0.043172210454940796,
-0.009995073080062866,
-0.018898440524935722,
0.00580979697406292,
0.042121823877096176,
0.0036124708130955696,
-0.049123674631118774,
0.013308881781995296,
0.007776251528412104,
-0.024525104090571404,
0.039076127111911774,
-0.03250064700841904,
-0.01722405105829239,
-0.06392429769039154,
0.013040454126894474,
-0.07612977176904678,
0.005422033369541168,
0.007610868662595749,
0.022845059633255005,
-0.00748942606151104,
-0.015850381925702095,
-0.013699596747756004,
-0.03897585719823837,
0.04551691561937332,
-0.04322146251797676,
0.042440757155418396,
0.025778349488973618,
0.05953540280461311,
0.05182984098792076,
0.023259369656443596,
0.017131268978118896,
0.05904269963502884,
0.051717359572649,
-0.032710153609514236,
-0.037550512701272964,
-0.015736645087599754,
-0.013358374126255512,
-0.009166098199784756,
-0.03204624354839325,
-0.011384483426809311,
-0.017344960942864418,
0.020151251927018166,
-0.0034399901051074266,
0.0014381062937900424,
-0.015381594188511372,
-0.018975192680954933,
-0.02496841922402382,
0.0268330667167902,
0.01930064894258976,
0.021824685856699944,
-0.009031469002366066,
-0.020495744422078133,
0.018611647188663483,
0.03254570811986923,
0.05998045578598976,
-0.014167451299726963,
0.022554215043783188,
0.032568078488111496,
0.04360624775290489,
-0.005586699116975069,
-0.016887931153178215,
0.07879022508859634,
0.02086448296904564,
0.02766905166208744,
0.034132760018110275,
-0.020053939893841743,
0.002049066126346588,
0.023410065099596977,
-0.03514649346470833,
-0.017034262418746948,
-0.011077875271439552,
-0.006152001209557056,
0.03997934237122536,
0.015699710696935654,
-0.04413871094584465,
-0.002744414145126939,
-0.051919352263212204,
-0.004133859649300575,
0.08746211230754852,
-0.017125088721513748,
-0.02306745946407318,
-0.04869997873902321,
0.007458684500306845,
-0.01959754154086113,
-0.04859637841582298,
-0.04306621477007866,
0.004298696294426918,
-0.023100899532437325,
-0.004081055521965027,
0.0018863555742427707,
-0.0017773689469322562,
-0.008609005250036716,
-0.03757527843117714,
0.014470016583800316,
0.06145641952753067,
0.052392829209566116,
-0.03272213786840439,
0.011997195892035961,
0.028921710327267647,
-0.08527415245771408,
0.05854463204741478,
0.005371741019189358,
-0.02495969831943512,
-0.037448763847351074,
-0.021479710936546326,
-0.022767197340726852,
0.00004216658999212086,
-0.00901185255497694,
0.014667916111648083,
0.02459081821143627,
-0.015674781054258347,
-0.07645487785339355,
-0.04003060981631279,
0.040304843336343765,
-0.014732562005519867,
-0.060469210147857666,
-0.09165702760219574,
0.022024141624569893,
0.027340363711118698,
0.07050570100545883,
0.0017731740372255445,
-0.00021681211364921182,
0.02836351841688156,
0.017940450459718704,
-0.03083057887852192,
-0.036966998130083084,
-0.055514462292194366,
-0.0037199747748672962,
-0.0308323185890913,
-0.03129569813609123,
-0.039506543427705765,
0.025462031364440918,
0.052915655076503754,
-0.001728992210701108,
-0.010801747441291809,
0.07493335753679276,
-0.029667725786566734,
0.00959151890128851,
0.03658111393451691,
0.01704353280365467,
-0.03368852287530899,
0.0554492361843586,
-0.006267178803682327,
0.054785046726465225,
0.020829670131206512,
0.012934685684740543,
-0.010513407178223133,
0.01096772775053978,
0.03109169378876686,
0.035550739616155624,
0.0020726658403873444,
-0.008960756473243237,
-0.0029055627528578043,
-0.006575691979378462,
0.03445844724774361,
-0.016877751797437668,
-0.03393286466598511,
-0.005849847570061684,
-0.002126189647242427,
-0.011460449546575546,
0.07056239992380142,
0.0046785203740000725,
-0.029957856982946396,
-0.04420923814177513,
-0.04541350528597832,
-0.0005780056235380471,
-0.08428367227315903,
0.032581012696027756,
-0.018370386213064194,
0.00514228455722332,
0.04972650855779648,
0.020765794441103935,
0.013306079432368279,
-0.04771553352475166,
-0.02900388464331627,
-0.013217611238360405,
0.03650573641061783,
0.019238345324993134,
-0.03316272422671318,
0.0038731324020773172,
0.021340932697057724,
0.07248704135417938,
0.02033744566142559,
-0.008170580491423607,
-0.0264686718583107,
-0.023955581709742546,
-0.023621996864676476,
-0.017314592376351357,
0.020236141979694366,
-0.016641343012452126,
-0.03396499529480934,
0.018121512606739998,
0.02635880745947361,
0.017453953623771667,
0.037308335304260254,
-0.028631219640374184,
0.0485774502158165,
0.07067297399044037,
0.01697767712175846,
-0.000003955458851123694,
0.044120922684669495,
0.026994824409484863,
0.02879176288843155,
-0.021224142983555794,
-0.031575411558151245,
-0.019037440419197083,
-0.016442352905869484,
0.06060146912932396,
0.016012199223041534,
-0.0284542515873909,
-0.03171313926577568,
0.06651479750871658,
0.03000515140593052,
0.04467790201306343,
0.024869512766599655,
0.016886495053768158,
-0.029432253912091255,
0.0599917434155941,
-0.006778002716600895,
0.03362027183175087,
-0.01490398496389389,
0.023400945588946342,
0.04912395775318146,
0.03551807254552841,
0.007232251577079296,
-0.0014091554330661893,
0.011662260629236698,
-0.0027081898879259825,
0.004843283910304308,
-0.014150714501738548,
-0.0133746936917305,
0.03260139748454094,
-0.02929537370800972,
0.00901741161942482,
0.03180874139070511,
0.007385841105133295,
-0.001970574725419283,
-0.01903057098388672,
-0.003686603158712387,
0.005574813578277826,
0.014460747130215168,
0.014343791641294956,
-0.004761194810271263,
0.030643431469798088,
-0.048987433314323425,
-0.011295627802610397,
-0.009401746094226837,
-0.03883567452430725,
-0.010759372264146805,
0.031058305874466896,
0.01692076399922371,
-0.0009699288057163358,
0.033891744911670685,
-0.014144289307296276,
-0.03003806620836258,
0.02537737973034382,
-0.015748079866170883,
-0.0264454185962677,
0.03404129669070244,
-0.051596011966466904,
0.020444221794605255,
-0.01328031811863184,
-0.018444400280714035,
0.03666960448026657,
0.010765907354652882,
0.005146321374922991,
-0.023572251200675964,
0.0063237883150577545,
-0.02356848306953907,
-0.03004014678299427,
-0.030268825590610504,
0.002015696605667472,
0.007221773266792297,
0.009304456412792206,
0.019821198657155037,
0.003664715215563774,
-0.05044557526707649,
0.03554152697324753,
-0.022150835022330284,
-0.05354023724794388,
-0.020848991349339485,
-0.009847616776823997,
0.04164977744221687,
-0.01951272413134575,
0.03393281623721123,
0.05584128946065903,
-0.05635892599821091,
-0.008901257067918777,
-0.05943906679749489,
-0.049112554639577866,
0.03835556283593178,
-0.01584467664361,
0.03612947091460228,
0.011415624059736729,
-0.054936107248067856,
0.10997235029935837,
-0.0184022169560194,
-0.03644045069813728,
0.03272814303636551,
0.009628018364310265,
0.0032275181729346514,
-0.04703304171562195,
0.009396395646035671,
0.040700994431972504,
-0.038344088941812515,
0.019606905058026314,
0.012278230860829353,
0.016103722155094147,
0.02501113899052143,
0.01108946930617094,
-0.0066260662861168385,
-0.0017877774080261588,
-0.0005026853759773076,
0.02421846240758896,
0.049338873475790024,
0.013979075476527214,
0.003198890248313546,
0.03306111320853233,
0.01957709528505802,
0.03758014366030693,
0.07009784877300262,
-0.05776866897940636,
0.04177580401301384,
-0.021202154457569122,
-0.017059383913874626,
-0.02816505916416645,
0.03723636269569397,
0.020351897925138474,
-0.04307599365711212,
0.019310947507619858,
0.05040968582034111,
0.03571728244423866,
-0.035735633224248886,
-0.016451720148324966,
0.037384551018476486,
0.04749317094683647,
-0.03197011724114418,
-0.052244145423173904,
0.003377782879397273,
-0.006815371569246054,
0.024169398471713066,
-0.02391115576028824,
0.005599057301878929,
0.03994317352771759,
0.0026898705400526524,
0.017452040687203407,
-0.04205368086695671,
-0.05106844753026962,
0.0006961858016438782,
-0.0501568429172039,
-0.0036900651175528765,
-0.023079533129930496,
0.06130250170826912,
-0.007734033744782209,
0.06403475999832153,
0.01355198584496975,
0.027492040768265724,
0.04007053002715111,
0.024322889745235443,
-0.05488184094429016,
0.0020751236006617546,
0.002935088938102126,
-0.03930438682436943,
-0.03154782950878143,
-0.011901346035301685,
0.03488117456436157,
-0.05064141005277634,
-0.005114469677209854,
-0.007369322702288628,
-0.00967639870941639,
-0.043895795941352844,
-0.0109883863478899,
-0.034783683717250824,
-0.04289674386382103,
-0.030188964679837227,
0.04110381752252579,
0.04994679242372513,
-0.031104864552617073,
-0.0029242809396237135,
0.04600208252668381,
0.002428631763905287,
-0.01171081978827715,
-0.03334616869688034,
-0.008240468800067902,
-0.001590910367667675,
0.04941968619823456,
0.03824543207883835,
-0.018299294635653496,
0.03667738288640976,
0.058663081377744675,
0.014672241173684597,
0.053458984941244125,
-0.02611548826098442,
0.0043913936242461205,
-0.03147744759917259,
-0.08152510225772858,
0.0017547727329656482,
-0.00940838921815157,
0.07097697257995605,
-0.010835853405296803,
-0.0034428562503308058,
0.02739865332841873,
-0.022944189608097076,
-0.04300357401371002,
0.07208813726902008,
0.060164276510477066,
0.023534487932920456,
-0.03523700684309006,
-0.018642032518982887,
-0.0070471386425197124,
-0.026471909135580063,
-0.01144860964268446,
0.0029176753014326096,
0.02542078122496605,
-0.04423648491501808,
0.028679758310317993,
0.01430221926420927,
-0.002910602604970336,
-0.025899598374962807,
-0.039874061942100525,
0.018274841830134392,
0.055762846022844315,
-0.00013780186418443918,
-0.021937614306807518,
-0.005199986509978771,
0.03570191189646721,
0.014852226711809635,
-0.0374622568488121,
0.009529408998787403,
-0.09845135360956192,
0.005471058655530214,
0.022839663550257683,
0.010798856616020203,
0.007572792936116457,
0.0055971392430365086,
-0.05471160635352135,
0.006207584403455257,
0.04894420504570007,
-0.037741273641586304,
-0.004946875385940075,
-0.018471408635377884,
-0.03205956891179085,
-0.009372737258672714,
-0.020574161782860756,
-0.01979268714785576,
0.011616437695920467,
-0.023526029661297798,
0.03135664016008377,
-0.04256084933876991,
0.008218028582632542,
-0.013671433553099632,
0.025799380615353584,
-0.011348566971719265,
0.06081333011388779,
-0.004968875553458929,
-0.027609441429376602,
-0.01457362249493599,
0.033555276691913605,
-0.0428038127720356,
-0.05150122568011284,
-0.0016162539832293987,
0.023200470954179764,
0.04181809350848198,
0.00985705852508545,
-0.02215859852731228,
-0.04769613966345787,
0.05042338743805885,
0.0275894608348608,
-0.02028230018913746,
0.008460703305900097,
-0.006408624351024628,
0.0317387692630291,
0.04324661195278168,
0.00046948634553700686,
0.03964788466691971,
0.06532472372055054,
-0.010280167683959007,
-0.03508089482784271,
-0.017513927072286606,
0.038131214678287506,
-0.00640597939491272,
-0.027331281453371048,
-0.04138175770640373,
0.01479806937277317,
-0.001434901263564825,
0.040395546704530716,
-0.019235173240303993,
0.040963467210531235,
0.010664178058505058,
-0.0782255157828331,
-0.039954692125320435,
0.01429110299795866,
0.04884761944413185,
-0.03047100082039833,
0.040450867265462875,
0.01183122768998146,
0.025990165770053864,
0.006630626041442156,
-0.007269628811627626,
0.003150672186166048,
-0.0036978155840188265,
-0.0004790326056536287,
-0.022605208680033684,
0.03069138340651989,
-0.012268148362636566,
-0.0007920032949186862,
0.04702228680253029,
-0.062559574842453,
0.04125915467739105,
0.002634454518556595,
0.014271169900894165,
0.004941792692989111,
-0.029193496331572533,
0.0012150987749919295,
-0.004897469189018011,
0.010606265626847744,
0.022255748510360718,
-0.059994280338287354,
0.010168253444135189,
0.03255733847618103,
0.029679110273718834,
-0.0648525282740593,
-0.06246434897184372,
0.034736134111881256,
-0.008271617814898491,
-0.03987789526581764,
-0.02114059589803219,
0.023175837472081184,
-0.025603774935007095,
-0.0038783629424870014,
0.009952944703400135,
0.02886347286403179,
-0.019674206152558327,
-0.058502472937107086,
0.02915215492248535,
0.05554215610027313,
0.036673977971076965,
-0.00738403107970953,
0.0223852451890707,
0.01933589205145836,
-0.04286220297217369,
0.0032549144234508276,
0.019032727926969528,
0.06050703674554825,
-0.018731333315372467,
0.020080972462892532,
-0.008440532721579075,
-0.033468570560216904,
0.04930177330970764,
-0.002409324049949646,
0.02779746986925602,
0.004581626504659653,
0.014379551634192467,
-0.011216066777706146,
-0.009954589419066906,
-0.01476037222892046,
-0.004226806107908487,
0.05389402061700821,
0.025995656847953796,
0.012490938417613506,
-0.02481197565793991,
0.004622419364750385,
0.008723284117877483,
-0.001643568160943687,
-0.008561129681766033,
-0.001861676573753357,
0.1044732928276062,
0.0031777264084666967,
0.023059919476509094,
0.050411298871040344,
0.011360324919223785,
0.06676177680492401,
0.027912020683288574,
-0.010070226155221462,
0.023611560463905334,
0.00008495962538290769,
-0.018139660358428955,
-0.062032539397478104,
-0.022639116272330284,
-0.00043969080434180796,
0.048477355390787125,
-0.032773248851299286,
0.05647061765193939,
0.013437818735837936,
-0.005794293247163296,
0.007206927984952927,
-0.024816207587718964,
-0.026623908430337906,
0.0009690946899354458,
-0.03789609298110008,
0.0569942481815815,
-0.020616695284843445,
-0.011359353549778461,
-0.003466308582574129,
0.031178072094917297,
-0.03242400661110878,
0.009442777372896671,
0.006618781480938196,
0.03187166154384613,
0.02083653211593628,
-0.007899980992078781,
-0.009767066687345505,
0.04111526161432266,
-0.027880756184458733,
0.006738441064953804,
-0.030013425275683403,
-0.012235550209879875,
0.056867290288209915,
-0.00000443026510765776,
0.03139197826385498,
-0.04086212441325188,
-0.006880864966660738,
0.0024407014716416597,
0.0070969825610518456,
0.011349907144904137,
0.00456843851134181,
0.029908984899520874,
-0.007777818012982607,
0.025459222495555878,
0.011339368298649788,
0.004060145001858473,
-0.03580165281891823,
-0.04980694502592087,
-0.022085513919591904,
-0.058234766125679016,
-0.03964708000421524,
0.02943900041282177,
0.04583381861448288,
-0.01120757032185793,
0.019380535930395126,
-0.020732756704092026,
0.025489166378974915,
0.020186766982078552,
-0.008273085579276085,
-0.022472364827990532,
0.07026486098766327,
-0.021241581067442894,
0.033000167459249496,
-0.008035222068428993,
0.014014539308845997,
0.1050785556435585,
0.06948163360357285,
0.030387073755264282,
-0.06401372700929642,
0.013431661762297153,
-0.0036986039485782385,
-0.0006670635775662959,
-0.060172367841005325,
0.0627853125333786,
0.009889361448585987,
0.009802733547985554,
-0.03315360099077225,
0.059747014194726944,
-0.025031648576259613,
0.023139892145991325,
0.029725681990385056,
-0.07868583500385284,
-0.003603528719395399,
0.022317662835121155,
-0.007442348171025515,
-0.02805386297404766,
0.050740234553813934,
-0.03891618549823761,
0.013316933996975422,
-0.00883739348500967,
-0.015119836665689945,
-0.025800900533795357,
-0.030420443043112755,
0.028835467994213104,
-0.0015864671440795064,
-0.040336813777685165,
0.00969395600259304,
-0.020422618836164474,
0.020008912310004234,
-0.021539947018027306,
0.0008474388741888106,
0.01688295230269432,
-0.04578199237585068,
0.006214872468262911,
-0.014894249849021435,
-0.005569774657487869,
0.0004946754197590053,
-0.003396525513380766,
0.011560466140508652,
-0.038565970957279205,
-0.011614085175096989,
-0.04128081724047661,
0.05755941569805145,
-0.034650642424821854,
0.016459381207823753,
-0.01240411028265953,
-0.010515168309211731,
0.009449999779462814,
-0.0497005432844162,
-0.03617901727557182,
0.0034225983545184135,
0.023578006774187088,
0.02474580705165863,
0.001497968565672636,
-0.04075760394334793,
0.014561888761818409,
-0.00413191132247448,
0.023225579410791397,
0.03083670511841774,
-0.033148787915706635,
-0.0028133229352533817,
0.01057474035769701,
0.03220565989613533,
-0.01723407208919525,
-0.031703319400548935,
0.003518142504617572,
-0.00503508560359478,
-0.06762179732322693,
-0.006834080908447504,
0.006209356710314751,
0.013475419953465462,
-0.0033831114415079355,
0.0004844290961045772,
0.008160648867487907,
-0.0075711593963205814,
-0.0890919491648674,
0.01774667762219906,
-0.04393639788031578,
0.00877476204186678,
-0.036106012761592865,
-0.020911289379000664,
0.023469574749469757,
0.026460351422429085,
-0.01472347229719162,
-0.048661909997463226,
-0.006647344212979078,
0.02823016233742237,
0.035318903625011444,
-0.004534482024610043,
-0.0382939912378788,
-0.015461482107639313,
-0.006427408661693335,
0.03558298572897911,
0.015959667041897774,
0.02877281978726387,
0.016703937202692032,
0.018682727590203285,
0.015860412269830704,
0.03214568644762039,
-0.03135208413004875,
0.024831779301166534,
0.01271318644285202,
-0.010957714170217514,
-0.01579613797366619,
-0.010051493532955647,
0.013850248418748379,
-0.015386699698865414,
0.004015972372144461,
0.0008603032329119742,
0.008361701853573322,
-0.008668235503137112,
-0.010936912149190903,
-0.048356469720602036,
0.007856105454266071,
-0.03197276219725609,
0.002435619942843914,
-0.040059853345155716,
-0.004043357912451029,
-0.05527189001441002,
-0.012954731471836567,
-0.010618717409670353,
0.01784188486635685,
-0.01519852876663208,
0.009343506768345833,
-0.05819832906126976,
0.010286835953593254,
0.01290304958820343,
0.016216738149523735,
0.01772289164364338,
0.009345515631139278,
0.0311087928712368,
-0.006790535524487495,
0.00835318025201559,
-0.04641946405172348,
-0.05638694763183594,
0.03139296919107437,
-0.0342249870300293,
-0.043110523372888565,
-0.014257070608437061,
0.02302870713174343,
0.04985607787966728,
0.0365847572684288,
-0.02043023891746998,
-0.014768247492611408,
0.032616905868053436,
-0.007131460588425398,
0.038901906460523605,
-0.021456697955727577,
-0.023082267493009567,
-0.019707685336470604,
-0.03997974470257759,
0.0703464075922966,
0.013520373962819576,
0.021464543417096138,
0.014321490190923214,
0.0005654051783494651,
-0.0587715245783329,
-0.0018558251904323697,
0.030707502737641335,
-0.010091356933116913,
0.009723743423819542,
0.02444695681333542,
0.006080367136746645,
0.041266415268182755,
0.01982656680047512,
-0.034893181174993515,
0.02615341544151306,
0.020794019103050232,
0.0003772855270653963,
-0.09045025706291199,
0.007619872689247131,
0.0019980445504188538,
0.012136967852711678,
0.004214290529489517,
-0.06254205107688904,
-0.007831737399101257,
0.008172953501343727,
-0.03589770942926407,
-0.007956638000905514,
-0.031513653695583344,
0.021025797352194786,
-0.035727664828300476,
-0.014239116571843624,
-0.01011696457862854,
0.0672643855214119,
0.0210493765771389,
0.010580348782241344,
0.00995909795165062,
-0.0042061591520905495,
0.012017123401165009,
-0.006869009230285883,
0.017815720289945602,
0.03300940617918968,
-0.027731765061616898,
-0.05005747079849243,
0.03222716599702835,
-0.02622690610587597,
-0.01156044565141201,
-0.018067151308059692,
-0.011181012727320194,
-0.02681822143495083,
0.004896741360425949,
0.011609219945967197,
-0.029544739052653313,
0.020449310541152954,
0.001339644892141223,
-0.026217514649033546,
-0.016131941229104996,
0.04513896629214287,
-0.02634413354098797,
0.015107800252735615,
0.005062062293291092,
-0.031368665397167206,
0.016652923077344894,
-0.043385133147239685,
-0.062158070504665375,
0.029967060312628746,
-0.040660008788108826,
-0.002061947248876095,
-0.00005785196117358282,
-0.0036380046512931585,
0.029268668964505196,
-0.03170765936374664,
0.021554311737418175,
-0.04548145458102226,
0.022737622261047363,
0.021732937544584274,
0.0073742917738854885,
-0.006847532466053963,
0.052867043763399124,
-0.005207681097090244,
-0.026232995092868805,
-0.014132213778793812,
0.0029951692558825016,
-0.040162593126297,
-0.09372053295373917,
0.002444351091980934,
0.022649621590971947,
-0.05730792135000229,
-0.03173856809735298,
-0.01116550900042057,
0.010633970610797405,
0.04288493096828461,
0.019726306200027466,
0.027796687558293343,
-0.01296399999409914,
-0.022567033767700195,
-0.013903308659791946,
-0.047726139426231384,
0.027667755261063576,
0.007818151265382767,
-0.017730513587594032,
-0.0007448130054399371,
-0.01776946894824505,
0.002018578117713332,
-0.003523831954225898,
0.06359207630157471,
0.01996014267206192,
-0.01902279257774353,
0.029701175168156624,
-0.0022885354701429605,
-0.00664106709882617,
0.009655020199716091,
-0.02074355259537697,
-0.026157956570386887,
-0.0049104513600468636,
-0.0018403595313429832,
0.0067879860289394855,
0.01056669931858778,
0.0005226131179369986,
0.004035321995615959,
0.007718429435044527,
0.023159578442573547,
-0.004817016422748566,
-0.0435926727950573,
0.008348563686013222,
0.015236714854836464,
-0.023944756016135216,
0.06059872731566429,
-0.002483632415533066,
0.024637455120682716,
0.006068617571145296,
-0.012607241049408913,
-0.044875193387269974,
0.02458280697464943,
-0.03531910479068756,
-0.010498201474547386,
-0.0363958440721035,
-0.01589527353644371,
0.013123154640197754,
-0.023036494851112366,
0.023930352181196213,
0.026676487177610397,
-0.020978465676307678,
0.014136239886283875,
0.04098786413669586,
0.012158920988440514,
-0.014615444466471672,
-0.01917983405292034,
0.011125677265226841,
0.03390837460756302,
0.004915859550237656,
-0.015552026219666004,
0.039707284420728683,
0.07740484178066254,
0.017933210358023643,
0.010907232761383057,
0.053505465388298035,
-0.019074346870183945,
0.012693683616816998,
0.03007456846535206,
-0.024590644985437393,
0.005287281237542629,
-0.03224017471075058,
0.007944113574922085,
-0.032834626734256744,
0.009036574512720108,
-0.005577840842306614,
-0.0098503939807415,
0.07260942459106445,
0.004130193963646889,
0.029225269332528114,
-0.04077078029513359,
0.011216743849217892,
0.017845777794718742,
0.01202001515775919,
0.0025255922228097916,
0.05565943196415901,
-0.01534601952880621,
-0.007768654730170965,
0.0007755556143820286,
0.0039915465749800205,
-0.02083621919155121,
-0.01423586905002594,
0.041093602776527405,
0.02315995842218399,
0.02706202305853367,
-0.0271750520914793,
-0.01584494300186634,
-0.0016115485923364758,
-0.015041286125779152,
0.026808928698301315,
0.04574252665042877,
0.02056671865284443,
0.03188155218958855,
-0.023802733048796654,
-0.02645563706755638,
0.055240482091903687,
-0.0594174861907959,
-0.050926122814416885,
0.018227800726890564,
0.023530296981334686,
0.007626596372574568,
-0.00455814553424716
] |
<p>It is simple to show that under the gauge transformation $$\begin{cases}\vec A\to\vec A+\nabla\chi\\
\phi\to\phi-\frac{\partial \chi}{\partial t}\\
\psi\to \psi \exp\left(\frac{iq\chi}{\hbar}\right)\end{cases}$$
The Schrodinger equation $$\left[-\frac{\hbar^2}{2m}\left(\nabla-\frac{iq\vec A}{\hbar}\right)^2+q\phi \right]\psi=i\hbar\frac{\partial}{\partial t}\psi$$
gives back the same equation.</p>
<p>How does it follow that the probability current is gauge invariant?</p> | 2,832 | [
-0.021288380026817322,
0.009546814486384392,
0.02608153596520424,
-0.0418100543320179,
0.03664780035614967,
0.006589587777853012,
-0.03298093378543854,
0.001128238975070417,
0.01379841286689043,
-0.02038358524441719,
0.03722361475229263,
0.023496897891163826,
0.09024734795093536,
0.0075772227719426155,
0.006245407275855541,
0.04421690106391907,
0.02076093666255474,
0.00022130942670628428,
-0.02218172699213028,
-0.028592396527528763,
-0.03517819195985794,
0.06568977236747742,
0.036245785653591156,
0.013158230111002922,
-0.03477897867560387,
0.04581248760223389,
-0.018136795610189438,
0.016699977219104767,
-0.005368278827518225,
0.1148165687918663,
0.013167662546038628,
-0.021167872473597527,
0.0084783174097538,
0.02595323882997036,
-0.029625367373228073,
-0.0030372990295290947,
-0.05067123845219612,
-0.034025829285383224,
0.039058342576026917,
-0.004476597532629967,
-0.06501074135303497,
0.004886179696768522,
-0.021921224892139435,
0.03189072012901306,
-0.01804438978433609,
0.007942435331642628,
-0.003159700660035014,
0.0065775904804468155,
0.041384004056453705,
-0.06207595765590668,
0.04997079446911812,
0.014286664314568043,
0.03764179348945618,
0.01796654611825943,
-0.026987332850694656,
-0.029217077419161797,
0.02867906168103218,
0.06712525337934494,
0.004732712171971798,
-0.03197093680500984,
-0.0011233317200094461,
-0.050329532474279404,
0.0036001999396830797,
-0.036388326436281204,
-0.010750245302915573,
0.01364581473171711,
0.016228914260864258,
-0.042414285242557526,
0.010961209423840046,
-0.027218298986554146,
0.00852086953818798,
-0.00506557198241353,
-0.01410920824855566,
-0.0142819844186306,
0.0259011909365654,
0.00814666785299778,
-0.007289278320968151,
0.027628425508737564,
0.01345362700521946,
0.032350070774555206,
0.02449141815304756,
0.008832189254462719,
0.04173826426267624,
0.01869712769985199,
-0.00827079638838768,
-0.042046189308166504,
0.06939323991537094,
-0.008481538854539394,
-0.009318278171122074,
0.026789896190166473,
-0.012645312584936619,
0.027234405279159546,
0.023763151839375496,
-0.004652836825698614,
-0.017181068658828735,
0.06179247051477432,
0.02073211967945099,
0.04982900992035866,
-0.0005749507108703256,
-0.024850819259881973,
-0.017475882545113564,
-0.031044134870171547,
0.027152571827173233,
0.039181020110845566,
-0.023244105279445648,
0.02625974453985691,
-0.022985542193055153,
-0.009022940881550312,
-0.01609247364103794,
-0.011205371469259262,
-0.05948304757475853,
0.0258842371404171,
0.0056898524053394794,
0.007200602442026138,
-0.002656684024259448,
-0.03990418091416359,
0.0112399160861969,
-0.028069181367754936,
0.03294459357857704,
0.040710486471652985,
-0.005136799532920122,
-0.01893485337495804,
-0.00496323499828577,
-0.022170700132846832,
-0.02314070612192154,
0.023864559829235077,
0.042122967541217804,
0.0351400189101696,
-0.03389019891619682,
0.011145549826323986,
-0.0069366986863315105,
-0.028707634657621384,
0.007982142269611359,
0.00023314407735597342,
-0.00651867501437664,
-0.020909594371914864,
-0.11080485582351685,
-0.05056558921933174,
0.044775575399398804,
-0.030608488246798515,
-0.01678008958697319,
-0.07550473511219025,
-0.006775603163987398,
0.056348007172346115,
0.0939539223909378,
-0.03320768475532532,
0.048535268753767014,
-0.0005966756725683808,
0.0057249972596764565,
0.011746044270694256,
-0.011490185745060444,
-0.02465854585170746,
0.0036966735497117043,
-0.018447473645210266,
-0.031290363520383835,
-0.06205712631344795,
0.030395928770303726,
0.017311424016952515,
-0.01959790289402008,
-0.014718561433255672,
0.0695209950208664,
-0.021443720906972885,
-0.011707458645105362,
-0.0002307315298821777,
-0.003569679567590356,
-0.013525529764592648,
0.11860819905996323,
0.034354981034994125,
-0.011902239173650742,
0.024693001061677933,
0.007601561024785042,
0.018263498321175575,
0.003973468206822872,
0.010208459571003914,
0.021267419680953026,
-0.050811443477869034,
-0.001195907942019403,
0.0005601776647381485,
-0.002854440128430724,
-0.005578989628702402,
-0.0023539692629128695,
0.00014562465366907418,
-0.056958749890327454,
0.01590280793607235,
0.028484905138611794,
0.01385014969855547,
-0.009800118394196033,
-0.02064250409603119,
-0.02121054008603096,
-0.036176227033138275,
-0.010539930313825607,
-0.05723430588841438,
0.03247317299246788,
0.0036831162869930267,
-0.021060960367321968,
0.025974448770284653,
0.016382092610001564,
-0.0012187018292024732,
0.018430110067129135,
-0.04692016541957855,
0.02586517482995987,
0.010918314568698406,
-0.03177890554070473,
0.00484514283016324,
0.011539103463292122,
0.028569163754582405,
0.04290652275085449,
-0.0027432567439973354,
0.038913529366254807,
-0.0011124862357974052,
-0.06792762875556946,
-0.01461792178452015,
-0.003051134990528226,
0.046378087252378464,
0.023326439782977104,
-0.021314015612006187,
-0.000059985381085425615,
0.017857646569609642,
-0.02870003879070282,
0.025954730808734894,
-0.023620814085006714,
0.04614084213972092,
0.05439632758498192,
0.006711080204695463,
-0.012303181923925877,
0.048521146178245544,
-0.0021504703909158707,
0.03748895227909088,
0.008404114283621311,
-0.03230975940823555,
-0.022384025156497955,
0.006060703191906214,
0.014195460826158524,
0.03154052793979645,
-0.02193591557443142,
0.02380531281232834,
0.017992548644542694,
0.021776942536234856,
0.025639591738581657,
-0.0034053034614771605,
-0.009873908944427967,
-0.05252423882484436,
0.031061604619026184,
0.01824164018034935,
-0.006002647336572409,
-0.06637460738420486,
0.00845703762024641,
-0.021057138219475746,
-0.001396473846398294,
-0.023395223543047905,
-0.031721748411655426,
0.027471475303173065,
-0.04624627158045769,
-0.0009209807612933218,
0.004137134645134211,
-0.03349137306213379,
0.04589013010263443,
-0.009228451177477837,
0.03718145564198494,
0.031228050589561462,
-0.019555589184165,
0.008668316528201103,
-0.04474710300564766,
-0.029450397938489914,
0.02517804503440857,
-0.026819756254553795,
0.021573467180132866,
0.009492950513958931,
-0.007991040125489235,
-0.0030746720731258392,
-0.008687971159815788,
0.002351249335333705,
0.00592432264238596,
-0.031141581013798714,
0.0017317519523203373,
0.03856799378991127,
0.017381533980369568,
0.03247758746147156,
-0.04516207054257393,
-0.056065283715724945,
0.030660327523946762,
0.012173720635473728,
0.0355045311152935,
0.05036969110369682,
-0.01407108549028635,
0.0033866234589368105,
-0.058595020323991776,
-0.007198587991297245,
0.05799941346049309,
-0.008797853253781796,
0.019175995141267776,
-0.041190940886735916,
-0.008901827037334442,
-0.05303407087922096,
0.03177361562848091,
-0.0033598365262150764,
-0.013346049003303051,
-0.025993915274739265,
-0.02120068669319153,
0.06089277192950249,
-0.0032952860929071903,
-0.014330076985061169,
0.014561336487531662,
-0.011551957577466965,
-0.05738009512424469,
0.010031810961663723,
0.010972236283123493,
0.0034260444808751345,
-0.03294692561030388,
0.07316763699054718,
0.04216983914375305,
-0.07022850960493088,
-0.04500487819314003,
-0.051780544221401215,
-0.014067515730857849,
0.013651872053742409,
0.0286055076867342,
0.024707434698939323,
0.008475026115775108,
-0.028623808175325394,
0.07943667471408844,
0.04583229124546051,
-0.05366244539618492,
0.011382843367755413,
0.014878448098897934,
-0.018129024654626846,
-0.026486748829483986,
-0.012578881345689297,
0.05591375753283501,
-0.01377604715526104,
0.0402812734246254,
0.018835153430700302,
0.04734509810805321,
0.004556715488433838,
0.0005532260984182358,
-0.011123305186629295,
0.033672552555799484,
-0.0032954206690192223,
0.0142369968816638,
0.07848788797855377,
-0.0063563622534275055,
-0.0025521523784846067,
-0.030427580699324608,
0.039062727242708206,
0.012937366031110287,
0.017778009176254272,
-0.045109156519174576,
0.07378019392490387,
-0.014499107375741005,
0.020240332931280136,
-0.04113685339689255,
0.04505230858922005,
-0.016184847801923752,
0.00407342379912734,
-0.0008088000467978418,
0.015483340248465538,
0.023561080917716026,
-0.02232399955391884,
0.0009512213873676956,
0.009028895758092403,
0.025822598487138748,
-0.008876382373273373,
-0.03889370337128639,
-0.013500310480594635,
-0.029936453327536583,
0.06011809781193733,
-0.04761630669236183,
-0.048133641481399536,
0.03432735800743103,
0.024849625304341316,
0.006309756077826023,
-0.02525627613067627,
-0.020889516919851303,
-0.027169393375515938,
-0.04256584122776985,
0.012049863114953041,
-0.01564975641667843,
0.03411431610584259,
0.041414618492126465,
0.040359944105148315,
0.036332134157419205,
0.016658110544085503,
0.005490903742611408,
0.01492412481456995,
-0.07924874871969223,
-0.020048070698976517,
-0.017696024850010872,
0.005542142782360315,
-0.0338103286921978,
-0.02119981311261654,
0.009263291023671627,
-0.03812728449702263,
-0.023249713703989983,
-0.01283101737499237,
-0.01601518876850605,
-0.03901885822415352,
0.0006041945889592171,
-0.04313839226961136,
-0.030098794028162956,
-0.03700612112879753,
0.038207683712244034,
0.027918241918087006,
-0.011694103479385376,
0.00473652221262455,
0.0452694296836853,
-0.03317906707525253,
-0.02975517511367798,
0.002409309381619096,
0.006586558185517788,
0.03338228166103363,
0.026400165632367134,
0.023316171020269394,
-0.009865887463092804,
-0.01018935814499855,
0.0006443083984777331,
0.014426964335143566,
0.035679399967193604,
0.0023711901158094406,
-0.006245806813240051,
0.002292148070409894,
-0.059363823384046555,
-0.0337008498609066,
0.0022519254125654697,
0.05024261772632599,
0.04478711262345314,
0.0007695984095335007,
0.034922581166028976,
0.023286977782845497,
-0.048641737550497055,
0.03121974691748619,
0.038246046751737595,
0.007442291360348463,
-0.0010386117501184344,
-0.042460404336452484,
0.022101404145359993,
-0.0016522029181942344,
-0.023803846910595894,
-0.011700531467795372,
-0.032752666622400284,
-0.009465784765779972,
-0.00654590455815196,
0.018575508147478104,
0.0424930639564991,
0.013668142259120941,
-0.046861086040735245,
0.00040548216202296317,
0.00005469873212859966,
0.04911487549543381,
0.01275183167308569,
0.029751580208539963,
0.012964287772774696,
0.009919451549649239,
-0.016831625252962112,
0.00689163152128458,
-0.039343785494565964,
-0.0006818283582106233,
0.029440106824040413,
0.03675428777933121,
-0.020418981090188026,
-0.013404808938503265,
-0.057192202657461166,
-0.007845002226531506,
0.036204028874635696,
0.005292721092700958,
0.019115837290883064,
0.014616013504564762,
-0.06211874261498451,
0.007361693307757378,
-0.06741749495267868,
-0.02047186717391014,
0.017224982380867004,
0.023165641352534294,
0.006502499803900719,
-0.032512497156858444,
-0.03417225927114487,
-0.002518477151170373,
-0.006274452432990074,
0.0015633152797818184,
0.05142809450626373,
0.007809690199792385,
0.013559119775891304,
-0.02177133411169052,
0.05786597356200218,
-0.03052826225757599,
-0.077996626496315,
-0.0026096603833138943,
-0.004079559817910194,
0.020127251744270325,
0.04217786714434624,
-0.04105612635612488,
-0.05645520240068436,
0.013683242723345757,
-0.008427436463534832,
-0.011346274055540562,
0.016468709334731102,
-0.0356036052107811,
0.056287653744220734,
0.006281381007283926,
0.0002946394379250705,
0.05945128574967384,
0.013141117058694363,
0.009852046146988869,
-0.019380098208785057,
-0.02120089717209339,
0.04713152348995209,
-0.04236702620983124,
0.014324655756354332,
-0.028659524396061897,
0.02746364288032055,
-0.025013430044054985,
0.060782596468925476,
-0.0028394372202455997,
0.006750297732651234,
-0.007609921041876078,
0.003912199754267931,
-0.0015964015619829297,
-0.019580073654651642,
-0.016186831519007683,
-0.042528506368398666,
-0.009129921905696392,
0.038039084523916245,
0.02799997292459011,
-0.017586853355169296,
0.035262882709503174,
-0.013125286437571049,
0.006630062125623226,
0.0029947864823043346,
-0.01644647866487503,
-0.003287625964730978,
-0.02975918911397457,
-0.00029464508406817913,
-0.0021470326464623213,
-0.046329133212566376,
0.00684802932664752,
-0.003546611638739705,
0.0036262620706111193,
0.017741449177265167,
-0.007983695715665817,
-0.054585881531238556,
0.01753767766058445,
-0.004145309329032898,
-0.00008892500045476481,
-0.05156340077519417,
0.018077559769153595,
0.04525628313422203,
0.01944882422685623,
-0.10698933154344559,
-0.028178073465824127,
-0.012443319894373417,
-0.003909020684659481,
0.011484868824481964,
-0.03158225119113922,
-0.011276907287538052,
-0.02260296419262886,
-0.03215429559350014,
-0.005056875292211771,
0.041750021278858185,
-0.009436220861971378,
-0.012556038796901703,
0.009104292839765549,
0.051919206976890564,
0.049836814403533936,
-0.03343188390135765,
-0.004878841806203127,
0.020996075123548508,
-0.046337272971868515,
-0.005365767981857061,
0.01453909371048212,
0.05810201168060303,
-0.008190428838133812,
-0.030495181679725647,
0.007779201492667198,
-0.038601893931627274,
0.0016806232742965221,
0.0040407064370810986,
-0.009594369679689407,
0.021374190226197243,
-0.01626645028591156,
-0.012005145661532879,
-0.019891975447535515,
-0.027603602036833763,
0.021674329414963722,
0.04156782105565071,
0.008145097643136978,
0.003486114554107189,
-0.029571492224931717,
-0.014659068547189236,
0.07759175449609756,
0.011780898086726665,
-0.018906617537140846,
0.010058942250907421,
0.05668482556939125,
-0.011764568276703358,
-0.01551334373652935,
0.03586212545633316,
-0.0012928310316056013,
-0.023522894829511642,
-0.039296720176935196,
0.019653918221592903,
0.008414661511778831,
-0.019038304686546326,
-0.043138690292835236,
-0.03357306495308876,
-0.03555271029472351,
0.022451579570770264,
0.04487736150622368,
0.0067077986896038055,
0.060262709856033325,
-0.007150805089622736,
-0.001547951134853065,
-0.023027237504720688,
-0.01596883125603199,
0.011570203118026257,
0.021705197170376778,
-0.010894028469920158,
0.002333531156182289,
-0.022912904620170593,
0.015323895029723644,
0.011732140555977821,
0.04798637703061104,
-0.048801444470882416,
-0.035272832959890366,
0.022160572931170464,
0.03850838169455528,
0.030838364735245705,
0.006329819094389677,
-0.024817943572998047,
0.047671929001808167,
-0.03969063609838486,
0.07337559759616852,
-0.002111385576426983,
0.0010275847744196653,
0.0282859168946743,
0.008319784887135029,
-0.03492800518870354,
-0.016607994213700294,
0.005152922123670578,
-0.02675412781536579,
0.022853361442685127,
0.005045692902058363,
0.011726339347660542,
0.04461599886417389,
0.035007599741220474,
0.05554911494255066,
-0.009349208325147629,
-0.0012125072535127401,
-0.0026601648423820734,
-0.04587810859084129,
0.0016134310280904174,
-0.03941480442881584,
-0.041445791721343994,
0.05290383845567703,
-0.024595195427536964,
-0.016282664611935616,
-0.04280416667461395,
-0.02714255265891552,
0.009832731448113918,
0.020866652950644493,
0.010338096879422665,
-0.01705262064933777,
0.07262486219406128,
-0.012101690284907818,
0.010593331418931484,
-0.01610781066119671,
0.0007326298509724438,
0.11672373861074448,
0.05365052819252014,
0.0403161346912384,
-0.07047891616821289,
0.019160306081175804,
0.0003350925981067121,
0.012998007237911224,
-0.017761029303073883,
0.016490058973431587,
-0.01568259857594967,
0.026613211259245872,
-0.005868846550583839,
0.058185797184705734,
0.027691543102264404,
-0.022702155634760857,
0.03608761727809906,
-0.04973356053233147,
-0.054634079337120056,
0.011709851212799549,
-0.014919896610081196,
-0.026439616456627846,
0.02107962779700756,
-0.03910353034734726,
0.010325592011213303,
-0.031888432800769806,
0.01963081955909729,
-0.025122910737991333,
-0.019290484488010406,
0.004350475501269102,
0.000543748727068305,
-0.032173607498407364,
-0.01124134473502636,
0.005134798586368561,
-0.018908096477389336,
-0.02836064249277115,
0.014599908143281937,
-0.007407496217638254,
-0.002020270563662052,
0.057487912476062775,
0.018488353118300438,
0.017484351992607117,
0.007746029179543257,
0.01272093877196312,
0.019364943727850914,
-0.03277531638741493,
0.00009968818631023169,
-0.011429672129452229,
0.07763320952653885,
-0.012513961642980576,
-0.020815152674913406,
0.0212253388017416,
-0.055348124355077744,
-0.004713171627372503,
-0.018272392451763153,
-0.031129823997616768,
-0.018990114331245422,
0.0023928098380565643,
-0.008827732875943184,
0.03459663316607475,
-0.024658238515257835,
0.028460640460252762,
-0.0075246794149279594,
0.021698111668229103,
-0.011804867535829544,
-0.01395722758024931,
-0.019631586968898773,
0.0034632522147148848,
0.0063981181010603905,
-0.0010474519804120064,
-0.012942996807396412,
-0.03667975217103958,
-0.02406230941414833,
-0.06243817135691643,
-0.06591875851154327,
-0.0005102399154566228,
-0.00172523595392704,
0.06589727103710175,
-0.016094032675027847,
0.007644317112863064,
-0.009392863139510155,
-0.10364096611738205,
0.0017386563122272491,
-0.00012602872448042035,
-0.00020602384756784886,
-0.030898530036211014,
0.005742860492318869,
0.004464170429855585,
0.050724174827337265,
-0.022239765152335167,
-0.007956410758197308,
-0.006732843816280365,
0.04476649686694145,
0.031410589814186096,
-0.008024130016565323,
0.003767328104004264,
0.017212551087141037,
-0.0063012405298650265,
0.0152450455352664,
0.021996598690748215,
0.004869220778346062,
0.0036228960379958153,
0.03435226529836655,
-0.023018615320324898,
0.025285765528678894,
0.0005904329591430724,
-0.01306965108960867,
0.006135096307843924,
-0.0032198927365243435,
0.01592041552066803,
0.025318287312984467,
0.044514674693346024,
-0.01103582140058279,
-0.015734007582068443,
-0.012636635452508926,
0.01775871217250824,
0.019789816811680794,
-0.01749914512038231,
-0.030307352542877197,
-0.012148209847509861,
-0.015704017132520676,
0.04349139332771301,
-0.045121874660253525,
-0.006711747031658888,
-0.03755106031894684,
0.02789529785513878,
-0.017546938732266426,
0.005916159134358168,
0.0037767922040075064,
0.05489668622612953,
-0.014422781765460968,
-0.03824237361550331,
0.02963203191757202,
0.03160816803574562,
-0.022561518475413322,
0.003121335990726948,
-0.0036318027414381504,
0.0038191915955394506,
0.02555074729025364,
-0.025138255208730698,
-0.029377635568380356,
0.06164231523871422,
-0.023693861439824104,
0.0244277473539114,
0.037083327770233154,
0.020265739411115646,
0.031329043209552765,
0.034434158354997635,
-0.04413001239299774,
0.014191672205924988,
0.011056678369641304,
0.001353361294604838,
-0.024093179032206535,
-0.004783532116562128,
-0.07065572589635849,
0.010392902418971062,
-0.03291264548897743,
-0.005104357842355967,
0.001623795717023313,
-0.011545426212251186,
0.032321758568286896,
0.008671400137245655,
-0.026002012193202972,
-0.009018388576805592,
0.032304201275110245,
0.011170055717229843,
0.04407147690653801,
0.05121319741010666,
0.013494279235601425,
0.0003537464654073119,
0.05979541316628456,
-0.025968626141548157,
0.01704670488834381,
-0.027117831632494926,
0.01885039359331131,
-0.07909733057022095,
-0.010172734968364239,
0.044168148189783096,
0.0006996362935751677,
0.0412423349916935,
-0.06546256691217422,
0.010159485042095184,
0.04858243837952614,
-0.09179199486970901,
-0.002996549243107438,
-0.03142513334751129,
-0.029101373627781868,
-0.009933187626302242,
0.027646824717521667,
-0.025118879973888397,
0.07049828767776489,
0.038011759519577026,
0.02570955455303192,
0.02169427089393139,
0.027184737846255302,
-0.002770512830466032,
-0.01327306218445301,
-0.04676253721117973,
0.03511713817715645,
0.025386417284607887,
-0.027226310223340988,
0.04177495092153549,
-0.00894362572580576,
0.010616213083267212,
0.018019095063209534,
0.0060549271292984486,
-0.027624769136309624,
-0.0047804866917431355,
0.023072892799973488,
0.027714839205145836,
0.00970548391342163,
0.018101705238223076,
-0.0028848268557339907,
0.014517824165523052,
-0.017119862139225006,
0.05166773870587349,
0.02069181762635708,
-0.04362217336893082,
-0.01967724598944187,
0.016622617840766907,
-0.020334217697381973,
-0.024477185681462288,
0.03872286155819893,
-0.013281363062560558,
-0.02367376908659935,
0.02890847623348236,
-0.022139864042401314,
0.004701903555542231,
-0.0057354276068508625,
0.018335217610001564,
-0.037648435682058334,
-0.0035057615023106337,
0.03868038207292557,
-0.008244243450462818,
0.03596120327711105,
-0.010144458152353764,
-0.017755677923560143,
-0.0525367446243763,
0.05515214055776596,
0.0199960395693779,
-0.021817393600940704,
-0.07602087408304214,
0.01227518729865551,
-0.020808061584830284,
0.007026545703411102,
0.0255352221429348,
-0.07417991757392883,
-0.034936051815748215,
0.02704646810889244,
-0.0011535651283338666,
0.018897028639912605,
-0.06690645217895508,
-0.013688318431377411,
-0.013973994180560112,
-0.04495184123516083,
0.029154738411307335,
0.02498764544725418,
-0.017927588894963264,
-0.030414503067731857,
-0.01811850629746914,
-0.029393592849373817,
0.030397949740290642,
0.0702781081199646,
0.0009714804473333061,
-0.019257687032222748,
0.04163234680891037,
-0.008729014545679092,
0.011571388691663742,
-0.049729928374290466,
-0.009090256877243519,
-0.017339643090963364,
0.018602192401885986,
0.0031195308547466993,
0.016278771683573723,
-0.001968350727111101,
0.0426221564412117,
-0.03272697702050209,
-0.00811721570789814,
0.039537932723760605,
0.0055901724845170975,
-0.07905314862728119,
0.04490084573626518,
-0.022809388116002083,
-0.008125947788357735,
0.07510576397180557,
-0.01715693809092045,
0.020104385912418365,
-0.001954790437594056,
0.004130326211452484,
-0.02599201910197735,
0.02609035186469555,
-0.0337105318903923,
-0.008912354707717896,
0.023507680743932724,
0.02307857759296894,
0.02466508373618126,
-0.03096633031964302,
-0.012769055552780628,
0.0008747831452637911,
-0.016150377690792084,
-0.04122744873166084,
0.06909751892089844,
0.02068258263170719,
0.030924340710043907,
0.01619821973145008,
0.008766385726630688,
-0.007195858284831047,
0.044211726635694504,
0.0225017461925745,
0.04721847176551819,
0.029103009030222893,
-0.035042617470026016,
0.008893579244613647,
0.04413182660937309,
-0.01810312084853649,
-0.0028065054211765528,
0.02631760574877262,
0.011983798816800117,
-0.05744517222046852,
-0.013289830647408962,
0.0524405762553215,
-0.0071089607663452625,
0.02753133699297905,
0.02101258747279644,
-0.05172012373805046,
0.0663423016667366,
-0.038249421864748,
0.022410839796066284,
0.020394479855895042,
0.020056599751114845,
-0.025859178975224495,
0.031596627086400986,
0.022202223539352417,
0.05814388394355774,
0.0019459062023088336,
-0.025454971939325333,
-0.015358475036919117,
-0.01009061187505722,
-0.019221380352973938,
-0.06014351174235344,
0.01444976031780243,
0.01426671538501978,
-0.03436144441366196,
-0.0069134775549173355,
-0.011838083155453205,
0.018411310389637947,
-0.020631952211260796,
-0.03317882865667343,
0.038484860211610794,
0.02884504571557045,
-0.0008477019728161395,
-0.02702743373811245,
-0.03861023485660553,
0.08003347367048264,
-0.045834317803382874,
-0.0175856314599514,
-0.037002768367528915,
-0.004979151766747236,
-0.027844486758112907,
-0.011909637600183487
] |
<p>Quantum fields are presented as operator-valued <em>distributions</em>, so that the <em>operators</em> in the theory are linear functionals of some test function space. This works well for free fields, giving us a particular form for VEVs, in which the 2-point connected correlation function determines the whole theory, and a trivial S-matrix.</p>
<p>For interacting fields, however, the VEVs and the statistics of S-matrix observables that are predicted by the theory depend not only on the test functions (generally given for the S-matrix in terms of pure, improper wave-number modes of the free field at $t=\pm\infty$) but also on the "energy scale of measurements". One obtains a different functional form at different energy scales.</p>
<p>The energy scales at which one is measuring are already encoded in the wave-numbers associated with the test functions, so it seems that the test functions play extra duty, to determine the functional form of the VEVs (at least in their S-matrix form) both by linearly smearing the quantum field and, more indirectly, by determining the renormalization scale. As a consequence, the VEVs, the Wightman functions, seem clearly to be nonlinear functionals of the test functions for interacting QFTs.</p>
<p>I've worried at this for a while. The argument as put brings into question the Wightman axioms' insistence that a quantum field must be a linear map from the test function space to the space of operators, although I suppose the effect would be only logarithmic in some measure of the frequencies of the test functions. The Haag-Kastler additivity axiom also seems problematic. I'm not aware of weakening this particular aspect of the Wightman or Haag-Kastler axioms so as to be able to construct models of the axioms that parallel empirically successful QFT having been discussed in the literature, but have they?</p>
<p>[Note that dropping the linearity of the map from test functions to operators in the algebra of observables does not affect the linearity of the algebra. There's still a perfectly good probability interpretation of a state over a *-algebra and a perfectly good Hilbert space, but the relationship of measurements to space-time is somewhat modified.]</p>
<p>EDIT: I'll <em>attempt</em> to make the Question slightly more accessible. It turns out that what follows makes it significantly longer. The Wightman functions (effectively a different name for Vacuum Expectation Values (VEVs)) allow the reconstruction of a Wightman (quantum) field. That is, given the vacuum state over the algebra one can construct the Wightman functions, $$W(x_1,x_2,...x_n)=\left<0\right|\hat\phi(x_1)\hat\phi(x_2)...\hat\phi(x_n)\left|0\right>,$$ but also, given the Wightman functions one can construct the algebra. Wightman functions satisfy somewhat arcane relationships, so that just any function $VV(x_1,x_2,...,x_n)$ is almost certainly not a Wightman function and cannot be used to reconstruct a Wightman field.</p>
<p>The object $\hat\phi(x)$ is not an operator in the algebra of observables, it is an <em>operator-valued distribution</em>, so that if we have a well-behaved "test function" $f(x)$, where "well-behaved" most often means that it is smooth (infinitely differentiable) and has a smooth fourier transform, then $\hat\phi_f=\int\hat\phi(x)f(x)\mathrm{d}^4x$ <em>is</em> an operator. This is often called "smearing" with the test function $f(x)$. The test function $f(x)$ effectively tells us what relative amplification we apply to the field at each point in space-time for a given measurement, and its fourier transform $\tilde f(k)$ tells us what relative amplification we apply to the field at each point in momentum space. In signal analysis the same object is called a "window function", which can be looked up on Wikipedia. One can talk about the bandwidth of a measurement, or say that a signal transformation is high-pass or low-pass. If it were not for non-commutativity of measurement operators at time-like separation, quantum field theory would be <em>exactly</em> what one would want for a mathematical formalism for modeling stochastic signal processing. If one only talks about measurements that are space-like separated —admittedly a tight constraint—, QFT <em>is</em> a stochastic signal processing formalism.</p>
<p>In contrast to $\hat\phi(x)$, $\hat\phi_f$ is not a singular mathematical object; the difference is comparable to the difference between a smooth function and the Dirac delta function. In terms of these operators, the Wightman functions become $$W(f_1,f_2,...,f_n)=\left<0\right|\hat\phi_{f_1}\hat\phi_{f_2}...\hat\phi_{f_n}\left|0\right>,$$
which is linear in all the test functions.
When we move to the practical formalisms of interacting QFT, however, the VEVs predicted by the bare theory are infinite. Renormalization fixes that in a Lorentz invariant way, but it leaves the VEVs a function of the energy scale $\mu$ of the measurements that are involved in an experiment. Thus, one finds that the Wightman functions are now a function of $\mu$ as well as of the points $x_i$, $W_\mu(x_1,x_2,...x_n)$, or, in terms of operators, $W_\mu(f_1,f_2,...f_n)$. [It's perhaps worth noting that we don't know whether these $W_\mu(...)$ satisfy the relationships required for them to be Wightman functions, so that we could reconstruct a Wightman field, but I've never seen a discussion of perturbative QFT conducted in such terms.] The Wightman functions in terms of positions do not encode energy scales, but they are <em>not</em> observables, they are only a template for constructing observables. The fourier transforms of the test functions, $\tilde f_i(k)$, however, already determine various energy scales at which the measurements made in an experiment operate, potentially in <em>much</em> more detail than a single number $\mu$. We could just say that the energy scale of measurements $\mu$ is separate from the energy scales determined by the test functions $f_i$, but it seems more natural <em>to me</em> to say that $\mu$ is a functional of the test functions $f_i$, in which case we can write $W'(f_1,f_2,...f_n)=W_\mu(f_1,f_2,...f_n)$, where $W'$ is now a non-linear functional of the $f_i$. I suppose we expect $W'$ to be a symmetric function of each of the $f_i$.</p>
<p>For a more-or-less trivial example, suppose we have two ordinary quantized Klein-Gordon fields $\hat\phi_f$ and $\hat\xi_f$, not necessarily having the same mass spectrum, then we could construct a quantum field $\hat\Phi_f=\hat\phi_f+\hat\xi_{f+\epsilon f^2}$ (where the square $f^2$ is $[f^2](x)=[f(x)]^2$, so that $\hat\Phi_f$ satisfies microcausality), so that $\hat\Phi:\mathcal{S}\rightarrow\mathcal{A};\hat\Phi:f\mapsto\hat\Phi_f$ is a nonlinear map from the test function space into the algebra of observables. This is still a Gaussian field, so not interacting. Already there start to be significant complications. One of the most fundamental Wightman axioms is the restriction to positive spectrum, which in terms of test functions is a projection to forward light-cone components of the test functions. Only components of $\tilde f(k)$ for which $k_\alpha$ is in the forward light-cone have any effect on measurement results. In the above, however, forward light-cone components of $f^2(x)$ contribute, which in fourier space, where $f^2(x)$ is a convolution, means that negative frequency components of $f(x)$ will contribute. Although this means that this kind of nonlinearity apparently does not satisfy positivity of the energy, it's not clear that this means such a system is not <strong><em>stable</em></strong>, which is the (non-axiomatic) reason why we insist on positivity of the energy as an axiom. Which, whoops, brings into question positivity of the energy, one of the <em>big</em> axioms, which I asked about <a href="http://physics.stackexchange.com/q/5812/2451">here</a>.</p>
<p>Now, of course, I'm trying out doing research here as if it was a virtual blackboard. Many of the ideas above ought to be rubbed out, different ideas tried and equally or more vigorously discarded. I've got lots of pieces of paper that have discarded ideas on them that you don't want to see, because I hope you have your own discarded ideas, as anyone who doesn't get too fixed in their ways should, most of which I probably don't want to see (not that I'm not a little fixed in my ways, but I've discarded <em>some</em> ideas). The trouble is that I can't see how we can go forward from me just typing away, I think the feedback loop may be too long for this to work. Still, the alternative is to write a paper and get feedback six months later. This introduces Questions that I may try to put on meta.</p>
<p>By the way, making a Question Favorite counts for no Reps, but it's much appreciated. </p> | 2,833 | [
-0.028407536447048187,
-0.004946231842041016,
0.010310589335858822,
-0.02779671922326088,
0.04739538952708244,
0.01031065359711647,
-0.042060233652591705,
-0.014009702950716019,
0.021398484706878662,
-0.04484451934695244,
0.030841678380966187,
-0.0038853466976433992,
0.021341323852539062,
0.0030566900968551636,
0.006371538154780865,
0.01227966882288456,
-0.028065204620361328,
-0.020472312346100807,
-0.01620631292462349,
-0.006488248240202665,
0.002040633000433445,
0.05504576116800308,
0.004409705754369497,
-0.02469421550631523,
-0.0026671146042644978,
-0.0005482016713358462,
-0.007534306030720472,
0.009177601896226406,
0.028361963108181953,
0.0477573424577713,
0.016728434711694717,
-0.05584700033068657,
-0.012087960727512836,
0.02015558071434498,
0.019386883825063705,
-0.01657901145517826,
-0.0006277633947320282,
0.015515079721808434,
0.011247705668210983,
0.009136684238910675,
-0.021445661783218384,
0.0010041731875389814,
-0.018841229379177094,
0.025413593277335167,
0.017630547285079956,
0.01532873883843422,
0.023864690214395523,
-0.010019424371421337,
0.06151233986020088,
-0.04300089552998543,
0.0647086352109909,
-0.018326662480831146,
-0.0015114342095330358,
0.0076111131347715855,
-0.03733048215508461,
-0.00973217748105526,
0.04073388874530792,
0.050573498010635376,
0.012518470175564289,
-0.050710905343294144,
-0.005807330831885338,
-0.01655632257461548,
-0.01191501785069704,
-0.01649448834359646,
0.002617672784253955,
0.01919328048825264,
0.0315423347055912,
0.0005464652203954756,
0.011705533601343632,
-0.03620642051100731,
-0.0020435547921806574,
0.02756921388208866,
0.03959792107343674,
-0.02046508900821209,
0.005909800063818693,
0.035804349929094315,
0.014111646451056004,
0.015383260324597359,
0.03001244366168976,
0.011944360099732876,
0.008746332488954067,
0.037036437541246414,
0.00986757967621088,
0.018321780487895012,
0.03869394585490227,
-0.00045842205872759223,
0.04469495639204979,
-0.007694259285926819,
-0.0020211655646562576,
0.05874745547771454,
-0.012359213083982468,
-0.006003291811794043,
0.035735100507736206,
0.0024349542800337076,
-0.06741202622652054,
0.02730410173535347,
-0.003634439315646887,
0.04602702334523201,
-0.004372393246740103,
-0.0017915505450218916,
-0.018868381157517433,
-0.038549378514289856,
-0.028368348255753517,
0.050247639417648315,
-0.02942427434027195,
-0.01376376859843731,
-0.02910872921347618,
0.02145211212337017,
-0.03284478560090065,
-0.041834570467472076,
-0.059543266892433167,
0.009687833487987518,
-0.0075243739411234856,
0.02932700701057911,
-0.0030429556500166655,
-0.019435251131653786,
0.006820425391197205,
-0.05306725203990936,
0.061930324882268906,
0.0811406821012497,
0.06356852501630783,
-0.029411522671580315,
-0.00612987857311964,
-0.002141867997124791,
-0.02989150583744049,
0.028284437954425812,
0.039731450378894806,
-0.016309987753629684,
-0.03343228995800018,
-0.005059431307017803,
0.05015360936522484,
-0.00046666141133755445,
0.021245501935482025,
0.014615270309150219,
0.027877474203705788,
-0.05820045247673988,
-0.08638852834701538,
-0.023447087034583092,
0.02455040253698826,
0.008692602626979351,
-0.0005102292052470148,
-0.0559309683740139,
-0.0065156398341059685,
0.03766763210296631,
0.07035918533802032,
-0.048104189336299896,
0.015384540893137455,
-0.016772445291280746,
0.04256134107708931,
0.01598331145942211,
-0.02085864543914795,
-0.024142557755112648,
-0.03179129213094711,
-0.03751513734459877,
-0.040052011609077454,
-0.01883159577846527,
0.06260350346565247,
0.02983321063220501,
-0.014448525384068489,
0.0131252221763134,
0.041215915232896805,
0.004670366179198027,
-0.01815061829984188,
0.01101723313331604,
-0.001249596942216158,
-0.028746817260980606,
0.05857119709253311,
-0.0022179652005434036,
0.03851759061217308,
0.05035775527358055,
-0.02827451191842556,
-0.005390366539359093,
0.04187992960214615,
0.015565811656415462,
0.032982125878334045,
-0.04575882852077484,
-0.020819490775465965,
-0.02268495038151741,
0.023633727803826332,
-0.005411237012594938,
-0.04599147289991379,
-0.017611011862754822,
-0.0577252060174942,
0.009952112101018429,
-0.013774593360722065,
0.01480330340564251,
-0.020045453682541847,
-0.018626948818564415,
0.00589374266564846,
-0.07277950644493103,
-0.031262774020433426,
-0.060584329068660736,
0.02060249261558056,
0.013634484261274338,
0.0005279958131723106,
0.09653870761394501,
-0.015313380397856236,
-0.0006253211759030819,
-0.016627704724669456,
-0.04569350555539131,
0.018980590626597404,
0.0374317541718483,
0.03399750217795372,
0.004748098086565733,
0.05508295074105263,
0.01994028128683567,
0.06971152871847153,
0.016821736469864845,
0.044904790818691254,
-0.023782525211572647,
-0.06028229370713234,
0.023098669946193695,
-0.021456023678183556,
0.018345871940255165,
0.010857252404093742,
0.006317146122455597,
-0.0004471450811251998,
-0.006342371925711632,
-0.00360502814874053,
0.02249542996287346,
-0.054844945669174194,
0.03331223130226135,
0.023691920563578606,
-0.039800841361284256,
-0.008120812475681305,
0.06139937788248062,
-0.019229019060730934,
0.031444668769836426,
-0.004303185734897852,
-0.007475606165826321,
-0.06096009537577629,
-0.031359463930130005,
0.0449555329978466,
0.06545789539813995,
0.013991517014801502,
0.017140956595540047,
0.06598305702209473,
0.03112158179283142,
-0.0077566122636199,
0.023162301629781723,
-0.043303024023771286,
-0.03206706419587135,
0.028327658772468567,
-0.014684784226119518,
0.03542556241154671,
-0.014513269066810608,
-0.015220152214169502,
0.006684667896479368,
0.013987156562507153,
0.014281396754086018,
-0.04544016346335411,
0.012080447748303413,
-0.049306683242321014,
-0.0032879516948014498,
-0.025066956877708435,
-0.025276124477386475,
-0.010790734551846981,
-0.0239508468657732,
0.007105597294867039,
0.05528602749109268,
-0.027702992781996727,
0.015663526952266693,
-0.005934074055403471,
-0.0027974986005574465,
0.03565612807869911,
0.0012191960122436285,
-0.02068031206727028,
0.02298043482005596,
0.037869732826948166,
-0.03757062181830406,
-0.008372161537408829,
-0.020739175379276276,
0.004078676458448172,
-0.01835694909095764,
0.011673854663968086,
0.027949253097176552,
-0.01877657324075699,
0.01915784366428852,
-0.03327681124210358,
0.0021130205132067204,
0.03668142482638359,
-0.008069994859397411,
0.04467332363128662,
0.035080842673778534,
-0.006441398058086634,
-0.004312560893595219,
-0.08376510441303253,
-0.04241480305790901,
0.011315224692225456,
-0.04019742086529732,
0.012733283452689648,
-0.013701928779482841,
-0.02300403267145157,
-0.023179832845926285,
-0.039679061621427536,
-0.011242865584790707,
0.014815915375947952,
-0.004981054924428463,
-0.005369783844798803,
0.05585779994726181,
0.035150520503520966,
-0.04927263408899307,
0.02359391748905182,
-0.0000907546273083426,
-0.009809993207454681,
-0.022035999223589897,
-0.007000703364610672,
0.017905736342072487,
-0.04896790534257889,
0.056790173053741455,
0.03418257087469101,
-0.05393194034695625,
-0.004874149803072214,
-0.07953273504972458,
-0.044234275817871094,
-0.012766620144248009,
0.009817879647016525,
0.050639498978853226,
0.0050671580247581005,
-0.02430189959704876,
0.07620783150196075,
0.04500478506088257,
-0.007813581265509129,
-0.011625616811215878,
0.01648731343448162,
-0.011466944590210915,
-0.006050444208085537,
0.04261025786399841,
0.016472114250063896,
0.020554812625050545,
0.08268043398857117,
-0.0007767563802190125,
0.011866808868944645,
0.010870344005525112,
-0.018109753727912903,
-0.018067900091409683,
0.03375351428985596,
0.000019758639609790407,
-0.0158883947879076,
0.06482348591089249,
0.0010002627968788147,
0.009393054991960526,
-0.028181109577417374,
0.013147862628102303,
-0.0073671117424964905,
0.015101264230906963,
-0.03140004351735115,
0.06756711006164551,
0.041633546352386475,
0.016481731086969376,
-0.02408374845981598,
0.009125305339694023,
0.018476570025086403,
-0.010567453689873219,
-0.008546991273760796,
-0.0070215435698628426,
0.008372650481760502,
0.004599685315042734,
0.045041654258966446,
0.013897941447794437,
0.0720120221376419,
-0.03416574001312256,
-0.0350581519305706,
-0.03910456597805023,
-0.004711369052529335,
0.024559739977121353,
-0.021578796207904816,
-0.0452391617000103,
0.04238184168934822,
0.05837322771549225,
0.01719292439520359,
-0.01876046322286129,
-0.010521184653043747,
-0.015481396578252316,
-0.016953259706497192,
-0.015532371588051319,
-0.013919571414589882,
0.01702755130827427,
0.04535914212465286,
0.03101220168173313,
0.019000306725502014,
-0.014608246274292469,
-0.016481030732393265,
-0.015309513546526432,
-0.08158641308546066,
-0.034900665283203125,
-0.025140931829810143,
-0.030010564252734184,
0.035167984664440155,
-0.01213239599019289,
0.008797905407845974,
-0.013153128325939178,
-0.031388502568006516,
-0.024130217730998993,
0.0005041282856836915,
-0.053346216678619385,
-0.007268793415278196,
-0.02808956988155842,
-0.05828837305307388,
0.0003059808223042637,
0.0199505016207695,
0.050836216658353806,
-0.038747794926166534,
0.013116165064275265,
0.012169115245342255,
-0.04712308943271637,
0.02383454330265522,
0.008081458508968353,
0.024694984778761864,
0.008578930050134659,
0.033859316259622574,
0.006822654977440834,
0.010623696260154247,
-0.04524478316307068,
-0.004148064646869898,
0.04104634001851082,
0.0358901210129261,
0.02654844895005226,
-0.030111897736787796,
-0.0050240736454725266,
-0.0404672734439373,
-0.02020310051739216,
0.014324183575809002,
0.04903680831193924,
0.03629693016409874,
-0.019366886466741562,
0.058554571121931076,
0.04497785493731499,
-0.016464240849018097,
0.01034540869295597,
0.03787039592862129,
-0.01759771816432476,
0.010320901870727539,
-0.01880815252661705,
-0.0275869183242321,
-0.01692817732691765,
-0.0009582404745742679,
-0.024284815415740013,
0.017421158030629158,
-0.017997626215219498,
0.00951539259403944,
0.045652225613594055,
0.016086764633655548,
-0.06089998409152031,
-0.01120056677609682,
0.035451363772153854,
-0.026800956577062607,
-0.022021494805812836,
-0.024114737287163734,
-0.008324389345943928,
0.03841840848326683,
0.020927898585796356,
0.014916472136974335,
0.014966909773647785,
-0.05852222442626953,
-0.005194361321628094,
0.0646524429321289,
-0.005791341420263052,
0.03866676613688469,
-0.008806990459561348,
-0.03218049556016922,
-0.02792343683540821,
0.0501469187438488,
0.010182615369558334,
0.02337758243083954,
0.04057116433978081,
0.010720477439463139,
-0.06416799128055573,
-0.04713354632258415,
-0.05531300604343414,
0.012402396649122238,
0.025826936587691307,
-0.013853608630597591,
-0.05516527220606804,
-0.027070453390479088,
-0.023083187639713287,
0.012345433235168457,
0.008394281379878521,
0.030902795493602753,
0.003376223146915436,
-0.010907434858381748,
-0.009875064715743065,
-0.00647546024993062,
-0.029047930613160133,
-0.05384939908981323,
0.021844135597348213,
0.013989078812301159,
0.007688285317271948,
0.013888241723179817,
0.005693384446203709,
-0.04928163066506386,
0.032145265489816666,
-0.019981542602181435,
-0.027302201837301254,
0.03822382912039757,
-0.028449730947613716,
0.10421353578567505,
-0.005896316841244698,
0.05066780373454094,
0.026634888723492622,
0.021135469898581505,
-0.038944683969020844,
0.028772825375199318,
-0.0028313128277659416,
0.005178673658519983,
-0.009128994308412075,
0.026765180751681328,
-0.06918708235025406,
-0.03530966490507126,
-0.007481956388801336,
0.016869308426976204,
-0.030722148716449738,
0.02519391104578972,
-0.01957719586789608,
-0.030950000509619713,
-0.0077121322974562645,
0.014679967425763607,
-0.012007486075162888,
-0.0348723828792572,
0.02062155120074749,
0.05938372015953064,
0.005881323013454676,
0.003301623510196805,
0.014419672079384327,
0.012932037003338337,
0.028760066255927086,
0.03190348669886589,
-0.004033504985272884,
0.0043128603138029575,
-0.02231481671333313,
0.007120468188077211,
-0.007427075877785683,
-0.044215381145477295,
0.02767975628376007,
-0.018330713734030724,
-0.004555040970444679,
-0.030766084790229797,
-0.019243832677602768,
-0.0275554396212101,
0.003470783121883869,
-0.031125182285904884,
0.023129690438508987,
0.0008538785623386502,
-0.022117897868156433,
0.0456509105861187,
0.00009887827764032409,
-0.07490357756614685,
-0.01708064414560795,
0.00446521257981658,
0.0015653427690267563,
-0.0007014577859081328,
-0.02701265551149845,
0.03221685066819191,
-0.03354381024837494,
0.010047022253274918,
-0.00925274658948183,
0.05454117804765701,
-0.04205407202243805,
0.017942188307642937,
0.03306681662797928,
0.029124051332473755,
0.03799836337566376,
0.005875805392861366,
-0.008558690547943115,
0.03404201567173004,
-0.004477959591895342,
0.004173708148300648,
0.003749894443899393,
-0.008732588961720467,
-0.04169166833162308,
-0.0354132242500782,
-0.016355857253074646,
-0.007777604274451733,
0.008352747187018394,
-0.01672135666012764,
-0.01842467486858368,
0.02378397062420845,
0.02015085704624653,
0.0032750398386269808,
0.00005333009175956249,
-0.0013576979981735349,
0.01227483619004488,
0.017686627805233,
0.0017004001419991255,
-0.03717394918203354,
-0.02058934047818184,
-0.014829589985311031,
0.02210584655404091,
-0.04334467276930809,
-0.03336341306567192,
-0.004278476350009441,
0.004609784577041864,
0.0033282465301454067,
-0.005559558514505625,
0.02045857533812523,
-0.040075819939374924,
0.004547773860394955,
-0.007750826887786388,
0.028138047084212303,
0.001969020813703537,
0.010738088749349117,
-0.01692066714167595,
-0.042365461587905884,
-0.04418717697262764,
-0.038778237998485565,
0.04584207758307457,
0.019729861989617348,
0.027678918093442917,
0.005937299225479364,
0.01201634295284748,
-0.014600403606891632,
-0.035165123641490936,
-0.021638832986354828,
0.0019206139259040356,
0.005013307090848684,
0.01655261218547821,
-0.03739871084690094,
0.002570749493315816,
0.026880575343966484,
0.04226929321885109,
-0.039242006838321686,
0.009870009496808052,
-0.0023199310526251793,
0.02919057570397854,
0.05772458761930466,
-0.053139425814151764,
-0.05724678933620453,
0.06689215451478958,
-0.05011465772986412,
0.013498472981154919,
0.016592491418123245,
0.009956047870218754,
0.0067020258866250515,
0.04511398822069168,
-0.00032647233456373215,
0.007163829170167446,
-0.030503520742058754,
-0.03579765558242798,
-0.03037033975124359,
0.015197585336863995,
0.014696881175041199,
0.01567317731678486,
-0.020852774381637573,
0.02685895375907421,
0.01687130518257618,
0.017716698348522186,
0.003912125248461962,
-0.05108802020549774,
0.0002748170227278024,
-0.01728365570306778,
-0.039993781596422195,
0.048834096640348434,
-0.015684014186263084,
-0.01588677614927292,
-0.024501271545886993,
-0.022061849012970924,
0.043080564588308334,
0.024580661207437515,
0.040964532643556595,
-0.03196674957871437,
0.05956285074353218,
-0.041220638900995255,
0.01364237442612648,
-0.058373939245939255,
0.004701510071754456,
0.13131287693977356,
0.048695169389247894,
0.018077094107866287,
-0.04820999875664711,
0.006703790742903948,
0.0005882455152459443,
0.020517772063612938,
-0.028244279325008392,
0.0211081113666296,
-0.015474899671971798,
-0.03706891089677811,
0.022906091064214706,
0.04954081401228905,
0.0011486544972285628,
-0.02614509128034115,
0.03590577840805054,
-0.040568239986896515,
-0.023857686668634415,
0.002056725788861513,
0.02940596453845501,
-0.033162862062454224,
-0.0068327197805047035,
-0.03838450089097023,
-0.015193897299468517,
0.012166345492005348,
0.026335226371884346,
0.01300977822393179,
-0.014815587550401688,
0.02759275957942009,
0.0016755505930632353,
-0.05213028937578201,
-0.03185848519206047,
0.015643758699297905,
0.03026239573955536,
-0.025348380208015442,
-0.00803518295288086,
-0.00008566149335820228,
-0.00034945763763971627,
0.037106212228536606,
0.027166513726115227,
-0.0017704801866784692,
0.004869966302067041,
-0.010200564749538898,
0.026297608390450478,
-0.03770986199378967,
-0.02826661802828312,
-0.034630630165338516,
0.06692091375589371,
-0.037061624228954315,
-0.055801160633563995,
-0.014114297926425934,
-0.0497150756418705,
0.02817911095917225,
-0.03495052084326744,
-0.012528186663985252,
-0.006543347612023354,
0.03962863236665726,
-0.014851877465844154,
0.01620539464056492,
0.002198521513491869,
0.037767067551612854,
-0.012326781637966633,
0.026758389547467232,
-0.01038940716534853,
-0.030149400234222412,
0.013481898233294487,
0.0050963060930371284,
0.04895281046628952,
0.024865146726369858,
-0.027116380631923676,
0.016950473189353943,
-0.014979646541178226,
-0.038579247891902924,
0.0025273733772337437,
0.012361391447484493,
0.012577666901051998,
0.0737379640340805,
0.0035511350724846125,
0.012508132494986057,
-0.031463153660297394,
-0.06664467602968216,
-0.009810228832066059,
-0.04344881325960159,
-0.03484916314482689,
-0.00850443635135889,
0.02545466460287571,
-0.0007492729928344488,
0.045336220413446426,
-0.00038116323412396014,
-0.007655755616724491,
0.02486218698322773,
0.04591438174247742,
0.011374366469681263,
-0.04796674847602844,
-0.007767615374177694,
-0.007040097378194332,
-0.015589823015034199,
-0.01917991042137146,
-0.0075429026037454605,
0.02281898818910122,
0.036927271634340286,
0.01837017387151718,
-0.009045670740306377,
0.013364884071052074,
-0.00751092005521059,
-0.011789536103606224,
0.04871417209506035,
-0.018988776952028275,
-0.040476806461811066,
0.010278450325131416,
0.006912393029779196,
-0.02307526208460331,
-0.07347802072763443,
-0.02850532718002796,
-0.001621378818526864,
-0.0007277522818185389,
0.007762263063341379,
-0.035042401403188705,
-0.014344670809805393,
0.0028337151743471622,
0.022065313532948494,
-0.02496148645877838,
0.011391600593924522,
-0.0019135319162160158,
0.03302064165472984,
-0.03673669323325157,
0.02930646948516369,
0.030521409586071968,
0.03919167071580887,
-0.037615228444337845,
-0.027049429714679718,
0.017517510801553726,
0.04671069607138634,
-0.0322989858686924,
-0.0018959137378260493,
0.004809387493878603,
0.01686115935444832,
0.044985439628362656,
0.024072784930467606,
-0.015685461461544037,
0.05973285809159279,
-0.05021053925156593,
-0.03186914324760437,
0.03529396280646324,
-0.0050298855639994144,
0.027972470968961716,
0.03757453337311745,
-0.007760939188301563,
-0.04650551453232765,
0.019443120807409286,
-0.03373871371150017,
0.015820642933249474,
0.015368567779660225,
-0.04371548071503639,
-0.01325653400272131,
-0.004304800648242235,
0.04605837166309357,
0.002491304650902748,
0.008023010566830635,
0.020395586267113686,
-0.00712583540007472,
-0.02867397479712963,
0.0008260438335128129,
0.023930523544549942,
-0.07043576240539551,
0.027264416217803955,
0.007910202257335186,
-0.03755461797118187,
0.01299985684454441,
0.029854489490389824,
-0.010832620784640312,
0.048579148948192596,
0.00661737285554409,
0.01470466423779726,
-0.10732599347829819,
-0.03351083770394325,
0.019589096307754517,
0.028427863493561745,
0.04841502010822296,
-0.028667118400335312,
-0.015674976631999016,
-0.013850958086550236,
-0.07897673547267914,
0.0789613276720047,
0.002117385622113943,
-0.017311865463852882,
-0.048731040209531784,
0.010449792258441448,
-0.06674294918775558,
0.03128809109330177,
0.0074998801574110985,
0.03236977756023407,
-0.02975693717598915,
0.039185650646686554,
0.00867023691534996,
-0.00414247764274478,
-0.047775205224752426,
0.015842556953430176,
0.007838498800992966,
0.010562206618487835,
0.0891924798488617,
-0.010330922901630402,
0.0060242838226258755,
0.02454499527812004,
0.024281853809952736,
0.014607814140617847,
-0.026249241083860397,
0.002592256758362055,
0.02196964994072914,
0.054951898753643036,
0.03325191140174866,
-0.03819027543067932,
-0.013084015808999538,
-0.0014736182056367397,
0.010844942182302475,
0.03405638784170151,
0.00010952012235065922,
-0.004888475406914949,
0.0028263067360967398,
-0.054420117288827896,
-0.026925047859549522,
0.025473913177847862,
0.025317369028925896,
0.01238983403891325,
-0.017002342268824577,
0.013290951028466225,
0.04122423753142357,
-0.005179272033274174,
0.009358950890600681,
-0.061380039900541306,
-0.023056549951434135,
0.013763220980763435,
-0.0008354873862117529,
-0.042002562433481216,
0.0027203375939279795,
-0.02712477557361126,
-0.024551531299948692,
0.016856878995895386,
0.009502200409770012,
0.030113520100712776,
-0.06199243664741516,
-0.009137178771197796,
-0.012501170858740807,
0.009708675555884838,
-0.0007273249211721122,
-0.026037434116005898,
-0.02825912833213806,
0.028520269319415092,
-0.03228053078055382,
0.03858647495508194,
-0.03424353152513504,
-0.024596204981207848,
0.000578894920181483,
-0.08346480876207352,
0.02843412756919861,
-0.0008508279570378363,
0.013551431708037853,
-0.0015357461525127292,
0.012764032930135727,
0.013478312641382217,
0.015915850177407265,
0.05705267935991287,
0.0014008983271196485,
-0.05734711140394211,
-0.0010539274662733078,
0.006780767813324928,
0.019831223413348198,
-0.014371045865118504,
-0.016380956396460533,
-0.03495315834879875,
0.021978532895445824,
-0.025351038202643394,
-0.038036227226257324,
0.016855426132678986,
0.004356068558990955,
0.018333373591303825,
-0.05318530648946762,
-0.025776198133826256,
-0.015464399941265583,
-0.0697343721985817,
0.07768916338682175,
0.01288822665810585,
0.010423194617033005,
0.0323566235601902,
-0.04228196293115616,
0.027306202799081802,
0.03687882423400879,
-0.02609214559197426,
-0.023435842245817184,
-0.0037381979636847973,
-0.019016118720173836,
-0.039988789707422256,
0.01723347418010235,
0.05083756893873215,
0.03175973519682884,
0.015725748613476753,
-0.017217272892594337,
0.07017070800065994,
-0.014215405099093914,
-0.04184705391526222,
0.04919488728046417,
-0.0009174711303785443,
0.029804682359099388,
0.01646527461707592,
0.0317109078168869,
0.025855351239442825,
0.0293508879840374,
0.009850473143160343,
0.03886222839355469,
0.06391965597867966,
0.03057851456105709,
-0.0029983199201524258,
0.04807787016034126,
-0.04820876196026802,
0.027216795831918716,
0.0356723852455616,
0.0308874249458313,
-0.037139520049095154,
0.0076037002727389336,
0.019494248554110527,
-0.011340834200382233,
-0.006754312664270401,
0.032395269721746445,
-0.035136185586452484,
0.08898422122001648,
-0.010046727024018764,
-0.003322754753753543,
-0.06817779690027237,
0.009810584597289562,
-0.008600135333836079,
0.029289186000823975,
0.027371710166335106,
0.038914214819669724,
-0.04937439039349556,
0.023465512320399284,
0.018752247095108032,
0.01045960932970047,
-0.01179574429988861,
-0.027903204783797264,
-0.028525695204734802,
-0.004356174264103174,
-0.013925479725003242,
0.012278454378247261,
-0.001580190029926598,
-0.0236271470785141,
0.002794942120090127,
-0.008915042504668236,
0.0690690204501152,
0.012720681726932526,
0.009215540252625942,
0.018501710146665573,
-0.024736449122428894,
0.05328751727938652,
-0.04139647260308266,
0.010921670123934746,
-0.026569942012429237,
0.04782802611589432,
0.027425354346632957,
-0.018398819491267204
] |
<p>Source:
<a href="http://www.engineeringtoolbox.com/sound-power-intensity-pressure-d_57.html" rel="nofollow">http://www.engineeringtoolbox.com/sound-power-intensity-pressure-d_57.html</a></p>
<p>Both sound intesity and pressure level are measured in dB. Given a specific sound, are these two dB values the same?</p> | 2,834 | [
-0.030234569683670998,
-0.041286811232566833,
-0.00019705355225596577,
-0.022772572934627533,
0.03700859844684601,
0.03526477515697479,
-0.02265632525086403,
-0.04104606807231903,
0.06398481875658035,
-0.014328690245747566,
0.02735193446278572,
0.040824901312589645,
0.044757165014743805,
0.0020321982447057962,
0.015589224174618721,
0.026646409183740616,
-0.029321495443582535,
0.03639592230319977,
0.015435406938195229,
-0.005851867143064737,
-0.032443489879369736,
0.037448279559612274,
-0.0068290336057543755,
0.008614391088485718,
-0.03348740190267563,
0.048529304563999176,
0.03377535194158554,
-0.003910511266440153,
0.019851962104439735,
0.030863361433148384,
0.0022214644122868776,
-0.013948270119726658,
0.007926602847874165,
0.02700866013765335,
0.05036019906401634,
-0.014937165193259716,
-0.024463579058647156,
0.0057114968076348305,
-0.0609673373401165,
0.0411066859960556,
0.0022541333455592394,
-0.021812928840517998,
0.030100995674729347,
0.026784874498844147,
-0.02994486503303051,
0.021256238222122192,
0.004410684108734131,
-0.0461626760661602,
-0.007472427561879158,
-0.04122985899448395,
0.06071050465106964,
0.0028458882588893175,
0.06888473033905029,
0.03854615241289139,
-0.03267645090818405,
-0.0075643016025424,
0.08329598605632782,
0.08298569172620773,
-0.042615316808223724,
-0.045445531606674194,
-0.009821348823606968,
-0.023022282868623734,
-0.013196888379752636,
-0.0017048903973773122,
-0.0385809950530529,
0.00738372141495347,
0.01992708444595337,
-0.011690684594213963,
0.009313137270510197,
0.009385979734361172,
-0.002469882369041443,
0.017712345346808434,
0.051907144486904144,
-0.05816073715686798,
0.026502327993512154,
-0.04056533798575401,
0.028190653771162033,
0.02806212566792965,
0.02352325990796089,
0.057959821075201035,
-0.02385297790169716,
0.033462151885032654,
0.022968435660004616,
0.018543364480137825,
0.04345397651195526,
0.00012895143299829215,
0.06953097134828568,
-0.02054573968052864,
-0.029968341812491417,
0.03786763548851013,
-0.011653679423034191,
-0.027770640328526497,
-0.0038393731229007244,
-0.0186492707580328,
0.019633660092949867,
0.003293642308562994,
-0.044835131615400314,
0.06633379310369492,
0.02860998921096325,
-0.05683154985308647,
0.035144805908203125,
0.016812639310956,
0.06227767467498779,
0.04641837999224663,
-0.006683163344860077,
-0.04383782297372818,
-0.014171143062412739,
0.0061894794926047325,
-0.011265265755355358,
0.0041046664118766785,
-0.020062999799847603,
0.010968347080051899,
-0.021799223497509956,
-0.011470927856862545,
0.008800763636827469,
-0.02035786770284176,
-0.04505017027258873,
-0.010282870382070541,
0.05603165552020073,
0.01847376488149166,
0.07807709276676178,
-0.034469664096832275,
0.035873495042324066,
-0.03733786195516586,
-0.023326899856328964,
0.003035126719623804,
-0.02269470877945423,
-0.018717629835009575,
-0.08137691766023636,
0.035065650939941406,
-0.007560365833342075,
-0.006334621924906969,
0.006972045637667179,
-0.006938498932868242,
0.03934372216463089,
0.0005646240315400064,
-0.05145477503538132,
-0.046344928443431854,
0.011342445388436317,
0.013473568484187126,
-0.01706172525882721,
-0.08734933286905289,
-0.00156473892275244,
0.011906937696039677,
0.023693060502409935,
0.022427771240472794,
0.048636436462402344,
0.01521383412182331,
-0.002044121967628598,
0.03270478919148445,
0.02688833698630333,
0.0039535644464194775,
-0.02201344259083271,
-0.0020481469109654427,
0.0004212904314044863,
-0.06839204579591751,
-0.017169304192066193,
0.030728697776794434,
-0.012492279522120953,
-0.017831047996878624,
0.04503472149372101,
-0.01155763678252697,
-0.00590719236060977,
0.002022801199927926,
0.044698566198349,
-0.02213432639837265,
0.04932311922311783,
-0.009267541579902172,
-0.02005046419799328,
0.0340091697871685,
0.007965399883687496,
0.013494880869984627,
0.0019068963592872024,
0.0093317162245512,
0.06881838291883469,
-0.029100870713591576,
-0.02072579599916935,
-0.059279732406139374,
0.05514780059456825,
-0.0042609358206391335,
-0.034340277314186096,
-0.027908047661185265,
-0.01435807254165411,
-0.004471657797694206,
-0.0015544898342341185,
0.043815579265356064,
0.012636394239962101,
0.01741790771484375,
0.007110606878995895,
-0.02788269892334938,
-0.008710624650120735,
-0.07346910238265991,
0.05741170421242714,
-0.011080387979745865,
0.015769440680742264,
0.02851133421063423,
0.04124909266829491,
0.04296758770942688,
-0.05495845153927803,
0.03191549330949783,
0.01311520580202341,
0.0217440128326416,
0.03782248869538307,
-0.035379741340875626,
0.009662155993282795,
0.03759076073765755,
0.05231664702296257,
-0.01469862274825573,
-0.004000054206699133,
-0.0047258599661290646,
-0.025493836030364037,
0.056191012263298035,
-0.053715310990810394,
0.0003992494021076709,
-0.008853188715875149,
-0.01488988846540451,
0.04189496114850044,
-0.009365445002913475,
-0.013917006552219391,
0.030862728133797646,
-0.03082488663494587,
0.05376849323511124,
0.05011866241693497,
-0.004035410936921835,
0.027766989544034004,
-0.01123929861932993,
0.01118741650134325,
0.027730010449886322,
-0.01720508188009262,
-0.014970394782721996,
-0.04159359261393547,
0.005687962751835585,
0.01780771091580391,
0.0475662499666214,
-0.02034490741789341,
0.003255604999139905,
-0.0027137238066643476,
-0.01984616182744503,
0.0487416572868824,
0.05727076530456543,
0.03371772915124893,
-0.03573383018374443,
0.019042225554585457,
0.06530961394309998,
-0.00897646602243185,
0.03496289625763893,
0.024737181141972542,
0.026167478412389755,
0.05786678194999695,
-0.03848063945770264,
0.038584716618061066,
0.04743681848049164,
0.008203079923987389,
0.0006967843510210514,
-0.002547245239838958,
-0.023815415799617767,
0.018527019768953323,
-0.03630119934678078,
-0.005287553649395704,
0.004148278851062059,
-0.016088679432868958,
-0.015492803417146206,
0.002439899602904916,
0.004716329276561737,
0.02554941549897194,
0.0006125784129835665,
0.002171340398490429,
-0.013113104738295078,
0.03848966956138611,
-0.03911935165524483,
0.0026449994184076786,
-0.04101744294166565,
0.02276892028748989,
-0.01474994607269764,
-0.02433827519416809,
0.01632530800998211,
-0.005586161743849516,
0.034380216151475906,
-0.05236748978495598,
-0.004724510479718447,
-0.027494197711348534,
-0.04889799281954765,
-0.019135914742946625,
0.0010176259092986584,
-0.026048118248581886,
-0.031404830515384674,
-0.02555873431265354,
-0.013106691651046276,
0.01151849515736103,
-0.021543728187680244,
-0.0071618822403252125,
0.06898003071546555,
-0.027456318959593773,
-0.07069415599107742,
-0.006262877956032753,
-0.04843590781092644,
0.03194815292954445,
-0.016378644853830338,
-0.02059812843799591,
0.0033971304073929787,
0.009941362775862217,
-0.013792208395898342,
0.030939597636461258,
-0.03440907597541809,
-0.03099822625517845,
-0.001583931385539472,
0.004901168867945671,
0.016033127903938293,
-0.025964654982089996,
-0.011159959249198437,
0.03858574852347374,
-0.0628015473484993,
-0.03407629579305649,
-0.03301839530467987,
-0.04409552365541458,
0.008158035576343536,
0.0021468105260282755,
0.050648417323827744,
-0.015542285516858101,
-0.07650534808635712,
0.0731782540678978,
0.01734093390405178,
-0.049563102424144745,
0.0016116652404889464,
-0.05125228315591812,
-0.011928598396480083,
-0.007753078825771809,
-0.028472406789660454,
0.04364442452788353,
-0.033066123723983765,
0.032073069363832474,
0.05496161803603172,
0.008127343840897083,
0.0503867007791996,
0.04725188389420509,
-0.037246912717819214,
-0.028662612661719322,
0.01897028088569641,
-0.041526783257722855,
0.0783727616071701,
0.025766801089048386,
-0.0322486013174057,
0.024600960314273834,
-0.025653650984168053,
0.03457951173186302,
0.023448755964636803,
-0.01095569971948862,
0.048530757427215576,
-0.009836438111960888,
0.0012576875742524862,
-0.08070697635412216,
0.023222198709845543,
0.007345571182668209,
-0.0006454605609178543,
-0.050273068249225616,
0.028620047494769096,
0.011196998879313469,
0.0014139312552288175,
-0.03368823230266571,
0.03178272768855095,
0.00999714806675911,
-0.00213087210431695,
-0.02229003794491291,
0.010694478638470173,
-0.015504609793424606,
0.047885168343782425,
0.010247363708913326,
-0.011434146203100681,
0.049391262233257294,
0.015524354763329029,
0.026374947279691696,
-0.012820865027606487,
-0.032494135200977325,
0.011721924878656864,
-0.08016958832740784,
-0.005835785996168852,
-0.02705417573451996,
0.029942288994789124,
0.011194144375622272,
0.07790125906467438,
0.012712540104985237,
-0.013604794628918171,
0.027570975944399834,
-0.044682517647743225,
-0.04141911491751671,
0.02503647468984127,
-0.028083540499210358,
0.0052327439188957214,
-0.0033253859728574753,
-0.03774195536971092,
-0.03147629648447037,
-0.05305483564734459,
0.01979905553162098,
-0.013784521259367466,
0.0229011382907629,
-0.06523995101451874,
-0.0007960238144733012,
-0.02639157511293888,
-0.031071912497282028,
0.0018848150502890348,
0.06229502707719803,
0.018399400636553764,
-0.02600921131670475,
0.0472833551466465,
0.043998219072818756,
-0.003656424582004547,
-0.000440275325672701,
-0.01190332043915987,
-0.00043476434075273573,
-0.033359941095113754,
0.046612631529569626,
0.036594852805137634,
0.0356619656085968,
-0.016760945320129395,
0.0185861773788929,
0.02125430665910244,
0.04059687256813049,
-0.0005109345074743032,
-0.03204154968261719,
-0.014801406301558018,
-0.03507773205637932,
-0.0013311170041561127,
-0.019632676616311073,
0.025149371474981308,
-0.02389983832836151,
0.000016382609828724526,
-0.005138888023793697,
0.014896227978169918,
-0.02477402240037918,
0.0642559751868248,
0.038134656846523285,
-0.008504381403326988,
-0.03373679518699646,
-0.07595076411962509,
-0.02773413434624672,
-0.061175379902124405,
-0.042156755924224854,
0.0031277001835405827,
0.028437284752726555,
-0.020903440192341805,
0.02041960321366787,
0.03381083533167839,
0.006384183652698994,
-0.025612426921725273,
0.02699955925345421,
0.020885346457362175,
-0.00885783601552248,
-0.04031577706336975,
0.011041538789868355,
0.013255021534860134,
0.058118484914302826,
0.04469086229801178,
0.016146022826433182,
-0.017062706872820854,
-0.07733242213726044,
0.011070427484810352,
0.006435151677578688,
0.046486206352710724,
0.019540293142199516,
0.012468087486922741,
-0.016889771446585655,
-0.034266870468854904,
0.04244867339730263,
0.02076660841703415,
0.017861921340227127,
-0.02381759136915207,
0.020227843895554543,
-0.0325944721698761,
-0.016647592186927795,
-0.005465393885970116,
0.019023461267352104,
0.01331294048577547,
-0.004819198045879602,
-0.014315417036414146,
0.0010871017584577203,
-0.004502532538026571,
0.042249906808137894,
0.033710870891809464,
0.04082858934998512,
-0.044066064059734344,
-0.01629905216395855,
0.005402024835348129,
0.02274361252784729,
-0.0036347638815641403,
-0.018209440633654594,
0.010942281223833561,
-0.007821542210876942,
0.026029888540506363,
0.0294561218470335,
0.0031298797111958265,
-0.0227676872164011,
0.041493043303489685,
-0.017751215025782585,
-0.038650382310152054,
0.037693992257118225,
0.00009444679744774476,
0.055922433733940125,
0.01355632022023201,
0.020961944013834,
0.036180295050144196,
0.03227648884057999,
-0.004516826011240482,
-0.007089093327522278,
-0.00010032816499006003,
0.021998874843120575,
-0.061420734971761703,
-0.019625304266810417,
-0.00029621741850860417,
0.009850699454545975,
-0.0328846201300621,
0.03689621761441231,
0.0050781480967998505,
0.03793846443295479,
-0.01125401072204113,
-0.008854822255671024,
0.019137484952807426,
0.024218467995524406,
0.016039928421378136,
0.011691594496369362,
0.014512757770717144,
0.03941940888762474,
0.017180737107992172,
-0.044415801763534546,
-0.034020960330963135,
-0.018085187301039696,
0.0011693388223648071,
-0.004700052086263895,
-0.024097831919789314,
0.04403255879878998,
0.01011104229837656,
-0.03701334074139595,
0.017052585259079933,
-0.003479332895949483,
0.0399792417883873,
-0.015309805981814861,
0.0003087314253207296,
0.03356556594371796,
-0.03875062242150307,
0.0023964608553797007,
0.03260291367769241,
-0.008452724665403366,
0.05628369003534317,
-0.048612914979457855,
0.07434147596359253,
0.025635866448283195,
-0.0001374369312543422,
-0.02769267000257969,
-0.013070509769022465,
0.03971012309193611,
0.02308901958167553,
-0.01432877965271473,
-0.0061124758794903755,
0.00917364377528429,
0.018580395728349686,
-0.0067908745259046555,
-0.01707378774881363,
0.06828499585390091,
0.006183316465467215,
-0.026841770857572556,
0.014255278743803501,
-0.029768314212560654,
0.0647776648402214,
0.012835442088544369,
0.001776793273165822,
-0.037679851055145264,
0.01129731722176075,
-0.01704246923327446,
-0.04429870843887329,
0.04458656907081604,
-0.014694126322865486,
-0.005790102761238813,
-0.005847000516951084,
-0.03999099135398865,
0.060348086059093475,
-0.014598723500967026,
0.004101160913705826,
-0.002646077424287796,
0.012455161660909653,
-0.018679490312933922,
0.014541000127792358,
0.018707944080233574,
-0.00889600906521082,
-0.0033434040378779173,
-0.019235363230109215,
-0.004604163579642773,
-0.062430646270513535,
0.008559668436646461,
-0.0422225296497345,
0.0085972361266613,
0.020784201100468636,
-0.04833875969052315,
0.06632226705551147,
0.007231180556118488,
0.0012958256993442774,
-0.0005313935107551515,
-0.04238446429371834,
0.0325266569852829,
-0.01544319000095129,
-0.03610800951719284,
0.005737509112805128,
0.028085069730877876,
-0.019446318969130516,
-0.04057792201638222,
-0.03647424280643463,
-0.011764838360249996,
0.07091895490884781,
-0.0239386186003685,
0.030239665880799294,
0.04872237145900726,
-0.001760487793944776,
0.011898815631866455,
-0.03372010961174965,
-0.007523647043853998,
0.002908996306359768,
-0.03982207924127579,
0.03973385691642761,
-0.03172139450907707,
-0.027510056272149086,
0.017897073179483414,
-0.00036763297975994647,
0.0007636349182575941,
0.004716244526207447,
0.02230750396847725,
0.034930940717458725,
-0.01873738132417202,
-0.04554412141442299,
-0.0354645662009716,
0.03965000808238983,
-0.05007534474134445,
0.018515292555093765,
-0.011737467721104622,
0.009446505457162857,
0.04015294089913368,
0.02113507315516472,
-0.0022446266375482082,
-0.07040125131607056,
0.015951549634337425,
0.00012968266673851758,
0.0015165605582296848,
0.03724129870533943,
0.027174852788448334,
0.009798431769013405,
0.01425444707274437,
0.012967586517333984,
-0.012537349946796894,
0.0030265352688729763,
-0.0029022765811532736,
-0.03417498245835304,
-0.03278056159615517,
0.006003068294376135,
-0.03453848883509636,
0.0336885079741478,
-0.034586306661367416,
-0.05935496464371681,
0.05560546740889549,
-0.04691791534423828,
0.021463582292199135,
-0.009831870906054974,
-0.0019199219532310963,
-0.01288126315921545,
0.04062940925359726,
0.004369175992906094,
0.007290635257959366,
-0.016908282414078712,
0.00018223776714876294,
0.11889630556106567,
0.0681828185915947,
0.03143216297030449,
-0.03169333562254906,
0.016973862424492836,
0.0027466081082820892,
0.010674664750695229,
-0.028316862881183624,
0.02204914391040802,
0.002841451670974493,
-0.0013115039328113198,
-0.0025504084769636393,
0.06761030852794647,
0.034626301378011703,
0.0006517464644275606,
0.05567653104662895,
0.009017529897391796,
-0.0006729596643708646,
0.02473311871290207,
0.043699003756046295,
-0.019969763234257698,
0.017269885167479515,
0.008867383934557438,
-0.02573731541633606,
0.001990454737097025,
0.009243221953511238,
-0.034019481390714645,
-0.01560876052826643,
0.032352298498153687,
-0.053239282220602036,
-0.02114698849618435,
-0.008014693856239319,
-0.00021462145377881825,
-0.008904372341930866,
-0.058572374284267426,
0.03554605320096016,
0.009181112982332706,
-0.0037248115986585617,
-0.015520402230322361,
0.02656940557062626,
0.007563149090856314,
-0.033652786165475845,
-0.024391165003180504,
0.020530249923467636,
-0.03301761671900749,
0.008463619276881218,
0.01102589163929224,
0.01815018430352211,
0.009292311035096645,
-0.008822011761367321,
0.017981702461838722,
0.02612060122191906,
-0.018946100026369095,
-0.06673305481672287,
-0.022378381341695786,
0.018775826320052147,
0.029826881363987923,
0.008298572152853012,
-0.04734371230006218,
-0.06414472311735153,
0.030399959534406662,
-0.019319090992212296,
-0.004935085773468018,
-0.03512861579656601,
-0.024438345804810524,
0.007578947581350803,
0.005876858253031969,
0.04832584410905838,
-0.034791555255651474,
-0.005621097516268492,
-0.03019407019019127,
0.0067042699083685875,
-0.04210195317864418,
-0.018139250576496124,
-0.006043245084583759,
0.027409618720412254,
0.04461590573191643,
0.03931255638599396,
-0.019454259425401688,
-0.025599632412195206,
-0.09173856675624847,
0.029169529676437378,
0.009476309642195702,
-0.007025421131402254,
-0.01728847809135914,
-0.006408745888620615,
0.04388006404042244,
0.03782512620091438,
0.006897917948663235,
0.02872762829065323,
0.005615958012640476,
0.0037886365316808224,
0.030883580446243286,
-0.06387388706207275,
-0.026963520795106888,
0.035860005766153336,
-0.02198180928826332,
0.03600253909826279,
0.014340500347316265,
0.0349787101149559,
-0.018510809168219566,
0.034809987992048264,
-0.029928868636488914,
0.038160692900419235,
-0.04594293609261513,
-0.0005421173409558833,
-0.021337522193789482,
-0.030385533347725868,
-0.02961171604692936,
0.003871914464980364,
0.03201361373066902,
-0.02425055205821991,
-0.02123090624809265,
-0.05126069486141205,
-0.0179457925260067,
-0.00941490475088358,
-0.019386064261198044,
0.0037819254212081432,
-0.011584235355257988,
-0.0006109721143729985,
-0.04503536596894264,
-0.027285786345601082,
-0.01027574110776186,
-0.0473056323826313,
-0.026224033907055855,
0.033950380980968475,
-0.018811112269759178,
-0.016307402402162552,
0.017660802230238914,
-0.07014381140470505,
-0.021014658734202385,
0.023953916504979134,
0.00100992014631629,
0.004443744197487831,
-0.012857435271143913,
0.023227613419294357,
-0.021164121106266975,
0.03313402831554413,
0.007153361104428768,
-0.05919777974486351,
0.04559164494276047,
-0.04210720583796501,
-0.04677879065275192,
0.051190488040447235,
0.01224716566503048,
0.021216295659542084,
0.009250732138752937,
0.030577650293707848,
-0.03620446100831032,
0.0541299544274807,
-0.014860788360238075,
0.0009826752357184887,
-0.0007297098636627197,
-0.020330043509602547,
0.01090883556753397,
0.017075907438993454,
0.06769226491451263,
0.020999673753976822,
-0.013389104045927525,
0.007519916165620089,
-0.0018990427488461137,
0.003575326642021537,
0.05913253873586655,
0.03419046849012375,
-0.024423429742455482,
0.0326688252389431,
-0.002718196250498295,
0.011149776168167591,
0.015340565703809261,
0.02317764423787594,
-0.01083472091704607,
0.007178100291639566,
0.023738699033856392,
-0.016037805005908012,
-0.09543044120073318,
0.03333493322134018,
0.012418782338500023,
0.0067050098441541195,
0.018372641876339912,
-0.04277288168668747,
0.03497879579663277,
-0.0026119400281459093,
-0.06803521513938904,
-0.009454938583076,
-0.007955553010106087,
-0.013742401264607906,
-0.03595404326915741,
0.0021321726962924004,
-0.016398634761571884,
0.016390087082982063,
0.03186242654919624,
0.024717044085264206,
0.005070066079497337,
0.005386274307966232,
-0.0004952007438987494,
0.014954143203794956,
-0.015708060935139656,
0.02073698118329048,
0.03296859562397003,
-0.0055663022212684155,
0.04793325439095497,
-0.04553963243961334,
-0.030581990256905556,
0.030244672670960426,
-0.03404488041996956,
0.0247514508664608,
-0.02616315707564354,
0.020753460004925728,
0.0189825426787138,
0.016013728454709053,
0.0021749737206846476,
-0.012089917436242104,
-0.0354449599981308,
0.004759731702506542,
-0.024490458890795708,
0.012718542478978634,
-0.03884653374552727,
-0.0346749946475029,
0.02572472207248211,
-0.0035500687081366777,
-0.035548269748687744,
0.021530508995056152,
-0.026098553091287613,
-0.011616053059697151,
-0.011143556796014309,
-0.018751172348856926,
-0.019248945638537407,
-0.006101041566580534,
-0.002870894968509674,
-0.0647367388010025,
-0.0018416850361973047,
0.014978798106312752,
0.0010420301696285605,
-0.03908737376332283,
0.01631702296435833,
0.04868118464946747,
-0.02619713917374611,
0.051705703139305115,
0.02815856970846653,
-0.05240572243928909,
-0.038852475583553314,
-0.039469148963689804,
-0.01312397513538599,
-0.005370352417230606,
0.0016879375325515866,
-0.031050486490130424,
-0.051957473158836365,
0.015653880313038826,
0.002921964041888714,
0.006372416391968727,
0.02630874142050743,
-0.02799193747341633,
-0.04454941675066948,
-0.053703803569078445,
0.04513345658779144,
-0.00016741604486014694,
-0.015005526132881641,
-0.06039257347583771,
-0.02717818319797516,
0.0016276671085506678,
0.005500996485352516,
0.059585873037576675,
0.012873353436589241,
-0.02073560655117035,
0.025642458349466324,
-0.03169262781739235,
0.005096133798360825,
-0.03510713949799538,
-0.020963585004210472,
0.01631961204111576,
-0.01653810776770115,
-0.0016750996001064777,
0.0018817164236679673,
-0.0007123073446564376,
0.01732720248401165,
0.03752584755420685,
-0.02755151130259037,
0.029358021914958954,
-0.020950254052877426,
0.01460276823490858,
0.03956766426563263,
0.03605969622731209,
-0.0334184356033802,
0.07376626878976822,
-0.0288187675178051,
-0.017268141731619835,
-0.01645924150943756,
-0.017379095777869225,
-0.036707282066345215,
0.032876916229724884,
0.011951911263167858,
-0.0011000217637047172,
0.003429486881941557,
0.05171920359134674,
0.00046436922275461257,
-0.05588674172759056,
-0.02477855049073696,
0.04608473926782608,
-0.05651064217090607,
-0.010627987794578075,
0.05587256699800491,
0.048632312566041946,
0.0053748697973787785,
-0.011158914305269718,
0.030613891780376434,
0.028632264584302902,
-0.0012941834283992648,
-0.002940297592431307,
0.022885164245963097,
0.01814926229417324,
0.0104945357888937,
-0.03174661472439766,
0.026674319058656693,
0.007257498800754547,
0.004788032732903957,
0.01285061240196228,
0.029534371569752693,
0.00492710480466485,
-0.054150816053152084,
-0.006019623950123787,
-0.010739907622337341,
-0.004923272877931595,
0.017962757498025894,
-0.013130494393408298,
0.052165161818265915,
-0.006331840995699167,
0.0005787650588899851,
-0.027485409751534462,
-0.037148743867874146,
-0.02692090906202793,
-0.02358354441821575,
0.05695647746324539,
0.003359073307365179,
-0.03729112818837166,
-0.02857515774667263,
0.007122305687516928,
-0.009810036979615688,
0.03657808154821396,
-0.055440064519643784,
-0.004425637889653444,
-0.0037399991415441036,
-0.006830946542322636,
-0.05213771387934685,
0.01272877398878336,
-0.06294865161180496,
0.010836235247552395,
0.05733402818441391,
0.021652311086654663,
-0.0035523646511137486,
0.05045803636312485,
-0.02438335306942463,
-0.009522661566734314,
0.03630727902054787,
-0.058266185224056244,
-0.000549230317119509,
-0.015404474921524525,
0.032429419457912445,
0.0193690974265337,
-0.024064762517809868
] |
<p>I read that </p>
<p>$(FF(f))(x)=2\pi f(-x)$, where $F$ is the Fourier transform</p>
<p><em>and</em> $F(f(x-a))(k)=\exp(-ika) X(k)$ where $X(k)=F(f(x))$</p>
<p><em>implies</em> $F(\exp(iax)f(x))(k)=X(k-a)$.</p>
<p>But I don't see how that is done... I am quite happy with getting $F^{-1}X(k-a)=\exp(iax)f(x)$ by brute force calculation. I would like to see how to use duality though.</p> | 2,835 | [
0.011897265911102295,
-0.010510118678212166,
0.02387569658458233,
-0.009745479561388493,
0.03760210797190666,
-0.01540169958025217,
-0.04956856369972229,
-0.04794185981154442,
0.025616319850087166,
-0.023666728287935257,
0.039133790880441666,
0.04580787941813469,
0.05371374264359474,
0.039187632501125336,
-0.0225108303129673,
0.04143066704273224,
-0.0383714996278286,
-0.017373977228999138,
-0.02731514163315296,
-0.020574510097503662,
0.030957762151956558,
0.032460324466228485,
-0.01132984645664692,
0.022317713126540184,
-0.03214153274893761,
0.030831608921289444,
0.00953848846256733,
-0.018224749714136124,
0.008524269796907902,
0.09515195339918137,
-0.011690950021147728,
-0.018245771527290344,
0.010887222364544868,
0.08721143752336502,
0.03260136395692825,
0.04537471383810043,
-0.042267344892024994,
-0.012234936468303204,
0.012121638283133507,
0.07283292710781097,
0.0009715407504700124,
-0.024648046121001244,
-0.0033505212049931288,
0.0417913943529129,
-0.012713034637272358,
0.04505861550569534,
0.01523486990481615,
-0.03140075132250786,
0.03473560884594917,
-0.044553179293870926,
0.08612588047981262,
-0.006470425054430962,
0.003339808201417327,
0.03543582931160927,
-0.005874441936612129,
-0.017784597352147102,
0.06207288056612015,
0.054940082132816315,
0.028787991032004356,
-0.04889008402824402,
-0.04558713361620903,
-0.028562430292367935,
-0.013213016092777252,
0.009330200962722301,
-0.03153753653168678,
-0.057369478046894073,
0.0209642443805933,
-0.035405829548835754,
0.014528834261000156,
-0.036903634667396545,
-0.0009946917416527867,
0.014741353690624237,
0.04356813803315163,
-0.04235934838652611,
0.00559355178847909,
-0.02627154253423214,
-0.009233049117028713,
0.030692825093865395,
0.031466834247112274,
0.011392224580049515,
-0.008325227536261082,
0.04598679021000862,
0.027507852762937546,
-0.027764081954956055,
0.0031841201707720757,
0.003925147000700235,
0.07428676635026932,
0.024355094879865646,
-0.006484825164079666,
0.01795072853565216,
-0.03657996654510498,
-0.028164619579911232,
0.0493033304810524,
-0.04543520510196686,
0.0030378252267837524,
0.028423910960555077,
0.03337494656443596,
-0.006266019307076931,
0.029237179085612297,
-0.021906014531850815,
0.006924327928572893,
-0.016924245283007622,
0.014290113002061844,
0.07283362001180649,
-0.008108644746243954,
0.0379517637193203,
0.00528762536123395,
0.012097526341676712,
-0.03325355052947998,
-0.0004205495642963797,
-0.04176616296172142,
0.031749654561281204,
-0.004217867273837328,
0.00817327480763197,
0.011242222972214222,
0.025988755747675896,
-0.008557737804949284,
-0.012942072935402393,
0.011413052678108215,
0.06085062026977539,
0.047275565564632416,
-0.03031052090227604,
0.02019200287759304,
-0.0372537262737751,
-0.057823728770017624,
-0.0034700289834290743,
0.03458237275481224,
0.02152501977980137,
-0.04980633035302162,
0.04039554297924042,
0.004332011565566063,
-0.0416773296892643,
0.03274443373084068,
0.018076950684189796,
-0.01740994118154049,
0.01068398728966713,
-0.08401969075202942,
-0.06789642572402954,
0.024860912933945656,
-0.025132689625024796,
0.006515471264719963,
-0.08083740621805191,
0.02065459080040455,
0.04313543811440468,
0.061045143753290176,
0.014747095294296741,
-0.0006030015065334737,
-0.026015397161245346,
0.0034800844732671976,
0.006667498033493757,
-0.0006622744840569794,
-0.002507758792489767,
-0.014545134268701077,
-0.043731044977903366,
-0.04168900474905968,
-0.019101548939943314,
0.011486661620438099,
0.02356245554983616,
-0.02310786023736,
-0.02315252460539341,
0.1253035068511963,
0.010519934818148613,
-0.02185147814452648,
-0.007498795632272959,
0.00041871299617923796,
-0.03886142745614052,
0.06757497042417526,
0.04866781085729599,
-0.0011248979717493057,
-0.012434879317879677,
-0.0022998801432549953,
0.01338713988661766,
-0.037062425166368484,
0.03452381119132042,
0.022017797455191612,
-0.05164958909153938,
-0.041169241070747375,
-0.03812069818377495,
0.01745794713497162,
0.007755732629448175,
-0.015533667989075184,
-0.013719418086111546,
0.007922920398414135,
-0.0014787837862968445,
0.025177933275699615,
0.01861463114619255,
-0.0022320100106298923,
-0.02468189038336277,
0.010731841437518597,
-0.038553014397621155,
0.009138708934187889,
-0.05389302223920822,
0.009093061089515686,
-0.007674917578697205,
-0.024378538131713867,
0.011635160073637962,
-0.009538915939629078,
0.009528915397822857,
-0.02260141633450985,
-0.009541054256260395,
0.00986073911190033,
-0.02545347809791565,
0.01634502410888672,
-0.04443323239684105,
0.001673552324064076,
0.05149519816040993,
0.05835296958684921,
-0.017569953575730324,
0.03921011835336685,
-0.020472662523388863,
-0.0036102805752307177,
-0.009956040419638157,
-0.04845389351248741,
0.024434078484773636,
0.008098660036921501,
0.017285523936152458,
-0.010214033536612988,
0.00442215520888567,
-0.02179127186536789,
-0.025625361129641533,
-0.06685276329517365,
0.06147240847349167,
0.09367098659276962,
0.019658181816339493,
0.0348920077085495,
0.047197457402944565,
0.02837446518242359,
0.03750485181808472,
0.021071497350931168,
-0.0611347071826458,
-0.041104402393102646,
-0.020747100934386253,
0.022949598729610443,
0.009558524936437607,
-0.007587376981973648,
0.03418421372771263,
0.08139939606189728,
0.0017836567712947726,
0.02030882239341736,
0.024764548987150192,
-0.010129053145647049,
0.013461078517138958,
-0.008719369769096375,
0.0014531202614307404,
0.01996275968849659,
0.019365033134818077,
0.01824311725795269,
-0.0025024120695888996,
0.019324013963341713,
0.011723911389708519,
-0.036308933049440384,
0.047445349395275116,
-0.029901009052991867,
0.031593240797519684,
0.011566019617021084,
-0.0056525785475969315,
0.01301310770213604,
-0.012452436611056328,
-0.011133869178593159,
0.014986650086939335,
-0.02210378646850586,
-0.032155491411685944,
-0.005559907294809818,
0.0018275538459420204,
0.05288441479206085,
-0.007328353822231293,
-0.03151354193687439,
0.00905896071344614,
0.02112901397049427,
-0.002476809313520789,
-0.0022115411702543497,
-0.01630430482327938,
0.011816208250820637,
0.0043486300855875015,
0.006484330166131258,
0.03415720537304878,
0.009465841576457024,
0.051571398973464966,
-0.025711797177791595,
-0.021718500182032585,
0.019451286643743515,
-0.029707206413149834,
0.028755564242601395,
0.02500157803297043,
-0.0414680577814579,
0.02243914268910885,
-0.02645798958837986,
-0.03049418330192566,
0.03421655669808388,
-0.032647110521793365,
0.017374591901898384,
-0.011156326159834862,
-0.002595817670226097,
-0.07594871520996094,
-0.0109119713306427,
-0.015627946704626083,
-0.00020784481603186578,
-0.023975910618901253,
-0.007146832998842001,
0.058783840388059616,
0.008342207409441471,
-0.02965151146054268,
0.008276627399027348,
-0.009487727656960487,
0.003400613786652684,
-0.031044799834489822,
-0.017176559194922447,
0.022098910063505173,
-0.026806429028511047,
-0.015396851114928722,
-0.01731356978416443,
-0.048538338392972946,
0.010022483766078949,
-0.03887653350830078,
-0.01316150464117527,
-0.0013434665743261576,
-0.008423740044236183,
0.03357117623090744,
0.019515346735715866,
-0.02979053370654583,
0.039299216121435165,
0.02550668455660343,
-0.03310544788837433,
-0.03366803750395775,
-0.0224633626639843,
-0.03301409259438515,
-0.007063881028443575,
-0.034298356622457504,
0.011647624894976616,
-0.03767311945557594,
0.059753675013780594,
0.027249928563833237,
-0.044915590435266495,
0.07250205427408218,
-0.00022733400692231953,
-0.03847256675362587,
0.01795443333685398,
-0.009527414105832577,
0.004441826604306698,
0.07418318837881088,
0.005334482993930578,
-0.002409460488706827,
0.018104948103427887,
0.014728137291967869,
-0.036022547632455826,
0.011448301374912262,
-0.009149061515927315,
-0.023161400109529495,
0.0067553273402154446,
-0.009548402391374111,
-0.05693377926945686,
0.034730806946754456,
-0.010611461475491524,
0.040534112602472305,
0.005902203265577555,
0.03860214352607727,
0.06093723699450493,
-0.03629545494914055,
0.025780295953154564,
0.021574899554252625,
0.0551142618060112,
0.01925066113471985,
-0.027144229039549828,
-0.036280035972595215,
0.004792929161339998,
0.03213561326265335,
-0.06563486158847809,
-0.025898782536387444,
0.04842540621757507,
0.013645615428686142,
0.0599946528673172,
0.010765901766717434,
-0.018124984577298164,
0.003027860075235367,
-0.036570265889167786,
0.007756897713989019,
0.009834320284426212,
0.05883122235536575,
0.012092942371964455,
0.03610196337103844,
0.06302346289157867,
0.011930839158594608,
-0.02209465764462948,
0.000894451339263469,
-0.09211743623018265,
0.004800783004611731,
-0.0011554691009223461,
0.005244103725999594,
-0.04023820161819458,
0.007814961485564709,
0.0268495324999094,
-0.012673198245465755,
-0.02405146136879921,
0.001025857636705041,
-0.04364267736673355,
-0.03759593144059181,
-0.015766261145472527,
-0.016853131353855133,
-0.03991222754120827,
-0.02202051505446434,
0.024279236793518066,
0.06601519137620926,
-0.013018478639423847,
0.025120291858911514,
0.014656358398497105,
-0.03668081760406494,
0.002669507171958685,
-0.014128189533948898,
0.030006801709532738,
0.021970344707369804,
0.030610257759690285,
-0.027949325740337372,
0.04034195840358734,
-0.004078484605997801,
0.03614286705851555,
-0.007286022417247295,
0.07510105520486832,
0.04910092428326607,
-0.05955741927027702,
-0.018759796395897865,
-0.022182593122124672,
-0.038530200719833374,
0.000861926528159529,
0.04765278473496437,
-0.011919522657990456,
0.020807836204767227,
-0.0020130116026848555,
0.023728791624307632,
-0.025631258264183998,
0.03207601606845856,
0.028485579416155815,
0.0019873117562383413,
0.0037626761477440596,
-0.03925035893917084,
0.01972675882279873,
0.015029201284050941,
0.012941907159984112,
-0.012835968285799026,
-0.011065748520195484,
-0.005991428159177303,
0.011966000311076641,
0.052603501826524734,
-0.016118472442030907,
0.020350391045212746,
0.02975761517882347,
-0.00977521575987339,
-0.004612485412508249,
-0.02820063941180706,
-0.0015883544692769647,
0.0018303325632587075,
0.04885939881205559,
0.038379937410354614,
0.023150213062763214,
0.007447218522429466,
-0.08894024789333344,
-0.011592220515012741,
0.06113449111580849,
0.03758168965578079,
0.006791951600462198,
-0.0026796222664415836,
-0.06673546880483627,
-0.05843346193432808,
0.014746841974556446,
-0.0037737712264060974,
0.06316394358873367,
0.019963305443525314,
0.039780013263225555,
0.020049944519996643,
-0.03719692677259445,
-0.016794715076684952,
0.030955489724874496,
0.021552376449108124,
0.009219581261277199,
-0.01789284683763981,
-0.01202240027487278,
-0.04128868132829666,
-0.0028271847404539585,
0.04761660844087601,
0.03771448880434036,
0.005374227650463581,
-0.05102409049868584,
-0.04012643173336983,
0.025276975706219673,
-0.03436584770679474,
-0.0792829766869545,
0.019070129841566086,
0.0032252504024654627,
-0.0009284468833357096,
0.057966381311416626,
-0.027561170980334282,
-0.040489502251148224,
0.0031046683434396982,
-0.016345549374818802,
-0.019452238455414772,
0.02301076240837574,
-0.004231820814311504,
0.03833211585879326,
0.022387871518731117,
0.010334543883800507,
0.056156259030103683,
0.022813988849520683,
-0.029759149998426437,
-0.005895970854908228,
-0.02095181681215763,
0.01493812445551157,
-0.01811092533171177,
0.005691397935152054,
-0.02003159187734127,
0.015170815400779247,
-0.028535686433315277,
0.003998997621238232,
-0.01147572509944439,
0.04495681822299957,
0.005768454167991877,
-0.0012839582050219178,
-0.016178380697965622,
0.018012169748544693,
-0.05094167962670326,
0.013613030314445496,
-0.01365235261619091,
0.015564484521746635,
-0.006236304063349962,
-0.0211394801735878,
0.0053758565336465836,
0.011365286074578762,
0.01876758597791195,
-0.021421032026410103,
-0.01388365775346756,
0.018374072387814522,
-0.01130623184144497,
-0.003227523062378168,
0.01325636263936758,
-0.03743981570005417,
0.04638412222266197,
-0.009894665330648422,
0.010029904544353485,
0.036694739013910294,
-0.04051083326339722,
0.00521969934925437,
-0.000003566342229532893,
0.00012141543993493542,
0.006313602440059185,
-0.06366175413131714,
0.02875158190727234,
0.009405858814716339,
-0.051439519971609116,
-0.053834058344364166,
-0.03184856101870537,
0.016463307663798332,
-0.017943741753697395,
-0.009959639050066471,
-0.0382007472217083,
0.011268026195466518,
-0.0057177795097231865,
-0.02345842868089676,
-0.005205793306231499,
0.06171104684472084,
-0.02462957054376602,
0.010493159294128418,
0.03096713125705719,
-0.011248687282204628,
0.049360405653715134,
0.0013098627096042037,
-0.01616857759654522,
0.0292496457695961,
-0.032494720071554184,
-0.03294145315885544,
0.012513672932982445,
0.03311498463153839,
-0.017567738890647888,
0.028399381786584854,
0.0020720663014799356,
-0.0064427414909005165,
0.04082169756293297,
-0.006393680814653635,
-0.02553737163543701,
0.0013412144035100937,
0.05066554993391037,
0.05645585432648659,
-0.008631231263279915,
-0.021675769239664078,
0.01388606522232294,
0.04230853542685509,
-0.012888520956039429,
0.01531158946454525,
-0.03985419496893883,
-0.006631271913647652,
-0.017865562811493874,
0.0013077313778921962,
0.028980981558561325,
0.00004125804844079539,
0.04872095212340355,
-0.04120283201336861,
-0.006480018142610788,
0.034667156636714935,
0.019487477838993073,
0.0346987321972847,
-0.012377901934087276,
0.02467828057706356,
0.006284708622843027,
-0.029838014394044876,
-0.05320345610380173,
-0.031965114176273346,
-0.05427692458033562,
-0.009853198193013668,
0.048106949776411057,
0.006859106011688709,
0.06407079100608826,
0.038398150354623795,
0.030665913596749306,
-0.03379928693175316,
0.0258362777531147,
-0.021528884768486023,
-0.011111707426607609,
-0.019051719456911087,
0.015251627191901207,
-0.03322156146168709,
0.011903392150998116,
0.028397755697369576,
0.04297869652509689,
-0.019955625757575035,
0.007624115329235792,
-0.012556818313896656,
0.030030786991119385,
-0.021623117849230766,
-0.0504472590982914,
-0.033210355788469315,
0.017091266810894012,
-0.017059030011296272,
0.03929704800248146,
0.015023773536086082,
-0.027240410447120667,
0.03746550902724266,
0.045683976262807846,
0.0007540473598055542,
-0.07518395781517029,
-0.015441518276929855,
-0.022663051262497902,
0.011178281158208847,
0.01715605892241001,
-0.0016969941789284348,
0.03746822476387024,
-0.016043948009610176,
0.04045020788908005,
0.0015465599717572331,
0.009180937893688679,
-0.03267648071050644,
-0.030214987695217133,
0.0014724122593179345,
-0.07005167007446289,
-0.06577306240797043,
0.040343161672353745,
-0.041183289140462875,
-0.04080938175320625,
0.036233410239219666,
0.003908807411789894,
0.02483784221112728,
0.041537586599588394,
0.04940963536500931,
0.003529043635353446,
0.07788386195898056,
0.000421368342358619,
-0.009230892173945904,
-0.02131158858537674,
0.016787026077508926,
0.11660313606262207,
0.053865548223257065,
0.03605719655752182,
-0.08073506504297256,
0.003492876188829541,
-0.05888945236802101,
0.023416200652718544,
-0.04637899994850159,
0.01948397047817707,
-0.0017465075943619013,
-0.0032211490906774998,
-0.011807541362941265,
0.06778411567211151,
-0.00938810408115387,
-0.02531234174966812,
0.014393880032002926,
0.008005273528397083,
-0.02660607174038887,
-0.02501741237938404,
-0.023464873433113098,
-0.006905602291226387,
-0.012337097898125648,
-0.04253855720162392,
-0.008285149931907654,
-0.02505193091928959,
-0.015506993979215622,
-0.03527095913887024,
-0.029152793809771538,
0.018067166209220886,
-0.033738553524017334,
-0.027725456282496452,
-0.004722831305116415,
0.08834255486726761,
-0.025695381686091423,
0.00870326068252325,
0.034187667071819305,
-0.006991048343479633,
-0.041624877601861954,
0.015262252651154995,
0.029547998681664467,
0.02417021058499813,
-0.018181126564741135,
0.008946818299591541,
-0.02439170330762863,
-0.015439937822520733,
-0.0339922159910202,
-0.052041683346033096,
0.02735842764377594,
0.012309039942920208,
-0.013977090828120708,
-0.02996242418885231,
-0.02140306681394577,
0.0031133131124079227,
-0.04422259330749512,
0.006067229900509119,
-0.01838103123009205,
0.021652525290846825,
-0.05638952925801277,
-0.03564242273569107,
-0.03354225680232048,
0.025726068764925003,
-0.001284759840928018,
0.03550427034497261,
-0.008662046864628792,
-0.000032017000194173306,
-0.011030935682356358,
-0.008439158089458942,
0.03938234969973564,
-0.032979343086481094,
-0.020726902410387993,
-0.022678326815366745,
-0.005153220612555742,
-0.04136303812265396,
-0.031781576573848724,
0.01897311583161354,
-0.013557251542806625,
0.07726366072893143,
-0.02009456604719162,
-0.014443926513195038,
-0.015398996882140636,
-0.07120510190725327,
-0.0258416086435318,
-0.017838560044765472,
0.009341116063296795,
0.014567727223038673,
0.007921106182038784,
0.035806361585855484,
0.013219322077929974,
-0.030282732099294662,
0.002231935504823923,
-0.0004196941154077649,
0.02309868484735489,
0.05169443041086197,
-0.06256359070539474,
-0.046160511672496796,
-0.0015527202049270272,
-0.01769629679620266,
-0.021769307553768158,
-0.020492248237133026,
0.038663096725940704,
0.024006763473153114,
-0.007904156111180782,
-0.0191080030053854,
0.051474444568157196,
-0.056759949773550034,
0.001015777001157403,
-0.003572606248781085,
0.0022124394308775663,
0.015558229759335518,
0.009310533292591572,
0.002457187045365572,
-0.06386473029851913,
-0.027922315523028374,
-0.004788112826645374,
0.0040919724851846695,
0.023540223017334938,
0.0016751535004004836,
-0.020621873438358307,
-0.011304604820907116,
-0.026758944615721703,
0.014839930459856987,
-0.03426184505224228,
0.005337105598300695,
0.0010662423446774483,
0.014753335155546665,
0.009299775585532188,
0.02190759964287281,
-0.03175656870007515,
0.020774800330400467,
-0.033213358372449875,
-0.016547828912734985,
0.05325882136821747,
0.023313025012612343,
0.016994543373584747,
-0.013532182201743126,
0.024866871535778046,
-0.03363985940814018,
0.038975801318883896,
0.025597356259822845,
0.004465270787477493,
0.051457252353429794,
-0.06742953509092331,
-0.004736046306788921,
0.017835749313235283,
-0.013321462087333202,
0.007452563848346472,
0.035792458802461624,
-0.01911570318043232,
-0.026760000735521317,
0.013604087755084038,
-0.004799900576472282,
-0.03220898285508156,
-0.00264798104763031,
0.012618587352335453,
-0.0029309976380318403,
0.009760507382452488,
0.013740264810621738,
-0.025831803679466248,
-0.007675705943256617,
-0.020719898864626884,
0.021000055596232414,
-0.016893519088625908,
-0.03130366653203964,
0.04290005564689636,
0.01122383400797844,
-0.011241253465414047,
0.01969113200902939,
-0.025022391229867935,
0.049740102142095566,
0.02100013755261898,
0.0007861481280997396,
0.0007478587795048952,
-0.04400680214166641,
0.01878439448773861,
-0.06039370968937874,
0.009013127535581589,
-0.007053904235363007,
0.006070652510970831,
0.04506402090191841,
-0.0387432724237442,
-0.043689366430044174,
0.0028102986980229616,
-0.023635931313037872,
0.022977540269494057,
-0.011505967006087303,
-0.007270308211445808,
-0.05888878181576729,
0.028956159949302673,
-0.03674948588013649,
0.030021723359823227,
0.001342920819297433,
0.0206365417689085,
0.03154812008142471,
0.026147617027163506,
0.011980446055531502,
-0.008219556882977486,
0.015296983532607555,
0.0039536720141768456,
0.028994044288992882,
-0.028784507885575294,
0.07669142633676529,
-0.0003577256284188479,
-0.04792783781886101,
0.022805752232670784,
-0.011257796548306942,
-0.0063581219874322414,
-0.016218386590480804,
0.03663436323404312,
0.03683430328965187,
0.035432085394859314,
0.003472340991720557,
-0.01809505932033062,
0.018876902759075165,
0.026273559778928757,
0.004708826541900635,
0.013406360521912575,
-0.05174843594431877,
0.01997380517423153,
0.03669200837612152,
0.0050691235810518265,
0.0053180609829723835,
0.03544003143906593,
-0.00219200667925179,
-0.02629055641591549,
-0.040786243975162506,
-0.023483870550990105,
-0.0005710186087526381,
-0.01913321763277054,
0.005923825781792402,
-0.006180713884532452,
-0.002105626044794917,
-0.0021264399401843548,
-0.02850319631397724,
-0.0015532905235886574,
0.01818203181028366,
-0.014367328956723213,
-0.07282215356826782,
0.10075213760137558,
0.0008591284858994186,
-0.033847626298666,
-0.01545398123562336,
-0.015702439472079277,
0.022237110882997513,
0.026863757520914078,
-0.017199555411934853,
-0.04919756203889847,
-0.03237142786383629,
0.011641067452728748,
-0.018246984109282494,
0.012066337279975414,
0.002654698444530368,
-0.03166666254401207,
0.006322185508906841,
-0.04765765741467476,
0.02383400686085224,
0.02678523026406765,
0.0020366469398140907,
-0.008542316034436226,
-0.010691684670746326,
0.01162819005548954,
0.022838247939944267,
0.04129163548350334,
-0.016907289624214172,
-0.025799104943871498,
-0.019688958302140236,
-0.001136443461291492,
0.010923582129180431,
-0.04693678021430969,
0.020821068435907364,
-0.0059041669592261314,
-0.003632182953879237,
-0.0026011699810624123,
0.00027704102103598416,
-0.036806173622608185,
0.035483285784721375,
-0.005587318446487188,
-0.03992335870862007,
0.00892466027289629,
-0.004069844260811806,
-0.03653942421078682,
-0.0036404342390596867,
0.013197134248912334,
0.010455328971147537,
0.053600940853357315,
0.04827640950679779,
0.0036358910147100687,
0.01619660295546055,
-0.00868737418204546,
-0.000941860256716609,
0.010837082751095295,
-0.043769411742687225,
-0.0320417582988739,
-0.0347750298678875,
0.017878586426377296,
0.038443807512521744,
-0.04620853438973427,
-0.033430300652980804,
0.0370376892387867,
-0.061020683497190475,
0.002172299660742283,
0.04474986717104912,
0.005208257585763931,
0.02241835743188858,
0.02092144638299942,
0.013683495111763477,
-0.00042562969611026347,
-0.005121534690260887,
0.026110919192433357,
0.007880592718720436,
0.051645249128341675,
-0.036256469786167145,
0.03672156482934952,
-0.01786058209836483,
-0.011327199637889862,
0.0027330319862812757,
-0.04563990235328674,
0.060844212770462036,
-0.03964262455701828,
-0.0025448668748140335,
0.01822967454791069,
-0.004159102216362953,
-0.008533863350749016,
0.0050031039863824844,
-0.041830457746982574,
0.055038418620824814,
0.011160691268742085,
0.0024238391779363155,
-0.0062646460719406605,
-0.015204308554530144,
-0.005018322262912989,
0.00774145545437932,
0.09006844460964203,
0.0391550213098526,
-0.0026288703083992004,
0.014870582148432732,
-0.024169767275452614,
-0.017517535015940666,
-0.0019322558073326945,
-0.05282032862305641,
0.0268572885543108,
-0.005914868321269751,
-0.008434278890490532,
0.010321366600692272,
-0.01581639237701893,
-0.013157605193555355,
-0.054782651364803314,
0.006364048924297094,
0.03239992633461952,
0.039881326258182526,
0.005782200023531914,
-0.016806475818157196,
-0.000967267609667033,
0.07525131106376648,
-0.06763727217912674,
-0.014685733243823051,
0.014163796789944172,
0.014243234880268574,
0.017089471220970154,
0.020704001188278198
] |
<p>Suppose you a have an ordinary Luttinger liquid with<br>
$$ H = \int dx \sum _{\eta= \pm 1 , \sigma =\uparrow,\downarrow } \psi^\dagger_{\eta, \sigma} (x) (-i v \eta \partial _x) \psi _{\eta,\sigma} (x). $$</p>
<p>You then bosonize it using
$$\psi_{\eta,\sigma}=\frac{1}{\sqrt{2 \pi \alpha}} F_{\eta ,\sigma} e^{-i \phi_{\eta, \sigma}}$$
where F is the Klein factor and $\phi$ a bosonic field.</p>
<p>My question is, what happens to F and $\phi$ under time reversal? </p>
<p>The problem here is that the usual result for fermions,
$$T c_{i,\uparrow} T^{-1}= c_{i,\downarrow}$$
$$T c_{i,\downarrow} T^{-1}=- c_{i,\uparrow}$$</p>
<p>where T is the time reversal operator,
is not so obvious when there is separation between the Klein factor and the phase.
I mean, why would $\phi_\uparrow$ turn into $\phi_\downarrow$ ?</p> | 2,836 | [
0.020729798823595047,
0.005895004142075777,
0.012321451678872108,
-0.0019172175088897347,
0.03736107423901558,
-0.004870693664997816,
-0.04277421161532402,
-0.00820660125464201,
-0.005374690983444452,
0.0031498242169618607,
0.026761198416352272,
-0.019395975396037102,
0.0447772853076458,
-0.0006914479308761656,
-0.008801558054983616,
0.0350126214325428,
-0.025540899485349655,
-0.00763958552852273,
-0.040901053696870804,
-0.05253772810101509,
0.017521044239401817,
0.05604446306824684,
-0.018385810777544975,
-0.00014220316370483488,
-0.020649194717407227,
0.03997011482715607,
-0.016896449029445648,
-0.006580584682524204,
0.020020028576254845,
0.041666287928819656,
0.004312349949032068,
-0.037734098732471466,
0.011158112436532974,
-0.00984661839902401,
0.013677962124347687,
-0.005654330365359783,
-0.04138686880469322,
-0.05546480789780617,
0.004515077918767929,
-0.0015205144882202148,
-0.041019171476364136,
-0.04184899479150772,
-0.01773943565785885,
0.061525266617536545,
0.026354694738984108,
-0.018150659278035164,
-0.02577337808907032,
-0.008965804241597652,
0.034525856375694275,
-0.0859292671084404,
0.012050908990204334,
0.014161882922053337,
0.0049999854527413845,
-0.012885335832834244,
-0.0003396566316951066,
-0.0013163341209292412,
0.05174322798848152,
0.05236213654279709,
0.030831271782517433,
-0.08427011966705322,
-0.014750353060662746,
-0.03428012505173683,
-0.012895656749606133,
-0.015002644620835781,
-0.03393402323126793,
-0.009829928167164326,
0.008764374069869518,
-0.01957584172487259,
0.008675603196024895,
-0.05200845003128052,
-0.01498282141983509,
-0.030056307092308998,
0.023073773831129074,
-0.029807308688759804,
-0.014654818922281265,
0.0008888758602552116,
0.007910653948783875,
0.02050638571381569,
0.03660239651799202,
0.01929984986782074,
-0.012490486726164818,
0.027172211557626724,
0.03938264399766922,
0.016152173280715942,
-0.004285754170268774,
0.005963632836937904,
0.07621556520462036,
-0.03398960828781128,
0.002917792648077011,
0.056541163474321365,
-0.013014628551900387,
0.03999669477343559,
0.03956828638911247,
-0.010395677760243416,
-0.02615201659500599,
-0.006024354137480259,
0.02281028963625431,
0.04081559553742409,
-0.009226823225617409,
0.014555267058312893,
-0.04329439252614975,
-0.004699770826846361,
0.006513112690299749,
0.047149285674095154,
-0.028112182393670082,
-0.008226307108998299,
-0.016360241919755936,
-0.01693347841501236,
-0.007144870236515999,
-0.010001272894442081,
-0.05946638807654381,
-0.014511914923787117,
-0.02553982101380825,
0.010165443643927574,
-0.021039865911006927,
-0.03455234691500664,
0.00022434860875364393,
-0.020335977897047997,
0.04410375654697418,
0.08235205709934235,
0.004812411032617092,
-0.021512191742658615,
0.03937898203730583,
-0.001734066870994866,
-0.06241322308778763,
0.008291661739349365,
0.02597835846245289,
-0.015597764402627945,
-0.045619040727615356,
0.014410758391022682,
0.03053888864815235,
0.01015574112534523,
0.015153919346630573,
0.024420643225312233,
0.021749448031187057,
-0.033769164234399796,
-0.10894440859556198,
-0.07174625247716904,
0.031543612480163574,
-0.03301999717950821,
-0.022564981132745743,
-0.06695028394460678,
-0.004708809312433004,
0.03821709379553795,
0.05558977648615837,
-0.004544838331639767,
0.017924081534147263,
0.03129439800977707,
0.024267159402370453,
0.05575431138277054,
0.002371337730437517,
-0.05058504268527031,
0.02208581380546093,
-0.03435816243290901,
-0.014423652552068233,
-0.016882244497537613,
0.04303736612200737,
0.02738756686449051,
0.007439897395670414,
0.013717418536543846,
0.05442701652646065,
-0.02889750897884369,
0.016148554161190987,
0.015214328654110432,
-0.05716542527079582,
-0.049407921731472015,
0.07092813402414322,
0.022610099986195564,
0.019674697890877724,
0.03273375332355499,
-0.024269333109259605,
0.012992151081562042,
0.0022054912988096476,
0.017877064645290375,
0.009642179124057293,
-0.03158675879240036,
-0.05521820858120918,
-0.019937759265303612,
-0.0011089120525866747,
-0.004455000627785921,
0.013106366619467735,
-0.01528165116906166,
-0.022564033046364784,
-0.01143871620297432,
0.005995576269924641,
-0.007048343773931265,
-0.005506542511284351,
0.011607539840042591,
-0.006088003516197205,
-0.07069558650255203,
-0.012228567153215408,
-0.04812866076827049,
-0.01941026747226715,
0.019903218373656273,
-0.007112974766641855,
0.04815320670604706,
0.02172442339360714,
0.028839869424700737,
0.01211303099989891,
-0.055672865360975266,
0.00006826462777098641,
0.01690828427672386,
0.010878628119826317,
-0.021380603313446045,
0.05029435083270073,
0.05266764387488365,
0.03623826801776886,
0.006832916755229235,
0.03424092009663582,
-0.011948212049901485,
-0.020961502566933632,
-0.03954390436410904,
-0.01586725562810898,
0.02315221168100834,
-0.023037845268845558,
-0.025257980450987816,
0.030396077781915665,
-0.02021174319088459,
-0.023227347061038017,
0.0027076308615505695,
-0.0552285760641098,
0.04354562982916832,
0.0928068682551384,
-0.013014709576964378,
-0.017287129536271095,
0.01705174706876278,
0.03645160049200058,
0.04134424775838852,
0.020463276654481888,
0.005113866180181503,
-0.05980219691991806,
-0.02667136862874031,
0.021332422271370888,
0.04293474555015564,
-0.03173094615340233,
0.04095456376671791,
0.03561900556087494,
-0.0010779259027913213,
0.04580057039856911,
-0.004200667142868042,
-0.011091448366641998,
-0.04664497449994087,
0.02431659772992134,
-0.02739785984158516,
0.023156752809882164,
-0.016011957079172134,
0.02259756252169609,
-0.05185607075691223,
0.012085836380720139,
-0.03392564132809639,
-0.011018635705113411,
-0.01669609732925892,
-0.03165305405855179,
0.011856426484882832,
0.004304912406951189,
-0.06113381311297417,
0.01596831902861595,
-0.019058221951127052,
0.033763814717531204,
0.026562552899122238,
-0.01809358038008213,
-0.005472660064697266,
-0.04553961381316185,
-0.01814364828169346,
0.018594957888126373,
-0.008742153644561768,
-0.0020005882252007723,
-0.009197098203003407,
0.02493966370820999,
-0.04089212045073509,
0.026551080867648125,
-0.03686569631099701,
0.05124891549348831,
-0.003750759409740567,
-0.014960185624659061,
0.0292682945728302,
0.014315390959382057,
0.011337406933307648,
-0.007935374975204468,
-0.00017436356574762613,
0.04834369197487831,
-0.02599327452480793,
0.0129801444709301,
0.014371203258633614,
-0.06473802030086517,
0.0017212412785738707,
-0.034943513572216034,
-0.0028502228669822216,
0.011776668950915337,
0.0071511035785079,
0.010743072256445885,
-0.02966110035777092,
-0.016968103125691414,
-0.035505037754774094,
-0.04783731326460838,
-0.01636272855103016,
0.0031256703659892082,
-0.037947699427604675,
0.014662280678749084,
0.00197205925360322,
0.014039229601621628,
-0.017063861712813377,
-0.005362173076719046,
0.004016968421638012,
-0.0457688570022583,
-0.03342834487557411,
-0.008820880204439163,
0.011038625612854958,
-0.05461854487657547,
0.026051830500364304,
0.012548844330012798,
-0.05800655484199524,
-0.007545928470790386,
-0.05200176313519478,
0.00729544460773468,
0.014472479932010174,
-0.000016336713088094257,
0.022189108654856682,
-0.009769253432750702,
-0.008328467607498169,
0.0976167768239975,
-0.005182468332350254,
-0.015270113945007324,
0.00561891682446003,
-0.014617395587265491,
-0.006035970989614725,
-0.043787017464637756,
0.021417904645204544,
0.011665692552924156,
-0.025476904585957527,
0.048430562019348145,
-0.018184317275881767,
0.05616963282227516,
0.05869821459054947,
0.02894080989062786,
-0.033992137759923935,
0.024457497522234917,
0.004844939801841974,
-0.0010736380936577916,
0.02993904799222946,
-0.03131944313645363,
0.02620682679116726,
-0.010262358002364635,
0.020965712144970894,
0.049084026366472244,
0.015877632424235344,
-0.05010231211781502,
0.05002069100737572,
0.017016442492604256,
-0.0052534365095198154,
-0.01645575277507305,
0.0421111099421978,
-0.026037853211164474,
0.013936740346252918,
-0.01716013438999653,
0.0022037040907889605,
0.04303126037120819,
-0.031472984701395035,
0.03008905239403248,
0.02645365707576275,
0.03957800194621086,
-0.010295730084180832,
-0.05444477126002312,
0.00305216945707798,
-0.01640724204480648,
0.039908502250909805,
-0.07454577833414078,
-0.024588042870163918,
0.03701039031147957,
0.025413278490304947,
0.0068087331019341946,
-0.004670488648116589,
-0.0196403618901968,
-0.005082911346107721,
-0.03927284851670265,
-0.016256719827651978,
-0.019514668732881546,
0.0953626036643982,
0.010735699906945229,
0.04685220122337341,
0.03917315974831581,
0.010828309692442417,
0.023109517991542816,
-0.014801830984652042,
-0.06983593851327896,
0.00027396116638556123,
0.027077075093984604,
0.021160291507840157,
-0.022810017690062523,
-0.021848326548933983,
0.01430180761963129,
-0.03635033965110779,
-0.029686912894248962,
-0.014922318048775196,
-0.0049648592248559,
-0.029537366703152657,
0.02640042081475258,
-0.021838054060935974,
-0.01856776513159275,
-0.036273662000894547,
0.04263656958937645,
0.03246471658349037,
-0.017704816535115242,
0.024073120206594467,
0.016446540132164955,
-0.016692163422703743,
0.0034268226008862257,
-0.024994278326630592,
0.02502349577844143,
0.03604331612586975,
0.0452922023832798,
0.06851385533809662,
0.018832216039299965,
-0.01213593315333128,
-0.019278474152088165,
0.0444999597966671,
0.03948604315519333,
0.011576062999665737,
-0.00977129302918911,
-0.006534677930176258,
-0.0043453313410282135,
-0.027807017788290977,
0.025304781273007393,
0.06930965930223465,
0.0012117160949856043,
0.012716054916381836,
0.014387082308530807,
0.02369094453752041,
-0.010668243281543255,
0.049976084381341934,
0.037816110998392105,
0.00801925454288721,
0.0032421485520899296,
-0.03355326130986214,
0.017990557476878166,
-0.0005391964805312455,
0.015767188742756844,
0.009740574285387993,
0.003099078545346856,
-0.00492433737963438,
0.013903518207371235,
0.00881260447204113,
0.05613423138856888,
-0.009340564720332623,
-0.017526069656014442,
-0.011081746779382229,
-0.02509767934679985,
0.015887504443526268,
0.0024647803511470556,
0.0027442616410553455,
0.0637681856751442,
0.049024879932403564,
0.04164538532495499,
0.0074461959302425385,
-0.07187007367610931,
-0.03469352796673775,
0.015360001474618912,
0.02473168447613716,
0.005688301753252745,
-0.009774933569133282,
-0.05514294281601906,
-0.013087059371173382,
0.03321859613060951,
-0.027590762823820114,
0.03241950273513794,
-0.018514981493353844,
-0.0023295592982321978,
-0.008726418949663639,
-0.04552829638123512,
-0.006349768023937941,
0.050715599209070206,
-0.015096842311322689,
0.04787816107273102,
-0.046893034130334854,
0.0012922425521537662,
-0.04868222028017044,
0.0039031209889799356,
-0.0302419513463974,
0.060997869819402695,
-0.013414773158729076,
0.014625675044953823,
0.010074802674353123,
-0.004489649087190628,
-0.011039203964173794,
-0.12390968203544617,
0.002759320894256234,
0.012119445949792862,
0.023368122056126595,
0.026008808985352516,
-0.01567753031849861,
-0.04172978177666664,
-0.004671657457947731,
0.031606465578079224,
-0.012364604510366917,
0.02510298416018486,
-0.018857307732105255,
0.05961053445935249,
-0.0017644875915721059,
-0.025200355798006058,
0.08538603037595749,
0.05186142399907112,
0.016848597675561905,
-0.009865465573966503,
0.014094280079007149,
0.03898843750357628,
-0.018642086535692215,
0.062444400042295456,
-0.028773268684744835,
0.03039536066353321,
-0.022534504532814026,
0.05648580938577652,
-0.032427817583084106,
0.05317213758826256,
0.019938040524721146,
-0.009396699257194996,
-0.03143265098333359,
0.017914051190018654,
-0.011594070121645927,
-0.041839078068733215,
-0.0017906639259308577,
-0.02353842556476593,
0.0008897591615095735,
-0.00913259107619524,
0.01841040514409542,
-0.021053582429885864,
0.010431827045977116,
0.038068730384111404,
-0.0007046645623631775,
0.0413055419921875,
0.01758667267858982,
-0.0221488568931818,
-0.01365669909864664,
-0.0388578437268734,
0.007300898898392916,
-0.002424543956294656,
0.018811780959367752,
-0.009658614173531532,
-0.037159889936447144,
0.008222975768148899,
0.02484080381691456,
-0.0012490424560382962,
-0.024225912988185883,
-0.03911304846405983,
0.005535026080906391,
0.024730229750275612,
0.01765379123389721,
-0.08610440790653229,
-0.06180131062865257,
-0.015169668942689896,
-0.019220849499106407,
-0.052630990743637085,
0.000977543881163001,
0.0020447492133826017,
0.0021471588406711817,
-0.040074773132801056,
0.025526592507958412,
0.03314189612865448,
-0.017130380496382713,
-0.002927725901827216,
0.03497368097305298,
0.008077485486865044,
0.0374004952609539,
-0.008582552894949913,
-0.001032166532240808,
0.02013208717107773,
-0.023367954418063164,
-0.004655936267226934,
0.021272696554660797,
0.02693869173526764,
-0.03490526229143143,
-0.03424741327762604,
-0.008453523740172386,
-0.01242142915725708,
0.014976565726101398,
0.02573060803115368,
0.000985038815997541,
0.016617706045508385,
0.022419849410653114,
0.011267218738794327,
-0.033986896276474,
-0.013996027410030365,
0.01005870383232832,
0.05399445816874504,
-0.008920463733375072,
-0.014650927856564522,
-0.009758900851011276,
-0.0316849909722805,
0.011176933534443378,
-0.0001057890331139788,
-0.009125928394496441,
-0.0036584255285561085,
0.04147399961948395,
0.025365184992551804,
0.003515901742503047,
0.03168721869587898,
0.008520676754415035,
0.02771924063563347,
0.034492868930101395,
0.005666006356477737,
0.031578682363033295,
0.00028615377959795296,
-0.034062307327985764,
-0.04307803884148598,
-0.034585140645504,
0.050412729382514954,
0.04825088009238243,
-0.017398860305547714,
0.011348025873303413,
0.011619610711932182,
-0.007562803570181131,
-0.009893659502267838,
-0.019571421667933464,
-0.003875807859003544,
0.03472317382693291,
-0.030544111505150795,
0.021563636139035225,
-0.043093010783195496,
-0.004712360445410013,
0.018727581948041916,
0.04729742929339409,
-0.027208544313907623,
0.021835055202245712,
0.017348669469356537,
0.017706723883748055,
0.007156286388635635,
-0.008026636205613613,
-0.0018207409884780645,
0.033650632947683334,
-0.047839123755693436,
0.024206018075346947,
0.00605472456663847,
0.020968934521079063,
0.06442873924970627,
0.006937756203114986,
0.05247100442647934,
-0.036894045770168304,
0.0000847108822199516,
-0.05372946336865425,
-0.029452478513121605,
0.02010652981698513,
-0.010297069326043129,
0.0355059839785099,
0.04407656192779541,
0.03742336854338646,
0.024013826623558998,
-0.029826786369085312,
0.001941594178788364,
-0.061206329613924026,
0.001249992405064404,
-0.02339600771665573,
-0.06603141874074936,
-0.0027703833766281605,
-0.027049757540225983,
0.007358727511018515,
0.0445442833006382,
-0.023452429100871086,
0.02131463587284088,
0.03566383570432663,
0.02102365717291832,
-0.02661208249628544,
0.03898099437355995,
-0.00949470978230238,
0.049290914088487625,
0.0017733053537085652,
0.0021695811301469803,
0.1407044380903244,
0.040764350444078445,
0.021870579570531845,
-0.08005984127521515,
0.001992667093873024,
0.0013810412492603064,
0.040660310536623,
-0.030321747064590454,
0.018528440967202187,
-0.005883910693228245,
-0.005843047983944416,
0.0029621575959026814,
0.07772417366504669,
0.01513910572975874,
-0.001720624160952866,
0.026024963706731796,
-0.03723504766821861,
-0.02548689767718315,
0.025119543075561523,
0.014806948602199554,
-0.02440311200916767,
-0.021162254735827446,
-0.029445698484778404,
0.004931368865072727,
-0.03606446832418442,
0.050566963851451874,
-0.014461742714047432,
-0.04073728621006012,
0.0019229465397074819,
-0.0177712794393301,
-0.028550010174512863,
0.007792688440531492,
-0.011905355378985405,
-0.006811971310526133,
-0.01882125250995159,
0.047395575791597366,
0.008075929246842861,
-0.008465259335935116,
0.0290839821100235,
0.06607696413993835,
-0.008955471217632294,
0.0035409622360020876,
0.011175815016031265,
0.001877508475445211,
-0.02722669392824173,
-0.04236474633216858,
-0.011075270362198353,
0.06597241014242172,
-0.018220707774162292,
-0.023823704570531845,
-0.0037525086663663387,
-0.027758095413446426,
0.07288768142461777,
-0.03419529274106026,
-0.02742847427725792,
0.01630893535912037,
0.03383242338895798,
-0.0033475987147539854,
0.00798153504729271,
-0.01714470610022545,
0.029139747843146324,
0.006544244010001421,
0.013323168270289898,
-0.04859748110175133,
0.0011041659163311124,
-0.01026083342730999,
-0.003915794193744659,
0.015951011329889297,
0.01873970218002796,
-0.024170247837901115,
-0.03238240256905556,
0.046605825424194336,
-0.07021795213222504,
-0.004075328819453716,
0.012447544373571873,
0.016974519938230515,
0.018254339694976807,
-0.008604018948972225,
-0.009440894238650799,
-0.04139532893896103,
-0.08374330401420593,
0.044410590082407,
-0.03697021305561066,
-0.03398452326655388,
0.03013424575328827,
-0.010072656907141209,
0.04212881624698639,
0.06235039606690407,
-0.029715703800320625,
-0.0071062068454921246,
-0.0010995609918609262,
0.015153158456087112,
0.03983708471059799,
0.003968142904341221,
-0.061694324016571045,
0.008250958286225796,
-0.03331379219889641,
-0.009755072183907032,
-0.030126262456178665,
-0.006860614288598299,
0.037803225219249725,
-0.024832280352711678,
-0.024008480831980705,
0.01988856866955757,
-0.01821034587919712,
-0.021366264671087265,
0.03333314508199692,
-0.009754195809364319,
-0.023912550881505013,
0.04380587488412857,
0.0399409644305706,
-0.03598468378186226,
-0.0659671276807785,
-0.03318915516138077,
0.002123120240867138,
-0.0056198155507445335,
0.0017730939434841275,
-0.02885671705007553,
-0.030696885660290718,
-0.003092736005783081,
0.03633219748735428,
0.0026352587155997753,
0.02714395523071289,
-0.03190196678042412,
0.01856650970876217,
-0.02203589864075184,
0.012282107025384903,
-0.0029062465764582157,
0.05031738430261612,
0.026349255815148354,
0.03419600427150726,
-0.006100047379732132,
0.018431281670928,
0.011056589893996716,
0.005113897379487753,
0.02749026007950306,
0.01595951057970524,
0.008130704052746296,
0.00789206475019455,
-0.0274012703448534,
0.04706991836428642,
-0.014341591857373714,
-0.055630873888731,
0.03879489749670029,
0.02009872905910015,
0.01726999320089817,
0.009280867874622345,
0.03220600262284279,
-0.016219785436987877,
0.02970874309539795,
-0.0049067470245063305,
-0.0027741307858377695,
0.0007346348720602691,
-0.02107069455087185,
0.023051561787724495,
-0.034538205713033676,
-0.030537521466612816,
-0.013184593990445137,
0.03388001024723053,
0.001305585727095604,
0.02842172235250473,
-0.003472182434052229,
0.010855461470782757,
-0.024289710447192192,
0.012204599566757679,
0.04450225457549095,
0.03733542189002037,
-0.027434194460511208,
0.0040018572472035885,
0.06962820887565613,
0.011594239622354507,
0.023489348590373993,
0.052395015954971313,
0.027498314157128334,
-0.09589124470949173,
-0.028747035190463066,
0.0008789816638454795,
-0.0034064201172441244,
0.004581710789352655,
-0.042013395577669144,
0.021334579214453697,
0.012086416594684124,
-0.05577576160430908,
0.039940547198057175,
-0.016613950952887535,
-0.009484677575528622,
-0.02164093777537346,
-0.0038901909720152617,
-0.0379873588681221,
0.06650584936141968,
0.04756458103656769,
0.0026318782474845648,
-0.006916740443557501,
0.010173660703003407,
0.0121303740888834,
-0.026234257966279984,
-0.016048137098550797,
0.008382466621696949,
0.0019595210906118155,
-0.015517390333116055,
0.05207930505275726,
-0.011875178664922714,
-0.031248658895492554,
-0.0003072217805311084,
0.03404037281870842,
-0.04875815659761429,
-0.031239381060004234,
0.021731631830334663,
-0.02005600929260254,
0.022822866216301918,
-0.02325020544230938,
-0.02439901791512966,
0.010183777660131454,
0.026133237406611443,
0.006031940691173077,
-0.009807621128857136,
0.017899999395012856,
-0.032759349793195724,
-0.013308114372193813,
-0.060734666883945465,
-0.012946954928338528,
0.0700606256723404,
-0.03972761705517769,
-0.03573497012257576,
-0.023661592975258827,
-0.02367009036242962,
-0.005262183956801891,
-0.012600445188581944,
0.015972306951880455,
-0.06497308611869812,
-0.024980194866657257,
0.04589208588004112,
0.015482009388506413,
-0.01587056554853916,
0.008221969939768314,
-0.03491422161459923,
-0.0787585973739624,
0.057017549872398376,
0.003624927718192339,
-0.04286874085664749,
-0.0174242053180933,
-0.01975889876484871,
0.0005986351752653718,
0.014233182184398174,
0.003364596050232649,
-0.010452982038259506,
-0.033515606075525284,
0.01366675179451704,
-0.0004956276970915496,
0.02573578432202339,
-0.05052286013960838,
-0.02435879595577717,
0.0037762769497931004,
-0.05846051871776581,
0.03142856806516647,
0.008096184581518173,
-0.005204236134886742,
-0.005380100570619106,
-0.040363673120737076,
-0.028903448954224586,
0.005612426437437534,
0.062176354229450226,
0.021741073578596115,
-0.014155960641801357,
0.002113241469487548,
0.013112322427332401,
0.020693957805633545,
-0.03526907041668892,
-0.032980602234601974,
-0.010240972973406315,
0.021435480564832687,
0.029161345213651657,
0.000014582795301976148,
-0.018755385652184486,
0.05985812842845917,
0.044285643845796585,
-0.01552954688668251,
-0.022889789193868637,
-0.018398160114884377,
-0.037643298506736755,
0.05023559182882309,
0.022937405854463577,
0.04602311551570892,
0.059353798627853394,
-0.035204339772462845,
0.034978464245796204,
0.02293268032371998,
-0.04260053485631943,
-0.029132381081581116,
-0.0005711066187359393,
-0.02410321682691574,
-0.005289440043270588,
0.0003600364725571126,
-0.0011475388891994953,
-0.006355714984238148,
-0.012517198920249939,
0.04256441444158554,
0.0486445277929306,
-0.03998143598437309,
0.0072058867663145065,
0.05813569575548172,
0.015117673203349113,
0.024064529687166214,
0.014026125892996788,
0.01555069349706173,
0.009322748519480228,
0.04092850908637047,
0.009383946657180786,
0.0265815369784832,
0.0029596153181046247,
0.017256729304790497,
0.030515361577272415,
-0.02207522839307785,
-0.03160194307565689,
0.017828650772571564,
-0.00507368054240942,
0.01680946722626686,
-0.022402212023735046,
0.046759769320487976,
0.054664790630340576,
-0.04218662530183792,
-0.006629907991737127,
0.005858211778104305,
-0.016224650666117668,
0.07694153487682343,
-0.0404505580663681,
0.008938943967223167,
-0.03511149063706398,
0.02725839801132679,
0.009539708495140076,
0.014235087670385838,
0.01722109690308571,
0.04690096154808998,
-0.03534739464521408,
-0.02375967428088188,
-0.05334695056080818,
0.01377776823937893,
0.001936881453730166,
-0.06330729275941849,
-0.04724721610546112,
0.02374378591775894,
0.002050319453701377,
0.010691570118069649,
-0.06674212962388992,
-0.036508217453956604,
-0.026777207851409912,
0.002352625597268343,
0.017791396006941795,
0.005192026495933533,
0.021680576726794243,
-0.027847770601511,
0.016886578872799873,
0.04132584482431412,
-0.012890388257801533,
-0.014540594071149826,
0.002302333014085889,
0.04738135635852814,
-0.017841218039393425,
0.019123069941997528
] |
<p>How can it be shown that the Dirac spinor is the direct sum of a right handed Weyl spinor and a left handed Weyl spinor?</p>
<p>EDIT:- Let $\psi_L$ and $\psi_R$ be 2 component left-handed and right-handed Weyl spinors. Their transformation properties are known. When I put these two spinors in a column and construct a four-component column which is a direct sum of $\psi_L$ and $\psi_R$ i.e., $\psi_D=\psi_L\oplus\psi_R$. This I <strong>define</strong> to be the dirac spinor. Right? Since it is a direct sum under Lorentz transformation, the corresponding Lorentz transformation matrix is diagonal. Right? Then it is easy to show that, it satisfies the Dirac equation in Chiral basis. Right? This is possible because we started from the definition of left-handed and right handed weyl spinors and their transformation properties are known. Right? This is explicitly carried out in the book by Lewis Ryder. But suppose I start the other way around. I solve the dirac equation in chiral basis. Then no one tells me that the upper two components are really left-handed and lower two are really right-handed. Suppose I take this chiral basis solution of dirac equation and now take that to be my <strong>definition</strong> of dirac spinor. Then how can I show the opposite, that it is made up of two irreps of Lorentz group i.e., $\psi_D=\psi_L\oplus\psi_R$ ? </p> | 2,837 | [
-0.025909423828125,
0.017062831670045853,
-0.01659853383898735,
-0.016331255435943604,
0.04822269082069397,
0.01566610485315323,
-0.0073026143945753574,
-0.024966247379779816,
0.004159262403845787,
-0.03397344425320625,
0.04429676756262779,
-0.0016974465688690543,
0.07589994370937347,
0.001547139836475253,
0.035899609327316284,
0.03330608829855919,
-0.03292091190814972,
-0.0066218990832567215,
-0.013637775555253029,
0.0003215459000784904,
0.016088245436549187,
0.0036367648281157017,
-0.0005984737654216588,
0.011820191517472267,
-0.022264601662755013,
0.03129884973168373,
0.005051399115473032,
0.012943251058459282,
0.007467429153621197,
0.05874788761138916,
-0.01504283957183361,
-0.030448412522673607,
0.009342288598418236,
0.023025451228022575,
0.004304614383727312,
-0.010944814421236515,
-0.04648136720061302,
-0.0023181180004030466,
-0.008319560438394547,
-0.003880617441609502,
0.00462338188663125,
-0.0018808117602020502,
-0.025551069527864456,
0.036728933453559875,
-0.0290505550801754,
0.010158568620681763,
-0.008630960248410702,
-0.008561031892895699,
0.06479597091674805,
-0.06946466118097305,
0.06926676630973816,
0.004164294805377722,
0.036859069019556046,
-0.0016974488971754909,
-0.03510770946741104,
-0.03236560896039009,
0.04598814994096756,
0.05537393316626549,
0.010032429359853268,
-0.00786623265594244,
0.013387031853199005,
-0.014440937899053097,
0.02943992428481579,
-0.01859842985868454,
-0.037757132202386856,
0.032875847071409225,
0.005946282763034105,
0.015969622880220413,
-0.0006988295936025679,
-0.013663495890796185,
0.00642791111022234,
-0.018675267696380615,
0.02904631569981575,
-0.00520731694996357,
-0.002660547848790884,
-0.024252895265817642,
-0.0015454095555469394,
0.060618806630373,
0.03353958576917648,
0.010491173714399338,
-0.029538968577980995,
0.05341212823987007,
0.01959161087870598,
-0.011201826855540276,
-0.0041191899217665195,
-0.048865534365177155,
0.06028253957629204,
0.03469931706786156,
-0.01638484187424183,
0.015599277801811695,
0.03142476826906204,
0.001038793590851128,
0.0347629152238369,
0.010216467082500458,
-0.0163114033639431,
0.05869945511221886,
-0.010961879976093769,
0.010414671152830124,
-0.0014242051402106881,
-0.03266346454620361,
0.0037525170482695103,
-0.01935921050608158,
-0.018772445619106293,
0.06371692568063736,
0.014456558041274548,
0.0001488964626332745,
-0.01505990419536829,
0.030692031607031822,
-0.0184385497123003,
-0.05248495563864708,
-0.02936897985637188,
0.01931525580585003,
-0.043339673429727554,
-0.0037585687823593616,
-0.007421547546982765,
-0.023565737530589104,
-0.02127727121114731,
-0.00977211631834507,
0.04823508858680725,
0.10411674529314041,
0.017793506383895874,
-0.01985405944287777,
0.004766239318996668,
-0.01596318744122982,
-0.0774741992354393,
0.01882605254650116,
0.02907361462712288,
-0.011484132148325443,
-0.036861103028059006,
0.0174560584127903,
0.03131401538848877,
-0.003204386681318283,
0.009299005381762981,
0.0245213620364666,
0.0082962391898036,
0.0010455772280693054,
-0.10835324227809906,
-0.047121088951826096,
-0.005919777788221836,
-0.037646155804395676,
-0.0118700060993433,
-0.08479968458414078,
0.013292999938130379,
0.010543422773480415,
0.11501843482255936,
-0.007989531382918358,
0.059107545763254166,
-0.02066587656736374,
0.010011720471084118,
0.02538806013762951,
-0.026425417512655258,
-0.0116682518273592,
-0.021970978006720543,
-0.04148034006357193,
-0.03870607912540436,
-0.04643590375781059,
0.00013825033965986222,
0.006569914519786835,
-0.017154423519968987,
-0.0031826430931687355,
0.06794765591621399,
-0.02309897541999817,
-0.010814188048243523,
0.04365942254662514,
0.00020445210975594819,
-0.023217132315039635,
0.04893928021192551,
0.008515853434801102,
-0.02207423932850361,
0.06326892226934433,
-0.03479672595858574,
0.02526548132300377,
-0.010477658361196518,
0.05815515294671059,
0.010321027599275112,
-0.04989882558584213,
-0.05150362476706505,
-0.0014011369785293937,
0.02507685497403145,
-0.04322073608636856,
-0.0685112401843071,
-0.04166559502482414,
-0.011466744355857372,
0.013942361809313297,
-0.005180837120860815,
0.046243857592344284,
0.018703322857618332,
-0.06516236811876297,
0.008936881087720394,
-0.0769878476858139,
-0.004060355480760336,
-0.060341931879520416,
0.0060211289674043655,
0.007282836362719536,
-0.048769183456897736,
0.03904799744486809,
0.018409088253974915,
0.020730065181851387,
-0.012339167296886444,
-0.008055595681071281,
-0.012284640222787857,
0.03359338641166687,
-0.001989568816497922,
0.007391372695565224,
0.0035644241143018007,
0.008777093142271042,
0.0574243888258934,
0.005808645859360695,
0.03507282957434654,
0.016290580853819847,
-0.02207651361823082,
0.052173107862472534,
0.008190963417291641,
-0.02064647153019905,
0.0316336564719677,
-0.00006285244307946414,
0.012986012734472752,
0.009973356500267982,
-0.006516647525131702,
0.04609687253832817,
-0.016401320695877075,
0.030581308528780937,
0.0385228656232357,
-0.001475995173677802,
-0.00488085625693202,
0.025816677138209343,
0.023603899404406548,
0.010020878165960312,
-0.034602947533130646,
-0.008601601235568523,
-0.026155730709433556,
0.03893004357814789,
0.024440454319119453,
0.005452680867165327,
-0.08279267698526382,
0.03563140705227852,
0.0037757502868771553,
0.019581714645028114,
0.026033803820610046,
0.030540646985173225,
-0.008073394186794758,
-0.021282998844981194,
0.02613999880850315,
-0.01814490184187889,
-0.00872544851154089,
0.015517081134021282,
0.0012575574219226837,
0.0114364018663764,
0.007379487622529268,
0.017037352547049522,
-0.05557652935385704,
0.034407902508974075,
-0.04925617575645447,
-0.01773708127439022,
0.010449298657476902,
-0.02687506005167961,
0.040706515312194824,
-0.013834027573466301,
0.0402882844209671,
0.016261456534266472,
-0.01386506762355566,
-0.02905074693262577,
-0.023731712251901627,
0.007324772886931896,
0.007155482191592455,
-0.011312308721244335,
-0.0439508818089962,
-0.008238330483436584,
0.01369642373174429,
-0.02704015001654625,
0.013813558965921402,
-0.028554927557706833,
-0.020964166149497032,
-0.01053379476070404,
-0.013790898956358433,
0.040686510503292084,
-0.000060594396927626804,
0.02083003893494606,
-0.004216668661683798,
-0.014085855334997177,
0.018498266115784645,
0.020485863089561462,
-0.0001045324606820941,
0.06173024699091911,
-0.04782576858997345,
0.015534487552940845,
-0.0614924393594265,
-0.046593740582466125,
0.048246342688798904,
0.010746986605226994,
0.012217632494866848,
-0.002324284752830863,
-0.010769500397145748,
-0.06490036845207214,
-0.010704456828534603,
-0.020372649654746056,
0.03762989863753319,
-0.01673193648457527,
0.010738073848187923,
0.044088106602430344,
-0.02232293225824833,
-0.0006327368319034576,
0.0004800462629646063,
0.012117123231291771,
-0.03113759309053421,
0.014823580160737038,
-0.04709459841251373,
0.009785274975001812,
-0.021549511700868607,
0.019989192485809326,
-0.0034202621318399906,
-0.04253094270825386,
0.0156100420281291,
-0.057143356651067734,
0.011580223217606544,
0.012661940418183804,
-0.002338200341910124,
0.00807155855000019,
0.025869959965348244,
-0.02791486494243145,
0.06906221807003021,
0.019724590703845024,
-0.04500321298837662,
-0.019593574106693268,
0.032460615038871765,
-0.024874985218048096,
-0.0520683154463768,
-0.007246491499245167,
0.03595668077468872,
0.050285015255212784,
0.06663736701011658,
0.02481100894510746,
-0.0013486651005223393,
0.03002062439918518,
0.007252740673720837,
-0.0351238027215004,
0.008758680894970894,
-0.021129712462425232,
-0.0011895123170688748,
0.03275331109762192,
-0.021402273327112198,
-0.019216636195778847,
0.0025932001881301403,
0.05529901757836342,
0.044069234281778336,
0.0137944919988513,
-0.035960257053375244,
0.0054532974027097225,
0.02255876548588276,
0.030912334099411964,
-0.029650036245584488,
0.07113946974277496,
0.005154914688318968,
-0.028896309435367584,
0.006881112232804298,
0.012229452840983868,
0.017857816070318222,
-0.03508298099040985,
0.02077161893248558,
0.048266682773828506,
0.015285925939679146,
-0.04884195700287819,
-0.02222825400531292,
-0.008343338966369629,
-0.015701361000537872,
0.03160066902637482,
-0.013112244196236134,
0.0030365230049937963,
0.039953239262104034,
0.0517309233546257,
0.007874127477407455,
-0.009735355153679848,
-0.01618071272969246,
0.02914348989725113,
-0.04782853275537491,
0.021261602640151978,
0.0228397399187088,
0.06254515796899796,
0.000696135510224849,
0.013404452241957188,
0.0541214719414711,
-0.003035781905055046,
-0.01944965124130249,
-0.012315013445913792,
-0.044473547488451004,
-0.01999475620687008,
-0.01183080580085516,
-0.007345195859670639,
0.0005475571379065514,
-0.02032303251326084,
0.004181521944701672,
-0.055655159056186676,
-0.027141153812408447,
-0.028913412243127823,
-0.045180827379226685,
-0.03139326721429825,
0.05832582339644432,
-0.013554240576922894,
-0.012363843619823456,
-0.0274807121604681,
0.06234630197286606,
0.08194281160831451,
-0.0013206112198531628,
0.004517119377851486,
0.06564681231975555,
-0.03330236300826073,
0.03549516573548317,
-0.01590409129858017,
0.029832294210791588,
0.01122305542230606,
0.012722578831017017,
0.0701461136341095,
0.033689748495817184,
-0.001056406181305647,
-0.030014794319868088,
-0.016111165285110474,
0.05117073282599449,
-0.006012784782797098,
-0.020334746688604355,
-0.014018918387591839,
-0.047791823744773865,
-0.009342086501419544,
-0.012545813806355,
0.07339859008789062,
0.025683535262942314,
0.022094201296567917,
0.03749077022075653,
0.017237605527043343,
-0.02528604492545128,
0.04199456423521042,
0.04853411391377449,
-0.01949460059404373,
-0.01897941343486309,
-0.028798680752515793,
-0.01976429484784603,
-0.032575804740190506,
-0.030314218252897263,
0.053761076182127,
-0.018008951097726822,
-0.005237247329205275,
-0.019701650366187096,
0.04106878116726875,
-0.00330591038800776,
-0.030879873782396317,
0.04112454503774643,
-0.02733498066663742,
0.029472388327121735,
0.028627630323171616,
-0.008187073282897472,
-0.01795525662600994,
0.04735756292939186,
0.0312496367841959,
-0.030799807980656624,
-0.03130572289228439,
-0.008961962535977364,
-0.005928876344114542,
0.035807039588689804,
0.01502872072160244,
-0.01729648932814598,
0.021388428285717964,
-0.042623136192560196,
-0.008068392053246498,
0.022315748035907745,
-0.04372242093086243,
0.05636370927095413,
-0.012174375355243683,
-0.04763772338628769,
-0.02575669251382351,
-0.03287430852651596,
-0.01642519235610962,
0.024744411930441856,
-0.015095026232302189,
0.011149432510137558,
-0.02443762496113777,
-0.006146394181996584,
-0.029134241864085197,
-0.009371128864586353,
0.029837602749466896,
0.020830975845456123,
0.014135071076452732,
0.03071248158812523,
-0.023424353450536728,
0.05501137301325798,
-0.03968825563788414,
-0.10114780068397522,
0.01915479078888893,
0.0023483477998524904,
-0.006434406619518995,
0.05281906574964523,
-0.050645262002944946,
-0.04070184379816055,
0.010989485308527946,
0.030722351744771004,
-0.01587609387934208,
0.03058263286948204,
-0.06853155791759491,
0.014651671051979065,
0.02052656188607216,
-0.010924864560365677,
0.0382189117372036,
-0.0066284118220210075,
-0.03305022791028023,
-0.0017620660364627838,
-0.027120810002088547,
-0.023030299693346024,
-0.040832389146089554,
0.0009441247093491256,
-0.023865362629294395,
0.004330046940594912,
-0.00009724557457957417,
0.06116073578596115,
-0.019368376582860947,
0.01591835543513298,
0.024935202673077583,
-0.013608153909444809,
-0.024614691734313965,
0.0035280936863273382,
0.00023928067821543664,
0.024413133040070534,
-0.010626380331814289,
0.03313832730054855,
0.0036323994863778353,
-0.03877224400639534,
0.030898598954081535,
-0.021033875644207,
-0.013077959418296814,
0.03126491978764534,
-0.009522546082735062,
0.06048868969082832,
-0.03161961957812309,
-0.00010671116615412757,
-0.00937240943312645,
-0.03826218843460083,
0.01702296733856201,
-0.02661646157503128,
0.003567649284377694,
-0.0018490739166736603,
-0.03225335106253624,
-0.05380186438560486,
-0.002989943604916334,
-0.024869810789823532,
-0.04471548646688461,
-0.05099843814969063,
-0.003626475343480706,
0.05661551654338837,
-0.014830172061920166,
-0.09678535908460617,
-0.049015045166015625,
0.012682058848440647,
-0.007883877493441105,
-0.01347334124147892,
-0.012985844165086746,
-0.002667835680767894,
-0.02785586193203926,
-0.03304629772901535,
-0.027019334957003593,
0.03480638191103935,
0.003427657298743725,
-0.021971004083752632,
0.009627729654312134,
0.03482936695218086,
0.03734816238284111,
-0.04042086377739906,
-0.00735167833045125,
0.009737805463373661,
-0.03740832209587097,
0.014169341884553432,
0.023751528933644295,
0.018964039161801338,
0.0010518437484279275,
-0.04208521917462349,
-0.02066562883555889,
-0.019271502271294594,
0.030080271884799004,
-0.02650250867009163,
0.005126500502228737,
0.0018431392963975668,
0.013849819079041481,
-0.013980861753225327,
-0.06614038348197937,
-0.015424147248268127,
0.006801501847803593,
0.04455010965466499,
0.009487856179475784,
-0.0005947671015746891,
-0.04082343354821205,
-0.045804712921381,
0.005160619970411062,
-0.03270001336932182,
0.007977848872542381,
-0.022500479593873024,
0.05650708079338074,
-0.01251834537833929,
0.02240658365190029,
0.015856819227337837,
-0.02185116894543171,
-0.004920394625514746,
0.010487685911357403,
0.052493903785943985,
0.037982236593961716,
0.014034667052328587,
-0.018660901114344597,
-0.027893735095858574,
-0.020997820422053337,
0.05869631469249725,
0.03448905423283577,
0.002271452685818076,
0.00903770886361599,
0.0380362831056118,
0.0023462821263819933,
-0.040279123932123184,
0.012592105194926262,
-0.00934674870222807,
0.0099906325340271,
0.009211736731231213,
0.04700398072600365,
-0.021633455529808998,
0.003303949721157551,
0.027600321918725967,
0.05362197756767273,
-0.026586828753352165,
-0.012233393266797066,
0.0734507143497467,
-0.011145318858325481,
-0.023270992562174797,
0.02096528187394142,
-0.010582557879388332,
0.02740521915256977,
-0.011622054502367973,
0.008506989106535912,
0.033727601170539856,
0.0024692583829164505,
0.003014066256582737,
0.019783833995461464,
0.01629340834915638,
-0.037955500185489655,
-0.03330808877944946,
-0.051851123571395874,
-0.014601485803723335,
0.036462098360061646,
0.03863295912742615,
0.0033853596542030573,
0.016194496303796768,
0.04702506586909294,
0.013893461786210537,
0.026035530492663383,
0.0046940697357058525,
-0.014907429926097393,
0.008438787423074245,
-0.02372547797858715,
-0.011311986483633518,
0.05591550096869469,
-0.019783977419137955,
0.015734253451228142,
-0.004852338694036007,
-0.031014999374747276,
-0.007089161779731512,
0.03901218622922897,
0.05529039725661278,
-0.02024100162088871,
0.05301922932267189,
-0.0010606985306367278,
0.0380975641310215,
0.0018595540896058083,
-0.02285558357834816,
0.1149507462978363,
0.02843336947262287,
0.01895308494567871,
-0.08025441318750381,
0.036396633833646774,
0.013256974518299103,
0.025778790935873985,
-0.03704184666275978,
0.045270904898643494,
-0.015813684090971947,
0.026818467304110527,
-0.026919888332486153,
0.04621708020567894,
-0.024124525487422943,
-0.00012530959793366492,
0.03180108591914177,
-0.058125872164964676,
-0.03973810374736786,
0.02790500596165657,
0.028533106669783592,
0.00477621890604496,
-0.008123748935759068,
-0.05902250483632088,
0.005056646186858416,
-0.004904158879071474,
0.008302819915115833,
-0.013059310615062714,
-0.02976636402308941,
0.028434621170163155,
-0.010276075452566147,
-0.05506933480501175,
0.01189750898629427,
0.02044709213078022,
-0.011985279619693756,
-0.03284589201211929,
-0.004518019035458565,
0.026223430410027504,
0.0043607368133962154,
0.04202819988131523,
0.030543755739927292,
0.0028093496803194284,
0.01699761301279068,
0.059265535324811935,
0.04532575234770775,
-0.025987189263105392,
0.007250736001878977,
-0.03885306790471077,
0.030283179134130478,
-0.03820425271987915,
-0.020435160025954247,
0.03477700799703598,
-0.0003420798748265952,
-0.01628056727349758,
-0.07636551558971405,
-0.008244222961366177,
-0.004605983849614859,
0.03501167148351669,
-0.0051362598314881325,
0.002168305916711688,
0.0020458954386413097,
0.05259164795279503,
-0.011122368276119232,
-0.005783035885542631,
-0.048954617232084274,
-0.02857697568833828,
0.004256846383213997,
-0.0004150807799305767,
0.03694373741745949,
0.026492493227124214,
-0.014742327854037285,
-0.04065055400133133,
-0.026563351973891258,
-0.009534567594528198,
-0.009106321260333061,
0.019286250695586205,
0.019981203600764275,
0.027199136093258858,
-0.02865724451839924,
0.0020351880230009556,
-0.018075911328196526,
-0.1074426993727684,
-0.004665957763791084,
-0.016632040962576866,
-0.0398452952504158,
0.02329523116350174,
-0.009289808571338654,
0.017605874687433243,
0.07120474427938461,
-0.04260741546750069,
-0.0031260608229786158,
-0.015560520812869072,
0.030868997797369957,
0.012577097862958908,
-0.061650846153497696,
-0.032545607537031174,
-0.010259823873639107,
-0.02327786386013031,
0.00045768494601361454,
-0.03175260126590729,
-0.0034087838139384985,
0.04910772666335106,
0.007949365302920341,
-0.032307807356119156,
0.0331275649368763,
-0.00748015521094203,
-0.021206071600317955,
0.024143530055880547,
-0.014071530662477016,
0.016896530985832214,
0.02519000507891178,
0.008173157460987568,
-0.026893652975559235,
-0.011464578099548817,
-0.01993006281554699,
-0.05023481696844101,
0.03523100167512894,
-0.0061294944025576115,
-0.04599349945783615,
0.010376747697591782,
-0.018023235723376274,
-0.015403681434690952,
-0.02597162500023842,
-0.02240617945790291,
-0.05116227641701698,
0.009986883960664272,
-0.0019135689362883568,
-0.04457300901412964,
-0.020554009824991226,
0.02508622407913208,
0.01394837535917759,
-0.045055076479911804,
0.05634629726409912,
0.057344354689121246,
-0.04315789043903351,
-0.017544886097311974,
0.013696527108550072,
0.02178424783051014,
0.029137834906578064,
0.019980356097221375,
-0.04206470772624016,
0.024647243320941925,
-0.03557618707418442,
-0.015218283049762249,
0.04036485031247139,
0.005791644565761089,
-0.004216501023620367,
0.015631595626473427,
-0.020901823416352272,
-0.004145788960158825,
0.04870332404971123,
-0.04597222059965134,
-0.02018139697611332,
0.02465832233428955,
-0.009843217208981514,
0.011990462429821491,
-0.008600927889347076,
0.023381708189845085,
-0.0006285425624810159,
-0.013741189613938332,
0.023625951260328293,
0.04256017878651619,
0.004326366353780031,
0.016852688044309616,
0.02094685472548008,
0.04015693813562393,
0.05490845441818237,
0.048400573432445526,
-0.02136896550655365,
0.0028701757546514273,
0.04865606129169464,
-0.036280784755945206,
0.011899726465344429,
0.00017303590720985085,
0.001953302649781108,
-0.09398563206195831,
-0.000551672070287168,
0.016450250521302223,
-0.011293377727270126,
0.04396869242191315,
-0.04967525973916054,
0.034243784844875336,
0.031590335071086884,
-0.04642584174871445,
-0.003738771891221404,
-0.047945693135261536,
-0.008881383575499058,
-0.019191959872841835,
-0.021830188110470772,
-0.03200957551598549,
0.08351416140794754,
0.025918807834386826,
0.056916091591119766,
0.0007768081850372255,
0.008928747847676277,
0.010997319594025612,
-0.04644457995891571,
-0.019298480823636055,
0.0323009118437767,
-0.005923130549490452,
-0.04919249191880226,
0.08718469738960266,
0.002443196950480342,
-0.04619881510734558,
0.022924302145838737,
0.01863209903240204,
0.004535440355539322,
-0.004236054141074419,
0.021513869985938072,
-0.0011365952668711543,
0.035493336617946625,
-0.008897349238395691,
-0.021543020382523537,
-0.006051178090274334,
0.030722813680768013,
0.019918864592909813,
0.006100477650761604,
-0.009641177952289581,
-0.013199036940932274,
-0.012034997344017029,
-0.05991508811712265,
0.02006331831216812,
0.049354437738657,
-0.04723925143480301,
-0.006543625146150589,
-0.045187272131443024,
0.006191207095980644,
0.04131270945072174,
-0.037350285798311234,
0.019211068749427795,
-0.017481518909335136,
-0.010862953029572964,
0.0424506850540638,
0.039666369557380676,
-0.00042372860480099916,
0.02471209317445755,
-0.010019686073064804,
-0.054503124207258224,
0.031101534143090248,
0.007395219057798386,
0.028257302939891815,
-0.021126100793480873,
-0.003856749041005969,
0.014706485904753208,
-0.01930590346455574,
0.0076303184032440186,
-0.027326464653015137,
-0.04410633444786072,
0.006603674963116646,
-0.015624777413904667,
0.025088878348469734,
-0.03267781063914299,
-0.019140632823109627,
0.021231964230537415,
-0.03269428014755249,
0.030367441475391388,
0.030877193436026573,
-0.015055819414556026,
0.006882586982101202,
0.013373365625739098,
-0.007142163813114166,
0.016426682472229004,
0.08253393322229385,
-0.007247958332300186,
-0.03778073564171791,
0.0332549586892128,
0.010224295780062675,
0.006329434458166361,
-0.014028327539563179,
-0.016251716762781143,
-0.02073129266500473,
-0.010990176349878311,
0.012537064962089062,
-0.021036481484770775,
0.007632981054484844,
0.03479279950261116,
-0.008048862218856812,
0.0165266003459692,
0.00035251033841632307,
0.016158197075128555,
-0.07150442898273468,
0.025111770257353783,
-0.005817077122628689,
-0.022339582443237305,
0.07094031572341919,
0.015131346881389618,
0.012663932517170906,
0.01669965870678425,
-0.024892698973417282,
-0.0031257173977792263,
0.032818086445331573,
-0.03329547122120857,
-0.0007928736740723252,
-0.005020900163799524,
-0.003529384033754468,
0.03853505104780197,
-0.04565070942044258,
-0.0018217647448182106,
0.056947946548461914,
-0.004273333121091127,
-0.021568411961197853,
0.04878075420856476,
-0.01874658092856407,
0.010454045608639717,
0.02941427193582058,
0.001242592465132475,
0.009998911991715431,
-0.002897531958296895,
0.028711840510368347,
0.03929371386766434,
0.006158194504678249,
0.04540461301803589,
-0.02310018800199032,
0.05572019889950752,
-0.009732536040246487,
0.01376290898770094,
-0.0009367036400362849,
0.040140800178050995,
-0.027101140469312668,
0.005782265681773424,
0.01289423555135727,
-0.035630542784929276,
0.015163231641054153,
0.0036815942730754614,
-0.0121698547154665,
0.07666841894388199,
-0.012619192712008953,
0.01033735927194357,
-0.03597334772348404,
0.009950393810868263,
-0.025947989895939827,
0.003546017687767744,
0.009963121265172958,
0.04462391138076782,
-0.00003556243609637022,
-0.03604871779680252,
-0.05804000422358513,
-0.017688829451799393,
0.008144358173012733,
-0.05251197889447212,
-0.010042021982371807,
0.011837824247777462,
-0.03209918737411499,
-0.027461253106594086,
0.004364887252449989,
-0.002306876704096794,
-0.009932576678693295,
0.04061358794569969,
0.031550999730825424,
0.015897545963525772,
-0.024028204381465912,
-0.034382324665784836,
-0.02013871818780899,
0.04656749591231346,
-0.03626415506005287,
-0.04623252525925636,
-0.008913807570934296,
0.010355274192988873,
-0.0009257704950869083,
0.004761312156915665
] |
<p>For two particles, $\langle {\mathcal T} a(t_1) a^\dagger (t_2) \rangle = \langle
a(t_1) a^\dagger (t_2)\rangle \theta (t_1-t_2) + \xi \langle a^\dagger (t_2)a(t_1) \rangle \theta (t_2-t_1)$ with $\xi$ is a plus sign for bosons and a minus sign for fermions.</p>
<p>How would I write, for example, $\langle {\mathcal T} a(t_1) a^\dagger (t_2) a(t_3) a^\dagger (t_4) \rangle$ ?</p> | 2,838 | [
0.02214387059211731,
-0.01568392477929592,
-0.007614853326231241,
0.011238189414143562,
0.02147630788385868,
0.04972115904092789,
-0.009478393942117691,
0.003252552356570959,
0.0185192059725523,
0.004089698661118746,
0.05737847089767456,
0.018166834488511086,
0.04151766747236252,
-0.004143786616623402,
0.018845897167921066,
0.033149395138025284,
-0.006238612812012434,
-0.03792387247085571,
-0.03271188214421272,
-0.029940148815512657,
0.034997906535863876,
0.015120337717235088,
-0.015960844233632088,
0.02147393859922886,
0.01560281403362751,
0.050320181995630264,
0.026060428470373154,
-0.014402135275304317,
0.013618729077279568,
0.057001546025276184,
-0.023613426834344864,
-0.02929963544011116,
0.06271924823522568,
0.005107079166918993,
0.012733989395201206,
-0.022043582051992416,
-0.024660281836986542,
-0.037533342838287354,
0.009792167693376541,
0.005135644692927599,
-0.048616427928209305,
-0.006300941109657288,
-0.029065784066915512,
0.03652528300881386,
-0.010152757167816162,
-0.039692338556051254,
-0.022148258984088898,
-0.005945165175944567,
0.03229605033993721,
-0.06123910844326019,
0.056439921259880066,
0.00169071601703763,
0.05602787435054779,
0.01852693036198616,
-0.02944188378751278,
-0.022823598235845566,
0.042986348271369934,
0.05391606688499451,
0.03538086637854576,
-0.06386132538318634,
-0.02602451853454113,
-0.011908624321222305,
0.0160721056163311,
-0.020829632878303528,
-0.004440660122781992,
-0.0014827363193035126,
-0.0031643433030694723,
-0.030080704018473625,
0.014383486472070217,
-0.03554319217801094,
0.03448844701051712,
-0.03295945003628731,
0.06257841736078262,
-0.041450802236795425,
-0.011825576424598694,
-0.02675442025065422,
0.011602047830820084,
0.029557839035987854,
0.03669246658682823,
0.038972824811935425,
0.011153611354529858,
0.05730399116873741,
0.03257494047284126,
0.014137138612568378,
-0.01990041695535183,
-0.014072434045374393,
0.038003455847501755,
-0.011304156854748726,
-0.0255727618932724,
0.0504402332007885,
0.008209850639104843,
0.019926145672798157,
0.05202142521739006,
-0.020140642300248146,
-0.012166010215878487,
0.008992637507617474,
0.007517928723245859,
0.021101243793964386,
0.020421339198946953,
0.0017969184555113316,
-0.04852515459060669,
-0.01292066927999258,
0.006736903451383114,
0.07005217671394348,
-0.01859557442367077,
0.025137225165963173,
-0.03468179330229759,
0.0058461748994886875,
-0.04069090634584427,
-0.009997458197176456,
-0.039553478360176086,
0.0027501429431140423,
-0.026123732328414917,
0.037979837507009506,
-0.007051962893456221,
-0.04078188166022301,
0.01082780584692955,
0.006296881940215826,
0.023242447525262833,
0.058815039694309235,
0.013492682948708534,
-0.04255663603544235,
0.023871691897511482,
-0.017762545496225357,
-0.0658363327383995,
0.023121250793337822,
0.06419140845537186,
-0.004067291505634785,
-0.05648782476782799,
0.015734413638710976,
0.034441761672496796,
0.016596002504229546,
0.006960263475775719,
-0.016659047454595566,
0.0027186672668904066,
-0.011025502346456051,
-0.10961008071899414,
-0.08341720700263977,
0.01909666508436203,
-0.021467510610818863,
-0.034945935010910034,
-0.05297091230750084,
0.021551527082920074,
0.07444237917661667,
0.10290780663490295,
0.009226194582879543,
0.010470990091562271,
0.0375424288213253,
-0.005208184011280537,
0.02355596050620079,
0.015145214274525642,
0.004627391695976257,
-0.003359165508300066,
-0.02852330170571804,
-0.02403244376182556,
-0.04417905956506729,
0.025459663942456245,
0.023235440254211426,
-0.030292334035038948,
0.020389067009091377,
0.10118760168552399,
-0.03861540928483009,
0.03113149292767048,
0.02059226483106613,
-0.01921440102159977,
-0.03526925668120384,
0.06989766657352448,
0.021198246628046036,
-0.019901802763342857,
0.03164055570960045,
-0.014346868731081486,
0.009748667478561401,
-0.03492439538240433,
0.0414009764790535,
0.05382859334349632,
-0.015790564939379692,
-0.021026242524385452,
-0.03923166170716286,
-0.008631045930087566,
-0.01759890839457512,
-0.01711909845471382,
-0.06190438196063042,
-0.054228395223617554,
0.009947150014340878,
0.009969073347747326,
0.0009760530083440244,
0.0152919702231884,
0.002007762435823679,
0.019309457391500473,
-0.0515889935195446,
-0.03902267664670944,
-0.0557151660323143,
0.010237972252070904,
0.015637535601854324,
-0.03467090055346489,
0.07570240646600723,
0.027144597843289375,
-0.017424238845705986,
-0.002653366420418024,
-0.05422899127006531,
-0.010426967404782772,
0.024589890614151955,
-0.0012357912492007017,
-0.009456547908484936,
0.02551019936800003,
0.04513150826096535,
0.07436110824346542,
0.0014990131603553891,
0.06067908927798271,
-0.010810647159814835,
0.0026545540895313025,
-0.0028723340947180986,
0.009007293730974197,
0.02126888744533062,
0.048538561910390854,
0.008615415543317795,
-0.01953950896859169,
-0.0023168132174760103,
-0.0688186064362526,
0.04058496654033661,
-0.03691741079092026,
0.06522084772586823,
0.04198017343878746,
-0.006390433758497238,
0.01490105502307415,
0.05696418508887291,
0.009824033826589584,
0.044440895318984985,
-0.0021298578940331936,
-0.0009301460231654346,
-0.027118461206555367,
-0.01618381217122078,
0.02277107909321785,
0.029148520901799202,
-0.041362661868333817,
0.029750900343060493,
0.014362422749400139,
0.013085420243442059,
0.015674617141485214,
0.0449250154197216,
-0.01741197519004345,
-0.03244664892554283,
0.01357273943722248,
0.003983335569500923,
-0.01239848230034113,
0.016466915607452393,
0.03752148896455765,
-0.03461325913667679,
0.0007863304344937205,
0.004357583820819855,
-0.04388245940208435,
0.0017789466073736548,
-0.019639234989881516,
0.024992428719997406,
0.006261209491640329,
-0.048617471009492874,
0.0540628619492054,
-0.014715266413986683,
0.05896890163421631,
0.001670917379669845,
-0.006966360844671726,
-0.014976791106164455,
0.006047623232007027,
-0.038326334208250046,
-0.0052030691877007484,
0.002744747092947364,
-0.005750423762947321,
0.006114687770605087,
0.02383069507777691,
-0.05224379152059555,
0.03001580201089382,
-0.022467443719506264,
-0.024641631171107292,
-0.01946888118982315,
-0.03146599978208542,
0.023499399423599243,
0.010143110528588295,
0.037143051624298096,
0.012000148184597492,
-0.026460761204361916,
0.05341330170631409,
0.011035400442779064,
0.038176555186510086,
0.021739112213253975,
-0.049676671624183655,
0.02703508548438549,
-0.04741885885596275,
-0.04702874645590782,
0.043510984629392624,
-0.0003252255264669657,
-0.01310882531106472,
-0.01133675780147314,
-0.020984729751944542,
-0.04004174843430519,
-0.03353910148143768,
-0.00671320129185915,
-0.0028909300453960896,
-0.06712274998426437,
-0.013712740503251553,
0.03069811873137951,
0.012783573009073734,
-0.029278919100761414,
-0.06275863200426102,
-0.026191813871264458,
-0.048340339213609695,
-0.020009515807032585,
-0.03195156902074814,
0.018956296145915985,
-0.01174392644315958,
0.042754415422677994,
0.019269654527306557,
-0.02650199458003044,
0.006745424121618271,
-0.07747020572423935,
-0.03000614605844021,
0.020150717347860336,
-0.008060775697231293,
0.010947545059025288,
-0.015865381807088852,
-0.036908894777297974,
0.09932498633861542,
0.02199460379779339,
0.00791259203106165,
0.001357148285023868,
0.01698211207985878,
-0.01895125024020672,
-0.024633022025227547,
0.010409168899059296,
0.022864913567900658,
-0.006390059366822243,
0.044395409524440765,
0.02078651450574398,
0.010692499577999115,
0.036008067429065704,
0.039333682507276535,
-0.013369258493185043,
0.01637851819396019,
-0.019423287361860275,
-0.01608479954302311,
0.0527677945792675,
-0.013222594745457172,
-0.01877356693148613,
0.01728939078748226,
0.012144281528890133,
-0.01462637446820736,
-0.016592973843216896,
-0.026131413877010345,
0.032199591398239136,
0.0036268022377043962,
0.012233204208314419,
0.0029516660142689943,
0.03721412643790245,
0.005602489225566387,
-0.03029397688806057,
-0.015670204535126686,
0.05883164331316948,
0.036542776972055435,
-0.031900495290756226,
0.004442806355655193,
0.03750456124544144,
0.045927196741104126,
-0.03218472748994827,
-0.025391513481736183,
0.006523912772536278,
-0.017980970442295074,
0.02392980083823204,
-0.05301029235124588,
-0.025295527651906013,
0.009969109669327736,
0.022289173677563667,
-0.0036466082092374563,
0.004838741850107908,
-0.0394589938223362,
-0.019456837326288223,
-0.06526172161102295,
-0.007626578211784363,
-0.024368885904550552,
0.057203538715839386,
0.010880629532039165,
0.03403882309794426,
0.01357077807188034,
0.012423965148627758,
0.0374460369348526,
-0.015439579263329506,
-0.07625483721494675,
0.021422691643238068,
-0.018804311752319336,
-0.024486280977725983,
0.007625522091984749,
-0.019332973286509514,
0.017586149275302887,
-0.04560818150639534,
-0.02426004409790039,
-0.008411123417317867,
-0.01884082704782486,
-0.0091685950756073,
0.028149424120783806,
-0.03248634189367294,
-0.06621794402599335,
0.011353585869073868,
0.02336735464632511,
0.04975385218858719,
-0.0048698922619223595,
0.05084774270653725,
0.049248211085796356,
-0.00795171782374382,
-0.004621381871402264,
-0.049265965819358826,
-0.0026134373620152473,
0.042377687990665436,
0.007636156864464283,
0.0718667209148407,
0.05552225187420845,
-0.035540319979190826,
-0.015825143083930016,
0.006372513715177774,
0.05020636320114136,
-0.0024046790786087513,
-0.008543171919882298,
0.01601148396730423,
-0.05114198476076126,
-0.029846740886569023,
0.0016794672701507807,
0.07375985383987427,
0.007793482393026352,
0.007215400692075491,
0.019397566094994545,
0.03868058696389198,
-0.0035547816660255194,
0.04167542606592178,
0.06076681241393089,
0.0014232725370675325,
-0.0016712198266759515,
-0.0211359690874815,
0.0239165797829628,
0.023404035717248917,
-0.001272873836569488,
-0.012900838628411293,
0.005883414763957262,
-0.02315654046833515,
0.020147791132330894,
0.014401666820049286,
-0.0015113858971744776,
-0.022812295705080032,
0.030725780874490738,
-0.040907200425863266,
-0.027396025136113167,
0.030602147802710533,
-0.02411773055791855,
-0.005666999612003565,
0.03779338672757149,
-0.030967222526669502,
0.022111177444458008,
0.011783333495259285,
-0.08148809522390366,
-0.03054485283792019,
0.0453108586370945,
0.07288330793380737,
0.006638818886131048,
-0.02973431721329689,
-0.012161551043391228,
-0.04063987731933594,
0.03915837034583092,
-0.010270093567669392,
0.05523788556456566,
-0.01994073949754238,
-0.02645384520292282,
-0.00016687279276084155,
-0.029445061460137367,
-0.008893352933228016,
0.055719710886478424,
-0.011338012292981148,
0.010215542279183865,
-0.03457192704081535,
0.0034794120583683252,
-0.03220650181174278,
0.0046155196614563465,
-0.013714093714952469,
0.026381095871329308,
-0.015109785832464695,
-0.037150342017412186,
0.008726384490728378,
0.004091179464012384,
-0.004670313559472561,
-0.07027079164981842,
0.03253337740898132,
0.009840899147093296,
0.009557714685797691,
0.05674539878964424,
0.0030706659890711308,
-0.005971421487629414,
-0.0007880026823841035,
0.009154925122857094,
-0.009776265360414982,
0.00893833115696907,
-0.040719714015722275,
0.06107955053448677,
0.05095662549138069,
-0.015354578383266926,
0.0606105662882328,
0.030735697597265244,
-0.007691249251365662,
0.020853949710726738,
-0.0316513292491436,
0.020928561687469482,
-0.02152138017117977,
0.05446409061551094,
-0.025801170617341995,
0.01282788161188364,
-0.035972654819488525,
0.012799588963389397,
-0.053576353937387466,
0.033910587430000305,
-0.004049353301525116,
-0.0368351973593235,
-0.04637683928012848,
-0.007568416651338339,
0.005046507343649864,
-0.029816394671797752,
0.006895394064486027,
0.0028656290378421545,
0.017770610749721527,
-0.02367645688354969,
-0.0005840913509018719,
-0.031361330300569534,
-0.005331629421561956,
0.018394403159618378,
-0.00855193194001913,
0.02867005579173565,
-0.029340626671910286,
-0.051382940262556076,
0.004661259241402149,
-0.06598024070262909,
0.035665418952703476,
-0.01528451219201088,
0.004315464291721582,
-0.015437117777764797,
-0.04836387559771538,
-0.07498215138912201,
0.04702642932534218,
0.025383245199918747,
0.009461311623454094,
-0.07211070507764816,
0.04232014715671539,
0.010843420401215553,
-0.024325653910636902,
-0.052228961139917374,
-0.02890072949230671,
-0.01877736859023571,
-0.024947678670287132,
-0.013488306663930416,
-0.003525608452036977,
0.0025467730592936277,
-0.0194544717669487,
-0.03200685605406761,
-0.004948409274220467,
0.04945117607712746,
-0.047359317541122437,
-0.013010096736252308,
0.02298683673143387,
0.008777757175266743,
0.055879659950733185,
-0.010906582698225975,
-0.011307282373309135,
0.006684647407382727,
-0.0312977097928524,
0.029727358371019363,
0.03327437862753868,
0.019902080297470093,
-0.044250909239053726,
-0.03813064470887184,
0.011870275251567364,
0.02671104669570923,
0.011288406327366829,
-0.009948858991265297,
0.029269682243466377,
-0.004170037340372801,
0.016253594309091568,
0.014269971288740635,
-0.015914475545287132,
0.001088747987523675,
-0.008303284645080566,
0.014933248050510883,
0.002386509906500578,
-0.009485512040555477,
-0.005666840821504593,
-0.01798052340745926,
0.015909230336546898,
0.009350551292300224,
-0.02670031599700451,
-0.012867262586951256,
0.05086207389831543,
0.027956444770097733,
0.010299918241798878,
0.05246482044458389,
0.01970086060464382,
0.025535231456160545,
-0.024497047066688538,
0.03869183734059334,
0.013849921524524689,
-0.026399239897727966,
-0.010462600737810135,
-0.018860384821891785,
-0.009481384418904781,
-0.015002594329416752,
0.06604494899511337,
-0.007558825425803661,
0.053727444261312485,
0.029689598828554153,
-0.003727065632119775,
0.013571596704423428,
0.0089267548173666,
-0.01209841389209032,
0.021862337365746498,
0.001051959814503789,
0.03251703456044197,
-0.06974326819181442,
0.013972408138215542,
0.014134718105196953,
0.050420328974723816,
-0.044296909123659134,
-0.007273739669471979,
-0.018219556659460068,
-0.008996526710689068,
0.014896857552230358,
-0.01465188805013895,
-0.02265012264251709,
0.04750270023941994,
-0.02321542240679264,
0.025622792541980743,
-0.020071422681212425,
-0.04103174805641174,
0.026018274948000908,
0.022909797728061676,
0.014388874173164368,
-0.030314836651086807,
-0.015229913406074047,
-0.06755797564983368,
0.002557384083047509,
0.03229677304625511,
-0.01337479893118143,
0.019099846482276917,
0.015489298850297928,
0.07412612438201904,
-0.005754274781793356,
-0.0025354709941893816,
-0.03888794779777527,
-0.03812329098582268,
-0.02642870880663395,
-0.06428839266300201,
-0.04621226340532303,
0.02859170362353325,
-0.039313629269599915,
0.00039565417682752013,
0.0038051200099289417,
-0.024195171892642975,
-0.008041386492550373,
0.0217229425907135,
0.01612689532339573,
-0.04765486717224121,
0.05274506285786629,
-0.01529325544834137,
0.05701452121138573,
0.050415538251399994,
-0.0028576101176440716,
0.11093856394290924,
0.044289931654930115,
0.01383198145776987,
-0.07867330312728882,
0.024038003757596016,
0.011603464372456074,
0.015938065946102142,
-0.02395130880177021,
0.027434373274445534,
-0.011193209327757359,
0.018964778631925583,
-0.027517352253198624,
0.05181994289159775,
-0.01787150651216507,
-0.04563809186220169,
0.030757322907447815,
-0.026479478925466537,
-0.04807867482304573,
-0.005779105704277754,
0.03826887160539627,
0.00013175075582694262,
0.012873995117843151,
-0.06705813109874725,
0.018070224672555923,
-0.019395992159843445,
0.05432793125510216,
-0.01142002735286951,
-0.01337860245257616,
0.025857461616396904,
0.039684128016233444,
-0.014000902883708477,
-0.006364156492054462,
0.013251331634819508,
0.025751611217856407,
0.010582130402326584,
0.009353533387184143,
0.008421847596764565,
-0.040866121649742126,
0.04085796698927879,
0.06597305834293365,
0.0003486406058073044,
0.00974003691226244,
0.01210856530815363,
-0.024571934714913368,
-0.049829740077257156,
-0.018313413485884666,
-0.013201744295656681,
0.06620154529809952,
-0.00958450697362423,
0.00047634702059440315,
-0.021371133625507355,
-0.017544236034154892,
0.021934032440185547,
-0.024525867775082588,
-0.04454222694039345,
0.0017369933193549514,
0.029130734503269196,
-0.03305748477578163,
0.0332007072865963,
-0.005711269564926624,
0.042652685195207596,
0.027461938560009003,
0.01371314749121666,
-0.011561252176761627,
-0.004731402266770601,
0.02546616643667221,
-0.008528073318302631,
0.007712520658969879,
0.025943072512745857,
-0.033149927854537964,
-0.011138570494949818,
0.020005283877253532,
-0.05321035161614418,
0.005495737306773663,
0.022061852738261223,
0.03505198657512665,
0.029311539605259895,
0.04518765211105347,
-0.001708405208773911,
-0.00939319096505642,
-0.021336864680051804,
0.03600849583745003,
-0.04461754485964775,
-0.03515637665987015,
0.028830185532569885,
-0.02531534805893898,
0.015225502662360668,
0.028458651155233383,
-0.03997759893536568,
-0.013190190307796001,
0.04260234907269478,
0.05374816432595253,
0.07702866941690445,
-0.01306193694472313,
-0.02273743599653244,
-0.007025156635791063,
0.009405341930687428,
-0.01838099956512451,
-0.020339833572506905,
0.007736113388091326,
0.02656078338623047,
-0.011592959985136986,
-0.011015709489583969,
0.03023378551006317,
0.006442890036851168,
-0.03198063746094704,
0.030194519087672234,
-0.012369917705655098,
-0.04807530716061592,
0.029223361983895302,
-0.010009330697357655,
-0.03712555766105652,
0.003207492409273982,
-0.009157562628388405,
0.0010818454902619123,
0.038299310952425,
0.000107932100945618,
-0.020113909617066383,
-0.01242860872298479,
-0.01996980980038643,
0.01767912693321705,
-0.02153840661048889,
0.030572645366191864,
-0.06277906894683838,
-0.0019603909458965063,
-0.013594136573374271,
-0.010605662129819393,
-0.018790969625115395,
0.039228927344083786,
0.009217104874551296,
-0.0029766818042844534,
0.017792727798223495,
0.025995686650276184,
0.00003218166239093989,
0.007711976766586304,
-0.0121273472905159,
-0.022287385538220406,
0.004873926751315594,
0.015798702836036682,
-0.008175319992005825,
0.02981635555624962,
-0.001656155800446868,
0.028118491172790527,
0.03126871585845947,
0.0014049482997506857,
0.029408413916826248,
0.043130774050951004,
-0.02884818986058235,
-0.012315993197262287,
0.022205637767910957,
-0.05697118118405342,
-0.012420671992003918,
-0.01447706576436758,
-0.027238059788942337,
-0.025116106495261192,
-0.04430277273058891,
-0.013573037460446358,
0.021220019087195396,
-0.011266433633863926,
-0.022175464779138565,
0.030058521777391434,
-0.011989204213023186,
-0.004207425285130739,
-0.014719869010150433,
0.00016848692030180246,
0.07837056368589401,
0.004619874060153961,
-0.029674513265490532,
0.017440205439925194,
0.01971588097512722,
-0.02676660381257534,
0.02967522107064724,
0.04585808143019676,
0.03630370274186134,
-0.05911644175648689,
0.0004452095599845052,
0.02505522593855858,
0.003157082013785839,
0.03739013522863388,
-0.03492659702897072,
0.02070712111890316,
-0.004714634735137224,
-0.03129370138049126,
0.03860035166144371,
-0.024069728329777718,
-0.012921166606247425,
-0.011466290801763535,
-0.006852020975202322,
-0.017770446836948395,
0.08596211671829224,
-0.011193793267011642,
0.03611666336655617,
-0.02786492370069027,
-0.0041620852425694466,
-0.036593783646821976,
-0.04133691266179085,
-0.019084418192505836,
-0.011580768041312695,
0.000025905563234118745,
-0.04894593730568886,
0.04534059017896652,
-0.04353360831737518,
-0.03790505230426788,
0.016848528757691383,
0.01852741464972496,
-0.029193416237831116,
-0.01719297282397747,
0.006823542527854443,
0.014616966247558594,
0.029660766944289207,
-0.02358940802514553,
-0.030297348275780678,
-0.004953199997544289,
0.004559407010674477,
0.030090216547250748,
0.016765205189585686,
0.0036335373297333717,
-0.012210482731461525,
-0.007795680779963732,
-0.009472792036831379,
-0.03667319193482399,
0.0655713677406311,
-0.003848971100524068,
-0.03379709646105766,
-0.02873201295733452,
-0.010512467473745346,
0.029522588476538658,
-0.008862425573170185,
-0.019189350306987762,
-0.057693831622600555,
0.003179560648277402,
0.019107099622488022,
0.007056191563606262,
-0.0034415109548717737,
0.012928848154842854,
-0.025706930086016655,
-0.03952059522271156,
0.030052537098526955,
0.014399793930351734,
-0.03221139684319496,
-0.02588081732392311,
-0.036918580532073975,
0.0289729256182909,
0.04014858603477478,
-0.0088801309466362,
-0.020411713048815727,
-0.045718688517808914,
0.0005061463452875614,
-0.03222765773534775,
0.03825145959854126,
-0.03100643865764141,
-0.02945719286799431,
0.02098340541124344,
-0.03909005597233772,
0.012492644600570202,
0.0471416674554348,
0.018637115135788918,
-0.02074340544641018,
-0.040951941162347794,
-0.027493230998516083,
0.04099806025624275,
0.05711863562464714,
0.025743139907717705,
-0.04056011885404587,
-0.00830900389701128,
-0.000505419506225735,
0.0160308089107275,
-0.043013591319322586,
0.011719047091901302,
-0.0061438800767064095,
0.006805906537920237,
-0.010922745801508427,
0.011912955902516842,
-0.03008364513516426,
0.022212469950318336,
0.030949117615818977,
-0.01465530414134264,
-0.016582470387220383,
0.011885350570082664,
-0.047104790806770325,
0.04068172350525856,
-0.006795164663344622,
-0.016212286427617073,
0.07678001374006271,
0.025084447115659714,
0.03784539923071861,
0.01710185967385769,
-0.031041081994771957,
-0.018743349239230156,
-0.014813545159995556,
-0.05285274609923363,
0.012488587759435177,
0.0003211435105185956,
-0.016524577513337135,
-0.01014671940356493,
-0.03783313184976578,
0.004002392757683992,
0.025457385927438736,
0.00015358357632067055,
-0.019839074462652206,
0.03755927458405495,
0.05747969448566437,
0.04958757758140564,
-0.0013410679530352354,
0.0032913782633841038,
0.0262737013399601,
0.016167014837265015,
0.01652511954307556,
0.02289307489991188,
0.0020021076779812574,
0.039483968168497086,
0.00613390514627099,
-0.01277065183967352,
-0.0473114512860775,
0.020818447694182396,
-0.0076392702758312225,
0.007006010506302118,
-0.0043506198562681675,
0.01894574984908104,
0.004527456592768431,
-0.012979435734450817,
0.02637244015932083,
0.020033597946166992,
-0.04195522516965866,
0.08954776078462601,
-0.02602798491716385,
0.0005294777802191675,
-0.023891178891062737,
0.014622493647038937,
-0.004487669561058283,
-0.0045034983195364475,
0.02892715111374855,
0.04778846353292465,
-0.050948210060596466,
-0.028309442102909088,
-0.04170743376016617,
-0.023792367428541183,
-0.026486216112971306,
-0.07210090756416321,
-0.013805023394525051,
0.014198078773915768,
0.02096184529364109,
0.0006624427624046803,
-0.02380087971687317,
-0.03659144788980484,
-0.03721645474433899,
0.016016336157917976,
0.03842490538954735,
0.015995295718312263,
-0.005557377822697163,
-0.019371356815099716,
0.02675006352365017,
-0.008928528055548668,
-0.028714226558804512,
-0.03819906339049339,
-0.000577462138608098,
-0.00008380386861972511,
0.008496771566569805,
0.01167047768831253
] |
<p>Consider that we have two balls, one white and one black, and two distant observers A and B with closed eyes. We give the first ball to the observer A and the second ball to the observer B. The observers don't know the exact color (state) of their balls, they know only the probability of having one or another color, until they look at them (measure). If the observer A looks at his ball he will see its color, which is white, so he immediately knows the color of the second ball. Lets call this “classical entanglement”.</p>
<p>My question is: What is the difference between this “classical entanglement” and the quantum entanglement, for example, of two entangled electrons with opposite spins states? Can this analogy be used to explain the quantum entanglement?</p> | 2,839 | [
-0.02886955626308918,
-0.02573004737496376,
0.0003875427646562457,
-0.03934267535805702,
0.017595073208212852,
0.0034263881389051676,
0.012768060900270939,
0.0049252803437411785,
0.01450416725128889,
0.016158126294612885,
0.04116624966263771,
0.03941316157579422,
0.011096869595348835,
0.01074170134961605,
0.017386607825756073,
-0.001783047802746296,
-0.025716686621308327,
-0.017528412863612175,
-0.00791982002556324,
-0.0035616953391581774,
0.017751330509781837,
0.029923126101493835,
0.027140885591506958,
0.004519442096352577,
-0.008448616601526737,
0.026690851897001266,
0.013410438783466816,
-0.024776792153716087,
0.0439324826002121,
0.09015797823667526,
0.00449769152328372,
-0.015357466414570808,
0.005464903544634581,
0.021813808009028435,
-0.004227490164339542,
-0.03742464259266853,
-0.03503275662660599,
-0.03751248121261597,
-0.01080591231584549,
-0.007068131119012833,
-0.03124990314245224,
-0.05859808251261711,
-0.012961405329406261,
0.04674149677157402,
-0.025345977395772934,
-0.018573438748717308,
0.00966582354158163,
-0.06536401063203812,
0.04301545023918152,
-0.05446919426321983,
0.05955565720796585,
-0.0037132264114916325,
0.023870933800935745,
0.0011768520344048738,
0.0006612726137973368,
0.0172475203871727,
0.05938407778739929,
0.09233655035495758,
-0.011204736307263374,
-0.03670130670070648,
-0.043520595878362656,
-0.009434905834496021,
0.011525902897119522,
-0.03757269307971001,
-0.03177111595869064,
0.01931626908481121,
0.024431293830275536,
-0.01601962372660637,
0.01806100644171238,
0.009524746797978878,
-0.00025885956711135805,
0.049517616629600525,
0.09346068650484085,
-0.007968008518218994,
0.021180814132094383,
-0.025984790176153183,
0.009578900411725044,
0.025851383805274963,
0.03630542755126953,
0.017901398241519928,
-0.01222116407006979,
-0.01070617325603962,
0.04268303140997887,
0.0287892185151577,
0.014995045959949493,
-0.014443967491388321,
0.053757261484861374,
-0.021098392084240913,
-0.0000014952066749174264,
0.04582067206501961,
-0.01551672164350748,
0.0313018374145031,
0.012670177035033703,
-0.011395014822483063,
-0.05956064537167549,
0.010552392341196537,
-0.018591763451695442,
0.029465481638908386,
0.003769827540963888,
-0.03335835039615631,
-0.006594584323465824,
-0.06027362495660782,
0.03928898647427559,
0.05079590901732445,
-0.012166188098490238,
-0.019783811643719673,
-0.0211488027125597,
0.03207666799426079,
0.016386281698942184,
-0.0006987063679844141,
-0.013786064460873604,
0.04334213584661484,
0.011230506002902985,
0.010924451984465122,
0.012975038029253483,
-0.00868573971092701,
0.0006027620402164757,
-0.013415719382464886,
0.05817868933081627,
0.054999351501464844,
0.0386180616915226,
-0.021232688799500465,
-0.005386246368288994,
-0.03181122615933418,
-0.051062874495983124,
0.018422571942210197,
0.029598811641335487,
-0.01767592318356037,
-0.03279741108417511,
0.026150520890951157,
-0.022473307326436043,
-0.028221508488059044,
0.018279867246747017,
0.027876239269971848,
0.013194002211093903,
-0.06444720178842545,
-0.13050049543380737,
-0.050157174468040466,
0.0597304105758667,
-0.0061637721955776215,
0.0031396637205034494,
-0.08226971328258514,
0.05585207790136337,
0.02305390127003193,
0.08715058118104935,
0.01609310321509838,
0.013885880820453167,
-0.003108387114480138,
0.01546988170593977,
0.019690869376063347,
-0.02021477371454239,
-0.0032032481394708157,
0.01493497658520937,
-0.023609882220625877,
0.00458949338644743,
-0.05917135626077652,
0.04415881261229515,
0.040281061083078384,
-0.0059181018732488155,
-0.024895964190363884,
0.03814222291111946,
-0.016019361093640327,
0.008481791242957115,
0.039172735065221786,
0.006009948905557394,
-0.0410495400428772,
0.0795164704322815,
-0.009801999665796757,
0.014357857406139374,
0.029690533876419067,
0.0035965365823358297,
0.014050119556486607,
0.005352990236133337,
0.029520025476813316,
-0.011437020264565945,
-0.0013010069960728288,
-0.023970596492290497,
0.019931428134441376,
0.027594128623604774,
-0.018322020769119263,
-0.03525209799408913,
-0.016109900549054146,
-0.00884877610951662,
0.016187498345971107,
-0.00956891942769289,
0.018223898485302925,
0.007855286821722984,
-0.0271005816757679,
-0.022433875128626823,
-0.0458415187895298,
-0.006729046814143658,
-0.07537105679512024,
0.02183849923312664,
-0.012685162015259266,
-0.026749897748231888,
0.07237803936004639,
0.027285823598504066,
0.015409649349749088,
-0.019215427339076996,
-0.041139353066682816,
-0.021290088072419167,
0.027417955920100212,
0.016005685552954674,
-0.04118813946843147,
0.005859788972884417,
0.06623303145170212,
0.03184378892183304,
0.008121450431644917,
0.02576613985002041,
-0.018585428595542908,
-0.06196003034710884,
-0.010939584113657475,
0.015594265423715115,
0.036487262696027756,
0.015414503403007984,
0.022600047290325165,
-0.004166587255895138,
0.0193986464291811,
-0.02930734120309353,
0.03959769010543823,
-0.055583853274583817,
0.03975876420736313,
-0.01068271417170763,
-0.024758081883192062,
-0.007190526928752661,
0.04599365219473839,
0.017216911539435387,
-0.01567908562719822,
-0.019810592755675316,
-0.01943701133131981,
-0.04474692419171333,
0.032047998160123825,
-0.0034985458478331566,
0.053311921656131744,
-0.02362913079559803,
-0.003116705920547247,
0.011857408098876476,
0.03602862358093262,
0.0015180339105427265,
0.009504987858235836,
-0.024819741025567055,
-0.017526540905237198,
-0.00299758929759264,
-0.0027483743615448475,
0.01857173442840576,
0.0074745239689946175,
0.02339773066341877,
-0.008392882533371449,
0.03117239661514759,
-0.01774219237267971,
-0.04523032158613205,
0.056028060615062714,
-0.03884578496217728,
0.016408825293183327,
-0.005116129759699106,
-0.015800589695572853,
-0.002085622865706682,
-0.013654956594109535,
0.004096809308975935,
-0.007032480556517839,
-0.0071173920296132565,
-0.012587841600179672,
-0.030221454799175262,
-0.029532086104154587,
-0.012776555493474007,
0.010482792742550373,
-0.038935307413339615,
0.003063826821744442,
0.021647382527589798,
-0.03307124972343445,
0.0014800351345911622,
0.01971544697880745,
-0.0008457619114778936,
-0.002047681249678135,
0.027701010927557945,
0.01122027263045311,
-0.025581786409020424,
0.02771175652742386,
-0.0234831515699625,
-0.08588597923517227,
-0.009496289305388927,
-0.025726567953824997,
0.02324257418513298,
0.01753178983926773,
-0.060244932770729065,
0.03972071781754494,
-0.0627669170498848,
0.011404940858483315,
0.01165695209056139,
-0.01778814196586609,
0.03217831999063492,
0.0006181568023748696,
-0.017930636182427406,
-0.025712504982948303,
-0.016468049958348274,
-0.020281987264752388,
0.005438569933176041,
-0.03025546856224537,
-0.0070565384812653065,
0.03242676332592964,
-0.027594896033406258,
-0.027464015409350395,
-0.032187964767217636,
-0.032019246369600296,
-0.07772491872310638,
0.0014584058662876487,
-0.004962034057825804,
0.04567219689488411,
-0.03815554827451706,
-0.030894091352820396,
0.03342511132359505,
-0.06548305600881577,
-0.028467312455177307,
-0.052575428038835526,
-0.07693647593259811,
0.06321001797914505,
0.019855240359902382,
0.011670496314764023,
0.0024276121985167265,
0.023060085251927376,
0.07117155194282532,
0.007780234795063734,
0.007338999304920435,
-0.02690458856523037,
-0.0007331575034186244,
-0.028235694393515587,
-0.02133706584572792,
-0.008367514237761497,
0.03238864615559578,
-0.001189668313600123,
0.021747637540102005,
0.017200609669089317,
0.012735403142869473,
0.039420124143362045,
0.013431149534881115,
-0.0046196551993489265,
0.015187304466962814,
-0.013925593346357346,
-0.009440536610782146,
0.04495735839009285,
0.017292851582169533,
-0.060644492506980896,
-0.020212147384881973,
0.007688479498028755,
0.034814901649951935,
-0.01033244002610445,
-0.037373583763837814,
0.07391832023859024,
0.004704472608864307,
0.018157076090574265,
-0.0176884476095438,
0.04045706242322922,
-0.015201142989099026,
0.015012688934803009,
-0.0013578594662249088,
0.012365667149424553,
0.010908509604632854,
-0.029396265745162964,
-0.01472953800112009,
0.05891060456633568,
-0.007548786699771881,
-0.03507273271679878,
0.005649217404425144,
-0.007062599528580904,
0.006312643643468618,
0.0424884632229805,
-0.016610318794846535,
-0.022901810705661774,
0.020515812560915947,
0.026125429198145866,
0.026674626395106316,
0.00053351407404989,
-0.019518399611115456,
-0.03004586696624756,
-0.040650319308042526,
0.006910788826644421,
0.013258862309157848,
0.04197946935892105,
0.037415869534015656,
0.08480969071388245,
0.020059823989868164,
0.004624790977686644,
-0.0030361274257302284,
-0.028470927849411964,
-0.08386208862066269,
0.00481568044051528,
-0.04026033356785774,
-0.013947801664471626,
0.008017373271286488,
-0.047130074352025986,
-0.00073770567541942,
-0.06912628561258316,
-0.061480700969696045,
-0.014604292809963226,
0.007180067244917154,
-0.06235828995704651,
0.021804170683026314,
-0.0016175658674910665,
-0.02076537162065506,
-0.023017555475234985,
0.039100926369428635,
-0.008742926642298698,
0.02122853510081768,
0.04716838151216507,
0.044140830636024475,
-0.0488111637532711,
0.05252612754702568,
0.007773291785269976,
0.04319103807210922,
0.045331921428442,
0.015019423328340054,
0.047528982162475586,
0.04148269072175026,
-0.023046093061566353,
0.0015592580894008279,
0.011225597001612186,
0.05377949774265289,
-0.009841617196798325,
-0.010241800919175148,
-0.012806105427443981,
-0.06910301744937897,
-0.012650697492063046,
-0.034011613577604294,
0.06349160522222519,
-0.02293938212096691,
-0.0036239728797227144,
0.03652246296405792,
0.0038818863686174154,
0.01911844126880169,
-0.004964284133166075,
0.03542983904480934,
0.01206481084227562,
-0.026539325714111328,
-0.028544530272483826,
-0.00042118350393138826,
-0.046851594001054764,
0.019779780879616737,
0.020770477131009102,
-0.01855521835386753,
-0.00822423305362463,
-0.0038242731243371964,
-0.0036305219400674105,
0.009637671522796154,
-0.029639966785907745,
-0.04904793202877045,
-0.016582077369093895,
0.008577237837016582,
-0.016828875988721848,
-0.020425133407115936,
-0.006427224259823561,
0.0309214498847723,
-0.006062978412955999,
0.009330476634204388,
-0.012359424494206905,
-0.048994675278663635,
-0.0030375183559954166,
0.02586914412677288,
-0.00014559134433511645,
0.020602338016033173,
-0.002753391396254301,
-0.048795364797115326,
-0.028904680162668228,
0.044144485145807266,
-0.0014118349645286798,
0.041515741497278214,
-0.04047336429357529,
0.0021774903871119022,
-0.03765694051980972,
-0.00433931453153491,
0.0058615864254534245,
0.030130362138152122,
0.007159709930419922,
0.01639329269528389,
-0.010588595643639565,
0.0004976635100319982,
-0.02613549306988716,
-0.0004418960597831756,
0.047306641936302185,
0.04855942726135254,
-0.013381561264395714,
0.005308196414262056,
0.00534715224057436,
0.01544256042689085,
-0.012174620293080807,
-0.11916174739599228,
0.020101504400372505,
-0.042754609137773514,
0.000016105503163998947,
0.0337848886847496,
-0.031145263463258743,
-0.030983665958046913,
-0.0056368159130215645,
-0.026686081662774086,
0.016666946932673454,
0.04204545170068741,
-0.03992561250925064,
0.05386049300432205,
-0.0015573203563690186,
0.002009936375543475,
0.03786447271704674,
-0.01533303689211607,
0.007938012480735779,
0.019601896405220032,
-0.019051209092140198,
0.046887289732694626,
-0.04017137363553047,
0.007306229323148727,
-0.02651352435350418,
0.012204241938889027,
-0.026851749047636986,
0.05849697068333626,
-0.009307396598160267,
0.02172974869608879,
-0.010107615031301975,
-0.08562491089105606,
-0.015779763460159302,
-0.016741489991545677,
0.02093813195824623,
0.0006053819670341909,
-0.03380301222205162,
0.0006298884400166571,
-0.001736752805300057,
-0.018572086468338966,
0.0072092595510184765,
0.00039516054675914347,
-0.009358744136989117,
0.020447539165616035,
-0.022446338087320328,
0.04266640543937683,
-0.04491754621267319,
-0.025292737409472466,
0.02713063918054104,
-0.08429481089115143,
0.026397647336125374,
-0.028272299095988274,
0.0075343600474298,
0.03019653633236885,
-0.06882496178150177,
-0.04285348206758499,
-0.016159188002347946,
-0.03655907139182091,
0.012470025569200516,
-0.05537906661629677,
0.013641837053000927,
0.027365505695343018,
-0.06309186667203903,
-0.07361545413732529,
-0.04622764512896538,
-0.007158325053751469,
0.01866290718317032,
-0.0005138607230037451,
-0.0013417621375992894,
0.05102245509624481,
-0.01867041178047657,
-0.005225128959864378,
-0.02638515830039978,
0.04579305648803711,
0.004955335520207882,
-0.019681734964251518,
0.007498123683035374,
-0.004274995066225529,
0.014178358018398285,
-0.009176557883620262,
-0.006716468371450901,
-0.038828227669000626,
-0.00678239343687892,
-0.010074695572257042,
-0.0022572583984583616,
0.05589621141552925,
-0.01730428822338581,
-0.0414324551820755,
-0.0008887480362318456,
0.0072837830521166325,
0.028573166579008102,
-0.033073119819164276,
-0.03513605147600174,
-0.003875328926369548,
0.030421555042266846,
0.007141112349927425,
-0.013856187462806702,
-0.0267673097550869,
0.004024570807814598,
0.028797883540391922,
-0.016653655096888542,
0.0010101392399519682,
-0.00266198324970901,
-0.04456813260912895,
0.036316774785518646,
0.005796757061034441,
0.004077585879713297,
-0.01839379407465458,
0.049025315791368484,
-0.0038122653495520353,
-0.005643865093588829,
0.010410274378955364,
-0.02398780733346939,
0.0007060663774609566,
-0.031212378293275833,
0.012530388310551643,
0.0023276200518012047,
0.02122829109430313,
-0.01224480103701353,
-0.004424572456628084,
-0.030736377462744713,
-0.013021031394600868,
0.061641011387109756,
-0.0058469586074352264,
0.055020127445459366,
0.057425256818532944,
0.00856959167867899,
0.004431471228599548,
-0.03665352985262871,
0.016591476276516914,
0.018789151683449745,
0.008411146700382233,
0.03519463166594505,
-0.04622412472963333,
0.0031499327160418034,
0.022493967786431313,
0.04923773556947708,
0.0002451101900078356,
0.049899883568286896,
0.04369650036096573,
0.028589602559804916,
0.036882951855659485,
0.019054055213928223,
-0.006653260439634323,
0.03041873872280121,
-0.016952605918049812,
0.01145067997276783,
-0.035565800964832306,
-0.029632825404405594,
0.05050807446241379,
0.012664079666137695,
0.011052857153117657,
-0.02112368680536747,
-0.04111127182841301,
-0.04793970286846161,
-0.0006408179178833961,
0.013376963324844837,
0.04328474402427673,
0.008666838519275188,
0.007106502540409565,
-0.01068144477903843,
0.003115116385743022,
0.01636316440999508,
-0.018151504918932915,
-0.06069390848278999,
-0.04234272241592407,
-0.042931824922561646,
-0.05438316613435745,
0.044426918029785156,
-0.004643317312002182,
-0.02366735227406025,
0.019237535074353218,
-0.0386083647608757,
0.039537932723760605,
-0.011749575845897198,
0.013933788985013962,
-0.03974460810422897,
0.0526701956987381,
-0.0027169319801032543,
0.03210572898387909,
-0.010384413413703442,
0.01715613342821598,
0.09456592798233032,
0.02775544486939907,
-0.008949863724410534,
-0.0823284238576889,
0.018890436738729477,
0.01037984061986208,
0.024900658056139946,
-0.02963975816965103,
0.03152376040816307,
-0.0046690963208675385,
0.03460846096277237,
-0.011175790801644325,
0.0647120326757431,
0.02558119222521782,
-0.012899620458483696,
0.04428422823548317,
-0.03293304517865181,
-0.02919364534318447,
0.0016878718743100762,
0.014371388591825962,
-0.00563947856426239,
0.016110243275761604,
-0.01501441653817892,
-0.0028480845503509045,
-0.04098587483167648,
0.014195377938449383,
-0.009340344928205013,
-0.039758894592523575,
0.015049661509692669,
0.029036737978458405,
-0.026536986231803894,
0.03490462899208069,
0.010379442013800144,
-0.019487017765641212,
-0.04420021176338196,
0.02783021703362465,
0.06883275508880615,
-0.01616046391427517,
0.0384192168712616,
0.007733752951025963,
0.025789378210902214,
0.015422717668116093,
0.0069591691717505455,
0.01766366697847843,
-0.052050694823265076,
-0.0009738554363138974,
-0.012702353298664093,
0.05285082384943962,
-0.02034321054816246,
-0.014698927290737629,
-0.01620348170399666,
-0.04827258735895157,
0.013871624134480953,
-0.04556379094719887,
-0.012111198157072067,
-0.0028798850253224373,
0.011141893453896046,
-0.028020035475492477,
-0.010523823089897633,
-0.032674308866262436,
0.012315760366618633,
-0.006723221857100725,
0.030429311096668243,
-0.02133703976869583,
0.0022170378360897303,
0.0008649935480207205,
0.0086429538205266,
0.016363849863409996,
0.018789729103446007,
-0.0010895399609580636,
-0.02468331903219223,
0.00235987501218915,
-0.04494529217481613,
-0.028165647760033607,
0.011935458518564701,
0.025418320670723915,
0.056906748563051224,
0.01647561974823475,
-0.016756325960159302,
0.014764086343348026,
-0.037947289645671844,
0.02049924060702324,
-0.004125294275581837,
-0.010740116238594055,
-0.007458953652530909,
0.0268408115953207,
0.06747622787952423,
0.04005507007241249,
-0.03062465973198414,
-0.008529148995876312,
0.03293091058731079,
-0.007632100023329258,
0.03465624153614044,
-0.001987790921702981,
0.03626406937837601,
0.02149076759815216,
-0.03751712664961815,
-0.006806828081607819,
-0.05079953745007515,
0.015364604070782661,
0.016195038333535194,
0.038147397339344025,
-0.0231246966868639,
0.0018002225551754236,
0.0007940950454212725,
0.014274923130869865,
-0.0003099857422057539,
-0.010546807199716568,
-0.03378710150718689,
0.027805322781205177,
0.023893041536211967,
-0.008594445884227753,
-0.026097184047102928,
-0.05175144970417023,
-0.019012441858649254,
-0.012040634639561176,
-0.012838137336075306,
-0.016719313338398933,
-0.0247367974370718,
0.017701847478747368,
0.06221204251050949,
0.014957992359995842,
-0.024096867069602013,
-0.0475517101585865,
0.014237988740205765,
0.026805223897099495,
-0.02336736209690571,
-0.001416557002812624,
0.045246969908475876,
0.01161434780806303,
-0.05024648830294609,
0.01360020786523819,
0.05163269117474556,
0.01536533236503601,
0.0093954186886549,
0.0312783382833004,
0.006439764518290758,
0.06545887887477875,
-0.009467015042901039,
-0.02773788757622242,
0.06207079067826271,
-0.022993862628936768,
-0.01885090582072735,
0.04973232001066208,
-0.0010571782477200031,
0.046358782798051834,
0.05360430106520653,
-0.016635287553071976,
-0.02068653516471386,
0.020673412829637527,
-0.029434002935886383,
0.0032730780076235533,
0.03913451358675957,
-0.033524513244628906,
-0.01416705921292305,
-0.01047002524137497,
0.0285357553511858,
0.006979425437748432,
-0.014973640441894531,
0.0640544518828392,
0.007958326488733292,
0.0389539860188961,
0.02207580953836441,
-0.0036694782320410013,
0.00891597755253315,
0.01678563840687275,
0.02767481654882431,
-0.004030490294098854,
0.034596916288137436,
0.031686682254076004,
-0.04074445366859436,
0.05394301563501358,
0.022219674661755562,
-0.005684044677764177,
-0.09091761708259583,
0.006034246180206537,
0.007047556806355715,
-0.013470010831952095,
0.029564175754785538,
-0.051081594079732895,
0.024586675688624382,
0.05331622064113617,
-0.06925254315137863,
0.02426900714635849,
-0.022187110036611557,
-0.039175912737846375,
-0.017177436500787735,
0.03965073823928833,
-0.02716614305973053,
0.043699994683265686,
0.027363000437617302,
0.02833172306418419,
0.01918593980371952,
0.016910888254642487,
-0.025371376425027847,
-0.03684784471988678,
-0.03582511842250824,
0.031479351222515106,
-0.004708938766270876,
-0.0174233578145504,
0.08966521173715591,
-0.03759041801095009,
-0.007078284397721291,
0.03775445744395256,
-0.01651494763791561,
0.0037568749394267797,
0.0028009768575429916,
-0.013664194382727146,
0.015783101320266724,
0.026308352127671242,
0.01602589152753353,
-0.0005745487869717181,
-0.00959390215575695,
0.014822326600551605,
0.04791952297091484,
0.011809439398348331,
0.003197832964360714,
-0.028800735250115395,
0.012398811988532543,
-0.011189077980816364,
-0.04686177894473076,
0.04914438724517822,
0.0016208956949412823,
0.009605811908841133,
-0.007785509340465069,
0.02126362919807434,
0.014494447968900204,
-0.02285867929458618,
0.033308498561382294,
-0.0405673012137413,
-0.006783585995435715,
0.00633060559630394,
0.0189767275005579,
-0.011974030174314976,
0.012474041432142258,
-0.030360084027051926,
-0.049818914383649826,
0.015128816477954388,
-0.0009660153300501406,
0.011647077277302742,
-0.027405593544244766,
-0.010282880626618862,
0.013970576226711273,
0.003456344362348318,
0.005687641445547342,
-0.04233505576848984,
-0.03949356824159622,
0.02544853277504444,
0.0014201233861967921,
0.010945543646812439,
-0.00033074794919230044,
-0.025542043149471283,
-0.05428805947303772,
-0.05515887960791588,
0.03722274303436279,
0.024474048987030983,
0.004928151611238718,
-0.044934969395399094,
-0.004525142256170511,
-0.019470451399683952,
0.011519534513354301,
0.06278614699840546,
0.007885029539465904,
-0.0044415853917598724,
0.009762803092598915,
0.014368817210197449,
0.053138334304094315,
-0.03168313950300217,
-0.0014113441575318575,
-0.0382634736597538,
0.013256307691335678,
-0.019926466047763824,
-0.010691437870264053,
-0.010231159627437592,
0.022768912836909294,
0.035557907074689865,
-0.006425201892852783,
-0.03260546177625656,
0.003572623711079359,
-0.039320725947618484,
0.08461713790893555,
0.0006945772911421955,
0.013396836817264557,
0.05731654912233353,
0.013277918100357056,
0.03771788254380226,
0.02708798088133335,
-0.01586737483739853,
-0.03785774111747742,
0.03473649173974991,
-0.001711269491352141,
-0.03146160766482353,
0.0038187771569937468,
0.0003827193286269903,
-0.004625537432730198,
-0.03268009424209595,
-0.01827498897910118,
0.03473002091050148,
-0.034875962883234024,
-0.009364073164761066,
0.04012050852179527,
-0.019124208018183708,
0.006720955017954111,
0.00210405420511961,
0.01826385408639908,
0.006380670703947544,
0.0172459427267313,
0.007636908907443285,
0.03631246089935303,
0.04221741110086441,
0.008559984154999256,
0.030697893351316452,
0.029609793797135353,
-0.022203883156180382,
0.024822521954774857,
0.009890548884868622,
0.04718387871980667,
0.005803327076137066,
-0.042183104902505875,
0.001097342581488192,
-0.0003565741644706577,
0.02895539067685604,
0.01517035998404026,
-0.03310602530837059,
0.08118537068367004,
-0.04113677144050598,
-0.003317977301776409,
0.0021755474153906107,
0.045914966613054276,
-0.0327661857008934,
-0.020718032494187355,
0.05758807808160782,
0.011920186690986156,
-0.0009478327119722962,
-0.031561389565467834,
-0.01779971458017826,
-0.007481718901544809,
0.0017526592127978802,
-0.03948986157774925,
0.03300032764673233,
0.004247973207384348,
-0.01803390309214592,
0.013280197978019714,
-0.04409920051693916,
-0.016082346439361572,
-0.010765895247459412,
0.06352381408214569,
0.02776411361992359,
0.04196585714817047,
-0.0024956415873020887,
-0.012219823896884918,
-0.018976541236042976,
0.05364638939499855,
-0.1143326684832573,
-0.008722053840756416,
-0.018080847337841988,
0.04455835744738579,
-0.03339303284883499,
-0.03211840242147446
] |
<p>The time is treated differently in special relativity and quantum mechanics. What is the exact difference and why relativistic quantum mechanics (Dirac equation etc.) works?</p> | 2,840 | [
0.0037614814937114716,
-0.0589626170694828,
-0.0174237247556448,
-0.031744275242090225,
0.013477792963385582,
-0.0012395138619467616,
-0.02222009189426899,
-0.018043331801891327,
0.0034300358965992928,
0.001850414671935141,
0.011168496683239937,
0.06712216138839722,
0.047680143266916275,
-0.03073160909116268,
0.0340719148516655,
0.004527727607637644,
0.006417939439415932,
-0.03704336658120155,
-0.021895132958889008,
0.0031933882273733616,
0.018066538497805595,
0.015398851595818996,
0.03308640420436859,
0.013712401501834393,
-0.027263695374131203,
0.037288930267095566,
0.022250736132264137,
0.024920828640460968,
0.03741272911429405,
0.03774462640285492,
-0.01756194233894348,
-0.03984437510371208,
0.0051491959020495415,
0.03704819083213806,
0.02446308359503746,
-0.024459149688482285,
-0.03604263439774513,
-0.043346576392650604,
-0.019013626500964165,
-0.016255289316177368,
-0.03347025066614151,
-0.023878522217273712,
-0.029458239674568176,
0.046204470098018646,
-0.031341712921857834,
0.04566774517297745,
-0.008653166703879833,
-0.0113811194896698,
0.04937087744474411,
-0.04412779211997986,
0.04411868751049042,
0.015079011209309101,
0.03794460371136665,
-0.006005335133522749,
-0.011900903657078743,
0.023795349523425102,
0.07596486806869507,
0.0867866799235344,
-0.005747137125581503,
-0.03797806426882744,
-0.03101796843111515,
-0.011424321681261063,
0.015071317553520203,
-0.019148025661706924,
-0.01913374289870262,
0.018628519028425217,
-0.0018954346887767315,
-0.03296414762735367,
0.015219730325043201,
-0.016372812911868095,
0.008438578806817532,
0.012816864997148514,
0.04656675457954407,
-0.014139746315777302,
0.023295007646083832,
-0.07201307266950607,
0.0315786749124527,
0.019942304119467735,
0.03762604296207428,
0.024625297635793686,
-0.0011042830301448703,
-0.005894097965210676,
0.020478971302509308,
0.006562143098562956,
-0.02084142155945301,
-0.029545733705163002,
0.06482352316379547,
0.04107712209224701,
-0.006541373673826456,
0.024001220241189003,
-0.03296547010540962,
0.05464887619018555,
0.014116251841187477,
-0.0034110869746655226,
-0.006775792688131332,
0.04325699061155319,
0.0021294034086167812,
0.033511146903038025,
0.020124584436416626,
-0.004836787935346365,
0.020491985604166985,
-0.051185086369514465,
0.030374670401215553,
0.07416944205760956,
0.01826298050582409,
0.008233184926211834,
-0.021200863644480705,
0.036364175379276276,
-0.009295676834881306,
0.005692068487405777,
-0.02238341234624386,
0.013369100168347359,
-0.023019200190901756,
0.016438357532024384,
0.007605335209518671,
-0.03919317200779915,
-0.0064959716983139515,
-0.02457636035978794,
0.08456085622310638,
0.060411643236875534,
0.009808674454689026,
-0.05014927685260773,
-0.005896802060306072,
-0.023445239290595055,
-0.04046785831451416,
0.001829950138926506,
0.01404778752475977,
-0.017072195187211037,
-0.03241996467113495,
0.023266872391104698,
-0.0009976071305572987,
-0.04483698308467865,
0.017847297713160515,
-0.002006250200793147,
0.04573008790612221,
-0.028879273682832718,
-0.1241946667432785,
-0.046184320002794266,
0.02145606093108654,
0.006199465598911047,
-0.02460373193025589,
-0.06796938925981522,
0.032765913754701614,
-0.005169704556465149,
0.07889147847890854,
0.014183859340846539,
0.00445507513359189,
0.017296532168984413,
0.012677404098212719,
0.0073067862540483475,
-0.02043433114886284,
-0.0013893665745854378,
0.028036190196871758,
-0.016246965155005455,
0.034414686262607574,
-0.05111144110560417,
-0.005387457087635994,
0.02879307046532631,
-0.015457703731954098,
-0.02926716022193432,
0.06067119166254997,
-0.031276822090148926,
-0.005840836092829704,
0.0426957830786705,
-0.001059817150235176,
-0.025248343124985695,
0.05437806248664856,
0.029433079063892365,
-0.009117393754422665,
0.07169000804424286,
0.02156131900846958,
0.037478819489479065,
0.018908068537712097,
0.055946629494428635,
-0.008885329589247704,
-0.026185907423496246,
-0.03422115743160248,
0.05154100060462952,
0.007214025594294071,
0.0025295244995504618,
-0.06708058714866638,
-0.01484241709113121,
0.006375438999384642,
0.012338005937635899,
-0.005345059093087912,
0.0499308705329895,
-0.010344662703573704,
0.02705983817577362,
-0.038725629448890686,
-0.03315151110291481,
-0.005555497948080301,
-0.08578731119632721,
0.023421918973326683,
0.00024305148690473288,
-0.015047730877995491,
0.039877187460660934,
0.02246030792593956,
0.02621184103190899,
-0.04393452778458595,
-0.044983766973018646,
-0.035901330411434174,
0.06175203248858452,
-0.0247469674795866,
-0.012288125231862068,
0.04971226304769516,
0.07591629773378372,
0.05581112578511238,
0.006755999755114317,
0.010787885636091232,
-0.011200952343642712,
-0.04588658735156059,
0.019231196492910385,
0.004391409922391176,
0.02524069882929325,
0.01439717598259449,
-0.02936970815062523,
-0.006028755102306604,
-0.03202933445572853,
-0.0017669058870524168,
0.05044613778591156,
0.015982646495103836,
0.05585695430636406,
-0.0004443282086867839,
-0.008203672245144844,
0.006249262951314449,
0.04701100289821625,
-0.0026474473997950554,
0.010636309161782265,
0.024816762655973434,
-0.06703134626150131,
-0.012752227485179901,
-0.007673400454223156,
0.042430486530065536,
0.034723784774541855,
-0.03288516029715538,
0.015484348870813847,
-0.010740315541625023,
0.04478708282113075,
0.03168272227048874,
0.03844374045729637,
-0.02950417622923851,
-0.04514153301715851,
0.0005620393785648048,
-0.02136804908514023,
-0.00686687184497714,
0.007554692216217518,
0.025489438325166702,
0.01001270953565836,
0.012366829439997673,
-0.009272921830415726,
-0.040778834372758865,
0.042808111757040024,
-0.034713514149188995,
0.0017055938951671124,
0.020805567502975464,
-0.057159360498189926,
0.02153937518596649,
-0.023229677230119705,
-0.0021830748300999403,
0.018389588221907616,
-0.02158423699438572,
-0.002196270739659667,
-0.03179194778203964,
-0.045026350766420364,
0.02990933693945408,
-0.0192977637052536,
0.0005866410210728645,
-0.010980375111103058,
0.025132210925221443,
-0.018916305154561996,
0.008713179267942905,
-0.016005314886569977,
0.000441994343418628,
-0.013325735926628113,
-0.024923168122768402,
0.03017875738441944,
-0.005238081328570843,
0.02783278375864029,
-0.0049877227284014225,
-0.0494246706366539,
0.01539191696792841,
-0.03775504603981972,
0.014327740296721458,
0.01853950507938862,
-0.0349423848092556,
0.06417077034711838,
-0.030379191040992737,
-0.06108463555574417,
0.052086684852838516,
-0.010588523000478745,
0.054036375135183334,
0.029013164341449738,
-0.027426231652498245,
-0.053740743547677994,
-0.0260538998991251,
-0.03386000171303749,
0.003388370852917433,
-0.010161740705370903,
0.006298938300460577,
0.07875952124595642,
-0.030384525656700134,
-0.008227280341088772,
0.01013074442744255,
-0.042458273470401764,
-0.04139282554388046,
-0.023182598873972893,
0.007572762668132782,
0.02838488481938839,
-0.03816413879394531,
-0.006117922253906727,
0.02485385537147522,
-0.0848749428987503,
-0.021064279600977898,
-0.020485050976276398,
-0.032308850437402725,
0.03561120480298996,
0.002059017773717642,
0.035040292888879776,
-0.007553619798272848,
-0.016475534066557884,
0.05885494500398636,
0.02030368149280548,
-0.005560428369790316,
-0.013761083595454693,
-0.0071280342526733875,
-0.007739407010376453,
-0.012891084887087345,
0.026215432211756706,
0.034562885761260986,
-0.004013953730463982,
0.01986139826476574,
0.025310853496193886,
0.013293055817484856,
0.02956566959619522,
0.02347027137875557,
-0.018027612939476967,
-0.010699257254600525,
0.0021462582517415285,
0.00012621967471204698,
0.031726542860269547,
-0.0013094564201310277,
-0.05043328180909157,
-0.015075989998877048,
0.01662350632250309,
0.04547207057476044,
-0.007548712193965912,
-0.04235603287816048,
0.06059915944933891,
-0.0027876407839357853,
0.007269320543855429,
-0.01589156500995159,
0.05714865401387215,
-0.04181912913918495,
-0.007801485247910023,
0.0018477372359484434,
0.012715199030935764,
0.026725584641098976,
-0.03358783572912216,
0.011773871257901192,
0.025399895384907722,
0.03952862322330475,
-0.04950156435370445,
-0.015560111030936241,
-0.008629471063613892,
-0.019878597930073738,
0.04731931909918785,
-0.04748091474175453,
-0.03294766694307327,
0.06542796641588211,
0.02659333311021328,
0.022297030314803123,
-0.005821922793984413,
-0.03577805683016777,
-0.03249964490532875,
-0.07785026729106903,
0.013851725496351719,
0.009669539518654346,
0.05632927268743515,
0.024078842252492905,
0.0570983923971653,
0.0312375258654356,
-0.0015029857167974114,
0.01206330955028534,
-0.015430047176778316,
-0.04262033477425575,
0.022990209981799126,
-0.05851174145936966,
-0.030894914641976357,
-0.015371105633676052,
-0.004534728825092316,
-0.01383714098483324,
-0.0483577698469162,
-0.028694462031126022,
-0.030180715024471283,
-0.033579155802726746,
-0.05754475295543671,
0.02296428754925728,
-0.045248355716466904,
-0.03184381499886513,
-0.027081234380602837,
0.0461045503616333,
0.01998322829604149,
0.0020193827804178,
0.0008883618284016848,
0.06906012445688248,
-0.027286987751722336,
0.016318567097187042,
-0.0007855840376578271,
-0.012274821288883686,
0.01735622249543667,
0.00340629112906754,
0.07163339853286743,
0.006664585787802935,
-0.03972058743238449,
0.025037143379449844,
0.025000127032399178,
0.0658726617693901,
-0.0009844473097473383,
-0.03363950550556183,
-0.03469183295965195,
-0.055621437728405,
0.003137747058644891,
-0.01229821890592575,
0.06514223664999008,
0.01036075223237276,
0.029615148901939392,
0.02440609410405159,
0.005246562883257866,
-0.00956664141267538,
0.024161476641893387,
0.024337351322174072,
-0.00892798975110054,
-0.036717504262924194,
-0.03970206901431084,
-0.007195541635155678,
-0.043622616678476334,
-0.0035464507527649403,
-0.0005678244051523507,
0.000569884548895061,
-0.026838313788175583,
0.009959887713193893,
-0.004923146218061447,
-0.022716248407959938,
-0.01756232976913452,
-0.014000533148646355,
0.017021268606185913,
-0.0010241983691230416,
0.022468848153948784,
0.008614386431872845,
-0.012101085856556892,
0.028896115720272064,
0.033226776868104935,
-0.02672199159860611,
0.02338740974664688,
-0.043889451771974564,
-0.016024557873606682,
0.03112644888460636,
0.004003881476819515,
-0.0061788009479641914,
-0.015696698799729347,
-0.05567648634314537,
-0.018808670341968536,
0.046980131417512894,
-0.022012686356902122,
0.030529972165822983,
-0.010692589916288853,
-0.03343498334288597,
-0.03814588487148285,
-0.014625536277890205,
0.007852955721318722,
0.0462365560233593,
0.013886614702641964,
0.015843238681554794,
0.011882019229233265,
0.005128010176122189,
-0.034104201942682266,
-0.012157997116446495,
0.060674164444208145,
0.042549628764390945,
0.019719181582331657,
0.027607832103967667,
-0.0046817585825920105,
0.04383460804820061,
-0.023637130856513977,
-0.0867978110909462,
-0.021813273429870605,
0.007323600351810455,
-0.017658907920122147,
0.046597786247730255,
-0.039419982582330704,
-0.04165644943714142,
0.00934707559645176,
0.0008402682142332196,
0.00111437460873276,
0.009932168759405613,
-0.04254390671849251,
0.008176743052899837,
0.013599767349660397,
-0.019854703918099403,
0.006197011098265648,
0.00972461886703968,
-0.009180254302918911,
-0.0072304303757846355,
0.007435247767716646,
0.04082082584500313,
-0.02188512496650219,
-0.007042371202260256,
-0.01422188151627779,
-0.01589294523000717,
-0.02655899152159691,
0.04910632222890854,
-0.021950429305434227,
0.002252923557534814,
0.012189251370728016,
-0.01963772065937519,
-0.04672859236598015,
0.03858325257897377,
-0.010727886110544205,
0.006547665689140558,
-0.0033012591302394867,
-0.020818253979086876,
-0.011321469210088253,
-0.04145069420337677,
-0.017829302698373795,
-0.0027287860866636038,
-0.017257481813430786,
0.020307281985878944,
-0.0023680224549025297,
0.05314544215798378,
-0.0031771312933415174,
-0.028955021873116493,
0.028065400198101997,
-0.041932590305805206,
0.008578907698392868,
-0.004168424755334854,
-0.021366870030760765,
0.002947296015918255,
-0.04281352087855339,
-0.025004032999277115,
-0.004722924903035164,
-0.03124338947236538,
0.02615184336900711,
-0.0560397244989872,
0.03870374709367752,
0.03658467158675194,
-0.010079799219965935,
-0.09114609658718109,
-0.06348538398742676,
0.01074269600212574,
-0.0025786920450627804,
-0.02171144261956215,
-0.021468913182616234,
0.030543938279151917,
-0.03376305103302002,
-0.019177893176674843,
-0.004529830999672413,
0.0647786483168602,
0.0028791355434805155,
-0.03727693483233452,
-0.026872217655181885,
-0.008667522110044956,
0.025250159204006195,
-0.03457945957779884,
0.004504588898271322,
-0.020905369892716408,
-0.01012530829757452,
0.005024737678468227,
0.0031074106227606535,
0.05712416395545006,
0.00012115243589505553,
-0.032215267419815063,
-0.016812961548566818,
0.0016140576917678118,
0.011375299654901028,
-0.046889763325452805,
0.013610155321657658,
0.043654028326272964,
0.03817204013466835,
0.008615152910351753,
-0.027974430471658707,
0.029118016362190247,
0.01469018217176199,
0.051438670605421066,
0.016230395063757896,
0.0000380683814000804,
-0.04887434467673302,
-0.05518139898777008,
0.02237742953002453,
-0.019823577255010605,
0.03221648931503296,
-0.005479488056153059,
0.038282666355371475,
0.008436961099505424,
0.020988645032048225,
0.007029141299426556,
0.0066121541894972324,
0.010348726995289326,
-0.030338414013385773,
0.002956563839688897,
0.02153066359460354,
0.0005644308985210955,
-0.013742120005190372,
-0.013610275462269783,
-0.0024268191773444414,
-0.0039676777087152,
0.05006808787584305,
-0.023356366902589798,
0.035152774304151535,
0.01683715172111988,
-0.012708455324172974,
-0.007117311004549265,
-0.032039958983659744,
-0.02140701375901699,
0.015093913301825523,
0.002524113282561302,
0.026242181658744812,
-0.0025631559547036886,
0.013032622635364532,
0.04360402002930641,
0.08323850482702255,
-0.013870321214199066,
0.01062232069671154,
0.0459308922290802,
0.04885459318757057,
0.006771677173674107,
0.014490353874862194,
-0.040939055383205414,
0.036708444356918335,
-0.00809760857373476,
0.008706255815923214,
0.010068546049296856,
-0.009860842488706112,
0.019505323842167854,
-0.015656527131795883,
0.0007150890305638313,
-0.041287828236818314,
-0.0041839550249278545,
-0.05101031810045242,
0.011369485408067703,
0.0022242660634219646,
0.019065914675593376,
-0.011472822166979313,
0.038330912590026855,
0.027330385521054268,
0.012925820425152779,
-0.00012298878573346883,
0.018259476870298386,
-0.05774291977286339,
-0.020375169813632965,
-0.04207317531108856,
-0.05509070307016373,
0.046456389129161835,
-0.02179584465920925,
-0.01565607078373432,
-0.01626940444111824,
-0.016370680183172226,
0.01425640657544136,
0.011772088706493378,
0.03201866149902344,
-0.03894968330860138,
0.06282386183738708,
0.02255343459546566,
-0.008973625488579273,
0.004723610822111368,
0.0006929154042154551,
0.09748844802379608,
0.0226504597812891,
0.0021115124691277742,
-0.05419473350048065,
0.01953941397368908,
-0.01766303926706314,
0.024465106427669525,
-0.01667070761322975,
0.030016029253602028,
0.005170441698282957,
0.013626784086227417,
0.01939311809837818,
0.03876844793558121,
0.0430874340236187,
-0.013278895057737827,
0.044657062739133835,
-0.041089899837970734,
-0.0388040728867054,
-0.012624005787074566,
0.02128579467535019,
0.03560032323002815,
0.017461800947785378,
-0.03442412614822388,
0.005348792765289545,
-0.06284269690513611,
0.016518687829375267,
-0.005998584907501936,
-0.007689403370022774,
0.026111653074622154,
-0.005185503046959639,
-0.021748488768935204,
0.02151014655828476,
-0.00035460529034025967,
-0.01030027586966753,
-0.060632530599832535,
0.04533752426505089,
0.034914661198854446,
-0.001757494523189962,
0.036958325654268265,
0.002796157728880644,
0.02063371241092682,
-0.003289811545982957,
0.00013123398821335286,
0.015163326635956764,
-0.07180339843034744,
0.020285557955503464,
-0.03778309002518654,
0.025118352845311165,
-0.033042509108781815,
-0.031895142048597336,
0.017095934599637985,
-0.010773440822958946,
0.004937801044434309,
-0.04410897567868233,
-0.019930845126509666,
0.0033704619854688644,
0.03605564311146736,
0.018482765182852745,
0.004889971110969782,
-0.05330313742160797,
0.03966904059052467,
-0.013762722723186016,
0.03481020778417587,
-0.012079842388629913,
-0.018006818369030952,
0.042206354439258575,
0.007981892675161362,
-0.030926857143640518,
-0.043853700160980225,
-0.005882482975721359,
0.014331047423183918,
-0.025270817801356316,
-0.04341017082333565,
-0.01741143688559532,
0.06653407216072083,
0.039279546588659286,
0.02783304452896118,
-0.015710018575191498,
0.011244469322264194,
-0.020197125151753426,
-0.07397069782018661,
0.02004973217844963,
-0.012431401759386063,
-0.031143492087721825,
0.0011442702962085605,
0.01677749678492546,
0.05737529322504997,
0.0501536950469017,
-0.04820781573653221,
0.047012150287628174,
-0.010298037901520729,
-0.027027757838368416,
0.01983313076198101,
-0.02878827229142189,
0.023113934323191643,
0.030942857265472412,
-0.012279077433049679,
0.0049536749720573425,
-0.06494749337434769,
0.0052231596782803535,
0.058905646204948425,
-0.009205291979014874,
-0.014992802403867245,
0.03091905452311039,
-0.027517307549715042,
-0.01079770177602768,
0.01798020303249359,
-0.032729197293519974,
0.00228068302385509,
0.005535589065402746,
0.03885294497013092,
-0.050686102360486984,
-0.04151362553238869,
-0.04415295645594597,
0.03005601093173027,
0.008881582878530025,
-0.003366453805938363,
-0.02202007547020912,
0.01754581555724144,
-0.003941692411899567,
0.026442034170031548,
-0.019331632182002068,
0.003275966038927436,
-0.07058118283748627,
0.055240727961063385,
-0.0035971461329609156,
-0.029319491237401962,
-0.010151409544050694,
0.030554424971342087,
0.0059363460168242455,
-0.02573237754404545,
0.024168772622942924,
0.024576690047979355,
-0.034443266689777374,
0.01223116647452116,
0.031363341957330704,
0.007310075219720602,
0.041362229734659195,
-0.005257953889667988,
-0.029711244627833366,
0.008819418959319592,
-0.03962438553571701,
-0.03908907249569893,
0.05198697745800018,
-0.012681124731898308,
-0.001032695989124477,
0.03800756111741066,
-0.006270749028772116,
0.01094664353877306,
0.06798025220632553,
-0.04556576535105705,
-0.02320404164493084,
0.025599606335163116,
-0.020619818940758705,
-0.0022213642951101065,
-0.011441665701568127,
0.01474046055227518,
0.005030466243624687,
-0.021377287805080414,
0.015793468803167343,
0.027581267058849335,
-0.0387643463909626,
0.014118438586592674,
0.011066803708672523,
-0.012216053903102875,
0.04393073916435242,
0.057855576276779175,
-0.02453504502773285,
0.02135252021253109,
0.051862895488739014,
-0.051478296518325806,
0.03845294937491417,
0.026025667786598206,
-0.009876823052763939,
-0.09941651672124863,
0.03454006463289261,
0.010390125215053558,
-0.022457145154476166,
0.03210530802607536,
-0.017263198271393776,
0.019473303109407425,
0.03888802230358124,
-0.07072585821151733,
0.04154626652598381,
-0.036389030516147614,
-0.01544865407049656,
0.0044281817972660065,
-0.0051349070854485035,
-0.008240144699811935,
0.08816806972026825,
0.0262820553034544,
0.029463427141308784,
0.03557578846812248,
-0.011705906130373478,
0.0063056726939976215,
-0.03511494770646095,
-0.025302158668637276,
0.030317582190036774,
0.001597347785718739,
-0.016228074207901955,
0.02795439399778843,
-0.03806307911872864,
-0.00945619773119688,
0.02859276346862316,
0.008637972176074982,
0.007232110947370529,
-0.012548750266432762,
0.0015868621412664652,
-0.023774929344654083,
0.010363607667386532,
0.021639730781316757,
-0.04038031026721001,
0.01919971965253353,
0.03143160790205002,
0.008484797552227974,
0.004512203857302666,
-0.016709836199879646,
-0.01781371422111988,
-0.013446016237139702,
-0.05523577332496643,
-0.03697182610630989,
0.019450850784778595,
0.020349577069282532,
-0.019859420135617256,
0.0010402166517451406,
0.029971735551953316,
0.02204866148531437,
-0.032157838344573975,
-0.0036574052646756172,
-0.02305326983332634,
-0.025243114680051804,
0.022124702110886574,
0.02527199126780033,
-0.006534931715577841,
0.005610687658190727,
-0.026823865249753,
-0.02049565315246582,
0.0037473589181900024,
0.02963137812912464,
-0.002707122592255473,
-0.0419386550784111,
0.002809287514537573,
0.036487989127635956,
0.0015015964163467288,
-0.009868121705949306,
-0.025015508756041527,
-0.02935897558927536,
0.04785560816526413,
0.02188899926841259,
0.01964397169649601,
-0.024227065965533257,
-0.024274321272969246,
-0.019769418984651566,
-0.0717453882098198,
0.039805468171834946,
-0.011998356319963932,
0.016988076269626617,
-0.07062839716672897,
0.005709621123969555,
-0.02409535087645054,
0.004693802446126938,
0.07165646553039551,
0.011584331281483173,
-0.02887638472020626,
0.016687557101249695,
-0.008602699264883995,
0.01938764937222004,
-0.006937623023986816,
-0.008019114844501019,
-0.02586609497666359,
-0.027049323543906212,
-0.015324012376368046,
-0.024737799540162086,
-0.034839652478694916,
0.021660715341567993,
-0.018446553498506546,
0.00229990528896451,
0.027219193056225777,
-0.003969554323703051,
-0.02766779065132141,
0.06134558096528053,
0.037715740501880646,
-0.015989216044545174,
0.06520780175924301,
-0.017590966075658798,
0.03513287752866745,
0.05453279986977577,
-0.01725972257554531,
-0.02530674822628498,
0.01464785635471344,
-0.0310479998588562,
-0.0147103825584054,
-0.011777514591813087,
-0.035859040915966034,
0.028006961569190025,
-0.04604737460613251,
0.005757346283644438,
0.04205387458205223,
-0.01767718605697155,
-0.0006362287094816566,
0.033946044743061066,
0.014140100218355656,
0.04023949056863785,
0.003251548856496811,
0.005553199909627438,
0.02781832218170166,
0.027202406898140907,
0.00450994772836566,
0.06335178762674332,
0.015580490231513977,
-0.007718319073319435,
0.03345087170600891,
0.03296211361885071,
-0.003758971579372883,
0.03569681942462921,
0.02497226744890213,
0.04220001772046089,
0.0009937622817233205,
-0.015381687320768833,
0.017665792256593704,
-0.04082966595888138,
0.019549360498785973,
0.02088209055364132,
-0.040729936212301254,
0.08707932382822037,
-0.03992709517478943,
0.029185837134718895,
-0.033025939017534256,
0.019850442185997963,
-0.01710166037082672,
0.00012739341764245182,
0.025119999423623085,
0.04151586815714836,
-0.014719350263476372,
-0.010925306007266045,
-0.022115103900432587,
0.009363245218992233,
0.01848887838423252,
-0.03563347086310387,
0.03280721604824066,
0.01354173757135868,
-0.023811187595129013,
-0.054511282593011856,
-0.011154777370393276,
-0.00040794728556647897,
-0.013635518029332161,
0.011957583948969841,
0.03685595467686653,
0.03854743391275406,
-0.021302038803696632,
-0.0004164417623542249,
-0.023983778432011604,
0.03445211052894592,
-0.0942458063364029,
-0.01572757214307785,
-0.015031815506517887,
0.02596760168671608,
-0.0538095198571682,
0.01088645774871111
] |
<p>Am I correct in assuming it is the weight of all that liquid + gravity?</p> | 2,841 | [
-0.04613371193408966,
-0.04200311005115509,
-0.01896410994231701,
-0.0138416001573205,
0.051126256585121155,
-0.006441401783376932,
-0.010677372105419636,
-0.014659592881798744,
-0.01146718580275774,
-0.005937904119491577,
0.024226196110248566,
0.061018206179142,
0.050825320184230804,
0.010924864560365677,
0.0069352383725345135,
0.028727876022458076,
0.00754984887316823,
0.009408640675246716,
0.02346387505531311,
-0.035946473479270935,
0.015525230206549168,
0.025302782654762268,
0.010533266700804234,
0.012781821191310883,
-0.038858942687511444,
0.0389191135764122,
0.03299069404602051,
-0.021128904074430466,
0.031195616349577904,
0.05685374140739441,
0.01969279535114765,
-0.031743455678224564,
0.018561730161309242,
0.03772738575935364,
0.05007493495941162,
0.005824356805533171,
-0.04143610596656799,
-0.012387524358928204,
-0.02914438024163246,
0.051202401518821716,
-0.03452486917376518,
-0.009457849897444248,
-0.01565050520002842,
0.04020422697067261,
-0.013483485206961632,
0.017871202901005745,
-0.013775617815554142,
-0.02100347727537155,
0.023512249812483788,
-0.09359491616487503,
0.06430799514055252,
0.028621375560760498,
0.04632054269313812,
0.0212754774838686,
-0.014426035806536674,
-0.005926001816987991,
0.09477783739566803,
0.052310798317193985,
-0.01223593670874834,
-0.038193479180336,
-0.015903010964393616,
0.013780076988041401,
-0.005064257886260748,
-0.02926342561841011,
0.005881165619939566,
-0.004106847103685141,
-0.025781484320759773,
-0.012652321718633175,
0.02202962152659893,
0.0031257872469723225,
0.0032311719842255116,
0.006892568431794643,
0.05041185021400452,
0.008063025772571564,
0.013284011743962765,
-0.011853812262415886,
0.008560818620026112,
0.04185689613223076,
0.009403114207088947,
0.03602961078286171,
-0.04051841422915459,
0.0010956476908177137,
0.025722777470946312,
0.05265985429286957,
0.019170695915818214,
0.009532059542834759,
0.06468655914068222,
0.00618967367336154,
0.01392076350748539,
0.05459556728601456,
-0.020847000181674957,
-0.007022436708211899,
-0.008174899034202099,
-0.021037615835666656,
-0.014032317325472832,
-0.029715808108448982,
-0.005738118197768927,
0.03544432669878006,
0.02299044281244278,
-0.015051988884806633,
0.02683187648653984,
-0.017244815826416016,
-0.00044770591193810105,
0.10508096218109131,
0.0008692991686984897,
-0.010923650115728378,
-0.03368920087814331,
0.006508153863251209,
0.019694466143846512,
-0.001045167911797762,
-0.026834579184651375,
-0.02722841687500477,
0.0020553837530314922,
-0.04773302376270294,
-0.003727409988641739,
-0.021460186690092087,
0.028803154826164246,
-0.005656410939991474,
0.024846985936164856,
0.03780069202184677,
0.01141927670687437,
-0.023336833342909813,
0.0371265709400177,
-0.004342859145253897,
-0.03860316053032875,
0.07501594722270966,
0.03460345044732094,
-0.03070259466767311,
-0.0463520810008049,
0.015579205006361008,
-0.025042839348316193,
-0.018724460154771805,
0.0067160543985664845,
-0.0002333436714252457,
0.022827913984656334,
-0.021138718351721764,
-0.09160564839839935,
-0.06902607530355453,
0.04311128705739975,
-0.03218933939933777,
-0.03660345822572708,
-0.06859920918941498,
0.016967110335826874,
0.028555145487189293,
0.04971764236688614,
-0.013108165003359318,
0.04052684083580971,
-0.008155505172908306,
-0.00007326495688175783,
0.009363126941025257,
-0.012439198791980743,
-0.018825994804501534,
0.009231320582330227,
-0.061600495129823685,
0.005697079934179783,
-0.07552023977041245,
-0.018274230882525444,
0.055126797407865524,
0.014791436493396759,
-0.02655082754790783,
0.037564877420663834,
-0.036089904606342316,
0.004431318491697311,
0.014909747056663036,
0.00838034600019455,
-0.06144675239920616,
0.07710609585046768,
0.00637774495407939,
-0.014025175012648106,
0.0267585888504982,
0.003159379353746772,
0.029849646613001823,
0.03280918300151825,
0.01168083120137453,
0.049337610602378845,
-0.024575987830758095,
-0.020605916157364845,
-0.05386890843510628,
0.011550438590347767,
0.015543369576334953,
-0.04268907755613327,
-0.03531408682465553,
-0.007963483221828938,
-0.012023404240608215,
0.025916097685694695,
0.060950689017772675,
-0.00014877962530590594,
-0.05048465356230736,
0.012613890692591667,
-0.03280385211110115,
-0.009741268120706081,
-0.05296247825026512,
0.012108497321605682,
-0.025367004796862602,
0.022432096302509308,
0.006860487628728151,
0.02510767988860607,
0.025618303567171097,
-0.04193972796201706,
-0.03391590714454651,
-0.0009321125107817352,
0.025305500254034996,
0.0009095947025343776,
-0.01569642312824726,
0.03054937534034252,
0.05618767812848091,
0.02196461521089077,
0.00015144917415454984,
-0.013140940107405186,
-0.01358936820179224,
-0.024314675480127335,
-0.01689866930246353,
-0.02644798904657364,
0.022687727585434914,
-0.04112258553504944,
-0.015576607547700405,
0.01810562051832676,
-0.0002223733754362911,
0.02835153229534626,
0.03680489957332611,
-0.021045759320259094,
0.08884934335947037,
0.03674108162522316,
-0.01263920683413744,
0.007615488953888416,
0.018175754696130753,
0.001914685359224677,
0.03743002563714981,
0.0033751565497368574,
-0.012933386489748955,
-0.04985357075929642,
-0.01602792739868164,
0.01640365459024906,
0.02239840291440487,
0.027519099414348602,
-0.0020103000570088625,
0.020449571311473846,
0.07026258111000061,
0.02910032868385315,
0.00046209964784793556,
-0.014652445912361145,
-0.003278049873188138,
-0.007172436453402042,
0.024274837225675583,
0.020123200491070747,
0.001203058985993266,
0.019352780655026436,
0.05794011056423187,
0.02059728279709816,
-0.034120310097932816,
-0.014794883318245411,
0.00937135424464941,
0.021805504336953163,
0.01845421828329563,
-0.026827985420823097,
-0.028033101931214333,
0.04839072376489639,
-0.0664430484175682,
0.022275704890489578,
0.015248813666403294,
0.0045144883915781975,
-0.01065991073846817,
-0.0617741122841835,
-0.029924895614385605,
0.02550474740564823,
0.004423647187650204,
-0.010249536484479904,
0.007764149457216263,
0.03710496798157692,
-0.039153631776571274,
0.017256498336791992,
-0.017320340499281883,
-0.0120084872469306,
0.016994142904877663,
0.037567075341939926,
0.008990219794213772,
-0.0025973087176680565,
0.03458932414650917,
-0.013098964467644691,
-0.033807020634412766,
0.0009547213558107615,
-0.03468981757760048,
-0.036908965557813644,
0.01997537538409233,
-0.0598926916718483,
-0.00047912559239193797,
-0.013929425738751888,
-0.014010963961482048,
0.07165088504552841,
0.022509945556521416,
0.006341021973639727,
0.01857849396765232,
-0.008259243331849575,
0.002404050901532173,
-0.0070221563801169395,
-0.03207017853856087,
0.009327549487352371,
-0.03494713827967644,
0.02176252193748951,
0.03224606439471245,
-0.006291782949119806,
-0.031178198754787445,
-0.0028903568163514137,
-0.030084963887929916,
-0.045898888260126114,
-0.005312440916895866,
0.02369370311498642,
-0.012569689191877842,
-0.06503406912088394,
0.018112532794475555,
0.026622576639056206,
-0.05711124837398529,
-0.0017476128414273262,
-0.043834686279296875,
-0.05362405627965927,
0.053297966718673706,
-0.02422317862510681,
0.04079710319638252,
-0.015147989615797997,
-0.06949608772993088,
0.06919826567173004,
-0.000008791533218754921,
-0.04656842723488808,
-0.030912179499864578,
-0.0069051883183419704,
0.013287468813359737,
-0.0010252007050439715,
0.017377803102135658,
0.03808494657278061,
0.0026709262747317553,
0.017253996804356575,
0.03866421431303024,
0.003138445084914565,
0.005508579779416323,
0.029136531054973602,
0.03548899665474892,
0.021996967494487762,
0.027764495462179184,
-0.003446748247370124,
0.042818520218133926,
-0.006050220690667629,
0.00023024015536066145,
0.028617022559046745,
-0.020980985835194588,
0.062449466437101364,
-0.007626747712492943,
-0.0313086062669754,
0.06007932499051094,
0.023382116109132767,
0.024884849786758423,
-0.014588851481676102,
0.0362677238881588,
-0.0068145133554935455,
-0.005631921347230673,
0.03342660143971443,
0.017912620678544044,
0.055126141756772995,
0.00797351635992527,
-0.024764129891991615,
0.027151616290211678,
0.05732358619570732,
-0.014565856195986271,
-0.08308101445436478,
-0.014429883100092411,
-0.022775139659643173,
0.017297301441431046,
-0.02948901616036892,
-0.014314144849777222,
0.047577500343322754,
-0.003788923379033804,
0.027461038902401924,
-0.020261075347661972,
-0.054017312824726105,
-0.017996707931160927,
-0.0807410478591919,
-0.023485513404011726,
0.008894992992281914,
0.011765766888856888,
-0.0074969870038330555,
0.0730503723025322,
0.017793597653508186,
0.033087313175201416,
0.014798352494835854,
0.01696162484586239,
-0.0837286114692688,
-0.02706247568130493,
-0.05061236768960953,
0.006235597189515829,
0.019028134644031525,
-0.027043361216783524,
-0.008990866132080555,
-0.040838196873664856,
-0.020449019968509674,
-0.027390023693442345,
0.012897086329758167,
-0.0248249638825655,
0.0177829060703516,
0.006020842585712671,
-0.007845623418688774,
0.008930938318371773,
0.011554775759577751,
0.024732889607548714,
-0.0030500786378979683,
0.01878887228667736,
0.044852402061223984,
0.005098931025713682,
-0.029928551986813545,
-0.012749522924423218,
0.03418365865945816,
0.005295973736792803,
0.010178789496421814,
0.01533606555312872,
0.002234202576801181,
-0.01709790900349617,
-0.0026218818966299295,
-0.038152262568473816,
0.0038940240629017353,
-0.008549937047064304,
-0.011108079925179482,
-0.051531966775655746,
-0.048115648329257965,
-0.01903451606631279,
0.026990104466676712,
0.004051217809319496,
-0.0033772368915379047,
0.03885340318083763,
0.025027964264154434,
-0.014905148185789585,
-0.027835946530103683,
0.06561358273029327,
0.08696486055850983,
0.01540772058069706,
-0.028531191870570183,
-0.030009809881448746,
-0.0016436638543382287,
-0.044345274567604065,
-0.00521397078409791,
0.03776034340262413,
0.03168409690260887,
-0.027629787102341652,
-0.012162863276898861,
0.016014620661735535,
-0.04587709903717041,
-0.023532267659902573,
-0.038945868611335754,
0.015315965749323368,
0.03847511485219002,
-0.05789244547486305,
0.0063606807962059975,
0.035349391400814056,
0.028614606708288193,
0.013906678184866905,
-0.002916236175224185,
-0.022942161187529564,
-0.10106665641069412,
-0.04249314218759537,
0.01477213017642498,
0.03711191937327385,
-0.014532427303493023,
-0.014372406527400017,
-0.042469143867492676,
-0.04970613121986389,
0.028503229841589928,
-0.016155380755662918,
0.020326385274529457,
0.005540916230529547,
0.022494478151202202,
0.0064992886036634445,
-0.045963726937770844,
0.021207593381404877,
0.012033599428832531,
-0.030725279822945595,
0.02474096044898033,
0.004373778123408556,
0.024002471938729286,
0.0002937562530860305,
0.03152984753251076,
0.007125203963369131,
0.03793695941567421,
0.043766554445028305,
-0.0078062089160084724,
-0.0282342117279768,
0.03267158195376396,
-0.06137080863118172,
-0.0660804733633995,
-0.0263751782476902,
-0.011083755642175674,
0.0015277297934517264,
0.011615527793765068,
-0.01849709264934063,
-0.08722689747810364,
0.039164233952760696,
0.02533046342432499,
0.0042060245759785175,
0.008135301992297173,
-0.04463646188378334,
0.0372794084250927,
0.0536196194589138,
0.015544268302619457,
0.0442802757024765,
-0.0015274507459253073,
-0.023050321266055107,
-0.020132867619395256,
-0.01730894297361374,
0.04312700033187866,
-0.04104866459965706,
-0.037197455763816833,
-0.00844087079167366,
0.04707394540309906,
-0.04531507194042206,
0.017081422731280327,
0.01592131331562996,
0.0034816546831279993,
0.016330985352396965,
-0.0620315745472908,
-0.0199472326785326,
-0.01186954416334629,
0.05441391468048096,
-0.027916014194488525,
0.00872700847685337,
0.009835412725806236,
0.02225540764629841,
-0.017313063144683838,
0.03448042273521423,
0.008061075583100319,
-0.004086385481059551,
0.021578945219516754,
-0.004911008756607771,
0.041821062564849854,
0.0022766515612602234,
-0.008088364265859127,
0.03242669254541397,
-0.03451632708311081,
0.04146788269281387,
-0.01865336298942566,
0.02654038742184639,
-0.015814214944839478,
-0.0744280070066452,
-0.026558097451925278,
0.00613554660230875,
0.0055240909568965435,
0.035693809390068054,
-0.028835341334342957,
0.0057860785163939,
0.025649569928646088,
0.019530875608325005,
-0.07161855697631836,
-0.03785734996199608,
0.05079582706093788,
0.03980552777647972,
-0.0027194726280868053,
-0.024248339235782623,
0.002316370140761137,
-0.02474396303296089,
-0.033138152211904526,
-0.007698934059590101,
0.014345234259963036,
-0.026793373748660088,
-0.009970000013709068,
0.023953888565301895,
0.01596161723136902,
0.058668121695518494,
0.03786039352416992,
-0.026217039674520493,
0.001295873080380261,
-0.031456854194402695,
-0.00572206312790513,
0.0004209585895296186,
0.04539669677615166,
-0.036697544157505035,
-0.0049627842381596565,
-0.02118709869682789,
-0.049185607582330704,
0.017273519188165665,
-0.0309902373701334,
0.016080331057310104,
0.012591298669576645,
0.03681710362434387,
-0.03451284021139145,
-0.017177319154143333,
0.037054091691970825,
-0.00240949634462595,
0.035672061145305634,
0.0030259417835623026,
-0.01803780533373356,
-0.014090757817029953,
0.001265538390725851,
0.03285801038146019,
0.007153273094445467,
-0.026836954057216644,
-0.01100939977914095,
0.06335138529539108,
0.017186706885695457,
-0.04633649066090584,
0.015091236680746078,
-0.01075520645827055,
0.012628906406462193,
0.029414763674139977,
-0.01697128266096115,
0.030285174027085304,
0.02629256248474121,
-0.024921393021941185,
-0.03453459218144417,
-0.06296607851982117,
0.01771802268922329,
0.05435405671596527,
-0.018409423530101776,
0.04379415884613991,
0.01870582066476345,
-0.016051216050982475,
0.02888685092329979,
-0.00903383269906044,
-0.005742387846112251,
0.029446076601743698,
-0.03810826689004898,
0.026451943442225456,
-0.026719100773334503,
-0.02648933231830597,
0.027741780504584312,
0.008656700141727924,
-0.03356831893324852,
0.002408654196187854,
0.05413967743515968,
-0.014716587029397488,
-0.015170655213296413,
-0.017834078520536423,
-0.061348624527454376,
0.03751571476459503,
-0.011116852052509785,
0.04049856215715408,
-0.017499126493930817,
-0.03120579943060875,
0.05480458214879036,
-0.0028392586391419172,
0.017216363921761513,
-0.047644954174757004,
-0.021158529445528984,
-0.01705218479037285,
-0.0018159790197387338,
0.026301709935069084,
0.028237011283636093,
0.009956181049346924,
0.009171673096716404,
0.004681429825723171,
0.027243545278906822,
0.015889810398221016,
0.008736776188015938,
-0.0525134839117527,
-0.00749613344669342,
-0.005829425062984228,
-0.04291258379817009,
0.0015834257937967777,
-0.006544778123497963,
-0.02262093313038349,
0.025312982499599457,
-0.021529965102672577,
-0.012415913864970207,
0.01926163211464882,
0.03045286051928997,
-0.022537827491760254,
0.08434110134840012,
-0.009332255460321903,
0.013533740304410458,
-0.021247433498501778,
0.00714363856241107,
0.12087584286928177,
0.054871637374162674,
0.006550658028572798,
-0.06977793574333191,
-0.024542324244976044,
-0.021361349150538445,
0.006485839374363422,
-0.030098287388682365,
-0.005718054249882698,
-0.023106198757886887,
0.009991733357310295,
0.000011748863471439108,
0.03039456345140934,
-0.02713540568947792,
0.002829901175573468,
0.008548961021006107,
-0.034606121480464935,
-0.02243860252201557,
0.019092675298452377,
-0.001039172406308353,
-0.028881411999464035,
0.003767105285078287,
-0.015766823664307594,
0.0416940376162529,
-0.005962997209280729,
-0.01604967564344406,
-0.02389044314622879,
-0.012974146753549576,
-0.011496725492179394,
0.008070406503975391,
-0.060790836811065674,
0.01782447099685669,
0.0025160093791782856,
-0.01875445432960987,
-0.055723801255226135,
0.048313241451978683,
0.020267657935619354,
-0.02507021091878414,
-0.0023341947235167027,
-0.0019920452032238245,
-0.006835006643086672,
0.009851984679698944,
-0.025555992498993874,
-0.013553759083151817,
-0.05435648187994957,
-0.018356114625930786,
-0.02740183286368847,
0.03297119587659836,
-0.0040885694324970245,
0.025608912110328674,
0.02579519897699356,
-0.009348787367343903,
-0.013644919730722904,
-0.08191743493080139,
0.00463218055665493,
0.0077819605357944965,
0.044003382325172424,
0.0019184616394340992,
-0.02998109720647335,
-0.015427281148731709,
-0.013102157041430473,
-0.004789335187524557,
0.013064992614090443,
0.010554603300988674,
0.0226370207965374,
0.005101238377392292,
-0.01611935906112194,
0.04024031385779381,
-0.005793141201138496,
-0.02132824994623661,
-0.03867466002702713,
-0.01722368225455284,
-0.06390871107578278,
-0.017278088256716728,
-0.006694135256111622,
0.03663627803325653,
0.01498498022556305,
-0.008804290555417538,
0.018019484356045723,
-0.017723824828863144,
-0.04029601439833641,
0.05918295681476593,
-0.04557620733976364,
-0.01930706575512886,
-0.05780957266688347,
0.008948254399001598,
-0.0018383290152996778,
0.0374467633664608,
-0.013833438977599144,
0.0477689653635025,
-0.011848545633256435,
0.0514264851808548,
0.009238970465958118,
-0.03503613546490669,
0.013560948893427849,
0.022162489593029022,
-0.02238171361386776,
0.021109357476234436,
0.03584922105073929,
0.02410634607076645,
0.03185868635773659,
0.007304886355996132,
-0.014331006444990635,
0.006810999475419521,
-0.025872133672237396,
0.026873981580138206,
-0.0018088751239702106,
-0.01742386631667614,
-0.029400983825325966,
0.016016632318496704,
-0.01975162886083126,
-0.028534291312098503,
-0.02751781977713108,
-0.04155617579817772,
-0.010504740290343761,
-0.004912679083645344,
0.02682684361934662,
-0.03854668512940407,
0.03748416155576706,
0.00295268464833498,
0.02026149071753025,
-0.04003467410802841,
0.039298560470342636,
-0.0635463073849678,
-0.02463686279952526,
0.018710438162088394,
-0.005403522402048111,
-0.010219098068773746,
0.018880201503634453,
-0.02891313098371029,
0.008514869026839733,
0.027927055954933167,
-0.013635031878948212,
0.02857004851102829,
-0.011361030861735344,
0.038986414670944214,
-0.005669853650033474,
0.05211329460144043,
-0.04221644997596741,
-0.012599993497133255,
0.04639056697487831,
-0.03246891871094704,
-0.01990147866308689,
0.027210868895053864,
-0.019201846793293953,
0.03645119443535805,
0.03712817281484604,
-0.008765134029090405,
-0.012054679915308952,
0.0677378922700882,
-0.017748208716511726,
-0.0004029185511171818,
-0.02369404025375843,
-0.006489183753728867,
0.03148491308093071,
-0.0026556311640888453,
-0.012852988205850124,
0.0275851059705019,
0.03325244411826134,
0.04066925123333931,
0.027997709810733795,
-0.0035637530963867903,
0.014263012446463108,
0.013389495201408863,
-0.011918316595256329,
0.002058830577880144,
0.0362243615090847,
-0.004567498341202736,
-0.0028385864570736885,
0.037035923451185226,
-0.05078916996717453,
0.02071303129196167,
0.01613095961511135,
-0.019832471385598183,
-0.09002272039651871,
-0.020732248201966286,
-0.034652743488550186,
-0.006835695821791887,
0.021484654396772385,
-0.06048007309436798,
0.03319351002573967,
0.009754923172295094,
-0.05204281210899353,
0.0006147888489067554,
-0.0629051923751831,
-0.009148109704256058,
-0.010511850006878376,
0.010740473866462708,
-0.0021083487663418055,
0.03725803270936012,
0.007551254704594612,
0.04518274590373039,
0.037205953150987625,
0.01025147084146738,
-0.00892174057662487,
-0.026786495000123978,
-0.00017590900824870914,
0.04013046622276306,
-0.021225804463028908,
0.004018704406917095,
0.03433636203408241,
-0.027072153985500336,
-0.02960933931171894,
0.04311145097017288,
0.021433528512716293,
0.040416132658720016,
-0.01263186801224947,
0.05265403166413307,
-0.0009490826050750911,
0.028648192062973976,
-0.004552486818283796,
-0.013594323769211769,
-0.031171441078186035,
0.046930063515901566,
0.011810295283794403,
0.05222533643245697,
-0.013683389872312546,
0.0073255631141364574,
-0.022070758044719696,
-0.04910473898053169,
-0.006289666518568993,
0.04149527847766876,
-0.03827033191919327,
0.025882676243782043,
-0.014127190224826336,
-0.0004911154392175376,
0.018516575917601585,
-0.025492561981081963,
-0.00020873923494946212,
-0.04416535794734955,
0.01394151896238327,
0.06391628086566925,
0.0039939479902386665,
-0.039855655282735825,
0.008036341518163681,
0.019237911328673363,
-0.01659606769680977,
-0.03854499012231827,
-0.011844014748930931,
-0.06641227006912231,
-0.03572364151477814,
-0.002338262740522623,
-0.022962123155593872,
-0.019915584474802017,
0.010170784778892994,
-0.043036606162786484,
-0.06623919308185577,
0.03168468177318573,
0.03127642348408699,
0.01724241115152836,
0.030298981815576553,
-0.03995044156908989,
-0.004590596072375774,
-0.0781257227063179,
0.036403920501470566,
-0.003915596287697554,
-0.004055639263242483,
-0.007817553356289864,
-0.030721932649612427,
0.029926149174571037,
0.014367897994816303,
0.06320782750844955,
0.015284165740013123,
-0.020231295377016068,
-0.00422088336199522,
-0.00912739522755146,
-0.003882387187331915,
-0.03251691907644272,
0.011413666419684887,
-0.019946016371250153,
-0.06287015229463577,
0.0023376354947686195,
0.006326515227556229,
0.019293012097477913,
-0.015786776319146156,
0.041096512228250504,
-0.016925189644098282,
0.012191235087811947,
-0.022747140377759933,
0.0025558534543961287,
0.052287884056568146,
-0.0023876058403402567,
-0.014433598145842552,
0.08612959086894989,
0.008047018200159073,
0.006566646043211222,
0.034972187131643295,
-0.0046429503709077835,
-0.0659056082367897,
0.06522597372531891,
-0.009007181040942669,
0.025604955852031708,
0.01022311020642519,
0.023058297112584114,
0.020533347502350807,
-0.027263475582003593,
0.00803245510905981,
0.038747455924749374,
-0.01191504392772913,
-0.042372629046440125,
0.040520962327718735,
0.02399241179227829,
0.03420586511492729,
-0.01446889340877533,
0.00627189502120018,
0.018005209043622017,
0.002223755931481719,
-0.00015523532056249678,
0.053176797926425934,
0.08713430166244507,
0.02104501612484455,
-0.02699577808380127,
0.025413870811462402,
0.004819421097636223,
0.01580604538321495,
0.031851138919591904,
-0.005782979540526867,
-0.054734013974666595,
-0.058660682290792465,
-0.015753841027617455,
-0.028913291171193123,
0.02309197187423706,
0.02073037438094616,
-0.004246689844876528,
0.08760597556829453,
0.024942096322774887,
-0.009063205681741238,
-0.00826506782323122,
-0.020453475415706635,
0.004991038702428341,
0.012424075044691563,
0.01232146192342043,
0.01949528232216835,
0.0027577292639762163,
-0.012911406345665455,
0.011776575818657875,
0.0030568537767976522,
-0.0035174652002751827,
-0.009957490488886833,
0.010328814387321472,
0.005916162859648466,
-0.000260919303400442,
-0.038539331406354904,
-0.027552619576454163,
-0.02520224265754223,
-0.017849119380116463,
0.019431956112384796,
0.03658207133412361,
0.004437913186848164,
0.025937743484973907,
-0.004625560250133276,
-0.016330191865563393,
0.06185481324791908,
-0.05301377922296524,
-0.011809366755187511,
-0.020073188468813896,
0.03609243780374527,
0.0164719820022583,
-0.018411563709378242
] |
<p>By chance(playing around really) I saw that a spring(mainly from a pen) placed on a neodymium hard-disk magnet(and then flicked by your finger at the top) makes a nice-effect (see youtube video ). It appears to oscillate in slow-motion(looks like tornado).</p>
<p>Of course, "slow-motion" is purposely simplistic and unscientific - I am very far from a physicist. </p>
<p>Here's the video - <a href="http://www.youtube.com/watch?v=n0OJQ1iXZg0&feature=channel_video_title" rel="nofollow">http://www.youtube.com/watch?v=n0OJQ1iXZg0&feature=channel_video_title</a> </p>
<p>I was too impatient in the video though, I should have zoomed in on the spring and waited. Sorry about that.. </p>
<p>Here's a page about the magnets used:
<a href="http://www.reuk.co.uk/Hard-Disk-Drive-Magnets-For-Wind-Turbines.htm" rel="nofollow">http://www.reuk.co.uk/Hard-Disk-Drive-Magnets-For-Wind-Turbines.htm</a></p>
<p>Here are the polarities, plus a horizontal profile below:</p>
<p><img src="http://i.stack.imgur.com/7krCW.jpg" alt="enter image description here"></p>
<p><img src="http://i.stack.imgur.com/fPLEl.png" alt="enter image description here"></p>
<p>More details: You really want to use a retractable pen spring, the thin kind. And Hard-drive magnets are key - I think it doesn't work with others. I think it's partly because of the 4-poles of a neodymium magnet. i.e, it's actually two-magnets-in-one.
Cigarette lighters also have a long delicate magnet, which is good but too tipsy.<br>
LBNL, supposedly you can stack these magnets, but they seem impossible to separate from the backing-piece. I appreciate any tips or advice.</p> | 2,842 | [
-0.053630754351615906,
-0.016515983268618584,
0.00027121230959892273,
-0.060141369700431824,
0.032961390912532806,
0.014302612282335758,
-0.051981255412101746,
-0.005023571662604809,
-0.019794177263975143,
-0.046138666570186615,
0.013497676700353622,
0.08327453583478928,
0.05280650407075882,
0.04255310446023941,
0.00967639684677124,
-0.02744470350444317,
0.021563725546002388,
-0.028247719630599022,
-0.009464854374527931,
-0.04025135934352875,
-0.003022925928235054,
-0.036660999059677124,
-0.054805707186460495,
0.006591986399143934,
0.0013087325496599078,
0.01195112057030201,
0.008267068304121494,
-0.00582240941002965,
-0.015571021474897861,
0.021305875852704048,
-0.0005335542373359203,
-0.041136518120765686,
-0.0003854001988656819,
-0.007756371051073074,
0.05927059426903725,
-0.01638137176632881,
-0.014473434537649155,
-0.003478058148175478,
0.00119405600707978,
0.02771334908902645,
-0.0033807626459747553,
-0.0021923366002738476,
-0.02608433924615383,
0.03029412031173706,
-0.029446713626384735,
-0.0015515589620918036,
0.01650271750986576,
-0.013882734812796116,
0.08849534392356873,
-0.03918176516890526,
0.04474053904414177,
-0.00646989606320858,
0.0020374306477606297,
0.004403827246278524,
0.010661795735359192,
-0.026563534513115883,
0.07841072231531143,
0.049180012196302414,
-0.03278949111700058,
-0.05112259089946747,
0.005500267259776592,
0.008837452158331871,
-0.00756906857714057,
-0.04533851891756058,
-0.01820943132042885,
0.02075181156396866,
0.047807954251766205,
0.01394256018102169,
0.05015196651220322,
0.024203361943364143,
0.012754715047776699,
-0.005575114861130714,
0.05511775240302086,
0.019142407923936844,
-0.030624408274888992,
-0.04132363572716713,
0.0020505168940871954,
-0.004852331709116697,
0.03791109472513199,
0.015740154311060905,
-0.04448024183511734,
0.021368440240621567,
0.018763085827231407,
0.02944866754114628,
0.03402708098292351,
0.031593263149261475,
0.0723094642162323,
-0.04888071492314339,
0.018484126776456833,
0.007487662136554718,
0.028492344543337822,
0.005957186687737703,
0.05678516998887062,
-0.03009042888879776,
-0.016037534922361374,
0.06606146693229675,
0.022509418427944183,
0.030729424208402634,
0.008299778215587139,
-0.004126927349716425,
-0.004909614101052284,
0.028839658945798874,
-0.0124819315969944,
0.07087548822164536,
0.036750275641679764,
-0.054073184728622437,
0.006113589741289616,
0.01498806569725275,
-0.02637018822133541,
-0.03535609692335129,
-0.035798002034425735,
0.007156187202781439,
-0.001672105398029089,
-0.027270445600152016,
-0.0039309002459049225,
-0.048899345099925995,
0.006424788851290941,
0.025891896337270737,
0.04962325841188431,
0.05079658702015877,
0.007196670398116112,
-0.05240795388817787,
0.004666805267333984,
-0.03589843958616257,
-0.035101886838674545,
-0.009603367187082767,
0.0690062865614891,
-0.022931445389986038,
-0.03291818127036095,
-0.00956715364009142,
0.0198031235486269,
-0.010239052586257458,
0.017703836783766747,
-0.0017140607815235853,
0.03446759283542633,
0.01870434172451496,
-0.07716218382120132,
-0.0026553452480584383,
0.06574688851833344,
-0.01679595187306404,
0.018865590915083885,
-0.05516688525676727,
-0.028124094009399414,
0.03925297036767006,
0.0662730410695076,
0.00529772974550724,
-0.0022338221315294504,
-0.05311748385429382,
0.02705243229866028,
-0.005487395450472832,
-0.029965544119477272,
0.011049527674913406,
-0.009850379079580307,
-0.07326193153858185,
-0.03596673905849457,
-0.03453940525650978,
0.03686947375535965,
0.06025693565607071,
0.02302217297255993,
-0.0015655625611543655,
0.03680534288287163,
-0.015027142129838467,
0.01639813371002674,
0.0033618456218391657,
-0.0015993118286132812,
-0.04387203976511955,
0.0336812362074852,
-0.020050328224897385,
0.006326782982796431,
0.011912744492292404,
-0.05513285472989082,
0.04722166806459427,
-0.01032949984073639,
-0.01095143985003233,
0.06650786101818085,
-0.026185443624854088,
-0.002778394380584359,
-0.031119152903556824,
0.012718282639980316,
-0.0026432396844029427,
-0.045041490346193314,
-0.026714667677879333,
-0.012080859392881393,
-0.020485475659370422,
-0.022738846018910408,
0.06025483459234238,
0.0003050159430131316,
-0.013756036758422852,
-0.00776216434314847,
-0.044278085231781006,
0.007830752991139889,
-0.009137080982327461,
0.026307381689548492,
-0.06548775732517242,
-0.01076362282037735,
0.023919830098748207,
-0.005094682332128286,
0.022274000570178032,
-0.006491625215858221,
-0.0499400794506073,
-0.016485469415783882,
0.02326895482838154,
0.030822468921542168,
0.015051278285682201,
-0.029486987739801407,
0.037296973168849945,
-0.007320717442780733,
-0.013269021175801754,
0.04678017273545265,
-0.013229427859187126,
-0.03247975930571556,
0.012291117571294308,
-0.016515439376235008,
-0.006661164574325085,
0.027528513222932816,
-0.04290850833058357,
0.028453975915908813,
0.03555743768811226,
0.021389711648225784,
-0.04020150005817413,
-0.02094578556716442,
0.0434260219335556,
0.05410347878932953,
-0.03358834609389305,
0.029298704117536545,
0.023034948855638504,
0.04801105707883835,
0.04360291361808777,
-0.012236402370035648,
0.006276371888816357,
-0.047428347170352936,
-0.006618510466068983,
0.05265986546874046,
0.05442265793681145,
-0.04844111576676369,
0.023669397458434105,
0.027290407568216324,
0.019419319927692413,
0.01986621879041195,
0.015642989426851273,
0.024635156616568565,
-0.0035181192215532064,
-0.027055297046899796,
0.04969234764575958,
-0.004089335445314646,
0.012034093029797077,
0.055706340819597244,
0.004838873166590929,
0.0179347675293684,
0.0007808682275936007,
-0.023572295904159546,
0.03151264414191246,
-0.016042066738009453,
0.0028471576515585184,
0.013124714605510235,
-0.02251862734556198,
0.035761214792728424,
0.000014899541383783799,
0.01354171708226204,
-0.019640404731035233,
0.031833481043577194,
0.0508321151137352,
0.014230388216674328,
0.0011983659351244569,
-0.01191425509750843,
-0.004769438877701759,
-0.0028487988747656345,
-0.03860236331820488,
0.043851643800735474,
-0.03189407289028168,
0.0035206342581659555,
-0.03266338258981705,
-0.014545775018632412,
0.016168273985385895,
-0.019282406195998192,
0.010656077414751053,
0.06677360832691193,
0.01131194643676281,
0.022502554580569267,
-0.007616107352077961,
-0.006457923911511898,
-0.01044484879821539,
-0.005715672858059406,
0.03540108725428581,
-0.06196393072605133,
0.005930469371378422,
-0.023446977138519287,
-0.023732515051960945,
0.03304300084710121,
0.027818240225315094,
-0.005362553987652063,
0.012471327558159828,
0.014356843195855618,
-0.05939799174666405,
-0.02216128446161747,
-0.02603892795741558,
0.00027714422321878374,
-0.06274008750915527,
0.005569193046540022,
0.035878535360097885,
-0.005768420174717903,
-0.05005360022187233,
0.016154712066054344,
-0.032913513481616974,
-0.026186242699623108,
-0.009098748676478863,
-0.02869781292974949,
0.012446778826415539,
-0.023725084960460663,
0.016635600477457047,
-0.00891371350735426,
-0.02237483486533165,
-0.012250065803527832,
-0.051258619874715805,
-0.0034994774032384157,
0.01034505944699049,
-0.00814119167625904,
0.08795753121376038,
-0.02258574217557907,
-0.01731373742222786,
0.08023073524236679,
0.026260046288371086,
-0.010974813252687454,
-0.017081737518310547,
-0.03539801016449928,
-0.04775835573673248,
-0.08175503462553024,
-0.010311807505786419,
0.05686339735984802,
-0.013131651096045971,
0.014648682437837124,
-0.006611861288547516,
0.008974048309028149,
0.025625450536608696,
0.008089739829301834,
-0.012929026037454605,
0.022499211132526398,
0.02268623188138008,
-0.02931688167154789,
0.08798646926879883,
0.01211100909858942,
0.004477424081414938,
0.006261177361011505,
-0.03967688977718353,
0.033966291695833206,
0.035673998296260834,
-0.036620061844587326,
0.047620952129364014,
0.005501663312315941,
0.013423284515738487,
0.0010294882813468575,
0.013445248827338219,
-0.00020196331024635583,
-0.03359748050570488,
-0.02363801747560501,
0.03755343332886696,
0.059023287147283554,
0.014542100951075554,
0.00711113540455699,
0.053876131772994995,
0.03521442040801048,
0.01849525049328804,
-0.008164070546627045,
-0.020747022703289986,
-0.02579639106988907,
-0.009501072578132153,
-0.005309574771672487,
0.008837427943944931,
0.006880364380776882,
0.012075696140527725,
-0.0010780439479276538,
0.03335107862949371,
0.007334389723837376,
0.02834588848054409,
-0.057562440633773804,
-0.0034100497141480446,
-0.008607804775238037,
0.008600622415542603,
0.02050323784351349,
0.03452010080218315,
0.027586646378040314,
0.032631538808345795,
0.0093877874314785,
-0.03269290551543236,
-0.06788503378629684,
0.05691947042942047,
-0.012506794184446335,
0.0015978660667315125,
0.0018398870015516877,
-0.001999495318159461,
-0.008747674524784088,
-0.002008710755035281,
0.024089369922876358,
-0.021076057106256485,
0.0009787851013243198,
-0.031353771686553955,
-0.013660678640007973,
0.01651332527399063,
-0.049332987517118454,
-0.013042068108916283,
0.04209388047456741,
0.03220365568995476,
-0.032035693526268005,
0.020108578726649284,
0.00694507360458374,
-0.019771071150898933,
0.014224220998585224,
-0.01576095074415207,
-0.03206767141819,
-0.01401351299136877,
0.003224714891985059,
0.02637849748134613,
-0.020731864497065544,
-0.04782240837812424,
-0.006468136794865131,
0.04398442432284355,
0.021017424762248993,
-0.0014619901776313782,
-0.005710138939321041,
-0.051683567464351654,
-0.018455998972058296,
0.005223781801760197,
0.005024508573114872,
0.07206188887357712,
-0.004968421999365091,
0.02333817258477211,
-0.009460619650781155,
-0.04666582867503166,
0.016731154173612595,
0.003426061710342765,
0.013311962597072124,
0.004239116329699755,
0.02559545263648033,
-0.056223828345537186,
-0.03915060684084892,
-0.006586592644453049,
0.008565007708966732,
-0.013014891184866428,
0.03239937126636505,
-0.012236534617841244,
-0.0009493664256297052,
0.06562773883342743,
0.008621017448604107,
-0.012311473488807678,
0.07638531178236008,
-0.011501274071633816,
-0.012658189050853252,
-0.018123457208275795,
-0.009533536620438099,
-0.018322434276342392,
0.02766355499625206,
0.03477313369512558,
-0.003967764787375927,
-0.03311070799827576,
-0.10822595655918121,
-0.017570486292243004,
0.04363635182380676,
0.016465282067656517,
-0.017416689544916153,
-0.007180265616625547,
-0.02153583988547325,
-0.02530013397336006,
0.02302410453557968,
-0.0536416620016098,
0.041433755308389664,
-0.021061653271317482,
-0.01281981635838747,
-0.04022304713726044,
-0.012526740320026875,
-0.014778485521674156,
0.014730780385434628,
-0.014763005077838898,
0.007959597744047642,
-0.020599063485860825,
-0.0400545634329319,
0.019675301387906075,
0.030232256278395653,
0.03740151226520538,
0.04051966220140457,
0.02060898207128048,
0.03427337482571602,
-0.008539186790585518,
-0.019463540986180305,
-0.05098266154527664,
-0.06880638003349304,
0.022776635363698006,
0.013734637759625912,
-0.03827090561389923,
0.02145969867706299,
-0.009768472984433174,
-0.03372066468000412,
0.005794439930468798,
-0.024880720302462578,
-0.020742783322930336,
0.009178348816931248,
-0.01668873429298401,
0.030808763578534126,
0.02542087808251381,
0.03454594314098358,
0.02990054339170456,
0.0842561423778534,
-0.04528217390179634,
0.022869296371936798,
0.00858699157834053,
-0.01681051403284073,
-0.031072551384568214,
0.007938387803733349,
-0.008866698481142521,
0.021565817296504974,
-0.0701596811413765,
0.026699645444750786,
-0.018763342872262,
0.001057245652191341,
0.0017051857430487871,
-0.0006224715616554022,
-0.031864993274211884,
0.057959508150815964,
-0.013381683267652988,
-0.0432584173977375,
0.002695399336516857,
-0.0006984686478972435,
-0.004190423525869846,
0.011226403526961803,
-0.016306711360812187,
-0.02297079935669899,
0.0022943979129195213,
0.08494355529546738,
-0.02005329728126526,
-0.026626676321029663,
-0.041404321789741516,
0.007272348739206791,
0.00559314526617527,
-0.013110257685184479,
0.05662690848112106,
-0.001229362445883453,
-0.01966763287782669,
0.020469924435019493,
-0.02742357924580574,
-0.00645348709076643,
0.013341360725462437,
-0.027527103200554848,
0.0037612030282616615,
-0.029596641659736633,
-0.040770240128040314,
0.020739814266562462,
0.007150589954108,
0.013523366302251816,
-0.04407468065619469,
0.043020084500312805,
-0.01879892311990261,
-0.011493873782455921,
-0.011294003576040268,
-0.01839369349181652,
-0.0025909501127898693,
-0.04799429327249527,
0.016641195863485336,
0.039699871093034744,
-0.06693274527788162,
-0.03132101893424988,
0.028775358572602272,
-0.004165113903582096,
0.07797928154468536,
-0.01582895591855049,
-0.03643949702382088,
0.01867225021123886,
-0.01913815177977085,
-0.015164091251790524,
-0.0506996214389801,
-0.028461387380957603,
-0.027620410546660423,
-0.02308485470712185,
0.004444355145096779,
-0.003969588782638311,
0.012829049490392208,
0.008737895637750626,
0.04696245864033699,
0.03444446250796318,
0.04410875216126442,
-0.028127258643507957,
-0.05594412237405777,
0.025894969701766968,
0.016421882435679436,
-0.007518088910728693,
-0.018256165087223053,
-0.006586400326341391,
-0.014238945208489895,
-0.07307462394237518,
0.023765042424201965,
0.025117190554738045,
-0.030684534460306168,
-0.033270757645368576,
0.08791819214820862,
-0.02463633567094803,
-0.04838573560118675,
0.02751214988529682,
-0.04593472182750702,
0.03170572221279144,
-0.01546181458979845,
0.02555641531944275,
-0.04629459232091904,
0.008056393824517727,
-0.009495404548943043,
-0.05048371106386185,
-0.019628029316663742,
0.008112192153930664,
0.04229574277997017,
-0.016342729330062866,
0.022002480924129486,
0.02521570213139057,
-0.021880127489566803,
-0.020754557102918625,
-0.017142076045274734,
-0.012632020749151707,
0.0037768047768622637,
-0.02371409721672535,
0.035599593073129654,
0.011940502561628819,
0.030366837978363037,
-0.003191738622263074,
0.01962018944323063,
0.015088008716702461,
-0.006419327110052109,
0.028919361531734467,
0.03700318560004234,
0.03608391806483269,
0.018246060237288475,
-0.028651345521211624,
0.041906651109457016,
-0.06137380376458168,
0.06641960144042969,
0.015935124829411507,
-0.019854607060551643,
-0.005179745610803366,
0.010804470628499985,
-0.013813327066600323,
-0.06446655839681625,
0.0225811917334795,
-0.04457709938287735,
-0.00196690927259624,
0.02178351581096649,
-0.03183531388640404,
-0.0013443314237520099,
-0.0061366967856884,
0.018211156129837036,
0.030765332281589508,
0.010000834241509438,
-0.00798727571964264,
-0.028547203168272972,
-0.0253128819167614,
-0.0012332748156040907,
-0.05878924950957298,
0.05501532554626465,
0.008071158081293106,
-0.01826748251914978,
0.01481359452009201,
-0.0017833338351920247,
0.05454181879758835,
0.049079738557338715,
0.017056917771697044,
-0.0033751418814063072,
0.04528196156024933,
0.002075331984087825,
0.011542941443622112,
-0.037067510187625885,
-0.027454014867544174,
0.17256110906600952,
-0.011291885748505592,
0.020974688231945038,
-0.02309435047209263,
-0.011655795387923717,
0.010772702284157276,
0.03739340975880623,
-0.018450547009706497,
-0.010177492164075375,
0.0011233979603275657,
0.01159737166017294,
0.017548127099871635,
0.0154092563316226,
-0.030198995023965836,
0.02867640182375908,
0.03882528468966484,
0.002634462434798479,
0.0020584836602211,
-0.03313733637332916,
0.005522766150534153,
-0.01140493806451559,
0.01854407787322998,
-0.05830909311771393,
0.008441398851573467,
-0.034427765756845474,
-0.004805027507245541,
0.025519395247101784,
-0.03727521002292633,
0.02194812521338463,
0.01467121671885252,
-0.028135206550359726,
0.013901429250836372,
-0.006585532799363136,
-0.02868467941880226,
0.022564327344298363,
0.026650846004486084,
0.0017125650774687529,
0.02648174948990345,
-0.019763929769396782,
0.017724476754665375,
-0.004174818284809589,
-0.0065328869968652725,
0.01147761382162571,
0.020639365538954735,
-0.045240651816129684,
-0.006357837934046984,
-0.04031308740377426,
0.004751688335090876,
-0.0016782243037596345,
0.0094407694414258,
-0.02430906891822815,
0.03559831157326698,
0.05976085737347603,
-0.028305750340223312,
-0.002120239892974496,
0.007328038103878498,
0.001003091805614531,
0.003556898096576333,
-0.017770681530237198,
0.034246478229761124,
-0.012242026627063751,
0.03185022622346878,
-0.013465974479913712,
0.004766002297401428,
-0.01188105158507824,
0.026364019140601158,
0.02205805666744709,
0.04425859823822975,
-0.017292913049459457,
-0.01072276383638382,
-0.034108951687812805,
0.013239068910479546,
-0.015570425428450108,
0.04339822754263878,
0.007914964109659195,
0.01902884803712368,
-0.03093571774661541,
-0.013383617624640465,
-0.01953224092721939,
-0.0009418213739991188,
-0.008999621495604515,
0.033670444041490555,
0.00798377301543951,
-0.007333699613809586,
-0.011528758332133293,
-0.028921879827976227,
0.004648897796869278,
0.020504234358668327,
-0.010772760026156902,
0.051021020859479904,
-0.005072396714240313,
0.04720937833189964,
0.0031530139967799187,
-0.03742116689682007,
-0.04105927795171738,
0.0028635109774768353,
-0.025730784982442856,
0.0031272447668015957,
-0.01695800945162773,
0.04990875720977783,
0.04515446349978447,
-0.004599160049110651,
0.008771192282438278,
0.024174131453037262,
-0.01001117192208767,
-0.02832402102649212,
0.040745772421360016,
-0.03597523272037506,
-0.025002997368574142,
-0.018350236117839813,
-0.05531900003552437,
-0.0548323392868042,
-0.003881994402036071,
-0.0030458313412964344,
-0.0006147081730887294,
-0.01977665349841118,
0.05181896314024925,
-0.004231276921927929,
0.001985980896279216,
-0.03398561105132103,
0.03487377613782883,
-0.012716391123831272,
-0.004476184491068125,
0.000017944013961823657,
0.037841882556676865,
-0.01627693884074688,
0.019991222769021988,
-0.010571070946753025,
0.019395407289266586,
0.0033131632953882217,
0.003116756910458207,
-0.01836237870156765,
0.018112167716026306,
0.018790777772665024,
0.011433713138103485,
0.058265142142772675,
0.033636242151260376,
-0.006763474550098181,
-0.00841182004660368,
-0.050143808126449585,
0.048795804381370544,
-0.023882482200860977,
-0.06521938741207123,
0.002803827403113246,
0.02437339536845684,
0.002940509235486388,
0.037016548216342926,
-0.005966573022305965,
0.0022556788753718138,
0.07374107092618942,
-0.01812719739973545,
-0.02712075039744377,
0.004424645099788904,
0.005463998299092054,
0.039049118757247925,
-0.0028671887703239918,
-0.00181816634722054,
-0.06290315836668015,
0.006663499865680933,
0.004307607654482126,
0.019651498645544052,
0.0076067689806222916,
-0.04362667351961136,
0.028416546061635017,
-0.0012838764814659953,
-0.027535077184438705,
-0.02568659745156765,
-0.006321829743683338,
0.022321779280900955,
0.04151303693652153,
-0.04101580008864403,
-0.013532014563679695,
-0.014856533147394657,
-0.011450421996414661,
-0.10144031047821045,
0.006112969946116209,
0.038619980216026306,
-0.012967102229595184,
0.011845376342535019,
-0.04424448311328888,
0.02415650151669979,
0.014188759960234165,
-0.06607557088136673,
-0.021203018724918365,
-0.019010769203305244,
-0.007058111019432545,
-0.025924157351255417,
0.005071505904197693,
-0.014360889792442322,
0.01284637302160263,
0.008803628385066986,
0.07132813334465027,
0.04216698929667473,
0.02337309904396534,
-0.03936748951673508,
-0.02265228144824505,
-0.016831224784255028,
0.040982574224472046,
0.01624579355120659,
-0.029582617804408073,
0.06638489663600922,
-0.03068268485367298,
0.0038856000173836946,
0.060993775725364685,
-0.03127920255064964,
0.014534395188093185,
-0.03553395718336105,
0.06481987237930298,
0.02188989706337452,
0.031698938459157944,
0.039027612656354904,
0.004730613436549902,
0.033233750611543655,
-0.011741763912141323,
0.028518402948975563,
0.03630112111568451,
0.0007502185762859881,
0.034044597297906876,
0.0450320839881897,
-0.020962102338671684,
0.0073340716771781445,
0.0033286032266914845,
-0.0655565932393074,
0.011598109267652035,
-0.001286406652070582,
0.003760707564651966,
0.020675789564847946,
-0.019817503169178963,
-0.029080837965011597,
0.002409865614026785,
-0.0259692445397377,
-0.016115617007017136,
-0.04465808719396591,
0.0026239098515361547,
0.07900400459766388,
-0.013888091780245304,
-0.005738798528909683,
-0.005898128729313612,
-0.01610255427658558,
-0.025271408259868622,
-0.029391394928097725,
-0.006575531326234341,
0.0048198942095041275,
0.04992414265871048,
-0.014781303703784943,
0.02497130259871483,
-0.032650090754032135,
0.022113598883152008,
0.02357012964785099,
0.033363714814186096,
-0.015819741412997246,
-0.010095296427607536,
-0.005722755566239357,
-0.06152953952550888,
0.04271981492638588,
-0.0031286701560020447,
-0.01173890195786953,
-0.04896128922700882,
-0.0020477697253227234,
0.018821507692337036,
0.023829858750104904,
0.03867429867386818,
-0.02684592641890049,
-0.006786851678043604,
0.05023235082626343,
-0.017384067177772522,
0.03860576078295708,
-0.03227134421467781,
0.002140528056770563,
-0.0013906174572184682,
-0.02772432193160057,
0.048992518335580826,
-0.000851755088660866,
-0.02126723900437355,
-0.001384936971589923,
0.027238214388489723,
0.016019493341445923,
0.015077945776283741,
0.002468924503773451,
-0.052134305238723755,
0.006304706912487745,
-0.02246396243572235,
-0.005713305436074734,
0.04000066965818405,
-0.014361469075083733,
0.003239243058487773,
-0.047086648643016815,
-0.05382129177451134,
-0.045759327709674835,
0.035352859646081924,
-0.024415478110313416,
0.018143927678465843,
-0.04451300948858261,
-0.06158633902668953,
0.02402522973716259,
-0.052698567509651184,
-0.029911013320088387,
-0.003974869381636381,
-0.024526581168174744,
0.0030937360133975744,
0.028802087530493736,
-0.01907588168978691,
0.0007821465842425823,
0.010513732209801674,
0.050829581916332245,
0.006458262447267771,
-0.030176162719726562,
0.026360079646110535,
0.00143869174644351,
-0.0017985730664804578,
0.021336840465664864,
-0.03681527078151703,
0.02124253287911415,
0.028967272490262985,
0.031526267528533936,
0.03802026808261871,
0.004802285693585873,
0.005272127687931061,
-0.058115169405937195,
0.06161477416753769,
-0.017812516540288925,
-0.04893280565738678,
0.05981339141726494,
-0.012131220661103725,
0.07807379215955734,
-0.039896946400403976,
-0.030164562165737152,
-0.024518612772226334,
0.010664541274309158,
0.03226599097251892,
-0.0011305093066766858,
-0.020348405465483665,
0.008968699723482132,
-0.0389791764318943,
0.008996127173304558,
0.007056585047394037,
0.006331056822091341,
0.023194020614027977,
-0.02701922319829464,
0.02671257220208645,
-0.015988372266292572,
0.04764077067375183,
0.041135337203741074,
-0.010260934941470623,
-0.03132706135511398,
-0.06811383366584778,
0.010375499725341797,
-0.00864832941442728,
-0.01646786369383335,
0.0043058618903160095,
-0.008630985394120216,
0.00966308917850256,
0.05227522552013397,
-0.06459654867649078,
0.009430564939975739,
0.008122495375573635,
0.030271394178271294,
0.0368957594037056,
0.034037817269563675
] |
<p>Will <a href="http://en.wikipedia.org/wiki/Timbre" rel="nofollow">timbre</a>/quality be different if two different people play the same guitar? Assume that frequency/pitch and amplitude are same.</p> | 2,843 | [
-0.03259490057826042,
-0.028885794803500175,
0.01738905906677246,
-0.02098364755511284,
0.002900706371292472,
0.03301553800702095,
-0.019756034016609192,
0.009265321306884289,
0.02087380178272724,
-0.01841351017355919,
0.013713236898183823,
0.023107068613171577,
0.05825921148061752,
0.027711648494005203,
0.0009515135316178203,
-0.015540863387286663,
-0.010490287095308304,
-0.003695037215948105,
-0.03348461911082268,
-0.0013789781369268894,
-0.0396893136203289,
0.03436078131198883,
0.026629015803337097,
0.015652764588594437,
-0.022948335856199265,
0.02941756322979927,
0.04331664368510246,
0.0034833841491490602,
0.03422035649418831,
0.04157776013016701,
0.0018063040915876627,
-0.005415935069322586,
0.014298053458333015,
0.05040416494011879,
0.04169903323054314,
-0.04104018956422806,
-0.033948492258787155,
-0.01848438009619713,
0.01610492542386055,
0.007483644876629114,
-0.014959911815822124,
0.006820496637374163,
-0.007081369869410992,
0.03759568929672241,
-0.029295561835169792,
0.0010573862819001079,
0.0003331007028464228,
-0.038534726947546005,
0.018789760768413544,
-0.03836707025766373,
0.07821395993232727,
0.019234366714954376,
0.020234040915966034,
0.036212801933288574,
0.007845873013138771,
0.02173863723874092,
0.06515463441610336,
0.07414951175451279,
-0.009803042747080326,
-0.06346925348043442,
-0.01979270577430725,
-0.027049794793128967,
0.0015653278678655624,
-0.004141179379075766,
-0.06141073256731033,
0.03598252311348915,
0.0002663703926373273,
-0.019197572022676468,
-0.0008888462907634676,
-0.008400165475904942,
0.013492725789546967,
0.045622650533914566,
0.05701395124197006,
-0.0632726177573204,
0.028239473700523376,
-0.05479295551776886,
0.036336444318294525,
0.0294285137206316,
0.026604458689689636,
0.04130621626973152,
-0.014979753643274307,
-0.006518503185361624,
-0.0022651103790849447,
0.02445629984140396,
0.056749533861875534,
-0.0039016841910779476,
0.05804220959544182,
-0.028655333444476128,
-0.0014603453455492854,
0.03681069612503052,
0.03905583173036575,
-0.003593772416934371,
0.020045427605509758,
-0.02465074323117733,
-0.015763146802783012,
-0.0032834464218467474,
-0.03983059152960777,
0.04491635039448738,
0.028770150616765022,
-0.04412316903471947,
0.03624187409877777,
-0.01677088625729084,
0.03448113799095154,
0.029876165091991425,
-0.0064165107905864716,
-0.023183003067970276,
-0.014748089015483856,
-0.015940839424729347,
0.009995880536735058,
-0.0131152905523777,
-0.05382344126701355,
-0.0044890702702105045,
-0.024297485128045082,
-0.012262104079127312,
0.023270102217793465,
-0.0017112168716266751,
0.0024727163836359978,
-0.017979027703404427,
0.08892964571714401,
0.06671914458274841,
0.051920194178819656,
-0.05528317391872406,
0.027240794152021408,
-0.02912294492125511,
-0.013275555334985256,
0.011338994838297367,
-0.00888766162097454,
-0.0024119338486343622,
-0.06924399733543396,
0.02416112646460533,
-0.028033075854182243,
-0.01852237805724144,
-0.011630427092313766,
-0.016444899141788483,
0.05061493068933487,
0.0005093103391118348,
-0.10095689445734024,
-0.05636177211999893,
0.025150548666715622,
-0.032366178929805756,
-0.008156703785061836,
-0.06805319339036942,
0.0006700312369503081,
-0.00016579541261307895,
0.015215282328426838,
0.028869515284895897,
0.050439395010471344,
0.01946861296892166,
0.029398810118436813,
0.05133740231394768,
-0.006130884401500225,
-0.025923848152160645,
0.0007411700789816678,
-0.02296285331249237,
0.015678375959396362,
-0.03174291551113129,
0.0012314767809584737,
0.023069432005286217,
-0.03531380370259285,
-0.04631274938583374,
0.03873063251376152,
0.010227688588202,
-0.008456298150122166,
0.037423498928546906,
0.028132721781730652,
-0.01255240011960268,
0.06652101129293442,
0.0082023274153471,
-0.009851165115833282,
-0.01024380698800087,
0.025777386501431465,
0.014488202519714832,
0.005203320644795895,
0.0017216249834746122,
0.01679367385804653,
-0.02324003167450428,
-0.02560609020292759,
-0.017086874693632126,
0.03954948112368584,
0.020479416474699974,
-0.054145973175764084,
-0.02497432939708233,
-0.015362933278083801,
0.028571853414177895,
0.019558081403374672,
0.04357318580150604,
0.0001286737824557349,
-0.00682025495916605,
0.022590210661292076,
-0.02188458852469921,
0.005239018239080906,
-0.06894300132989883,
0.051797740161418915,
0.024800606071949005,
-0.013938997872173786,
0.015004069544374943,
0.010273748077452183,
0.06839026510715485,
-0.052986592054367065,
0.011895231902599335,
0.01605418138206005,
0.0038305430207401514,
0.02850097045302391,
-0.014708909206092358,
0.008586904034018517,
0.07259766012430191,
0.05933535471558571,
-0.012317593209445477,
0.0640416070818901,
-0.025558864697813988,
-0.08480006456375122,
0.058824632316827774,
-0.026166537776589394,
0.06397313624620438,
-0.014223472215235233,
0.014262533746659756,
0.023860927671194077,
0.0157249104231596,
-0.0020060022361576557,
0.03176482766866684,
-0.018795643001794815,
0.045586470514535904,
0.022431662306189537,
-0.02825280837714672,
0.02658199705183506,
0.010261114686727524,
0.001040880219079554,
0.02144884690642357,
-0.04051847755908966,
-0.03201775625348091,
-0.04301281273365021,
-0.01192724984139204,
0.054123979061841965,
0.03272788226604462,
-0.03462729603052139,
0.03649294376373291,
0.016356028616428375,
0.018490804359316826,
0.03887829929590225,
0.004044472239911556,
0.0030698678456246853,
-0.024819673970341682,
-0.007491479627788067,
0.049322403967380524,
0.03335835784673691,
0.06428394466638565,
0.008154330775141716,
0.013989108614623547,
0.03375016152858734,
-0.019519561901688576,
0.01227047573775053,
0.05483446270227432,
-0.019460296258330345,
0.009317302145063877,
0.01759966090321541,
-0.024236006662249565,
0.011467340402305126,
-0.04516506940126419,
0.01926335133612156,
0.012294676154851913,
0.0021842974238097668,
-0.05142614617943764,
0.004156336188316345,
-0.02997393161058426,
0.015131473541259766,
0.0034628803841769695,
0.008953070268034935,
0.008467323146760464,
0.02039974555373192,
-0.012467868626117706,
0.0013533252058550715,
0.018575571477413177,
0.023337846621870995,
0.0036203665658831596,
-0.006616446655243635,
0.04453704506158829,
-0.005786950699985027,
0.04832201823592186,
-0.05137048661708832,
-0.03628331795334816,
-0.01058323122560978,
-0.011645196005702019,
0.008408332243561745,
-0.041500773280858994,
-0.04615780711174011,
-0.005788037553429604,
0.012025139294564724,
0.0013042815262451768,
-0.0005253970739431679,
-0.0023101461119949818,
0.009412656538188457,
0.019867319613695145,
-0.03374120965600014,
-0.07117298990488052,
0.014741186052560806,
-0.024498529732227325,
0.05300586298108101,
-0.0008191171218641102,
-0.00005973742372589186,
0.011700840666890144,
-0.011044382117688656,
-0.012115889228880405,
-0.00023741988115943968,
-0.05264157056808472,
-0.046821095049381256,
0.008049876429140568,
0.003193279728293419,
0.03673667460680008,
-0.016547061502933502,
0.003881184384226799,
0.04151086509227753,
-0.05073850601911545,
-0.034300047904253006,
-0.04903135821223259,
-0.03800613060593605,
0.04712080582976341,
-0.004073087591677904,
0.06256022304296494,
0.01946125738322735,
-0.046005189418792725,
0.05732199177145958,
0.01670086197555065,
-0.05816124379634857,
-0.020912371575832367,
-0.011419144459068775,
-0.008094769902527332,
-0.04209847375750542,
0.03049704246222973,
0.042650219053030014,
-0.024418888613581657,
0.039543312042951584,
0.06097863242030144,
-0.017486881464719772,
0.06036490947008133,
0.009287803433835506,
-0.032558247447013855,
-0.011821362189948559,
-0.00297552696429193,
-0.019517522305250168,
0.041847944259643555,
0.004142441786825657,
-0.03445564955472946,
-0.010709181427955627,
-0.02389027178287506,
0.048973143100738525,
0.01998319663107395,
0.007904227823019028,
0.026352442800998688,
-0.015971597284078598,
-0.0018645810196176171,
-0.05676272511482239,
0.025495946407318115,
0.00801040232181549,
-0.016986116766929626,
-0.03826216235756874,
0.014263538643717766,
0.0276847742497921,
0.010275201871991158,
0.014935493469238281,
0.01952507346868515,
0.019047541543841362,
-0.009463769383728504,
-0.03435775265097618,
0.01760733872652054,
0.010624358430504799,
0.018032131716609,
-0.028292791917920113,
-0.05978022888302803,
-0.0018067281926050782,
-0.010889866389334202,
-0.013968695886433125,
0.006931731011718512,
-0.05082732066512108,
0.004412918351590633,
-0.10506276786327362,
0.0012314156629145145,
-0.022766930982470512,
0.013777819462120533,
-0.008443272672593594,
0.07371318340301514,
0.0056232549250125885,
-0.015731219202280045,
-0.004595575854182243,
0.025876536965370178,
-0.10153091698884964,
0.009298248216509819,
-0.01795843616127968,
-0.02644849568605423,
-0.002204091288149357,
-0.02419503591954708,
-0.039195768535137177,
-0.03843173384666443,
-0.0110405832529068,
-0.026519756764173508,
-0.0004276740946806967,
-0.06895798444747925,
0.004277567379176617,
-0.011956317350268364,
-0.0531526580452919,
0.00873440969735384,
0.04119424149394035,
0.003397794207558036,
-0.008417731150984764,
0.056883495301008224,
0.013692924752831459,
-0.04169212281703949,
0.009832789190113544,
-0.027381306514143944,
0.007718619890511036,
-0.03065410442650318,
0.006965277716517448,
0.006283881142735481,
0.045498013496398926,
-0.004722781479358673,
0.014726892113685608,
-0.012401624582707882,
0.017786115407943726,
0.021085871383547783,
-0.024339623749256134,
0.004426042549312115,
-0.05774717032909393,
-0.013632708229124546,
0.014438644982874393,
0.012438027188181877,
0.0065593421459198,
0.014677125960588455,
0.019900133833289146,
0.022854074835777283,
-0.0382428839802742,
0.041201166808605194,
0.007465128321200609,
0.010516145266592503,
-0.028711894527077675,
-0.04616619646549225,
-0.008486825972795486,
0.004739005584269762,
-0.040389131754636765,
0.005903672892600298,
0.040234144777059555,
-0.024452852085232735,
0.007414605002850294,
0.015188561752438545,
0.004697307478636503,
-0.031775012612342834,
0.024626828730106354,
-0.017849842086434364,
-0.004868815187364817,
-0.027222799137234688,
-0.020371627062559128,
0.0015318519435822964,
0.008165305480360985,
0.04654914140701294,
0.023181850090622902,
-0.06020943820476532,
-0.08876898884773254,
-0.01160903088748455,
-0.0005617436254397035,
0.014122181572020054,
-0.03407974913716316,
0.02966945245862007,
-0.0032176508102566004,
-0.0603758804500103,
0.0234963521361351,
0.004746113903820515,
0.013322683051228523,
-0.031961601227521896,
-0.0009233409073203802,
-0.05806000530719757,
-0.025109857320785522,
-0.0200178325176239,
0.03101951628923416,
-0.000204716096050106,
-0.00502779521048069,
-0.014002698473632336,
-0.004145151004195213,
-0.013994076289236546,
0.02750086598098278,
0.04587037116289139,
0.0462033748626709,
0.0015618292381986976,
0.020843124017119408,
-0.03065064735710621,
0.028618909418582916,
-0.011090111918747425,
-0.03859268128871918,
0.04954539239406586,
-0.016673456877470016,
-0.0336206890642643,
0.011228474788367748,
-0.0049002086743712425,
-0.02739107795059681,
0.041461601853370667,
0.02257235161960125,
0.005435695871710777,
0.032218970358371735,
-0.009368997998535633,
0.046719085425138474,
0.01780196838080883,
-0.010560594499111176,
0.09115878492593765,
0.037167247384786606,
-0.02109755203127861,
-0.003035398432984948,
0.008058051578700542,
0.028795983642339706,
-0.05876652151346207,
0.003919376526027918,
-0.010165139101445675,
-0.01796533539891243,
-0.049164626747369766,
0.028978833928704262,
-0.011895040050148964,
0.04179225489497185,
-0.05271059647202492,
-0.014377115294337273,
-0.030736686661839485,
0.004464366007596254,
0.0154415899887681,
0.028071889653801918,
0.017944924533367157,
0.027779044583439827,
-0.012453543953597546,
-0.003475092351436615,
0.015674935653805733,
-0.007645993493497372,
0.01088463794440031,
0.0021042414009571075,
-0.005779867060482502,
0.06925090402364731,
-0.032776232808828354,
-0.03223950043320656,
-0.015206767246127129,
-0.02226622775197029,
0.04076366499066353,
-0.013482191599905491,
0.0498218834400177,
0.01964482106268406,
-0.026057571172714233,
-0.002906504785642028,
0.05401258543133736,
-0.0025469218380749226,
0.05563639476895332,
-0.033868301659822464,
0.06977534294128418,
0.005867574829608202,
-0.009662488475441933,
-0.052672699093818665,
-0.02626432292163372,
0.000774007523432374,
0.03659430146217346,
0.03165752813220024,
0.004734839778393507,
0.003158205421641469,
0.0006182019133120775,
-0.007217690348625183,
0.022976838052272797,
0.048061687499284744,
0.00036938191624358296,
0.011159340851008892,
-0.015134398825466633,
-0.028285905718803406,
0.09344436973333359,
0.05651697516441345,
-0.02024354226887226,
-0.020240802317857742,
-0.04661865904927254,
0.006314569618552923,
-0.04680522531270981,
0.03124893829226494,
-0.028695274144411087,
0.00787932425737381,
-0.01159053947776556,
-0.0061760894022881985,
0.047424666583538055,
-0.005213581025600433,
-0.021099954843521118,
-0.034430380910634995,
0.018216680735349655,
0.009122872725129128,
-0.025074442848563194,
0.034953486174345016,
-0.0027605288196355104,
0.011046781204640865,
-0.04034597426652908,
-0.02621890977025032,
-0.010171933099627495,
-0.0351283960044384,
-0.039292771369218826,
0.046129390597343445,
-0.01975204236805439,
-0.011762953363358974,
0.08024291694164276,
-0.0030624382197856903,
-0.005666680634021759,
0.018469875678420067,
-0.050347816199064255,
0.05080343782901764,
-0.044819995760917664,
-0.009089876897633076,
-0.02133757807314396,
0.020075354725122452,
0.00047421452472917736,
-0.0163122545927763,
-0.0062917014583945274,
-0.034329481422901154,
0.04054952785372734,
0.04230046272277832,
0.0276106595993042,
0.08819061517715454,
0.002981499070301652,
0.0053937374614179134,
-0.0054603503085672855,
0.014984594658017159,
-0.04138105735182762,
-0.07113490253686905,
0.05426418036222458,
-0.008911127224564552,
-0.003575056791305542,
0.01800229400396347,
0.019467489793896675,
0.010865505784749985,
0.04452379047870636,
0.028958555310964584,
0.04560086131095886,
0.012639951892197132,
-0.021693000569939613,
-0.029946643859148026,
0.009991556406021118,
-0.0388277992606163,
0.019320078194141388,
-0.0013291062787175179,
-0.00617730338126421,
0.04970604181289673,
0.06154545024037361,
0.010901709087193012,
-0.019571052864193916,
-0.013228177092969418,
-0.043831292539834976,
0.006681176368147135,
-0.005411249585449696,
0.03132615238428116,
0.01568012684583664,
-0.009604968130588531,
0.009297141805291176,
-0.004899730905890465,
0.030015116557478905,
-0.039556100964546204,
-0.07387369126081467,
-0.016911111772060394,
-0.04270666465163231,
-0.016831984743475914,
0.029302828013896942,
-0.004309006966650486,
-0.08657488226890564,
0.061149559915065765,
-0.0282876119017601,
0.064336858689785,
-0.03945900872349739,
0.03893521428108215,
-0.038615308701992035,
0.021511973813176155,
-0.015455019660294056,
0.04722065478563309,
-0.005204102490097284,
0.0046876054257154465,
0.09313476085662842,
0.05663635581731796,
0.03912593796849251,
-0.018174821510910988,
0.021856240928173065,
-0.03353124111890793,
-0.01375578809529543,
0.011898930184543133,
-0.004515409469604492,
0.006809636019170284,
0.012784061022102833,
0.038362327963113785,
0.061776529997587204,
0.03475809097290039,
-0.04003794118762016,
0.06354224681854248,
-0.017166925594210625,
0.010644146241247654,
-0.0012793331407010555,
0.018384123221039772,
-0.0042967600747942924,
0.01844770647585392,
-0.023791354149580002,
-0.012217216193675995,
-0.0283755324780941,
0.0021822715643793344,
-0.02687167190015316,
-0.013770860619843006,
0.06014378368854523,
-0.0006434476235881448,
-0.016420409083366394,
0.009466971270740032,
0.003546116640791297,
0.0002854158519767225,
-0.04404238983988762,
0.019514882937073708,
0.029167309403419495,
0.011849798262119293,
-0.009356174618005753,
0.020782137289643288,
0.00805981270968914,
-0.021120183169841766,
0.018385181203484535,
-0.018506690859794617,
-0.04677770286798477,
-0.024408672004938126,
-0.015666628256440163,
-0.01007778849452734,
0.029340647161006927,
-0.030006252229213715,
-0.010648571886122227,
-0.008217227645218372,
-0.028547687456011772,
-0.0659644678235054,
-0.03994002193212509,
0.01101036835461855,
0.028106188401579857,
-0.019139321520924568,
-0.013968389481306076,
-0.049860402941703796,
0.010543997399508953,
-0.01501987874507904,
0.004633418284356594,
-0.0022901680786162615,
-0.038230158388614655,
-0.031097115948796272,
0.02642604522407055,
0.010982153937220573,
-0.0007759378640912473,
-0.03244173899292946,
-0.03827144578099251,
-0.024527225643396378,
-0.03092888928949833,
-0.0465799905359745,
0.005020082928240299,
0.06474585831165314,
0.05735350027680397,
0.023297321051359177,
0.012013329192996025,
0.007639178540557623,
-0.056968316435813904,
0.059028662741184235,
0.027008147910237312,
-0.01225592102855444,
-0.0051850019954144955,
0.02412877231836319,
0.05183282494544983,
0.010285217314958572,
0.013567833229899406,
0.0504891499876976,
0.0033190050162374973,
0.034492164850234985,
0.0328524075448513,
-0.025157922878861427,
-0.021634384989738464,
0.015106762759387493,
-0.03216930851340294,
0.0019720925483852625,
0.024484464898705482,
0.04250862076878548,
-0.017773419618606567,
0.03291754424571991,
-0.02534320019185543,
0.011283055879175663,
-0.03650159761309624,
0.017403069883584976,
-0.024088701233267784,
-0.03451923653483391,
-0.025627486407756805,
0.024230074137449265,
0.01865483820438385,
-0.005949275568127632,
-0.04342499002814293,
-0.016197072342038155,
0.016615867614746094,
0.0020359084010124207,
-0.010760214179754257,
-0.017592625692486763,
0.004837134387344122,
0.008240836672484875,
0.003753913100808859,
-0.023259997367858887,
-0.0024493650998920202,
-0.04390358924865723,
-0.012671452946960926,
0.016627224162220955,
0.037212666124105453,
0.026538029313087463,
0.029737869277596474,
-0.05401374772191048,
-0.01904277503490448,
0.03468652069568634,
0.008411693386733532,
0.02021699957549572,
0.002230346202850342,
0.013257589191198349,
-0.02273598313331604,
0.047730736434459686,
-0.061454176902770996,
-0.05168156325817108,
0.04520402476191521,
-0.06731066852807999,
0.014828044921159744,
0.02884858287870884,
-0.02746083028614521,
0.030855825170874596,
-0.007237649522721767,
-0.007106361910700798,
0.02503088116645813,
0.044562261551618576,
-0.010638546198606491,
-0.00899491272866726,
0.012842247262597084,
0.026443907991051674,
-0.008951140567660332,
0.020118821412324905,
0.003427723189815879,
-0.0021153867710381746,
-0.02979627065360546,
0.0664375051856041,
0.044970519840717316,
0.013884061016142368,
-0.016240861266851425,
0.013064775615930557,
-0.003565957536920905,
0.0025567058473825455,
0.0015670835273340344,
0.013711617328226566,
0.004806591663509607,
0.006862761452794075,
-0.00898131262511015,
0.03541352227330208,
0.009042592719197273,
-0.03310806676745415,
-0.08284668624401093,
-0.03592962771654129,
0.008509887382388115,
0.029883647337555885,
0.009195951744914055,
-0.02864830009639263,
0.02442788891494274,
-0.0062912022694945335,
-0.05401941388845444,
0.0210496187210083,
0.0015913264360278845,
-0.0065013328567147255,
-0.05133349820971489,
0.009206761606037617,
-0.012522699311375618,
-0.0050821141339838505,
0.029027195647358894,
0.039162300527095795,
0.001313611282967031,
0.034014519304037094,
-0.011307732202112675,
0.0028359368443489075,
-0.015045042149722576,
0.0038594903890043497,
-0.02006760612130165,
-0.03339453041553497,
0.04695975035429001,
-0.04202636331319809,
-0.03887408599257469,
0.02337932586669922,
-0.01649399660527706,
0.0286877378821373,
-0.008367981761693954,
0.03852267563343048,
0.007852737791836262,
-0.0012610285775735974,
-0.01446513831615448,
-0.04779539257287979,
-0.03102823719382286,
0.014949562959372997,
-0.002728631952777505,
0.0320308543741703,
-0.009126846678555012,
-0.020676709711551666,
0.016233576461672783,
-0.017619963735342026,
-0.021437525749206543,
0.018376009538769722,
-0.03714778646826744,
-0.04322349652647972,
0.002661620732396841,
0.02665577083826065,
0.015517446212470531,
-0.0026900460943579674,
0.01194522064179182,
-0.01865125633776188,
-0.015260107815265656,
0.029742058366537094,
-0.013134293258190155,
0.0014866299461573362,
0.01394135132431984,
0.0019019697792828083,
-0.046065885573625565,
0.04510074481368065,
0.04310544580221176,
-0.03259029984474182,
-0.021031642332673073,
-0.02080651931464672,
0.01960557885468006,
0.004666411317884922,
0.02639688365161419,
-0.03331628814339638,
-0.025572629645466805,
0.02747698500752449,
0.025363739579916,
0.008778494782745838,
-0.01457362249493599,
-0.0277189239859581,
-0.03858322277665138,
-0.0576777458190918,
0.03366632014513016,
0.024618923664093018,
-0.028113171458244324,
-0.08128717541694641,
0.0025746801402419806,
-0.022404640913009644,
0.02569732442498207,
0.0367119163274765,
0.0012597820023074746,
-0.06491434574127197,
0.01343604177236557,
-0.00022134935716167092,
0.03409620746970177,
-0.05033078044652939,
0.002037603873759508,
0.02118256688117981,
-0.02189016155898571,
0.0011403692187741399,
0.001546810264699161,
-0.0395965538918972,
0.016494296491146088,
0.005341189447790384,
-0.04785679280757904,
0.014263265766203403,
-0.010097300633788109,
-0.009381181560456753,
0.0848790854215622,
0.03188187628984451,
-0.014835415408015251,
0.07943261414766312,
-0.020472722128033638,
0.02559947595000267,
0.0011742414208129048,
-0.01746584102511406,
-0.05962018296122551,
0.04095998406410217,
-0.034906186163425446,
0.022739872336387634,
0.015069057233631611,
0.008541541174054146,
-0.01743663288652897,
-0.014520661905407906,
-0.0015714375767856836,
0.03806564584374428,
-0.004201503004878759,
-0.0374259389936924,
0.04467007890343666,
0.04185926541686058,
0.023898927494883537,
-0.019695771858096123,
0.01637357845902443,
0.008821421302855015,
-0.030593911185860634,
-0.02806513011455536,
0.0008785577374510467,
0.011267191730439663,
-0.0022659155074507,
-0.0038401591591537,
-0.006727220024913549,
-0.023430634289979935,
-0.00206947885453701,
0.03316504508256912,
0.008860079571604729,
-0.017736468464136124,
-0.027676504105329514,
0.02093268372118473,
0.007868540473282337,
-0.01745835319161415,
0.012522830627858639,
-0.029840415343642235,
0.0704013779759407,
-0.026778655126690865,
-0.010647045448422432,
0.017400795593857765,
0.023276057094335556,
-0.02884569577872753,
-0.019843684509396553,
0.033845458179712296,
0.010192585177719593,
-0.01913672313094139,
-0.04317723587155342,
-0.020743638277053833,
0.00044347153743728995,
0.02340640500187874,
-0.0665326714515686,
0.0019292879151180387,
0.0031765757594257593,
-0.024773169308900833,
-0.01614287495613098,
0.034212902188301086,
-0.030682886019349098,
-0.03022089973092079,
0.041173290461301804,
0.02720048278570175,
0.04264640808105469,
-0.017483845353126526,
-0.04100996255874634,
-0.01305471919476986,
0.02768738381564617,
-0.07045948505401611,
-0.0004777724388986826,
-0.015536145307123661,
0.022032195702195168,
0.0016868170350790024,
-0.014066377654671669
] |
<blockquote>
<p>Four rods A, B, C, D of same length and material but of different
radii r, 2r , 3r and 4r respectively are held between two rigid
walls. The temperature of all rods is increased by same amount. If the
rods do not bend, then which of these are correct:</p>
<ol>
<li>The stress in the rods are in the ratio 1 : 2 : 3 : 4.</li>
<li>The force on the rod exerted by the wall are in the ratio 1 : 2 : 3 : 4.</li>
<li>The energy stored in the rods due to elasticity are in the ratio 1 : 2 : 3 : 4.</li>
<li>The strains produced in the rods are in the ratio 1 : 2 : 3 : 4.</li>
</ol>
</blockquote>
<p><em>Four rods A, B, C, D of same length and material</em> => Same Youngs Modulus, Same coefficient of linear expansion, Same Length.</p>
<p>Also, <em>The temperature of all rods is increased by same amount.</em> </p>
<p>Before answering the above question I've few other questions:</p>
<ol>
<li><p>Suppose rods were not held between two rigid walls. Then there would have been change in length. In that case, would there be stress? Intuitively it feels like stress would be zero, as there seems to be no restoring forces developed. But Stress = Youngs modulus * strain. Strain is definitely not zero. So, stress should not be zero. Confused!</p></li>
<li><p>No say, rods were held between two rigid walls. Assuming rods are not bending. There length will not change. So, strain would be zero. Stress = Youngs modulus * strain. So, Stress must be zero. But intuitively it seems there will be stress, because there will be restoring forces in the rod pushing walls away. Again confused!</p></li>
</ol>
<p>Now coming back to the original problem. The above two confusions are causing trouble. But just going by intuition. There will be stress developed even though there is no strain. But stress = Restoring Force/Area. Here areas for all rods are different pi*r^2, because r is different. But Restoring force is same. So, the ratio must be 1/1 : 1/4 : 1/9 : 1/16. Right?</p>
<p>Surprisingly answers are 3,4. There is lot of confusion. Kindly clarify</p> | 2,844 | [
-0.03441845253109932,
-0.006693125236779451,
-0.007805028930306435,
-0.05307697504758835,
0.01141064241528511,
-0.004218765068799257,
-0.038546305149793625,
-0.004041941836476326,
-0.006304857321083546,
-0.029672658070921898,
0.07643336802721024,
-0.005925016012042761,
0.033792756497859955,
0.014562590979039669,
0.0011356814065948129,
0.025977231562137604,
0.037758249789476395,
-0.023137973621487617,
0.010273524560034275,
-0.014340071938931942,
-0.001972641795873642,
-0.022163646295666695,
-0.012605971656739712,
-0.003648655954748392,
-0.04408562183380127,
0.03643188625574112,
0.044985584914684296,
-0.03290695697069168,
0.018901899456977844,
0.042577631771564484,
-0.01770690642297268,
-0.013563480228185654,
-0.006437125150114298,
-0.002264323877170682,
0.02571447752416134,
-0.0014242504257708788,
-0.045045558363199234,
-0.026294231414794922,
0.000834594015032053,
0.05231408029794693,
0.006992691662162542,
0.012115771882236004,
-0.02079017646610737,
0.03532197326421738,
-0.0006404484156519175,
0.017831068485975266,
0.020658506080508232,
0.02089809440076351,
0.06355569511651993,
-0.039113350212574005,
0.05989395081996918,
-0.028915850445628166,
0.019530178979039192,
0.037646688520908356,
-0.032887645065784454,
-0.027036897838115692,
0.034773651510477066,
0.04394124820828438,
-0.037259023636579514,
-0.054796043783426285,
-0.02678043767809868,
0.03802759572863579,
-0.024070823565125465,
-0.029036886990070343,
-0.009833117946982384,
0.01504475437104702,
-0.017026271671056747,
-0.022209245711565018,
0.036341506987810135,
-0.021054435521364212,
0.0064503769390285015,
0.01746160164475441,
0.045510321855545044,
-0.00865092407912016,
0.01144940871745348,
-0.009932270273566246,
-0.030647587031126022,
0.02316461130976677,
0.036283623427152634,
0.04844529554247856,
-0.016593512147665024,
0.0016818433068692684,
0.06458206474781036,
0.0649246796965599,
-0.01707773469388485,
-0.03856784105300903,
0.04258931800723076,
-0.010058751329779625,
0.016299717128276825,
0.02823164500296116,
0.04512267932295799,
-0.005205969326198101,
0.04125506430864334,
0.007392892148345709,
-0.0020744663197547197,
-0.0005610742955468595,
0.00834815576672554,
0.05730704590678215,
-0.009070917963981628,
0.006449130829423666,
0.012579616159200668,
-0.008165580220520496,
0.017374539747834206,
0.052856478840112686,
-0.023916123434901237,
-0.04116281494498253,
-0.032577965408563614,
0.005459125619381666,
0.0003899571020156145,
-0.0003774099750444293,
-0.0029383404180407524,
0.027271898463368416,
-0.020042160525918007,
-0.012555968947708607,
0.002806783188134432,
-0.027291979640722275,
0.027752915397286415,
-0.004490882158279419,
0.07517345249652863,
0.027053851634263992,
0.021156201139092445,
-0.0439315102994442,
0.0115676149725914,
0.00008868615259416401,
-0.06407173722982407,
0.014375663362443447,
0.006382222753018141,
-0.02402697317302227,
-0.016335386782884598,
0.0754520520567894,
0.007222497835755348,
-0.006366014946252108,
-0.041197460144758224,
0.025968540459871292,
0.030180277302861214,
0.0029340439941734076,
-0.08332902938127518,
-0.041838884353637695,
0.07732145488262177,
-0.0071367244236171246,
-0.0381680466234684,
-0.08322654664516449,
-0.004093070048838854,
0.006554740015417337,
0.08562487363815308,
-0.010462464764714241,
0.014670676551759243,
-0.0035673619713634253,
0.01993623748421669,
-0.020175330340862274,
-0.004651634022593498,
0.017970062792301178,
-0.009005450643599033,
-0.026333555579185486,
-0.01950155757367611,
-0.05080685019493103,
-0.008587255142629147,
0.017531992867588997,
-0.022350821644067764,
-0.01079585961997509,
0.01161041110754013,
-0.0007515437318943441,
0.02006746456027031,
0.01829361915588379,
-0.019498705863952637,
-0.016828516498208046,
0.07403857260942459,
-0.03390907496213913,
-0.02323007397353649,
0.03282841667532921,
-0.03081464022397995,
0.01597539708018303,
-0.027694229036569595,
0.034150898456573486,
0.022368639707565308,
-0.01477475930005312,
0.024555416777729988,
-0.007485641166567802,
-0.007943958975374699,
0.025628864765167236,
-0.03122672438621521,
-0.033676452934741974,
0.010141592472791672,
-0.0516897477209568,
0.01229142490774393,
0.06031637266278267,
0.03996346890926361,
-0.00032743276096880436,
-0.022922726348042488,
-0.03086547553539276,
-0.019109003245830536,
-0.08359111845493317,
0.013184785842895508,
-0.021195095032453537,
-0.035301174968481064,
-0.00016601098468527198,
0.02500109374523163,
0.009228216484189034,
-0.020739516243338585,
-0.007892271503806114,
-0.007794637698680162,
0.021732155233621597,
-0.01753818616271019,
-0.0002775622997432947,
0.04325908049941063,
0.03498104214668274,
0.05393262207508087,
0.01806345023214817,
-0.016095027327537537,
-0.040140874683856964,
0.016639025881886482,
0.031108848750591278,
-0.034147411584854126,
0.028335396200418472,
0.003501859726384282,
-0.004530465696007013,
0.024913055822253227,
-0.03081572987139225,
-0.01631990261375904,
0.02821572683751583,
-0.016527723520994186,
0.055831119418144226,
-0.0003787185123655945,
-0.019941221922636032,
-0.0054692961275577545,
0.06278169900178909,
0.0029127199668437243,
0.05562800168991089,
-0.03473742678761482,
-0.013730793260037899,
-0.0707242339849472,
-0.009464871138334274,
0.018853481858968735,
0.0688849613070488,
-0.04940284788608551,
0.03281854838132858,
-0.0014427837450057268,
0.022170722484588623,
-0.030627913773059845,
-0.03570543974637985,
0.0018748353468254209,
-0.044501177966594696,
0.059504393488168716,
0.027598727494478226,
-0.005650661885738373,
-0.004920449107885361,
-0.025496702641248703,
0.02882954478263855,
0.044601667672395706,
-0.015461895614862442,
0.015437527559697628,
0.015965797007083893,
0.031289778649806976,
0.034725893288850784,
-0.011135607957839966,
-0.005506522487848997,
0.019044179469347,
0.014429319649934769,
0.043306879699230194,
0.048650652170181274,
0.006514301523566246,
0.013513504527509212,
-0.01612538844347,
0.012889434583485126,
-0.005666447803378105,
0.03441881760954857,
-0.013092288747429848,
-0.05543564632534981,
0.03917481377720833,
-0.03080899640917778,
-0.014814747497439384,
-0.021892530843615532,
-0.03622518479824066,
-0.011031100526452065,
-0.044516727328300476,
-0.006951820570975542,
0.009909669868648052,
0.07010377198457718,
-0.06775615364313126,
0.026761217042803764,
0.02327396161854267,
-0.013301548548042774,
0.0015563624911010265,
0.0018911449005827308,
-0.02250300906598568,
0.006262054201215506,
-0.031274352222681046,
-0.019275406375527382,
0.009918555617332458,
0.013150216080248356,
-0.008145621046423912,
0.05985648185014725,
-0.0013676721137017012,
-0.06528463214635849,
-0.042624086141586304,
-0.026014795526862144,
0.013615941628813744,
-0.052930425852537155,
0.006230945698916912,
0.06109766662120819,
-0.0008740319171920419,
-0.005482254084199667,
-0.0031904401257634163,
-0.06164500489830971,
-0.002110193483531475,
-0.0195698793977499,
0.010593965649604797,
0.009996805340051651,
0.008021898567676544,
0.02741221711039543,
0.049914855509996414,
-0.009625684469938278,
-0.033131349831819534,
-0.05219104886054993,
-0.04136571288108826,
0.02319374307990074,
-0.010390156880021095,
0.04933977872133255,
-0.017643984407186508,
-0.06106911599636078,
0.06511062383651733,
-0.01226257998496294,
-0.004632369615137577,
-0.03580174595117569,
-0.030595634132623672,
-0.018452536314725876,
-0.06572768837213516,
0.03904154524207115,
0.04342783987522125,
-0.013364795595407486,
0.01789374276995659,
0.017996447160840034,
0.05569957196712494,
0.020358148962259293,
0.029528452083468437,
0.025471672415733337,
0.0023275366984307766,
0.03313058242201805,
-0.04105351120233536,
0.06240083649754524,
0.0023194956593215466,
0.04270169511437416,
-0.01714452914893627,
-0.015133033506572247,
0.04459245130419731,
0.01810990646481514,
-0.08482620865106583,
0.07089206576347351,
0.010173441842198372,
-0.011577196419239044,
-0.06491584330797195,
0.04965890571475029,
0.01376275159418583,
-0.018105989322066307,
0.006565111689269543,
-0.008245098404586315,
0.03252251818776131,
0.003624116303399205,
0.01111177820712328,
0.05535456910729408,
0.03533308953046799,
-0.0002561766596045345,
-0.006647746544331312,
0.008823529817163944,
-0.033442411571741104,
0.024251360446214676,
0.003106120740994811,
-0.01346522569656372,
0.05558484047651291,
-0.002975951647385955,
0.02305050939321518,
0.030198467895388603,
-0.03326108679175377,
0.02173588238656521,
-0.044992830604314804,
-0.021546732634305954,
-0.010583105497062206,
0.06748976558446884,
-0.004344930872321129,
0.05150735378265381,
0.027430018410086632,
0.04255906865000725,
0.03801747038960457,
-0.014057938009500504,
-0.07736681401729584,
0.00920590665191412,
-0.0233803428709507,
0.006456611678004265,
0.007225106004625559,
0.018383877351880074,
-0.007442542351782322,
-0.05065589025616646,
-0.009759373962879181,
-0.009283535182476044,
-0.023027261719107628,
-0.07293708622455597,
-0.005961365532130003,
-0.014098542742431164,
-0.03371978551149368,
0.037103936076164246,
0.024633895605802536,
0.026125505566596985,
-0.05404854565858841,
0.022497111931443214,
0.06636369228363037,
0.02199725992977619,
-0.00020160390704404563,
-0.002779194386675954,
0.004376730881631374,
0.04149152711033821,
0.04759667441248894,
0.000905076100025326,
0.013951974920928478,
-0.004948768299072981,
-0.00282976939342916,
0.041887033730745316,
0.005036809481680393,
0.00029412188450805843,
0.01213136501610279,
-0.029691366478800774,
-0.03221144527196884,
0.001183538231998682,
-0.011937962844967842,
0.05228690430521965,
-0.02243253029882908,
-0.013751910999417305,
0.0022204467095434666,
0.01927059143781662,
0.004760433454066515,
0.01852390542626381,
0.03169688954949379,
0.03155987709760666,
-0.035172801464796066,
-0.04690013825893402,
-0.015077806077897549,
-0.04724958911538124,
-0.021606896072626114,
0.000017218822904396802,
-0.0216467697173357,
-0.037937335669994354,
0.0024679324124008417,
0.05115073174238205,
0.02465664967894554,
0.0072768754325807095,
0.061336617916822433,
-0.04269539192318916,
0.0005599708529189229,
0.0089725898578763,
-0.02101094275712967,
0.03500664606690407,
0.011486245319247246,
0.025308720767498016,
0.0034419577568769455,
-0.004183785989880562,
-0.06817735731601715,
0.014800483360886574,
0.02578829601407051,
0.06869012117385864,
-0.02624334953725338,
0.04498552903532982,
-0.03503241017460823,
-0.04170200973749161,
0.030726660043001175,
-0.04676621034741402,
0.008551917038857937,
-0.0027605046052485704,
0.02661532163619995,
-0.013825681991875172,
-0.028923824429512024,
-0.041446786373853683,
-0.014900485053658485,
-0.012991888448596,
0.02854710817337036,
-0.014419681392610073,
0.013326381333172321,
0.04715883359313011,
-0.006681225262582302,
0.028713777661323547,
0.009420407935976982,
-0.05406028777360916,
-0.0032039766665548086,
-0.013124708086252213,
0.01272132620215416,
-0.04433124139904976,
-0.05461942404508591,
0.028559543192386627,
0.01173330657184124,
-0.046242985874414444,
0.029926741495728493,
-0.047544293105602264,
-0.024590231478214264,
0.03366216644644737,
-0.02170240692794323,
0.020235972478985786,
0.04118712618947029,
0.01100142765790224,
-0.006104561034590006,
0.0330476276576519,
-0.00107115029823035,
0.022746318951249123,
0.06462637335062027,
-0.02075193077325821,
-0.003762682667002082,
-0.03138171508908272,
0.03082425706088543,
-0.06050829961895943,
-0.0017328527756035328,
-0.03796647861599922,
0.004786231089383364,
-0.0038209406193345785,
0.030277272686362267,
-0.010764657519757748,
0.05476030707359314,
-0.024377217516303062,
-0.046773556619882584,
0.04449283704161644,
0.01842116005718708,
0.02797788381576538,
0.008638400584459305,
-0.006827158387750387,
0.003646634053438902,
0.0038778502494096756,
-0.05441952496767044,
0.0013918910408392549,
0.019196175038814545,
-0.01480056345462799,
0.020750610157847404,
-0.024067239835858345,
0.0329054556787014,
-0.019832827150821686,
0.003716695588082075,
-0.0018874328816309571,
-0.06674060225486755,
0.05288471654057503,
-0.017707712948322296,
0.05826571583747864,
0.01692766137421131,
0.004773056134581566,
0.030746247619390488,
0.01675775647163391,
-0.04233919084072113,
-0.00040584002272225916,
-0.000623625994194299,
0.029778337106108665,
-0.008038844913244247,
-0.006178604904562235,
-0.040003929287195206,
-0.04299096018075943,
0.0030941602308303118,
0.009853886440396309,
-0.02202966995537281,
-0.03244394063949585,
-0.03675189986824989,
-0.0010914618615061045,
-0.05225863680243492,
-0.016407731920480728,
0.0697164237499237,
-0.02928272634744644,
0.013169918209314346,
0.018899014219641685,
0.015106470324099064,
0.03740428388118744,
-0.03209784999489784,
-0.007502653170377016,
-0.03956669569015503,
-0.017624668776988983,
-0.02389742061495781,
-0.006328036077320576,
0.013774682767689228,
-0.020828723907470703,
-0.018458960577845573,
0.01591487042605877,
-0.00021075458789709955,
0.040089480578899384,
-0.011122767813503742,
0.012302643619477749,
0.0033065176103264093,
0.016229933127760887,
-0.043868228793144226,
-0.025103094056248665,
0.03216388449072838,
0.022817373275756836,
0.021879691630601883,
0.002219343790784478,
0.0300277266651392,
-0.022385157644748688,
-0.05528832599520683,
-0.004533526487648487,
-0.001235714415088296,
0.003459949279204011,
-0.0020078313536942005,
0.09864001721143723,
-0.023292474448680878,
-0.05154838040471077,
0.00035931580350734293,
-0.03629809245467186,
0.021782582625746727,
-0.011308270506560802,
-0.00090518913930282,
-0.024278800934553146,
-0.013285622000694275,
-0.04859001561999321,
-0.04432873800396919,
-0.008351452648639679,
0.023319797590374947,
0.05951371043920517,
-0.02143722027540207,
0.05692801997065544,
0.01309266872704029,
-0.03555288165807724,
0.04473141208291054,
-0.017641950398683548,
-0.004563707858324051,
0.00973476655781269,
-0.024235812947154045,
0.061019305139780045,
-0.04222404956817627,
-0.03341314569115639,
0.030291955918073654,
0.027277758345007896,
-0.03399491682648659,
-0.023497512564063072,
0.020389724522829056,
0.01488910336047411,
0.006843214388936758,
-0.05494549125432968,
-0.0453716441988945,
0.04777803272008896,
-0.04182591289281845,
0.03248968720436096,
0.007431541569530964,
0.00002167104867112357,
0.06626543402671814,
0.02185153216123581,
0.019753074273467064,
-0.043296489864587784,
0.011441684328019619,
-0.009912285953760147,
0.014526767656207085,
0.021847335621714592,
-0.015061515383422375,
-0.020904583856463432,
0.021015185862779617,
0.04002160206437111,
-0.0022381762973964214,
0.02877812087535858,
-0.02034843899309635,
-0.050304438918828964,
-0.020854711532592773,
0.0011334738228470087,
-0.023734746500849724,
0.04672917723655701,
0.010045710951089859,
-0.01057845912873745,
0.014656894840300083,
-0.02098933607339859,
0.02320989780128002,
0.012747357599437237,
0.023437345400452614,
-0.008743281476199627,
0.03270807862281799,
-0.005103051662445068,
0.05880975350737572,
-0.04737995192408562,
0.021670766174793243,
0.14342091977596283,
0.04538152366876602,
0.00626165047287941,
-0.03389803320169449,
0.015704073011875153,
-0.008616537787020206,
-0.008174587972462177,
-0.018476437777280807,
0.01607934571802616,
-0.02262060157954693,
0.009701975621283054,
0.013119533658027649,
0.061595503240823746,
-0.06078865006566048,
-0.02117510698735714,
0.020279642194509506,
-0.017445484176278114,
-0.016691729426383972,
-0.057190753519535065,
0.011444052681326866,
-0.00976079422980547,
-0.004905461799353361,
-0.0179563220590353,
0.017156703397631645,
-0.01632201112806797,
0.0012785226572304964,
-0.06927353888750076,
-0.05197335407137871,
0.019721781834959984,
0.00490693561732769,
-0.04255285486578941,
0.02904764749109745,
0.00132969138212502,
-0.048996154218912125,
-0.05303439870476723,
0.014565619640052319,
-0.011716384440660477,
-0.001618658658117056,
0.02898154966533184,
0.03579198941588402,
0.004827858880162239,
-0.009340661577880383,
0.010433762334287167,
0.03871538117527962,
-0.018924767151474953,
-0.00821117777377367,
-0.02197900414466858,
0.01811956614255905,
-0.011556845158338547,
-0.005557851400226355,
0.024075841531157494,
0.0007627772865816951,
-0.012516100890934467,
-0.027903005480766296,
-0.01444854773581028,
0.0025532664731144905,
0.0072985864244401455,
0.00878444965928793,
-0.029790828004479408,
0.002076112199574709,
0.02449851483106613,
0.01898767612874508,
0.020960664376616478,
-0.0031193222384899855,
-0.00848923996090889,
0.0025072169955819845,
-0.008589662611484528,
0.06183735653758049,
-0.009273911826312542,
0.026709241792559624,
-0.05988249182701111,
-0.008554295636713505,
0.009708842262625694,
-0.008033143356442451,
-0.043421462178230286,
0.04544973373413086,
0.058411501348018646,
-0.01790899969637394,
-0.023811446502804756,
-0.015560605563223362,
-0.03953517600893974,
0.007114138454198837,
-0.012178812175989151,
-0.01511302962899208,
-0.021695556119084358,
0.022346725687384605,
-0.008625774644315243,
0.06346429139375687,
-0.02765180543065071,
-0.019142229110002518,
0.01076220627874136,
0.020100731402635574,
0.023137204349040985,
-0.03614892065525055,
-0.037820301949977875,
0.0012805103324353695,
-0.029992729425430298,
0.00513449078425765,
0.015409416519105434,
0.001200284343212843,
0.046618569642305374,
0.009583329781889915,
0.015716195106506348,
0.051790185272693634,
-0.008800043724477291,
-0.0014341009082272649,
0.020402653142809868,
-0.03495614975690842,
0.023173414170742035,
0.020987221971154213,
-0.014664781279861927,
-0.0501297190785408,
-0.03372691199183464,
0.004818310029804707,
-0.03693583980202675,
-0.013229595497250557,
0.026457304134964943,
-0.004465953446924686,
-0.0007762982859276235,
-0.041451163589954376,
0.004569361452013254,
-0.02291892096400261,
-0.02181459777057171,
-0.01941370964050293,
-0.03166975826025009,
0.012344393879175186,
0.006476163398474455,
-0.021718990057706833,
0.017966296523809433,
-0.021533217281103134,
-0.015371355228126049,
0.0273559782654047,
0.0009923572652041912,
-0.012387534603476524,
-0.033610835671424866,
0.0027191867120563984,
-0.005291066598147154,
0.01828329637646675,
0.02005058340728283,
-0.061916548758745193,
0.010944305919110775,
-0.029976021498441696,
-0.0433061309158802,
-0.009229560382664204,
-0.0019515497842803597,
0.001060659415088594,
0.005084184929728508,
0.009311414323747158,
-0.015267262235283852,
0.07021620869636536,
-0.03355987370014191,
0.02184363268315792,
-0.03834329545497894,
-0.040359221398830414,
0.02612202800810337,
-0.03106788545846939,
0.015237981453537941,
-0.001063498784787953,
-0.011920889839529991,
0.02782311476767063,
0.03345516696572304,
-0.008327137678861618,
-0.039770860224962234,
0.015043950639665127,
0.0015289296861737967,
-0.021259600296616554,
-0.009203210473060608,
0.04085700213909149,
0.020183894783258438,
0.055339265614748,
0.011751070618629456,
0.015432344749569893,
0.01944507099688053,
-0.01213300321251154,
-0.10925564169883728,
-0.013794907368719578,
-0.0006206348189152777,
-0.019703004509210587,
-0.0165397971868515,
-0.03841978311538696,
0.02450770139694214,
0.02285139635205269,
-0.07174346596002579,
0.011140083894133568,
-0.04019486531615257,
-0.029773078858852386,
-0.012759676203131676,
-0.02269792929291725,
-0.0024229635018855333,
0.0495775006711483,
0.011642714962363243,
0.05766238644719124,
-0.022497504949569702,
0.04872148111462593,
-0.006948391441255808,
-0.0037401423323899508,
0.026607157662510872,
0.03017849661409855,
0.02667459100484848,
0.0116121219471097,
0.04916688799858093,
0.004132438451051712,
0.012531361542642117,
-0.003397060791030526,
0.0002321510255569592,
0.018916359171271324,
0.025787999853491783,
0.0109012546017766,
-0.004483222495764494,
0.05170170217752457,
-0.04051767289638519,
-0.018999647349119186,
-0.018618924543261528,
-0.002875897102057934,
-0.010707683861255646,
-0.0069588422775268555,
-0.04195505753159523,
0.0034530137199908495,
0.044053103774785995,
-0.0650743767619133,
-0.009069603867828846,
0.018142420798540115,
-0.03337094560265541,
0.031731169670820236,
0.003518072422593832,
0.00534954434260726,
-0.006580407731235027,
-0.01630050130188465,
0.0034899248275905848,
0.0005392773891799152,
-0.0032054230105131865,
0.04287096858024597,
0.029475536197423935,
-0.020613690838217735,
0.03161976486444473,
0.004644937813282013,
0.03861461207270622,
-0.02466076985001564,
-0.0398171991109848,
-0.037433553487062454,
-0.05688086524605751,
-0.01831207238137722,
0.003752518445253372,
-0.0011155514512211084,
-0.054777197539806366,
-0.02477840520441532,
-0.034256402403116226,
0.024952350184321404,
0.060850922018289566,
0.015439941547811031,
0.013702484779059887,
-0.022493701428174973,
-0.04580423980951309,
-0.0739155262708664,
0.021577831357717514,
-0.01153359841555357,
-0.05772875249385834,
-0.05821395665407181,
-0.01995333470404148,
-0.028592022135853767,
0.04559771344065666,
0.06406944990158081,
0.025023918598890305,
0.01684076525270939,
0.02049941197037697,
0.0007404226926155388,
0.0014347463147714734,
-0.033464785665273666,
0.014906859025359154,
0.029617125168442726,
0.045279305428266525,
0.03620442375540733,
0.024867862462997437,
0.01094137504696846,
-0.0044753882102668285,
0.0038791149854660034,
-0.06290819495916367,
0.026879332959651947,
0.011826211586594582,
-0.02230130508542061,
0.036897264420986176,
0.0038108944427222013,
-0.02379022352397442,
0.08359616249799728,
-0.026886561885476112,
-0.013760403729975224,
0.03478539362549782,
-0.026481257751584053,
-0.046944405883550644,
0.03441871330142021,
-0.03779461234807968,
0.01897636614739895,
-0.006906337570399046,
-0.009915999136865139,
0.05347896367311478,
0.011485695838928223,
-0.008227825164794922,
0.061038292944431305,
-0.049173664301633835,
-0.013206751085817814,
0.005820958409458399,
0.034272946417331696,
0.028849588707089424,
-0.05573239177465439,
0.023149289190769196,
0.0023863944225013256,
-0.001982436515390873,
0.04742514714598656,
0.034309323877096176,
0.006778357550501823,
0.00734210480004549,
-0.0031322019640356302,
0.05910363048315048,
-0.01771513558924198,
-0.0011166752083227038,
-0.0004675539385061711,
0.01876302808523178,
-0.04199458286166191,
-0.03012062795460224,
0.013664552941918373,
-0.02658016048371792,
-0.026110870763659477,
0.04709552228450775,
0.0019308060873299837,
0.05544304475188255,
0.001032804255373776,
-0.013524563983082771,
0.0030671737622469664,
0.017051013186573982,
0.011179805733263493,
0.027316495776176453,
0.04155592620372772,
0.02618807926774025,
-0.016316033899784088,
0.005232722498476505,
-0.019113674759864807,
-0.001426591770723462,
0.008906135335564613,
-0.020410750061273575,
-0.002215243875980377,
0.006152184680104256,
0.00958816334605217,
0.006897480692714453,
-0.024042276665568352,
-0.06379874795675278,
0.01045812014490366,
0.0741548091173172,
0.02172238938510418,
0.02071906253695488,
0.0004033684963360429,
0.01960786059498787,
-0.005076767411082983,
0.0248220507055521,
-0.023864183574914932,
-0.03767523169517517,
-0.0009171870769932866,
0.03764780983328819,
0.017797941341996193,
-0.03514673188328743
] |
<p>See this related question: <a href="http://physics.stackexchange.com/questions/118927/if-particles-are-excitations-what-are-their-fields">If particles are excitations what are their fields?</a></p>
<p>I ask this question because, according to a lecture, the higgs boson was frozen into a "matrix" at some point before recombination (otherwise we would not have atoms). Is this considered a field in the same way an electron field is a field? It was described that higgs was everywhere ... Is that another way of saying there is Higgs field?</p>
<p>This means the electron interacts with the higgs field and not with excitations of the higgs field? Or probably Higgs bosons are only excited momentarily. </p>
<p>Was the electron field also created like the higgs field at some point? </p>
<p>See here <a href="https://www.youtube.com/watch?v=hL2BLAOVbDA" rel="nofollow">https://www.youtube.com/watch?v=hL2BLAOVbDA</a></p> | 2,845 | [
0.018432581797242165,
0.014102659188210964,
0.05282280221581459,
-0.0496220737695694,
0.0513986274600029,
-0.022944806143641472,
-0.03561991825699806,
-0.039592377841472626,
0.023931149393320084,
-0.0251313503831625,
0.034164126962423325,
0.0017471195897087455,
0.03857406973838806,
-0.013840696774423122,
0.02384622022509575,
0.04003247618675232,
0.007613829802721739,
-0.023004774004220963,
-0.027792036533355713,
-0.012483801692724228,
-0.00344239198602736,
0.008508267812430859,
-0.005108176730573177,
0.03803994879126549,
-0.02170909382402897,
0.00867341086268425,
-0.00478869816288352,
0.038300223648548126,
0.0024615260772407055,
0.03331774100661278,
0.0022501470521092415,
-0.02954200841486454,
0.0250680111348629,
-0.0042732227593660355,
0.03127674385905266,
-0.0006550936377607286,
0.012017421424388885,
-0.06824791431427002,
0.024976780638098717,
-0.018475279211997986,
-0.010127986781299114,
-0.03344504162669182,
-0.009354599751532078,
0.06673050671815872,
-0.015749454498291016,
-0.0037457894068211317,
-0.037572428584098816,
0.009406648576259613,
0.08918321877717972,
-0.03749449923634529,
0.03153518587350845,
-0.006373022682964802,
0.044290874153375626,
0.02364777959883213,
0.011654171161353588,
-0.024924611672759056,
0.06238637492060661,
0.04247329384088516,
0.022579405456781387,
-0.051780834794044495,
-0.020827699452638626,
-0.05026683211326599,
-0.019852764904499054,
-0.04754568636417389,
-0.037245236337184906,
0.037976447492837906,
0.00821248721331358,
-0.03423206880688667,
0.04071320965886116,
-0.011905568651854992,
-0.012901190668344498,
-0.009374691173434258,
0.02421191893517971,
0.019469069316983223,
0.009112476371228695,
-0.010829376056790352,
0.022657476365566254,
-0.018769605085253716,
0.006836899556219578,
0.01700766570866108,
0.0018881895812228322,
0.017054574564099312,
0.024218076840043068,
0.01611744798719883,
0.025700554251670837,
-0.014469455927610397,
0.07935290038585663,
-0.05515413358807564,
0.020151862874627113,
0.04306318238377571,
-0.019112855195999146,
0.05612974241375923,
0.03030674159526825,
0.009749392047524452,
-0.05334251746535301,
-0.0031181706581264734,
0.009762950241565704,
0.025607872754335403,
0.010219885967671871,
0.0064813485369086266,
0.04058116301894188,
0.016717325896024704,
0.0172459464520216,
0.06645846366882324,
-0.004338865168392658,
-0.0041506001725792885,
-0.019254440441727638,
-0.0024987643118947744,
-0.059445083141326904,
-0.0342603474855423,
-0.04637262225151062,
0.02693265862762928,
-0.01466155331581831,
-0.00023104004503693432,
0.00585739454254508,
-0.04045028239488602,
0.005999225191771984,
0.006708427798002958,
0.09744556248188019,
0.06641560047864914,
0.030662335455417633,
-0.06501802802085876,
0.008769489824771881,
-0.040659014135599136,
-0.08094913512468338,
-0.00007460277993232012,
0.0008159146527759731,
0.033711422234773636,
-0.05275791510939598,
0.009507965296506882,
-0.01729317009449005,
-0.0007437678286805749,
-0.009397291578352451,
0.01815655454993248,
0.04744267463684082,
-0.024085165932774544,
-0.09049879759550095,
-0.054770469665527344,
0.0697169229388237,
-0.008295648731291294,
-0.009279871359467506,
-0.05963633209466934,
-0.002580707659944892,
0.03340770676732063,
0.058072928339242935,
-0.0014392508892342448,
-0.02281046472489834,
0.014828918501734734,
0.009333273395895958,
0.0008389557478949428,
0.004670094698667526,
-0.035678256303071976,
0.005816715303808451,
-0.03448287770152092,
-0.01917133666574955,
-0.034171316772699356,
0.005290820263326168,
0.028942599892616272,
0.007031680084764957,
0.023555196821689606,
0.052582576870918274,
0.0028996176552027464,
0.014269386418163776,
0.027953680604696274,
-0.019785676151514053,
-0.03867636248469353,
0.05472893640398979,
0.011154795996844769,
0.020815135911107063,
0.05316092073917389,
-0.026107678189873695,
0.037559423595666885,
-0.01090421061962843,
0.028688041493296623,
-0.010633320547640324,
-0.04485194385051727,
-0.04271547868847847,
0.002090134657919407,
0.026407791301608086,
-0.0031312897335737944,
-0.07767148315906525,
-0.0211162269115448,
0.006283028516918421,
0.035138584673404694,
0.01672978140413761,
0.06482898443937302,
-0.018405187875032425,
-0.024426303803920746,
0.00032554203062318265,
-0.04454556107521057,
-0.02447204850614071,
-0.07446300983428955,
-0.00036316344630904496,
-0.0013147792778909206,
0.0014432005118578672,
0.038688480854034424,
-0.00302430079318583,
0.03142375126481056,
-0.0315871499478817,
-0.0401691235601902,
0.007901515811681747,
0.031259339302778244,
0.005965937860310078,
0.013801992870867252,
0.010148442350327969,
0.050114791840314865,
0.0015928443754091859,
0.018422193825244904,
0.03851482272148132,
-0.028695615008473396,
-0.03250621259212494,
-0.02547132596373558,
-0.0387524776160717,
0.02688787132501602,
-0.003356773406267166,
0.022407250478863716,
-0.0010211067274212837,
-0.0017509220633655787,
-0.041399210691452026,
0.061652570962905884,
0.0006807094323448837,
0.055814601480960846,
-0.0025119951460510492,
0.008984612300992012,
-0.0002195129491155967,
0.026337722316384315,
0.010536670684814453,
0.023371199145913124,
-0.018024463206529617,
-0.011960482224822044,
-0.07831849157810211,
-0.010251408442854881,
0.07217996567487717,
0.018328892067074776,
-0.027299681678414345,
0.014563486911356449,
0.00953451357781887,
0.02582648955285549,
0.04991888254880905,
0.018408605828881264,
-0.05320270359516144,
-0.04369800537824631,
0.03188163787126541,
0.040790487080812454,
0.01952861063182354,
0.0007389678503386676,
0.015357519499957561,
-0.020130574703216553,
0.05280862748622894,
0.004303985740989447,
-0.015821948647499084,
0.028836531564593315,
-0.02957753650844097,
0.006927077192813158,
-0.011793074198067188,
-0.03717442974448204,
0.024803049862384796,
0.015294796787202358,
0.034600500017404556,
-0.004316341131925583,
-0.02275359071791172,
-0.006863207556307316,
-0.011279961094260216,
-0.00741152185946703,
0.020400308072566986,
-0.0026149170007556677,
-0.05151337385177612,
-0.037184156477451324,
0.020337553694844246,
-0.02823704294860363,
0.04771706089377403,
-0.006355824880301952,
-0.01923520490527153,
-0.004636174533516169,
0.0160461887717247,
0.03973512351512909,
-0.004945169668644667,
0.05787228047847748,
-0.0666579157114029,
-0.008817513473331928,
0.02393931895494461,
-0.05123041197657585,
0.011150828562676907,
0.03679612651467323,
-0.03209209814667702,
0.0011858149664476514,
-0.08183028548955917,
-0.027506906539201736,
0.01804039441049099,
-0.017633704468607903,
-0.0002912736963480711,
-0.00218767742626369,
-0.02196824736893177,
-0.02161289192736149,
0.004076245240867138,
-0.03554590791463852,
-0.0015921726590022445,
-0.01584833674132824,
-0.016141153872013092,
0.034594789147377014,
0.032696258276700974,
-0.018563590943813324,
0.04047120735049248,
-0.03259411081671715,
-0.032135725021362305,
-0.01705288328230381,
0.02407250925898552,
0.0183569248765707,
-0.03154408559203148,
0.07653875648975372,
0.02430671826004982,
-0.024484053254127502,
-0.015476061962544918,
-0.0211507398635149,
-0.012367639690637589,
-0.00566193088889122,
-0.021773606538772583,
0.007526461500674486,
0.003395628184080124,
-0.0438486784696579,
0.07163789868354797,
0.0219840407371521,
-0.04259292781352997,
-0.0064718895591795444,
-0.012919227592647076,
-0.023426253348588943,
-0.059895046055316925,
0.005051631014794111,
0.0021481008734554052,
-0.008474106900393963,
-0.016337838023900986,
0.017477823421359062,
0.04693842679262161,
0.02352123148739338,
0.00011077995441155508,
-0.007286978419870138,
-0.015511744655668736,
-0.012529270723462105,
0.015954820439219475,
0.07012535631656647,
-0.012298347428441048,
-0.006632429081946611,
-0.04464514181017876,
0.006854372099041939,
0.0349087156355381,
0.004395854193717241,
-0.02868356928229332,
0.07072029262781143,
0.0002856674836948514,
0.025834521278738976,
-0.031786613166332245,
0.02278849668800831,
0.02354515716433525,
-0.021022750064730644,
-0.0023072639014571905,
-0.0010416557779535651,
0.014171450398862362,
0.0009129396639764309,
0.014545006677508354,
0.04188261181116104,
0.038569118827581406,
-0.06462570279836655,
-0.0007887776591815054,
0.019479110836982727,
-0.0026624139863997698,
0.034225478768348694,
0.0002063125284621492,
-0.03709043934941292,
0.02247360348701477,
0.021551668643951416,
0.012804322876036167,
-0.017239052802324295,
-0.010218077339231968,
-0.025979479774832726,
-0.026639169082045555,
0.025646250694990158,
-0.00622138474136591,
0.014502976089715958,
0.026131223887205124,
0.07630207389593124,
0.014674141071736813,
0.020259710028767586,
0.010729738511145115,
0.018282035365700722,
-0.057893648743629456,
-0.04353085160255432,
-0.05225364863872528,
-0.0014732928248122334,
-0.060921937227249146,
-0.02583870105445385,
0.014060933142900467,
-0.001360848662443459,
-0.012236367911100388,
-0.029012005776166916,
-0.020618895068764687,
-0.052499234676361084,
0.00006885127368150279,
-0.06246258690953255,
0.0014357416657730937,
-0.04585433006286621,
0.01203980389982462,
0.04960983619093895,
-0.0069344537332654,
0.005910923238843679,
0.029921552166342735,
-0.033530671149492264,
0.044398996978998184,
0.03873236104846001,
0.008148177526891232,
0.013575331307947636,
0.005890672095119953,
0.06128717586398125,
0.03354036435484886,
-0.041618119925260544,
-0.03605847433209419,
0.03356301039457321,
0.04745230823755264,
-0.009336313232779503,
0.006855980958789587,
-0.033512525260448456,
-0.05222170427441597,
-0.017469225451350212,
0.0024851192720234394,
0.05266258865594864,
0.0003168946714140475,
0.008818304166197777,
0.04695701226592064,
0.030933618545532227,
0.00042673241114243865,
0.055199071764945984,
0.047371815890073776,
0.015910038724541664,
-0.020971819758415222,
-0.05819094926118851,
0.026744237169623375,
-0.05486617982387543,
-0.009837491437792778,
0.004309386480599642,
-0.02005132846534252,
-0.012505007907748222,
0.02596234530210495,
0.0024199921172112226,
0.018976764753460884,
0.003291302127763629,
0.02091137319803238,
-0.007650498766452074,
0.020075742155313492,
-0.0020620650611817837,
-0.030036913231015205,
-0.05457860231399536,
0.05392118915915489,
0.027474956586956978,
0.0012656992767006159,
-0.0050920648500323296,
-0.08276547491550446,
-0.010244777426123619,
0.0551522821187973,
0.026898443698883057,
-0.006593331228941679,
-0.012980773113667965,
-0.0719289481639862,
-0.025972213596105576,
0.023496335372328758,
-0.030890969559550285,
0.018074501305818558,
-0.02077442593872547,
0.01765148714184761,
-0.020337920635938644,
-0.008381901308894157,
-0.0164636243134737,
0.026671940460801125,
-0.03368286043405533,
0.03137320652604103,
-0.04322483763098717,
-0.00843939557671547,
0.007160754408687353,
0.021888231858611107,
0.015185466036200523,
0.026408007368445396,
0.02820499986410141,
0.022859979420900345,
-0.006679075304418802,
-0.00030293277814053,
-0.005678877234458923,
-0.10536590963602066,
-0.019529717043042183,
0.03975987061858177,
-0.028620107099413872,
0.031851429492235184,
-0.05170443654060364,
-0.04354375600814819,
0.015176852233707905,
-0.0005199289880692959,
0.013476628810167313,
0.027065768837928772,
-0.0394202396273613,
0.044497016817331314,
0.00745413638651371,
-0.011907738633453846,
0.08378888666629791,
0.03652032092213631,
-0.007708055432885885,
0.007938441820442677,
-0.020378245040774345,
0.030795546248555183,
-0.04650261253118515,
-0.006831702776253223,
-0.02064157836139202,
0.015602167695760727,
-0.03202386945486069,
0.08421620726585388,
0.003836608724668622,
0.01193950790911913,
0.02624646946787834,
-0.03965095803141594,
0.007451431825757027,
0.03377160429954529,
-0.02290995977818966,
-0.023152004927396774,
-0.06372162699699402,
0.014984158799052238,
-0.015607672743499279,
-0.016946004703640938,
0.018560832366347313,
0.013374537229537964,
0.022787069901823997,
0.012736727483570576,
-0.008521161042153835,
0.00505371717736125,
-0.002608852693811059,
-0.018017301335930824,
0.03888467699289322,
-0.02669905312359333,
0.03714297339320183,
-0.031982868909835815,
-0.018741197884082794,
-0.017300967127084732,
-0.05828172713518143,
-0.024299822747707367,
0.0018533187685534358,
0.02735746093094349,
0.002490722807124257,
0.00469852052628994,
0.013821808621287346,
0.013735894113779068,
0.005644011776894331,
-0.05938001349568367,
-0.06937257200479507,
-0.021650757640600204,
-0.001613900763913989,
0.007505367044359446,
-0.010433991439640522,
0.016093896701931953,
-0.03904087841510773,
-0.04670638218522072,
0.018880493938922882,
0.02482791431248188,
-0.06399139761924744,
-0.02598922699689865,
-0.0012533239787444472,
0.013938738033175468,
0.03301118686795235,
0.01759454980492592,
-0.016832077875733376,
0.01127393078058958,
0.034252095967531204,
0.011182878166437149,
0.031738005578517914,
0.05658590793609619,
0.005494473967701197,
-0.002128712134435773,
-0.009928498417139053,
-0.007832773961126804,
0.0551920011639595,
0.011885421350598335,
-0.04146454110741615,
0.059504952281713486,
0.013369649648666382,
0.01751118339598179,
-0.035252124071121216,
0.03242061659693718,
-0.00558421341702342,
0.007260557729750872,
0.016852661967277527,
-0.0017728732200339437,
0.01002836599946022,
-0.008596951141953468,
0.04359166696667671,
-0.030239790678024292,
0.020215338096022606,
0.010113254189491272,
0.029691504314541817,
-0.024091370403766632,
-0.0012573318090289831,
0.020829882472753525,
-0.026615379378199577,
0.052717018872499466,
-0.030249832198023796,
0.04298445209860802,
0.013258261606097221,
-0.006901196204125881,
-0.03632716089487076,
-0.03931795060634613,
-0.06137242913246155,
-0.025503363460302353,
0.06521578878164291,
-0.016323411837220192,
-0.0077325147576630116,
0.0014080636901780963,
-0.03246937319636345,
0.0034149931743741035,
-0.030278250575065613,
0.022414011880755424,
0.03243498131632805,
0.009543709456920624,
0.004708793479949236,
-0.03156476095318794,
-0.005709539633244276,
0.03711225837469101,
0.03136385604739189,
-0.03563954681158066,
-0.010245920158922672,
0.012420116923749447,
0.035744134336709976,
0.021024657413363457,
-0.007070564199239016,
-0.010699375532567501,
0.03851740062236786,
-0.01661350019276142,
0.03662636876106262,
0.004063828848302364,
-0.025699669495224953,
0.04730517789721489,
0.03231018781661987,
0.013524185866117477,
0.01987474597990513,
-0.020452408120036125,
-0.05452554300427437,
0.032099176198244095,
-0.0055395676754415035,
-0.005809583235532045,
-0.00593754043802619,
0.038422949612140656,
0.0382201112806797,
-0.0052788532339036465,
-0.04148687794804573,
0.011220511980354786,
-0.08138418942689896,
-0.01723976619541645,
-0.033947449177503586,
-0.010918300598859787,
0.04598304629325867,
0.01280022133141756,
-0.03240006044507027,
0.006508433260023594,
-0.024678541347384453,
-0.0017286253860220313,
-0.0023802928626537323,
0.05642423778772354,
-0.028887631371617317,
0.025054579600691795,
-0.030330441892147064,
0.022901030257344246,
-0.01774986833333969,
0.029918072745203972,
0.10896312445402145,
0.0709584429860115,
0.012339874170720577,
-0.04811607301235199,
0.00827714055776596,
-0.023086704313755035,
0.029951434582471848,
-0.05282127857208252,
-0.0024658343754708767,
-0.03954542800784111,
-0.01571926847100258,
0.012534660287201405,
0.0478551909327507,
0.021613135933876038,
0.04186910018324852,
0.03076131083071232,
-0.04110168293118477,
-0.014496922492980957,
-0.02597695402801037,
-0.005012297537177801,
0.0000924800697248429,
0.027988092973828316,
-0.03577438369393349,
0.015855863690376282,
-0.0008965000743046403,
0.02799818478524685,
-0.0478227362036705,
-0.025287538766860962,
0.025352036580443382,
-0.021329201757907867,
-0.015122273936867714,
-0.012443525716662407,
-0.008804620243608952,
-0.0019214038038626313,
-0.07865870743989944,
-0.02200126089155674,
0.005571089684963226,
0.023871658369898796,
0.05055889114737511,
0.04365305230021477,
0.020116128027439117,
-0.003755199257284403,
0.009229798801243305,
0.03061126545071602,
-0.027848748490214348,
-0.02322169952094555,
-0.02510049380362034,
0.07698194682598114,
-0.011128892190754414,
-0.015455689281225204,
0.004513747524470091,
0.004927514120936394,
0.00033741959487088025,
-0.02612150087952614,
-0.02315208874642849,
-0.008361808955669403,
0.01471687015146017,
-0.008811071515083313,
-0.011859778314828873,
-0.05717906355857849,
0.04243436083197594,
0.0016312916995957494,
-0.000232536782277748,
0.01625387743115425,
0.027582570910453796,
0.01572498120367527,
-0.02239193022251129,
0.04058576002717018,
-0.003876960836350918,
0.004225867800414562,
-0.01441341731697321,
-0.007542072329670191,
-0.04212380573153496,
-0.005395542364567518,
0.030660707503557205,
0.02182232029736042,
0.021432608366012573,
0.04414689540863037,
-0.01973642408847809,
-0.021764632314443588,
-0.04924876242876053,
0.03968755155801773,
0.02279176376760006,
-0.020880907773971558,
-0.01071933563798666,
0.02899775467813015,
-0.003764081746339798,
0.07104909420013428,
-0.032919708639383316,
0.011567522771656513,
0.023166755214333534,
-0.005643296055495739,
-0.015087500214576721,
-0.048952214419841766,
-0.010844530537724495,
0.0265401229262352,
-0.019087309017777443,
-0.025448109954595566,
-0.03896799311041832,
0.014362956397235394,
0.011394250206649303,
0.01063371542841196,
-0.01824563555419445,
0.041719548404216766,
0.0031015630811452866,
0.00939496885985136,
0.044653624296188354,
-0.008158358745276928,
0.001331535866484046,
0.030415942892432213,
0.014602468349039555,
-0.03365253657102585,
-0.0413682647049427,
-0.013387301005423069,
0.010423523373901844,
-0.0017865666886791587,
0.0367346815764904,
-0.0478147491812706,
-0.019559908658266068,
-0.02497289888560772,
0.0474151186645031,
-0.0313500314950943,
-0.035819608718156815,
-0.06387480348348618,
0.027649998664855957,
0.018168823793530464,
-0.042335592210292816,
-0.0052839526906609535,
0.033351294696331024,
0.029270494356751442,
-0.005738734733313322,
0.0344993993639946,
0.03441770002245903,
-0.02776876837015152,
-0.018892578780651093,
-0.0034891844261437654,
0.004369731992483139,
0.021144112572073936,
-0.00949019379913807,
-0.012678381986916065,
0.02619207091629505,
-0.024202361702919006,
-0.038192037492990494,
0.02528540976345539,
0.01226886734366417,
0.008487927727401257,
0.07923614233732224,
-0.001272727269679308,
0.014331011101603508,
0.05157150328159332,
-0.0264652781188488,
-0.010303489863872528,
0.01895696111023426,
-0.036041878163814545,
-0.033400122076272964,
-0.015948262065649033,
0.024738110601902008,
0.033802472054958344,
0.01571819745004177,
0.07530447095632553,
0.025994833558797836,
-0.021823277696967125,
-0.01863931678235531,
-0.013430659659206867,
0.005737348925322294,
0.028805522248148918,
0.039840009063482285,
0.0005337206530384719,
-0.02248278073966503,
0.02744193561375141,
-0.03686019033193588,
0.032209355384111404,
0.029284769669175148,
0.011628108099102974,
-0.09512235969305038,
-0.05558815598487854,
0.012312840670347214,
-0.0006731027970090508,
0.04262545332312584,
-0.021012183278799057,
-0.017832882702350616,
0.030767690390348434,
-0.06407956033945084,
0.008704021573066711,
0.02923840843141079,
-0.01598144881427288,
-0.008940364234149456,
-0.010562540963292122,
-0.03201231360435486,
0.028821660205721855,
0.0054684774950146675,
0.05937217175960541,
-0.001852450892329216,
0.006355030927807093,
0.008694902062416077,
-0.024638766422867775,
-0.06469066441059113,
0.04638245329260826,
0.023112356662750244,
-0.00012781922123394907,
0.05811736360192299,
-0.014056521467864513,
0.007406552322208881,
0.02424638904631138,
0.0409378707408905,
-0.046035148203372955,
-0.004647710360586643,
0.015769390389323235,
0.01952844113111496,
0.014902656897902489,
0.010927947238087654,
-0.025033876299858093,
0.0024107531644403934,
0.026454292237758636,
-0.00876758061349392,
0.019858790561556816,
0.01722317934036255,
-0.01150459237396717,
0.013816934078931808,
-0.00970999151468277,
-0.022892100736498833,
0.05320103093981743,
-0.042901553213596344,
-0.037240639328956604,
-0.02940933033823967,
0.03714930638670921,
-0.004968840628862381,
-0.004487032536417246,
0.0012351470068097115,
-0.05458482354879379,
0.021013565361499786,
-0.009592738933861256,
0.00550201116129756,
-0.019750576466321945,
-0.009315249510109425,
-0.006218635942786932,
0.01755695790052414,
0.023354273289442062,
0.02081156149506569,
-0.022245371714234352,
-0.06235072761774063,
-0.018548691645264626,
0.02872120961546898,
0.024376777932047844,
0.01613393798470497,
-0.0424320325255394,
-0.0560554563999176,
0.02726280689239502,
-0.013132452964782715,
0.05474544316530228,
-0.021156921982765198,
-0.03376135230064392,
-0.00020629291248042136,
-0.046312883496284485,
0.04405205696821213,
-0.009820142760872841,
-0.003777111880481243,
-0.03274429589509964,
0.00763075053691864,
0.007970403879880905,
0.026935109868645668,
0.03923194482922554,
-0.00749616464599967,
0.0051314388401806355,
0.03371354937553406,
0.008285285905003548,
0.020297711715102196,
-0.021381590515375137,
0.0063361735083162785,
-0.009422803297638893,
0.002436775481328368,
-0.005741693079471588,
-0.01846487633883953,
-0.03810730576515198,
0.054152872413396835,
0.0429733470082283,
0.005306497681885958,
0.027272189036011696,
-0.04578069597482681,
-0.056895483285188675,
0.02449181117117405,
0.023127954453229904,
-0.04504036530852318,
0.057700466364622116,
-0.01106838695704937,
0.02321670576930046,
0.04571559652686119,
-0.028082307428121567,
0.003634198335930705,
-0.010719513520598412,
-0.06615430861711502,
0.012243706732988358,
-0.00980385486036539,
-0.010158962570130825,
-0.0012255137553438544,
-0.04607010632753372,
0.034199975430965424,
0.02070816233754158,
-0.06305748969316483,
-0.006966612301766872,
0.029203657060861588,
0.004954973701387644,
0.02411041408777237,
0.04385790973901749,
-0.003832703223451972,
0.01268476527184248,
-0.010104943066835403,
0.006944181863218546,
0.029255090281367302,
0.017320159822702408,
0.00494572427123785,
0.002401668345555663,
-0.003268746891990304,
0.010928264819085598,
-0.005430020857602358,
0.011280841194093227,
0.01011546328663826,
-0.006983435712754726,
-0.016333092004060745,
0.003430758835747838,
0.002088323701173067,
-0.024831917136907578,
0.02201917953789234,
-0.01897113211452961,
0.08328653872013092,
-0.041098702698946,
0.015314782038331032,
0.007790422532707453,
0.030052844434976578,
0.010335971601307392,
0.01679307222366333,
0.009766343049705029,
0.04235953465104103,
-0.03038354218006134,
-0.03323082998394966,
-0.00499062379822135,
-0.012239556759595871,
0.01798449270427227,
-0.0886659100651741,
-0.01304932776838541,
-0.005113339051604271,
0.0013613217743113637,
-0.006671650800853968,
-0.02245495468378067,
-0.04118482768535614,
0.00069232884561643,
0.030694805085659027,
0.007402838673442602,
0.03604995086789131,
-0.017823560163378716,
-0.022131722420454025,
-0.005000898148864508,
0.030688147991895676,
-0.0355595238506794,
0.00003978280074079521,
-0.049374159425497055,
0.027818506583571434,
-0.059966061264276505,
0.014961453154683113
] |
<p>My home town (Iran, Lamerd) has very hot summer (always > 45+ degree) with dry weather and sharp sun shine. I used some black tubes under glassy box to heat up water. It was a natural thermal siphon and did not need pimping. definite volume of salty water in the container was connected to the tube glassy box. the empty space of the container was filled with hot humid. I have just connected this humid to a condenser. finally I had the distilled water but production rate was slow. Is that economically feasible to scale it up and be used for drinking water?<img src="http://i.stack.imgur.com/V0Qqz.jpg" alt="My home made apparatus"></p> | 2,846 | [
-0.014018778689205647,
-0.02298312820494175,
-0.0018380676629021764,
-0.0015674561727792025,
0.05532734841108322,
-0.009218242950737476,
-0.0244176983833313,
-0.006826010532677174,
0.013542361557483673,
-0.03241558000445366,
0.07789228111505508,
0.0581236258149147,
0.01853935793042183,
-0.006865462753921747,
0.00298540317453444,
0.03337554633617401,
0.01905663311481476,
-0.02395079843699932,
0.002075694501399994,
0.018804403021931648,
-0.008433325216174126,
0.040184177458286285,
-0.007977774366736412,
-0.01523374393582344,
-0.016779543831944466,
0.010631734505295753,
-0.006796638946980238,
-0.02221611887216568,
-0.025998780503869057,
0.037249740213155746,
0.010392882861196995,
-0.025314338505268097,
0.02234841138124466,
-0.0033381108660250902,
0.02784893848001957,
-0.002385481959208846,
-0.03059522435069084,
-0.012416242621839046,
-0.04007649049162865,
0.027405235916376114,
-0.012629813514649868,
0.001011253916658461,
-0.0026715253479778767,
0.03329351916909218,
-0.01480654627084732,
-0.0058287386782467365,
0.014419648796319962,
-0.02946494147181511,
0.05793391540646553,
-0.08474310487508774,
0.0025192357134073973,
0.009198801591992378,
0.03209342807531357,
0.03657440468668938,
0.002167126629501581,
-0.002875787438824773,
0.07047862559556961,
0.025804735720157623,
0.01745927706360817,
-0.019776958972215652,
0.016636114567518234,
0.0026825882960110903,
-0.01674010045826435,
-0.026156725361943245,
-0.0387527234852314,
-0.017951667308807373,
-0.03402484953403473,
-0.01576988399028778,
0.015350528061389923,
-0.018254222348332405,
0.057156383991241455,
0.0078058443032205105,
0.02841549552977085,
-0.0011399154318496585,
0.01694347709417343,
-0.016059361398220062,
0.001262362115085125,
0.03638942167162895,
-0.002542310394346714,
0.05136833339929581,
-0.0016748441848903894,
0.02690196968615055,
0.007429888937622309,
0.047060295939445496,
0.012997210025787354,
-0.02729106694459915,
0.04872797057032585,
-0.03215709328651428,
0.03148218244314194,
0.005371918436139822,
0.03510720655322075,
-0.0022206781432032585,
0.06490658223628998,
0.0490218885242939,
-0.006651720963418484,
-0.0029097101651132107,
-0.01138220727443695,
0.021466286852955818,
0.008893090300261974,
-0.05201513692736626,
0.02227269485592842,
-0.008123521693050861,
0.04068354144692421,
0.10863061994314194,
0.007958817295730114,
-0.0660683885216713,
-0.012817726470530033,
-0.016830869019031525,
-0.0028992679435759783,
0.02873356081545353,
-0.04911663383245468,
-0.017556024715304375,
0.010254202410578728,
-0.035437654703855515,
0.0010008963290601969,
-0.028447985649108887,
-0.009475398808717728,
-0.022697793319821358,
0.041473403573036194,
0.036875709891319275,
0.05197962000966072,
0.01681486703455448,
0.0614481121301651,
-0.04500063881278038,
-0.061086803674697876,
0.014078361913561821,
-0.037256624549627304,
-0.010506597347557545,
-0.025204667821526527,
0.04967913776636124,
0.024696331471204758,
0.012187245301902294,
0.008980386890470982,
-0.03873546048998833,
0.028727764263749123,
-0.036892570555210114,
-0.06636402010917664,
-0.027068331837654114,
0.0393558144569397,
-0.02293950319290161,
0.011095061898231506,
-0.061062201857566833,
0.024104595184326172,
0.024644162505865097,
0.07998961955308914,
-0.02236681990325451,
0.023990914225578308,
-0.020571665838360786,
0.05002804845571518,
0.007717568892985582,
-0.04656239598989487,
-0.003965720068663359,
0.013426350429654121,
-0.055012937635183334,
-0.011605842038989067,
-0.03562522679567337,
0.04418595880270004,
0.07336165755987167,
0.0010643383720889688,
-0.039995722472667694,
0.03850403055548668,
0.013529807329177856,
-0.002453562803566456,
0.009883714839816093,
-0.0037974410224705935,
-0.034406453371047974,
0.05729245766997337,
-0.026964113116264343,
-0.008861019276082516,
-0.019253650680184364,
0.006342517677694559,
0.015627790242433548,
0.03275937959551811,
0.014304254204034805,
0.05418629199266434,
-0.0038936410564929247,
0.004025772213935852,
-0.013129184953868389,
0.034734923392534256,
0.03491991385817528,
-0.01835581846535206,
0.025803836062550545,
-0.001008430728688836,
0.013822954148054123,
0.015067648142576218,
0.03527924790978432,
-0.0059814536944031715,
-0.03950716182589531,
0.025992101058363914,
-0.10260838270187378,
-0.027896234765648842,
-0.033889785408973694,
-0.0025580988731235266,
-0.015694251284003258,
0.013415343128144741,
-0.013827051967382431,
-0.010054078884422779,
0.037007711827754974,
0.006078843027353287,
-0.03864328935742378,
-0.021016787737607956,
-0.017501775175333023,
0.04827306792140007,
0.03956357017159462,
0.030638253316283226,
0.04120036959648132,
0.03515156731009483,
-0.04712729901075363,
0.007608333136886358,
-0.0431128665804863,
-0.03860286623239517,
-0.046223465353250504,
-0.014183503575623035,
-0.009659347124397755,
-0.03186849504709244,
-0.00716016162186861,
0.0017078046221286058,
0.015875132754445076,
0.02625163458287716,
0.03827720135450363,
-0.061267875134944916,
0.10951828211545944,
0.06537957489490509,
-0.011597364209592342,
0.048392750322818756,
0.0007802274194546044,
0.03266458958387375,
-0.015124711208045483,
-0.009244929999113083,
-0.02898532524704933,
-0.06638374924659729,
0.02517198771238327,
0.01048789732158184,
0.0048154378309845924,
-0.043210845440626144,
0.022520126774907112,
0.012373552657663822,
0.022349046543240547,
0.03432221710681915,
-0.01267971284687519,
-0.008479460142552853,
0.026286864653229713,
0.03336574509739876,
0.046095866709947586,
-0.011982428841292858,
0.03453952819108963,
-0.01604175753891468,
0.0234613548964262,
0.025784427300095558,
-0.05097842961549759,
0.03580706939101219,
0.032544322311878204,
-0.025401214137673378,
-0.00036421502591110766,
-0.021731702610850334,
-0.006122163496911526,
0.04294733330607414,
-0.06975456327199936,
-0.008193966932594776,
0.009130137041211128,
-0.013625881634652615,
0.054203931242227554,
-0.04267784580588341,
0.009201832115650177,
0.014165157452225685,
0.04992471635341644,
-0.02812390960752964,
-0.04706830158829689,
0.03648082911968231,
-0.05394754186272621,
0.014358208514750004,
-0.03063097596168518,
0.02734493836760521,
-0.031186794862151146,
0.020160498097538948,
0.01970169134438038,
-0.008576929569244385,
0.0011782583314925432,
-0.03159838169813156,
-0.013548878021538258,
-0.027967656031250954,
0.014648702926933765,
-0.008991943672299385,
0.01253257691860199,
-0.03767992928624153,
0.006248024757951498,
0.042834047228097916,
-0.023400327190756798,
0.03536192700266838,
-0.008072366006672382,
-0.02089867927134037,
0.010771157220005989,
0.029530618339776993,
-0.038775283843278885,
-0.007266972213983536,
-0.022375404834747314,
0.02875731885433197,
-0.002620463725179434,
-0.02239011786878109,
0.019299162551760674,
-0.03145622834563255,
-0.016248947009444237,
0.010674168355762959,
-0.08104615658521652,
-0.03219776600599289,
-0.015703123062849045,
0.007256921846419573,
-0.00004743439785670489,
-0.0527639165520668,
0.02922680974006653,
0.02426968701183796,
-0.04484117403626442,
0.027615811675786972,
-0.06767362356185913,
-0.08362507820129395,
0.025516614317893982,
0.01898360438644886,
0.019303718581795692,
0.014531424269080162,
-0.000057026314607355744,
0.034747347235679626,
0.02315634861588478,
-0.08157320320606232,
0.005036548245698214,
-0.016703585162758827,
-0.011999459937214851,
-0.02455788664519787,
-0.024650532752275467,
0.04308206960558891,
-0.03255612775683403,
0.02338222973048687,
0.0011447281576693058,
-0.012901748530566692,
0.04318607598543167,
0.03450876846909523,
-0.0019524074159562588,
0.007445231080055237,
-0.0004286619368940592,
0.013161752372980118,
0.06332609802484512,
0.019791219383478165,
-0.009697739034891129,
0.0028772372752428055,
-0.046184707432985306,
0.04658393934369087,
0.03260236233472824,
-0.04948138818144798,
0.013586790300905704,
0.03361092880368233,
-0.011649467051029205,
-0.06048259139060974,
0.015083725564181805,
-0.01642359420657158,
0.033160630613565445,
0.013253294862806797,
-0.015173890627920628,
0.02333131432533264,
0.024238545447587967,
-0.0031085414811968803,
0.013597877696156502,
0.0682394951581955,
-0.011570771224796772,
-0.048348959535360336,
0.005107871722429991,
0.015867052599787712,
-0.0014480656245723367,
0.021741829812526703,
-0.016233300790190697,
0.033185526728630066,
0.034505512565374374,
0.017865292727947235,
0.010681075975298882,
-0.009532539173960686,
0.009042784571647644,
-0.05939340963959694,
-0.015358342789113522,
-0.0022015764843672514,
0.05620379373431206,
0.03616451472043991,
0.0206746906042099,
-0.010003872215747833,
-0.020371779799461365,
0.0027257876936346292,
-0.019081778824329376,
-0.06375379860401154,
0.01668458618223667,
-0.004998343531042337,
0.0012435468379408121,
-0.017742786556482315,
-0.01841091923415661,
-0.007933719083666801,
0.006562677212059498,
-0.03817366436123848,
0.009191717021167278,
0.03410320729017258,
-0.02229861542582512,
0.011616774834692478,
0.0007160388631746173,
-0.008509723469614983,
0.003610030049458146,
-0.0017406933475285769,
0.008623727597296238,
-0.016599338501691818,
0.015512091107666492,
-0.00047282048035413027,
-0.0066767847165465355,
0.007770970463752747,
-0.01888027787208557,
0.021875351667404175,
0.04696785658597946,
0.02948867715895176,
0.0360640287399292,
0.04995676130056381,
-0.0039230892434716225,
-0.016138674691319466,
0.04734260216355324,
0.024379385635256767,
-0.023417267948389053,
0.008756599389016628,
-0.04067068174481392,
-0.02109936997294426,
-0.032393213361501694,
0.05545032024383545,
-0.00697306776419282,
-0.007217800244688988,
0.026233922690153122,
-0.002105321502313018,
-0.05131429806351662,
-0.031317245215177536,
0.039160940796136856,
0.0511971078813076,
-0.033433061093091965,
-0.006503221578896046,
-0.034356214106082916,
-0.05261855572462082,
-0.01732131838798523,
0.041670411825180054,
0.022932251915335655,
0.0059557161293923855,
0.0005138818523846567,
-0.030208399519324303,
0.04421573504805565,
0.0666562169790268,
-0.003387042786926031,
0.052153389900922775,
0.0317920483648777,
0.03701373562216759,
-0.019456420093774796,
-0.03332450985908508,
0.021241964772343636,
0.024436384439468384,
0.007682485971599817,
-0.027689097449183464,
-0.012101791799068451,
-0.0866272896528244,
-0.0002683950588107109,
0.010053843259811401,
0.06308367848396301,
-0.023771338164806366,
0.021504200994968414,
-0.04484756663441658,
-0.032891832292079926,
0.08064582943916321,
-0.01360856369137764,
0.024266138672828674,
-0.029192296788096428,
-0.01481150183826685,
-0.014799344353377819,
-0.028496941551566124,
-0.004846086725592613,
-0.02032800391316414,
-0.029341550543904305,
-0.0038042368832975626,
-0.019425638020038605,
-0.005194781813770533,
0.02085629478096962,
0.008837970905005932,
0.01023529190570116,
0.01676727831363678,
0.01186476368457079,
-0.005751384887844324,
0.0026509512681514025,
0.02985868602991104,
-0.007349601946771145,
-0.036294613033533096,
0.02199580706655979,
-0.019554438069462776,
0.0026051560416817665,
-0.0031917751766741276,
-0.005207099486142397,
0.030756911262869835,
0.03195205703377724,
0.041766222566366196,
0.009286296553909779,
0.01648818887770176,
-0.04107920452952385,
-0.008048541843891144,
0.006697921082377434,
0.02151554264128208,
0.00976531207561493,
0.03934086486697197,
-0.0007552457973361015,
0.004068697802722454,
-0.04496757686138153,
0.033924926072359085,
-0.04036060720682144,
-0.035968855023384094,
-0.015166619792580605,
0.018170971423387527,
-0.029341477900743484,
0.04288141056895256,
0.0021225805394351482,
0.03183021396398544,
-0.00916899461299181,
0.007661392912268639,
0.054922107607126236,
0.002143654739484191,
-0.0007456174353137612,
-0.03189099207520485,
-0.005541931837797165,
0.05379485338926315,
0.013708273880183697,
-0.045122116804122925,
0.01459032017737627,
-0.019520873203873634,
0.02605360560119152,
0.009846744127571583,
-0.054261256009340286,
0.03226490318775177,
-0.028799816966056824,
0.004669751040637493,
0.03353702649474144,
-0.0445728525519371,
0.02236129902303219,
-0.031169867143034935,
0.04970622435212135,
0.051647741347551346,
-0.08066359162330627,
0.020901832729578018,
0.05403159558773041,
0.002205277094617486,
-0.02702919766306877,
-0.07684913277626038,
0.03376494348049164,
0.0023836020845919847,
-0.011058136820793152,
-0.04840392619371414,
-0.019442306831479073,
0.07134175300598145,
-0.01590696908533573,
-0.015088295564055443,
-0.050897516310214996,
-0.01695011928677559,
-0.0005247531807981431,
-0.03274104371666908,
-0.051829252392053604,
0.03389723226428032,
0.02761990576982498,
0.013384529389441013,
-0.024032503366470337,
0.02440275438129902,
0.09361124783754349,
-0.020910043269395828,
-0.01658661477267742,
-0.00010330932127544656,
-0.028902936726808548,
-0.03804708272218704,
-0.047775160521268845,
0.012725194916129112,
-0.040157612413167953,
-0.01993604190647602,
-0.0035007346887141466,
-0.004926521331071854,
0.02635117620229721,
-0.006602081470191479,
0.0020171054638922215,
0.007244325242936611,
0.053498681634664536,
-0.007920834235846996,
0.009200540371239185,
0.04220206290483475,
0.018664207309484482,
0.01600777916610241,
-0.04005284607410431,
-0.016640182584524155,
-0.046529460698366165,
-0.02774137072265148,
-0.015698211267590523,
-0.03431286662817001,
-0.006007668096572161,
0.006681290455162525,
0.05538758635520935,
0.0014411569572985172,
0.008266312070190907,
0.02018844522535801,
-0.0027811930049210787,
0.0064459675922989845,
0.019300542771816254,
-0.012703021056950092,
-0.0363592691719532,
0.008894030004739761,
-0.04024685546755791,
-0.0262041836977005,
-0.02046142891049385,
-0.0008082339772954583,
0.035593003034591675,
-0.016425320878624916,
0.03494948893785477,
0.06644387543201447,
0.022138576954603195,
0.03222985565662384,
0.043296512216329575,
0.0003110601974185556,
0.017388099804520607,
-0.01095582265406847,
0.029393043369054794,
-0.023390784859657288,
-0.015566716901957989,
0.0007076202891767025,
0.02636440098285675,
0.01385817676782608,
0.026491796597838402,
0.05471227690577507,
0.016121521592140198,
-0.0037469130475074053,
-0.06076892092823982,
-0.06059928238391876,
-0.016259850934147835,
-0.047828927636146545,
0.024255787953734398,
-0.003859964432194829,
-0.035471443086862564,
0.03380289673805237,
0.00309292902238667,
-0.002292534103617072,
-0.06362593919038773,
0.013969231396913528,
-0.024945134297013283,
0.005659695249050856,
-0.007402750197798014,
0.009102790616452694,
-0.012921836227178574,
0.03567783534526825,
-0.002826009877026081,
0.038673970848321915,
0.08411087095737457,
-0.008656972087919712,
-0.03769395500421524,
0.014606327749788761,
-0.0356844961643219,
-0.02624579146504402,
0.04881234094500542,
0.0006717107607983053,
-0.003359938506036997,
-0.02670663595199585,
-0.007623840123414993,
0.0008263513445854187,
-0.01324385218322277,
-0.0012697145575657487,
0.034781165421009064,
0.012008431367576122,
0.003383949166163802,
0.035635799169540405,
0.014256118796765804,
0.009720763191580772,
0.11557696014642715,
0.026848604902625084,
-0.004460580181330442,
-0.049972452223300934,
0.022213177755475044,
-0.019685309380292892,
0.013134418055415154,
-0.01604919321835041,
-0.0031340476125478745,
-0.012371518649160862,
0.0003467811911832541,
0.00568170752376318,
0.044632069766521454,
-0.013053038157522678,
0.045995909720659256,
0.03468546271324158,
-0.0550088994204998,
-0.06882632523775101,
0.035079024732112885,
0.012956243008375168,
-0.051073912531137466,
0.012967774644494057,
-0.054545141756534576,
0.04122879356145859,
-0.02999943308532238,
-0.030909081920981407,
-0.013432984240353107,
-0.03011750988662243,
0.011906013824045658,
0.021821606904268265,
-0.04038625210523605,
0.013669588603079319,
-0.02852088212966919,
0.0009624905069358647,
-0.054275672882795334,
-0.026906387880444527,
0.02077261544764042,
-0.05180136486887932,
-0.02642839588224888,
0.04945255443453789,
0.05500952526926994,
-0.004662760067731142,
-0.0008122330182231963,
0.04686499759554863,
-0.047979339957237244,
0.0084659643471241,
-0.004402242600917816,
0.008361799642443657,
0.00003077035944443196,
-0.02058545872569084,
-0.013240203261375427,
-0.01373382844030857,
0.017908411100506783,
-0.051034774631261826,
-0.028247371315956116,
-0.00005316759416018613,
0.039966970682144165,
-0.034585025161504745,
-0.0282882247120142,
-0.004973884206265211,
0.02770540863275528,
-0.0182010717689991,
-0.00930324662476778,
-0.016202740371227264,
0.007866265252232552,
-0.024492742493748665,
-0.003691969672217965,
0.02530503086745739,
0.004636513534933329,
-0.02028667740523815,
-0.05323977395892143,
-0.01883070543408394,
0.004254948813468218,
0.009834283962845802,
-0.007099671754986048,
0.017356805503368378,
0.051237091422080994,
-0.0009752577752806246,
-0.013241232372820377,
-0.0004858358297497034,
-0.009171338751912117,
0.03191159665584564,
-0.04756062477827072,
-0.008076966740190983,
-0.05363849550485611,
0.009615307673811913,
-0.02028326317667961,
0.030476484447717667,
-0.020639726892113686,
-0.0022102524526417255,
0.00838217418640852,
0.05387571454048157,
0.043247874826192856,
-0.029568331316113472,
-0.03341231495141983,
-0.019615475088357925,
-0.0364135317504406,
-0.019074294716119766,
-0.00020238760043866932,
0.041430629789829254,
0.002165877027437091,
0.008095521479845047,
-0.018541492521762848,
-0.043162912130355835,
-0.013257486745715141,
0.02291753701865673,
0.020544283092021942,
-0.04671803116798401,
0.016339780762791634,
-0.03391081839799881,
-0.0005896352231502533,
-0.023232515901327133,
-0.03703860938549042,
-0.027532026171684265,
0.004113441798835993,
-0.020333174616098404,
-0.024699708446860313,
0.002971641719341278,
0.010673882439732552,
-0.01877736486494541,
0.03701025992631912,
-0.007142240647226572,
-0.015330402180552483,
-0.04839511588215828,
-0.043553151190280914,
-0.02457922324538231,
0.04369140416383743,
0.006231761071830988,
0.026466934010386467,
-0.03529832512140274,
-0.033894024789333344,
0.024203021079301834,
0.025073988363146782,
-0.01053048949688673,
-0.03187019005417824,
0.02553144283592701,
0.021510541439056396,
0.051379960030317307,
-0.052007224410772324,
-0.014016982167959213,
0.035472970455884933,
-0.017664026468992233,
0.01985752396285534,
0.03174937143921852,
-0.00882465299218893,
0.04000912234187126,
0.013846167363226414,
-0.022144585847854614,
0.03423203155398369,
0.08477526903152466,
-0.019351324066519737,
0.009240317158401012,
0.008733576163649559,
-0.026220595464110374,
0.012684122659265995,
0.017828194424510002,
-0.05736687034368515,
0.008185457438230515,
-0.02582113817334175,
0.047594595700502396,
0.04329568147659302,
0.04675504192709923,
-0.014643976464867592,
0.0007343579200096428,
-0.0059332773089408875,
-0.029312774538993835,
-0.005490671843290329,
-0.03575017303228378,
0.03756305202841759,
0.03012165054678917,
-0.05073738098144531,
0.014963694848120213,
0.014751700684428215,
-0.011720127426087856,
-0.0619020089507103,
0.016630234196782112,
-0.0005894495989196002,
-0.013844914734363556,
0.013476231135427952,
-0.024226056411862373,
0.00926673598587513,
0.01382502168416977,
-0.05222579091787338,
-0.04185984283685684,
-0.02446667104959488,
-0.027253255248069763,
-0.04848834499716759,
0.021059675142169,
-0.008939475752413273,
0.030176648870110512,
-0.009365133009850979,
0.02829062193632126,
0.020697956904768944,
0.06498666852712631,
-0.00839277170598507,
0.0067255739122629166,
0.012415692210197449,
0.003345893230289221,
0.0010760086588561535,
-0.028612781316041946,
0.03396010771393776,
-0.059257037937641144,
0.003611186286434531,
0.012517808936536312,
-0.05538399517536163,
0.01816580444574356,
0.031007342040538788,
0.013564983382821083,
-0.03336135298013687,
0.06714502722024918,
0.023245930671691895,
0.035509683191776276,
0.02470947988331318,
-0.017968960106372833,
0.06716278195381165,
0.022460104897618294,
-0.009535237215459347,
-0.0022184541448950768,
0.06807704269886017,
-0.009622737765312195,
0.005077906418591738,
0.040436938405036926,
-0.019372260197997093,
0.013574299402534962,
0.03858945146203041,
-0.05469757691025734,
0.03916475921869278,
0.0009637276525609195,
0.01764589175581932,
0.010705428197979927,
0.01718772202730179,
0.017907090485095978,
0.01045383419841528,
-0.006142178550362587,
-0.011187932454049587,
-0.01722295582294464,
-0.03862309828400612,
-0.007870007306337357,
-0.03174513205885887,
-0.012080798856914043,
-0.021871577948331833,
-0.013178987428545952,
0.010508928447961807,
-0.0027548533398658037,
-0.003958835266530514,
-0.03996311128139496,
-0.030418118461966515,
0.08682116121053696,
0.012460250407457352,
0.037889450788497925,
0.10599661618471146,
0.011514809913933277,
0.0021890171337872744,
-0.05104346573352814,
0.02467852644622326,
-0.02321147359907627,
0.020287638530135155,
-0.026858393102884293,
-0.02473807893693447,
0.011631693691015244,
0.016548670828342438,
0.03737178444862366,
-0.03319557383656502,
-0.012044386006891727,
-0.0260830819606781,
0.010078715160489082,
0.0332883857190609,
-0.021201850846409798,
0.0274336040019989,
0.02586154080927372,
-0.049807704985141754,
0.004380511119961739,
-0.014513194561004639,
-0.012660486623644829,
-0.02043350599706173,
0.051137685775756836,
-0.015864770859479904,
0.0016085359966382384,
-0.011660902760922909,
-0.02178408019244671,
0.025855401530861855,
-0.014136421494185925,
-0.031208792701363564,
0.08263961225748062,
-0.0313635990023613,
-0.030265159904956818,
0.04995722323656082,
0.0006939652375876904,
-0.036481671035289764,
0.01990612782537937,
-0.00896680448204279,
0.0057943109422922134,
0.02990727126598358,
-0.08049943298101425,
0.01655004546046257,
-0.017094731330871582,
-0.00027220018091611564,
0.017153771594166756,
-0.006047590170055628,
0.007573330774903297,
0.052674341946840286,
0.038285546004772186,
0.029551805928349495,
-0.0597166009247303,
-0.005871094763278961,
-0.026808805763721466,
0.02938281185925007,
-0.03118617832660675,
0.016961300745606422,
0.02896970696747303,
-0.003940621856600046,
0.015052669681608677,
0.005412759725004435,
0.00020895435591228306,
0.021700432524085045,
0.01500765047967434,
0.031762853264808655,
-0.031095005571842194,
-0.03797009587287903,
0.030777983367443085,
0.003644467331469059,
-0.01166751328855753,
0.02507312037050724,
-0.002846316434442997,
0.04747248440980911,
-0.009918706491589546,
0.004522344563156366,
-0.02858591638505459,
-0.01608825847506523,
-0.016598936170339584,
0.003890396561473608,
0.00458115478977561,
0.03577711805701256,
-0.007254458963871002,
-0.013146460987627506,
-0.011650563217699528,
-0.014311172068119049,
0.00626843236386776,
-0.018986964598298073,
0.033488549292087555,
-0.034474149346351624,
0.007151038385927677,
-0.03268416225910187,
-0.022286515682935715,
0.01774289272725582,
-0.0023022976238280535,
0.013842793181538582,
0.04575346037745476,
-0.009327673353254795,
0.023775842040777206,
-0.026497909799218178,
0.017540426924824715,
0.0403057336807251,
-0.06605498492717743,
0.0031926885712891817,
-0.012816512025892735,
-0.04059803858399391,
-0.008913417346775532,
-0.04645012691617012
] |
<p>When a polished piece of metal (or steel in particular) is heated to incandescence, how do its reflective properties change?</p>
<p>Given a mirror-like surface, would the object temporarily cease to act like a mirror at a certain temperature?
Would the specular reflection of light turn into diffuse reflection; in other words, would the surface temporarily become matte/dull?</p>
<p>I am not asking about permanent changes to the object such as melting, but rather can there be a temporary change in the reflectivity only while the the object is hot, that disappears when the object is cooled down?</p>
<p>Background of the question: I have a laser scanner that usually has trouble scanning shiny surfaces with high specular/ low diffuse reflectivity; and it seems to work a lot better for hot steel pieces than for cold ones. Glowing steel also <em>looks</em> less shiny to me than cold steel, but of course that is hard to tell with all the glowing </p> | 2,847 | [
-0.03203263878822327,
-0.06954818218946457,
0.0066199335269629955,
-0.01957102306187153,
0.03956581652164459,
0.015310523100197315,
-0.05802014842629433,
-0.03205868974328041,
-0.03571155667304993,
-0.03817097842693329,
0.03792193904519081,
0.06409532576799393,
0.05816539376974106,
-0.00013740530994255096,
0.01601569540798664,
-0.012403982691466808,
-0.0004311591910663992,
-0.04227839782834053,
-0.014891073107719421,
-0.01484716311097145,
-0.005665180739015341,
-0.009571285918354988,
0.019097212702035904,
-0.02948342077434063,
-0.07358680665493011,
0.009827043861150742,
-0.01966620609164238,
-0.011189219541847706,
0.0264744833111763,
0.00469030300155282,
-0.020241744816303253,
0.004426957573741674,
-0.012804271653294563,
-0.009093422442674637,
-0.005209865979850292,
-0.014681055210530758,
-0.025346845388412476,
-0.03649027273058891,
-0.04555760324001312,
0.047036681324243546,
0.006433997303247452,
-0.0030817980878055096,
-0.046184610575437546,
0.03855827823281288,
0.033722735941410065,
-0.05717599019408226,
-0.06307253241539001,
-0.01503421925008297,
0.023883039131760597,
-0.04048530012369156,
0.04585547745227814,
-0.020554129034280777,
0.013156935572624207,
0.03415605425834656,
0.001312196021899581,
0.0008384219836443663,
0.05252649262547493,
0.08773884177207947,
-0.0010182351106777787,
-0.008992831222712994,
-0.015628742054104805,
-0.004383140709251165,
-0.032722268253564835,
-0.0027212186250835657,
-0.02176002971827984,
0.014721142128109932,
-0.01275146845728159,
-0.06740126013755798,
0.03450433909893036,
0.015523857437074184,
0.011563080362975597,
-0.009585858322679996,
0.02321222424507141,
0.002202562987804413,
-0.001528251450508833,
-0.05190378427505493,
0.035703856498003006,
0.056094150990247726,
0.04566469416022301,
0.03648356720805168,
-0.003551927162334323,
-0.01736823096871376,
-0.010539817623794079,
0.015097050927579403,
0.029466934502124786,
0.0010038717882707715,
0.09130032360553741,
0.0037298158276826143,
0.05443291366100311,
0.05095069855451584,
0.012282152660191059,
0.007566694635897875,
0.004898267798125744,
0.026515666395425797,
-0.02351619489490986,
-0.008874408900737762,
-0.007005210034549236,
0.05360712110996246,
-0.019893012940883636,
-0.019323045387864113,
-0.011496132239699364,
0.05554669722914696,
0.03362562134861946,
0.02116767317056656,
0.006239333655685186,
-0.02017383463680744,
-0.012784278020262718,
-0.0002521323331166059,
0.021516969427466393,
-0.01302334200590849,
-0.010245822370052338,
0.016643889248371124,
-0.006822230760008097,
-0.04083409160375595,
0.04912952706217766,
-0.03266257420182228,
0.03937704488635063,
-0.016507931053638458,
0.02387889474630356,
0.051220837980508804,
-0.026669692248106003,
0.014358303509652615,
0.027485987171530724,
-0.006034324876964092,
-0.08321897685527802,
0.019894681870937347,
0.03568996489048004,
-0.024319572374224663,
-0.016734521836042404,
0.027762899175286293,
-0.015111919492483139,
-0.03833073005080223,
0.020533591508865356,
-0.03406250476837158,
-0.002992455381900072,
-0.013918745331466198,
-0.06711196899414062,
-0.0476607084274292,
0.014775090850889683,
0.005357828922569752,
0.0035846547689288855,
-0.08423371613025665,
-0.017413288354873657,
0.03212838992476463,
0.0736660361289978,
0.01419917494058609,
-0.006775360554456711,
-0.01790008135139942,
0.03506223112344742,
-0.008829504251480103,
-0.020395947620272636,
-0.04786759242415428,
0.021216508001089096,
-0.02958865277469158,
0.0004362609179224819,
-0.027280369773507118,
0.02549832873046398,
0.07542265951633453,
-0.021191049367189407,
-0.03931957110762596,
0.009733384475111961,
-0.026344137266278267,
0.04270405322313309,
0.05840831622481346,
0.03182906284928322,
-0.02482004649937153,
0.10206782072782516,
0.009124909527599812,
0.018107283860445023,
0.011218100786209106,
0.023845817893743515,
0.004242266993969679,
-0.0022197188809514046,
0.04539288580417633,
0.047309476882219315,
-0.021672073751688004,
-0.0010946800466626883,
0.023197682574391365,
0.028221117332577705,
0.037926752120256424,
-0.03791186213493347,
-0.014136485755443573,
-0.00044874250306747854,
-0.013875937089323997,
0.03911930322647095,
0.06594251841306686,
0.022945942357182503,
-0.03954114764928818,
0.014429530128836632,
-0.06046398729085922,
-0.026339765638113022,
-0.08663998544216156,
0.010034996084868908,
0.005813675466924906,
-0.013826649636030197,
0.004699183162301779,
0.002111179754137993,
0.012339329347014427,
-0.007722110487520695,
-0.058436352759599686,
0.03748636320233345,
0.034266404807567596,
0.010100442916154861,
-0.033010855317115784,
-0.013071581721305847,
0.02780897729098797,
0.03955507650971413,
0.008366512134671211,
0.03469878062605858,
-0.07073968648910522,
-0.011135702952742577,
-0.026025503873825073,
-0.012284974567592144,
0.00965890008956194,
0.005963191390037537,
-0.021060023456811905,
-0.004034734796732664,
0.011979549191892147,
-0.017385100945830345,
0.005502797197550535,
-0.0024200051557272673,
0.0530460961163044,
0.014442572370171547,
-0.019142108038067818,
-0.00962879415601492,
0.027264920994639397,
-0.004146914929151535,
0.012668353505432606,
0.00423605740070343,
-0.04251322150230408,
-0.03513799607753754,
-0.011074666865170002,
0.007017325609922409,
0.03709343075752258,
-0.07621286064386368,
0.02454519458115101,
0.012630141340196133,
0.028560960665345192,
0.038741420954465866,
0.003504806896671653,
-0.04328663647174835,
-0.0016909139230847359,
0.028288831934332848,
-0.03477413207292557,
0.013560200110077858,
0.015835106372833252,
0.001166840665973723,
0.027243994176387787,
0.027735386043787003,
-0.031782593578100204,
0.035928286612033844,
0.03259766846895218,
0.0046991934068500996,
0.030216163024306297,
-0.04980485141277313,
-0.02782641351222992,
0.05765177309513092,
0.013112214393913746,
-0.004328874871134758,
0.004031013231724501,
0.02791660465300083,
0.03232644870877266,
-0.05743957683444023,
-0.03740779310464859,
0.016074448823928833,
0.03836283087730408,
-0.01595337688922882,
-0.014507279731333256,
0.012296997010707855,
-0.0015084394253790379,
0.03933268412947655,
-0.03650525584816933,
0.025910696014761925,
-0.036982111632823944,
-0.004019096959382296,
0.009509457275271416,
0.0032716712448745966,
-0.0045604342594742775,
-0.06540562212467194,
-0.0573987253010273,
-0.04235708713531494,
-0.018534962087869644,
0.001640510163269937,
-0.0018692107405513525,
-0.07587690651416779,
-0.037227239459753036,
-0.004466018173843622,
-0.02249005436897278,
0.03389189764857292,
0.03395798057317734,
0.0036920884158462286,
0.022312544286251068,
0.002854331163689494,
-0.07639789581298828,
-0.005951437633484602,
0.028663434088230133,
-0.003584923455491662,
-0.06362450122833252,
0.005534104537218809,
0.06617487967014313,
0.0036462240386754274,
0.0006314501515589654,
0.006800757721066475,
-0.03703460842370987,
-0.04554060846567154,
0.015511748380959034,
-0.03495633229613304,
-0.02022732049226761,
-0.007860960438847542,
0.03510554879903793,
0.07233038544654846,
-0.05094286426901817,
0.02221682481467724,
-0.02522653341293335,
-0.04379473626613617,
0.035004399716854095,
0.0014516417868435383,
0.004311251919716597,
-0.010467040352523327,
-0.01578025333583355,
0.06953868269920349,
0.015003323554992676,
-0.017506692558526993,
-0.0416860468685627,
0.015573570504784584,
0.0050702025182545185,
-0.025914305821061134,
0.0007380057359114289,
0.019710620865225792,
-0.03828667104244232,
0.013438087888062,
-0.011206145398318768,
0.00803495291620493,
0.036559220403432846,
0.06404144316911697,
-0.019546782597899437,
0.03814956173300743,
-0.004141188692301512,
-0.0006844127201475203,
0.005226515233516693,
0.02488785982131958,
-0.0341717004776001,
-0.01801658608019352,
-0.003980697598308325,
0.030477318912744522,
0.06252322345972061,
-0.04385814070701599,
0.07886645942926407,
-0.008033698424696922,
-0.009084095247089863,
-0.025778690353035927,
0.06508521735668182,
-0.014934191480278969,
0.024181462824344635,
-0.041430167853832245,
0.018574582412838936,
0.03651368245482445,
0.0024250720161944628,
0.0007799900486133993,
0.034132424741983414,
0.02058013528585434,
0.0017034636111930013,
-0.0024421873968094587,
0.024818401783704758,
-0.04744797572493553,
0.0023649376817047596,
-0.021983085200190544,
0.006426035892218351,
0.04766567796468735,
0.03277355059981346,
0.016570815816521645,
0.008480893447995186,
-0.005344456993043423,
-0.01981155388057232,
-0.060524940490722656,
0.003439789405092597,
0.03884539380669594,
0.0628042072057724,
0.0038514838088303804,
0.015720468014478683,
0.06814078241586685,
0.044700320810079575,
0.023703159764409065,
-0.013342087157070637,
-0.10315273702144623,
0.028691934421658516,
-0.028619203716516495,
0.010499437339603901,
-0.03679875656962395,
0.01011577993631363,
-0.03286153823137283,
-0.025362268090248108,
-0.02473711594939232,
0.03181086480617523,
0.012763618491590023,
-0.04656613990664482,
0.005641316529363394,
-0.0046644872054457664,
-0.07271742075681686,
-0.03771204501390457,
0.05035633221268654,
0.026070941239595413,
-0.05157380923628807,
0.018775157630443573,
-0.006513937842100859,
-0.07275828719139099,
-0.006517046596854925,
-0.053986839950084686,
0.03243924304842949,
0.01456612627953291,
0.08393467962741852,
0.026464644819498062,
0.010572917759418488,
0.008494059555232525,
0.04249395802617073,
0.044950831681489944,
0.04121428728103638,
-0.025480449199676514,
-0.03198222815990448,
-0.012957251630723476,
-0.0615764781832695,
-0.048502273857593536,
0.01753517985343933,
0.04129573702812195,
-0.022240832448005676,
-0.0015978121664375067,
-0.018312795087695122,
-0.022727366536855698,
-0.02238452062010765,
-0.0203892532736063,
0.025579361245036125,
0.05380202829837799,
0.012511665001511574,
-0.012476411648094654,
0.025795502588152885,
-0.021137399598956108,
0.024345099925994873,
0.012008649297058582,
0.04375629872083664,
0.019961653277277946,
-0.004910988733172417,
-0.005229374393820763,
0.00017098154057748616,
0.013002992607653141,
-0.02390528842806816,
0.0016848203958943486,
0.0318775400519371,
0.006164742633700371,
0.013470079749822617,
0.02004174143075943,
0.06073182821273804,
0.07057172805070877,
0.0011378347408026457,
-0.02486608177423477,
-0.08373500406742096,
0.00322239613160491,
0.03740055486559868,
0.02461300604045391,
-0.058156657963991165,
-0.023778298869729042,
-0.05745348334312439,
-0.0227222740650177,
0.05988270789384842,
0.007989943958818913,
0.03170951083302498,
-0.03697408735752106,
-0.029390577226877213,
-0.019238876178860664,
0.011466431431472301,
0.0029593929648399353,
0.01634913496673107,
0.012543772347271442,
0.021138686686754227,
-0.03576042130589485,
-0.02947009913623333,
0.03754978999495506,
0.01281428150832653,
0.014559117145836353,
0.029238438233733177,
0.004067371599376202,
0.012488222680985928,
-0.016239086166024208,
0.005492394790053368,
-0.004682502243667841,
-0.054425016045570374,
-0.01761520840227604,
0.0027590682730078697,
-0.007835428230464458,
0.05169089511036873,
-0.008870147168636322,
-0.02976447343826294,
0.048396892845630646,
0.03270597383379936,
-0.018079020082950592,
0.006907300092279911,
-0.015596703626215458,
0.010651074349880219,
0.021891681477427483,
-0.025928471237421036,
0.05408450961112976,
0.028020689263939857,
0.008139993995428085,
0.016638686880469322,
0.03603111207485199,
0.02970750816166401,
-0.0593448244035244,
0.002469252562150359,
-0.004945272579789162,
-0.007635942660272121,
-0.030580684542655945,
0.07382623851299286,
-0.007583138067275286,
0.00361926993355155,
-0.006840042304247618,
-0.03259916231036186,
0.02576635032892227,
0.002595478668808937,
-0.0017487078439444304,
-0.019523365423083305,
-0.007650126703083515,
0.010662329383194447,
-0.01739986054599285,
-0.006099449936300516,
0.0016954931197687984,
-0.0063726091757416725,
0.02709992416203022,
-0.012117517180740833,
-0.04665493592619896,
0.06246153637766838,
-0.05554701015353203,
0.013420491479337215,
0.011503535322844982,
-0.005990863312035799,
0.06574394553899765,
-0.01551087573170662,
0.035452574491500854,
0.05001780763268471,
-0.06875281780958176,
0.041907597333192825,
-0.035255543887615204,
0.001790399313904345,
0.05323066934943199,
-0.05179721489548683,
0.04793695732951164,
0.013952704146504402,
-0.020464317873120308,
-0.03469005972146988,
-0.024443743750452995,
0.00353685743175447,
0.013048196211457253,
-0.016854844987392426,
-0.016567230224609375,
-0.02345266565680504,
-0.010174592956900597,
-0.058218006044626236,
0.024394942447543144,
0.018108762800693512,
-0.015900297090411186,
-0.0044179982505738735,
0.03607064485549927,
-0.0005859335651621222,
0.06009949371218681,
-0.009372013621032238,
-0.028358707204461098,
-0.0076558394357562065,
-0.0318031907081604,
-0.01506229117512703,
-0.002568622352555394,
0.0739758089184761,
-0.013623174279928207,
-0.01660141721367836,
-0.027398506179451942,
0.002445709891617298,
0.043318409472703934,
0.019745413213968277,
-0.004907432943582535,
0.012665011920034885,
0.050942834466695786,
0.014887182042002678,
-0.010649663396179676,
0.040846940129995346,
0.05153916776180267,
0.026770537719130516,
-0.00856521911919117,
0.02083502523601055,
0.01515323854982853,
-0.024803968146443367,
0.012467637658119202,
0.009603176265954971,
0.033171799033880234,
-0.004295552149415016,
0.028296295553445816,
-0.028742877766489983,
0.007418814580887556,
0.026609111577272415,
-0.010339402593672276,
0.012889345176517963,
-0.01257533859461546,
0.03618336096405983,
0.005981865338981152,
0.0006060008890926838,
0.011237864382565022,
-0.04987385869026184,
-0.02340867556631565,
-0.05546555668115616,
0.04530948027968407,
-0.0226516742259264,
0.03759869933128357,
0.02049344591796398,
-0.021560227498412132,
0.02302894927561283,
-0.03440573439002037,
-0.02631072886288166,
-0.0038744518533349037,
-0.017864331603050232,
0.0437757633626461,
-0.019973399117588997,
0.028442392125725746,
-0.008821571245789528,
0.052202001214027405,
0.007065198849886656,
0.04345521330833435,
0.004073087126016617,
0.029902590438723564,
0.024345330893993378,
-0.026958255097270012,
-0.03556123375892639,
0.0243682898581028,
-0.03557441756129265,
0.012662775814533234,
-0.020732952281832695,
0.028019463643431664,
0.03198691084980965,
-0.008882688358426094,
0.025871220976114273,
-0.05589485168457031,
-0.03917574882507324,
-0.05839027836918831,
0.014089449308812618,
0.012519612908363342,
0.015475736930966377,
-0.012454933486878872,
0.031346868723630905,
0.0011981403222307563,
-0.013928906992077827,
0.017403997480869293,
-0.006945655681192875,
-0.034831833094358444,
-0.025847092270851135,
-0.015779390931129456,
-0.018870366737246513,
0.02782902680337429,
-0.010453039780259132,
-0.01718135178089142,
0.025510625913739204,
-0.05389133095741272,
-0.011698408052325249,
0.02550027146935463,
0.035026442259550095,
-0.013613163493573666,
0.02022569626569748,
-0.01645185425877571,
0.030346596613526344,
0.006208463106304407,
0.046638261526823044,
0.1068529337644577,
0.05239758640527725,
0.012976156547665596,
-0.03353419154882431,
0.01622573658823967,
-0.03313548490405083,
-0.005927712190896273,
-0.0104907201603055,
-0.0023378466721624136,
-0.03596474230289459,
0.02224905416369438,
0.014886421151459217,
0.06081536039710045,
0.01476607657968998,
0.023526016622781754,
-0.01016364898532629,
-0.03183714300394058,
0.0042182160541415215,
-0.011334242299199104,
0.0001586044381838292,
-0.013950720429420471,
0.05544847249984741,
-0.04360221326351166,
0.011183717288076878,
-0.004235310945659876,
-0.009797287173569202,
-0.017108594998717308,
-0.015635240823030472,
-0.010070216841995716,
0.0037777561228722334,
-0.01665809005498886,
0.030135612934827805,
0.015673194080591202,
-0.012912017293274403,
-0.050851862877607346,
0.02286963351070881,
0.0457291416823864,
0.018474487587809563,
0.02068326063454151,
0.0004314160905778408,
0.04217217490077019,
-0.002722900127992034,
0.017577119171619415,
0.018319888040423393,
-0.05267468839883804,
-0.021272830665111542,
-0.018283776938915253,
0.015435533598065376,
-0.014134579338133335,
-0.019456632435321808,
-0.01558592263609171,
-0.01822005584836006,
0.03687234967947006,
-0.017039628699421883,
0.004043419845402241,
0.005871525965631008,
-0.005208744201809168,
-0.013058274984359741,
-0.06259935349225998,
-0.009905734099447727,
0.04854010418057442,
0.009778188541531563,
-0.0029367120005190372,
0.021298954263329506,
0.008673243224620819,
-0.004038655199110508,
0.012255390174686909,
0.02899523638188839,
0.009299036115407944,
-0.03151743486523628,
-0.029044993221759796,
0.0001724393223412335,
0.006964212749153376,
-0.04173405468463898,
-0.011219820007681847,
0.03236698731780052,
0.021129054948687553,
0.011341381818056107,
-0.014748663641512394,
-0.02808159403502941,
-0.08360018581151962,
0.04707816615700722,
-0.029104603454470634,
-0.01532877516001463,
-0.04578525573015213,
0.016634946689009666,
0.04649452865123749,
-0.008341535925865173,
-0.018401598557829857,
-0.00810931995511055,
0.04786483570933342,
0.05517319589853287,
0.03784509003162384,
-0.02112511172890663,
-0.0014864957192912698,
0.026170236989855766,
-0.02407650463283062,
0.012929798103868961,
-0.027707461267709732,
0.05306502804160118,
0.015264214016497135,
-0.026976831257343292,
0.042479436844587326,
0.03108935058116913,
-0.04307851940393448,
-0.002833988983184099,
-0.00029656352126039565,
-0.020571686327457428,
0.0029817947652190924,
-0.007180402986705303,
-0.02017882466316223,
0.013256874866783619,
-0.03668443486094475,
-0.03734663128852844,
-0.02060178481042385,
-0.03454196825623512,
0.005246077198535204,
0.018646031618118286,
0.012620377354323864,
-0.00801585428416729,
0.02886400930583477,
-0.003911311738193035,
-0.04220316931605339,
-0.03395023196935654,
0.001704548834823072,
0.05351904779672623,
-0.000384844170184806,
0.006385178305208683,
0.006305619142949581,
0.004931365605443716,
-0.032417602837085724,
0.003944405820220709,
0.011637275107204914,
0.012193764559924603,
-0.01520835142582655,
0.007652795407921076,
0.01653764583170414,
0.040727972984313965,
-0.022983796894550323,
0.009495600126683712,
0.056992076337337494,
-0.02590538002550602,
-0.024828558787703514,
0.033894430845975876,
-0.011310138739645481,
0.037625569850206375,
0.02721700817346573,
0.0381624810397625,
0.01599605195224285,
0.06893926858901978,
0.015752563253045082,
-0.03302830830216408,
-0.030747950077056885,
-0.002719602547585964,
0.009187226183712482,
0.0036963229067623615,
0.02471528947353363,
-0.014746585860848427,
-0.036070361733436584,
0.05316304787993431,
0.003498181002214551,
-0.023390863090753555,
-0.008511790074408054,
-0.02541099674999714,
-0.0014192385133355856,
-0.023432012647390366,
0.03158259764313698,
0.025969505310058594,
0.026624994352459908,
0.00721427658572793,
-0.011621523648500443,
0.015397850424051285,
0.0074143121019005775,
-0.036319054663181305,
-0.08886557817459106,
-0.006894410587847233,
0.007610304746776819,
-0.00670125475153327,
0.03375710919499397,
-0.04336646944284439,
0.007582627236843109,
0.014886481687426567,
-0.08078168332576752,
0.0013696941314265132,
-0.013449817895889282,
-0.06078594550490379,
-0.05372944846749306,
0.01686726324260235,
-0.003082857932895422,
0.015789827331900597,
0.011574110016226768,
0.057987771928310394,
0.02832648530602455,
0.05339617654681206,
-0.020746072754263878,
-0.005820814520120621,
-0.011911049485206604,
0.031867291778326035,
0.008591124787926674,
-0.01741117052733898,
0.05426689609885216,
-0.04146001115441322,
-0.007466908078640699,
0.02343841642141342,
-0.01075469795614481,
0.03865918517112732,
-0.021653758361935616,
-0.031184909865260124,
-0.04267904907464981,
-0.002997560892254114,
-0.014813072048127651,
-0.015061954036355019,
-0.0038296410348266363,
0.02809763513505459,
0.02959194779396057,
0.019897667691111565,
0.006349784787744284,
-0.009352477267384529,
0.01568123698234558,
-0.0584527812898159,
-0.0058380370028316975,
0.01459210179746151,
-0.007814005948603153,
-0.01751728355884552,
0.029791925102472305,
0.0323013998568058,
0.044919148087501526,
-0.00464411498978734,
-0.022610483691096306,
-0.05228768289089203,
0.0069228713400661945,
-0.021319229155778885,
0.02892208844423294,
0.028372785076498985,
0.018276751041412354,
-0.024448709562420845,
-0.038473233580589294,
0.011920345947146416,
0.006392406299710274,
-0.05244794860482216,
-0.015232272446155548,
-0.0288898553699255,
0.017372319474816322,
-0.0008528060861863196,
-0.0196340624243021,
0.026970745995640755,
-0.014644898474216461,
0.025769848376512527,
0.016957342624664307,
0.012033125385642052,
-0.01534687913954258,
-0.04638787731528282,
-0.09062319248914719,
-0.04435895383358002,
0.021717660129070282,
-0.03061593696475029,
-0.0378238819539547,
-0.04466327279806137,
-0.009610598906874657,
-0.006552054081112146,
0.05250479653477669,
0.015196803025901318,
-0.05316724628210068,
-0.012107297778129578,
0.005831094924360514,
-0.010187320411205292,
0.013005122542381287,
-0.04148804396390915,
0.040954239666461945,
-0.0004349510418251157,
0.002691684989258647,
-0.020793670788407326,
0.018419204279780388,
-0.0068833488039672375,
0.0011291474802419543,
0.025814374908804893,
0.00763124180957675,
-0.034447457641363144,
-0.026441019028425217,
-0.02121017873287201,
0.07975666970014572,
0.03166303411126137,
-0.05145765468478203,
0.07451504468917847,
-0.006702691316604614,
-0.002631156938150525,
0.0072190603241324425,
0.0036943950690329075,
-0.020619815215468407,
0.007022660691291094,
-0.02834816463291645,
-0.004158835392445326,
-0.007613074034452438,
-0.03956412151455879,
-0.004409166984260082,
-0.04063224792480469,
0.04909105598926544,
0.0071347723715007305,
-0.002194782253354788,
-0.04524770379066467,
0.038874831050634384,
-0.00014095554070081562,
0.03127048909664154,
0.022953957319259644,
-0.0054938592948019505,
-0.013258296065032482,
0.029942084103822708,
-0.0019482312491163611,
0.04193153232336044,
0.004301321692764759,
-0.0033744603861123323,
0.00870839785784483,
-0.011949550360441208,
-0.025116952136158943,
-0.0034545829985290766,
-0.00317372172139585,
0.039188023656606674,
-0.05578380823135376,
-0.0075835478492081165,
0.03867340460419655,
0.010131333023309708,
-0.030817216262221336,
0.01480857189744711,
-0.023492028936743736,
0.06641888618469238,
-0.01749594882130623,
-0.013945414684712887,
-0.02382076345384121,
-0.0020370730198919773,
0.007709892001003027,
0.01600111648440361,
0.023770563304424286,
0.03255133330821991,
-0.01222777646034956,
0.019776128232479095,
-0.004671287722885609,
0.015509168617427349,
0.031356122344732285,
-0.05196719989180565,
0.02235187031328678,
-0.03759462758898735,
-0.017177637666463852,
0.006543314550071955,
0.004396907519549131,
-0.002936065662652254,
0.0034007346257567406,
-0.001022885786369443,
0.03231004253029823,
0.01492576114833355,
0.022545916959643364,
-0.02271406352519989,
-0.016961850225925446,
0.023877790197730064,
-0.07642515003681183,
-0.016766859218478203,
0.001169341616332531,
0.026792777702212334,
-0.011207092553377151,
-0.032342731952667236
] |
<p>According to the definition of potential energy, we use $U= mhg .
$
In the figure below , </p>
<p><strong>A thin uniform rod of mass m and length h is positioned vertically above an anchored frictionless pivot point.</strong></p>
<p>Why does a author say that potential energy is $U =\dfrac{mgh}2$ why not $U =mgh$</p>
<p><img src="http://i.stack.imgur.com/DfGcJ.png" alt="enter image description here"></p>
<p>Similar problem I faced on a problem, when I had to find out the potential energy for lifting water from a hole with height h.</p>
<blockquote>
<p>So my problem is, when should I consider center of mass and when I should not?</p>
</blockquote> | 2,848 | [
-0.01401805505156517,
-0.01753382571041584,
-0.018789080902934074,
0.0008250729879364371,
0.027359288185834885,
-0.006557114887982607,
-0.02811914123594761,
-0.054071974009275436,
0.011145745404064655,
-0.01747862622141838,
0.030770668759942055,
0.027260230854153633,
0.05038190260529518,
0.009628850035369396,
0.030043281614780426,
0.04654783755540848,
0.010074477642774582,
-0.011045851744711399,
-0.019100645557045937,
0.009514547884464264,
-0.010662191547453403,
0.011340871453285217,
-0.006211191415786743,
0.0007440508343279362,
-0.005020162556320429,
0.029861092567443848,
0.00985334999859333,
-0.014135697856545448,
0.0033711441792547703,
0.046582747250795364,
-0.02919602207839489,
-0.030552400276064873,
0.0024393098428845406,
0.006362126208841801,
-0.0008346413960680366,
0.01334100030362606,
-0.018595917150378227,
-0.010861743241548538,
-0.020900094881653786,
0.030635328963398933,
-0.003296470269560814,
0.019380128011107445,
0.008475666865706444,
0.05458524823188782,
-0.04601169005036354,
0.05032720789313316,
-0.033768899738788605,
-0.03526381775736809,
0.018596967682242393,
-0.029781397432088852,
0.04311410337686539,
0.020426098257303238,
0.026201115921139717,
0.04302363097667694,
-0.0061307866126298904,
-0.008940359577536583,
0.03752372786402702,
0.04015804082155228,
-0.024390950798988342,
-0.05294543877243996,
-0.01898791454732418,
-0.021250616759061813,
-0.03145657852292061,
-0.05251186713576317,
0.011094324290752411,
0.009907234460115433,
-0.010503066703677177,
0.011069592088460922,
0.023455152288079262,
-0.01753993332386017,
-0.014174053445458412,
-0.01482485607266426,
0.005827224347740412,
-0.01953570730984211,
0.013664726167917252,
-0.0341796875,
0.011181950569152832,
0.025103146210312843,
0.027987979352474213,
0.021848203614354134,
-0.003621145384386182,
0.0099564790725708,
0.0649980679154396,
0.06586101651191711,
0.015283810906112194,
-0.013677791692316532,
0.043404970318078995,
0.011632137931883335,
0.028987767174839973,
0.015847455710172653,
-0.0010343294125050306,
0.0010444852523505688,
0.0091767692938447,
-0.02553487941622734,
0.029854504391551018,
-0.004727799445390701,
0.007959447801113129,
0.02410821244120598,
0.031179197132587433,
-0.004169607535004616,
0.0001842562633100897,
-0.034888386726379395,
0.022912537679076195,
0.07522023469209671,
0.0006707953289151192,
-0.06534948199987411,
-0.027542641386389732,
0.024014027789235115,
0.0006410747882910073,
-0.023747708648443222,
-0.057010114192962646,
0.0037468168884515762,
-0.03372613340616226,
-0.02638285420835018,
0.006108890753239393,
-0.006665343418717384,
0.02580559067428112,
-0.017100203782320023,
0.09664226323366165,
-0.023238766938447952,
0.04583752155303955,
-0.04142574965953827,
0.02822115272283554,
-0.04586669057607651,
-0.05769599974155426,
0.02063538320362568,
0.05155462399125099,
0.01302377786487341,
-0.03765978664159775,
0.024644890800118446,
0.019257115200161934,
0.04518362134695053,
0.002161037642508745,
0.03823139891028404,
0.022946463897824287,
0.019519787281751633,
-0.09176028519868851,
-0.053903717547655106,
0.05389057844877243,
-0.027545414865016937,
-0.0341876819729805,
-0.06666956841945648,
-0.008830207400023937,
0.04223998263478279,
0.07277864962816238,
-0.011194124817848206,
0.016157109290361404,
-0.003928801976144314,
0.03366851061582565,
-0.014331931248307228,
-0.0023694003466516733,
-0.07017280906438828,
-0.021653754636645317,
-0.06195993348956108,
-0.01744992844760418,
-0.05028069391846657,
-0.01703392155468464,
0.008931316435337067,
0.019754275679588318,
-0.025778034701943398,
0.060734763741493225,
0.023695344105362892,
-0.0007173374178819358,
0.0018200052436441183,
-0.01960369013249874,
-0.027371102944016457,
0.07252831757068634,
-0.0046279774978756905,
-0.01984967291355133,
0.048783667385578156,
0.029444720596075058,
0.04764313995838165,
-0.011605069041252136,
0.015090993605554104,
0.05068138986825943,
-0.02977336384356022,
0.00277934898622334,
-0.034942664206027985,
0.023727769032120705,
-0.010112816467881203,
-0.0499139279127121,
-0.04756792262196541,
0.0011386481346562505,
-0.015008805319666862,
0.022935966029763222,
0.06522724032402039,
0.006140047684311867,
-0.009455117397010326,
0.0012732043396681547,
-0.011271401308476925,
0.013603899627923965,
-0.04267453774809837,
0.06500288099050522,
0.002589942654594779,
0.02579016610980034,
0.013897884637117386,
0.010650761425495148,
0.016643766313791275,
-0.04834897071123123,
0.02948952093720436,
0.005096823908388615,
0.02821708470582962,
-0.016746604815125465,
-0.014693445526063442,
0.022254757583141327,
0.03356117382645607,
0.013070515356957912,
0.05341120436787605,
-0.011935398913919926,
-0.021103544160723686,
-0.021183982491493225,
0.0071059032343328,
-0.025894228368997574,
0.004113082308322191,
0.0077001494355499744,
-0.013636698946356773,
0.0050455438904464245,
-0.028322702273726463,
-0.024264542385935783,
0.04265974089503288,
-0.02055719867348671,
0.08318351954221725,
0.034257542341947556,
-0.019135257229208946,
0.01622825488448143,
0.02979329228401184,
0.03274647518992424,
0.022390490397810936,
0.012603803537786007,
0.009082295931875706,
-0.04240787401795387,
-0.011315451003611088,
0.012392771430313587,
0.018717143684625626,
-0.042541347444057465,
-0.005392164923250675,
0.03148474916815758,
0.017690157517790794,
0.009252169169485569,
-0.009471135213971138,
-0.027393167838454247,
-0.05700869485735893,
0.04412738233804703,
0.060541361570358276,
-0.032994359731674194,
0.03852366656064987,
0.05600983276963234,
0.020133981481194496,
0.028941281139850616,
-0.029132435098290443,
0.01367761567234993,
0.043460652232170105,
-0.007996111176908016,
0.02758534625172615,
0.0023491026367992163,
-0.00002627246612973977,
0.036913685500621796,
-0.04341793432831764,
0.022042179480195045,
0.032454680651426315,
-0.011447258293628693,
-0.030383367091417313,
-0.06927630305290222,
-0.035141926258802414,
-0.007135527674108744,
0.003097990993410349,
-0.03602154552936554,
-0.015720784664154053,
0.029664691537618637,
-0.030199849978089333,
0.0280020572245121,
-0.05208541452884674,
-0.012841807678341866,
-0.018524030223488808,
-0.005812105722725391,
0.041481658816337585,
0.008051487617194653,
0.0298173725605011,
-0.027479838579893112,
-0.000779067981056869,
-0.03235793113708496,
-0.0064546773210167885,
-0.018166054040193558,
-0.013441348448395729,
-0.04574572667479515,
-0.014714550226926804,
-0.036168236285448074,
0.023636791855096817,
0.06396755576133728,
0.019980264827609062,
-0.015146550722420216,
-0.0031364012975245714,
0.03445688262581825,
-0.03419109806418419,
-0.0037363942246884108,
-0.024360917508602142,
0.014303796924650669,
-0.01696660928428173,
-0.055774349719285965,
0.03578518331050873,
-0.03661935776472092,
-0.023604055866599083,
0.03187541291117668,
-0.030052123591303825,
-0.05146099254488945,
-0.015362956561148167,
0.015310317277908325,
0.051967818289995193,
0.01733066886663437,
0.03380768001079559,
-0.013779801316559315,
-0.02329493686556816,
0.013078918680548668,
-0.06863269209861755,
-0.039233773946762085,
0.0006526862271130085,
-0.016556527465581894,
0.06231314316391945,
0.003802852239459753,
-0.03690345585346222,
0.08501369506120682,
0.02772003598511219,
-0.05893797427415848,
0.006064011715352535,
-0.016785919666290283,
-0.03169610723853111,
-0.003709210781380534,
-0.0023761168122291565,
0.04590078070759773,
-0.04121531546115875,
-0.003681608010083437,
-0.00843049492686987,
0.024215050041675568,
0.04501371458172798,
0.027370348572731018,
0.03700260818004608,
-0.011537669226527214,
0.01308181881904602,
0.019398100674152374,
0.05744370073080063,
-0.014001830480992794,
-0.00678970804437995,
0.010580784641206264,
-0.01914994977414608,
0.03283245116472244,
0.00934735219925642,
-0.06432206928730011,
0.07333815842866898,
-0.03924000263214111,
0.013963829725980759,
-0.04511556774377823,
0.055514391511678696,
0.04073838144540787,
-0.045106153935194016,
0.03511152043938637,
-0.021019211038947105,
0.056915316730737686,
-0.013709469698369503,
-0.0070698074996471405,
0.06019850820302963,
0.03813944011926651,
0.00016351995873264968,
-0.014446135610342026,
0.01422595139592886,
-0.014827747829258442,
0.02975807711482048,
-0.03254606947302818,
-0.03342294692993164,
0.030966131016612053,
0.04199841991066933,
0.035522766411304474,
0.005784057546406984,
-0.06405509263277054,
-0.01701393909752369,
-0.07589533179998398,
0.0217741709202528,
-0.012746241874992847,
0.0428038015961647,
-0.019461428746581078,
0.03848253935575485,
0.019361549988389015,
0.014628610573709011,
0.004246900789439678,
0.020668916404247284,
-0.06006433442234993,
0.01068153791129589,
-0.03743406757712364,
0.035420842468738556,
0.008759005926549435,
-0.019637463614344597,
-0.024137672036886215,
-0.06815303862094879,
-0.0016892645508050919,
0.004161232151091099,
-0.00040796707617118955,
-0.025259921327233315,
0.030418720096349716,
-0.040115099400281906,
-0.04328792169690132,
-0.012580717913806438,
0.003031747182831168,
0.044696636497974396,
-0.007694682572036982,
0.013274742290377617,
0.06404874473810196,
-0.004536525346338749,
-0.02906399592757225,
-0.019175518304109573,
-0.006455863360315561,
-0.005123604089021683,
0.02671811543405056,
0.006823042873293161,
0.02200615592300892,
0.0083879129961133,
-0.011095535941421986,
0.015543927438557148,
0.01543131098151207,
-0.022889764979481697,
-0.02234908565878868,
-0.030334556475281715,
-0.039568398147821426,
0.010405904613435268,
0.007512383162975311,
0.07213320583105087,
-0.04071637615561485,
0.020322490483522415,
0.011742576956748962,
-0.017646463587880135,
-0.028091706335544586,
0.07201292365789413,
0.055422667413949966,
0.03138572722673416,
-0.01302268449217081,
-0.07193001359701157,
-0.010223299264907837,
-0.027105366811156273,
-0.041402868926525116,
0.01578349433839321,
-0.0028406681958585978,
-0.05300667881965637,
-0.003548427252098918,
0.004949014168232679,
0.021234719082713127,
0.01265756692737341,
0.01796509511768818,
0.013450166210532188,
0.02110799215734005,
-0.009822574444115162,
-0.022883858531713486,
0.03221555054187775,
0.0043638963252305984,
0.039212338626384735,
-0.014889474958181381,
0.010856371372938156,
-0.04221947863698006,
-0.05393523350358009,
0.05278180539608002,
0.036969248205423355,
-0.03478918597102165,
0.00017051678150892258,
-0.033088501542806625,
-0.023732610046863556,
0.04779789596796036,
-0.04007529839873314,
0.03622759133577347,
-0.02392805740237236,
0.022055411711335182,
0.015388560481369495,
-0.009162113070487976,
-0.05606507882475853,
-0.0255533866584301,
0.026973780244588852,
0.0467059351503849,
-0.03642392158508301,
0.016556719318032265,
-0.011470615863800049,
-0.0005418850341811776,
0.018453221768140793,
0.04810723662376404,
0.02252671681344509,
-0.03565457463264465,
0.010135206393897533,
0.016820590943098068,
0.010076330974698067,
-0.06904855370521545,
-0.014730572700500488,
0.015025872737169266,
-0.005348723381757736,
0.004183816723525524,
-0.02791779674589634,
-0.08707965910434723,
0.05534032732248306,
0.015030238777399063,
0.01912608928978443,
0.01737743243575096,
-0.011905654333531857,
-0.015424031764268875,
0.07232639193534851,
0.010585812851786613,
0.06285937130451202,
0.017145637422800064,
-0.05723578855395317,
-0.03670395910739899,
-0.0668129250407219,
0.040152862668037415,
-0.022238098084926605,
-0.04876428470015526,
-0.06821059435606003,
0.012758007273077965,
-0.03284726291894913,
0.046880073845386505,
0.019417721778154373,
0.031568314880132675,
-0.01496544387191534,
-0.02607615664601326,
-0.005263433326035738,
0.019761057570576668,
0.025588853284716606,
-0.005139320157468319,
0.025989826768636703,
0.0109518151730299,
-0.00019036934827454388,
0.00018444655870553106,
0.0032727986108511686,
0.0006587637471966445,
-0.013963107950985432,
-0.002406846499070525,
0.012791006825864315,
0.018620533868670464,
-0.02004126086831093,
-0.025126127526164055,
0.011896264739334583,
-0.03333573788404465,
0.04806844890117645,
-0.016685698181390762,
0.023111438378691673,
-0.01346906553953886,
-0.03159453347325325,
-0.059358205646276474,
0.02997749112546444,
0.014245024882256985,
0.0007815825520083308,
-0.030748488381505013,
0.02939422056078911,
0.03153605759143829,
0.0443105511367321,
-0.02956569567322731,
-0.017048761248588562,
0.01660391315817833,
0.03341551497578621,
-0.004231186117976904,
-0.013674560934305191,
0.03414040058851242,
-0.021191025152802467,
-0.02516883611679077,
-0.024479951709508896,
0.046769075095653534,
0.006349124014377594,
-0.017104901373386383,
0.013847162947058678,
0.03151162713766098,
0.08543673157691956,
-0.014530333690345287,
-0.01569613441824913,
0.02403193712234497,
-0.03103545494377613,
-0.018856685608625412,
-0.016594357788562775,
0.05620899423956871,
-0.01044231653213501,
-0.04489487037062645,
-0.009223341010510921,
-0.028528012335300446,
0.05560779199004173,
-0.02207007445394993,
0.010736677795648575,
0.03122141771018505,
0.03728364780545235,
-0.021941429004073143,
0.011653409339487553,
0.015756480395793915,
-0.0025687890592962503,
0.029475489631295204,
0.01894967630505562,
0.015479760244488716,
-0.011204936541616917,
-0.055975575000047684,
0.027007926255464554,
-0.00860518403351307,
-0.0018691160948947072,
0.009970036335289478,
0.06057984009385109,
-0.04458692669868469,
-0.006840838585048914,
0.022716986015439034,
-0.0032124011777341366,
0.02971949614584446,
0.012261013500392437,
-0.011632665991783142,
0.015255232341587543,
0.01424943283200264,
-0.03298644721508026,
-0.04066263139247894,
-0.018128827214241028,
0.041136689484119415,
0.052327707409858704,
0.03154138848185539,
0.053312383592128754,
0.008091156370937824,
-0.011128170415759087,
0.023148376494646072,
-0.011048835702240467,
-0.012828943319618702,
-0.023832207545638084,
-0.0023208765778690577,
0.01439076941460371,
-0.03764202073216438,
-0.004614494275301695,
0.04837139695882797,
0.012793712317943573,
-0.034590259194374084,
0.009165110066533089,
0.018080323934555054,
0.014556337147951126,
0.0015819485997781157,
-0.02498587965965271,
-0.03524135425686836,
0.03651859611272812,
-0.02791481465101242,
0.042110711336135864,
-0.015405098907649517,
-0.03717462718486786,
0.04441279172897339,
0.02990136109292507,
-0.014635705389082432,
-0.06092699617147446,
0.015490910038352013,
-0.007792102172970772,
-0.0006963318446651101,
0.010978122241795063,
-0.015289139933884144,
-0.035631004720926285,
0.04175099357962608,
0.008973119780421257,
-0.018448572605848312,
0.031142426654696465,
-0.022605855017900467,
-0.05099846422672272,
-0.018676212057471275,
-0.02315192110836506,
-0.08224616199731827,
0.022826822474598885,
0.01159906666725874,
-0.03560899198055267,
0.03972818702459335,
-0.03836502879858017,
-0.007125783711671829,
0.01160972286015749,
0.027438420802354813,
-0.029642557725310326,
0.05586174875497818,
0.0007420508773066103,
0.003998477011919022,
0.01502891443669796,
0.010092455893754959,
0.12711560726165771,
0.05822772532701492,
0.013666165992617607,
-0.07327444106340408,
-0.003931010141968727,
-0.029841739684343338,
-0.014479139819741249,
-0.019668662920594215,
-0.009494424797594547,
-0.02725665643811226,
0.006299855187535286,
0.0031937502790242434,
0.017247792333364487,
-0.016292797401547432,
0.0009700842783786356,
0.03464765474200249,
-0.03662336617708206,
-0.015434532426297665,
0.017759626731276512,
0.02142184041440487,
-0.05185122787952423,
-0.01077229529619217,
0.03287198394536972,
0.02848004177212715,
0.007305896375328302,
0.012272778898477554,
-0.003407515585422516,
-0.0467291995882988,
-0.004940364975482225,
-0.003901856020092964,
-0.024612069129943848,
0.00203491048887372,
-0.02156822197139263,
-0.02676432579755783,
-0.014697286300361156,
0.04207339137792587,
-0.019388370215892792,
-0.07067432254552841,
0.005308587569743395,
0.042870208621025085,
-0.018567558377981186,
0.0020083030685782433,
0.03287172317504883,
0.013316134922206402,
-0.05462001636624336,
-0.007578365039080381,
-0.036794498562812805,
0.02496269717812538,
0.0023244465701282024,
0.003001577453687787,
0.011219399981200695,
0.008663486689329147,
0.0024766947608441114,
-0.04620155319571495,
-0.007060167845338583,
-0.019815394654870033,
0.048799145966768265,
0.017727063968777657,
-0.0193600133061409,
-0.03135515749454498,
0.012175269424915314,
0.009637214243412018,
0.02588479220867157,
0.014867224730551243,
-0.02772016078233719,
-0.007013864349573851,
0.0026333241257816553,
0.030965758487582207,
0.0011244186898693442,
0.0011818778002634645,
-0.01638723351061344,
-0.021945618093013763,
-0.022908786311745644,
-0.035612914711236954,
-0.02770019881427288,
0.010487331077456474,
0.034733254462480545,
-0.009686223231256008,
0.04108630120754242,
-0.005864487960934639,
-0.06103288754820824,
0.0367114394903183,
-0.010528798215091228,
-0.015152777545154095,
-0.05560129135847092,
0.021758755668997765,
-0.035247258841991425,
0.06536965072154999,
0.021128423511981964,
-0.004436849616467953,
-0.008141105063259602,
0.0000838522391859442,
0.005276081617921591,
-0.017958497628569603,
-0.047388382256031036,
0.010985109023749828,
-0.03783658891916275,
0.030684538185596466,
-0.027582312002778053,
-0.034862834960222244,
0.01707305572926998,
0.02502504363656044,
-0.0028412044048309326,
0.005350783932954073,
-0.03045453131198883,
0.0015249624848365784,
-0.005710682366043329,
0.002691202564164996,
-0.0180171150714159,
0.045767638832330704,
-0.01643300987780094,
-0.020653482526540756,
-0.028340520337224007,
-0.010295445099473,
-0.017936326563358307,
-0.013153801672160625,
0.05505723878741264,
-0.033315449953079224,
0.027157606557011604,
-0.035936202853918076,
0.00628611771389842,
-0.024371834471821785,
-0.023316573351621628,
-0.05501697212457657,
-0.01219749916344881,
0.028174487873911858,
-0.01503397524356842,
-0.05276987701654434,
0.028615687042474747,
-0.013483199290931225,
0.01505537424236536,
-0.00008641125168651342,
-0.027983389794826508,
-0.020669763907790184,
-0.03306250274181366,
0.054139960557222366,
-0.026646524667739868,
0.05619318038225174,
-0.01256184745579958,
-0.003832054790109396,
0.023673681542277336,
0.00343541637994349,
-0.003573870984837413,
0.006692785304039717,
-0.004378753714263439,
0.023382488638162613,
0.01800892874598503,
-0.0025079953484237194,
0.02282092534005642,
0.018951203674077988,
-0.009035324677824974,
0.014953033067286015,
-0.02271946705877781,
-0.027926277369260788,
-0.014892668463289738,
-0.0002939444384537637,
-0.006224218290299177,
-0.0409495010972023,
-0.016261259093880653,
0.019022995606064796,
0.01577768288552761,
-0.000035938963264925405,
-0.03828061744570732,
0.022875862196087837,
0.011874910444021225,
-0.0025814722757786512,
0.028879160061478615,
0.02313966117799282,
-0.004406395368278027,
0.06113659217953682,
-0.0421551913022995,
0.00486014224588871,
0.02778106927871704,
0.001175290672108531,
-0.1082460805773735,
-0.05061791464686394,
0.02748226933181286,
0.011138912290334702,
0.03063833713531494,
-0.032320622354745865,
-0.0026692247483879328,
0.02868245542049408,
-0.06119627505540848,
0.03408943861722946,
-0.02842267043888569,
0.0166897252202034,
-0.00898013450205326,
-0.023072266951203346,
0.01310634147375822,
0.03494029492139816,
0.010021576657891273,
0.022704454138875008,
-0.014236390590667725,
0.012416122481226921,
-0.011443586088716984,
-0.020603802055120468,
0.011540244333446026,
0.057922277599573135,
-0.03347184136509895,
-0.021312495693564415,
0.06570058315992355,
-0.004136080387979746,
-0.04500715434551239,
0.022830132395029068,
-0.04193432629108429,
-0.003804075298830867,
0.017938612028956413,
0.007597411051392555,
-0.00824429839849472,
0.07017020881175995,
0.044036976993083954,
-0.014369487762451172,
-0.04734775424003601,
0.04281408339738846,
0.018474403768777847,
0.02779453806579113,
-0.009345446713268757,
-0.03457427769899368,
-0.011153205297887325,
-0.04634053632616997,
-0.03244027495384216,
0.03689856454730034,
-0.05234462022781372,
-0.017971530556678772,
0.032304827123880386,
0.012429340742528439,
-0.010459649376571178,
-0.030294425785541534,
0.013642683625221252,
-0.054604265838861465,
0.007223899941891432,
0.06200247257947922,
-0.024143755435943604,
0.009860052727162838,
0.01469261571764946,
0.03870786353945732,
-0.019401131197810173,
0.033581048250198364,
0.013007406145334244,
-0.04985266923904419,
-0.06314700841903687,
-0.009954345412552357,
0.005235294811427593,
-0.022230202332139015,
-0.013434017077088356,
-0.03943909332156181,
-0.041406821459531784,
0.034139204770326614,
0.030428560450673103,
0.02269350178539753,
0.008768577128648758,
-0.02211812324821949,
-0.02952389605343342,
-0.08951348811388016,
0.015747329220175743,
0.03266749531030655,
-0.0238636527210474,
-0.008083186112344265,
-0.023674240335822105,
0.000698038493283093,
0.005472088232636452,
0.06959003955125809,
0.003580651478841901,
-0.04551481083035469,
0.05493390932679176,
-0.04333887994289398,
0.015954282134771347,
-0.01313328929245472,
-0.02134104259312153,
0.028537509962916374,
-0.01245874259620905,
0.03827985003590584,
0.008461711928248405,
-0.001956871012225747,
0.033815640956163406,
0.015742463991045952,
-0.02291291020810604,
0.04331135377287865,
0.01757868193089962,
0.014977501705288887,
0.034058865159749985,
0.004544964525848627,
-0.011526547372341156,
0.06187468767166138,
-0.0008199148578569293,
0.006324674468487501,
0.015456927008926868,
-0.0631893053650856,
-0.04235855117440224,
0.03390101343393326,
-0.006667372304946184,
-0.019368968904018402,
0.010770509950816631,
0.013416912406682968,
0.03661799058318138,
-0.04401955381035805,
-0.007824715226888657,
0.03042590245604515,
-0.061615634709596634,
-0.004663296043872833,
0.005233644042164087,
0.051933128386735916,
0.02567402645945549,
-0.009765274822711945,
0.05197066813707352,
0.014059615321457386,
-0.029269596561789513,
0.01831078715622425,
0.016952164471149445,
0.06636981666088104,
0.027563760057091713,
-0.00611509382724762,
0.04251973330974579,
0.017706017941236496,
0.014954066835343838,
0.010080221109092236,
0.02916184440255165,
-0.03698200732469559,
-0.007428300101310015,
0.016709787771105766,
0.00616708118468523,
-0.03276297450065613,
0.007889710366725922,
-0.004802640061825514,
0.05343274772167206,
0.03027585707604885,
-0.014762775041162968,
-0.03336402773857117,
0.016626233235001564,
0.017120804637670517,
0.008057177066802979,
-0.007559094578027725,
0.035625576972961426,
-0.0006262237438932061,
-0.0060009039007127285,
-0.027594318613409996,
-0.008913612924516201,
-0.0011060223914682865,
0.02362910285592079,
0.029791230335831642,
0.015250473283231258,
0.006495730951428413,
-0.04042018949985504,
-0.02446676976978779,
-0.010143319144845009,
-0.01197683997452259,
0.04056381806731224,
0.05694182589650154,
0.029001040384173393,
0.021942567080259323,
-0.01359995361417532,
-0.013742315582931042,
0.03627927601337433,
-0.04946054890751839,
-0.021934224292635918,
-0.03219500556588173,
0.006140328478068113,
0.01690499298274517,
-0.0043503278866410255
] |
<p>It is said that in Minkowski spacetime, the current conservation law for the number current $N^\mu$ where $N^0$ is the number density and $N^i, i=1,2,3$ is the particle flux in the $x^i $ direction, is given by </p>
<p>$$\partial_\mu N^\mu=0 ....................(*)$$</p>
<p>What I don't understand is he following.</p>
<p>I would have thought that $$\partial_t N^0=-\nabla\cdot \vec N$$ where $\vec N$ has components $N^i, i=1,2,3$.</p>
<p>But using the Minkowski metric, $(*)$ reads
$$\partial_t N^0=\nabla\cdot \vec N$$</p>
<p>Why is there not a minus sign on the RHS?</p>
<p>Thank you.</p> | 2,849 | [
-0.04792638123035431,
-0.01254609227180481,
-0.009302317164838314,
-0.056468382477760315,
0.033619821071624756,
0.01449218112975359,
-0.04197223111987114,
0.013806425966322422,
-0.015041735023260117,
-0.03190512955188751,
0.016171623021364212,
0.02827705629169941,
0.09730780124664307,
0.03353722020983696,
0.047464173287153244,
0.011489944532513618,
-0.014243591576814651,
-0.015455817803740501,
-0.00851553212851286,
-0.05738444998860359,
0.006770584732294083,
0.01951783522963524,
0.037083256989717484,
0.014577292837202549,
-0.03993575647473335,
0.022415226325392723,
0.02931106835603714,
0.0173223614692688,
-0.0032708407379686832,
0.04319167882204056,
-0.010824708268046379,
-0.049936432391405106,
0.007090992759913206,
0.0183698832988739,
-0.004290105774998665,
0.027390971779823303,
-0.04355568811297417,
-0.02358976937830448,
0.012791512534022331,
0.00007562016980955377,
-0.017037145793437958,
-0.03961944580078125,
0.0251997672021389,
0.04605012387037277,
-0.045310333371162415,
0.029574071988463402,
0.044628508388996124,
0.011727339588105679,
0.02592579461634159,
-0.052863381803035736,
0.04952925443649292,
0.0432828888297081,
0.06951820105314255,
0.007176626473665237,
-0.04180233180522919,
-0.019871773198246956,
0.07688899338245392,
0.0634455531835556,
0.00399149302393198,
-0.043415334075689316,
0.004512566141784191,
-0.01583029143512249,
-0.014558685012161732,
-0.021534135565161705,
0.002408288884907961,
0.03484633192420006,
-0.007188872434198856,
0.00014342422946356237,
0.018180616199970245,
-0.029209304600954056,
0.0008940058178268373,
-0.02244831621646881,
-0.01053755171597004,
-0.03333202004432678,
-0.012871360406279564,
-0.011275279335677624,
0.05330556631088257,
-0.014591892249882221,
0.03625054657459259,
0.03211801499128342,
0.015477755106985569,
0.01059917826205492,
0.027720771729946136,
0.041912395507097244,
-0.02361409366130829,
-0.0177414882928133,
0.04721853882074356,
0.027060799300670624,
0.02819574996829033,
0.051151975989341736,
0.014823531731963158,
0.025712376460433006,
0.057156018912792206,
-0.008331879042088985,
-0.02227102965116501,
0.05481001362204552,
-0.013515937142074108,
0.010761342942714691,
-0.010100011713802814,
-0.0008150598150677979,
-0.041870903223752975,
-0.010672558099031448,
0.007179575506597757,
0.01919332891702652,
-0.01402980275452137,
-0.026513833552598953,
-0.05390321835875511,
0.022162554785609245,
-0.054486148059368134,
0.002956612268462777,
-0.047181982547044754,
0.011709652841091156,
-0.006322757340967655,
-0.016234716400504112,
0.027915870770812035,
-0.034061893820762634,
0.015999767929315567,
-0.0016585502307862043,
0.025841373950242996,
0.04223695397377014,
0.044646862894296646,
-0.02342204749584198,
0.039594341069459915,
0.005260122008621693,
-0.11799664795398712,
0.02595663070678711,
0.016031557694077492,
0.003684114431962371,
-0.0035240405704826117,
-0.012592222541570663,
-0.010963676497340202,
0.003953872248530388,
0.029758546501398087,
0.010889975354075432,
0.041660044342279434,
-0.007908694446086884,
-0.0806271955370903,
-0.06679930537939072,
0.012090176343917847,
-0.022633571177721024,
-0.03200862184166908,
-0.08277887105941772,
-0.019418863579630852,
0.046290624886751175,
0.06637334823608398,
-0.02760959416627884,
-0.003627242986112833,
0.023645268753170967,
0.05466610938310623,
-0.0015959386946633458,
-0.031416572630405426,
-0.01528905425220728,
-0.006997876800596714,
-0.05455268919467926,
-0.0349634625017643,
-0.03849778324365616,
0.051299791783094406,
0.036482442170381546,
0.01982441172003746,
-0.04673994332551956,
0.06830692291259766,
-0.020618142560124397,
0.024513591080904007,
0.009874174371361732,
-0.021679766476154327,
-0.021349355578422546,
0.0625547543168068,
0.024841176345944405,
0.0070158992893993855,
0.023849928751587868,
0.013039088808000088,
0.01265933271497488,
-0.03218638896942139,
0.04695659503340721,
0.07524973154067993,
-0.047412045300006866,
-0.025403082370758057,
-0.004886601120233536,
0.00393736083060503,
0.018442386761307716,
-0.030011966824531555,
-0.0430467464029789,
-0.020800761878490448,
0.0008103027939796448,
0.024314891546964645,
0.04745886102318764,
-0.02718077041208744,
0.008347872644662857,
-0.005935372319072485,
-0.026801718398928642,
-0.018907638266682625,
-0.0540638267993927,
0.02542397379875183,
-0.005490066017955542,
-0.05633877217769623,
0.03100384771823883,
-0.025850676000118256,
0.004206077661365271,
-0.013416810892522335,
-0.031587015837430954,
0.025214076042175293,
0.009402148425579071,
-0.029399950057268143,
-0.019833296537399292,
0.0023802360519766808,
0.018105747178196907,
0.035493165254592896,
0.029755067080259323,
0.02502996101975441,
-0.006992431823164225,
-0.01017958577722311,
0.006634141784161329,
0.007843507453799248,
0.01434769295156002,
0.033251143991947174,
-0.0386422760784626,
0.0038137598894536495,
-0.024414340034127235,
0.008739403448998928,
0.055608004331588745,
-0.06061740964651108,
0.025155991315841675,
0.05910166725516319,
0.011736135929822922,
0.011620339937508106,
0.02318909391760826,
-0.035088613629341125,
0.017153698951005936,
-0.002063466003164649,
0.010529798455536366,
-0.0035630171187222004,
0.012398837134242058,
0.03838980942964554,
0.02481873705983162,
-0.059066470712423325,
-0.03273773193359375,
0.037762321531772614,
0.0222760122269392,
-0.004786162171512842,
0.013676701113581657,
0.014635751023888588,
-0.057385098189115524,
0.03127054497599602,
0.0012618734035640955,
-0.04071654751896858,
0.009936995804309845,
0.04250401258468628,
-0.022315844893455505,
0.015344308689236641,
0.02118009701371193,
-0.05320984497666359,
0.019514229148626328,
-0.04284534603357315,
0.008555128239095211,
-0.015036056749522686,
-0.006738806143403053,
0.010509089566767216,
-0.007778518833220005,
0.0319310799241066,
0.025125784799456596,
0.009592684917151928,
0.016240311786532402,
-0.015552635304629803,
0.01322211790829897,
0.004774637520313263,
0.00803601834923029,
0.0028505083173513412,
-0.02675246261060238,
0.005401033442467451,
-0.06414900720119476,
-0.007165390066802502,
0.002911656629294157,
-0.015794865787029266,
-0.032037146389484406,
0.0021265631075948477,
0.056687045842409134,
0.01614636927843094,
0.017149358987808228,
-0.019329719245433807,
-0.0005656426656059921,
0.020437270402908325,
-0.00908974464982748,
-0.012254802510142326,
0.04446222260594368,
-0.044145144522190094,
0.016894124448299408,
-0.04739883542060852,
-0.016570573672652245,
0.06499612331390381,
0.018865039572119713,
0.0006756751681677997,
0.008628727868199348,
-0.040922556072473526,
-0.07020124047994614,
-0.03599187731742859,
-0.014509621076285839,
0.018647443503141403,
0.005305138416588306,
0.018479501828551292,
0.06217547133564949,
-0.012413839809596539,
-0.03790166229009628,
-0.008813084103167057,
-0.03394945338368416,
-0.06483851373195648,
-0.03402485325932503,
-0.02681821770966053,
0.03710545599460602,
-0.029892968013882637,
0.031613241881132126,
0.029851263388991356,
-0.035990484058856964,
0.0005706907249987125,
-0.04008806124329567,
-0.002596910111606121,
-0.008167905732989311,
-0.001565840095281601,
0.030637705698609352,
0.009456581436097622,
-0.05665298178792,
0.050939470529556274,
0.03309781104326248,
-0.024564241990447044,
-0.002041843021288514,
0.018734442070126534,
-0.03776267543435097,
-0.058935098350048065,
0.010107009671628475,
0.023211758583784103,
0.002657923847436905,
0.026020321995019913,
-0.007202832959592342,
0.043722622096538544,
0.016515139490365982,
0.013967825099825859,
0.0032518510706722736,
0.013025933876633644,
-0.015705497935414314,
0.00542644876986742,
0.07007227092981339,
0.019508587196469307,
-0.02395867183804512,
0.011157065629959106,
0.005232606548815966,
0.01843487285077572,
0.05142345279455185,
-0.016838887706398964,
0.05226835235953331,
0.009458365850150585,
0.0003672669699881226,
-0.033078912645578384,
0.023455023765563965,
0.0022685276344418526,
0.010801485739648342,
-0.00631537102162838,
0.019628480076789856,
0.019997697323560715,
-0.04186338931322098,
-0.024229004979133606,
-0.006327399518340826,
0.03616178408265114,
-0.04411805421113968,
-0.007206903304904699,
-0.00948254019021988,
0.01693691872060299,
0.01796078123152256,
0.014750339090824127,
0.02135535702109337,
0.006558848544955254,
0.004744136705994606,
0.0164114311337471,
0.008156969211995602,
-0.0269998237490654,
0.006429350934922695,
-0.034848298877477646,
-0.024033255875110626,
-0.003061989787966013,
0.012634113430976868,
-0.011767543852329254,
0.04410200193524361,
-0.001777296420186758,
0.03806377202272415,
0.03998226299881935,
0.0020736062433570623,
-0.05489286780357361,
0.023737112060189247,
-0.023541998118162155,
-0.043558519333601,
-0.0011262870393693447,
-0.02039702981710434,
-0.03810423985123634,
-0.04079081490635872,
0.009831655770540237,
0.04446030780673027,
0.003990937490016222,
-0.0626172125339508,
0.022857801988720894,
-0.05243898555636406,
-0.017227109521627426,
-0.023940235376358032,
0.0485939122736454,
0.05749092996120453,
-0.04596550390124321,
0.015614653006196022,
0.030285872519016266,
0.0020534272771328688,
-0.04141790792346001,
-0.03848804160952568,
-0.0012597768800333142,
0.06708499789237976,
0.006490079686045647,
0.010388629510998726,
0.005047614220529795,
0.02129667066037655,
0.03274917230010033,
0.03925517201423645,
0.03544846549630165,
0.02243545651435852,
-0.004059228114783764,
-0.018877563998103142,
-0.02490258775651455,
-0.021717850118875504,
-0.0117345517501235,
0.0674094706773758,
0.042343951761722565,
0.029250498861074448,
0.01602841354906559,
0.019326774403452873,
0.0070915804244577885,
0.015219733119010925,
0.026182496920228004,
0.00011903109407285228,
-0.0014816164039075375,
-0.037421539425849915,
0.021170131862163544,
-0.012224781326949596,
0.025112783536314964,
0.010393795557320118,
0.010217697359621525,
-0.016124708577990532,
-0.01199000608175993,
0.024544628337025642,
-0.017355183139443398,
-0.025423703715205193,
-0.00044544259435497224,
-0.011142500676214695,
-0.003468572860583663,
-0.02268568053841591,
-0.009227872826159,
0.028759831562638283,
0.05297407880425453,
0.02466997690498829,
0.010869772173464298,
0.020631004124879837,
-0.0739661306142807,
-0.062065694481134415,
-0.011249910108745098,
0.024034962058067322,
-0.010558799840509892,
-0.021241823211312294,
-0.07438906282186508,
-0.004142693243920803,
0.025813059881329536,
-0.021471964195370674,
0.028734080493450165,
-0.002343808300793171,
0.00027683094958774745,
-0.010180304758250713,
-0.03825153037905693,
-0.04892196133732796,
-0.0015171011909842491,
-0.03804783895611763,
0.03847486898303032,
-0.013587365858256817,
0.025486689060926437,
-0.005891036707907915,
0.013630775734782219,
-0.0035095561761409044,
0.031697046011686325,
0.0026448562275618315,
0.005334583576768637,
0.00024842299171723425,
0.04477492719888687,
-0.03803972527384758,
-0.04631577059626579,
0.0005876559298485518,
0.020649965852499008,
-0.011075492948293686,
0.06497523188591003,
-0.013736932538449764,
-0.0027362299151718616,
0.00590017344802618,
0.022271616384387016,
-0.000034657979995245114,
0.007976774126291275,
-0.040624409914016724,
0.030620068311691284,
0.010288838297128677,
-0.0115814795717597,
0.04918309301137924,
0.0019619124941527843,
0.02331644669175148,
-0.022608352825045586,
-0.02208232693374157,
0.050381850451231,
-0.0334094800055027,
0.03124910593032837,
-0.018161682412028313,
-0.007081097457557917,
-0.017181772738695145,
0.0436752624809742,
-0.012715457938611507,
0.022880934178829193,
-0.006975334603339434,
-0.04575969651341438,
-0.0025712528731673956,
0.02228810451924801,
0.02445467747747898,
-0.008838881738483906,
0.05094247683882713,
0.0028405403718352318,
0.023747699335217476,
-0.033490169793367386,
0.036947883665561676,
-0.027777330949902534,
-0.011795717291533947,
0.04829523712396622,
0.01322502177208662,
0.039472807198762894,
-0.000034513050195528194,
-0.030100475996732712,
0.040346428751945496,
-0.01655312441289425,
0.017012260854244232,
0.01129046082496643,
0.012208367697894573,
-0.006566071882843971,
-0.020461466163396835,
-0.04480976238846779,
-0.010862048715353012,
-0.02455105260014534,
0.020108481869101524,
-0.06208213046193123,
0.03335551917552948,
0.07293389737606049,
0.05479712784290314,
-0.07589637488126755,
-0.020026803016662598,
-0.006492799613624811,
-0.016644779592752457,
-0.0030563403852283955,
-0.01324937678873539,
-0.02207528054714203,
-0.02260464057326317,
-0.03360898047685623,
-0.0022843435872346163,
0.07142705470323563,
-0.053298696875572205,
-0.026421647518873215,
-0.001151937642134726,
0.036923568695783615,
0.029857615008950233,
-0.01928924024105072,
-0.02300286665558815,
0.05380149930715561,
-0.006237621419131756,
-0.028724856674671173,
-0.0158710740506649,
0.06241120398044586,
-0.009435622952878475,
-0.014902652241289616,
0.02390523999929428,
-0.02731860987842083,
0.018341831862926483,
-0.013601443730294704,
0.03252832964062691,
0.02477862313389778,
-0.0009706579730845988,
-0.034438252449035645,
-0.026651188731193542,
-0.007605402264744043,
-0.02775709144771099,
0.02068186178803444,
-0.015938837081193924,
-0.03169583901762962,
-0.024193722754716873,
-0.035952333360910416,
0.0451311357319355,
0.005088845733553171,
0.02532486617565155,
-0.010813772678375244,
0.03408368304371834,
-0.0028556212782859802,
-0.030126258730888367,
0.009538444690406322,
-0.005180071108043194,
0.006510592065751553,
0.0015137989539653063,
0.027856742963194847,
-0.016720663756132126,
-0.008564210496842861,
-0.036423638463020325,
-0.00014555193774867803,
-0.039224401116371155,
0.0663071721792221,
0.03312590345740318,
-0.032101064920425415,
0.033315837383270264,
-0.023881861940026283,
-0.024234572425484657,
0.003189896000549197,
-0.020571453496813774,
-0.022017229348421097,
-0.010706007480621338,
0.0005990666104480624,
0.0326879620552063,
-0.014231988228857517,
0.015428345650434494,
0.02962431125342846,
0.03751019015908241,
-0.025240583345294,
-0.02163853496313095,
0.011442319490015507,
-0.03550134226679802,
-0.018926560878753662,
0.00727347144857049,
-0.04232638329267502,
0.04109878093004227,
-0.01881430111825466,
0.019544288516044617,
-0.0030651940032839775,
-0.018273798748850822,
0.0448773019015789,
-0.014648123644292355,
0.019796371459960938,
-0.04932339861989021,
-0.015064362436532974,
-0.03539925813674927,
-0.018116658553481102,
0.04860939458012581,
-0.002553286962211132,
-0.03728979825973511,
0.008542372845113277,
0.044177114963531494,
0.015112688764929771,
0.022753441706299782,
0.016759134829044342,
-0.020682701840996742,
-0.016519075259566307,
-0.05679197236895561,
-0.03456586226820946,
0.04266779124736786,
-0.017387986183166504,
-0.015411666594445705,
0.01658065803349018,
-0.02975696139037609,
0.04089423269033432,
0.04265723004937172,
0.010065016336739063,
-0.01566317491233349,
0.09777354449033737,
0.027497975155711174,
0.056429844349622726,
-0.002819651737809181,
0.007399505469948053,
0.1398594081401825,
0.042918477207422256,
-0.0006334626814350486,
-0.033564355224370956,
0.007102229632437229,
-0.017078103497624397,
-0.026691213250160217,
-0.02976136840879917,
0.04914190620183945,
-0.00717524066567421,
0.0467386431992054,
0.01496952399611473,
0.019218841567635536,
-0.008566760458052158,
-0.03019767813384533,
0.016167186200618744,
-0.030640555545687675,
-0.07662968337535858,
-0.013042610138654709,
0.016423679888248444,
0.015904929488897324,
-0.0011505933944135904,
-0.023601390421390533,
0.031095733866095543,
0.015171727165579796,
0.00885166134685278,
-0.01199472974985838,
-0.017607608810067177,
0.004484221339225769,
0.019906846806406975,
-0.052960511296987534,
0.013485284522175789,
0.02516619861125946,
-0.035622093826532364,
-0.023191120475530624,
-0.032690294086933136,
0.027142204344272614,
0.0019200693350285292,
0.03517330065369606,
0.07007484138011932,
-0.0062163034453988075,
0.015535828657448292,
0.007875148206949234,
0.023714765906333923,
-0.07001262903213501,
0.052499059587717056,
-0.03630732372403145,
0.040785033255815506,
-0.01886461116373539,
0.013597950339317322,
-0.013519278727471828,
0.009498972445726395,
-0.019794367253780365,
-0.059943925589323044,
0.001889134873636067,
0.002908990951254964,
0.03290633484721184,
0.0063206953927874565,
-0.009656378999352455,
0.0006089212838560343,
-0.010624232701957226,
0.02538543939590454,
-0.01225165743380785,
0.01370498351752758,
0.001887966995127499,
0.02017580345273018,
-0.02254810743033886,
0.019347447901964188,
-0.025442514568567276,
-0.011125653982162476,
-0.019347164779901505,
-0.01396909635514021,
-0.04662802442908287,
-0.029844481498003006,
0.01855447329580784,
0.004377692937850952,
0.042875200510025024,
0.004116699565201998,
-0.004183893091976643,
-0.010436774231493473,
-0.06986092031002045,
0.031179022043943405,
-0.03031637705862522,
0.0006338170496746898,
-0.025147682055830956,
0.025722594931721687,
-0.04619065299630165,
0.0393228754401207,
-0.012611228972673416,
-0.020261209458112717,
0.02130443975329399,
0.04340251162648201,
-0.004131237044930458,
0.02104617841541767,
-0.035451099276542664,
0.019977031275629997,
0.011801456101238728,
0.02068927325308323,
-0.00383556867018342,
-0.00530772702768445,
0.07253540307283401,
0.020183291286230087,
0.0057599241845309734,
0.07355290651321411,
0.009095212444663048,
-0.04850040748715401,
0.011863022111356258,
-0.027052685618400574,
0.03346214443445206,
0.010498752817511559,
0.016848793253302574,
-0.031836967915296555,
-0.016561249271035194,
-0.020368412137031555,
0.029828093945980072,
0.009691840969026089,
0.04058988019824028,
-0.0358506441116333,
-0.038164280354976654,
-0.009103714488446712,
-0.00009322199912276119,
-0.018820922821760178,
-0.01786823943257332,
-0.021446656435728073,
0.038645464926958084,
-0.0331587940454483,
-0.005565065890550613,
-0.00637798709794879,
0.010402661748230457,
-0.03410007804632187,
-0.012530433014035225,
0.02726687677204609,
0.01067589782178402,
-0.01638275943696499,
-0.012058059684932232,
0.022443169727921486,
0.031113620847463608,
0.03334258124232292,
0.006994794588536024,
-0.041949015110731125,
0.03021642379462719,
-0.05195339396595955,
-0.0744248628616333,
0.026088319718837738,
0.03194446489214897,
0.026250675320625305,
-0.011057856492698193,
0.014661078341305256,
-0.03566514700651169,
0.04451047629117966,
-0.011521725915372372,
0.013771970756351948,
-0.0010212046327069402,
-0.06259345263242722,
-0.005177723243832588,
-0.08079859614372253,
0.01980253867805004,
-0.0031070199329406023,
0.016297709196805954,
0.01654605008661747,
0.03156134858727455,
-0.031225919723510742,
-0.016456427052617073,
-0.011065345257520676,
-0.01822492480278015,
-0.020967284217476845,
0.03532254323363304,
0.0035346474032849073,
-0.02167441137135029,
0.02433423139154911,
-0.047489963471889496,
0.008806776255369186,
0.014610945247113705,
0.0026341925840824842,
-0.08148425072431564,
-0.02838682383298874,
-0.002941032638773322,
0.008584286086261272,
0.02253606915473938,
-0.06082974374294281,
0.03296069800853729,
0.01657102443277836,
-0.05039050430059433,
0.03770817071199417,
-0.015246550552546978,
-0.03833355754613876,
-0.040142688900232315,
-0.005097926594316959,
0.005769603885710239,
0.06594017148017883,
0.03462357446551323,
0.06366991996765137,
0.03598581999540329,
0.00580926239490509,
-0.03592700883746147,
-0.045048560947179794,
-0.03980240970849991,
0.02690853923559189,
-0.01303894817829132,
-0.038582272827625275,
0.05350271612405777,
0.0012387157185003161,
-0.025066586211323738,
0.030527571216225624,
-0.03278676047921181,
-0.017369620501995087,
0.014524434693157673,
0.05865510180592537,
0.043202392756938934,
0.02060214802622795,
0.023180212825536728,
0.007649583742022514,
-0.019361896440386772,
0.037300750613212585,
0.021406060084700584,
-0.005657772999256849,
-0.002211273182183504,
-0.018177246674895287,
0.01703476719558239,
-0.04784390330314636,
0.00676476676017046,
0.048790961503982544,
-0.03329987823963165,
-0.005565627012401819,
-0.027487076818943024,
-0.03961348533630371,
0.02518487349152565,
-0.019503889605402946,
-0.0028576268814504147,
-0.0492379292845726,
-0.019963547587394714,
0.019818464294075966,
-0.007872749119997025,
-0.005089879035949707,
-0.017081696540117264,
0.005439436994493008,
-0.060983333736658096,
0.0032789469696581364,
-0.014054951258003712,
0.03153727948665619,
-0.05059580132365227,
-0.04787357151508331,
0.0241854190826416,
-0.00030933102243579924,
-0.01744106039404869,
-0.024274110794067383,
-0.008190708234906197,
0.03483795002102852,
0.04349709674715996,
-0.007214789278805256,
0.00399049324914813,
-0.040211211889982224,
-0.01594635471701622,
-0.06775573641061783,
-0.026765502989292145,
0.032615646719932556,
-0.0016424964414909482,
-0.019304733723402023,
-0.02440602518618107,
-0.05230254679918289,
0.025137966498732567,
0.06222011521458626,
0.009217336773872375,
-0.012157839722931385,
0.039769429713487625,
-0.0046508884988725185,
0.02718184143304825,
-0.053839847445487976,
0.003808093722909689,
-0.002732161432504654,
-0.023559261113405228,
-0.0016687785973772407,
0.02309351973235607,
-0.022989271208643913,
0.05934222415089607,
-0.004863073583692312,
0.032882947474718094,
-0.0165523961186409,
-0.02700692228972912,
-0.030400369316339493,
0.019453536719083786,
-0.010820015333592892,
-0.025029655545949936,
0.07451392710208893,
0.02389737218618393,
0.04125479608774185,
0.06301668286323547,
-0.006612946279346943,
-0.052334874868392944,
-0.028121359646320343,
-0.01647336222231388,
-0.01811237819492817,
-0.00037194695323705673,
-0.016566449776291847,
0.04163581505417824,
-0.016369294375181198,
-0.038845259696245193,
0.0528707318007946,
-0.009629331529140472,
-0.023535653948783875,
0.0656685158610344,
0.04960886389017105,
0.04936733841896057,
0.015279958955943584,
-0.0005028113955631852,
0.02369976043701172,
0.0016496803145855665,
0.020026853308081627,
0.05752637982368469,
-0.001056936802342534,
-0.009893546812236309,
-0.020801739767193794,
0.04114099591970444,
-0.025890851393342018,
-0.01943180523812771,
0.03492164984345436,
0.04190290346741676,
-0.02715477906167507,
0.003931589890271425,
0.05548727139830589,
-0.03243695944547653,
0.0063780853524804115,
0.007251172326505184,
-0.02622632496058941,
0.0908564031124115,
-0.028770064935088158,
0.023917371407151222,
-0.018749626353383064,
0.04305476322770119,
-0.003031068481504917,
0.015611098147928715,
0.0006219242350198328,
0.05718664079904556,
0.010546881705522537,
-0.0406639501452446,
-0.015263071283698082,
-0.03078152984380722,
0.01456182450056076,
-0.07729335129261017,
0.00852152332663536,
0.003849871689453721,
0.0054436614736914635,
-0.01755240000784397,
-0.020178070291876793,
-0.023524662479758263,
-0.03565666824579239,
0.009041905403137207,
0.004546680022031069,
0.04007812216877937,
-0.007309312000870705,
0.011719873175024986,
-0.022890040650963783,
0.045461442321538925,
-0.006430554669350386,
-0.03718186542391777,
-0.00256750057451427,
0.0007615840877406299,
0.009778495877981186,
-0.023959334939718246
] |
<p>I'm investigating the velocity field induced by a continuous distribution of 2D vortex points distributed along an ellipse $\{a\cos\theta,b\sin\theta\}$. I'm interested in the field inside the ellipse, and I need some help to prove whether this field is zero or not.</p>
<p>The intensity of each vortex point is proportional to $d\theta$ and not to the length along the ellipse. A vortex point located at a point $\boldsymbol{x'}$ induces a velocity field $\boldsymbol{u}(\boldsymbol{x})=\frac{d\theta}{2\pi |\boldsymbol{x}-\boldsymbol{x'}|} \boldsymbol{e}_\perp$ where ${e}_\perp$ is the unitary vector orthogonal to $(\boldsymbol{x}-\boldsymbol{x'})$ which is in 2D: $\boldsymbol{e}_z\times(\boldsymbol{x}-\boldsymbol{x'})/|\boldsymbol{x}-\boldsymbol{x'}|$.
The total velocity field at a point $(x,y)$ inside the ellipse is obtained by integration over $\theta$. Numerical experiments seem to show that the field is zero inside the ellipse, but I cannot prove it. Dropping the factor $2\pi$, the field is in cartesian coordinates:</p>
<p>$$\boldsymbol{u}=\int_0^{2\pi} \left\{\frac{-y + b \sin\theta}{(x - a \cos\theta)^2 + (y -
b \sin\theta)^2}, \frac{x - a \cos\theta}{(x - a \cos\theta)^2 + (y -
b \sin\theta)^2}\right\} d\theta \stackrel{?}{=}\{0,0\}$$</p>
<p>Is the field really zero?</p>
<p>Maybe there is no need for the integrals to prove it. Maybe complex analysis is of help?
I should mention that the following property is true in this problem: For any closed contour inside the ellipse the circulation is zero:
$$\oint \boldsymbol{u}\cdot\boldsymbol{dl} =0$$</p>
<p>Since we are in a simply connected region, the velocity is the gradient of a potential which is single valued. But then is this potential constant?...</p>
<p>I'm able to prove that the velocity is zero on both the $x$ and the $y$ axis. Also $u_x$ is an even function of $x$ and an odd function of $y$. The opposite applies for $u_y$. I'm able to prove the result for a circle $a=b$.
Can somebody help me for the ellipse? Any idea?</p> | 2,850 | [
-0.0013533893506973982,
-0.014215261675417423,
0.01899847947061062,
-0.03507668152451515,
0.06981682032346725,
0.006639471743255854,
-0.0257896576076746,
-0.040174130350351334,
0.01661701127886772,
-0.006406902335584164,
0.05546063184738159,
0.059640735387802124,
0.06184279918670654,
0.05177649110555649,
0.005620066542178392,
-0.007586054503917694,
-0.049937654286623,
0.0040183160454034805,
-0.006756233517080545,
-0.002806594595313072,
-0.0391618087887764,
0.01147998683154583,
0.013441202230751514,
-0.004937898367643356,
-0.01389475166797638,
0.015660246834158897,
0.019368290901184082,
-0.017350956797599792,
-0.02161712385714054,
0.08242840319871902,
-0.020857691764831543,
-0.036902185529470444,
0.0017465176060795784,
0.02175888791680336,
0.010788197629153728,
0.022895004600286484,
-0.046412114053964615,
-0.009483500383794308,
-0.030055006965994835,
0.01716155745089054,
-0.015614955686032772,
0.00463147833943367,
-0.02065964601933956,
0.08092711120843887,
0.010308310389518738,
-0.014857304282486439,
0.02352485992014408,
0.014561289921402931,
0.045349474996328354,
-0.0321199893951416,
0.055467236787080765,
-0.022997306659817696,
0.04131219908595085,
0.01925809308886528,
0.02466929890215397,
-0.022445011883974075,
0.06705739349126816,
0.04574031010270119,
-0.006833147723227739,
-0.04727829247713089,
0.003535263007506728,
-0.018175309523940086,
0.003537250217050314,
-0.03343002498149872,
-0.011504442431032658,
0.009509825147688389,
-0.0011581896105781198,
-0.03253405541181564,
-0.002822832902893424,
-0.012070799246430397,
0.015560433268547058,
-0.02094949409365654,
-0.02074391208589077,
-0.03711014613509178,
0.0004407269589137286,
-0.026402553543448448,
-0.0016040033660829067,
0.03524880111217499,
0.007379255257546902,
0.025871504098176956,
-0.025432463735342026,
0.02756454423069954,
0.03541257977485657,
0.0249724593013525,
0.005283116828650236,
0.02061466872692108,
0.05896805599331856,
-0.02374326065182686,
0.017919080331921577,
0.022589560598134995,
-0.0022781752049922943,
0.022261634469032288,
0.0016331735532730818,
-0.0181378535926342,
-0.0324268639087677,
0.03965459018945694,
-0.008114563301205635,
0.0336109884083271,
0.007091074716299772,
-0.05475934222340584,
-0.018047703430056572,
-0.026624072343111038,
-0.017407046630978584,
0.10476116091012955,
-0.011817462742328644,
0.013070914894342422,
-0.032567188143730164,
0.021961530670523643,
-0.04517538473010063,
-0.019414715468883514,
-0.054647304117679596,
0.05273714289069176,
-0.00857489462941885,
-0.00013061474601272494,
-0.014995948411524296,
-0.016317415982484818,
0.013595490716397762,
-0.01978071965277195,
0.02866339683532715,
0.03757225349545479,
0.08245661854743958,
-0.016040699556469917,
-0.01936512626707554,
-0.010165117681026459,
-0.05948512628674507,
0.020060071721673012,
0.011001414619386196,
0.03043634444475174,
-0.027606302872300148,
0.02817501127719879,
0.03878438472747803,
-0.0002317536127520725,
0.0056007904931902885,
0.04890204221010208,
-0.0023800658527761698,
0.028164179995656013,
-0.09307702630758286,
-0.06417588889598846,
0.062110938131809235,
-0.01846763677895069,
0.032076235860586166,
-0.05463699996471405,
-0.036236684769392014,
0.0539269857108593,
0.0931202694773674,
-0.02788998931646347,
-0.023598887026309967,
-0.025687048211693764,
0.032459408044815063,
-0.020440882071852684,
-0.023646898567676544,
-0.005591758526861668,
-0.012761341407895088,
-0.07384026795625687,
0.00010827962250914425,
-0.02919776923954487,
0.028779521584510803,
0.02175130695104599,
-0.016503848135471344,
-0.011668151244521141,
0.06763093918561935,
-0.028398338705301285,
0.019194653257727623,
0.01751813478767872,
-0.02087998203933239,
-0.038826197385787964,
0.07138066738843918,
0.03523788973689079,
0.007741871289908886,
0.02124907448887825,
-0.016534384340047836,
0.014042730443179607,
0.017583144828677177,
0.02939864620566368,
0.05960142984986305,
-0.053882207721471786,
0.0045003583654761314,
-0.007372899912297726,
0.012830865569412708,
0.013274733908474445,
-0.05597623437643051,
-0.04776076599955559,
-0.03988082334399223,
0.0005493864300660789,
-0.00043451812234707177,
0.07638432830572128,
0.029206637293100357,
0.007411161903291941,
0.010246997699141502,
-0.03939902037382126,
0.011015618219971657,
-0.027973631396889687,
0.02360335737466812,
0.021171191707253456,
-0.04000360891222954,
0.0540178045630455,
-0.011739926412701607,
0.014056006446480751,
-0.07395942509174347,
0.007640891242772341,
-0.006007171701639891,
-0.01072414219379425,
0.009371740743517876,
0.001409765100106597,
0.04422374814748764,
0.014834323897957802,
0.01732214353978634,
0.011262134648859501,
0.03517112135887146,
0.011826897971332073,
0.004838540218770504,
-0.03450921177864075,
-0.023168543353676796,
0.023875657469034195,
-0.003012713510543108,
0.007681150920689106,
0.011502913199365139,
0.03902076929807663,
-0.019897572696208954,
0.014110369607806206,
-0.04646385461091995,
0.060733649879693985,
0.061502084136009216,
0.030943742021918297,
0.008893228136003017,
0.015184495598077774,
0.031338442116975784,
0.016940375789999962,
0.003576199524104595,
-0.02909655123949051,
-0.05336148291826248,
0.04052935913205147,
0.07400494068861008,
0.04564150795340538,
-0.02341974712908268,
-0.012385295704007149,
0.03943189978599548,
0.013477817177772522,
0.016939977183938026,
0.017532359808683395,
-0.011821751482784748,
-0.05860024690628052,
0.01594610884785652,
0.039194777607917786,
-0.0008705242071300745,
0.03158203884959221,
0.02785835973918438,
0.018946416676044464,
0.033544208854436874,
-0.0016056345775723457,
-0.054399579763412476,
0.05013022571802139,
0.0030447638127952814,
-0.006275541614741087,
-0.012199603952467442,
0.04041852802038193,
0.018638301640748978,
0.006471208296716213,
0.05630363151431084,
0.0010286013130098581,
0.004932391922920942,
-0.004410681314766407,
-0.017963431775569916,
0.01390459667891264,
0.05379093438386917,
0.022062528878450394,
0.013734498992562294,
-0.02358986996114254,
0.012211489491164684,
-0.004031607881188393,
-0.005698390305042267,
-0.03216073662042618,
-0.04355831816792488,
-0.03519660606980324,
-0.009509794414043427,
0.0027496146503835917,
0.03429221361875534,
-0.01910390332341194,
0.0023748453240841627,
-0.011345124803483486,
-0.02916526608169079,
0.013738979585468769,
-0.005701943300664425,
0.01548434142023325,
-0.05922330170869827,
0.011713682673871517,
-0.046790797263383865,
0.029218439012765884,
0.05768747255206108,
-0.00925072655081749,
-0.0011357448529452085,
-0.02133604884147644,
-0.008254677057266235,
-0.04450629651546478,
0.0003589108819141984,
-0.037354469299316406,
-0.02003752999007702,
-0.03410104662179947,
-0.011512073688209057,
0.015662049874663353,
0.016693519428372383,
-0.050426315516233444,
0.007925225421786308,
-0.013863485306501389,
-0.024914748966693878,
-0.011862946674227715,
0.015251273289322853,
0.0538998581469059,
-0.014760608784854412,
0.04201941564679146,
-0.024991029873490334,
0.013133534230291843,
0.004651185590773821,
-0.01837148144841194,
-0.04855396971106529,
-0.011163994669914246,
-0.008826478384435177,
-0.008503558114171028,
-0.019216176122426987,
-0.0526912696659565,
0.06974427402019501,
0.003810072084888816,
-0.025019394233822823,
0.025563690811395645,
0.010750378482043743,
0.01636117324233055,
-0.0033618060406297445,
0.008838902227580547,
0.0397503599524498,
-0.02807558886706829,
0.021949440240859985,
-0.02786090224981308,
0.015580584295094013,
-0.007477124221622944,
0.01401393860578537,
-0.012789566069841385,
0.038469333201646805,
0.01715140976011753,
-0.008816166780889034,
0.044456128031015396,
0.04113103821873665,
-0.016373256221413612,
0.020450297743082047,
0.007121359463781118,
0.008579503744840622,
0.01701970398426056,
-0.047330982983112335,
0.004934531636536121,
-0.03569037839770317,
0.017157623544335365,
0.005439078435301781,
0.05472132936120033,
-0.010438002645969391,
-0.025661775842308998,
-0.03846735507249832,
0.002235819585621357,
0.04100351780653,
0.02342519350349903,
0.011859842576086521,
0.04276081547141075,
-0.005307510029524565,
0.007886029779911041,
-0.0101547259837389,
-0.04297259822487831,
0.011048258282244205,
0.05045569688081741,
-0.04630054533481598,
-0.037122588604688644,
0.01820243149995804,
0.07105332612991333,
0.0014797791372984648,
0.0027005132287740707,
-0.005373266059905291,
0.005501629319041967,
-0.030732544139027596,
0.019922737032175064,
-0.029703635722398758,
0.027883514761924744,
0.025804752483963966,
0.041971344500780106,
-0.026043178513646126,
0.013357286341488361,
-0.014819811098277569,
-0.0034764520823955536,
-0.04614365100860596,
0.017623549327254295,
-0.023657457903027534,
-0.007014188915491104,
-0.008282830007374287,
-0.014255642890930176,
0.03298231586813927,
-0.04518583416938782,
-0.019381769001483917,
-0.02397584542632103,
-0.028430471196770668,
-0.052747078239917755,
0.014101714827120304,
-0.0013107541017234325,
-0.03419928625226021,
-0.03955135494470596,
0.07884006947278976,
0.03448911011219025,
-0.07728615403175354,
0.025020839646458626,
0.00932798720896244,
-0.048135075718164444,
0.0328521803021431,
-0.03997069224715233,
0.0088593615218997,
0.007693399675190449,
0.008825298398733139,
-0.006241146940737963,
0.0009102286421693861,
-0.024957040324807167,
0.004386465530842543,
-0.0014012913452461362,
0.0437341146171093,
-0.011474997736513615,
0.0001830812107073143,
-0.056696902960538864,
-0.030172618106007576,
-0.0035556380171328783,
0.013325759209692478,
0.04865868017077446,
0.026555027812719345,
-0.004264066461473703,
0.0473955012857914,
0.014002432115375996,
0.007655852008610964,
0.015417596325278282,
0.0015069161308929324,
-0.0028008855879306793,
0.04292995110154152,
-0.03387605771422386,
-0.02642725594341755,
-0.00718179764226079,
0.00786851067095995,
-0.006443028338253498,
-0.037777893245220184,
-0.02601655386388302,
-0.02730955369770527,
0.018265319988131523,
0.043233472853899,
0.0266793891787529,
0.02300145849585533,
-0.010146668180823326,
-0.009231748059391975,
-0.015851682052016258,
0.005705047864466906,
0.04512227326631546,
0.01200393307954073,
0.017879193648695946,
0.02441144362092018,
-0.022990457713603973,
-0.023008134216070175,
-0.015539505518972874,
0.03216524422168732,
0.04192569851875305,
-0.0005027299048379064,
-0.001337569672614336,
-0.034322045743465424,
-0.05061900243163109,
0.03335379809141159,
-0.021142490208148956,
0.021061575040221214,
-0.010086179710924625,
0.015360122546553612,
-0.028030913323163986,
-0.07867598533630371,
-0.05487637221813202,
-0.014694396406412125,
-0.037905253469944,
-0.005002974532544613,
-0.04235156625509262,
-0.03210814669728279,
-0.004859455861151218,
0.0024893954396247864,
0.013845513574779034,
0.018790513277053833,
0.03247029334306717,
-0.028279954567551613,
-0.008445215411484241,
0.00169744819868356,
-0.014116913080215454,
-0.053417157381772995,
0.032102420926094055,
0.006656148005276918,
0.011733430437743664,
0.0450156070291996,
-0.039253026247024536,
-0.08452533930540085,
0.023689741268754005,
0.004938820842653513,
0.005362626165151596,
0.05890573561191559,
-0.006753101013600826,
0.03943989798426628,
0.044059742242097855,
0.011479913257062435,
0.016988279297947884,
0.036168236285448074,
0.017213372513651848,
-0.026511721312999725,
-0.026103802025318146,
-0.006159027572721243,
-0.019162492826581,
-0.007266574073582888,
-0.037547316402196884,
0.04381132498383522,
-0.010504812933504581,
0.0637689009308815,
-0.04336008056998253,
0.021953513845801353,
-0.04631097987294197,
0.0007591876783408225,
0.009618420153856277,
0.058952394872903824,
0.01816372200846672,
-0.0003237916389480233,
0.0013931415742263198,
0.006962668150663376,
0.04078130051493645,
-0.016462069004774094,
0.0075372676365077496,
-0.05052684247493744,
0.04412693902850151,
0.022179115563631058,
0.019252613186836243,
-0.008019765838980675,
-0.0022472916170954704,
0.00785242859274149,
-0.033575233072042465,
-0.06511355191469193,
0.016921062022447586,
-0.004786582197993994,
-0.015393862500786781,
0.020793134346604347,
-0.05955556035041809,
-0.030442828312516212,
0.010517108254134655,
0.04155134782195091,
0.010890910401940346,
-0.040587928146123886,
-0.03481429070234299,
0.023074494674801826,
0.01989668793976307,
-0.031189927831292152,
-0.034938257187604904,
0.007826353423297405,
0.018450135365128517,
0.009105254895985126,
-0.06783217936754227,
-0.017035366967320442,
0.0009030502988025546,
-0.044718556106090546,
0.015570657327771187,
0.013541193678975105,
-0.04436292499303818,
-0.02109021320939064,
-0.00249651912599802,
0.014455958269536495,
0.06996091455221176,
-0.022052397951483727,
-0.03169765695929527,
0.036683544516563416,
0.02700032852590084,
0.008028248324990273,
0.03293348103761673,
0.01405212003737688,
-0.01671574078500271,
-0.012500199489295483,
0.018265919759869576,
-0.020856289193034172,
0.026359859853982925,
0.008607628755271435,
-0.03181932494044304,
0.0027661528438329697,
0.004165759310126305,
0.0058839223347604275,
-0.001429715775884688,
-0.03731837123632431,
0.007862770929932594,
0.0034990867134183645,
-0.01060012448579073,
-0.029168760403990746,
-0.04758454114198685,
-0.017713800072669983,
-0.0020941169932484627,
-0.013288653455674648,
-0.007952080108225346,
-0.05648127198219299,
0.04191172868013382,
-0.007982641458511353,
0.007179631851613522,
-0.00709948968142271,
-0.0027495315298438072,
-0.01094046700745821,
-0.001507228473201394,
-0.021015407517552376,
0.0164162777364254,
0.010267151519656181,
-0.07391595095396042,
0.0008696164004504681,
-0.05787041410803795,
0.008611330762505531,
0.07270320504903793,
-0.018297318369150162,
0.038541436195373535,
0.02810315415263176,
-0.007300686091184616,
-0.036925021559000015,
-0.04763432592153549,
-0.006866639479994774,
0.011958682909607887,
-0.028300749137997627,
0.02697848156094551,
-0.035882771015167236,
-0.04840874299407005,
0.02229289337992668,
0.03867753967642784,
-0.002078549936413765,
0.023579105734825134,
-0.008997025899589062,
0.012460104189813137,
0.01687568426132202,
-0.012675629928708076,
-0.04207327216863632,
0.022651787847280502,
-0.008760975673794746,
0.05530550330877304,
0.007814901880919933,
-0.020529640838503838,
0.04048764333128929,
0.026137735694646835,
0.018179023638367653,
-0.002734430832788348,
-0.018386732786893845,
0.00012991568655706942,
-0.010519319213926792,
0.008847517892718315,
-0.010409471578896046,
-0.013330240733921528,
0.019765982404351234,
0.018528340384364128,
0.011278573423624039,
-0.03125650808215141,
-0.017649002373218536,
-0.0666009932756424,
-0.011341044679284096,
-0.015184919349849224,
-0.03349762409925461,
0.07021918892860413,
-0.0020351482089608908,
0.0206310898065567,
0.013707751408219337,
0.00569117022678256,
0.01644228585064411,
0.02108548767864704,
0.010913060046732426,
-0.025714054703712463,
0.03853157162666321,
-0.011487370356917381,
-0.0010188891319558024,
-0.03147076442837715,
0.014764114283025265,
0.1266569197177887,
0.006723730359226465,
0.028231943026185036,
-0.03976355865597725,
-0.007547594141215086,
-0.015515582635998726,
0.03278437629342079,
-0.0780683308839798,
0.023606980219483376,
-0.004095318261533976,
-0.05265091359615326,
0.011548242531716824,
0.05265871807932854,
0.021686019375920296,
-0.0689375177025795,
0.014506365172564983,
0.002369076246395707,
-0.04875434935092926,
-0.013437202200293541,
0.058138515800237656,
-0.05862040817737579,
0.015023591928184032,
-0.06604631245136261,
0.010784830898046494,
-0.04504188895225525,
0.003061902243643999,
-0.05857640132308006,
-0.004632818978279829,
-0.013626963831484318,
-0.006005283910781145,
-0.03789979964494705,
-0.008260037750005722,
0.017548227682709694,
-0.017482005059719086,
-0.055719394236803055,
-0.006055189296603203,
0.019188420847058296,
0.0027291779406368732,
0.061825234442949295,
0.0424264594912529,
-0.002480168826878071,
0.013690435327589512,
0.0255831778049469,
0.035394951701164246,
-0.018000727519392967,
-0.02552959695458412,
-0.009837614372372627,
0.11179550737142563,
0.007195460144430399,
0.022224681451916695,
-0.01499471440911293,
-0.0013130288571119308,
0.014124344103038311,
-0.04070374742150307,
-0.0016930081183090806,
-0.022693529725074768,
0.013817939907312393,
0.004240595269948244,
-0.015037083066999912,
0.01369507610797882,
0.020897608250379562,
0.01898570917546749,
-0.015428395010530949,
-0.005164723843336105,
-0.0036594707053154707,
-0.01129203848540783,
0.03388914093375206,
0.06123553588986397,
0.012664375826716423,
0.006030293181538582,
0.0020097759552299976,
0.016382792964577675,
-0.03967051953077316,
0.005832834634929895,
0.011548632755875587,
-0.039180316030979156,
0.018433600664138794,
0.03516983240842819,
-0.04690626636147499,
-0.0014886283315718174,
-0.07678860425949097,
0.013578861020505428,
0.02931204065680504,
0.014218566939234734,
0.018090013414621353,
0.0010549605358392,
0.01136461365967989,
0.06401501595973969,
-0.03232225775718689,
-0.032048460096120834,
0.032274264842271805,
0.06192352995276451,
0.012639516964554787,
-0.015881109982728958,
-0.05995479226112366,
-0.0003441860608290881,
-0.028865506872534752,
-0.015642886981368065,
0.019513113424181938,
0.029200637713074684,
0.03924810141324997,
0.061993297189474106,
-0.0004901428474113345,
0.039264976978302,
-0.017443515360355377,
-0.03139166906476021,
0.03664534166455269,
-0.02051176317036152,
-0.011836720630526543,
0.04178328439593315,
0.03234807401895523,
-0.03395581617951393,
-0.01074137818068266,
-0.005593843292444944,
0.012778239324688911,
0.006192628759890795,
-0.009632783941924572,
-0.01759437844157219,
-0.04803306609392166,
-0.018590619787573814,
-0.024571401998400688,
-0.031174959614872932,
0.0017694421112537384,
-0.00442742882296443,
0.029676012694835663,
-0.0067623513750731945,
0.009626812301576138,
-0.012483570724725723,
0.04015336558222771,
-0.03164319321513176,
0.011398045346140862,
0.001411682111211121,
0.005890178494155407,
-0.0011978261172771454,
-0.00866222195327282,
0.04005666449666023,
-0.02402826026082039,
0.031457237899303436,
0.05129377171397209,
-0.05393727496266365,
0.03448166698217392,
0.006055859848856926,
-0.007533268537372351,
0.006900823675096035,
-0.027548406273126602,
0.013769639655947685,
0.010266193188726902,
-0.01216532476246357,
-0.038194261491298676,
0.03602082282304764,
0.005821616854518652,
-0.0006432105437852442,
-0.01452221255749464,
-0.031781166791915894,
0.013201544992625713,
-0.04008657857775688,
0.054455261677503586,
0.0036712156143039465,
0.0006200504139997065,
0.04366367682814598,
0.007719318848103285,
-0.010284211486577988,
0.023437151685357094,
0.025558339431881905,
-0.047638989984989166,
0.024329200387001038,
0.03161551058292389,
-0.009565329179167747,
0.060424380004405975,
0.03928760439157486,
-0.02731321193277836,
0.021284999325871468,
-0.014934835955500603,
0.0006496591377072036,
-0.11540493369102478,
-0.016965094953775406,
0.023990867659449577,
0.04911624267697334,
0.014257770963013172,
-0.041197504848241806,
-0.019560853019356728,
0.03746215999126434,
-0.059858862310647964,
-0.0278326328843832,
-0.025386113673448563,
-0.004933448508381844,
-0.047964584082365036,
-0.02822832204401493,
-0.032131921499967575,
0.015702450647950172,
0.0267062708735466,
0.03003728576004505,
0.004836892709136009,
0.012851232662796974,
-0.01091630756855011,
-0.0460224375128746,
-0.014116054400801659,
0.00967790000140667,
-0.002082864986732602,
-0.00940302200615406,
0.058898914605379105,
0.015849720686674118,
0.019087422639131546,
0.02244645729660988,
0.004663822706788778,
-0.023590993136167526,
-0.013522591441869736,
0.0014999391278252006,
-0.006166036706417799,
0.01722097210586071,
0.017449254170060158,
0.027775978669524193,
0.04485544562339783,
-0.02377822808921337,
-0.01949281431734562,
0.022769197821617126,
-0.07332044839859009,
-0.0064621674828231335,
0.04569161683320999,
-0.010545722208917141,
-0.07069000601768494,
0.03631962090730667,
-0.004182823933660984,
-0.005663319490849972,
0.018975330516695976,
-0.011870850808918476,
0.013671054504811764,
-0.037144698202610016,
0.033214204013347626,
-0.03253421187400818,
0.0029011638835072517,
0.02590702474117279,
-0.000929361442103982,
-0.008924263529479504,
-0.0035793958231806755,
-0.004139463417232037,
-0.051416076719760895,
0.02505902200937271,
-0.01818779483437538,
0.01847151666879654,
-0.04725318029522896,
0.006937460508197546,
-0.034060683101415634,
-0.001968642231076956,
0.026972206309437752,
-0.019501864910125732,
-0.027505993843078613,
0.001048626028932631,
0.03980173170566559,
-0.005549383349716663,
-0.017606563866138458,
-0.0007019342156127095,
-0.05727562680840492,
-0.05173330381512642,
0.034090571105480194,
0.013322144746780396,
-0.04285774007439613,
-0.02666703425347805,
-0.010358575731515884,
0.009023389779031277,
0.05029556527733803,
0.029173534363508224,
0.025832995772361755,
0.025025658309459686,
0.05877169221639633,
0.011933577246963978,
0.03630456700921059,
-0.06406458467245102,
0.010093534365296364,
-0.011711136437952518,
-0.0391751304268837,
-0.01012288685888052,
-0.01131261233240366,
-0.00986710749566555,
0.02528264746069908,
0.035851944237947464,
0.006479702424257994,
0.0402335524559021,
0.009578736498951912,
-0.05817282199859619,
0.02611083909869194,
-0.017510613426566124,
-0.022753093391656876,
0.06486576795578003,
0.004336422309279442,
0.016708992421627045,
-0.017098143696784973,
-0.05021537095308304,
-0.04266051575541496,
0.019017906859517097,
-0.03324097767472267,
0.0003587508399505168,
-0.0025929466355592012,
-0.020440280437469482,
0.022472819313406944,
-0.023463191464543343,
0.004911042749881744,
0.05417695641517639,
-0.06490525603294373,
-0.03266802057623863,
0.022651726379990578,
-0.0069007971324026585,
0.045984458178281784,
0.018970292061567307,
0.02925490029156208,
-0.0008941090782172978,
-0.005294637754559517,
0.0726398304104805,
0.022119099274277687,
0.02847583219408989,
0.002778547117486596,
-0.04116491600871086,
0.024959035217761993,
-0.017597971484065056,
0.03988432511687279,
-0.02093767188489437,
-0.012457158416509628,
-0.0072707561776041985,
-0.01255715824663639,
0.004736807197332382,
-0.06678445637226105,
-0.007005495019257069,
0.03553003445267677,
-0.012942076660692692,
0.0676218643784523,
0.007770260330289602,
0.03954063355922699,
-0.012946009635925293,
-0.009785284288227558,
-0.02183173969388008,
0.025829631835222244,
0.060588229447603226,
0.05461039021611214,
-0.01284256111830473,
-0.020517053082585335,
0.005402765236794949,
-0.04790237545967102,
0.0036323124077171087,
-0.004783842712640762,
-0.015727465972304344,
0.041304104030132294,
0.013933785259723663,
0.00990079902112484,
-0.019962409511208534,
-0.04223689064383507,
-0.032108843326568604,
0.03144044801592827,
0.04489917308092117,
0.013184183277189732,
-0.01014961302280426,
-0.007667058613151312,
-0.020538881421089172,
0.045412372797727585,
-0.055678222328424454,
0.001299919793382287,
0.004425494931638241,
0.025930486619472504,
0.018008466809988022,
0.0012614831794053316
] |
<p>Consider a "wavefunction" $\psi(x)$, which has a Fourier transform $\tilde \psi(p)$</p>
<p>Suppose that we know, for each $x$, $|\psi(x)|^2$, and that we know, for each $p$, $|\tilde \psi(p)|^2$.</p>
<p>Have we enough information to reconstruct the "wavefunction" $\psi(x)$, that is, obtain the phase of the "wavefunction" for all $x$ (up to a global phase, we are only interesting to the relative phases between the $x$)?</p> | 2,851 | [
-0.005160280968993902,
-0.005653809290379286,
-0.003536114702001214,
-0.035413097590208054,
0.05036439001560211,
0.013032795861363411,
-0.055200811475515366,
-0.0496872179210186,
0.008809291757643223,
-0.039163123816251755,
0.02586366981267929,
0.05953901261091232,
0.049762923270463943,
0.0006811463972553611,
0.004448119550943375,
0.03731551393866539,
-0.029511084780097008,
0.009295452386140823,
-0.03171640634536743,
-0.02655375935137272,
0.0019445266807451844,
0.04198374226689339,
0.005920476280152798,
-0.022770989686250687,
-0.03191022202372551,
0.022293001413345337,
0.023400679230690002,
-0.004430361092090607,
0.03828708827495575,
0.0918906182050705,
0.006231348495930433,
-0.01639765128493309,
0.01580069772899151,
0.04283185303211212,
0.020876532420516014,
-0.0364261269569397,
-0.0457802452147007,
-0.003800037782639265,
0.021888921037316322,
0.0088282385841012,
-0.07436943054199219,
-0.03140939772129059,
-0.0005648607620969415,
0.0333796963095665,
-0.0016390932723879814,
0.021219095215201378,
0.002235317835584283,
-0.041860181838274,
0.022209633141756058,
-0.03140804171562195,
0.04910331964492798,
-0.024153513833880424,
0.014416007325053215,
0.0015665085520595312,
-0.005400559864938259,
0.006501082330942154,
0.05025316774845123,
0.06307611614465714,
0.017355026677250862,
-0.05024569481611252,
-0.032605212181806564,
-0.006105526816099882,
0.02038176730275154,
0.002707576844841242,
-0.059215642511844635,
-0.0032580262050032616,
-0.008697657845914364,
-0.002395416609942913,
0.006239396054297686,
-0.025612862780690193,
-0.012871691957116127,
0.031146494671702385,
0.04232398793101311,
-0.01746026799082756,
0.004933499731123447,
-0.0023594398517161608,
0.002987847663462162,
-0.0075342245399951935,
0.02012517675757408,
0.021384568884968758,
0.006696104537695646,
0.028040090575814247,
0.014821496792137623,
-0.009076742455363274,
0.026975266635417938,
0.005237383767962456,
0.058933403342962265,
0.000002971617504954338,
0.0057023135013878345,
0.028832240030169487,
-0.0002771372674033046,
-0.005471854005008936,
0.032462988048791885,
-0.043615903705358505,
-0.04247831925749779,
0.005157161969691515,
-0.004009020049124956,
0.016290273517370224,
0.00368512119166553,
-0.06311051547527313,
0.01634036935865879,
-0.02731647901237011,
-0.00958266668021679,
0.0702725499868393,
-0.029115911573171616,
-0.03628552332520485,
-0.041167002171278,
0.016149425879120827,
0.0021606588270515203,
-0.020153990015387535,
0.003525726031512022,
0.0546201653778553,
-0.0018659153720363975,
0.016612527891993523,
0.006602374371141195,
-0.008118024095892906,
-0.0132328225299716,
-0.015511387959122658,
0.06600871682167053,
0.09032245725393295,
0.02980361320078373,
-0.02211102843284607,
0.0024888694752007723,
-0.021419689059257507,
-0.076113760471344,
0.025375526398420334,
0.029716165736317635,
-0.021367715671658516,
-0.05655447393655777,
0.028708841651678085,
0.015616880729794502,
0.011014279909431934,
0.03836071863770485,
0.01094119343906641,
0.010137503035366535,
-0.03607210889458656,
-0.12979190051555634,
-0.04522724822163582,
0.008558149449527264,
-0.01941031962633133,
-0.03861144930124283,
-0.07048917561769485,
0.025535324588418007,
0.02070481702685356,
0.09483789652585983,
-0.005024025682359934,
0.0323801264166832,
-0.003522447543218732,
0.01911536045372486,
0.011099412105977535,
0.0207257941365242,
-0.020995909348130226,
-0.0010906871175393462,
-0.04243480786681175,
-0.019246188923716545,
-0.032017484307289124,
0.013320650905370712,
0.055370576679706573,
-0.04090878739953041,
-0.02774233929812908,
0.051438506692647934,
0.010260384529829025,
-0.010419980622828007,
0.013011407107114792,
0.002297702245414257,
-0.027444999665021896,
0.09554307907819748,
0.014351855032145977,
0.01793183758854866,
0.018956156447529793,
0.0007699253619648516,
0.010371907614171505,
0.00443863682448864,
0.0061058588325977325,
0.02880358323454857,
-0.023392517119646072,
-0.018690338358283043,
-0.01640324480831623,
0.03384246677160263,
-0.001838513882830739,
0.009187542833387852,
-0.021763820201158524,
0.004368369467556477,
0.01488792710006237,
0.024401219561696053,
0.04674552008509636,
0.005782991647720337,
-0.025873446837067604,
0.019643472507596016,
-0.05736547335982323,
0.0014964492293074727,
-0.05935778096318245,
0.015519137494266033,
0.017833929508924484,
-0.011042255908250809,
0.027995480224490166,
0.02388809807598591,
-0.0066491723991930485,
0.007494906894862652,
-0.04263991490006447,
-0.00745881674811244,
0.040369775146245956,
0.013408982194960117,
-0.01776977628469467,
0.05300386995077133,
0.04919271543622017,
0.04793250188231468,
0.0023559113033115864,
0.03645002841949463,
-0.0248147901147604,
-0.03989644721150398,
-0.01059022918343544,
-0.03135860711336136,
0.019501782953739166,
-0.03089883178472519,
-0.004102802369743586,
-0.012172631919384003,
0.041804928332567215,
-0.006205258425325155,
-0.012746634893119335,
-0.044314369559288025,
0.05446687713265419,
0.05277465283870697,
0.01077643595635891,
-0.012815406545996666,
0.03864477574825287,
0.023375362157821655,
0.029181502759456635,
0.014696181751787663,
-0.03953774645924568,
-0.0706910789012909,
-0.025989098474383354,
0.017137601971626282,
0.06393460184335709,
-0.031632449477910995,
0.04574844241142273,
0.04100301116704941,
0.05921993404626846,
0.03964710980653763,
0.026157600805163383,
-0.002983858110383153,
-0.0076017482206225395,
-0.007808521389961243,
0.012799595482647419,
0.010155802592635155,
0.02263781428337097,
0.019365478307008743,
0.005208705086261034,
-0.005833716597408056,
-0.009920896962285042,
-0.017788678407669067,
0.026577556505799294,
-0.024876793846488,
-0.0024434051010757685,
0.000729690189473331,
-0.046197809278964996,
0.0032636658288538456,
-0.029076769948005676,
0.006297247484326363,
-0.03768782690167427,
-0.03577723354101181,
-0.015493504703044891,
-0.041964951902627945,
-0.016130466014146805,
0.028462564572691917,
0.007742392830550671,
-0.06933777034282684,
0.018952716141939163,
0.03513449430465698,
-0.03771870210766792,
-0.017099836841225624,
-0.0010013269493356347,
0.006209001410752535,
-0.0017187311314046383,
-0.007914606481790543,
0.05086241662502289,
-0.011312754824757576,
0.05182735249400139,
-0.02428688295185566,
-0.06559546291828156,
0.03903250768780708,
0.004869984462857246,
0.00491808308288455,
0.01328896451741457,
-0.03809921815991402,
0.005533725023269653,
-0.0026797098107635975,
0.0030273885931819677,
0.02760058455169201,
0.019230950623750687,
0.030777232721447945,
-0.0040978435426950455,
-0.007259307894855738,
-0.06271520256996155,
0.007317790295928717,
-0.024335302412509918,
0.010488452389836311,
-0.04433503374457359,
0.04538961499929428,
0.017250655218958855,
-0.011055322363972664,
-0.046999741345644,
0.012955758720636368,
-0.02095866948366165,
-0.03450985625386238,
-0.013515038415789604,
0.009300881065428257,
0.036834072321653366,
-0.027637047693133354,
0.012266891077160835,
0.011884354054927826,
-0.03378574922680855,
-0.019897302612662315,
-0.04310445860028267,
-0.07692711800336838,
0.03633015230298042,
0.006222605239599943,
0.029267264530062675,
-0.014727059751749039,
0.012288280762732029,
0.09332109987735748,
-0.014388141222298145,
-0.053973715752363205,
-0.020826837047934532,
0.015902727842330933,
0.00797334499657154,
0.01935379020869732,
-0.031194351613521576,
0.0202200785279274,
0.005006952676922083,
0.08647727966308594,
-0.012547563761472702,
0.014638623222708702,
0.03249721601605415,
0.04669160395860672,
-0.024942466989159584,
0.024342264980077744,
0.015062707476317883,
0.008387498557567596,
0.006771982181817293,
-0.012387028895318508,
-0.019991904497146606,
-0.00005530280395760201,
0.026950497180223465,
-0.012296922504901886,
0.02310228906571865,
-0.010407749563455582,
0.03009820729494095,
-0.009440467692911625,
0.009064541198313236,
-0.03207891061902046,
0.03549570217728615,
-0.002461249940097332,
-0.009727444499731064,
-0.010675031691789627,
0.021442655473947525,
0.034047625958919525,
0.03506266698241234,
-0.0357128269970417,
0.0466700978577137,
0.0018934846157208085,
-0.02263878658413887,
0.021675702184438705,
-0.023254331201314926,
-0.005832679569721222,
0.013085603713989258,
-0.008238023146986961,
-0.06562996655702591,
0.01857849583029747,
0.05123593658208847,
0.046752411872148514,
0.006538293324410915,
0.0008489134488627315,
-0.019327932968735695,
-0.023594263941049576,
0.002888527698814869,
0.004734237212687731,
0.02206720970571041,
-0.01260110829025507,
0.06213955208659172,
0.045221250504255295,
0.029245276004076004,
-0.027367139235138893,
0.04735095426440239,
-0.0719815343618393,
-0.013317672535777092,
-0.002852844540029764,
0.022092433646321297,
0.00014409134746529162,
0.010508386418223381,
0.04509451240301132,
-0.03279256820678711,
-0.03833867236971855,
-0.007779316511005163,
-0.026724234223365784,
-0.062008265405893326,
0.004309662617743015,
-0.01410876214504242,
-0.029409134760499,
-0.017335793003439903,
0.04364800453186035,
0.043426528573036194,
-0.014158817008137703,
-0.0021481066942214966,
0.05003900080919266,
-0.043471116572618484,
0.039891235530376434,
0.012760143727064133,
-0.003925378434360027,
-0.0027456101961433887,
0.03868432343006134,
0.03869205713272095,
0.04212819039821625,
-0.007401042617857456,
0.004177987575531006,
-0.007273805793374777,
0.08503521978855133,
0.019004657864570618,
-0.006655244622379541,
0.024514151737093925,
-0.00942742358893156,
-0.0017456996720284224,
-0.010226324200630188,
0.04172602668404579,
-0.028895430266857147,
0.0016914232401177287,
0.005832824390381575,
-0.009706374257802963,
-0.019687019288539886,
0.034579116851091385,
0.06484608352184296,
-0.024645885452628136,
0.01980660669505596,
-0.04652292653918266,
0.01405839342623949,
-0.005280650220811367,
-0.004856458865106106,
0.033331774175167084,
-0.03550463914871216,
-0.003904914017766714,
-0.014311015605926514,
-0.008669602684676647,
0.032255273312330246,
-0.006272709928452969,
-0.01919463649392128,
-0.009548000991344452,
0.018024491146206856,
0.011688075959682465,
-0.009663713164627552,
-0.004536723252385855,
0.0027139950543642044,
0.030990734696388245,
0.02904067002236843,
-0.030492685735225677,
-0.07271430641412735,
0.001842126832343638,
0.009825225919485092,
0.05126725509762764,
0.011141208931803703,
-0.013284697197377682,
-0.047452330589294434,
-0.05460149049758911,
0.047360315918922424,
-0.00740177882835269,
0.02042343281209469,
0.0012100731255486608,
-0.030708514153957367,
-0.006033865734934807,
-0.035657163709402084,
0.01289075892418623,
0.0046377102844417095,
-0.026397772133350372,
-0.01163291186094284,
-0.026597218587994576,
-0.011380154639482498,
-0.027064591646194458,
0.017375417053699493,
0.011759404093027115,
0.0568653866648674,
0.012107882648706436,
-0.017639942467212677,
-0.032262202352285385,
0.025077862665057182,
-0.036325737833976746,
-0.06740055978298187,
-0.008543098345398903,
0.00830648560076952,
-0.004626116249710321,
0.045327335596084595,
-0.04471922293305397,
-0.06971808522939682,
0.04359738528728485,
-0.006554176099598408,
-0.02706146612763405,
0.03448307514190674,
-0.032693274319171906,
0.035471029579639435,
0.023905150592327118,
0.04530927911400795,
0.05699722096323967,
0.031111164018511772,
0.009301402606070042,
-0.0038920664228498936,
-0.0043431231752038,
0.028516869992017746,
-0.027799854055047035,
0.03756522759795189,
-0.008369878865778446,
-0.013715594075620174,
-0.0154827069491148,
0.04238073527812958,
-0.001148936222307384,
0.015844402834773064,
0.02182726003229618,
-0.00147060991730541,
-0.018924521282315254,
0.007695975247770548,
-0.009608172811567783,
0.016548391431570053,
0.002735183108597994,
0.02851708233356476,
-0.000584205670747906,
-0.03755811229348183,
-0.01760164648294449,
0.02188248373568058,
0.014518454670906067,
0.01745520532131195,
0.028104213997721672,
0.035257432609796524,
-0.07689373195171356,
-0.0014281735057011247,
0.00995597243309021,
-0.030327098444104195,
0.013395910151302814,
-0.007741577457636595,
0.027216657996177673,
0.04994168132543564,
-0.07473058253526688,
-0.037364739924669266,
0.0018859008559957147,
-0.0053069875575602055,
0.027246981859207153,
-0.019631395116448402,
-0.013822793960571289,
0.03083702363073826,
0.01781703531742096,
-0.0830436646938324,
-0.04352320358157158,
0.02817089483141899,
0.0401010625064373,
-0.004935042001307011,
-0.024906238541007042,
0.023348653689026833,
-0.002134740585461259,
-0.004360752180218697,
-0.03691868856549263,
0.010311768390238285,
0.009456892497837543,
-0.012103431858122349,
0.012295346707105637,
-0.009888052940368652,
0.018228253349661827,
-0.01194713357836008,
-0.00394423445686698,
0.020487233996391296,
0.0016165084671229124,
0.017377600073814392,
0.006807092111557722,
0.010532460175454617,
-0.033454347401857376,
-0.024803368374705315,
-0.029417775571346283,
-0.015210684388875961,
0.020649230107665062,
-0.0076075708493590355,
-0.029701000079512596,
0.003971542697399855,
0.0035887574777007103,
-0.005335671361535788,
-0.008291540667414665,
-0.01817822828888893,
-0.0035580757539719343,
0.03306176885962486,
-0.0009463481837883592,
0.004742697346955538,
-0.018176743760704994,
-0.04076256975531578,
0.0015370999462902546,
-0.010828573256731033,
-0.007277571130543947,
0.013583201915025711,
0.03164057433605194,
-0.010180603712797165,
0.00625508651137352,
0.030773499980568886,
0.006586048752069473,
-0.010630634613335133,
0.0019336814293637872,
0.03299684822559357,
-0.005348012316972017,
0.015018105506896973,
-0.018833650276064873,
-0.016772696748375893,
-0.031962327659130096,
0.006827339064329863,
0.08543098717927933,
0.022585595026612282,
0.037561703473329544,
0.0203501358628273,
0.016947245225310326,
-0.016913216561079025,
0.019518127664923668,
-0.010372324846684933,
0.01955355517566204,
-0.0017676667775958776,
0.013338519260287285,
-0.029192233458161354,
-0.028255410492420197,
0.029629172757267952,
0.016188137233257294,
-0.02416478469967842,
0.015622799284756184,
-0.014906530268490314,
0.028616176918148994,
0.031915564090013504,
-0.05021071434020996,
-0.04302576929330826,
0.02820492908358574,
-0.05269867926836014,
0.022566262632608414,
-0.019135480746626854,
-0.0017310809344053268,
0.045255396515131,
0.004199807532131672,
0.030841467902064323,
-0.018018024042248726,
-0.021276459097862244,
-0.03928926959633827,
-0.004300458822399378,
-0.0030351041350513697,
0.02128133364021778,
0.032616741955280304,
-0.0070340922102332115,
0.005576990079134703,
0.019760938361287117,
0.011639322154223919,
-0.00247737648896873,
-0.08537869900465012,
-0.04401111230254173,
-0.013836521655321121,
-0.07370465248823166,
0.032577626407146454,
0.019576942548155785,
-0.0008594013634137809,
0.01861167699098587,
-0.028327669948339462,
0.017350396141409874,
0.015559105202555656,
0.06094849854707718,
-0.05069785565137863,
0.0511220321059227,
0.023786578327417374,
0.023617932572960854,
0.006708105094730854,
-0.006092926021665335,
0.10167678445577621,
0.06215047091245651,
0.03690090402960777,
-0.05516596511006355,
0.015356243588030338,
-0.04459720477461815,
-0.008041329681873322,
-0.021106822416186333,
0.019412273541092873,
-0.013017220422625542,
-0.00891678873449564,
-0.008093451149761677,
0.06290867924690247,
0.02190168760716915,
0.010722444392740726,
0.03157795965671539,
-0.05630912631750107,
-0.03569280356168747,
0.004310615826398134,
0.008138155564665794,
-0.024002334102988243,
0.02946586161851883,
-0.0007215581135824323,
-0.010656168684363365,
-0.0516253225505352,
-0.038862425833940506,
-0.012140676379203796,
-0.029212281107902527,
0.015984466299414635,
0.009373842738568783,
-0.044045064598321915,
0.017029358074069023,
0.009527510963380337,
-0.01647552102804184,
-0.04370030760765076,
0.03599615395069122,
0.03399210050702095,
-0.006010583136230707,
0.025685220956802368,
0.0229803416877985,
0.009384622797369957,
0.017035480588674545,
-0.01922997646033764,
-0.00654204236343503,
-0.0316038504242897,
-0.040583640336990356,
-0.02066653221845627,
0.06414761394262314,
-0.03593333065509796,
-0.005419922061264515,
-0.012248608283698559,
-0.03699600324034691,
0.001491402625106275,
-0.0595083087682724,
-0.011861034668982029,
0.016638072207570076,
0.025281943380832672,
-0.028106987476348877,
-0.029164211824536324,
-0.008814413100481033,
0.0435955636203289,
-0.01637958735227585,
0.0319511778652668,
-0.04178236052393913,
-0.029008422046899796,
-0.006311408244073391,
0.025212395936250687,
0.018472379073500633,
0.01656549982726574,
-0.015359590761363506,
-0.02318894863128662,
-0.015988869592547417,
-0.02750750631093979,
-0.03627025708556175,
0.06424926966428757,
0.014305251650512218,
0.04391932860016823,
-0.011622661724686623,
-0.011259099468588829,
-0.0231012012809515,
-0.07752761244773865,
0.012949678115546703,
-0.05913970619440079,
-0.05464152246713638,
0.027906134724617004,
0.03579864650964737,
0.029855677857995033,
0.08195512741804123,
-0.03733834996819496,
0.010168477892875671,
-0.0008211235399357975,
-0.018432287499308586,
0.06280255317687988,
-0.04531928896903992,
-0.016349447891116142,
0.014877240173518658,
-0.015013518743216991,
0.011355544440448284,
-0.016747554764151573,
0.02756117656826973,
0.03305080533027649,
0.030657341703772545,
0.005862541496753693,
0.05706486478447914,
-0.04966255649924278,
0.031199462711811066,
-0.005462270230054855,
-0.019247915595769882,
-0.01321946457028389,
0.017956743016839027,
0.028363684192299843,
-0.029553882777690887,
-0.053522009402513504,
-0.024452077224850655,
0.0029330013785511255,
0.006703599821776152,
0.002055137185379863,
-0.02756611444056034,
-0.01452114898711443,
0.02277759090065956,
0.033192649483680725,
-0.03384527564048767,
-0.014750968664884567,
-0.03695918619632721,
-0.007246135268360376,
-0.014137394726276398,
-0.036910995841026306,
0.0019498229958117008,
0.026253540068864822,
-0.008185363374650478,
-0.04003576934337616,
0.018610911443829536,
0.04659993201494217,
-0.03182138502597809,
-0.015912581235170364,
0.00554421404376626,
0.008627473376691341,
0.028209710493683815,
-0.012712960131466389,
-0.011794188991189003,
0.03484001383185387,
-0.04955381155014038,
-0.03470160812139511,
0.036336176097393036,
-0.022188253700733185,
0.04637717828154564,
0.03669905290007591,
0.020779825747013092,
-0.0053630308248102665,
0.0067617096938192844,
-0.018436333164572716,
0.0018167149974033237,
0.023328615352511406,
0.002588557079434395,
-0.00462309131398797,
0.007770112715661526,
0.02120167948305607,
-0.038110289722681046,
-0.02144639566540718,
0.07171349972486496,
0.00616499874740839,
0.030690088868141174,
0.02189061790704727,
0.03590979427099228,
0.011302660219371319,
0.053686950355768204,
0.02334623783826828,
-0.01259655598551035,
0.03574712574481964,
0.008333680219948292,
-0.023720376193523407,
0.04887239262461662,
0.03385838866233826,
-0.009682878851890564,
-0.11095505952835083,
-0.016946205869317055,
0.015653524547815323,
0.02660994976758957,
0.04211534932255745,
0.0009709768346510828,
0.012577992863953114,
0.01651642471551895,
-0.09565240144729614,
0.06588656455278397,
-0.03382405638694763,
-0.012554065324366093,
-0.022063883021473885,
0.026127953082323074,
-0.0454096794128418,
0.06774797290563583,
0.05295449495315552,
0.06463202089071274,
0.027785582467913628,
-0.015102607198059559,
0.005436593666672707,
-0.015058770775794983,
-0.016208278015255928,
-0.008694102987647057,
-0.026648815721273422,
-0.009488330222666264,
0.04225439205765724,
-0.026778338477015495,
-0.024048926308751106,
0.003767580259591341,
-0.020846981555223465,
0.0333721749484539,
-0.026798730716109276,
0.020392892882227898,
0.0010977541096508503,
-0.0018971997778862715,
0.0031824701000005007,
-0.005401944741606712,
-0.014467289671301842,
-0.0017178275156766176,
0.0018932981183752418,
0.014076163992285728,
-0.012241508811712265,
-0.02061857469379902,
-0.020071089267730713,
-0.031111089512705803,
-0.035622913390398026,
0.021143164485692978,
0.012093261815607548,
-0.005592270288616419,
0.015939274802803993,
0.014693133533000946,
-0.019111057743430138,
-0.016008010134100914,
0.018367918208241463,
-0.04806649312376976,
-0.00975156668573618,
0.018630025908350945,
0.02048669196665287,
-0.04303094744682312,
0.012755443342030048,
-0.02651752158999443,
-0.07601162046194077,
0.05050654336810112,
0.0015899596037343144,
-0.044348012655973434,
-0.07111861556768417,
-0.026475535705685616,
0.033134810626506805,
0.000519969966262579,
0.01900799758732319,
-0.0336793027818203,
-0.020369114354252815,
0.01695479452610016,
0.006698167882859707,
0.025873854756355286,
-0.022038307040929794,
-0.03748822957277298,
-0.042777784168720245,
-0.06070492044091225,
0.04413982853293419,
0.03237348794937134,
0.012926905415952206,
-0.027823708951473236,
-0.008844032883644104,
0.01094813458621502,
0.003565409453585744,
0.01807570643723011,
-0.025219324976205826,
0.004196412395685911,
-0.016628621146082878,
0.011801176704466343,
0.0190974660217762,
-0.03502071648836136,
-0.021839763969182968,
-0.02904343418776989,
-0.023558901622891426,
-0.02860521525144577,
-0.02137927897274494,
-0.004694652743637562,
0.018308140337467194,
0.011577984318137169,
-0.0028043074999004602,
0.008628283627331257,
-0.0025128850247710943,
0.001874313922598958,
0.07308490574359894,
-0.026545492932200432,
-0.0034600587096065283,
0.05620879679918289,
0.015884149819612503,
0.012732239440083504,
0.013489172793924809,
-0.037085745483636856,
-0.046526312828063965,
0.016035355627536774,
-0.040012259036302567,
-0.053060051053762436,
-0.027877360582351685,
0.03060123510658741,
0.01958128809928894,
-0.009847383946180344,
-0.032786015421152115,
0.04735589772462845,
-0.04062502831220627,
0.0029115667566657066,
0.07987600564956665,
-0.006861114874482155,
0.018543792888522148,
0.021866310387849808,
-0.007801682222634554,
-0.0022484504152089357,
-0.0014689278323203325,
0.002633520867675543,
0.04693985730409622,
0.031106354668736458,
-0.02754773013293743,
0.03140019625425339,
0.03487971052527428,
-0.018943578004837036,
-0.018562693148851395,
-0.004425050690770149,
0.08028364181518555,
-0.06984954327344894,
-0.002916026161983609,
-0.012043583206832409,
-0.01933804713189602,
0.001699083368293941,
0.013300442136824131,
-0.0345187745988369,
0.09708817303180695,
0.01694554090499878,
0.00948385801166296,
-0.056511424481868744,
0.01484841201454401,
-0.020471446216106415,
0.013096184469759464,
0.04030079394578934,
0.04473007470369339,
-0.01732620596885681,
-0.00009878205310087651,
-0.04285036399960518,
0.01857084408402443,
0.019263913854956627,
-0.022302964702248573,
-0.013567322865128517,
-0.023347485810518265,
-0.000136300761369057,
-0.015818612650036812,
-0.012141037732362747,
-0.046203549951314926,
-0.04999355599284172,
0.00807634275406599,
0.0341213084757328,
0.04152565449476242,
0.017166849225759506,
-0.0017846905393525958,
-0.04371500760316849,
0.04914656654000282,
-0.0631806030869484,
0.01989598199725151,
-0.016409896314144135,
0.03656387701630592,
0.009274370968341827,
0.005657291039824486
] |
<p>The PACER project is described in this question: <a href="http://physics.stackexchange.com/questions/21405/how-much-of-the-energy-from-1-megaton-h-bomb-explosion-could-we-capture-to-do-us">How much of the energy from 1 megaton H Bomb explosion could we capture to do useful work?</a></p>
<p>Why was it abandoned? It seems that it is the only readily economical and engineeringwise useful path to fusion power, and it seems that its breeder possibilities can easily let it pay for itself for generating fissile elements and helium (which is getting to be rare too nowadays!) </p>
<p>Was it political or technical limitations that killed it? Is there hope for a renewed interest in this in todays energy conscious politics?</p> | 2,852 | [
-0.03228133171796799,
-0.044087186455726624,
-0.013714986853301525,
-0.0485350526869297,
0.04356744885444641,
-0.01538018323481083,
-0.05338286980986595,
-0.04295869916677475,
-0.005907134618610144,
-0.024981588125228882,
0.05274874344468117,
0.015675194561481476,
0.045142266899347305,
-0.002734184032306075,
-0.016353506594896317,
0.006945643573999405,
0.03421613201498985,
-0.04558054730296135,
0.0007012165733613074,
0.006714979186654091,
-0.0034381139557808638,
-0.038367144763469696,
-0.013912846334278584,
0.017466288059949875,
0.0013150821905583143,
0.029742101207375526,
-0.008828203193843365,
0.00408458337187767,
0.018007852137088776,
0.05553758516907692,
0.010161059908568859,
-0.017142830416560173,
-0.0017696499126031995,
-0.029972346499562263,
-0.009131102822721004,
0.03273192420601845,
-0.017917534336447716,
-0.04519656300544739,
-0.008013908751308918,
0.02751629427075386,
-0.034685902297496796,
-0.006682590581476688,
0.008799315430223942,
0.022022567689418793,
-0.016205793246626854,
-0.020898552611470222,
-0.006872936617583036,
-0.020967744290828705,
0.036810897290706635,
-0.07091173529624939,
-0.021123094484210014,
0.02587122842669487,
-0.033842671662569046,
-0.012288637459278107,
0.00294237001799047,
-0.029301978647708893,
0.07582300901412964,
0.06678920984268188,
0.015226490795612335,
-0.041336920112371445,
-0.05552715063095093,
0.02448098361492157,
-0.015260351821780205,
-0.01771780662238598,
-0.02293512225151062,
0.015442193485796452,
-0.023770786821842194,
-0.01642206311225891,
0.02105436846613884,
0.02195296622812748,
0.010662085376679897,
0.03293279558420181,
0.020955784246325493,
0.024110041558742523,
0.03007076308131218,
-0.015078353695571423,
0.015516112558543682,
0.004463456105440855,
0.035266850143671036,
0.09766075760126114,
-0.0490114800632,
-0.006933538243174553,
0.037437546998262405,
0.024912692606449127,
0.03275461122393608,
0.012848315760493279,
0.05798012763261795,
-0.014411567710340023,
0.009716360829770565,
0.002741794567555189,
0.005812079180032015,
0.00496998056769371,
0.05839281156659126,
0.030409201979637146,
-0.02209693007171154,
0.018411802127957344,
0.015775278210639954,
0.09211934357881546,
0.01970728114247322,
-0.007819222286343575,
0.03302416205406189,
0.00528008071705699,
0.0256437286734581,
0.016558464616537094,
0.03536960855126381,
-0.015028231777250767,
-0.015215807594358921,
0.011410108767449856,
-0.029928380623459816,
0.006886563263833523,
-0.044323381036520004,
0.03871522098779678,
0.03223774582147598,
0.0016750260256230831,
-0.024293767288327217,
-0.04948661848902702,
0.0025959089398384094,
-0.017871880903840065,
0.09310780465602875,
0.047650087624788284,
0.016390953212976456,
0.011133401654660702,
0.025993799790740013,
-0.04251386597752571,
-0.03595942258834839,
-0.03396202251315117,
0.017746251076459885,
-0.02418562024831772,
-0.006737236864864826,
0.04043712839484215,
-0.0159417986869812,
-0.01611095480620861,
0.016960253939032555,
0.043573856353759766,
0.022398313507437706,
-0.029375318437814713,
-0.09460070729255676,
-0.055890295654535294,
0.06361740082502365,
-0.012405389919877052,
-0.027199601754546165,
-0.07288439571857452,
-0.009119920432567596,
-0.019326934590935707,
0.06526511907577515,
-0.02911774069070816,
-0.041917264461517334,
0.01433567050844431,
0.06013165041804314,
0.0009614555747248232,
-0.05351632460951805,
-0.010871929116547108,
0.015235520899295807,
-0.016045836731791496,
-0.01767531968653202,
-0.06461406499147415,
0.012753798626363277,
0.007832403294742107,
-0.008314728736877441,
-0.00929772574454546,
0.0042236740700900555,
0.026688478887081146,
-0.025510458275675774,
-0.015960780903697014,
-0.02685806341469288,
-0.022954631596803665,
0.09771759808063507,
0.012677613645792007,
-0.013516362756490707,
-0.015992527827620506,
0.037365928292274475,
0.029397327452898026,
0.042554955929517746,
0.022186506539583206,
0.028263388201594353,
-0.0496630035340786,
0.009443382732570171,
-0.018058814108371735,
-0.01833781972527504,
-0.010909702628850937,
-0.025856416672468185,
-0.017745831981301308,
0.0005424070404842496,
-0.002870123367756605,
0.03263819217681885,
0.03571442514657974,
0.020001793280243874,
0.013413124717772007,
0.035539720207452774,
-0.03535369038581848,
-0.03499831631779671,
-0.05525314435362816,
-0.007875395938754082,
0.030778169631958008,
-0.01791088841855526,
0.006294356193393469,
-0.015529705211520195,
0.013752073980867863,
0.01129304338246584,
-0.01844814419746399,
0.0428473986685276,
0.05791325494647026,
0.01166465226560831,
0.034131091088056564,
-0.024543842300772667,
0.040588948875665665,
-0.00839970726519823,
0.005403218790888786,
0.019109342247247696,
-0.009298539720475674,
-0.039801135659217834,
-0.048473309725522995,
-0.021890299394726753,
0.01206901390105486,
0.041292451322078705,
-0.009997119195759296,
-0.004316101782023907,
-0.0195640716701746,
0.005096288863569498,
0.029284514486789703,
-0.00260595022700727,
0.08951396495103836,
-0.010041964240372181,
0.015066600404679775,
0.01474410854279995,
0.0606737956404686,
0.022750793024897575,
0.018414437770843506,
0.00760246766731143,
-0.011005887761712074,
-0.04833684489130974,
0.023283198475837708,
-0.002407532185316086,
0.020879756659269333,
-0.04506997391581535,
0.015345219522714615,
-0.020794443786144257,
-0.00032928198925219476,
0.045321401208639145,
-0.008778239600360394,
-0.03255297988653183,
-0.020759792998433113,
0.045036058872938156,
0.012692629359662533,
-0.03345973417162895,
-0.00043435324914753437,
-0.004500434268265963,
0.014843050390481949,
-0.026989715173840523,
0.014119891449809074,
0.007054012268781662,
0.03518107905983925,
-0.005790763068944216,
-0.0633181631565094,
0.011437099426984787,
-0.038381874561309814,
0.051881298422813416,
-0.04692276939749718,
0.03055967018008232,
0.006662952248007059,
-0.001076120650395751,
0.03785599395632744,
-0.015010586939752102,
-0.029273636639118195,
-0.02292611263692379,
0.01040906086564064,
-0.00478703249245882,
-0.026021670550107956,
0.05007855221629143,
-0.023143228143453598,
0.0378679484128952,
-0.05326896160840988,
0.03738647699356079,
-0.0444033220410347,
-0.008885398507118225,
-0.011856053955852985,
-0.02524975687265396,
0.018771640956401825,
-0.05513857305049896,
-0.038494911044836044,
0.01948370970785618,
-0.030758550390601158,
0.0050663696601986885,
-0.003006444312632084,
-0.045979373157024384,
-0.02177978679537773,
-0.0023896535858511925,
-0.00975650455802679,
-0.002938798861578107,
-0.008401951752603054,
-0.018011825159192085,
0.01919582299888134,
0.027568263933062553,
-0.05378321185708046,
0.007730001118034124,
-0.04202146455645561,
-0.0008555491804145277,
-0.026244429871439934,
-0.006362906191498041,
0.048120561987161636,
0.017251772806048393,
-0.00173848622944206,
0.04597418010234833,
-0.005029086023569107,
-0.03181250020861626,
-0.020196085795760155,
0.02167203649878502,
0.013914190232753754,
0.0022014514543116093,
0.017952365800738335,
0.06671145558357239,
-0.04056243225932121,
-0.024926314130425453,
-0.039891064167022705,
-0.049097124487161636,
0.0071007320657372475,
-0.015542710199952126,
0.03455543890595436,
-0.031121307983994484,
-0.015226613730192184,
0.03822629898786545,
0.030655981972813606,
-0.04397726058959961,
-0.002265470800921321,
-0.008048608899116516,
0.03238460794091225,
0.009478122927248478,
0.0173413697630167,
0.037878409028053284,
0.042150430381298065,
0.008519347757101059,
-0.014018814079463482,
0.061444997787475586,
0.028048573061823845,
0.03916780650615692,
-0.04201164469122887,
0.014673528261482716,
-0.019288314506411552,
0.014783196151256561,
0.04404308646917343,
0.015764635056257248,
-0.05256309360265732,
0.03501775860786438,
-0.028789788484573364,
0.04656441882252693,
0.01906103827059269,
-0.03757756948471069,
0.01790991611778736,
0.0164962075650692,
0.010916274040937424,
-0.03660675883293152,
0.013733414001762867,
0.014241529628634453,
-0.04320845007896423,
0.016666295006871223,
0.028481684625148773,
0.03866754099726677,
0.015064498409628868,
-0.007477364502847195,
0.02056884765625,
0.02121838554739952,
-0.012805335223674774,
-0.017595000565052032,
-0.0006117432494647801,
0.004683900158852339,
0.00279477471485734,
0.0651538297533989,
-0.030542541295289993,
0.03274305909872055,
0.047920338809490204,
0.016199959442019463,
0.0010014029685407877,
0.0037820206489413977,
0.0008728281245566905,
-0.07525857537984848,
-0.03416278958320618,
-0.023832762613892555,
0.07528842240571976,
0.0013654048088937998,
0.032460495829582214,
0.021958909928798676,
0.03408384695649147,
-0.046039652079343796,
-0.015245504677295685,
-0.036345530301332474,
0.00898784026503563,
-0.0626690536737442,
0.004632836207747459,
-0.01634671911597252,
-0.010848671197891235,
-0.0022946654353290796,
-0.010213320143520832,
-0.014506831765174866,
-0.0681687444448471,
0.0016331439837813377,
-0.0457550585269928,
0.07437305152416229,
0.028080690652132034,
-0.01807178556919098,
-0.033980272710323334,
0.02522106096148491,
0.07057535648345947,
0.010379202663898468,
0.024097956717014313,
0.016411053016781807,
-0.061343759298324585,
0.010365310125052929,
-0.008368400856852531,
-0.012457739561796188,
-0.03554615005850792,
0.0565057098865509,
0.0043267481960356236,
0.02139206789433956,
-0.03783386945724487,
0.00421548867598176,
0.023387297987937927,
0.03868360444903374,
-0.008713913150131702,
0.03241189569234848,
0.0009224676759913564,
-0.016873961314558983,
-0.022438202053308487,
0.0371074415743351,
0.019715934991836548,
-0.02512485906481743,
0.032825130969285965,
-0.014246129430830479,
-0.0064426688477396965,
0.00621665408834815,
0.03355354070663452,
0.058179158717393875,
-0.004545369651168585,
0.003499626647680998,
-0.060846563428640366,
-0.007992167957127094,
-0.016005970537662506,
-0.006120877806097269,
0.006044492591172457,
-0.010483927093446255,
0.013159324415028095,
0.006250631995499134,
0.01450438890606165,
0.05425513908267021,
-0.05174430459737778,
0.032289497554302216,
-0.02117607370018959,
0.004711976274847984,
0.0022831668611615896,
-0.006791405379772186,
0.025024360045790672,
-0.010297759436070919,
0.04572082683444023,
-0.002963255625218153,
0.03290810063481331,
-0.10344866663217545,
-0.024807754904031754,
0.01698467507958412,
0.02176055870950222,
-0.011834275908768177,
-0.013535442762076855,
-0.06659401208162308,
0.028011558577418327,
0.04370427876710892,
-0.03882082551717758,
0.00880357250571251,
-0.03576422855257988,
-0.022761834785342216,
-0.004228152800351381,
-0.027952466160058975,
0.00980730727314949,
-0.0013287061592563987,
0.006013961974531412,
0.0007186824223026633,
-0.018782256171107292,
-0.00776105560362339,
0.04087890684604645,
0.014531135559082031,
0.009253941476345062,
0.03827210143208504,
-0.019404519349336624,
0.017081858590245247,
-0.019996315240859985,
0.020215705037117004,
-0.007399301510304213,
-0.07979118078947067,
-0.01827646605670452,
-0.029274366796016693,
-0.031069673597812653,
0.026178615167737007,
-0.06590435653924942,
-0.07589490711688995,
0.03394419699907303,
0.008606803603470325,
-0.01739819534122944,
-0.02110069803893566,
-0.06154084578156471,
0.004166982602328062,
0.03641340509057045,
-0.02078637294471264,
0.028049735352396965,
0.0857648029923439,
-0.02346993423998356,
0.007587325293570757,
-0.0030206642113626003,
0.0029497945215553045,
-0.05238658934831619,
0.038916073739528656,
0.022689875215291977,
0.012502303346991539,
-0.04815410077571869,
0.04109703004360199,
-0.012747942470014095,
0.014160659164190292,
-0.009844529442489147,
-0.008255942724645138,
-0.000053364288760349154,
0.015623638406395912,
-0.03521624580025673,
-0.016793325543403625,
-0.006640619598329067,
0.038317978382110596,
-0.006703837774693966,
-0.01912657916545868,
0.0089466143399477,
-0.010191359557211399,
0.022418739274144173,
0.01589888334274292,
-0.02717817947268486,
0.007546895649284124,
-0.019207045435905457,
0.0002404667902737856,
0.05963662266731262,
-0.007343745324760675,
0.04114065319299698,
-0.013151517137885094,
0.030769288539886475,
0.009430774487555027,
-0.0514606237411499,
-0.030507415533065796,
-0.02514537237584591,
0.007521325722336769,
0.00494347233325243,
-0.02149648778140545,
0.04515908658504486,
-0.024067113175988197,
0.014218494296073914,
-0.07456737756729126,
-0.03661774471402168,
0.0310317762196064,
0.024666380137205124,
-0.05140502005815506,
-0.02817429043352604,
-0.02228526584804058,
0.011372581124305725,
-0.015042989514768124,
-0.020166276022791862,
0.022037025541067123,
-0.025370778515934944,
0.0459330677986145,
0.014049793593585491,
0.012195409275591373,
0.0702657699584961,
-0.029648857191205025,
-0.0054094865918159485,
0.036393988877534866,
0.006574451923370361,
-0.03176281973719597,
-0.023605071008205414,
0.017123712226748466,
-0.04787502437829971,
-0.03414538502693176,
0.021308500319719315,
0.0013599337544292212,
0.01068810187280178,
0.02755259908735752,
-0.002815251937136054,
0.0637272447347641,
-0.03280171751976013,
-0.015181101858615875,
0.008176668547093868,
0.0189987663179636,
-0.017201684415340424,
0.006836233660578728,
-0.023315779864788055,
0.009385297074913979,
0.000988459913060069,
-0.05033784359693527,
0.015481536276638508,
-0.01763194613158703,
-0.02888394147157669,
-0.004292334895581007,
0.009020787663757801,
0.007276178803294897,
0.002408867934718728,
0.05558165907859802,
-0.026316454634070396,
0.036695223301649094,
-0.03646958991885185,
0.03495095670223236,
0.005809559021145105,
-0.02545478194952011,
-0.01885625533759594,
-0.043027639389038086,
-0.01955861784517765,
0.01927156187593937,
0.03266847878694534,
-0.001647010212764144,
0.01350180059671402,
-0.06287789344787598,
-0.05115498602390289,
-0.001318309921771288,
-0.021905913949012756,
0.022582391276955605,
0.01560461800545454,
0.01507782842963934,
-0.01921190693974495,
0.009887994267046452,
-0.0011303236242383718,
0.03719019517302513,
0.02805490978062153,
0.0008795229368843138,
0.010323439724743366,
0.03815453127026558,
0.03752228245139122,
0.00758830551058054,
-0.032950837165117264,
-0.03928003087639809,
0.009742454625666142,
0.001459071529097855,
-0.001539316726848483,
-0.0020470547024160624,
-0.028914906084537506,
0.014998674392700195,
-0.013586053624749184,
-0.02974863536655903,
-0.037810225039720535,
-0.004255281295627356,
-0.020047133788466454,
0.037482958287000656,
0.024834781885147095,
-0.01870223507285118,
0.0021693245507776737,
0.0005011868779547513,
0.000718548079021275,
-0.012623364105820656,
0.03339986503124237,
-0.00047380515024997294,
-0.05834866687655449,
-0.01898946985602379,
-0.03326273709535599,
-0.08051013946533203,
0.05388718470931053,
0.0014040899695828557,
-0.008772981353104115,
0.00934381689876318,
0.00011615658877417445,
0.0018604531651362777,
-0.03555353358387947,
0.035448551177978516,
-0.024043872952461243,
0.060213420540094376,
-0.001947565353475511,
-0.005851316265761852,
-0.04268750175833702,
0.06165993586182594,
0.12200415879487991,
0.04570670798420906,
0.0023606051690876484,
-0.06742916256189346,
0.03443218022584915,
-0.045543041080236435,
-0.017045749351382256,
-0.03166768699884415,
0.015744982287287712,
0.024121403694152832,
0.0019674699287861586,
0.02163669280707836,
0.021796414628624916,
0.03166680783033371,
0.06477057933807373,
0.02969886176288128,
0.0024228952825069427,
-0.05346372351050377,
0.041147153824567795,
0.0014427396235987544,
-0.020268723368644714,
-0.016023706644773483,
-0.012376541271805763,
0.022174563258886337,
0.008655224926769733,
-0.001201090170070529,
-0.037423230707645416,
-0.03823476284742355,
0.043241772800683975,
0.00572680588811636,
-0.01144954189658165,
-0.000884742708876729,
-0.000824481772724539,
0.016864953562617302,
-0.0035633808001875877,
-0.01316008623689413,
0.0008061534608714283,
0.016406914219260216,
-0.01907338947057724,
0.056268397718667984,
0.03779812157154083,
-0.03497859835624695,
-0.00638904282823205,
0.02687094174325466,
-0.041401129215955734,
0.0007200294057838619,
-0.026942718774080276,
0.01833385042846203,
-0.03391502425074577,
0.02628263272345066,
0.01593506895005703,
-0.044654857367277145,
-0.013076569885015488,
0.0026403856463730335,
-0.05890767648816109,
-0.03448910638689995,
0.024332167580723763,
0.006236149929463863,
-0.04065778851509094,
-0.014151499606668949,
0.011131257750093937,
-0.04941907897591591,
-0.007005627267062664,
-0.019451318308711052,
-0.017499200999736786,
-0.0044165668077766895,
0.003039719071239233,
0.016358686611056328,
0.029498307034373283,
-0.02201061323285103,
-0.03877867013216019,
-0.012610584497451782,
-0.05684022605419159,
-0.029332449659705162,
0.017423130571842194,
0.06273741275072098,
0.04608108475804329,
0.020962346345186234,
-0.0286440197378397,
-0.05886432155966759,
-0.04254141449928284,
0.055409181863069534,
0.015835916623473167,
-0.02678622491657734,
-0.010489770211279392,
0.004111138172447681,
0.03234066814184189,
0.013276956975460052,
-0.03782525658607483,
-0.0056291427463293076,
-0.018699368461966515,
0.029056690633296967,
-0.005762020125985146,
-0.008433153852820396,
0.014863194897770882,
-0.016298120841383934,
-0.06808681041002274,
-0.0026242949534207582,
-0.022522829473018646,
0.028091957792639732,
0.003772496711462736,
-0.004751636181026697,
0.008331222459673882,
0.022895213216543198,
0.024248242378234863,
0.00843089446425438,
0.06717346608638763,
-0.019915329292416573,
-0.01820865459740162,
-0.03213561698794365,
0.03452103212475777,
-0.022644829005002975,
-0.0019358566496521235,
-0.04296569526195526,
-0.0014681883621960878,
0.018519841134548187,
0.023880235850811005,
-0.005943987052887678,
0.001737552578561008,
-0.030317658558487892,
0.03096361644566059,
0.03666526451706886,
0.04468986392021179,
-0.048379085958004,
-0.011969475075602531,
-0.027704212814569473,
0.00476418761536479,
0.011638661846518517,
0.017913229763507843,
-0.0023771640844643116,
0.03420773893594742,
0.023884261026978493,
0.0015510439407080412,
-0.024754807353019714,
0.011800176464021206,
-0.0005485801957547665,
0.06927263736724854,
0.03038349375128746,
-0.008623918518424034,
-0.023840555921196938,
0.04154834523797035,
-0.03442562371492386,
-0.06764385104179382,
0.0396159403026104,
-0.001427398412488401,
0.03557642921805382,
0.034764546900987625,
-0.012886946089565754,
-0.029831960797309875,
0.08003504574298859,
-0.022341156378388405,
0.008730659261345863,
0.0645890161395073,
0.002217085799202323,
0.032591313123703,
0.04555119201540947,
-0.056538429111242294,
-0.012219584546983242,
0.0028995240572839975,
0.01662955991923809,
0.03186626359820366,
-0.019411196932196617,
0.04298989474773407,
-0.0575130395591259,
0.015400880947709084,
0.0401221439242363,
0.0034820737782865763,
0.023009156808257103,
0.004530081059783697,
0.04399746656417847,
-0.033423375338315964,
-0.019505543634295464,
0.015519825741648674,
0.002117390977218747,
-0.08709171414375305,
-0.019445709884166718,
-0.023897245526313782,
-0.006675414741039276,
0.000014203505088516977,
-0.003955285530537367,
0.02359483577311039,
0.02830517664551735,
-0.06674402207136154,
-0.017491405829787254,
-0.01371351070702076,
-0.049646563827991486,
-0.02883654646575451,
-0.0011120284907519817,
-0.034061696380376816,
0.05073263496160507,
0.018922841176390648,
0.022287195548415184,
0.04323572292923927,
0.05183368921279907,
-0.011565711349248886,
0.03381803259253502,
-0.013058202341198921,
-0.03119007498025894,
-0.012513844296336174,
0.006372569594532251,
0.05313121899962425,
-0.04608076438307762,
-0.03773730620741844,
0.05576656386256218,
-0.02668299712240696,
0.03516474366188049,
-0.027987344190478325,
0.023956919088959694,
0.013508191332221031,
0.048955801874399185,
0.048496633768081665,
-0.003876267932355404,
-0.03297996520996094,
0.0214206762611866,
-0.003999033942818642,
0.02259390614926815,
0.018368437886238098,
0.010177331045269966,
0.04373009130358696,
-0.014711768366396427,
0.011665859259665012,
0.04369663447141647,
-0.006929746363312006,
-0.005127498880028725,
0.010007849894464016,
-0.018915964290499687,
0.05061464011669159,
0.004220108035951853,
0.02100146934390068,
-0.037003517150878906,
-0.03004693053662777,
0.016462773084640503,
-0.004456607159227133,
0.0006889058859087527,
0.026711421087384224,
-0.06465444713830948,
-0.005566497799009085,
0.03176978975534439,
-0.018813541159033775,
-0.04355386644601822,
-0.041272539645433426,
-0.011370822787284851,
0.013185614719986916,
0.03158409893512726,
-0.001445185742340982,
-0.002248175209388137,
-0.04208685830235481,
0.033813342452049255,
0.023384559899568558,
0.06403706967830658,
0.04791291803121567,
-0.03701271116733551,
-0.007751841098070145,
-0.0473303496837616,
0.031800176948308945,
-0.04095574468374252,
0.01210086140781641,
0.011298730038106441,
-0.07523324340581894,
0.009076093323528767,
0.00906023383140564,
0.022302888333797455,
-0.016391947865486145,
-0.005316998343914747,
0.04336875304579735,
-0.02383161149919033,
0.019416015595197678,
-0.021061178296804428,
0.03111075609922409,
0.009608537890017033,
0.03396878391504288,
-0.013467526063323021,
-0.02698933146893978,
-0.011475936509668827,
0.027849024161696434,
0.014581214636564255,
0.03813515231013298,
-0.03648632764816284,
-0.002240904839709401,
0.00008739460463402793,
0.03450123220682144,
-0.006775233428925276,
-0.005519550293684006,
0.06880421936511993,
0.0005271316040307283,
0.022702442482113838,
-0.016649959608912468,
-0.023244470357894897,
-0.021561432629823685,
0.04138020798563957,
-0.0378585085272789,
-0.02223425917327404,
0.02134297788143158,
-0.024406172335147858,
0.018553709611296654,
-0.02740067057311535,
0.013101684860885143,
0.04567316174507141,
-0.016364820301532745,
0.02879122644662857,
0.04673682153224945,
0.028136851266026497,
-0.00791260041296482,
-0.007374522276222706,
0.013136603869497776,
-0.004649966489523649,
-0.0019134097965434194,
-0.016456708312034607,
0.06455517560243607,
0.015737270936369896,
0.019756972789764404,
0.00767398439347744,
0.003707798197865486,
0.00922725535929203,
-0.0072442893870174885,
0.027077127248048782,
-0.004251725040376186,
-0.021391460672020912,
-0.05230696126818657,
0.05229147896170616,
-0.015639740973711014,
-0.014046208001673222,
0.0353584960103035,
-0.02462962083518505,
0.07262645661830902,
0.03628285229206085,
0.014601771719753742,
-0.009229063056409359,
-0.01043731439858675,
-0.00286039337515831,
0.014569198712706566,
-0.03712467849254608,
0.04078177735209465,
-0.02744681015610695,
-0.011394811794161797,
-0.02128472551703453,
0.03190341964364052,
0.04111719876527786,
-0.024797363206744194,
-0.006240459159016609,
-0.051911018788814545,
-0.019243374466896057,
-0.021663038060069084,
-0.021150017157197,
-0.027669399976730347,
-0.0061928448267281055,
0.011022352613508701,
0.03258436173200607,
0.0234274510294199,
0.00012096160207875073,
-0.018242059275507927,
-0.016613828018307686,
0.05606925114989281,
-0.03339461237192154,
0.013303929008543491,
-0.03857160359621048,
0.01118781790137291,
-0.005233513191342354,
0.024261612445116043
] |
<p>The other day I was wondering: When a <a href="http://en.wikipedia.org/wiki/Tachyon" rel="nofollow">tachyon</a> is coming towards you faster than the speed of light, will you see it before it hits you? Then I thought of course not, since the light waves aren't traveling faster than the tachyon then how could you see it before it hits you? Now I thought today, if an tachyon is traveling away from you faster than the speed of light, would you see it?</p>
<p>If you fire a ball at an initial velocity of 20mph south out of a car that is going 50mph north, the final velocity of the ball would be 30mph north, is this also how light acts when the initial velocity of the object it is reflecting off is not equal to 0? </p>
<p>So in my case, if the speed of light were 100mph (dummy math) and a tachyon was traveling at 110mph north that means the light reflecting off the tachyon would be traveling at 10mph north, so then really would you be able to see it?
More generally, how does <a href="http://en.wikipedia.org/wiki/Velocity-addition_formula" rel="nofollow">relativistic addition of velocities</a> work for tachyons?</p>
<p>update:</p>
<p>This question is a hypothetical question: IF tachyons exist, then what would happen? After a few hours of research I see why a usual massive object CAN'T travel faster than (or even reach) the speed of light, but this question is about tachyons.</p> | 2,853 | [
-0.02174905687570572,
-0.06318192183971405,
-0.02208048850297928,
-0.037153832614421844,
0.053071215748786926,
0.0002693914866540581,
0.011047477833926678,
-0.0027773783076554537,
0.01699538342654705,
0.010283756069839,
0.03060493990778923,
0.07760446518659592,
0.036895982921123505,
0.01511457096785307,
0.03622768819332123,
0.028837883844971657,
-0.03528955951333046,
-0.022500991821289062,
0.022627856582403183,
-0.04381551966071129,
0.0001138092193286866,
0.020314177498221397,
0.05014210566878319,
0.013063179329037666,
-0.025055475533008575,
0.01774238608777523,
0.0193256177008152,
0.003949351143091917,
0.0028951552230864763,
0.024392059072852135,
0.04360637068748474,
-0.020184306427836418,
0.01577238366007805,
0.025387253612279892,
0.0027655200101435184,
0.03438748046755791,
-0.018103906884789467,
-0.0120264682918787,
-0.021104371175169945,
-0.0019571417942643166,
0.023081738501787186,
-0.010571548715233803,
0.002226575743407011,
0.05875161662697792,
-0.04464571550488472,
0.006206399295479059,
0.007180114276707172,
-0.022984802722930908,
0.08390729129314423,
-0.058363836258649826,
0.042239926755428314,
0.0282466821372509,
0.026334719732403755,
0.026110246777534485,
-0.019646933302283287,
-0.007059464696794748,
0.036559220403432846,
0.08562098443508148,
-0.025637678802013397,
-0.03386842459440231,
-0.017408927902579308,
-0.009464429691433907,
-0.014882709830999374,
-0.009950865060091019,
-0.02950223721563816,
0.03380158543586731,
-0.04817618802189827,
-0.030542368069291115,
0.0052939048036932945,
-0.021045710891485214,
-0.0022069436963647604,
-0.012098505161702633,
0.011125314980745316,
0.003852758090943098,
-0.02001328021287918,
-0.06182420626282692,
0.009493284858763218,
0.014586481265723705,
0.06350844353437424,
0.051570773124694824,
-0.030696092173457146,
0.006001641973853111,
0.022534789517521858,
0.02938535064458847,
0.027745824307203293,
0.015854112803936005,
0.062203824520111084,
0.013830549083650112,
0.011470307596027851,
0.016871865838766098,
-0.036563534289598465,
0.029271380975842476,
0.005131684243679047,
-0.017873220145702362,
-0.0113016776740551,
0.019044188782572746,
-0.01606013812124729,
0.05472749099135399,
0.010342909023165703,
-0.03647345304489136,
-0.024952398613095284,
0.006272174883633852,
0.008451013825833797,
0.05795945227146149,
-0.01978224888443947,
-0.05636972934007645,
-0.023319650441408157,
0.035467371344566345,
-0.00550443772226572,
-0.030931798741221428,
-0.034351591020822525,
0.008949946612119675,
0.007435962557792664,
0.02434597909450531,
0.003158047329634428,
-0.042852770537137985,
0.010438297875225544,
-0.0023473487235605717,
0.06416163593530655,
0.03427105396986008,
0.06431857496500015,
-0.013441854156553745,
0.03457607328891754,
-0.006031809840351343,
-0.04272070899605751,
-0.0067635802552104,
0.006378459744155407,
-0.016613928601145744,
0.00807163119316101,
0.01888669840991497,
0.01421110238879919,
-0.04942405968904495,
0.008713695220649242,
-0.03813488781452179,
0.05790489539504051,
-0.01720401644706726,
-0.07424826920032501,
-0.03515031933784485,
0.04685813561081886,
0.01550188660621643,
-0.03603173792362213,
-0.07083446532487869,
0.007367769256234169,
0.015592021867632866,
0.09470010548830032,
0.00013756530825048685,
-0.011447399854660034,
-0.012317863292992115,
0.04683936387300491,
0.00987034197896719,
-0.02342985011637211,
-0.013130243867635727,
-0.01078727189451456,
-0.026504123583436012,
0.0014060194371268153,
-0.07195869833230972,
-0.01260487549006939,
0.011182467453181744,
-0.014623459428548813,
-0.026274174451828003,
0.0821223258972168,
-0.020816456526517868,
0.031212586909532547,
0.02771383710205555,
-0.037171754986047745,
-0.011253399774432182,
0.1248299852013588,
0.03768093138933182,
-0.038855914026498795,
0.06320131570100784,
0.013395815156400204,
0.038198962807655334,
0.006300781387835741,
-0.0009119146270677447,
0.037348419427871704,
-0.03033788874745369,
-0.014710391871631145,
0.008022734895348549,
0.015707172453403473,
-0.016567615792155266,
-0.007263654842972755,
-0.05141761526465416,
-0.004386342596262693,
0.014200043864548206,
0.05342106148600578,
0.03562525287270546,
0.0028668507002294064,
0.01485461089760065,
0.020180335268378258,
-0.011742834933102131,
-0.011256130412220955,
-0.06167493015527725,
0.012466921471059322,
0.021694796159863472,
0.019840534776449203,
-0.00979075487703085,
-0.017250899225473404,
0.01416696049273014,
-0.023816393688321114,
-0.006258530076593161,
-0.021821221336722374,
0.050340063869953156,
-0.0012182611972093582,
0.02369053103029728,
-0.006963646039366722,
0.07026059925556183,
0.029761118814349174,
-0.00628636172041297,
0.01240397710353136,
-0.027423730120062828,
-0.025063833221793175,
0.007832597009837627,
0.0026610225904732943,
0.02597631886601448,
-0.004168680403381586,
-0.021687015891075134,
0.008532347157597542,
0.008745881728827953,
-0.0038712932728230953,
0.04234270378947258,
-0.028624258935451508,
0.07521216571331024,
0.03325190395116806,
0.0368758887052536,
-0.037977185100317,
0.06392986327409744,
-0.0019368664361536503,
0.0004089904250577092,
0.011163950897753239,
-0.013255232013761997,
-0.05981194227933884,
-0.0031401081942021847,
0.02007456310093403,
-0.005901349242776632,
-0.026590809226036072,
-0.019111795350909233,
0.04188944399356842,
0.030090080574154854,
0.024704795330762863,
0.041771795600652695,
-0.020318761467933655,
-0.04420836642384529,
-0.010987265035510063,
-0.012188299559056759,
0.009474659338593483,
0.010058470070362091,
0.04694773256778717,
0.02491096779704094,
-0.01590092107653618,
-0.013088795356452465,
-0.04760807007551193,
0.011900372803211212,
-0.021488822996616364,
0.018797501921653748,
-0.009945829398930073,
-0.017322374507784843,
0.0414813794195652,
0.010467673651874065,
0.014905543066561222,
0.023066474124789238,
0.015519080683588982,
-0.0028430758975446224,
-0.0441368967294693,
0.026262374594807625,
-0.015516473911702633,
0.0013014472788199782,
-0.007137593813240528,
-0.028165673837065697,
0.01901109889149666,
-0.041304249316453934,
-0.023040831089019775,
0.009634625166654587,
0.009449169039726257,
-0.05455689877271652,
0.00949131790548563,
0.01886938139796257,
0.05404609814286232,
0.049940381199121475,
-0.026229944080114365,
-0.058007948100566864,
0.013298929668962955,
-0.03606046363711357,
0.018394870683550835,
0.006188774015754461,
-0.0416727289557457,
0.051958803087472916,
-0.03163328766822815,
-0.07695143669843674,
0.0393216647207737,
-0.010246728546917439,
-0.005673548672348261,
0.01422462984919548,
-0.03664083033800125,
-0.07298503071069717,
0.0002756782341748476,
-0.010824007913470268,
-0.006140050012618303,
-0.053394850343465805,
0.003431747667491436,
0.02202143520116806,
-0.004265649244189262,
-0.028846092522144318,
-0.009900463744997978,
-0.027582766488194466,
-0.03743579611182213,
-0.020514145493507385,
0.01599586382508278,
0.014468890614807606,
-0.03683290630578995,
0.03267551586031914,
-0.003461871761828661,
-0.06357292085886002,
0.03110811486840248,
-0.03459440916776657,
-0.02627914398908615,
0.019343340769410133,
0.0159896332770586,
0.0466332845389843,
-0.01567390374839306,
-0.02124742977321148,
0.03812938556075096,
0.044513992965221405,
0.007928816601634026,
-0.016952184960246086,
0.01545439288020134,
0.031533095985651016,
-0.025943391025066376,
-0.012060197070240974,
0.018811609596014023,
-0.010843277908861637,
0.01602966897189617,
0.019054774194955826,
0.015376759693026543,
0.026908453553915024,
0.032998036593198776,
-0.007062125951051712,
-0.023279575631022453,
-0.026989100500941277,
-0.007789620663970709,
0.03516963869333267,
0.03213939815759659,
-0.055066417902708054,
0.04589366912841797,
-0.03485627844929695,
0.04719989746809006,
0.042048487812280655,
-0.021567342802882195,
0.051423899829387665,
0.04517257958650589,
-0.006143871229141951,
-0.017930129542946815,
0.06088976189494133,
0.0004567329597193748,
0.0401802696287632,
-0.02695818431675434,
0.014517503790557384,
0.050628021359443665,
-0.01811363361775875,
0.008561885915696621,
-0.0006837600958533585,
0.01970900595188141,
-0.05649181827902794,
-0.02286592684686184,
-0.02198590151965618,
0.00766503531485796,
0.03227820619940758,
-0.034507352858781815,
0.0008069993345998228,
0.03455205634236336,
0.04693252593278885,
0.0064396667294204235,
0.014076133258640766,
-0.0013283139560371637,
0.0072900401428341866,
-0.0578882060945034,
-0.008098351769149303,
-0.02436947077512741,
0.04313497245311737,
0.030781343579292297,
0.014464205130934715,
-0.0008008008007891476,
0.02399090863764286,
0.028836041688919067,
-0.008062263019382954,
-0.10913572460412979,
0.01007300429046154,
-0.040141358971595764,
-0.047208596020936966,
-0.02472887933254242,
-0.025295227766036987,
-0.005419876892119646,
-0.019176213070750237,
-0.02452770434319973,
-0.005041567143052816,
-0.029651816934347153,
-0.07768194377422333,
0.02729770541191101,
-0.03219631686806679,
-0.02658112719655037,
-0.010786882601678371,
0.011870612390339375,
0.044128693640232086,
0.00910905934870243,
0.002929468173533678,
0.035129040479660034,
-0.03567369654774666,
-0.0060662031173706055,
-0.020366424694657326,
0.0019759065471589565,
0.041613854467868805,
0.020875202491879463,
0.025355178862810135,
0.0038633500225842,
-0.04305598512291908,
0.055892348289489746,
0.028070848435163498,
0.02718733623623848,
0.0148677509278059,
-0.006177951581776142,
-0.06487727910280228,
-0.050463806837797165,
-0.005000125616788864,
-0.014346511103212833,
0.06241687759757042,
-0.003548121079802513,
0.010615606792271137,
0.046605367213487625,
0.0020108800381422043,
0.02148538827896118,
0.016732320189476013,
0.01132169645279646,
-0.006700597237795591,
0.008758350275456905,
-0.03367702662944794,
-0.019163263961672783,
-0.03411403298377991,
-0.010737528093159199,
0.02820410020649433,
-0.019429074600338936,
-0.01204011496156454,
0.020841084420681,
0.0036553493700921535,
-0.01959259994328022,
0.0013300844002515078,
0.0059980065561831,
-0.03075837530195713,
-0.03530044108629227,
0.02182813361287117,
-0.006780516356229782,
-0.03681403771042824,
0.06525292247533798,
0.023444289341568947,
-0.04052724316716194,
-0.015238954685628414,
-0.08927136659622192,
0.004267923999577761,
0.03579866141080856,
0.023879358544945717,
-0.013753484934568405,
-0.023219233378767967,
-0.046809934079647064,
-0.008198165334761143,
0.05111021548509598,
-0.04296429827809334,
0.05154876038432121,
-0.014933444559574127,
0.017632711678743362,
-0.024275342002511024,
-0.028633182868361473,
0.004164685029536486,
0.019173918291926384,
-0.029074886813759804,
-0.020840425044298172,
0.008847617544233799,
0.015573107637465,
-0.006425860337913036,
-0.02288072742521763,
0.02753947302699089,
0.01882883906364441,
-0.032456301152706146,
0.0035786102525889874,
-0.03042450360953808,
0.00021989706146996468,
-0.01390526071190834,
-0.10448353737592697,
0.01140760350972414,
0.011200951412320137,
-0.019807640463113785,
0.06843627244234085,
-0.04690039902925491,
0.009234808385372162,
0.0719686970114708,
0.01746807061135769,
-0.04486186429858208,
0.012599325738847256,
-0.06187543272972107,
0.02875223383307457,
0.002973119029775262,
0.01993585005402565,
0.01725989393889904,
0.02323077619075775,
0.013690740801393986,
-0.009517460130155087,
0.01913774386048317,
0.009085141122341156,
-0.010580744594335556,
-0.00003003586425620597,
-0.0002351788862142712,
0.0007430735277011991,
-0.019456135109066963,
0.04414897784590721,
-0.04715361073613167,
-0.018722349777817726,
0.003145018592476845,
-0.016919394955039024,
-0.008068356662988663,
0.034797485917806625,
0.022257164120674133,
0.035608869045972824,
-0.008289000950753689,
-0.009334210306406021,
0.008091072551906109,
-0.04402973875403404,
0.003794768126681447,
-0.013211368583142757,
0.016328128054738045,
0.04117549955844879,
0.0020907989237457514,
0.01241915114223957,
0.009549007751047611,
0.006382441613823175,
0.02049165405333042,
-0.03529997915029526,
0.015592481009662151,
0.0017563316505402327,
-0.0004293072852306068,
0.02754426747560501,
-0.009622031822800636,
-0.024421200156211853,
-0.012622825801372528,
-0.013272718526422977,
0.018082493916153908,
-0.05405997857451439,
0.03440311178565025,
0.040736984461545944,
0.021192479878664017,
-0.048524126410484314,
-0.05697101727128029,
0.034277088940143585,
0.0056707244366407394,
-0.0384620726108551,
-0.004117409698665142,
-0.023765770718455315,
-0.04818571358919144,
-0.03517112508416176,
-0.0075282445177435875,
0.06060241162776947,
0.01663239486515522,
-0.04329065605998039,
0.02140902355313301,
-0.012554300017654896,
0.04009081795811653,
0.00797942839562893,
-0.03154631331562996,
-0.0032071643508970737,
-0.03770894929766655,
-0.018741851672530174,
0.008399219252169132,
0.07430997490882874,
-0.022928433492779732,
-0.034570880234241486,
-0.03584896773099899,
-0.0065018292516469955,
0.019826499745249748,
-0.010963289067149162,
0.033454760909080505,
0.050394609570503235,
0.013957091607153416,
0.02577621303498745,
-0.04171757027506828,
0.02816079743206501,
-0.006618790794163942,
0.0036240944173187017,
0.01466043945401907,
-0.00993973109871149,
-0.015245610848069191,
-0.03962411358952522,
0.04521789401769638,
-0.00417845556512475,
0.03041151911020279,
-0.04133574292063713,
0.048335712403059006,
-0.02377649024128914,
-0.0020626462064683437,
-0.005958404392004013,
0.017521457746624947,
0.041453201323747635,
-0.016486836597323418,
-0.014771505258977413,
0.026261935010552406,
-0.020888376981019974,
-0.028284858912229538,
-0.00970029179006815,
-0.01574213244020939,
-0.004366538021713495,
0.09720828384160995,
-0.05631764605641365,
0.03143879398703575,
-0.029490910470485687,
-0.009626512415707111,
-0.003088600467890501,
-0.01717962510883808,
-0.024423418566584587,
0.00032834321609698236,
-0.008959684520959854,
0.010262738913297653,
-0.04171639308333397,
-0.012346180155873299,
-0.003945014905184507,
0.07545392960309982,
0.014674060046672821,
0.010930884629487991,
0.0390995591878891,
0.013573246076703072,
0.016967814415693283,
0.03168172389268875,
-0.010463397949934006,
0.010474640876054764,
-0.025757888332009315,
-0.01449201162904501,
-0.003162786364555359,
-0.01772976480424404,
0.04728887602686882,
-0.013191064819693565,
0.037634797394275665,
-0.02763548493385315,
-0.022651344537734985,
-0.04424339905381203,
-0.02536267787218094,
0.004071190021932125,
0.026842843741178513,
0.0010633161291480064,
-0.012750218622386456,
0.014650764875113964,
0.029508672654628754,
0.05131145194172859,
-0.02631470188498497,
-0.06471849977970123,
-0.05710066482424736,
-0.038564980030059814,
-0.010556327179074287,
0.055193863809108734,
0.03971577808260918,
0.007080696988850832,
-0.005474934354424477,
-0.043445147573947906,
0.01583380438387394,
0.033105961978435516,
0.053886257112026215,
0.0028716048691421747,
0.06685221940279007,
0.0034140110947191715,
0.022366488352417946,
0.002700651064515114,
0.01962982304394245,
0.10355361551046371,
0.032710056751966476,
-0.0001519184443168342,
-0.016258491203188896,
0.026338910683989525,
-0.008777051232755184,
0.018824109807610512,
-0.04012591764330864,
0.01916542835533619,
-0.01802668534219265,
0.003297095885500312,
0.02652113512158394,
0.05958038195967674,
-0.02340475097298622,
-0.008998697623610497,
0.043494295328855515,
-0.05732674151659012,
-0.04620445519685745,
0.013308401219546795,
0.024026181548833847,
0.004701119381934404,
0.023113258183002472,
-0.0437750518321991,
0.03357413783669472,
-0.013656836934387684,
-0.0009031728841364384,
-0.022937830537557602,
-0.03282669931650162,
0.014721374958753586,
0.04419365152716637,
-0.054866719990968704,
0.019373474642634392,
0.04564497992396355,
-0.024876786395907402,
-0.03616837412118912,
0.0013578555081039667,
0.06777973473072052,
0.00041196902748197317,
0.031105751171708107,
0.021069439128041267,
0.02453906461596489,
0.01384282298386097,
-0.001859487616457045,
0.01323087140917778,
-0.03901029750704765,
0.03804301470518112,
-0.015591861680150032,
0.05292769521474838,
-0.04454540088772774,
0.01285626646131277,
-0.028437664732336998,
-0.009315943345427513,
0.028403999283909798,
-0.06517977267503738,
-0.014014182612299919,
-0.01468062773346901,
0.0026880691293627024,
0.031972773373126984,
-0.009539106860756874,
-0.02122713439166546,
0.029043693095445633,
0.029440121725201607,
0.01626642234623432,
0.021432165056467056,
0.023735295981168747,
-0.00237209047190845,
-0.021066492423415184,
0.03853711485862732,
-0.022594274953007698,
-0.05606348067522049,
-0.005957753863185644,
0.007351110223680735,
-0.06806082278490067,
-0.0008585861069150269,
0.03338896855711937,
0.0372975692152977,
0.01155017875134945,
-0.009217675775289536,
-0.0004994543851353228,
0.0014256387948989868,
-0.06974697858095169,
-0.011898270808160305,
-0.0011346278479322791,
-0.018204011023044586,
-0.012852254323661327,
0.006892605684697628,
0.031098313629627228,
0.022305235266685486,
-0.04226090386509895,
0.011576006188988686,
-0.002084767911583185,
0.07605983316898346,
0.006126864813268185,
-0.00038031526491977274,
-0.03509429097175598,
0.028636807575821877,
-0.004080004058778286,
0.001969741890206933,
-0.0400124192237854,
0.020604733377695084,
0.0460219644010067,
-0.0010405087377876043,
-0.00005878392403246835,
0.0016780700534582138,
-0.020352782681584358,
-0.004136910196393728,
0.014098942279815674,
-0.034349024295806885,
0.0065417359583079815,
-0.004520015325397253,
0.01444624736905098,
-0.01345880702137947,
0.006110937334597111,
-0.022375423461198807,
-0.020683659240603447,
0.003773365169763565,
0.0021436584647744894,
-0.015443477779626846,
0.00866044219583273,
-0.022787882015109062,
0.001783358515240252,
-0.045779816806316376,
0.001514424686320126,
-0.02218949981033802,
0.04111120104789734,
-0.015621508471667767,
-0.020945236086845398,
-0.0326167568564415,
0.03135554865002632,
-0.061664432287216187,
-0.025164667516946793,
-0.01063393335789442,
0.02734864316880703,
-0.00786389596760273,
-0.035951852798461914,
-0.005715124309062958,
-0.009854073636233807,
0.03320698440074921,
0.0010619013337418437,
-0.042756423354148865,
0.04750628396868706,
-0.04028696566820145,
-0.02972467429935932,
0.06386028975248337,
-0.02133304812014103,
0.023976586759090424,
0.052676618099212646,
-0.025176767259836197,
-0.003167834598571062,
0.08882078528404236,
-0.015307968482375145,
-0.009183203801512718,
0.02380077727138996,
-0.03201825171709061,
-0.005276117939502001,
0.0028617025818675756,
0.019571453332901,
-0.013393748551607132,
-0.00945973675698042,
0.02094324678182602,
0.032140836119651794,
-0.016668131574988365,
0.04490085318684578,
0.011119113303720951,
-0.03265293315052986,
-0.02762417681515217,
-0.0136359091848135,
-0.035075679421424866,
-0.016278401017189026,
0.06391698867082596,
-0.030098771676421165,
0.040145158767700195,
0.013916355557739735,
-0.003718448569998145,
-0.11163204908370972,
0.035204820334911346,
0.018096880987286568,
0.014333534054458141,
0.053146399557590485,
-0.032490625977516174,
0.025033462792634964,
0.03185754641890526,
-0.06881679594516754,
0.0057626147754490376,
-0.0553324818611145,
-0.008076416328549385,
-0.043495964258909225,
0.02228112332522869,
0.019524797797203064,
0.01482277549803257,
0.02271568961441517,
0.03554866835474968,
0.004653990268707275,
-0.010071366094052792,
-0.033983293920755386,
-0.06535603851079941,
-0.021520452573895454,
0.05826551467180252,
0.0013780120061710477,
0.04494630545377731,
0.08825778216123581,
-0.023087773472070694,
-0.011668029241263866,
0.04284568130970001,
-0.005050664767622948,
0.02376261167228222,
-0.027515539899468422,
-0.017551904544234276,
0.01571812853217125,
0.025022344663739204,
0.006986099295318127,
0.02397613786160946,
0.0010184720158576965,
0.053707968443632126,
0.0436229482293129,
0.02936895191669464,
-0.030711814761161804,
-0.011652029119431973,
0.04777481406927109,
-0.02678220346570015,
-0.02932007610797882,
0.016253666952252388,
-0.0001022633514367044,
-0.00646119425073266,
0.007970210164785385,
0.029870282858610153,
0.0354485847055912,
-0.005154936574399471,
-0.011797751300036907,
-0.034456491470336914,
-0.008006328716874123,
-0.0038148658350110054,
-0.015601353719830513,
-0.018172796815633774,
0.009332534857094288,
-0.03322957828640938,
-0.03179939091205597,
-0.0045834798365831375,
-0.021155493333935738,
0.007062493357807398,
-0.013351662084460258,
-0.012416516430675983,
0.026625804603099823,
0.010179144330322742,
0.03440864011645317,
-0.043984465301036835,
-0.0030449898913502693,
0.028774581849575043,
-0.0028918785974383354,
-0.00008668351074447855,
-0.007600526791065931,
-0.037002984434366226,
-0.012928907759487629,
-0.053560931235551834,
0.04067055135965347,
0.006911820266395807,
-0.01728273555636406,
-0.04082409292459488,
-0.024575533345341682,
-0.013513019308447838,
0.020481819286942482,
0.04655176401138306,
-0.03629334270954132,
-0.023841511458158493,
0.037460654973983765,
-0.006442869082093239,
0.006645520683377981,
-0.03422185778617859,
-0.026444410905241966,
0.026519861072301865,
-0.04930438846349716,
-0.04461025446653366,
0.01209211628884077,
-0.004394287709146738,
0.012958299368619919,
0.013395696878433228,
0.004981790203601122,
0.011775691993534565,
-0.012317967601120472,
-0.05283408612012863,
0.07151822745800018,
0.0018261481309309602,
-0.010908463038504124,
0.04791990667581558,
0.02587861195206642,
0.025398578494787216,
0.015763888135552406,
-0.01743268221616745,
-0.006592870689928532,
0.005146654322743416,
-0.017608480527997017,
-0.019130032509565353,
0.004992741160094738,
-0.0295991413295269,
0.015660667791962624,
-0.030121270567178726,
0.02224034257233143,
0.04956343024969101,
0.0016318566631525755,
-0.017109273001551628,
0.05344686284661293,
-0.011466207914054394,
0.04558951035141945,
0.0007287788321264088,
0.02268434315919876,
-0.0019966051913797855,
-0.021753961220383644,
-0.019567832350730896,
0.01066966075450182,
-0.02657647803425789,
0.003841181518509984,
0.006563176866620779,
0.05463040992617607,
-0.0013611650792881846,
0.00669193034991622,
-0.028147496283054352,
0.014062591828405857,
-0.031744834035634995,
-0.013205236755311489,
-0.00431404635310173,
-0.0379737950861454,
0.030408354476094246,
0.006935878656804562,
0.008622069843113422,
0.07928552478551865,
-0.005127564072608948,
0.04262085631489754,
0.005407015793025494,
-0.023040633648633957,
-0.014812042936682701,
0.023155007511377335,
-0.016610655933618546,
-0.0021430959459394217,
-0.018827151507139206,
-0.017533233389258385,
-0.02032242901623249,
-0.005927830934524536,
0.04569844529032707,
-0.07982121407985687,
0.0009516006102785468,
-0.025263240560889244,
-0.0025234948843717575,
-0.00825570710003376,
-0.018180083483457565,
-0.009293251670897007,
0.018203143030405045,
0.007932323962450027,
0.022259525954723358,
-0.008177703246474266,
-0.006860452238470316,
-0.015240362845361233,
0.0007325574988499284,
0.02186536230146885,
-0.06891440600156784,
-0.012513281777501106,
-0.020314084365963936,
0.0007918998599052429,
-0.011517975479364395,
-0.06717926263809204
] |
<p>Given a parallel plate capacitor of width $w$, length $l$, with a dielectric moving along the length $l$. Let the dielectric be from $x$ onwards.</p>
<p>The capacitance will be $\frac{w \epsilon_0}{d} (\epsilon_r l - \chi_e x)$. Griffiths (p. 195) says that the total charge $Q$ in the $C=\frac{Q}{V}$ expression is constant as the dielectric moves. But $Q$ here refers to the free charge, and the free charge definitely increases as you move the dielectric in increasing $x$. What am I misunderstanding?</p> | 2,854 | [
0.005034168716520071,
-0.020814966410398483,
0.02183927595615387,
0.013891649432480335,
0.029413381591439247,
0.017045123502612114,
0.025246532633900642,
0.028738778084516525,
0.02781686745584011,
-0.027424218133091927,
-0.005521985702216625,
0.06776023656129837,
0.07668282091617584,
0.01316048763692379,
0.029701407998800278,
0.023290932178497314,
-0.01843571476638317,
-0.00017543183639645576,
0.024300765246152878,
-0.02358417958021164,
-0.00791425071656704,
0.06228908523917198,
0.017258387058973312,
-0.006182263605296612,
0.0018838043324649334,
0.0400749035179615,
-0.01774732954800129,
-0.03820022568106651,
0.020208338275551796,
0.03223075717687607,
-0.008971597999334335,
-0.011305710300803185,
-0.010875318199396133,
-0.014920122921466827,
0.012230289168655872,
-0.011842739768326283,
-0.03591054305434227,
-0.06275280565023422,
-0.0030012743081897497,
0.028060901910066605,
-0.02398627996444702,
0.016574135050177574,
-0.002470429753884673,
0.030387194827198982,
-0.03365423530340195,
0.006545158103108406,
0.040060240775346756,
-0.031330227851867676,
0.015103265643119812,
-0.05109721049666405,
0.0617557168006897,
-0.004313663113862276,
0.05316007137298584,
0.03335700184106827,
-0.005615487229079008,
0.00996464304625988,
0.0722823366522789,
0.05456596240401268,
-0.04120834916830063,
-0.0037023196928203106,
-0.04069076478481293,
-0.04864370450377464,
0.01591254211962223,
-0.029003096744418144,
-0.009908188134431839,
0.0290482509881258,
0.01776009239256382,
0.0006215604953467846,
0.010575993917882442,
-0.004945619963109493,
0.014423870481550694,
0.05660473182797432,
-0.0007650270126760006,
-0.03416161984205246,
0.006644522771239281,
0.01290898211300373,
-0.01603849045932293,
0.05045799911022186,
0.004069064743816853,
0.03768496960401535,
-0.006777338683605194,
0.0026811875868588686,
0.030218107625842094,
0.05409517511725426,
0.011494258418679237,
-0.011710071004927158,
0.043371137231588364,
0.022709883749485016,
-0.0015439260751008987,
0.03110373578965664,
0.01920245587825775,
0.018443403765559196,
0.022599564865231514,
-0.0048080068081617355,
-0.010098231956362724,
0.038637928664684296,
-0.031241295859217644,
0.033727534115314484,
0.009608599357306957,
-0.03508327156305313,
0.013441183604300022,
-0.005568963475525379,
0.01570393703877926,
0.03391091898083687,
0.024977944791316986,
-0.035050131380558014,
-0.014254978857934475,
0.024213481694459915,
-0.03113335371017456,
-0.041475262492895126,
-0.08856029063463211,
0.011930153705179691,
0.01882525347173214,
0.033688485622406006,
-0.001043378608301282,
-0.019999830052256584,
-0.0073371040634810925,
-0.017807969823479652,
0.03180292993783951,
0.03900294378399849,
0.0048651848919689655,
-0.026956111192703247,
0.026025352999567986,
-0.028309741988778114,
-0.06713979691267014,
0.053129926323890686,
0.013944044709205627,
-0.014585950411856174,
-0.0487065315246582,
-0.0019769661594182253,
0.009363795630633831,
0.01503330934792757,
-0.003256501629948616,
0.009226216934621334,
0.011582871899008751,
0.004794278182089329,
-0.0924294963479042,
-0.03196384012699127,
-0.005727583076804876,
-0.00035251633380539715,
-0.0009073069086298347,
-0.08528944849967957,
-0.019103998318314552,
0.03152019530534744,
0.10803642123937607,
-0.02772611752152443,
0.000035017386835534126,
-0.01994957961142063,
-0.0010139882797375321,
-0.014186561107635498,
-0.04131094366312027,
-0.05870956555008888,
0.025170691311359406,
-0.005136147607117891,
-0.022052107378840446,
-0.06828714907169342,
0.0034362557344138622,
0.046873122453689575,
0.02230987511575222,
-0.0033548681531101465,
0.050191279500722885,
-0.021973252296447754,
-0.028819698840379715,
-0.007373375352472067,
-0.05319037660956383,
-0.036886900663375854,
0.07558803260326385,
0.02826644852757454,
0.03919272497296333,
0.010454759001731873,
0.05066491663455963,
0.03592604398727417,
0.003270881250500679,
0.024603212252259254,
0.09012569487094879,
-0.032486576586961746,
0.011028528213500977,
-0.01835346780717373,
0.017606280744075775,
0.03284110501408577,
-0.04032377526164055,
-0.04597855359315872,
-0.009128818288445473,
0.03298556059598923,
0.039223600178956985,
0.031452152878046036,
-0.03138919174671173,
-0.00023724876518826932,
-0.0026301799807697535,
-0.044591110199689865,
-0.038164082914590836,
-0.0630468875169754,
0.06618793308734894,
0.023773489519953728,
-0.012552815489470959,
0.019686702638864517,
-0.0007859558681957424,
-0.005558195058256388,
-0.030840331688523293,
-0.023169441148638725,
0.024477722123265266,
0.03410817310214043,
-0.028669120743870735,
-0.01604502648115158,
0.017911257222294807,
0.03302831947803497,
0.033262867480516434,
0.05032389611005783,
0.007831643335521221,
-0.017240114510059357,
-0.01183081790804863,
0.026264764368534088,
-0.01703958958387375,
0.05185313895344734,
-0.004916165489703417,
-0.011073610745370388,
0.01823292300105095,
0.0033705481328070164,
-0.018403632566332817,
0.036081429570913315,
-0.011263854801654816,
0.055847082287073135,
0.0769190713763237,
0.005404709838330746,
-0.0045687309466302395,
0.019984373822808266,
-0.02794741280376911,
0.017054134979844093,
-0.02256486378610134,
-0.0466872863471508,
-0.03950479254126549,
0.009471678175032139,
0.020700674504041672,
0.00591510534286499,
-0.015808748081326485,
0.014460207894444466,
0.023735549300909042,
0.0005149728385731578,
0.046200159937143326,
-0.006067164242267609,
0.007906467653810978,
-0.04451444372534752,
0.036433491855859756,
-0.000553194317035377,
-0.016440661624073982,
-0.038517288863658905,
-0.0007369759259745479,
-0.01841726154088974,
0.010110104456543922,
-0.015619686804711819,
-0.013282530009746552,
0.010100587271153927,
0.03382540121674538,
0.05700789391994476,
0.028713932260870934,
-0.05014201998710632,
0.032552570104599,
-0.05323532223701477,
0.03101417049765587,
0.030940288677811623,
0.0017832674784585834,
0.004561204928904772,
-0.0200093574821949,
0.008332774043083191,
0.014607071876525879,
0.009768353775143623,
-0.035194117575883865,
-0.002280997345224023,
0.02180188149213791,
-0.04386065900325775,
0.055237483233213425,
-0.02202320471405983,
-0.029182193800807,
0.012470615096390247,
-0.012272757478058338,
0.0312897153198719,
0.043369509279727936,
0.08087343722581863,
-0.04180251806974411,
-0.012256335467100143,
0.006881336681544781,
-0.02391837164759636,
0.02293926663696766,
0.024690281599760056,
-0.04108108580112457,
-0.007500205188989639,
-0.030051155015826225,
-0.04657489433884621,
0.03489366173744202,
0.015584266744554043,
0.020341098308563232,
0.027103422209620476,
-0.038550954312086105,
-0.03736633434891701,
-0.011048323474824429,
-0.008740905672311783,
-0.005758369341492653,
-0.03404141589999199,
0.016397306695580482,
0.07234293967485428,
-0.0040712845511734486,
-0.032908935099840164,
-0.006855499930679798,
-0.04179229214787483,
-0.025446513667702675,
0.01991150714457035,
0.010148241184651852,
0.03798642009496689,
-0.027500513941049576,
0.02093110792338848,
0.003799592610448599,
-0.027580782771110535,
0.01120719313621521,
-0.03144677355885506,
-0.07691200077533722,
0.054229721426963806,
-0.034771937876939774,
0.05805665999650955,
-0.01550350058823824,
-0.03479703143239021,
0.07421815395355225,
0.0029066423885524273,
-0.0037170774303376675,
-0.006900789216160774,
-0.032056525349617004,
-0.012731689028441906,
-0.027871428057551384,
-0.03359023854136467,
0.04511990398168564,
-0.02802291326224804,
0.013562829233705997,
0.01911778561770916,
0.0503934770822525,
0.025052927434444427,
0.0034256966318935156,
0.006197142414748669,
-0.0004657534882426262,
0.02908727340400219,
-0.015601351857185364,
0.04997292906045914,
0.024413414299488068,
0.003662119386717677,
0.010903301648795605,
0.027166292071342468,
0.02653389237821102,
0.026550976559519768,
-0.036757949739694595,
0.04020523652434349,
-0.011274079792201519,
-0.013944294303655624,
-0.004185361787676811,
0.06883462518453598,
0.005017234943807125,
-0.017868712544441223,
0.013492977246642113,
0.028501063585281372,
0.025416504591703415,
-0.056217923760414124,
-0.02478678897023201,
0.029002467170357704,
0.03680041432380676,
-0.012241478078067303,
-0.038645826280117035,
-0.036303214728832245,
-0.04400845617055893,
0.027598893269896507,
-0.021279938519001007,
-0.02149178273975849,
0.020097728818655014,
0.007597685791552067,
0.01570875383913517,
-0.005277898628264666,
-0.04512276500463486,
-0.003272463334724307,
-0.05591370537877083,
-0.024480005726218224,
-0.011536800302565098,
0.03353781998157501,
0.021235588937997818,
0.037028275430202484,
0.014352713711559772,
-0.022836966440081596,
0.009213894605636597,
0.013143130578100681,
-0.07957663387060165,
0.0026482536923140287,
-0.004141960293054581,
-0.005475848447531462,
-0.005180207546800375,
0.00087320915190503,
0.004255588632076979,
-0.010129913687705994,
-0.02375786192715168,
-0.03683047741651535,
-0.003944068215787411,
-0.05825551226735115,
0.04230433702468872,
-0.01971542276442051,
-0.048280540853738785,
-0.000014731533156009391,
0.02037419006228447,
0.010995744727551937,
-0.053630225360393524,
-0.0040827603079378605,
0.02720397710800171,
-0.032098956406116486,
0.015240342356264591,
0.022510899230837822,
-0.003277083393186331,
0.014471014961600304,
-0.024949736893177032,
0.0004952622693963349,
-0.005084540694952011,
0.012960933148860931,
0.022536631673574448,
0.03320911154150963,
0.04931576922535896,
0.013408844359219074,
-0.036692917346954346,
-0.04558151960372925,
-0.05540380999445915,
-0.027417004108428955,
-0.031054401770234108,
0.050604451447725296,
0.013704218901693821,
-0.00016822245379444212,
0.04675763100385666,
0.024243582040071487,
-0.007887029089033604,
0.029330143705010414,
0.05139102041721344,
0.031288065016269684,
-0.025777233764529228,
-0.05308566242456436,
0.03505373001098633,
-0.0036691175773739815,
-0.008030706085264683,
0.02527627907693386,
0.002825363539159298,
-0.007578787859529257,
0.014938827604055405,
0.009043202735483646,
-0.014371068216860294,
-0.02841809391975403,
0.009321175515651703,
0.012223663739860058,
-0.016873955726623535,
-0.002074929652735591,
-0.01713547110557556,
0.001960260095074773,
-0.003917512949556112,
0.022774631157517433,
0.013063871301710606,
-0.019679686054587364,
-0.10738655924797058,
-0.017685705795884132,
0.022814983502030373,
0.03243524208664894,
-0.01247339230030775,
0.002054942538961768,
-0.056146290153265,
-0.014010810293257236,
0.011418739333748817,
-0.025137461721897125,
0.03164210170507431,
-0.012437345460057259,
0.0019044233486056328,
-0.0012620765483006835,
-0.009041860699653625,
-0.03122103214263916,
0.029560444876551628,
-0.000191587969311513,
0.03057321161031723,
-0.02731040120124817,
0.019610514864325523,
-0.009476236067712307,
0.016846641898155212,
0.05073009803891182,
0.07618448138237,
0.016226908192038536,
-0.01861822046339512,
-0.0004951357841491699,
0.01682755909860134,
-0.010110168717801571,
-0.05806676298379898,
-0.0006803993019275367,
-0.007137484848499298,
0.025515714660286903,
0.025756116956472397,
-0.014700044877827168,
-0.05439325422048569,
0.007163078058511019,
0.028186853975057602,
0.008728343062102795,
-0.015828028321266174,
-0.010948722250759602,
0.09498883038759232,
0.03299754485487938,
-0.004148809239268303,
0.07083947211503983,
0.024014579132199287,
-0.0504118911921978,
0.014323526993393898,
-0.012165703810751438,
0.06711894273757935,
0.0017059965757653117,
0.011391323991119862,
-0.020501889288425446,
0.006132534705102444,
-0.02791110798716545,
0.05069718137383461,
-0.013328404165804386,
0.010017960332334042,
-0.03510689735412598,
-0.02928422950208187,
0.01119988039135933,
-0.012455837801098824,
0.036753032356500626,
-0.0043214899487793446,
-0.02024848759174347,
0.03512119501829147,
0.04178459197282791,
-0.00853622704744339,
-0.0014754210133105516,
0.011496976017951965,
0.0048672789707779884,
0.0556860975921154,
0.014526581391692162,
-0.011550265364348888,
-0.0357455350458622,
0.011407952755689621,
-0.005690204910933971,
-0.022653702646493912,
0.03046482242643833,
0.01752565987408161,
-0.014614046551287174,
0.014783534221351147,
-0.024084730073809624,
-0.05214574560523033,
0.009168228134512901,
-0.0020126088056713343,
-0.0025008749216794968,
-0.08920438587665558,
-0.005753328558057547,
0.026335712522268295,
0.027308164164423943,
-0.07659020274877548,
-0.05222227796912193,
0.019702749326825142,
-0.004466325044631958,
-0.004089205525815487,
-0.014130126684904099,
-0.014576119370758533,
0.015333003364503384,
-0.05741356313228607,
-0.000918214675039053,
0.02937285415828228,
-0.036965806037187576,
0.027959270402789116,
-0.00017962486890610307,
0.004153926856815815,
0.04003625363111496,
-0.01149857696145773,
-0.005011932924389839,
-0.003863094374537468,
-0.0537356361746788,
-0.008826482109725475,
-0.014115436002612114,
0.034648966044187546,
-0.0438857302069664,
-0.01682758331298828,
-0.016858506947755814,
-0.02438381128013134,
0.046795789152383804,
-0.03804250806570053,
-0.06555495411157608,
0.004835936240851879,
0.016398916020989418,
-0.031117264181375504,
-0.002025514841079712,
0.0074099707417190075,
-0.004077553749084473,
0.025606073439121246,
0.015423780307173729,
-0.009105417877435684,
-0.09114856272935867,
-0.012625808827579021,
0.004302497021853924,
0.012201962992548943,
0.01949493959546089,
-0.04480449855327606,
0.06014275178313255,
-0.046091228723526,
-0.028961848467588425,
0.03695129603147507,
-0.0006855796091258526,
0.03570261225104332,
0.004116374533623457,
-0.044100090861320496,
0.012309186160564423,
-0.005775212775915861,
-0.0120084835216403,
0.007848989218473434,
-0.04686993360519409,
0.028899526223540306,
0.06532768160104752,
0.006121931131929159,
0.06682146340608597,
0.014459631405770779,
-0.05794166773557663,
-0.009172236546874046,
-0.008816401474177837,
-0.04313411936163902,
-0.018450431525707245,
-0.0021364002022892237,
-0.01745561696588993,
-0.009544532746076584,
-0.029566334560513496,
0.00815962627530098,
0.06362385302782059,
-0.04824348911643028,
-0.02670987881720066,
0.03811119124293327,
0.04349229484796524,
0.003644372336566448,
-0.012525327503681183,
-0.04954497516155243,
0.058723315596580505,
-0.018790228292346,
0.03551790118217468,
-0.00828609336167574,
-0.05285650119185448,
0.05350756272673607,
0.026377491652965546,
-0.0030135309789329767,
-0.0390470027923584,
-0.016042275354266167,
-0.025322090834379196,
0.02271221950650215,
0.003475831588730216,
0.05779487267136574,
0.0014356470201164484,
0.025768645107746124,
0.05083037167787552,
0.006519368849694729,
0.024922434240579605,
-0.034308500587940216,
-0.052175216376781464,
0.008589833043515682,
0.0032646742183715105,
0.008474741131067276,
0.011307396925985813,
0.0011903931153938174,
-0.01006338931620121,
-0.006520092952996492,
-0.03300001099705696,
0.05111636966466904,
0.026453398168087006,
0.01753227412700653,
-0.0036105532199144363,
0.050803977996110916,
-0.035555317997932434,
-0.007128228899091482,
-0.04595141112804413,
0.0010097210761159658,
0.12114586681127548,
0.03415467217564583,
-0.012903561815619469,
-0.060692302882671356,
-0.0012998987222090364,
-0.020693080499768257,
-0.007535211741924286,
-0.03947814553976059,
0.025883106514811516,
-0.024021092802286148,
-0.017399024218320847,
-0.000665330677293241,
0.03003096394240856,
-0.0065319957211613655,
0.02960755117237568,
0.05683638155460358,
0.010190600529313087,
-0.03283718600869179,
0.03532237932085991,
0.02090342529118061,
-0.0020378688350319862,
0.04821782186627388,
-0.05248371139168739,
0.0330490879714489,
-0.028909053653478622,
-0.018291065469384193,
-0.04183023422956467,
-0.030048128217458725,
0.00589592382311821,
0.004977669101208448,
-0.06145130842924118,
0.0027099077124148607,
0.025109071284532547,
0.0005192748503759503,
-0.056871198117733,
0.04730335250496864,
0.02743988297879696,
0.02406124211847782,
-0.009486178867518902,
0.009841705672442913,
0.020067960023880005,
0.022515105083584785,
0.03354240208864212,
0.015871761366724968,
-0.028470613062381744,
0.016526104882359505,
-0.05530809983611107,
0.044891346246004105,
0.0018939098808914423,
0.007782599423080683,
0.028550993651151657,
0.016429144889116287,
-0.013287365436553955,
-0.06583669781684875,
0.0001744897454045713,
0.01947498694062233,
0.008454469032585621,
0.02490212209522724,
0.026550231501460075,
-0.046443693339824677,
0.02637084387242794,
-0.026528043672442436,
-0.01024733204394579,
-0.020049341022968292,
-0.046979621052742004,
0.01778315007686615,
-0.01778373308479786,
0.011932357214391232,
-0.036304887384176254,
-0.028294557705521584,
-0.01811661384999752,
-0.0037005983758717775,
-0.02438328042626381,
-0.023056304082274437,
-0.019962895661592484,
0.006264501716941595,
0.036146197468042374,
-0.04892418533563614,
-0.007319252472370863,
0.020327625796198845,
-0.09701329469680786,
0.049123216420412064,
-0.0028229951858520508,
-0.022642826661467552,
-0.0398445650935173,
0.015963982790708542,
-0.012203233316540718,
0.04586273431777954,
-0.04825153201818466,
-0.0016417574370279908,
-0.019382618367671967,
0.04217366874217987,
0.004718841519206762,
-0.029316561296582222,
-0.010924289003014565,
-0.011688089929521084,
-0.03832319378852844,
-0.00047945010010153055,
0.00014032484614290297,
-0.008997845463454723,
0.012189775705337524,
0.0388493686914444,
-0.023553598672151566,
0.031686943024396896,
-0.011491211131215096,
0.015243738889694214,
-0.003163789864629507,
0.009224512614309788,
0.011991120874881744,
0.010426238179206848,
0.02617962658405304,
-0.006345757748931646,
-0.03737642988562584,
-0.02268896996974945,
-0.007133270613849163,
-0.019976191222667694,
0.010461057536303997,
-0.009951794520020485,
-0.011412220075726509,
-0.03002980165183544,
0.0119412150233984,
-0.029806826263666153,
-0.02410489320755005,
-0.03486563265323639,
0.027810825034976006,
0.04598468914628029,
0.03257892653346062,
0.010589809156954288,
0.021557141095399857,
-0.037970393896102905,
0.018711287528276443,
0.011074589565396309,
-0.014137182384729385,
0.0019616037607192993,
-0.005342462565749884,
0.02829936146736145,
0.020012585446238518,
0.04245171695947647,
-0.06715076416730881,
-0.03282277658581734,
0.036636825650930405,
-0.004842828493565321,
-0.06340620666742325,
-0.00955157820135355,
-0.02053702436387539,
0.02014852687716484,
0.018211951479315758,
0.008268549107015133,
0.017030982300639153,
0.017773529514670372,
-0.010032114572823048,
0.008612655103206635,
-0.02074357122182846,
-0.0540463887155056,
0.020951880142092705,
-0.052814602851867676,
-0.011005549691617489,
-0.0056003485806286335,
0.033424895256757736,
0.04788138344883919,
0.02631746418774128,
-0.03265929967164993,
-0.007359360810369253,
0.016893351450562477,
-0.019831037148833275,
-0.03892167657613754,
0.016038265079259872,
0.030116697773337364,
0.007152189034968615,
0.046474993228912354,
-0.029650239273905754,
-0.0035330592654645443,
-0.0167336855083704,
0.01152822095900774,
-0.07901167124509811,
-0.024982746690511703,
0.0013515612808987498,
0.0155039606615901,
0.0256632212549448,
-0.04888352006673813,
0.01653490960597992,
0.020245596766471863,
-0.08662552386522293,
0.01611338183283806,
-0.062301091849803925,
0.022714661434292793,
-0.03443070128560066,
0.008929288946092129,
0.011750549077987671,
0.035798005759716034,
0.052211929112672806,
0.0340188592672348,
0.028037529438734055,
-0.022403135895729065,
0.00998763833194971,
-0.051890432834625244,
-0.003002293175086379,
0.007964770309627056,
0.006154532078653574,
-0.037059929221868515,
0.057658471167087555,
-0.00380318402312696,
-0.03002496063709259,
0.034125957638025284,
0.005401389207690954,
-0.01858402229845524,
0.023600716143846512,
0.020637456327676773,
0.02035589888691902,
0.03072570450603962,
0.018937047570943832,
-0.017783520743250847,
-0.013112332671880722,
-0.03266240283846855,
0.0227464959025383,
0.014949820935726166,
-0.0007290283683687449,
0.0055423304438591,
0.015839973464608192,
-0.0063204276375472546,
-0.03735215961933136,
0.01914556883275509,
-0.0711618959903717,
-0.018708670511841774,
0.01618221402168274,
0.04513029381632805,
0.01796317659318447,
-0.01783762313425541,
0.025729000568389893,
-0.030531849712133408,
-0.026242047548294067,
0.024281583726406097,
0.02913842350244522,
0.004647289868444204,
-0.021143710240721703,
0.01411295123398304,
-0.0070886267349123955,
0.0060370624996721745,
0.03799576312303543,
0.02553996443748474,
-0.059856925159692764,
-0.021620173007249832,
-0.025472989305853844,
-0.006422595586627722,
-0.006752062123268843,
-0.03329943120479584,
-0.04663855582475662,
0.03363844007253647,
-0.021171968430280685,
0.0011590158101171255,
-0.008843831717967987,
0.00268559786491096,
-0.009063453413546085,
-0.059490904211997986,
0.02561776526272297,
0.012503252364695072,
-0.05980437248945236,
-0.007303804159164429,
-0.0453123077750206,
-0.050317417830228806,
-0.026203680783510208,
0.06829429417848587,
-0.002480923430994153,
-0.01518630888313055,
0.01915878988802433,
0.010172171518206596,
0.05034556984901428,
-0.04433205723762512,
-0.0037095658481121063,
0.01784362830221653,
0.0032426847610622644,
0.006774176377803087,
0.00045620009768754244,
-0.012738959863781929,
0.01743929088115692,
0.0012667110422626138,
0.03552067652344704,
0.02539953961968422,
-0.00923794973641634,
-0.0013314749812707305,
0.033669888973236084,
0.04206988587975502,
-0.008952484466135502,
0.06080905348062515,
0.007504261564463377,
0.018483610823750496,
0.006153466645628214,
-0.013098100200295448,
-0.05855530500411987,
-0.014572801999747753,
-0.02786436304450035,
0.0040743970312178135,
-0.026423512026667595,
0.055553704500198364,
0.04037818685173988,
-0.02186249941587448,
-0.01779346540570259,
0.026871884241700172,
-0.03210825100541115,
-0.02752782218158245,
0.07225349545478821,
-0.011580219492316246,
-0.0135737843811512,
0.023003598675131798,
0.002385207684710622,
0.0055882902815938,
0.009365561418235302,
-0.004127833526581526,
0.038461681455373764,
0.05671171471476555,
-0.0075428904965519905,
0.03477296233177185,
0.08039996773004532,
-0.00891932938247919,
0.005840587895363569,
-0.017424577847123146,
-0.0001978849759325385,
0.007033696398139,
-0.031390056014060974,
-0.0020691491663455963,
-0.002976828021928668,
-0.029390038922429085,
0.03640377148985863,
-0.036176905035972595,
0.064583919942379,
-0.0008936377125792205,
0.019227152690291405,
0.03843025118112564,
0.016090936958789825,
-0.00021998729789629579,
0.0074503133073449135,
-0.001955291721969843,
0.02127739042043686,
-0.006540801376104355,
-0.026786258444190025,
-0.032233331352472305,
-0.03282713517546654,
0.012983162887394428,
-0.031110525131225586,
-0.001868905033916235,
0.025680411607027054,
0.008782400749623775,
-0.01537003368139267,
-0.0207456536591053,
-0.025950873270630836,
0.016586758196353912,
0.033133089542388916,
0.049596529453992844,
-0.003441890235990286,
0.007686716038733721,
-0.00980436336249113,
-0.025112001225352287,
0.07312793284654617,
-0.04524088278412819,
0.010430943220853806,
0.009377852082252502,
0.014395947568118572,
0.030863502994179726,
0.015254883095622063
] |
<p>I was just wondering... I believe that if a car travelling 50 miles per hour crashes into a wall, the result should be the same as crashing to another car also travelling 50 miles per hour (but in the other direction of course)</p>
<p>Is this true? Why is that?</p> | 58 | [
-0.054732587188482285,
0.004704664461314678,
-0.030169043689966202,
-0.020509544759988785,
0.030699370428919792,
0.017734073102474213,
-0.0279824398458004,
0.0059150150045752525,
0.02064364030957222,
0.03371773287653923,
0.0017006713896989822,
0.059625156223773956,
0.013092962093651295,
0.014599906280636787,
0.02373524382710457,
0.02622746303677559,
-0.014635938219726086,
-0.000863264431245625,
0.005123636685311794,
-0.045105885714292526,
0.0008701325277797878,
-0.008441798388957977,
0.009299516677856445,
-0.005702564958482981,
-0.02595103718340397,
0.008286603726446629,
0.02382602170109749,
-0.0039054863154888153,
0.016168400645256042,
0.02598145604133606,
0.020167989656329155,
0.0003227794368285686,
0.003528932575136423,
0.062276922166347504,
0.037042513489723206,
0.006159116048365831,
-0.006825894117355347,
0.0174635611474514,
-0.03683008626103401,
0.00944956298917532,
-0.0015007448382675648,
-0.014096973463892937,
0.0019183697877451777,
0.08808677643537521,
-0.039900559931993484,
0.029676057398319244,
0.020447729155421257,
-0.03789761662483215,
0.008357254788279533,
-0.05932173132896423,
0.10163145512342453,
-0.020767657086253166,
0.015742653980851173,
0.0012525547062978148,
-0.006096932105720043,
-0.011398710310459137,
0.04371128976345062,
0.06671760231256485,
-0.041649866849184036,
-0.027710406109690666,
-0.0292314775288105,
0.013784115202724934,
-0.005204284563660622,
0.010924247093498707,
-0.035620465874671936,
0.04859444871544838,
-0.042304877191782,
-0.04316316172480583,
0.0507180318236351,
-0.007395564578473568,
-0.026534901931881905,
-0.001287285820581019,
0.04369717836380005,
-0.004782705567777157,
0.03860912472009659,
-0.03537974879145622,
0.02123548462986946,
0.0032391948625445366,
0.05634831637144089,
0.029094843193888664,
-0.02825835905969143,
-0.008303944952785969,
0.07836512476205826,
0.04630354046821594,
0.04406744986772537,
-0.012033418752253056,
0.06300757080316544,
-0.004601981025189161,
0.014979047700762749,
0.047911398112773895,
0.02147173136472702,
-0.004238534718751907,
-0.010211948305368423,
-0.0022754196543246508,
0.016707925125956535,
0.04402858391404152,
0.009687285870313644,
0.057012345641851425,
0.0031286696903407574,
0.017105933278799057,
-0.013117361813783646,
0.006754800211638212,
-0.005421017296612263,
0.007972038350999355,
0.009859472513198853,
-0.016410496085882187,
-0.031196899712085724,
0.013963509351015091,
0.0023203277960419655,
0.028243722394108772,
-0.0020995622035115957,
0.03592800348997116,
0.002420025411993265,
0.010129748843610287,
0.005849706940352917,
-0.00487423874437809,
0.05058161914348602,
-0.006425058469176292,
0.02305646426975727,
0.02629910036921501,
0.011423342861235142,
-0.04867390915751457,
0.02367144264280796,
-0.033362243324518204,
-0.022216934710741043,
0.022548265755176544,
0.009523773565888405,
-0.01734466664493084,
-0.02738061361014843,
0.02443069778382778,
0.014012176543474197,
-0.021692020818591118,
-0.0008183970930986106,
0.007435852196067572,
0.06907951086759567,
-0.012899907305836678,
-0.08853161334991455,
-0.053213320672512054,
0.021655432879924774,
0.01890946552157402,
-0.03605896607041359,
-0.07268664985895157,
-0.0038326906505972147,
-0.0019091753056272864,
0.04649227112531662,
-0.00004952436574967578,
0.03302031382918358,
0.04612840712070465,
0.02963813580572605,
0.011280636303126812,
0.02247030660510063,
-0.04162199795246124,
-0.016189439222216606,
-0.061031997203826904,
0.01041143573820591,
-0.05963430553674698,
0.011618424206972122,
0.019018420949578285,
-0.016648156568408012,
-0.0048774066381156445,
0.0248578991740942,
-0.01305051613599062,
-0.04118501394987106,
0.025471823289990425,
-0.014932646416127682,
-0.00013366957136895508,
0.07972581684589386,
0.020894715562462807,
-0.009597929194569588,
0.030692555010318756,
0.025050802156329155,
0.03244074434041977,
-0.01244912575930357,
0.005203345324844122,
0.04528840631246567,
-0.045406196266412735,
-0.029137644916772842,
-0.042877551168203354,
0.016213010996580124,
-0.029765266925096512,
-0.041136935353279114,
-0.04032503813505173,
-0.004735833499580622,
0.021260682493448257,
0.006040578708052635,
0.009558762423694134,
0.01972157135605812,
0.009040254168212414,
0.016149774193763733,
0.00018588262901175767,
-0.018191102892160416,
-0.04572170600295067,
0.023368149995803833,
-0.030991656705737114,
-0.01093336846679449,
-0.004418894182890654,
-0.0058471327647566795,
0.021960096433758736,
-0.043279170989990234,
-0.032649558037519455,
0.020391017198562622,
0.009468590840697289,
-0.006309391465038061,
-0.0463230237364769,
-0.0293290913105011,
0.05597970262169838,
0.02362622134387493,
-0.011461962945759296,
0.015321648679673672,
-0.045533012598752975,
-0.007792999502271414,
0.017008796334266663,
-0.0005350100109353662,
-0.004065447952598333,
-0.012071222998201847,
-0.019361311569809914,
0.058773186057806015,
-0.012882884591817856,
0.027892371639609337,
0.022484229877591133,
-0.04888373613357544,
0.09094246476888657,
0.0442470982670784,
0.021498894318938255,
0.012541215866804123,
0.005845687352120876,
-0.014185996726155281,
-0.017271555960178375,
-0.01837707869708538,
-0.0354323647916317,
-0.0460270419716835,
0.013399736024439335,
-0.004007597919553518,
-0.028960049152374268,
-0.019956933334469795,
-0.02717059664428234,
0.039510101079940796,
0.029973439872264862,
0.02771792933344841,
0.04154368117451668,
0.015313846059143543,
-0.0665757954120636,
-0.018188336864113808,
-0.004258554894477129,
0.02357952669262886,
-0.018010372295975685,
0.005648485384881496,
-0.017417212948203087,
-0.013263942673802376,
-0.050575606524944305,
-0.0352095328271389,
0.03331710770726204,
-0.015091833658516407,
0.06442412734031677,
0.04378652200102806,
-0.04377256706357002,
0.015390828251838684,
-0.04186297580599785,
0.0008066223235800862,
0.022635726258158684,
0.01668155938386917,
-0.020681994035840034,
-0.023648671805858612,
0.03296470642089844,
-0.03492870554327965,
0.041369810700416565,
-0.02542032301425934,
0.03043157421052456,
0.04641973227262497,
-0.007562838029116392,
0.015556109137833118,
-0.0045050824992358685,
0.011971181258559227,
-0.008752564899623394,
0.008616897277534008,
0.028891118243336678,
-0.007965671829879284,
0.0383177176117897,
-0.05692237615585327,
-0.00591264758259058,
-0.02931799739599228,
-0.051095593720674515,
-0.04062891751527786,
-0.011801349930465221,
-0.03352353349328041,
0.05688846483826637,
-0.05177329108119011,
-0.04228292405605316,
0.030221780762076378,
-0.018709348514676094,
0.006164023652672768,
0.04673420637845993,
-0.008660689927637577,
-0.040565360337495804,
-0.0234803669154644,
-0.05373156815767288,
0.0034796863328665495,
-0.04726484790444374,
0.021104058250784874,
0.0554744116961956,
0.004445079248398542,
-0.04936826974153519,
0.016625231131911278,
-0.03115670755505562,
-0.029984768480062485,
-0.028898296877741814,
-0.05607117712497711,
0.015768010169267654,
-0.009794971905648708,
0.0016136921476572752,
0.034214284271001816,
-0.06298407167196274,
-0.016101520508527756,
-0.00021985729108564556,
-0.06580428034067154,
0.024973195046186447,
-0.0023091856855899096,
0.05701445788145065,
-0.03151754289865494,
-0.01695941388607025,
0.0251200869679451,
-0.014165143482387066,
-0.04239194840192795,
-0.04662645608186722,
-0.003138821804895997,
-0.01125330850481987,
-0.026675982400774956,
-0.002736010355874896,
0.05120233818888664,
-0.027668487280607224,
0.02163158357143402,
0.021439993754029274,
0.029200255870819092,
0.015417613089084625,
0.01049108523875475,
-0.035049956291913986,
-0.013017446734011173,
0.027761690318584442,
0.007506867870688438,
0.009390406310558319,
0.01731501705944538,
-0.04648048058152199,
0.038085710257291794,
0.005836655851453543,
0.05805087834596634,
0.0261040348559618,
-0.04257900267839432,
0.06872457265853882,
-0.005196759011596441,
0.0031978734768927097,
-0.03362179920077324,
0.015772277489304543,
-0.0046434830874204636,
0.027907298877835274,
-0.03340277820825577,
0.01636216603219509,
0.04068882763385773,
0.0003062471514567733,
0.017155716195702553,
0.01107739843428135,
0.020915422588586807,
-0.04128851741552353,
-0.043078359216451645,
-0.014530915766954422,
-0.014123192057013512,
0.018037205561995506,
-0.014677775092422962,
-0.026617970317602158,
0.05278278887271881,
0.025330422446131706,
0.03035244531929493,
0.03288452699780464,
-0.033522896468639374,
0.012726341374218464,
-0.057811297476291656,
-0.052714135497808456,
0.0183856263756752,
0.03693700581789017,
0.006689024157822132,
0.059426091611385345,
0.02140727825462818,
0.020053524523973465,
0.019314033910632133,
-0.02966342493891716,
-0.08409538120031357,
0.009840733371675014,
-0.027289068326354027,
-0.04594472423195839,
0.006251128390431404,
-0.06363046914339066,
0.018324103206396103,
-0.031024517491459846,
-0.0014552709180861712,
0.006407030858099461,
-0.013259503990411758,
-0.053157124668359756,
-0.002816787688061595,
-0.020605526864528656,
-0.06437406688928604,
0.01287833321839571,
0.07765909284353256,
0.03176893666386604,
-0.006726754363626242,
0.03332303464412689,
0.03586156293749809,
0.006354940589517355,
-0.03305608406662941,
-0.0012482660822570324,
0.014150510542094707,
0.014378998428583145,
0.052359480410814285,
0.0011471320176497102,
-0.009896654635667801,
-0.03319200500845909,
0.022453809157013893,
-0.016922935843467712,
0.017041277140378952,
-0.007713140919804573,
-0.023487115278840065,
-0.023510444909334183,
-0.044843561947345734,
-0.01461769174784422,
-0.04276463761925697,
0.03380083292722702,
-0.013067499734461308,
-0.02479221671819687,
0.030829062685370445,
0.03738422691822052,
0.002157714683562517,
0.021983768790960312,
0.017868751659989357,
0.04221690446138382,
0.01655193418264389,
-0.03859167918562889,
-0.03346295282244682,
-0.01815398782491684,
-0.003288698848336935,
-0.0051973783411085606,
-0.01778559200465679,
-0.020506959408521652,
0.020498977974057198,
0.0329909510910511,
0.0186543557792902,
-0.007982666604220867,
0.009200521744787693,
-0.060767870396375656,
-0.023127593100070953,
-0.0017693343106657267,
0.006364589091390371,
-0.010806100443005562,
0.007199772167950869,
0.023086678236722946,
0.04834497347474098,
-0.037150800228118896,
-0.08212745934724808,
0.02533571422100067,
0.0007561785168945789,
0.03460150212049484,
-0.03743480145931244,
-0.024011246860027313,
-0.014189501293003559,
-0.0007757509592920542,
0.04611998423933983,
-0.005881317891180515,
0.01958649605512619,
0.006476519163697958,
0.03714815154671669,
-0.02258491702377796,
-0.05589020997285843,
-0.0032481488306075335,
0.020916910842061043,
-0.0026619008276611567,
0.030298037454485893,
0.0012150800321251154,
0.006519616115838289,
-0.029181668534874916,
-0.010215065442025661,
0.04668949171900749,
0.04028754308819771,
-0.0007569866720587015,
0.020194116979837418,
-0.05184498801827431,
0.04568183794617653,
-0.037679772824048996,
-0.06337431818246841,
0.018297355622053146,
-0.011879605241119862,
0.00872846506536007,
0.019110115244984627,
-0.0056277671828866005,
0.012608400546014309,
0.025458255782723427,
-0.018440674990415573,
-0.025722038000822067,
0.033888764679431915,
-0.0112887192517519,
0.06249745190143585,
0.022164426743984222,
0.012788474559783936,
0.029571499675512314,
0.0009029792854562402,
0.007444256916642189,
-0.020785421133041382,
-0.007480153348296881,
0.046622149646282196,
-0.04641975834965706,
-0.010142331942915916,
-0.03607536107301712,
-0.008823469281196594,
-0.02719433419406414,
0.021416274830698967,
0.015927251428365707,
0.05657042935490608,
-0.03306838124990463,
-0.04469175636768341,
0.0115298330783844,
0.006695745047181845,
0.011731795035302639,
0.007871687412261963,
-0.03209242597222328,
0.009755813516676426,
0.02095058746635914,
-0.06634636968374252,
0.01130801159888506,
0.023625873029232025,
-0.036896660923957825,
0.04511340335011482,
-0.016146710142493248,
-0.004479783121496439,
-0.007135720457881689,
-0.02676190435886383,
0.011880040168762207,
-0.043614309281110764,
0.03720324859023094,
-0.03372151404619217,
-0.020796820521354675,
0.031203189864754677,
-0.019492018967866898,
-0.0037333820946514606,
0.03015955165028572,
-0.011424366384744644,
0.03428684175014496,
-0.04185069352388382,
0.03157294541597366,
0.0047831907868385315,
0.009359708055853844,
-0.045727964490652084,
-0.045299723744392395,
0.0391838364303112,
-0.01430952362716198,
-0.02413717284798622,
-0.026955028995871544,
-0.02925824373960495,
-0.03921588137745857,
-0.08011190593242645,
-0.0005691915284842253,
0.05578949674963951,
-0.004197616130113602,
-0.022912027314305305,
0.02131563425064087,
-0.013594158925116062,
0.046027570962905884,
0.02141382358968258,
-0.017911585047841072,
-0.004922407679259777,
-0.038099318742752075,
0.0025149481371045113,
-0.00821906328201294,
0.05215757340192795,
-0.013133591040968895,
0.0016653808997943997,
0.0067497966811060905,
-0.04343930259346962,
0.041453443467617035,
0.01528532151132822,
0.03254816308617592,
0.03656081482768059,
0.008685833774507046,
0.001964436611160636,
-0.010385608300566673,
0.060783736407756805,
-0.001077163266018033,
0.004865975584834814,
-0.013615387491881847,
0.004339192528277636,
-0.03485962748527527,
-0.02100382000207901,
0.012302779592573643,
0.011328676715493202,
0.022126508876681328,
0.0017234808765351772,
0.0744701698422432,
-0.008091654628515244,
-0.024106455966830254,
-0.007412169594317675,
-0.03530645743012428,
0.03676876053214073,
-0.040654733777046204,
-0.0034140674397349358,
-0.006848224904388189,
0.003918429370969534,
-0.029604794457554817,
-0.029142888262867928,
-0.003586813108995557,
0.009620306082069874,
0.007205934729427099,
-0.06333983689546585,
0.02521493472158909,
0.0018853956134989858,
0.01048709824681282,
-0.011292705312371254,
-0.016602277755737305,
-0.0005442776018753648,
0.03205246478319168,
0.02440783567726612,
0.03634842112660408,
-0.026614394038915634,
-0.014264479279518127,
0.0369705930352211,
0.05634516105055809,
0.00246130651794374,
-0.01234915666282177,
0.024439165368676186,
0.006434950511902571,
0.06471909582614899,
0.009882168844342232,
-0.012599551118910313,
0.03735513985157013,
-0.02999386563897133,
0.00815256405621767,
-0.03507712110877037,
0.00423230417072773,
0.07962778210639954,
-0.005508742295205593,
-0.011301294900476933,
-0.02426624484360218,
0.007150765974074602,
-0.004473624750971794,
0.01838637702167034,
0.00044472384615801275,
0.01753978803753853,
0.01674816571176052,
0.0023892654571682215,
0.0242376197129488,
0.001706754439510405,
0.011490830220282078,
-0.022470470517873764,
-0.025421978905797005,
-0.025343725457787514,
-0.046389393508434296,
-0.012386351823806763,
0.013757411390542984,
0.013996357098221779,
0.0036679988261312246,
0.018997101113200188,
-0.04743945226073265,
-0.01020297035574913,
0.013456097804009914,
0.0611141212284565,
0.012776165269315243,
0.06158292293548584,
0.01437326055020094,
0.03971034660935402,
-0.028851225972175598,
0.002707910491153598,
0.12012360990047455,
0.025004930794239044,
0.028842195868492126,
0.0034788076300174,
0.0011039207456633449,
-0.017317986115813255,
0.018836963921785355,
-0.004984813742339611,
0.04743034765124321,
0.00832618772983551,
0.0043095313012599945,
0.05807254835963249,
0.08927126973867416,
0.007843849249184132,
-0.036181338131427765,
0.03310081735253334,
-0.012347894720733166,
-0.0026272942777723074,
-0.018077772110700607,
0.03254463151097298,
-0.007300382014364004,
0.00040282748523168266,
0.019169477745890617,
-0.017478492110967636,
-0.02853434905409813,
0.015488515608012676,
0.00212147762067616,
-0.04079649597406387,
-0.0015161515912041068,
0.01862403191626072,
-0.07306596636772156,
0.03598596528172493,
0.04608452692627907,
-0.02619558945298195,
-0.045573800802230835,
0.01883789338171482,
0.05142495036125183,
-0.004208127502351999,
-0.016869451850652695,
0.03310732543468475,
0.019962243735790253,
0.02993597835302353,
-0.023620616644620895,
0.010854600928723812,
-0.0448630265891552,
0.020264074206352234,
-0.0420033223927021,
0.034968916326761246,
-0.0036194303538650274,
0.013800738379359245,
-0.028575673699378967,
0.012972169555723667,
0.017591698095202446,
-0.05145929008722305,
-0.01668439991772175,
-0.016030203551054,
0.02278352901339531,
0.022301357239484787,
-0.01627325266599655,
-0.026061395183205605,
0.010678796097636223,
-0.008396788500249386,
0.001635352848097682,
0.03346753492951393,
-0.021681681275367737,
-0.026141924783587456,
-0.008840402588248253,
0.10581416636705399,
-0.04012792184948921,
-0.01502369437366724,
-0.032245904207229614,
-0.00930296815931797,
-0.06346698105335236,
-0.013807935640215874,
-0.022635480388998985,
0.06793583929538727,
0.059868644922971725,
-0.008364053443074226,
-0.003349681617692113,
-0.009275650605559349,
-0.024315282702445984,
0.07495090365409851,
0.009169493801891804,
-0.028071429580450058,
-0.04502703249454498,
-0.0027246512472629547,
0.042723678052425385,
0.04533578082919121,
-0.062347471714019775,
0.0007528652204200625,
-0.01388308685272932,
0.06015952676534653,
-0.012151682749390602,
0.0007089254213497043,
-0.017540279775857925,
0.019512087106704712,
-0.04319976270198822,
0.026736173778772354,
0.013953005895018578,
0.011997977271676064,
0.02870367467403412,
-0.00028054844005964696,
0.011330226436257362,
0.04393298551440239,
0.0052233487367630005,
0.0128462640568614,
0.01989690586924553,
-0.054747145622968674,
-0.036288514733314514,
0.036545928567647934,
0.020242948085069656,
-0.02039090171456337,
0.005796436220407486,
-0.021907906979322433,
0.013676051050424576,
-0.026065826416015625,
0.03466102480888367,
-0.005061499308794737,
0.010151424445211887,
-0.023549512028694153,
0.0492638498544693,
-0.041837047785520554,
-0.014652589336037636,
-0.06624330580234528,
0.00321462145075202,
0.008073030039668083,
-0.05240798369050026,
-0.04868871346116066,
0.020511094480752945,
-0.026588665321469307,
0.024166027083992958,
0.030614955350756645,
0.0013916586758568883,
-0.05529193952679634,
-0.008498904295265675,
0.029641641303896904,
-0.006763771641999483,
0.0515022911131382,
-0.03224451467394829,
-0.023890884593129158,
0.036204684525728226,
-0.04289065673947334,
-0.04716067016124725,
0.02763136476278305,
-0.005146539304405451,
0.023313261568546295,
-0.003644351614639163,
0.0076530566439032555,
-0.01615278609097004,
0.12054119259119034,
-0.007784842047840357,
-0.012101894244551659,
-0.003672943916171789,
-0.01087178010493517,
-0.00868843775242567,
-0.005006263963878155,
0.03842403367161751,
-0.0381971150636673,
-0.010507272556424141,
0.008161814883351326,
0.057080820202827454,
-0.04514969140291214,
0.04740850254893303,
-0.02643294259905815,
-0.0006924931076355278,
-0.0014020957751199603,
0.004346886649727821,
0.019037535414099693,
0.041569240391254425,
0.04032110050320625,
-0.013543793931603432,
0.028094854205846786,
0.011242084205150604,
-0.002748096827417612,
-0.04738897830247879,
0.005487232003360987,
0.022802205756306648,
0.006006916053593159,
0.04473629966378212,
-0.045291949063539505,
0.023629721254110336,
0.040014058351516724,
-0.09904498606920242,
-0.005298309959471226,
-0.016963530331850052,
-0.03192455694079399,
-0.07243421673774719,
-0.0100637162104249,
-0.003941080067306757,
0.030791576951742172,
0.017914732918143272,
0.02441648580133915,
-0.012679137289524078,
0.021380500867962837,
-0.025458622723817825,
-0.0032634371891617775,
-0.026118025183677673,
0.021522078663110733,
-0.02313724346458912,
0.043005432933568954,
0.046772558242082596,
-0.02816264145076275,
-0.01459340937435627,
0.000798277382273227,
-0.012889186851680279,
0.023127863183617592,
-0.01280299387872219,
-0.008021864108741283,
0.03646935895085335,
-0.022605184465646744,
-0.013447907753288746,
-0.0005897572846151888,
0.009215605445206165,
0.033776864409446716,
0.0013411660911515355,
0.021830596029758453,
-0.006716675125062466,
-0.02037782594561577,
0.020446045324206352,
-0.03489771485328674,
-0.051762767136096954,
-0.003221402643248439,
0.0045368606224656105,
0.0222096536308527,
-0.016915330663323402,
0.01911320351064205,
0.02474375255405903,
-0.018682993948459625,
-0.013347238302230835,
-0.018445180729031563,
-0.03706672042608261,
0.03581617400050163,
-0.023351818323135376,
0.006616896018385887,
0.03089756891131401,
-0.017721403390169144,
0.004120032303035259,
-0.009299371391534805,
-0.00775382062420249,
-0.010341687127947807,
-0.060769300907850266,
-0.011130089871585369,
0.000638772442471236,
0.0024537306744605303,
-0.009295188821852207,
-0.07298898696899414,
0.006663628853857517,
0.03148345276713371,
0.03463566303253174,
0.021574251353740692,
0.016443489119410515,
-0.026918992400169373,
-0.016080083325505257,
-0.0402175635099411,
0.044913746416568756,
-0.05142936855554581,
-0.023048069328069687,
-0.06711289286613464,
-0.04691705480217934,
-0.010307330638170242,
0.016489677131175995,
0.06150888651609421,
-0.008056813850998878,
0.021353023126721382,
0.02343694306910038,
-0.004143726080656052,
0.018604034557938576,
-0.03448546305298805,
-0.0301410760730505,
-0.020902356132864952,
-0.006747380364686251,
0.01294016558676958,
0.02173120342195034,
-0.021445928141474724,
-0.01732436940073967,
0.0134006692096591,
-0.033563870936632156,
0.018630992621183395,
-0.007876463234424591,
-0.025348355993628502,
0.010169741697609425,
0.025953052565455437,
-0.01690257340669632,
0.05942700430750847,
0.011406982317566872,
0.03914700448513031,
0.032387763261795044,
-0.030144277960062027,
-0.05704892799258232,
-0.008225012570619583,
-0.03956548497080803,
0.000978477648459375,
-0.03452964499592781,
-0.027881167829036713,
0.03643258661031723,
-0.026809971779584885,
0.028347602114081383,
0.025246020406484604,
-0.030016331002116203,
-0.019097203388810158,
0.05423995852470398,
0.05375165492296219,
0.03711913898587227,
-0.04373380169272423,
0.04296436905860901,
0.01918998546898365,
-0.047807469964027405,
-0.02669859491288662,
0.0327535979449749,
0.0063571445643901825,
0.03153345733880997,
0.01948820985853672,
0.05092884972691536,
0.0091496417298913,
0.02666334994137287,
0.03726893663406372,
0.050040993839502335,
-0.008766280487179756,
-0.024853862822055817,
-0.0041335285641252995,
-0.022405264899134636,
0.024516182020306587,
0.04332808405160904,
-0.021929603070020676,
0.0433182530105114,
-0.011171210557222366,
0.016513710841536522,
0.0004405435756780207,
0.01781938038766384,
-0.02236190252006054,
0.020810648798942566,
-0.005160030443221331,
0.020143022760748863,
0.004043572582304478,
-0.02485806867480278,
0.010000676847994328,
-0.0140901580452919,
0.0302459504455328,
-0.024345092475414276,
0.007088273297995329,
-0.008425530977547169,
-0.0024294310715049505,
-0.04037041217088699,
-0.012874587439000607,
-0.03271865472197533,
0.0005182932363823056,
0.032537855207920074,
0.059294041246175766,
-0.011967496946454048,
-0.028726676478981972,
0.004584174603223801,
-0.022493096068501472,
0.056181151419878006,
-0.06728159636259079,
-0.046698667109012604,
-0.031110916286706924,
0.04329243302345276,
-0.005857924930751324,
0.004580494482070208
] |
<p>Let's say there is a fin that is 1mm thick, extends 8mm from the surface, and is 10 mm wide. The fin is exposed to a moving fluid. Can we assume the adiabatic tip condition and use the characteristic, "Corrected", length for calculations?</p> | 2,855 | [
0.016705172136425972,
-0.04041942581534386,
-0.00043204016401432455,
-0.002658811630681157,
0.06412947922945023,
0.006282752845436335,
-0.0560910701751709,
-0.00641500623896718,
-0.023913701996207237,
-0.021268706768751144,
0.024115998297929764,
0.06182686239480972,
0.04264451935887337,
0.02621871419250965,
0.014046095311641693,
0.01751944236457348,
0.00221672048792243,
-0.010324005037546158,
0.005107628647238016,
-0.051390476524829865,
-0.015943016856908798,
0.02910708636045456,
0.04299573600292206,
-0.04187346249818802,
-0.04846028611063957,
-0.0030636463779956102,
0.01590966247022152,
-0.026615675538778305,
-0.012965509667992592,
0.0022436114959418774,
-0.011442017741501331,
-0.043615277856588364,
0.04219677671790123,
0.02826640196144581,
-0.004766140133142471,
0.0007188101881183684,
-0.034330930560827255,
-0.03391343727707863,
-0.03130645677447319,
0.022579655051231384,
-0.023601237684488297,
-0.01077758427709341,
0.01475522480905056,
0.03780492767691612,
-0.003698828862980008,
-0.009374652057886124,
-0.029086461290717125,
-0.04893980175256729,
0.04702633619308472,
-0.04722622036933899,
0.04814040660858154,
0.017211100086569786,
0.019434750080108643,
0.038825344294309616,
-0.02613822929561138,
0.0005190986557863653,
0.05872068926692009,
0.03703003004193306,
-0.056542910635471344,
-0.008605842478573322,
-0.0023503797128796577,
0.01839364320039749,
0.010513072833418846,
-0.0076364874839782715,
-0.005591204855591059,
0.01376374065876007,
-0.0173273254185915,
-0.004761763848364353,
0.011621779762208462,
-0.014602850191295147,
0.005772601347416639,
-0.012290799990296364,
0.031130565330386162,
0.020829791203141212,
0.022519776597619057,
-0.04718096926808357,
0.001979757798835635,
0.05106286332011223,
0.06791277974843979,
0.04301922395825386,
-0.023787416517734528,
0.036842506378889084,
0.02664295770227909,
0.045913565903902054,
0.005015921778976917,
-0.01019799429923296,
0.04796319827437401,
-0.023706866428256035,
0.032983362674713135,
0.0493541918694973,
-0.037356846034526825,
-0.013000069186091423,
0.043838463723659515,
-0.021396229043602943,
0.015352186746895313,
-0.009578093886375427,
0.003026397665962577,
0.011410175822675228,
-0.017463410273194313,
-0.018442803993821144,
-0.010174757800996304,
-0.020567286759614944,
0.005996404215693474,
0.05225088447332382,
-0.008381226100027561,
-0.010788713581860065,
-0.023148568347096443,
0.038364969193935394,
-0.020598461851477623,
0.009905412793159485,
-0.0646824911236763,
0.005245351232588291,
-0.023051735013723373,
0.010793397203087807,
0.008188815787434578,
-0.0007928565028123558,
0.018857114017009735,
-0.011502993293106556,
0.027693698182702065,
0.04286561906337738,
-0.007299158722162247,
-0.01561371423304081,
0.005476187448948622,
0.03828384354710579,
-0.0510103702545166,
0.036050815135240555,
0.007493928540498018,
-0.021632153540849686,
-0.02478330209851265,
0.021476058289408684,
-0.0013954826863482594,
0.0012577897869050503,
0.016102755442261696,
-0.011798425577580929,
0.015604211017489433,
-0.0015498213469982147,
-0.06277023255825043,
-0.06321614235639572,
0.04202768951654434,
0.01838148944079876,
-0.07256783545017242,
-0.09487780183553696,
0.007251071278005838,
0.07652297616004944,
0.10098622739315033,
0.004942979663610458,
0.029955502599477768,
-0.029556769877672195,
-0.008278013207018375,
-0.047886550426483154,
-0.022901106625795364,
-0.060181740671396255,
0.011078599840402603,
-0.00886603444814682,
-0.03404970094561577,
-0.054330021142959595,
0.026380185037851334,
0.05314391478896141,
-0.0009228638955391943,
-0.017975369468331337,
0.04202741011977196,
0.006583075970411301,
-0.005202192347496748,
0.015107370913028717,
0.0019452793058007956,
-0.03287740796804428,
0.09089098125696182,
0.01799514703452587,
-0.012948188930749893,
0.0029067446012049913,
0.010682969354093075,
0.02849501557648182,
-0.03314604610204697,
-0.025993984192609787,
0.049093928188085556,
-0.011086046695709229,
0.01210753433406353,
-0.030942711979150772,
0.015392811968922615,
0.06591945141553879,
-0.02224513702094555,
-0.05821043625473976,
-0.03360123932361603,
-0.04801454767584801,
0.010042672976851463,
0.026039838790893555,
0.020445385947823524,
0.01855398155748844,
0.028302954509854317,
-0.05534890666604042,
-0.01226990669965744,
-0.04206135869026184,
0.010213869623839855,
0.0035849104169756174,
0.014630037359893322,
0.0053198193199932575,
-0.0052768210880458355,
0.010218326933681965,
-0.050973232835531235,
-0.05434444174170494,
-0.005204671993851662,
-0.006260125897824764,
0.016390949487686157,
-0.01701611466705799,
0.03737501800060272,
0.028799250721931458,
0.03355948254466057,
0.013551163487136364,
-0.004989773966372013,
-0.013479388318955898,
-0.04932701215147972,
-0.01566658914089203,
-0.042815618216991425,
0.02401452139019966,
0.012603471986949444,
-0.021025564521551132,
0.018888330087065697,
0.013123111799359322,
0.0010230977786704898,
0.05126136913895607,
0.008140427060425282,
0.09990616142749786,
0.06358274817466736,
-0.013084981590509415,
0.008098814636468887,
0.03253473341464996,
0.019330667331814766,
-0.006510381121188402,
-0.000337081088218838,
-0.04044371843338013,
-0.04195569455623627,
-0.01802220195531845,
0.05733499675989151,
0.011077338829636574,
-0.05830039083957672,
-0.024638233706355095,
0.06683753430843353,
-0.004270222503691912,
0.05960182473063469,
0.007498917169868946,
-0.003110229503363371,
-0.013991904444992542,
0.027257487177848816,
0.03975421190261841,
-0.0013402431504800916,
-0.013231057673692703,
0.04484272748231888,
0.026162568479776382,
-0.0024794740602374077,
-0.030466768890619278,
0.028481675311923027,
-0.008045644499361515,
0.014853174798190594,
0.0008576425025239587,
-0.03166019544005394,
-0.02169201336801052,
0.03329326584935188,
-0.043070901185274124,
0.01919044554233551,
0.009139468893408775,
-0.0010448824614286423,
0.013971722684800625,
-0.024641340598464012,
0.051715221256017685,
0.010123246349394321,
-0.04694540053606033,
0.002468463033437729,
-0.059090036898851395,
0.042818233370780945,
-0.006030483637005091,
0.0009395439410582185,
-0.05204687640070915,
-0.004016156308352947,
0.009434647858142853,
0.012799983844161034,
0.06748835742473602,
0.013816905207931995,
0.01593419723212719,
-0.015626264736056328,
-0.02266612835228443,
0.004414583556354046,
0.01642104983329773,
0.01393502950668335,
0.01582675613462925,
-0.0817098319530487,
0.01918117143213749,
-0.029844991862773895,
-0.02604995295405388,
0.060164060443639755,
-0.0032143129501491785,
0.00969533808529377,
-0.005348297767341137,
0.021911295130848885,
-0.025117890909314156,
-0.02641165815293789,
-0.0050797234289348125,
-0.03286224976181984,
-0.04282413795590401,
0.0060135130770504475,
0.04955711588263512,
0.008994285017251968,
-0.04108404740691185,
0.03196136653423309,
-0.03563523665070534,
-0.024873539805412292,
0.009034231305122375,
-0.01539304107427597,
0.047947537153959274,
0.0017024630215018988,
0.05376458540558815,
0.04649072512984276,
-0.05921974033117294,
-0.014204682782292366,
-0.0271407850086689,
-0.06985241174697876,
0.05301836133003235,
0.006632520351558924,
0.07738113403320312,
0.007968293502926826,
0.001232223934493959,
0.045823805034160614,
-0.0066807870753109455,
-0.022267984226346016,
0.006463727913796902,
0.009693785570561886,
-0.0014878679066896439,
-0.010822220705449581,
-0.015912240371108055,
0.019309332594275475,
-0.024904821068048477,
-0.011293040588498116,
0.014842746779322624,
0.022043287754058838,
0.0405527763068676,
0.018951738253235817,
0.02352510765194893,
-0.002714411122724414,
0.003516086144372821,
0.028504284098744392,
0.022291608154773712,
-0.008202479220926762,
-0.010030124336481094,
0.01624472066760063,
-0.023396579548716545,
0.054002661257982254,
0.043051961809396744,
-0.03314213827252388,
0.080199234187603,
-0.02426479384303093,
0.029492605477571487,
-0.0016165090491995215,
0.039626479148864746,
-0.025895394384860992,
-0.008476299233734608,
-0.03721027076244354,
0.03642917424440384,
0.01828904077410698,
-0.022537002339959145,
0.012384808622300625,
0.07306690514087677,
0.027999434620141983,
0.0008005618583410978,
-0.03605944290757179,
-0.005456062033772469,
-0.035132765769958496,
0.046237021684646606,
-0.062461428344249725,
-0.04411837458610535,
0.06068940460681915,
0.049080658704042435,
0.03995053842663765,
-0.012524530291557312,
0.02991502918303013,
-0.018659576773643494,
-0.05040678754448891,
-0.00425448315218091,
-0.007148095406591892,
0.05003610625863075,
0.005313070025295019,
0.02498188056051731,
0.032863181084394455,
0.06457780301570892,
0.017290128394961357,
0.03505347669124603,
-0.07930663228034973,
-0.012808801606297493,
-0.022753598168492317,
-0.0536983497440815,
-0.02211594581604004,
-0.0014487085863947868,
-0.0034238065127283335,
-0.050378840416669846,
-0.013217715546488762,
0.011863567866384983,
0.02504790760576725,
-0.0503992922604084,
0.022162003442645073,
-0.021143855527043343,
-0.034996870905160904,
0.0025025762151926756,
0.0055142599157989025,
0.04787160083651543,
-0.04093366116285324,
0.004871552810072899,
0.05043950304389,
0.008568935096263885,
-0.032504089176654816,
-0.01540636271238327,
0.03854891657829285,
-0.03240140154957771,
0.05045226216316223,
0.038862552493810654,
-0.011506247334182262,
-0.05004897713661194,
0.049955401569604874,
0.021962061524391174,
0.033810898661613464,
0.006246647797524929,
0.000560999964363873,
-0.024631060659885406,
-0.05705735459923744,
0.026290254667401314,
0.012796089984476566,
0.06736812740564346,
-0.013043861836194992,
-0.024421479552984238,
-0.003977836575359106,
-0.021877627819776535,
-0.03594370558857918,
0.010060161352157593,
0.052653539925813675,
0.04249877110123634,
0.017087871208786964,
-0.06696576625108719,
0.0219765342772007,
-0.012581614777445793,
-0.012157044373452663,
0.023042846471071243,
0.01861625164747238,
-0.005993610713630915,
0.029267974197864532,
0.019451376050710678,
0.01754072681069374,
0.01007118634879589,
0.03560933470726013,
0.002574054291471839,
-0.00957019254565239,
0.02408757247030735,
0.03308406472206116,
0.015039738267660141,
0.028468474745750427,
0.04197591543197632,
-0.0009499813313595951,
-0.019479557871818542,
-0.09455617517232895,
0.025669921189546585,
0.04468302056193352,
0.03295877203345299,
-0.01912749744951725,
0.03690531104803085,
-0.07130656391382217,
-0.003862270386889577,
0.07705017179250717,
0.0324990339577198,
0.03686826676130295,
-0.022981693968176842,
-0.004154361318796873,
0.0049705603159964085,
-0.017466837540268898,
-0.008081497624516487,
0.024098295718431473,
-0.011606316082179546,
-0.0007432958809658885,
-0.024929476901888847,
-0.04249780252575874,
0.021561268717050552,
-0.021455369889736176,
0.04115772619843483,
0.05572711303830147,
0.010117018595337868,
-0.03513774275779724,
-0.0022866239305585623,
-0.016551055014133453,
-0.061341166496276855,
-0.05691599100828171,
0.0013458254979923368,
0.0018866899190470576,
-0.00024351992760784924,
0.012869364582002163,
-0.048760801553726196,
-0.04010694473981857,
0.06431369483470917,
0.024640092626214027,
-0.019909704104065895,
-0.0066991206258535385,
-0.01907019130885601,
0.07306185364723206,
0.02598656341433525,
0.022036802023649216,
0.04637187719345093,
0.07572868466377258,
-0.013185903429985046,
-0.06793814152479172,
0.0002663866907823831,
0.0011992803774774075,
0.01256292313337326,
-0.023192256689071655,
-0.016028838232159615,
-0.012666955590248108,
-0.002396903932094574,
0.03542429581284523,
-0.04147648438811302,
0.027472902089357376,
-0.007034684531390667,
-0.027200894430279732,
0.014160067774355412,
0.016468068584799767,
0.00734985014423728,
-0.03356689587235451,
0.008048688992857933,
0.01660199835896492,
0.011583114974200726,
-0.004910898860543966,
-0.0016019829781726003,
-0.004313300363719463,
-0.009173384867608547,
0.04676033556461334,
0.0017262593610212207,
0.0084677217528224,
-0.0115132424980402,
0.009839393198490143,
-0.0017404707614332438,
-0.0070665073581039906,
0.07006215304136276,
-0.02140936255455017,
-0.00554663548246026,
-0.008251669816672802,
-0.02676987834274769,
0.020842688158154488,
0.019530782476067543,
-0.011827853508293629,
0.03569949045777321,
-0.0675094872713089,
0.028417769819498062,
0.024636248126626015,
0.009741938672959805,
-0.049102894961833954,
-0.0023285828065127134,
0.02487049624323845,
0.06407156586647034,
0.010879289358854294,
-0.05895625799894333,
-0.014915398322045803,
-0.0331139974296093,
-0.04067160189151764,
0.03235175833106041,
-0.005347783211618662,
-0.00242303847335279,
-0.040116842836141586,
-0.0023806747049093246,
-0.006959458347409964,
0.044253021478652954,
-0.03156344220042229,
-0.023366330191493034,
0.02683432213962078,
-0.05469126254320145,
-0.0030682894866913557,
-0.017812125384807587,
0.037136998027563095,
-0.029995497316122055,
0.018265001475811005,
-0.006178395822644234,
-0.03830735757946968,
0.046346452087163925,
0.025417881086468697,
-0.01743127405643463,
0.02089286781847477,
-0.004576677922159433,
-0.006052722223103046,
-0.027516717091202736,
0.006971938535571098,
-0.0028542056679725647,
0.03344205021858215,
0.017740173265337944,
0.022678954526782036,
0.017545143142342567,
0.0007933240267448127,
0.008975530974566936,
0.0032134156208485365,
0.005298111587762833,
0.0016280836425721645,
0.042212024331092834,
-0.040707655251026154,
-0.01654035411775112,
0.026703082025051117,
0.019285669550299644,
0.022718753665685654,
-0.006524340249598026,
-0.002124302089214325,
-0.04023522511124611,
0.017782915383577347,
-0.003899978008121252,
-0.054479219019412994,
-0.026341082528233528,
-0.012738187797367573,
0.05553312972187996,
-0.0024977438151836395,
0.003974093124270439,
-0.01657215878367424,
-0.006684226915240288,
0.011885174550116062,
-0.004804837983101606,
-0.03146681562066078,
-0.009133361279964447,
-0.045078981667757034,
0.07464094460010529,
-0.03623855113983154,
-0.03513043373823166,
0.017217202112078667,
0.04066086560487747,
-0.029809433966875076,
0.026996633037924767,
0.0366269089281559,
0.0058120121248066425,
0.015463612042367458,
0.01911032944917679,
-0.05036436766386032,
0.03181862086057663,
-0.04384562000632286,
0.031016239896416664,
-0.022255320101976395,
0.01753106899559498,
0.03184108808636665,
0.03764021024107933,
0.020864048972725868,
-0.05177133530378342,
-0.0026204781606793404,
-0.012897517532110214,
0.025655219331383705,
-0.0023669919464737177,
0.04250752553343773,
-0.0011301733320578933,
0.007623323239386082,
0.05089088901877403,
-0.017564812675118446,
0.0272215586155653,
-0.001760418526828289,
-0.01876416616141796,
-0.025083892047405243,
-0.03695408254861832,
-0.02309837006032467,
0.04592881351709366,
0.019521186128258705,
-0.038380466401576996,
0.029298700392246246,
-0.0009420157875865698,
0.03291945904493332,
-0.026494178920984268,
0.03520422801375389,
-0.01958334818482399,
0.06664741039276123,
-0.013921011239290237,
0.01311176922172308,
-0.034097474068403244,
0.02262333780527115,
0.13496823608875275,
0.049378085881471634,
0.03000880777835846,
-0.03874491900205612,
0.016324790194630623,
-0.014358234591782093,
-0.015859749168157578,
-0.0384136401116848,
0.0009299914818257093,
-0.037168558686971664,
-0.016527125611901283,
-0.00673732440918684,
0.037772152572870255,
-0.048870477825403214,
0.005929641891270876,
0.01016723457723856,
-0.04750170558691025,
-0.02138805016875267,
0.02924816682934761,
-0.018775999546051025,
-0.0011419933289289474,
0.01425552275031805,
-0.03597201779484749,
-0.012614835985004902,
-0.022540362551808357,
0.009118282236158848,
-0.002112237038090825,
-0.021368369460105896,
0.035629451274871826,
0.04400163143873215,
-0.06224675476551056,
0.0017802603542804718,
0.0252405796200037,
-0.02221040613949299,
-0.029391691088676453,
-0.010102536529302597,
-0.0033405099529772997,
-0.025509843602776527,
0.0058725508861243725,
0.036284852772951126,
0.034192655235528946,
-0.012824416160583496,
-0.004449720028787851,
-0.01253093034029007,
-0.00808509811758995,
-0.005051797721534967,
-0.01427355408668518,
0.005837982054799795,
0.010182969272136688,
-0.04239649325609207,
0.005576769821345806,
-0.010506424121558666,
0.023698460310697556,
-0.04634995758533478,
-0.015737954527139664,
0.007462938781827688,
0.027951516211032867,
0.021316519007086754,
0.007958631031215191,
-0.006198648829013109,
0.03480486571788788,
0.006969095207750797,
-0.0055712624453008175,
0.046334173530340195,
0.02343425527215004,
0.015435567125678062,
-0.0020674970000982285,
0.030406404286623,
-0.0006034534890204668,
-0.044718582183122635,
-0.03314154967665672,
-0.026868341490626335,
-0.03639551252126694,
-0.02773984894156456,
0.013638940639793873,
0.02718500979244709,
0.01701418310403824,
-0.0036026649177074432,
0.01440858468413353,
-0.028235865756869316,
-0.04448122903704643,
0.043372925370931625,
0.004991971421986818,
-0.038344111293554306,
-0.02662358619272709,
0.02104034461081028,
0.020018253475427628,
0.06155328080058098,
-0.03849025443196297,
0.006779031828045845,
-0.027066439390182495,
0.06714678555727005,
0.025612829253077507,
0.008619136177003384,
-0.009247048757970333,
-0.029523367062211037,
-0.02198610082268715,
0.05158368870615959,
0.0034104844089597464,
0.020722152665257454,
0.04961315914988518,
0.005564502440392971,
-0.0003069647355005145,
0.012421759776771069,
-0.036195021122694016,
0.020204437896609306,
0.01657782308757305,
0.01118799764662981,
-0.04825877770781517,
-0.015558685176074505,
0.008317277766764164,
-0.05880362167954445,
-0.057030655443668365,
-0.035992853343486786,
-0.012829380109906197,
0.0012862709118053317,
0.017194358631968498,
-0.035907309502363205,
0.004699090961366892,
-0.012336076237261295,
-0.028637545183300972,
-0.056929800659418106,
0.021900780498981476,
-0.04197140410542488,
-0.0011741314083337784,
-0.017248643562197685,
0.016881177201867104,
-0.005631124135106802,
-0.006593053694814444,
-0.08513466268777847,
-0.008195842616260052,
0.00891156680881977,
-0.0007583089754916728,
0.03140086308121681,
-0.0066174669191241264,
0.015006173402071,
0.017526092007756233,
0.06339424103498459,
-0.05016256123781204,
0.014801215380430222,
0.014037582091987133,
-0.031363047659397125,
-0.012343033216893673,
0.022736931219697,
-0.012093239463865757,
0.036177169531583786,
-0.011973533779382706,
0.027942374348640442,
0.010106663219630718,
0.05934904143214226,
0.004337820690125227,
-0.021319666877388954,
-0.007296318653970957,
-0.01256607472896576,
-0.007027692627161741,
-0.04037744551897049,
0.027604911476373672,
-0.03798074275255203,
0.005549538414925337,
-0.006856723688542843,
0.016726208850741386,
0.008794957771897316,
-0.04013356193900108,
0.0119194146245718,
-0.013749553821980953,
-0.04041370376944542,
0.019032545387744904,
-0.006649359129369259,
0.03736356273293495,
0.07216911017894745,
0.011019222438335419,
0.011655864305794239,
-0.033980634063482285,
0.0029248676728457212,
-0.1198752149939537,
-0.03378475084900856,
0.0074762701988220215,
0.013959711417555809,
-0.011112012900412083,
0.0016812508692964911,
0.032524723559617996,
0.01109795831143856,
-0.06377477198839188,
0.008397171273827553,
-0.03210301324725151,
0.0019684925209730864,
-0.026693200692534447,
0.029184434562921524,
0.00009922813478624448,
0.04311341047286987,
0.005877623800188303,
0.009520941413939,
-0.0012465354520827532,
0.007001649122685194,
-0.04577714204788208,
-0.05388107895851135,
0.0005239957827143371,
0.022511107847094536,
-0.008136504329741001,
-0.04806121438741684,
0.040483225136995316,
0.002210170729085803,
0.012068336829543114,
-0.012123804539442062,
-0.026332546025514603,
-0.00434351759031415,
-0.011431282386183739,
0.015904223546385765,
0.0023159990087151527,
0.02214927226305008,
0.006333672441542149,
-0.007738060783594847,
-0.003345595207065344,
0.029764823615550995,
-0.012258422560989857,
0.01579512096941471,
-0.00456251110881567,
-0.008034813217818737,
0.01564509980380535,
-0.0556216798722744,
-0.022777270525693893,
0.022856414318084717,
-0.014428268186748028,
-0.021946415305137634,
0.025822313502430916,
0.004619543440639973,
0.024000825360417366,
-0.029974358156323433,
0.013555018231272697,
-0.014877830632030964,
-0.012837829999625683,
0.01123846136033535,
0.0011375900357961655,
-0.0279387254267931,
0.012012106366455555,
0.001539960503578186,
-0.05143817514181137,
-0.03212578967213631,
-0.011176023632287979,
-0.006375563330948353,
-0.05499282106757164,
-0.01222580298781395,
-0.004144732840359211,
-0.039854276925325394,
-0.026331616565585136,
-0.021388549357652664,
0.008059432730078697,
0.018789993599057198,
0.04214723780751228,
-0.01606343872845173,
0.030880535021424294,
-0.0008213475812226534,
-0.046675972640514374,
-0.0705084353685379,
0.02267494425177574,
-0.016402311623096466,
-0.019310226663947105,
-0.022468335926532745,
-0.01235730666667223,
-0.022945621982216835,
0.005976040847599506,
0.07052966952323914,
-0.028391847386956215,
-0.02249884232878685,
0.03790687397122383,
-0.014645076356828213,
-0.020415639504790306,
-0.04010865092277527,
-0.014125709421932697,
-0.004778295289725065,
-0.030838994309306145,
0.015390744432806969,
0.01444314606487751,
-0.004062999039888382,
-0.05504355952143669,
-0.014125260524451733,
0.007046078331768513,
0.044895753264427185,
0.025894861668348312,
-0.03335558623075485,
0.00812860019505024,
0.009409664198756218,
0.019685711711645126,
0.04350314289331436,
0.014902866445481777,
0.014528629370033741,
0.010651892982423306,
-0.022312713786959648,
-0.08872967958450317,
0.0027765356935560703,
-0.05665474385023117,
0.002273083897307515,
-0.030104557052254677,
0.007243528962135315,
-0.0007433599093928933,
-0.03989884629845619,
0.034091074019670486,
0.008852371014654636,
-0.019562188535928726,
-0.018640965223312378,
0.04358341544866562,
-0.0007107069250196218,
0.0261672455817461,
-0.027058091014623642,
0.01933290995657444,
0.020670613273978233,
-0.028641745448112488,
0.009503576904535294,
0.02054019831120968,
0.020113475620746613,
-0.007620830088853836,
0.0025187411811202765,
0.019680825993418694,
-0.01686079055070877,
0.023437432944774628,
0.017300888895988464,
-0.03473832458257675,
-0.0023115621879696846,
-0.038603994995355606,
0.03268444165587425,
-0.01106446236371994,
-0.01767158694565296,
0.03768393024802208,
-0.00795032363384962,
0.09057667851448059,
0.014504075050354004,
0.03820861130952835,
-0.017377514392137527,
-0.005530481226742268,
0.012980673462152481,
0.019394095987081528,
0.007718323729932308,
0.06323529034852982,
-0.01784416101872921,
-0.019071752205491066,
0.00845426321029663,
-0.02980741113424301,
0.0059406026266515255,
-0.014406779780983925,
-0.00035512089380063117,
0.005831895396113396,
0.02460702694952488,
-0.005934827961027622,
-0.03350173309445381,
-0.028743889182806015,
-0.00615790206938982,
0.03664322942495346,
0.040487032383680344,
0.006203078664839268,
0.012712432071566582,
0.003002393990755081,
0.004312832839787006,
0.043536145240068436,
-0.09105989336967468,
-0.007171114441007376,
0.015151899307966232,
0.01676812395453453,
0.018703799694776535,
-0.008424193598330021
] |
<p>Can you trigger a thermonuclear explosion from a smaller thermonuclear explosion in a scaling way, so that starting from a small laser ignited fusion within a small fissile container, using the X-rays from the first explosion to implode a tiny adjacent Li-d wire, which is then used to implode a bigger wire, and so on to a big explosion after a few cycles? Or does the Teller-Ulam design not scale to miniature explosions?</p>
<p>If there is a russian-doll design, can you then trigger the first explosion using a free-electron x-ray laser available today? Any other laser trigger? I am asking because from the answer to this question: <a href="http://physics.stackexchange.com/questions/21405/how-much-of-the-energy-from-1-megaton-h-bomb-explosion-could-we-capture-to-do-us">How much of the energy from 1 megaton H Bomb explosion could we capture to do useful work?</a> , the PACER power-plant design presumably relies on a fission triggered bombs, and fission resources are limited and non-renewable. Further, the PACER folks suggested that future thermonuclear explosions can be laser-triggered, and this was the only way I could think of doing this. Is this really possible?</p>
<p>(I should add that it would also help with regards to proliferation and terrorism safety if the trigger was an expensive bulky free electron laser, as opposed to a standalone explosive nuclear bomb.)</p> | 2,856 | [
-0.002931723603978753,
-0.05032723769545555,
-0.0037881340831518173,
-0.025237437337636948,
-0.001021023839712143,
-0.009591057896614075,
-0.07642640173435211,
-0.0420089028775692,
0.036366432905197144,
-0.025419509038329124,
0.0549386702477932,
0.008496435359120369,
0.0394449308514595,
-0.010032999329268932,
-0.024488434195518494,
0.033813200891017914,
0.018294187262654305,
-0.0664869025349617,
0.007601508405059576,
-0.045604005455970764,
0.02164638228714466,
-0.015135171823203564,
-0.02749243937432766,
0.01844228431582451,
-0.03209405392408371,
0.05029129609465599,
0.011579375714063644,
-0.017403289675712585,
0.03499998897314072,
0.05965862050652504,
0.0015346388099715114,
-0.04791963845491409,
-0.000004270044883014634,
-0.002236349042505026,
0.0037099099718034267,
0.03199607878923416,
-0.035081129521131516,
-0.02878374606370926,
0.003959278576076031,
0.013035211712121964,
-0.02688666805624962,
0.013790504075586796,
-0.0039529213681817055,
0.05360797792673111,
-0.00597468251362443,
0.0017267981311306357,
-0.05794890224933624,
-0.05423435568809509,
0.04143592715263367,
-0.06993886828422546,
-0.002769231563434005,
0.0011897870572283864,
0.0016356571577489376,
0.004271020647138357,
-0.001460174098610878,
-0.02780996449291706,
0.07472605258226395,
0.05898245796561241,
0.02577746845781803,
-0.04267137497663498,
-0.009168188087642193,
0.032225821167230606,
-0.017850754782557487,
-0.007455499842762947,
-0.005345749203115702,
0.017297782003879547,
-0.008183605968952179,
-0.010062689892947674,
-0.006518194451928139,
-0.0015593438874930143,
0.010108728893101215,
0.010819274000823498,
0.024653978645801544,
-0.004075049888342619,
0.00724242115393281,
0.013244850561022758,
0.02275865152478218,
0.008026906289160252,
0.04218854382634163,
0.04010287672281265,
-0.03047909028828144,
-0.0010464207734912634,
0.04129527136683464,
0.04006937891244888,
0.017054008319973946,
0.00015208107652142644,
0.06518323719501495,
0.023707512766122818,
0.03882564604282379,
0.001074085128493607,
0.013258346356451511,
0.041959844529628754,
0.05040993541479111,
0.013929701410233974,
-0.028351787477731705,
0.030597057193517685,
0.01782866008579731,
0.09788372367620468,
0.022538214921951294,
0.008266424760222435,
0.05334901437163353,
0.006272349040955305,
0.01564120315015316,
0.0508313924074173,
0.035717226564884186,
-0.02405654266476631,
0.010497890412807465,
0.0512697733938694,
-0.015735676512122154,
0.0015331930480897427,
-0.06558647006750107,
0.06036336347460747,
0.006170621607452631,
-0.007328017149120569,
-0.029317570850253105,
-0.05930137261748314,
0.026022441685199738,
-0.017488205805420876,
0.05859341844916344,
0.05638374388217926,
0.00928455963730812,
-0.00011618474673014134,
0.021009599789977074,
-0.044804491102695465,
-0.055928368121385574,
-0.028855955228209496,
0.04561750590801239,
-0.011820274405181408,
-0.00881201308220625,
0.02783721312880516,
-0.006666412577033043,
-0.015040242113173008,
0.007424597162753344,
0.0060295285657048225,
0.0406653918325901,
-0.03603998199105263,
-0.08476005494594574,
-0.032111383974552155,
0.015592548996210098,
0.02632289193570614,
-0.05982062965631485,
-0.0641477033495903,
-0.015737812966108322,
-0.014792085625231266,
0.06400969624519348,
-0.02317807264626026,
-0.021339379251003265,
0.004030445124953985,
0.03976430743932724,
0.011460126377642155,
-0.06117977574467659,
0.01868719793856144,
0.028431609272956848,
-0.04302885755896568,
-0.03572186455130577,
-0.02965364046394825,
0.032803796231746674,
0.03675762191414833,
0.016430184245109558,
0.002461493480950594,
0.021931085735559464,
0.0029260199517011642,
-0.0017253244295716286,
-0.0004707316984422505,
0.0011126139434054494,
-0.01676306501030922,
0.09288881719112396,
0.04325898364186287,
-0.02905365079641342,
0.0388043150305748,
0.025178199633955956,
0.015105456113815308,
0.0288222786039114,
0.0056297313421964645,
0.031217005103826523,
-0.06974341720342636,
-0.005076555535197258,
-0.04815689101815224,
-0.005730724427849054,
0.010900958441197872,
-0.03025592677295208,
-0.012923731468617916,
-0.03178374841809273,
-0.015010516159236431,
0.033288344740867615,
0.05564940348267555,
0.026842327788472176,
-0.002599271945655346,
-0.0020520396064966917,
-0.05127895250916481,
-0.006313657853752375,
-0.0234527550637722,
0.021438630297780037,
0.01724640652537346,
-0.02423330955207348,
0.00474726315587759,
-0.016643041744828224,
0.013504905626177788,
-0.008182784542441368,
-0.026830358430743217,
-0.0036873463541269302,
0.064741350710392,
0.010220038704574108,
0.02513597160577774,
-0.001661323825828731,
0.07893075048923492,
0.007173503283411264,
0.0013220463879406452,
0.025543397292494774,
-0.027441496029496193,
-0.015312380157411098,
-0.02869565039873123,
-0.016777878627181053,
0.02567036636173725,
0.03598722815513611,
0.0022773228120058775,
-0.006980525329709053,
0.008925944566726685,
0.003961620852351189,
0.018217947334051132,
-0.0065512582659721375,
0.07316837459802628,
0.060335446149110794,
0.01231754757463932,
-0.010373944416642189,
0.021816769614815712,
0.03812282159924507,
0.006551278289407492,
0.029740851372480392,
-0.028580406680703163,
-0.07340934872627258,
-0.008404717780649662,
-0.0001847018429543823,
0.02710569277405739,
-0.047879621386528015,
0.04463319852948189,
0.030286861583590508,
0.01941658742725849,
0.03267768397927284,
-0.016524193808436394,
-0.042967211455106735,
0.0037066861987113953,
0.020190542563796043,
0.004744525533169508,
-0.03594956547021866,
-0.024420663714408875,
0.0006364855216816068,
0.006666138768196106,
-0.010413758456707,
0.01872706413269043,
0.008367255330085754,
0.00798781868070364,
-0.00491762813180685,
-0.04448854178190231,
7.681518354729633e-7,
-0.04664316400885582,
0.06474614888429642,
-0.02621135488152504,
0.0204356387257576,
0.006082027684897184,
-0.02469048649072647,
0.017660990357398987,
-0.023491432890295982,
-0.024930208921432495,
-0.03950715810060501,
0.007607574108988047,
-0.031221449375152588,
0.0004485389217734337,
0.03488308563828468,
-0.034072183072566986,
0.01323198527097702,
-0.0011593456147238612,
0.010372349992394447,
-0.03425650671124458,
0.0028336786199361086,
-0.015202175825834274,
0.0024854764342308044,
0.041610803455114365,
-0.07516071200370789,
-0.02751602791249752,
-0.006944144610315561,
-0.0074563524685800076,
0.012091848067939281,
-0.009674585424363613,
-0.04194236919283867,
0.006081413943320513,
-0.02070966735482216,
-0.03490378335118294,
0.0221367459744215,
-0.01087536197155714,
0.019134320318698883,
0.0316602997481823,
0.0011662773322314024,
-0.07178262621164322,
0.01218000054359436,
-0.03310270607471466,
0.01817650906741619,
-0.0164653230458498,
-0.005480615887790918,
0.04380200058221817,
0.022661155089735985,
-0.030784757807850838,
0.027678541839122772,
0.013338075950741768,
0.001818509423173964,
-0.03165498375892639,
0.0026836374308913946,
-0.019842592999339104,
-0.014796996489167213,
0.014728513546288013,
0.028595121577382088,
-0.034268420189619064,
0.0012971604010090232,
-0.04834137484431267,
-0.03451453894376755,
0.02852986380457878,
-0.006865461822599173,
0.0744197890162468,
-0.031266070902347565,
-0.03657966107130051,
0.046483125537633896,
0.05320451408624649,
-0.05261440575122833,
-0.02748721092939377,
-0.0032581256236881018,
0.015458890236914158,
-0.026424076408147812,
0.02356521598994732,
0.003903646720573306,
0.02290092594921589,
0.0047934288159012794,
0.034309256821870804,
0.029430177062749863,
0.03207176551222801,
0.03708112612366676,
-0.02515617199242115,
-0.0009620506316423416,
0.015097320079803467,
0.010080551728606224,
0.04619135335087776,
0.020218629390001297,
-0.02741866372525692,
0.034662749618291855,
-0.025211423635482788,
0.02326015569269657,
0.02526908554136753,
-0.05302061885595322,
0.030965151265263557,
0.023457901552319527,
-0.023599404841661453,
-0.024642430245876312,
0.02031150460243225,
-0.0003488241054583341,
-0.03789695352315903,
0.01723620668053627,
0.022059455513954163,
0.03512916341423988,
-0.007120109163224697,
-0.03218090161681175,
-0.02016572654247284,
0.05342424288392067,
0.002439275849610567,
0.004222109913825989,
0.005763296503573656,
0.010912172496318817,
-0.004886159207671881,
0.05847443267703056,
0.020801713690161705,
0.026896195486187935,
0.04613705724477768,
0.02882547304034233,
0.010533607564866543,
0.02072448842227459,
0.0000808950571808964,
-0.09558763355016708,
-0.004343898501247168,
-0.036891691386699677,
0.08148233592510223,
0.007835421711206436,
0.048685140907764435,
0.040938448160886765,
-0.002269048010930419,
-0.01865546964108944,
-0.04106411710381508,
-0.09919413924217224,
0.0157809816300869,
-0.06032571196556091,
-0.008523251861333847,
-0.009769624099135399,
0.0006184940575622022,
-0.014184310100972652,
-0.0004199601535219699,
-0.04623488709330559,
-0.04025750607252121,
-0.015666604042053223,
-0.024593621492385864,
0.04003702104091644,
-0.00970065500587225,
-0.04131050407886505,
0.013848509639501572,
0.04252689331769943,
0.05727406591176987,
0.01718384586274624,
0.014448968693614006,
0.011411499232053757,
-0.021227356046438217,
0.010603037662804127,
0.022490935400128365,
-0.0000789767800597474,
-0.04302872344851494,
0.07458499073982239,
-0.00018803482817020267,
0.007500232197344303,
-0.03192197531461716,
-0.0016227312153205276,
0.039782099425792694,
0.020827101543545723,
-0.00441026221960783,
-0.01710558868944645,
-0.0232330821454525,
-0.005133524537086487,
-0.030905133113265038,
0.045522239059209824,
0.025792468339204788,
-0.014929883182048798,
0.012150445953011513,
0.018893320113420486,
-0.023575812578201294,
0.012723235413432121,
0.03692251443862915,
0.0468965545296669,
-0.031035596504807472,
-0.03359946608543396,
-0.048688724637031555,
0.0039933524094522,
-0.016377443447709084,
-0.01089203730225563,
-0.0059727332554757595,
0.003945623058825731,
0.021725067868828773,
0.00499350018799305,
0.022249041125178337,
0.0386066697537899,
-0.027922827750444412,
0.029218390583992004,
-0.003126668743789196,
0.0158403180539608,
0.0007130884914658964,
0.001353622879832983,
0.028219524770975113,
-0.01893443427979946,
0.03523432835936546,
-0.021469013765454292,
0.0315554253757,
-0.12179413437843323,
-0.022367674857378006,
0.0068959458731114864,
0.04103776440024376,
-0.024364659562706947,
-0.04562297463417053,
-0.07440388947725296,
0.008543495088815689,
0.02629701979458332,
-0.024915212765336037,
0.03451910614967346,
-0.009185921400785446,
-0.0019032363779842854,
-0.02240396849811077,
-0.03508929908275604,
-0.016915148124098778,
0.006741807796061039,
0.023371465504169464,
0.008962818421423435,
-0.02384830079972744,
-0.010240173898637295,
0.04684450849890709,
0.04050573334097862,
0.04013742879033089,
0.056657787412405014,
-0.01405682135373354,
-0.015734145417809486,
-0.018636541441082954,
0.013962654396891594,
-0.001416381448507309,
-0.07710503786802292,
-0.009873858653008938,
-0.0187112707644701,
-0.05872592702507973,
0.03439220041036606,
-0.0411745123565197,
-0.042898304760456085,
0.054156456142663956,
0.043698135763406754,
-0.02300264872610569,
-0.02047375589609146,
-0.025272829458117485,
0.04592178389430046,
0.05855872109532356,
0.020961059257388115,
0.0023493629414588213,
0.06910238415002823,
-0.02163662575185299,
0.00020290218526497483,
0.002107517560943961,
0.01574687846004963,
-0.028719354420900345,
0.03013532981276512,
0.009827870875597,
0.04212304577231407,
-0.01909843273460865,
0.015016329474747181,
-0.04251894727349281,
-0.03610937297344208,
0.03553199768066406,
0.012444732710719109,
0.01629328727722168,
0.03973844647407532,
-0.0141135947778821,
-0.00432730745524168,
-0.020625222474336624,
0.04893115162849426,
-0.004210036713629961,
0.01226935163140297,
0.022053617984056473,
-0.004439143929630518,
0.03684009984135628,
0.005413735285401344,
-0.0132836839184165,
0.005177665501832962,
-0.058431386947631836,
0.027325928211212158,
0.05063215643167496,
-0.03591860085725784,
0.05339217931032181,
-0.02512318268418312,
0.023667965084314346,
0.026820221915841103,
-0.032526370137929916,
0.0006825694581493735,
-0.04445522651076317,
0.012237746268510818,
0.007091648411005735,
-0.03404729813337326,
0.04966995492577553,
-0.05331344157457352,
-0.0061501204036176205,
-0.05387017875909805,
-0.034884583204984665,
0.014599274843931198,
-0.005333054810762405,
-0.030230771750211716,
-0.04238373786211014,
-0.023150229826569557,
-0.008581922389566898,
-0.02383527345955372,
-0.024864085018634796,
0.04765690490603447,
-0.0353284515440464,
0.0030919252894818783,
-0.003284287406131625,
0.015839142724871635,
0.025909626856446266,
-0.030632713809609413,
-0.04584315046668053,
0.018153458833694458,
-0.01102893240749836,
-0.005825134925544262,
0.019810469821095467,
0.016531579196453094,
-0.041047144681215286,
-0.03135282173752785,
0.004329306073486805,
0.027111554518342018,
0.036153391003608704,
0.0036823400296270847,
-0.00047427750541828573,
0.06136377528309822,
0.012947875075042248,
-0.010368132032454014,
-0.010388593189418316,
0.014158077538013458,
-0.02558855153620243,
-0.022584017366170883,
-0.028204001486301422,
0.011792481876909733,
-0.008874217048287392,
-0.04587431624531746,
0.02165430225431919,
-0.0019719989504665136,
0.00042969678179360926,
-0.0252966471016407,
0.03372284770011902,
0.007359520997852087,
0.002374184550717473,
0.03039482980966568,
-0.03789093717932701,
0.07220494747161865,
-0.041316404938697815,
0.01711869239807129,
0.00081721565220505,
-0.03941168636083603,
-0.004176363814622164,
-0.041068073362112045,
-0.018716320395469666,
0.026389043778181076,
0.04249478876590729,
-0.01910824328660965,
0.043667759746313095,
0.00740814721211791,
-0.010322407819330692,
0.016130570322275162,
-0.04220244660973549,
0.00987918023020029,
-0.01636415347456932,
-0.002570650540292263,
-0.014162939041852951,
-0.018660148605704308,
-0.03322220221161842,
0.04271349683403969,
0.03496183082461357,
-0.0015456863911822438,
-0.0011686006328091025,
0.03603723272681236,
0.013256597332656384,
0.019678259268403053,
-0.04778878018260002,
-0.022986935451626778,
0.04506939277052879,
-0.05977673828601837,
0.01448505837470293,
0.019640425220131874,
-0.007873105816543102,
-0.008853975683450699,
0.00726058566942811,
-0.0019180916715413332,
-0.048749055713415146,
-0.017056914046406746,
-0.048741407692432404,
0.0390084870159626,
0.012037523090839386,
-0.0036628921516239643,
0.0021289419382810593,
0.009022612124681473,
0.014927458949387074,
-0.016250653192400932,
-0.008103855885565281,
0.001542543526738882,
-0.05710957944393158,
-0.012331248261034489,
-0.0346728079020977,
-0.07215215265750885,
0.0678437277674675,
-0.0026801247149705887,
-0.01710621640086174,
0.03216373175382614,
-0.028686674311757088,
0.006706048268824816,
-0.006554796360433102,
0.057959333062171936,
0.010846962220966816,
0.05836918205022812,
-0.04433131963014603,
0.0065588378347456455,
-0.03860795497894287,
0.03913065046072006,
0.12886273860931396,
0.01651209592819214,
-0.03727903589606285,
-0.03909427300095558,
0.02944013848900795,
-0.06519056111574173,
0.021718623116612434,
-0.005312405992299318,
-0.033952921628952026,
0.012235140427947044,
-0.025581253692507744,
0.045215457677841187,
0.02860352024435997,
-0.028991755098104477,
0.030325835570693016,
0.026203088462352753,
-0.02695600688457489,
-0.02830771915614605,
0.056413087993860245,
-0.0056348624639213085,
0.01750233583152294,
0.01696092262864113,
-0.011802637949585915,
0.009594778530299664,
-0.008991526439785957,
-0.02076021023094654,
-0.03484064340591431,
-0.05140124261379242,
0.043873004615306854,
0.025830870494246483,
-0.02535179816186428,
-0.02830476313829422,
0.0030389237217605114,
-0.010641665197908878,
0.005695786792784929,
0.012346144765615463,
0.008198720403015614,
0.01285630650818348,
-0.01740523986518383,
0.033800672739744186,
0.027410276234149933,
-0.01568283699452877,
0.015031195245683193,
0.019473081454634666,
-0.045553360134363174,
0.001737560029141605,
-0.03496633470058441,
-0.0009100179886445403,
-0.010972014628350735,
0.005152186844497919,
-0.004220535978674889,
-0.012509265914559364,
0.02414902299642563,
-0.001394086517393589,
-0.0414857491850853,
0.005645474418997765,
0.04399761185050011,
0.0067397537641227245,
-0.03364567086100578,
-0.012186556123197079,
0.0301889069378376,
-0.042395446449518204,
-0.012276371009647846,
-0.020435739308595657,
0.008272436447441578,
0.012684639543294907,
-0.004311676137149334,
0.0332779660820961,
-0.00006984068750170991,
-0.031191008165478706,
-0.04744821786880493,
-0.01690329611301422,
-0.02838660404086113,
-0.02156360261142254,
0.019803013652563095,
0.041134290397167206,
0.035486094653606415,
0.02227657288312912,
0.00427744397893548,
-0.04416441544890404,
-0.04200679436326027,
0.043284688144922256,
0.011628647334873676,
-0.021439775824546814,
-0.011806834489107132,
0.027453448623418808,
0.02828058786690235,
0.029479430988430977,
-0.015183036215603352,
0.017968637868762016,
0.013424183242022991,
0.05026308074593544,
0.01299296971410513,
-0.01919376477599144,
-0.022751087322831154,
0.010611237026751041,
0.018263045698404312,
0.0041269417852163315,
0.002051973482593894,
0.01437252014875412,
-0.0011604101164266467,
-0.013965836726129055,
0.033515188843011856,
0.009952876716852188,
-0.02081686072051525,
0.009067492559552193,
0.024124516174197197,
0.007507551461458206,
-0.033083878457546234,
0.00019332142255734652,
0.015402107499539852,
-0.009193782694637775,
-0.03844885155558586,
-0.00012816431990358979,
-0.023386411368846893,
-0.004467597231268883,
0.038588352501392365,
0.004913087468594313,
0.014638904482126236,
-0.04085363820195198,
0.00962118525058031,
0.0005885348073206842,
-0.010699275881052017,
-0.04182633385062218,
-0.014889969490468502,
-0.010472258552908897,
-0.015947522595524788,
0.00644438061863184,
0.03167703002691269,
-0.015016946941614151,
-0.017208676785230637,
0.024891065433621407,
0.03913354128599167,
-0.0490497350692749,
0.0010515997419133782,
-0.0117097869515419,
0.058731306344270706,
0.016586167737841606,
-0.027649713680148125,
-0.023735705763101578,
0.03749430552124977,
-0.03153093159198761,
-0.03312511742115021,
0.0639910101890564,
0.01468290388584137,
0.01624455861747265,
0.03185952082276344,
-0.004827427212148905,
-0.015959875658154488,
0.07874199748039246,
-0.00994095765054226,
-0.013498187996447086,
0.050845544785261154,
0.0050605968572199345,
0.008737053722143173,
0.032477159053087234,
-0.004026394337415695,
-0.030553767457604408,
-0.008062451146543026,
0.017601918429136276,
0.0377422496676445,
-0.04118986427783966,
0.025396328419446945,
-0.03646150231361389,
-0.010228329338133335,
0.02221754379570484,
-0.0059861778281629086,
-0.0040474762208759785,
0.033074647188186646,
0.01993061602115631,
-0.026242168620228767,
-0.007430210243910551,
0.0011858998332172632,
-0.0102840606123209,
-0.11359643191099167,
-0.018522225320339203,
-0.007914501242339611,
-0.02397947385907173,
-0.001434659818187356,
-0.026207242161035538,
-0.008063236251473427,
0.013212298974394798,
-0.0732090100646019,
-0.016807710751891136,
0.00032821536296978593,
-0.03889991343021393,
-0.06086771935224533,
0.017397860065102577,
-0.008762581273913383,
0.04117234796285629,
0.014610394835472107,
0.06570347398519516,
0.044497180730104446,
0.02890712395310402,
-0.0067879450507462025,
-0.028660515323281288,
0.018801623955368996,
-0.005305803846567869,
0.01846824213862419,
0.007588271051645279,
0.02916724421083927,
-0.07558878511190414,
-0.023429131135344505,
0.006873855367302895,
0.0030913257505744696,
0.04388454928994179,
-0.015609433874487877,
-0.0022387730423361063,
-0.008675536140799522,
0.05315067991614342,
0.026515847072005272,
0.012505868449807167,
0.0113728241994977,
0.041038062423467636,
0.012379427440464497,
0.027208328247070312,
-0.004900083877146244,
0.029537564143538475,
0.057754188776016235,
-0.02391846477985382,
0.006312176119536161,
0.05683339387178421,
0.0042506069876253605,
-0.03943372890353203,
0.019090674817562103,
0.018602296710014343,
0.021058199927210808,
-0.005765465088188648,
-0.02112477459013462,
-0.05499355122447014,
-0.031783729791641235,
-0.02034013904631138,
0.0014115110971033573,
0.029170731082558632,
0.02574784867465496,
-0.059297677129507065,
0.02633429318666458,
0.024979425594210625,
-0.01225106231868267,
-0.06666107475757599,
-0.05138799920678139,
-0.007421231362968683,
0.017047885805368423,
0.01756732165813446,
-0.0058354465290904045,
-0.02979094721376896,
-0.04516865313053131,
0.05020911991596222,
-0.002714897971600294,
0.05382969230413437,
0.05601285398006439,
-0.017641574144363403,
-0.014027833007276058,
-0.03927958011627197,
0.027889486402273178,
-0.030872927978634834,
0.02382158488035202,
-0.018805351108312607,
-0.08933035284280777,
0.019940633326768875,
0.011986481957137585,
-0.0024360469542443752,
-0.01739983819425106,
-0.0010861140908673406,
0.04626355692744255,
-0.029895996674895287,
0.012189507484436035,
-0.015982268378138542,
-0.005984100513160229,
-0.004606651142239571,
0.028586726635694504,
-0.03832989186048508,
-0.014774343930184841,
-0.028998486697673798,
0.0246404018253088,
0.06263549625873566,
0.03361600637435913,
-0.001976261381059885,
-0.033557869493961334,
0.004165433347225189,
0.03529759496450424,
-0.005290189757943153,
-0.010100341401994228,
0.04534550756216049,
0.022471990436315536,
0.0017587891779839993,
-0.006098636891692877,
-0.04085402563214302,
-0.03752916306257248,
0.02449675463140011,
-0.04199095070362091,
0.007840042002499104,
-0.014080068096518517,
-0.029222890734672546,
0.04800175502896309,
-0.012035121209919453,
0.023191086947917938,
0.014744365587830544,
0.0015061977319419384,
0.009276309981942177,
0.025679558515548706,
0.0036758293863385916,
0.0010072733275592327,
-0.015862634405493736,
0.03197102248668671,
-0.012074890546500683,
0.010579059831798077,
-0.049244094640016556,
0.029944084584712982,
0.019974127411842346,
-0.0014829423744231462,
0.0198923721909523,
-0.00309312017634511,
0.010572470724582672,
-0.026411104947328568,
0.020923569798469543,
0.0031108176335692406,
-0.00509389815852046,
-0.03321627900004387,
0.03873611241579056,
-0.0007966880802996457,
-0.012654590420424938,
0.014659587293863297,
-0.02610577829182148,
0.06615089625120163,
0.013194404542446136,
-0.016403356567025185,
-0.0346352681517601,
0.009308511391282082,
0.012580730952322483,
0.015179172158241272,
-0.015729209408164024,
0.04803696647286415,
-0.026788379997015,
0.0028847409412264824,
-0.030375611037015915,
0.011057528667151928,
0.03840489685535431,
-0.057716306298971176,
-0.004785867873579264,
-0.052365612238645554,
-0.004964705090969801,
-0.026286916807293892,
-0.027575969696044922,
-0.0375976487994194,
-0.047270361334085464,
0.017671754583716393,
0.04410557821393013,
-0.004009542986750603,
0.02577040158212185,
-0.0648689791560173,
0.0014992798678576946,
0.07045183330774307,
-0.03339843451976776,
0.004949536174535751,
-0.026628687977790833,
0.02058575302362442,
0.014900635927915573,
0.020379390567541122
] |
<p>One method of introducing electric field is based on the measurement of the force acting on moving charged particle. By equating F to qE we determine the electric field E if the electric charge q is known. Similarly, one can determine magnetic field. </p>
<p>This approach is fine for vacuum but it generally fails for fields in a medium, especially for dispersive medium since one needs first to distigush Lorentz force from other forces that act on a particle there, e.g., from friction force. Once I met the above cited description somewhere but I forgot where it was written. Could some one direct me to an approriate reference? I also cannot remember tha name of scientist who pointed out on the above cited difficulty in determining the field. Perhaps, it was Rosenfeld or something like that. And finally, is there a better definition of the electric / magnetic field in a medium?</p> | 2,857 | [
-0.009432892315089703,
0.006848354823887348,
0.007337638176977634,
-0.04247402027249336,
0.03664827719330788,
0.008051807060837746,
0.0034370380453765392,
-0.026086753234267235,
-0.015735279768705368,
-0.01092520821839571,
0.0377020463347435,
0.02618235908448696,
0.07084192335605621,
-0.000046011144149815664,
0.028606247156858444,
0.007864325307309628,
-0.003230032278224826,
0.0017489651218056679,
-0.01868434064090252,
-0.05793941020965576,
-0.003678919980302453,
0.022423548623919487,
-0.014372178353369236,
0.01311903353780508,
-0.010327307507395744,
0.026861513033509254,
0.027620455250144005,
0.02475162409245968,
0.026695970445871353,
0.044336073100566864,
-0.004452866967767477,
-0.03396845608949661,
0.013490498997271061,
-0.009441578760743141,
0.02308610826730728,
-0.01986614800989628,
-0.022661717608571053,
-0.0659017339348793,
-0.01232901494950056,
-0.0001513670285930857,
-0.05544993653893471,
-0.01560105662792921,
-0.00007686347089475021,
0.037502359598875046,
-0.0386497937142849,
0.013100938871502876,
0.04142898693680763,
-0.026155175641179085,
0.06872981786727905,
-0.06582474708557129,
0.05271171033382416,
0.0052978224121034145,
0.05836404487490654,
-0.0037039066664874554,
-0.008317937143146992,
-0.0334174819290638,
0.08929033577442169,
0.06414087116718292,
-0.013292195275425911,
-0.06227034702897072,
-0.03348439186811447,
-0.009587172418832779,
-0.0066593545489013195,
-0.04737565666437149,
-0.04260801523923874,
0.04038368910551071,
-0.017206376418471336,
-0.00082472461508587,
0.016636833548545837,
0.02509584091603756,
0.00002813619539665524,
0.009417259134352207,
0.03964395821094513,
0.016598334535956383,
0.007811001967638731,
-0.02400864101946354,
0.014344899915158749,
0.00818253867328167,
0.003309504361823201,
0.014761090278625488,
-0.029719185084104538,
0.003488692454993725,
0.025263868272304535,
0.03531883656978607,
-0.006772641092538834,
-0.02787822112441063,
0.048767562955617905,
-0.04074150323867798,
0.020744742825627327,
0.026469586417078972,
-0.029065193608403206,
0.032497603446245193,
0.027578584849834442,
-0.009230656549334526,
-0.055617209523916245,
0.02640588767826557,
-0.000002137277533620363,
0.04109529033303261,
0.008837302215397358,
-0.02441493049263954,
0.02996346540749073,
0.010035491548478603,
0.0058091068640351295,
0.0746162161231041,
0.005711854435503483,
-0.04766598343849182,
-0.01196432113647461,
0.0359664186835289,
-0.036577071994543076,
-0.0018868218176066875,
-0.017267679795622826,
0.02728842757642269,
-0.0007660586852580309,
0.005499657243490219,
0.002094153081998229,
-0.03179368004202843,
0.011660785414278507,
0.006495216395705938,
0.06447024643421173,
0.07238440960645676,
0.03552456945180893,
-0.04682786762714386,
0.003049626015126705,
-0.0030012766364961863,
-0.07454784214496613,
-0.018656980246305466,
0.02801717072725296,
0.008860291913151741,
0.0015933249378576875,
0.01720552146434784,
0.0031610128935426474,
-0.008708476088941097,
-0.020550113171339035,
0.015255898237228394,
0.05049770325422287,
-0.04010261222720146,
-0.0903811827301979,
-0.02450566738843918,
0.02846144512295723,
-0.013496140949428082,
0.022375846281647682,
-0.0651208832859993,
-0.012447408400475979,
0.0013464642688632011,
0.05450686812400818,
0.030332542955875397,
0.016676688566803932,
-0.028055155649781227,
0.05720427632331848,
-0.002573674311861396,
-0.02822933718562126,
-0.029736332595348358,
-0.0021833174396306276,
-0.03116598166525364,
0.009999359957873821,
-0.031599048525094986,
0.003329290309920907,
0.010215988382697105,
-0.03107559308409691,
-0.021490780636668205,
0.07176417857408524,
-0.025687325745821,
-0.02257353812456131,
0.029282931238412857,
-0.01006130501627922,
-0.018127895891666412,
0.08608046174049377,
0.005258927587419748,
0.038484666496515274,
0.03965884447097778,
-0.012954681180417538,
0.04089543968439102,
0.007845290005207062,
0.0018371401820331812,
0.06565965712070465,
-0.051676612347364426,
-0.042991749942302704,
-0.010146542452275753,
0.04467925801873207,
0.0035101203247904778,
-0.06043913587927818,
-0.048285044729709625,
0.014003876596689224,
0.026898974552750587,
-0.01792365126311779,
0.05704103037714958,
-0.0018103765323758125,
0.012761815451085567,
0.009507207199931145,
-0.06284521520137787,
-0.004000952001661062,
-0.034840695559978485,
0.022839119657874107,
0.015634173527359962,
-0.028184810653328896,
0.031492795795202255,
-0.000575660727918148,
0.01574620045721531,
-0.06095052883028984,
-0.057896655052900314,
-0.006215072702616453,
0.027833614498376846,
0.00491294264793396,
-0.045887794345617294,
0.019784417003393173,
0.015457098372280598,
0.010233979672193527,
-0.00013555421901401132,
0.02024158090353012,
-0.0308667179197073,
-0.05714987590909004,
0.01944137178361416,
-0.03987003117799759,
0.0415167436003685,
0.021783022210001945,
-0.024938108399510384,
0.012563325464725494,
-0.001306398306041956,
-0.02032994106411934,
0.031097909435629845,
-0.013632377609610558,
0.06339707970619202,
0.062454964965581894,
0.026825156062841415,
-0.022564344108104706,
0.0601942352950573,
0.017474057152867317,
-0.00020465573470573872,
-0.02180510386824608,
-0.03641669452190399,
-0.061126697808504105,
0.003600301453843713,
0.06847105175256729,
-0.004950796719640493,
-0.037689775228500366,
0.01661580428481102,
0.019549256190657616,
0.05890697240829468,
0.030087029561400414,
0.05335351824760437,
-0.03813900798559189,
-0.06339772790670395,
0.028406022116541862,
0.033890627324581146,
-0.017757045105099678,
0.022824948653578758,
0.04206838458776474,
0.00953203346580267,
0.0023868796415627003,
0.00691674929112196,
-0.021221447736024857,
0.03457948565483093,
-0.034267883747816086,
0.008776159957051277,
0.006868664640933275,
-0.036513734608888626,
0.028833188116550446,
-0.04457974433898926,
0.030540136620402336,
0.00413126777857542,
-0.027291037142276764,
0.010571545921266079,
-0.01674276404082775,
-0.004362940322607756,
0.019301731139421463,
-0.04328882321715355,
-0.045479029417037964,
-0.010673616081476212,
0.015180817805230618,
-0.05392694100737572,
-0.03555945307016373,
-0.01160131674259901,
0.0006416696705855429,
-0.009770701639354229,
-0.020114198327064514,
0.01981160044670105,
0.0271714236587286,
0.04800458252429962,
-0.01785988174378872,
-0.007613687310367823,
-0.021019436419010162,
-0.053976476192474365,
-0.004112018272280693,
0.03623959794640541,
-0.013962918892502785,
0.026992039754986763,
-0.029127981513738632,
-0.052822139114141464,
0.04618093743920326,
-0.022037720307707787,
0.008269451558589935,
-0.007093260996043682,
-0.009029436856508255,
-0.0410010889172554,
0.02187434211373329,
-0.02711520344018936,
-0.00228332681581378,
0.0038052713498473167,
-0.021496186032891273,
0.043898239731788635,
-0.003824746934697032,
-0.033667657524347305,
0.011107056401669979,
-0.049627192318439484,
-0.06568717956542969,
-0.03750186040997505,
-0.00017115498485509306,
0.02650338038802147,
-0.02173178270459175,
0.04298612102866173,
0.024183785542845726,
-0.03576679527759552,
-0.02933119237422943,
-0.02572977915406227,
-0.0571819469332695,
0.0169015284627676,
0.009222171269357204,
0.032980870455503464,
-0.002673090435564518,
-0.04365544021129608,
0.057161636650562286,
0.010194879025220871,
-0.03964555263519287,
-0.035576287657022476,
-0.008539097383618355,
-0.02038612589240074,
-0.005563071463257074,
-0.016469508409500122,
0.016057712957262993,
-0.009472713805735111,
0.02281199023127556,
0.0012339111417531967,
-0.010850287973880768,
0.008806836791336536,
0.004298747051507235,
-0.005923507269471884,
-0.012672186829149723,
0.0030248367693275213,
-0.01069088838994503,
0.06150728836655617,
0.003492626827210188,
-0.022998647764325142,
0.005647338926792145,
0.013405906967818737,
0.038511279970407486,
0.03115343675017357,
-0.007913538254797459,
0.024592390283942223,
0.012520140036940575,
0.0037903792690485716,
-0.020853964611887932,
0.017593931406736374,
-0.01610877737402916,
0.006758071947842836,
0.048424459993839264,
0.0042716278694570065,
-0.007692706771194935,
-0.027348380535840988,
-0.024137474596500397,
0.022655971348285675,
0.033188823610544205,
-0.046219419687986374,
-0.0443694144487381,
-0.01199218537658453,
0.003241920145228505,
0.03240372613072395,
-0.052024293690919876,
-0.011386090889573097,
0.033914804458618164,
0.02163897082209587,
0.023312872275710106,
0.01028739009052515,
-0.026006879284977913,
-0.029268033802509308,
-0.039729390293359756,
-0.012304555624723434,
0.020191743969917297,
0.043991487473249435,
0.013534070923924446,
0.05117393285036087,
0.037905093282461166,
0.010930979624390602,
0.02776535227894783,
0.0061778961680829525,
-0.10696116089820862,
0.02610994316637516,
-0.017697051167488098,
-0.018410231918096542,
-0.043659694492816925,
-0.007166245486587286,
-0.010390076786279678,
0.005492077674716711,
-0.009764282964169979,
-0.02245095558464527,
-0.027667803689837456,
-0.07485567033290863,
0.029991604387760162,
-0.02591865137219429,
-0.04310285300016403,
-0.03571552783250809,
0.03165112063288689,
0.022679399698972702,
-0.04285092279314995,
-0.01979573629796505,
0.04022637754678726,
-0.01555578876286745,
-0.0068664844147861,
-0.012718194164335728,
-0.022718466818332672,
0.03799981623888016,
0.020936058834195137,
0.009559391997754574,
0.011885284446179867,
-0.03190058469772339,
0.020897265523672104,
-0.01527245994657278,
0.055055826902389526,
0.024058975279331207,
-0.008835452608764172,
-0.04628691077232361,
-0.02257058583199978,
0.005561037454754114,
-0.02671412192285061,
0.045276932418346405,
-0.020922137424349785,
0.009057952091097832,
0.022595945745706558,
0.013791635632514954,
-0.013777037151157856,
0.031071912497282028,
0.03026439994573593,
-0.007115679327398539,
-0.009955501183867455,
-0.06569407135248184,
0.056838300079107285,
-0.03567490726709366,
-0.011663476005196571,
0.016382427886128426,
0.025085994973778725,
0.0020067007280886173,
-0.028681710362434387,
0.028737230226397514,
-0.009154045954346657,
-0.009760701097548008,
0.021407607942819595,
-0.008443538099527359,
-0.02938876673579216,
-0.0004850295663345605,
-0.023514332249760628,
0.0003942620533052832,
0.03736792877316475,
0.055448055267333984,
0.020016837865114212,
-0.048244409263134,
-0.07154024392366409,
-0.001421444583684206,
0.04353209584951401,
0.019107148051261902,
0.006174053531140089,
-0.011047675274312496,
-0.05035184323787689,
0.005155949853360653,
0.032710883766412735,
-0.04036466032266617,
0.001514858566224575,
-0.03914044797420502,
-0.004648841917514801,
-0.03993626683950424,
-0.032975535839796066,
-0.03906751051545143,
0.04764622449874878,
-0.0034600046928972006,
-0.0005689722020179033,
-0.028051558881998062,
0.02056507021188736,
0.010011871345341206,
0.04324771463871002,
0.006125536747276783,
0.052475038915872574,
0.009568263776600361,
-0.0039003086276352406,
0.009088307619094849,
-0.003464224049821496,
-0.03553549200296402,
-0.07002357393503189,
0.00037264564889483154,
-0.0023411635775119066,
-0.0035960099194198847,
0.018169475719332695,
-0.02515668235719204,
-0.0490279458463192,
-0.01284085027873516,
0.011923369020223618,
0.016956957057118416,
0.0063389805145561695,
-0.03183899447321892,
0.05049804225564003,
0.002393465954810381,
0.009510481730103493,
0.0901932343840599,
0.013966337777674198,
-0.0348949059844017,
-0.014362250454723835,
-0.009893660433590412,
0.019354552030563354,
-0.020101454108953476,
0.0007479939376935363,
-0.001229401445016265,
0.015869298949837685,
-0.02115548960864544,
0.07885836064815521,
-0.03191697597503662,
-0.015101908706128597,
-0.012685180641710758,
-0.0334477499127388,
-0.01805894635617733,
-0.026485081762075424,
0.00013342250895220786,
-0.0004982553073205054,
-0.023024331778287888,
0.04419466853141785,
-0.01795656979084015,
-0.039301756769418716,
0.018584154546260834,
0.04052561894059181,
0.006385744549334049,
0.036573585122823715,
-0.003226927714422345,
0.02526836469769478,
-0.033887796103954315,
-0.011527209542691708,
-0.00013942529039923102,
-0.055496104061603546,
0.04867741838097572,
-0.033105868846178055,
-0.004046332556754351,
-0.020009750500321388,
-0.07449878752231598,
-0.041195254772901535,
0.00930002797394991,
-0.019179994240403175,
0.02250802516937256,
-0.07015206664800644,
-0.010038048960268497,
-0.0030776485800743103,
0.012214981950819492,
-0.07980886846780777,
-0.06234355270862579,
0.02136138640344143,
0.005717787425965071,
0.005324020981788635,
-0.028271876275539398,
0.019887883216142654,
-0.02899084985256195,
-0.04408137500286102,
0.04486718028783798,
0.05929170176386833,
-0.011814472265541553,
-0.007660998962819576,
0.0017775784945115447,
0.02084978111088276,
0.035954415798187256,
-0.009874205105006695,
-0.034767523407936096,
0.02089112065732479,
0.0018145883223041892,
0.01309349574148655,
0.016994282603263855,
0.009522685781121254,
-0.005807033274322748,
-0.0246133953332901,
-0.009458793327212334,
0.018074484542012215,
0.010780041106045246,
0.008405614644289017,
-0.02221793495118618,
0.05057110637426376,
-0.0011302682105451822,
-0.025906013324856758,
-0.034383270889520645,
0.021503569558262825,
0.032306820154190063,
0.03491058945655823,
-0.03834908455610275,
-0.003089170902967453,
-0.028239810839295387,
-0.03561822697520256,
0.033145658671855927,
0.0007218645769171417,
0.04599422588944435,
0.0031749987974762917,
0.05537578463554382,
0.003417149418964982,
0.011571552604436874,
0.03955559432506561,
0.0032112575136125088,
0.004514174070209265,
0.011471635662019253,
0.0020683100447058678,
0.011405096389353275,
0.024568699300289154,
0.004992771428078413,
-0.015204750932753086,
-0.020070111379027367,
0.0060547818429768085,
0.0586230531334877,
-0.03116074576973915,
0.08885477483272552,
0.048151761293411255,
0.011164030991494656,
-0.008125079795718193,
0.007882603444159031,
-0.022447843104600906,
0.006125219631940126,
-0.020267412066459656,
0.05379747599363327,
-0.00045841120299883187,
-0.009292122907936573,
0.025224434211850166,
0.057134438306093216,
-0.020726198330521584,
0.021632693707942963,
0.012757508084177971,
0.07531310617923737,
0.027926156297326088,
-0.0012291903840377927,
-0.06937698274850845,
0.03467707335948944,
-0.013552745804190636,
0.022016914561390877,
0.016570840030908585,
-0.021168598905205727,
0.04881051927804947,
-0.006353430915623903,
-0.009465480223298073,
0.002829039003700018,
-0.017198821529746056,
-0.02022409625351429,
0.028145762160420418,
0.011135234497487545,
0.01167189422994852,
0.006522096693515778,
0.03194631263613701,
0.01873108558356762,
0.01190350390970707,
0.005218773614615202,
0.043921466916799545,
-0.038118451833724976,
-0.01727987825870514,
-0.057529475539922714,
-0.04140331223607063,
0.04610476270318031,
0.010058455169200897,
-0.03664642199873924,
0.007461441680788994,
-0.0031817546114325523,
0.033674027770757675,
0.02798512578010559,
-0.0028908969834446907,
-0.013093523681163788,
0.042851097881793976,
-0.029400736093521118,
0.0014228431973606348,
-0.03517298400402069,
0.042957011610269547,
0.1064627543091774,
0.059003446251153946,
0.019778555259108543,
-0.03484400734305382,
0.013016360811889172,
-0.05323003977537155,
0.020132767036557198,
-0.033042434602975845,
0.04177580773830414,
-0.05264195427298546,
0.022656090557575226,
-0.00863274373114109,
0.06563585251569748,
-0.003636374371126294,
0.017141267657279968,
0.04693840444087982,
-0.06469257175922394,
-0.06902094930410385,
0.004138675052672625,
0.04659157618880272,
-0.029211705550551414,
-0.0071150874719023705,
-0.04707616567611694,
0.045287810266017914,
-0.0317864790558815,
0.008451974019408226,
-0.002988006453961134,
-0.03188224509358406,
-0.025427890941500664,
0.0027800712268799543,
-0.06456555426120758,
-0.0022173409815877676,
0.0010347635252401233,
-0.005166889168322086,
-0.06002495810389519,
-0.0033078959677368402,
0.05915573239326477,
-0.0002558999403845519,
0.004104321822524071,
0.01606377586722374,
0.020564625039696693,
0.0046252780593931675,
0.01544678583741188,
0.05717405676841736,
-0.005747785326093435,
0.00679068872705102,
-0.0299404114484787,
0.053737327456474304,
-0.024785365909337997,
0.012623398564755917,
0.044886231422424316,
0.014081012457609177,
-0.01091708429157734,
-0.022382494062185287,
-0.02751346491277218,
-0.032296571880578995,
0.016213521361351013,
-0.018497562035918236,
0.008439619094133377,
-0.008681529201567173,
0.04911667853593826,
0.014001843519508839,
0.010838543996214867,
0.0005885750288143754,
0.009058303199708462,
0.02262876182794571,
0.039121393114328384,
0.03267644718289375,
-0.010328155942261219,
-0.01945926621556282,
-0.025280212983489037,
-0.054402999579906464,
-0.027173588052392006,
0.007141112349927425,
0.024985209107398987,
0.04950845614075661,
0.05385875329375267,
-0.022397935390472412,
-0.016973117366433144,
0.003373744199052453,
-0.06881032884120941,
0.05762431398034096,
-0.013532277196645737,
-0.026076272130012512,
-0.029847029596567154,
0.020273244008421898,
0.015922727063298225,
0.05222715809941292,
-0.03127178177237511,
0.02436230517923832,
0.026159314438700676,
-0.03862001374363899,
0.020281905308365822,
-0.03503180667757988,
-0.0022426145151257515,
-0.01649262197315693,
-0.006083535496145487,
0.011425934731960297,
-0.010671685449779034,
-0.011982543393969536,
0.03821980953216553,
0.0007908978732302785,
-0.01594926044344902,
0.0445237010717392,
-0.02323133870959282,
0.01614825613796711,
0.024433519691228867,
0.007255931850522757,
-0.008863122202455997,
-0.000030417277230299078,
0.012570556253194809,
-0.03010539896786213,
-0.01088802795857191,
-0.029665006324648857,
0.0013898643665015697,
-0.012368913739919662,
0.012520850636065006,
-0.04180791229009628,
-0.02777109108865261,
-0.01811518892645836,
-0.022353170439600945,
-0.051186688244342804,
-0.009031250141561031,
-0.03704523667693138,
0.007138865999877453,
-0.027541643008589745,
0.012213723734021187,
-0.04732365161180496,
0.017094045877456665,
-0.0391877181828022,
0.005333688575774431,
0.018443217501044273,
0.0037218029610812664,
-0.009657938964664936,
0.021682128310203552,
0.009565189480781555,
-0.004039451014250517,
0.0520382784307003,
-0.03709050267934799,
-0.013998324982821941,
0.022431552410125732,
-0.04503844305872917,
-0.052352819591760635,
0.02645202912390232,
0.028153585270047188,
0.006088187452405691,
0.05545654892921448,
0.00016998793580569327,
-0.006307343952357769,
0.060778599232435226,
0.010830029845237732,
0.007641722448170185,
-0.007152195554226637,
-0.054589223116636276,
-0.0025532946456223726,
-0.03337951377034187,
0.01236884854733944,
0.0006186202517710626,
-0.015263441950082779,
0.0360243134200573,
0.018563533201813698,
0.021631205454468727,
-0.025891417637467384,
0.04497121274471283,
0.017219962552189827,
-0.008855863474309444,
0.0500614270567894,
-0.0028452607803046703,
0.04650906100869179,
0.08155054599046707,
-0.03397708013653755,
0.004497204907238483,
0.008248064666986465,
0.042120978236198425,
-0.1272030770778656,
-0.03002047725021839,
0.009622781537473202,
0.02546834386885166,
0.03046487644314766,
-0.05835774913430214,
-0.015135361813008785,
0.022576170042157173,
-0.07100245356559753,
-0.013725759461522102,
-0.021973425522446632,
0.010343037545681,
-0.018991952762007713,
-0.0030393218621611595,
0.00555419921875,
0.05309048295021057,
0.03878935053944588,
0.02522878348827362,
0.012980137951672077,
0.015965254977345467,
-0.0023701456375420094,
-0.01366856973618269,
-0.05225145444273949,
0.06484176963567734,
-0.001345028285868466,
-0.021115725859999657,
0.06799164414405823,
-0.004232835955917835,
-0.019012833014130592,
0.052400778979063034,
0.016158107668161392,
0.013682031072676182,
0.0006803030846640468,
0.005765555426478386,
-0.016236910596489906,
0.021841399371623993,
-0.002261134097352624,
-0.019066404551267624,
0.0052490029484033585,
0.023644376546144485,
0.016719304025173187,
0.014429240487515926,
0.001921950955875218,
-0.018248705193400383,
0.034532397985458374,
-0.01947636529803276,
-0.0071120732463896275,
0.04284856095910072,
-0.03963180258870125,
-0.013680621050298214,
0.0059504141099750996,
0.019994622096419334,
0.0009438598644919693,
0.005057156551629305,
0.007923952303826809,
-0.05758830904960632,
-0.022070521488785744,
0.024067509919404984,
-0.006898699793964624,
-0.029555873945355415,
0.0172122772783041,
-0.011320793069899082,
-0.03726407513022423,
0.02495589666068554,
0.006766666192561388,
0.04005661979317665,
-0.04491536691784859,
0.02707080915570259,
0.034828197211027145,
-0.010699203237891197,
-0.001610240084119141,
-0.0607064850628376,
-0.03523538261651993,
0.004532001446932554,
0.012511308304965496,
0.006357820238918066,
-0.013689377345144749,
-0.027420727536082268,
0.028828822076320648,
-0.04483146220445633,
0.03698648139834404,
0.01623576693236828,
-0.018329160287976265,
-0.009947307407855988,
-0.03064424730837345,
0.011869472451508045,
0.030393170192837715,
0.0489443801343441,
-0.02629479393362999,
-0.040157563984394073,
0.011769233271479607,
-0.012739240191876888,
0.01108580082654953,
-0.03957383707165718,
-0.018380340188741684,
-0.019599970430135727,
-0.03308873996138573,
0.018556123599410057,
0.013663030229508877,
-0.013860324397683144,
0.020399566739797592,
-0.0032934839837253094,
0.020426969975233078,
0.03389773145318031,
-0.008550112135708332,
-0.021994873881340027,
0.021144285798072815,
0.011991561390459538,
-0.028535570949316025,
0.03970307111740112,
-0.03294294700026512,
0.023570338264107704,
0.014494210481643677,
0.004927346017211676,
-0.015100633725523949,
0.003012353554368019,
-0.05405928194522858,
0.004673670046031475,
0.01736844703555107,
-0.008220426738262177,
0.0038235895335674286,
-0.027556290850043297,
-0.004277050029486418,
0.03672999143600464,
-0.043103959411382675,
0.0007029646076261997,
0.029490971937775612,
-0.007603658828884363,
0.039537228643894196,
-0.008626388385891914,
0.023138869553804398,
0.018130168318748474,
-0.0036825449205935,
-0.010671031661331654,
0.044089220464229584,
0.04198724403977394,
0.030396316200494766,
0.032938502728939056,
0.05559723451733589,
-0.01747521571815014,
0.024734878912568092,
0.011655906215310097,
0.020795250311493874,
-0.000034820444852812216,
0.031221549957990646,
-0.0007332605891861022,
-0.005239022895693779,
-0.009643612429499626,
0.02354607731103897,
-0.01866229623556137,
0.08773670345544815,
-0.03723280876874924,
0.021597743034362793,
-0.025189092382788658,
0.029051948338747025,
-0.0006319051026366651,
0.025856342166662216,
0.013917001895606518,
0.048302020877599716,
-0.004844172392040491,
-0.0013134917244315147,
-0.016057826578617096,
-0.020896930247545242,
-0.0066770147532224655,
-0.02142672799527645,
0.020976249128580093,
-0.01658427156507969,
0.03232035040855408,
-0.013725756667554379,
-0.011535828933119774,
-0.02677946723997593,
0.004024514928460121,
0.04229949042201042,
0.014860231429338455,
0.05614972114562988,
-0.015354962088167667,
0.003772605210542679,
-0.030819401144981384,
0.06870296597480774,
-0.08190206438302994,
0.015111922286450863,
-0.011629502288997173,
0.026638729497790337,
-0.017933504655957222,
0.021323367953300476
] |
<p>Please help me with an answer to my dilemma:</p>
<p>Is there a liquid that could be used to fill an ice rink (non-explosive, non-poisonous, etc), and have the freezing point above 0 Celsius?</p> | 2,858 | [
-0.025586165487766266,
-0.024890564382076263,
-0.03815090283751488,
0.00854428205639124,
0.06957775354385376,
-0.01593758352100849,
-0.02757066674530506,
-0.04435289278626442,
-0.01920173689723015,
-0.013158715330064297,
0.04049954190850258,
0.036902591586112976,
0.015786658972501755,
0.04223477840423584,
-0.0008817865746095777,
0.00525392172858119,
-0.01216332707554102,
-0.022162599489092827,
0.016002152115106583,
-0.02023339830338955,
-0.0061419447883963585,
-0.014743771404027939,
-0.012753128074109554,
0.01797872968018055,
-0.027358002960681915,
0.02745179831981659,
0.017143918201327324,
-0.04521605744957924,
0.0013971624430269003,
0.044065605849027634,
-0.018796712160110474,
-0.04354558885097504,
0.015805622562766075,
0.018963223323225975,
0.04302862659096718,
-0.012750674970448017,
-0.03816282004117966,
0.014962932094931602,
-0.01545107364654541,
0.021069655194878578,
-0.051391635090112686,
-0.04739576205611229,
0.017426853999495506,
0.025347281247377396,
-0.002692369744181633,
-0.010489484295248985,
-0.011669912375509739,
-0.048472411930561066,
0.029181646183133125,
-0.0724891796708107,
0.025130128487944603,
0.014221763238310814,
0.03662257269024849,
0.028248824179172516,
0.009511800482869148,
-0.0015362020349130034,
0.07181201130151749,
0.05321922525763512,
-0.002439972246065736,
-0.059438999742269516,
0.0010116291232407093,
-0.00284741073846817,
-0.01897156424820423,
-0.028364865109324455,
-0.0092474315315485,
0.02145335078239441,
-0.02897847257554531,
0.028470907360315323,
0.002415226772427559,
-0.022216089069843292,
0.002688926411792636,
0.006761969067156315,
0.015903126448392868,
-0.004435322247445583,
0.03332354500889778,
-0.02041911706328392,
0.011717586778104305,
0.02759036421775818,
0.039190325886011124,
0.045250579714775085,
-0.03443225100636482,
0.01185238640755415,
0.03992799296975136,
0.023736391216516495,
0.023622428998351097,
-0.035706907510757446,
0.054316889494657516,
-0.017073627561330795,
0.04603559523820877,
0.057768069207668304,
-0.005734709091484547,
-0.012494347058236599,
0.04883880913257599,
0.02354062721133232,
0.0003181609499733895,
-0.04018038511276245,
-0.02257131040096283,
0.09381743520498276,
-0.018127156421542168,
-0.016263240948319435,
0.04360155388712883,
0.032639842480421066,
-0.004126154351979494,
0.0645906999707222,
-0.0012917625717818737,
-0.02637615241110325,
-0.036134421825408936,
-0.010617375373840332,
0.053359273821115494,
-0.00642042001709342,
-0.015202751383185387,
0.008432390168309212,
-0.0011324678780511022,
-0.015799900516867638,
-0.019153054803609848,
-0.04264703020453453,
-0.02785545401275158,
-0.0272324588149786,
0.027703875675797462,
0.036848295480012894,
0.033439092338085175,
-0.005397621542215347,
0.023587603121995926,
-0.015493134967982769,
-0.0488952212035656,
0.010863197967410088,
-0.020368145778775215,
0.03231245279312134,
-0.036010000854730606,
0.03518323972821236,
-0.019108206033706665,
0.02907080203294754,
0.0314750075340271,
-0.007617689669132233,
0.06703846901655197,
-0.052374277263879776,
-0.0638929083943367,
-0.07998206466436386,
0.04373425990343094,
-0.009457843378186226,
-0.08106538653373718,
-0.07680000364780426,
-0.00007538835052400827,
-0.01480891928076744,
0.04475913196802139,
0.0029251507949084044,
0.006198481190949678,
-0.016240548342466354,
0.013455945067107677,
0.012083573266863823,
-0.02771456353366375,
-0.017410214990377426,
-0.01963138021528721,
-0.030744651332497597,
0.021418564021587372,
-0.04670564457774162,
0.03807293623685837,
0.05644083395600319,
0.005936609581112862,
-0.00861840508878231,
-0.009574600495398045,
-0.05057520791888237,
0.008407586254179478,
0.025146441534161568,
0.028536800295114517,
-0.03193969279527664,
0.055511344224214554,
-0.027683617547154427,
-0.008238522335886955,
0.029542554169893265,
0.020151587203145027,
0.04625079035758972,
0.04312682896852493,
0.0029970169998705387,
0.04851903021335602,
-0.01673044264316559,
0.015909308567643166,
-0.027351072058081627,
0.02307736501097679,
0.05269772186875343,
-0.05001632496714592,
0.013158537447452545,
0.005346691235899925,
0.0125017324462533,
0.000423658755607903,
0.07421832531690598,
0.005973740480840206,
0.0063224188052117825,
0.0482296347618103,
-0.060810983180999756,
-0.01571516878902912,
-0.07451096177101135,
0.001825443934649229,
0.009449471719563007,
0.040834467858076096,
0.0512303002178669,
0.038455989211797714,
0.05855005234479904,
-0.06176471710205078,
-0.009570264257490635,
0.0017252591205760837,
0.024789083749055862,
0.021578243002295494,
-0.0009145649382844567,
0.04754061996936798,
0.05453575775027275,
0.03478609025478363,
-0.04319995269179344,
-0.020229095593094826,
-0.01548051368445158,
-0.006667126435786486,
-0.06406906247138977,
-0.02090563252568245,
0.05100206285715103,
-0.018639355897903442,
-0.008999766781926155,
0.018731072545051575,
0.01593846082687378,
0.003797024954110384,
0.05669916421175003,
-0.02962835319340229,
0.0648142471909523,
-0.007013989146798849,
-0.0012643069494515657,
0.005781717598438263,
0.006232972722500563,
0.02563762292265892,
-0.010691963136196136,
0.059269051998853683,
-0.03444761782884598,
-0.05749618634581566,
0.03527886047959328,
0.04928820580244064,
0.031777068972587585,
-0.06254664808511734,
-0.004266223404556513,
0.017743214964866638,
0.005006424151360989,
0.03106546588242054,
0.013533774763345718,
-0.0331118069589138,
0.004111303016543388,
0.014508295804262161,
0.015465724281966686,
0.041192591190338135,
0.014482171274721622,
0.001654268242418766,
0.03830286115407944,
-0.0013258534017950296,
-0.009801344014704227,
-0.025878220796585083,
-0.03779945522546768,
0.004786391742527485,
0.015547516755759716,
-0.01153641752898693,
-0.004028956405818462,
0.03748296573758125,
-0.035199303179979324,
0.027909159660339355,
0.007827210240066051,
0.028784532099962234,
-0.005829477217048407,
-0.01792699098587036,
-0.035265374928712845,
0.018093926832079887,
0.01963542401790619,
-0.021710293367505074,
-0.0006828255136497319,
0.034310974180698395,
-0.02467425726354122,
-0.004573273938149214,
0.02843027561903,
0.0053480807691812515,
-0.02708219178020954,
0.036394137889146805,
0.021529948338866234,
0.011979954317212105,
0.024444136768579483,
-0.03343959152698517,
-0.021879520267248154,
-0.004170815460383892,
-0.027507439255714417,
-0.036559320986270905,
0.031294822692871094,
-0.05572773888707161,
0.023565271869301796,
0.00006135923467809334,
-0.023284099996089935,
0.03739447891712189,
-0.01231446210294962,
-0.015807146206498146,
0.009830361232161522,
-0.0016222280682995915,
-0.025163980200886726,
-0.009921601042151451,
-0.014220069162547588,
0.03184323385357857,
-0.016292709857225418,
-0.004437847062945366,
0.04672103747725487,
-0.024320010095834732,
-0.05340445786714554,
0.02337123639881611,
-0.06921692937612534,
-0.03825168311595917,
-0.01932985894382,
-0.02009311132133007,
0.03518684208393097,
-0.041718531399965286,
-0.003005422418937087,
0.018242234364151955,
-0.03153793141245842,
0.026414964348077774,
-0.030151430517435074,
-0.06137857213616371,
0.02404603734612465,
-0.0022284400183707476,
0.03351878374814987,
-0.00754068186506629,
-0.017359493300318718,
0.046766217797994614,
0.006505455356091261,
-0.04208143800497055,
-0.03184279426932335,
-0.03696887567639351,
-0.027178354561328888,
-0.04855659604072571,
0.0001091224912670441,
0.010095705278217793,
-0.01528897974640131,
0.0174606591463089,
0.022420283406972885,
0.038296155631542206,
-0.00033321318915113807,
0.05179585516452789,
-0.016174999997019768,
0.008778938092291355,
0.028939636424183846,
0.04697432368993759,
0.04004787653684616,
-0.0014635707484558225,
-0.028894539922475815,
-0.0044519370421767235,
-0.013766600750386715,
0.03343236446380615,
0.055526599287986755,
-0.01815684325993061,
0.020492468029260635,
-0.01153433509171009,
0.017951365560293198,
-0.01673821359872818,
0.02533411793410778,
-0.006328284740447998,
0.006382777355611324,
0.03599218651652336,
0.040749482810497284,
0.0031857509166002274,
-0.005787009838968515,
0.01358751580119133,
0.04035024344921112,
0.032533399760723114,
-0.06080732122063637,
-0.03791157156229019,
0.01972537860274315,
0.00033806555438786745,
0.011958505026996136,
0.02034025453031063,
0.026443038135766983,
0.01738269254565239,
0.008832719177007675,
0.04531538859009743,
-0.013101549819111824,
0.0018525212071835995,
0.008840286172926426,
-0.06551031023263931,
-0.010863161645829678,
-0.012251297943294048,
0.017744731158018112,
0.009981006383895874,
0.05010208114981651,
0.011357021518051624,
0.03217228874564171,
0.042620282620191574,
0.024101626127958298,
-0.04647884890437126,
0.023534584790468216,
-0.05843467637896538,
0.04979146644473076,
0.0002378798817517236,
-0.009008020162582397,
-0.016945019364356995,
-0.044885486364364624,
-0.03155561909079552,
0.022140750661492348,
0.012864644639194012,
-0.016002340242266655,
0.021000344306230545,
-0.01289732102304697,
-0.018098248168826103,
-0.004519525449723005,
-0.013664321042597294,
-0.02894424833357334,
-0.030627381056547165,
0.0075477175414562225,
0.0197535939514637,
0.008372870273888111,
-0.025363342836499214,
-0.00002546328141761478,
0.019543712958693504,
0.012105201371014118,
0.04093068465590477,
-0.012182298116385937,
0.028897840529680252,
-0.011017067357897758,
-0.029081035405397415,
-0.007513318210840225,
0.01573498733341694,
-0.030052077025175095,
-0.0015367233427241445,
-0.055528756231069565,
-0.07376576960086823,
-0.006127562373876572,
-0.0007025642553344369,
0.03361057490110397,
0.010684972628951073,
0.017605939880013466,
-0.02858804725110531,
-0.03783959522843361,
-0.01769581250846386,
0.021249430254101753,
0.08463801443576813,
0.02809370867908001,
-0.016019949689507484,
-0.011421426199376583,
-0.046655938029289246,
-0.025908153504133224,
0.0076399873942136765,
0.03980457782745361,
0.004237848799675703,
-0.0004326874332036823,
-0.023880593478679657,
0.01950259692966938,
0.017955627292394638,
-0.0503561906516552,
-0.001111737103201449,
0.015131352469325066,
0.009558062069118023,
-0.01274739857763052,
-0.003100711852312088,
-0.0031370518263429403,
-0.004856091924011707,
0.008539753966033459,
-0.004371441435068846,
-0.01561711635440588,
-0.08891173452138901,
-0.005638682283461094,
0.057032328099012375,
0.06379981338977814,
-0.0036657352466136217,
-0.01267374586313963,
-0.08130935579538345,
-0.025421641767024994,
0.028158392757177353,
-0.03425666689872742,
-0.0051559824496507645,
-0.016590017825365067,
-0.017186105251312256,
-0.019235670566558838,
-0.012186040170490742,
0.008798233233392239,
-0.021937303245067596,
-0.011516934260725975,
0.030847914516925812,
0.0012314463965594769,
-0.016162093728780746,
0.03325972706079483,
0.03591020032763481,
0.039254188537597656,
0.07034025341272354,
0.02152109146118164,
-0.016531771048903465,
0.005518672522157431,
-0.004786242730915546,
-0.0383826307952404,
-0.06488826870918274,
-0.013588822446763515,
0.027019275352358818,
0.019206194207072258,
0.026343541219830513,
-0.028680631890892982,
-0.08958102017641068,
0.03755553066730499,
-0.01516403816640377,
-0.017160866409540176,
0.04233894124627113,
-0.03315812349319458,
0.02932884730398655,
0.029970606788992882,
0.01899144984781742,
0.019519459456205368,
0.058081936091184616,
-0.0061234282329678535,
-0.021902721375226974,
-0.031612757593393326,
0.019641345366835594,
-0.033203233033418655,
0.009240048006176949,
-0.01799151673913002,
0.02784791588783264,
-0.04816659912467003,
0.004888670053333044,
-0.03714458644390106,
0.02723071537911892,
0.011585277505218983,
-0.024625489488244057,
-0.004974960815161467,
0.0315023697912693,
0.025132782757282257,
-0.04598318040370941,
-0.014099334366619587,
-0.021146435290575027,
-0.015752021223306656,
0.002151524880900979,
0.039430584758520126,
-0.028846375644207,
-0.006711442954838276,
0.04585934057831764,
-0.03461474925279617,
0.059512678533792496,
0.007015605457127094,
-0.0007876571617089212,
-0.027224047109484673,
-0.08250337094068527,
0.05311960354447365,
-0.033725906163454056,
0.03463488072156906,
0.03161715343594551,
-0.06671532243490219,
0.00435402849689126,
0.022707723081111908,
0.048638515174388885,
0.013845150358974934,
-0.02323729358613491,
0.024898216128349304,
-0.014685921370983124,
0.029550746083259583,
-0.04271324351429939,
-0.0423455648124218,
0.008742349222302437,
0.036895669996738434,
-0.015269042924046516,
-0.06131605803966522,
-0.023378431797027588,
0.00925789400935173,
0.007310093380510807,
0.008127636276185513,
0.051252610981464386,
-0.004039206076413393,
-0.02870846353471279,
0.04932490736246109,
0.019907306879758835,
0.032529316842556,
0.030064035207033157,
-0.019267018884420395,
0.02652888186275959,
-0.024757735431194305,
-0.022637799382209778,
0.023960934951901436,
0.055973805487155914,
-0.040871888399124146,
-0.006208909675478935,
0.015093069523572922,
0.004087749868631363,
0.06626700609922409,
0.018321018666028976,
0.011260832659900188,
0.024917377158999443,
0.017339831218123436,
-0.041162073612213135,
-0.0551653616130352,
0.022430771961808205,
0.014199357479810715,
-0.0013339832657948136,
-0.00883532129228115,
-0.0009268384892493486,
-0.025607705116271973,
-0.024586476385593414,
-0.003973312675952911,
0.018593275919556618,
-0.005487803835421801,
-0.017372051253914833,
0.060376107692718506,
0.0221484936773777,
-0.044600993394851685,
0.039888493716716766,
-0.012549618259072304,
0.0435214526951313,
0.023352213203907013,
-0.009450435638427734,
0.022544967010617256,
0.019649721682071686,
-0.031922440975904465,
-0.07241535931825638,
-0.0011387602426111698,
0.006616097874939442,
-0.015574593096971512,
-0.023580554872751236,
0.021808017045259476,
0.0278795026242733,
0.0012232408626005054,
-0.018499065190553665,
0.010086214169859886,
-0.007438653148710728,
0.07799393683671951,
0.009323889389634132,
-0.01141655258834362,
0.01391735952347517,
0.015415126457810402,
0.024011753499507904,
0.027107158675789833,
0.020194031298160553,
0.035605039447546005,
0.05340183153748512,
-0.014431487768888474,
0.015796281397342682,
-0.014371570199728012,
-0.05002092942595482,
0.043993230909109116,
-0.028356006368994713,
0.06521598249673843,
0.00496565131470561,
-0.05237627029418945,
0.04004456475377083,
-0.01589498296380043,
0.03195725381374359,
-0.06173039972782135,
-0.013208047486841679,
-0.026026558130979538,
0.009482723660767078,
0.016692278906702995,
-0.004943879321217537,
-0.006491510197520256,
0.02912353165447712,
0.0038155498914420605,
0.015592973679304123,
-0.003988428507000208,
-0.03649190813302994,
-0.07926832139492035,
0.01574239321053028,
-0.015921415761113167,
-0.032615043222904205,
0.00015005319437477738,
0.021188590675592422,
-0.007289768662303686,
0.006389113143086433,
-0.03753459081053734,
0.0031008110381662846,
-0.024549750611186028,
0.01116522029042244,
0.0064967600628733635,
0.025038616731762886,
0.023158565163612366,
0.02243376150727272,
-0.009890430606901646,
0.023187652230262756,
0.11929059773683548,
0.03163513168692589,
0.0088271489366889,
-0.08171365410089493,
-0.019084515050053596,
-0.008336619473993778,
-0.019035784527659416,
-0.04301433637738228,
-0.002740436466410756,
-0.03298306092619896,
0.014427078887820244,
0.01309285033494234,
0.040276654064655304,
-0.0419326089322567,
0.04235073924064636,
0.028960859403014183,
-0.04137644171714783,
-0.02349809557199478,
-0.017171630635857582,
0.01692996732890606,
0.00155502965208143,
-0.005370177328586578,
0.016386603936553,
0.05541408807039261,
0.017734618857502937,
0.003130830591544509,
-0.026278730481863022,
-0.03119896911084652,
0.07476156204938889,
0.054097048938274384,
-0.05189330875873566,
0.015849122777581215,
0.004454978741705418,
0.029643064364790916,
-0.0649532675743103,
0.016252441331744194,
0.010419868864119053,
-0.01959797739982605,
-0.00734494486823678,
0.03424868360161781,
0.051737844944000244,
-0.00004739758514915593,
0.03109041601419449,
-0.000017457210560678504,
-0.03175063803792,
-0.00046303245471790433,
-0.04755207523703575,
0.002586403163149953,
-0.020631520077586174,
-0.006409286055713892,
-0.009656550362706184,
0.0036143548786640167,
0.002558490727096796,
-0.034353408962488174,
-0.05003174766898155,
-0.016712531447410583,
0.03976299613714218,
-0.010399481281638145,
-0.003473243210464716,
-0.051271747797727585,
0.02930796891450882,
-0.01297367550432682,
-0.021709129214286804,
0.02010124735534191,
0.009624931961297989,
-0.01039059553295374,
-0.008588670752942562,
0.03841204568743706,
-0.00221203058026731,
-0.02082972228527069,
-0.01351772341877222,
-0.009512421675026417,
-0.016309259459376335,
-0.009229270741343498,
-0.004665393847972155,
0.0259189885109663,
0.0188971608877182,
0.018531665205955505,
0.0018175559816882014,
-0.014125233516097069,
-0.010285062715411186,
0.03924009948968887,
-0.01619524508714676,
-0.013849898241460323,
0.008952259086072445,
-0.003878671443089843,
-0.009996576234698296,
0.04992222785949707,
-0.018664680421352386,
0.015424344688653946,
0.014148690737783909,
0.040313467383384705,
0.02745436504483223,
-0.004670960363000631,
-0.036727290600538254,
-0.03328979015350342,
-0.07492837309837341,
0.05716612935066223,
0.021279819309711456,
0.03515895456075668,
0.017019974067807198,
-0.00852335337549448,
0.053314778953790665,
-0.03307737410068512,
-0.034399207681417465,
0.01752678118646145,
-0.029434923082590103,
-0.028250493109226227,
-0.041155070066452026,
0.010121814906597137,
0.0162520594894886,
0.004093128722161055,
-0.07546290010213852,
-0.03988117352128029,
-0.030449876561760902,
-0.01266840286552906,
0.03428764268755913,
-0.027002472430467606,
0.012830235064029694,
0.01565312221646309,
-0.013261501677334309,
-0.0411822572350502,
0.01900644227862358,
-0.03739192709326744,
-0.020462453365325928,
0.05181407928466797,
-0.005267135798931122,
-0.006455633323639631,
-0.0071638599038124084,
-0.031347133219242096,
0.006205471232533455,
0.03911761939525604,
-0.005951168481260538,
-0.04814978316426277,
-0.03394787013530731,
0.0018592305714264512,
0.023917777463793755,
0.07350604236125946,
-0.06267428398132324,
-0.01852593943476677,
0.044993333518505096,
-0.033109359443187714,
-0.03563421964645386,
0.011644169688224792,
0.006171258166432381,
0.025924459099769592,
0.029836876317858696,
0.01932852901518345,
-0.005188074894249439,
0.06531539559364319,
0.0020714104175567627,
-0.0006859273998998106,
-0.003746712813153863,
0.01154955942183733,
0.014424755237996578,
-0.0022009429521858692,
-0.021403152495622635,
-0.029578668996691704,
0.022649195045232773,
0.03506080433726311,
0.014323880895972252,
0.019205357879400253,
-0.02173611894249916,
-0.016156315803527832,
-0.00951391365379095,
-0.02142990194261074,
0.051240891218185425,
0.005067931488156319,
-0.026452792808413506,
0.030806709080934525,
-0.01959945634007454,
0.0019772297237068415,
0.01917797140777111,
-0.017118196934461594,
-0.08965514600276947,
0.003356197150424123,
0.005215307231992483,
-0.04989880695939064,
0.011477292515337467,
-0.0370059497654438,
0.03708089515566826,
0.0605846606194973,
-0.07482332736253738,
-0.014799061231315136,
-0.03295003995299339,
-0.03598505258560181,
-0.03305185213685036,
-0.003538573859259486,
-0.012240353971719742,
0.011578750796616077,
0.02206507883965969,
0.04252147674560547,
0.01705806888639927,
0.0042120954021811485,
-0.006604291964322329,
-0.03854638710618019,
0.0262020044028759,
0.045002955943346024,
0.011221040040254593,
-0.012471768073737621,
0.02594670094549656,
-0.05083080008625984,
-0.018933530896902084,
0.02446850948035717,
-0.019616879522800446,
0.009678860194981098,
0.011541876941919327,
-0.004780646413564682,
-0.06386953592300415,
0.054295748472213745,
0.02779436856508255,
0.0213431715965271,
-0.001155545120127499,
0.04270804300904274,
-0.006640089675784111,
0.03903072699904442,
0.013029048219323158,
0.024067314341664314,
0.019159939140081406,
-0.048893626779317856,
-0.023736722767353058,
0.06423331052064896,
-0.03641176223754883,
-0.0032637128606438637,
0.02472623437643051,
0.0001808131783036515,
0.03864317014813423,
-0.02502419427037239,
-0.04863320291042328,
-0.04945001378655434,
-0.021474381908774376,
0.014105084352195263,
-0.010818036273121834,
0.009952411986887455,
-0.010891578160226345,
-0.030170833691954613,
0.00658454792574048,
-0.020892640575766563,
0.011722195893526077,
-0.05672958120703697,
-0.03400824964046478,
-0.007055260241031647,
-0.01678750477731228,
-0.033567558974027634,
-0.02538306452333927,
-0.011979327537119389,
-0.04925401136279106,
0.024636980146169662,
0.029802175238728523,
0.05391348898410797,
0.054185640066862106,
-0.004235502798110247,
-0.017833910882472992,
-0.06435780972242355,
0.03263438493013382,
-0.015866033732891083,
0.03355800360441208,
-0.0093943290412426,
-0.01696060225367546,
-0.004084316082298756,
-0.014471343718469143,
0.05936647206544876,
-0.02306722104549408,
-0.0028008304070681334,
0.022684646770358086,
-0.008209715597331524,
0.02386929839849472,
-0.026087718084454536,
-0.007636926602572203,
0.018068363890051842,
-0.048740748316049576,
0.033169712871313095,
-0.0036986391060054302,
0.0189344584941864,
-0.03333194553852081,
0.02966163493692875,
-0.0044448464177548885,
0.005831693299114704,
-0.02710149437189102,
-0.009477870538830757,
0.024126751348376274,
-0.0002693258284125477,
-0.02968013659119606,
0.06058242917060852,
-0.03335241600871086,
0.0015393529320135713,
-0.021372836083173752,
-0.019606225192546844,
-0.04739973321557045,
0.061418093740940094,
-0.022022152319550514,
0.027093209326267242,
-0.025354091078042984,
-0.04331927374005318,
-0.028276002034544945,
-0.02064904198050499,
0.03949635475873947,
0.027920806780457497,
-0.027260757982730865,
0.0031871888786554337,
0.04046505689620972,
0.022376129403710365,
0.0499795600771904,
-0.016042960807681084,
-0.014238105155527592,
0.001649990095756948,
0.004839156288653612,
-0.02059941552579403,
0.028650278225541115,
0.031586118042469025,
0.003967268392443657,
-0.01694375090301037,
-0.002430378459393978,
0.03613021969795227,
-0.0032921219244599342,
0.08036892861127853,
0.017460744827985764,
-0.034784089773893356,
-0.03600331395864487,
0.03047359734773636,
0.011719777248799801,
0.041745755821466446,
-0.013506806455552578,
-0.018216772004961967,
0.06686843931674957,
0.007127412594854832,
0.020564908161759377,
-0.062114495784044266,
0.02157471515238285,
0.011946186423301697,
0.008638790808618069,
-0.01950276643037796,
0.02134251408278942,
-0.027254221960902214,
-0.002783719915896654,
-0.011570240370929241,
0.03782166913151741,
0.0004091514565516263,
-0.043963249772787094,
-0.006382233463227749,
-0.01068144477903843,
0.008353373035788536,
-0.02529802918434143,
-0.011965730227530003,
0.019562365487217903,
0.0012812308268621564,
0.022057421505451202,
0.03397921845316887,
-0.004281748551875353,
0.01024988666176796,
-0.015026204288005829,
-0.04145009443163872,
0.05321114510297775,
-0.033062368631362915,
-0.008364102803170681,
-0.0029845184180885553,
0.03451330587267876,
-0.002277753548696637,
0.016982225701212883
] |
<p>A recent paper, titled <a href="http://arxiv.org/abs/1302.2775">Inertia from an Asymmetric Casimir Effect</a>, discusses the universal horizons relative to an accelerating observer (Rindler space). A figure it used to demonstrate its point challenged a view I held.</p>
<p><img src="http://i.stack.imgur.com/BAWzq.png" alt="Figure 1"></p>
<p>I previously asked a question about Rindler space, <a href="http://physics.stackexchange.com/questions/10811/do-apparent-event-horizons-have-hawking-radiation">Do apparent event horizons have Hawking radiation?</a>. My take-away from the (very good) answers was that an the Rindler Horizon (in the above figure) emits Hawking radiation in the same way that a black hole or the cosmic horizon does. This is called Unruh radiation.</p>
<p>This leads me to the obvious question: Does the accelerating observer see the new Unruh radiation <strong>and</strong> the old cosmic horizon's radiation?</p>
<p>As you accelerate to the <em>right</em>, then you replace the cosmic horizon to you <em>left</em> with a new horizon, closer to you. Radiation thus appears out of nowhere, but does that mean that the existing radiation from the prior horizon disappears?</p>
<hr>
<p>EDITED, new material follows:</p>
<p>In my first version of this question I referenced <em>both</em> the CMB and cosmic horizon radiation. These are two different things, but I treated them as the same thing. The question was answered for the CMB - it remains just as the light from any galaxy would.</p>
<p>I've reformulated this so it can be about the Rindler Horizon's radiation versus radiation from the original cosmic horizon. To illustrate this, I made my own version of Figure 1 above, with more detail for the old versus new horizon. Here:</p>
<ul>
<li>Cosmic horizon - horizon according to an inertial observer </li>
<li>Cosmic horizon prime - horizon according to an accelerating observer with same position and velocity as the inertial one</li>
</ul>
<p><img src="http://i.stack.imgur.com/UJ1wg.png" alt="My Figure 1"></p>
<p>This corresponds to Figure 1, since his surface labeled "COSMIC HORIZON" is the rightmost part of the horizon that remains the same for the accelerating observer as well as the inertial observer. His "RINDLER HORIZON" on the left is only the new horizon, leaving out the old horizon, which I have included.</p>
<p>If we say that $O$ <em>just started</em> accelerating, then what do we expect? Logical possibilities include:</p>
<ul>
<li>Sees Hawking radiation from both horizons</li>
<li>Sees Hawking radiation from old horizon, which transforms into the characteristic of the new horizon over time</li>
<li>Instantly sees Hawking radiation from new horizon</li>
</ul>
<p>I'm also not sure if I've drawn the new horizon correctly. I would think that you couldn't "reveal" any galaxy beyond the cosmic horizon at the rightmost point, but to $O$, its dark-energy acceleration is less than to the inertial observer. Maybe I should have just moved the horizon to the right instead of shrinking it? I'm not sure, but I <em>think</em> the paper assumed no change in the cosmic horizon Hawking radiation from the right.</p> | 2,859 | [
-0.001516837510280311,
-0.05314508453011513,
0.032012827694416046,
-0.023505762219429016,
-0.0007061808719299734,
0.01450180634856224,
-0.05253250151872635,
-0.032033126801252365,
-0.030244559049606323,
-0.04813137650489807,
-0.00024552992545068264,
0.008825864642858505,
0.0561600923538208,
0.049623336642980576,
0.0016471819253638387,
0.0008800369105301797,
-0.01632656529545784,
-0.016165437176823616,
-0.022993257269263268,
-0.048932790756225586,
0.028139807283878326,
0.02185194566845894,
-0.0005117027903907001,
0.014730661176145077,
-0.0562024749815464,
0.0012801099801436067,
0.010353369638323784,
0.021175529807806015,
0.0004772250249516219,
0.027857715263962746,
-0.05614728108048439,
-0.011617757380008698,
-0.02452625334262848,
0.004005131311714649,
0.017444070428609848,
-0.00857574213296175,
-0.003349261125549674,
-0.03150641545653343,
-0.007958343252539635,
0.020841002464294434,
-0.02420494705438614,
-0.002254429506137967,
-0.019451919943094254,
0.08638699352741241,
-0.07439427077770233,
-0.024922482669353485,
-0.035620711743831635,
0.0348648764193058,
0.03034384921193123,
-0.03406837582588196,
0.06129235401749611,
-0.021032866090536118,
0.03664054349064827,
0.008067450486123562,
-0.036481257528066635,
-0.015401058830320835,
0.07949475944042206,
0.07718820869922638,
0.006137058604508638,
-0.02463390678167343,
-0.0051387008279562,
-0.010961747728288174,
-0.029136432334780693,
0.011056099086999893,
-0.014157232828438282,
0.029721925035119057,
0.026302652433514595,
0.0039003200363367796,
0.016417156904935837,
-0.010030285455286503,
0.021498821675777435,
-0.008792058564722538,
0.001417488674633205,
-0.021579602733254433,
0.024751482531428337,
-0.05190010741353035,
0.004387881141155958,
0.02220829203724861,
0.03189217671751976,
0.031435564160346985,
-0.010485058650374413,
-0.004249771125614643,
0.06298889219760895,
0.009525538422167301,
0.043407559394836426,
0.025388916954398155,
0.10170523822307587,
-0.008497733622789383,
0.008734499104321003,
0.019908729940652847,
-0.021776247769594193,
0.004908819682896137,
0.006408638786524534,
-0.027867836877703667,
-0.02138110250234604,
0.026852166280150414,
-0.0055110277608036995,
0.046852461993694305,
-0.03161880746483803,
0.014172970317304134,
-0.0018230475252494216,
0.01909756287932396,
-0.02234445884823799,
0.08441049605607986,
0.021404465660452843,
-0.018773432821035385,
-0.05095459148287773,
0.03461238369345665,
-0.06660370528697968,
-0.03951328992843628,
-0.05674608796834946,
0.027271125465631485,
-0.009608842432498932,
-0.008263183757662773,
0.01477566733956337,
-0.039194256067276,
0.0057040005922317505,
-0.033681660890579224,
0.0693177804350853,
0.06072954460978508,
0.05232352390885353,
0.012062864378094673,
-0.013359610922634602,
0.00022728569456376135,
-0.030347032472491264,
0.033501237630844116,
0.038390565663576126,
-0.01984194479882717,
-0.03996353968977928,
-0.011364790610969067,
-0.007268956862390041,
0.011134968139231205,
0.029395658522844315,
0.01158960908651352,
0.023244651034474373,
-0.012531287968158722,
-0.07233162969350815,
-0.05395324155688286,
0.013995323330163956,
0.008786610327661037,
0.014131863601505756,
-0.056041523814201355,
0.007444149348884821,
0.054646361619234085,
0.08295299112796783,
-0.0028736398089677095,
-0.023801619186997414,
-0.021786771714687347,
0.05864035338163376,
0.024822069332003593,
-0.022875666618347168,
0.014199519529938698,
-0.019694466143846512,
-0.037352681159973145,
-0.017069313675165176,
-0.06878414005041122,
-0.0053244163282215595,
0.04782769829034805,
0.01812010630965233,
-0.01643751747906208,
0.1173764020204544,
-0.0056091295555233955,
0.011421545408666134,
0.007090755272656679,
0.006930181290954351,
-0.014346860349178314,
0.09671691805124283,
0.011067594401538372,
-0.019998986274003983,
0.005358790513128042,
0.028249138966202736,
0.03545013442635536,
0.0012164837680757046,
-0.04152527078986168,
0.018192628398537636,
-0.04954446107149124,
0.00806098710745573,
-0.020724454894661903,
-0.01777212880551815,
-0.02459798939526081,
-0.046986471861600876,
-0.021387577056884766,
-0.03291108459234238,
-0.03228782117366791,
0.0044852993451058865,
0.01869686134159565,
0.021759264171123505,
-0.03720724582672119,
0.020532727241516113,
-0.038085855543613434,
-0.012750023975968361,
-0.03862830251455307,
-0.03555271774530411,
-0.011962861754000187,
0.020569423213601112,
-0.00399148790165782,
0.02440754882991314,
-0.007704917341470718,
0.003624094882979989,
-0.019293654710054398,
0.04646969959139824,
0.035441067069768906,
-0.0397767648100853,
0.016786281019449234,
-0.014696608297526836,
0.0493287667632103,
0.005352213513106108,
-0.010498137213289738,
-0.0015142394695430994,
-0.00813318882137537,
-0.019802598282694817,
0.015642233192920685,
-0.021914534270763397,
0.02054867148399353,
-0.024595092982053757,
0.036850616335868835,
0.02486933022737503,
0.025589197874069214,
0.021023118868470192,
0.03518166020512581,
-0.027039164677262306,
0.07757028937339783,
0.021552948281168938,
0.0031554412562400103,
-0.01506605464965105,
0.02265351265668869,
0.0023629488423466682,
-0.0005200849263928831,
-0.0068490589037537575,
-0.030760861933231354,
-0.08521897345781326,
-0.0132235586643219,
0.031178070232272148,
-0.0006145154475234449,
-0.03898242488503456,
0.030244484543800354,
0.0045508136972785,
0.014624605886638165,
-0.008022193796932697,
0.017297344282269478,
0.004985840525478125,
-0.04286941885948181,
0.026187485083937645,
-0.02110491320490837,
0.01902819611132145,
0.0041535384953022,
0.023581257089972496,
-0.0339558944106102,
0.007656657136976719,
-0.0011103199794888496,
0.018772490322589874,
0.0029403148218989372,
0.004393286537379026,
0.015549521893262863,
-0.03146344795823097,
-0.0013684927253052592,
0.018320798873901367,
-0.02325338125228882,
0.021553482860326767,
0.01209127064794302,
-0.00016078766202554107,
-0.02081824094057083,
-0.0571705661714077,
-0.015145234763622284,
0.007239875849336386,
-0.007394689600914717,
-0.005343376658856869,
0.016271788626909256,
0.02772562764585018,
-0.0702536404132843,
0.030596258118748665,
-0.01596837490797043,
-0.03790193796157837,
-0.008598970249295235,
0.011634689755737782,
-0.022687092423439026,
0.041873347014188766,
0.01950082555413246,
-0.05747438594698906,
-0.02994626946747303,
0.010382183827459812,
-0.002715175971388817,
0.0013828198425471783,
0.030848968774080276,
-0.03787606209516525,
0.04646655544638634,
-0.03949495032429695,
-0.0321926511824131,
0.03956739604473114,
0.009209063835442066,
0.005172640550881624,
0.041936781257390976,
-0.014477270655333996,
-0.05253172665834427,
0.0009880901779979467,
-0.05462392047047615,
0.024555977433919907,
-0.044871021062135696,
-0.015002517029643059,
0.08849406987428665,
-0.02449977397918701,
-0.043655261397361755,
0.04136663302779198,
-0.02047840505838394,
-0.01973983645439148,
-0.005764931906014681,
0.02360941842198372,
0.0006676907069049776,
-0.030315419659018517,
0.02527134120464325,
0.019672801718115807,
-0.01391717977821827,
0.0012101525207981467,
-0.05506910756230354,
-0.07218807190656662,
0.03634703904390335,
0.005937368609011173,
0.010469400323927402,
0.004058147314935923,
0.003301297314465046,
0.03012988343834877,
0.037410084158182144,
-0.01364392600953579,
-0.02782471664249897,
0.02171589620411396,
-0.02092100866138935,
-0.029443912208080292,
-0.028256908059120178,
0.0039298804476857185,
0.00663538696244359,
0.005217107478529215,
0.010858593508601189,
0.03694167733192444,
0.023982971906661987,
0.034705229103565216,
-0.022545531392097473,
-0.016361456364393234,
0.008382312953472137,
0.01768518052995205,
0.03594131022691727,
-0.013264905661344528,
-0.028596775606274605,
-0.0025814520195126534,
-0.017240634188055992,
0.026767471805214882,
0.013564459048211575,
-0.043307945132255554,
0.039020538330078125,
0.01734202355146408,
0.01581663265824318,
-0.01719217747449875,
0.02608475461602211,
-0.021330369636416435,
-0.02450697124004364,
-0.0008642266620881855,
-0.01815887726843357,
0.05528860539197922,
0.017114097252488136,
0.048503756523132324,
0.0371723510324955,
0.03278172388672829,
-0.0031202102545648813,
-0.02055233158171177,
0.012113142758607864,
-0.0039040313567966223,
0.013899380341172218,
-0.03226352483034134,
-0.007497022859752178,
0.04556029662489891,
0.03151697292923927,
-0.020026419311761856,
0.06272939592599869,
-0.02962997928261757,
-0.029453005641698837,
-0.03822242096066475,
0.0067291283048689365,
-0.007106636185199022,
0.026063861325383186,
0.037104543298482895,
0.030514858663082123,
-0.0026136990636587143,
0.012519704177975655,
0.00032070890301838517,
-0.020333968102931976,
-0.11814462393522263,
-0.0074862162582576275,
-0.033618420362472534,
-0.02131274715065956,
-0.01482576783746481,
0.009891520254313946,
0.0014705437934026122,
-0.0030901157297194004,
-0.027110690250992775,
0.0061072115786373615,
-0.0072803134098649025,
-0.0699191689491272,
0.032934144139289856,
-0.0418558269739151,
-0.07433952391147614,
0.010867995209991932,
0.01667887158691883,
0.06543637812137604,
-0.00975640956312418,
-0.00820770300924778,
0.011025742627680302,
-0.026800056919455528,
0.0009373528882861137,
-0.02915896661579609,
0.006309169810265303,
-0.0016832529800012708,
0.01829327829182148,
0.02266072668135166,
-0.014709885232150555,
-0.0390680693089962,
0.00856519304215908,
0.04754997044801712,
0.021010635420680046,
-0.019152287393808365,
-0.01772349886596203,
-0.020039347931742668,
-0.04053177312016487,
-0.03205256536602974,
-0.04667454585433006,
0.06126488372683525,
-0.014547649770975113,
0.002087878528982401,
0.015322535298764706,
-0.010290877893567085,
0.019134845584630966,
0.05367877334356308,
0.0190361887216568,
-0.030116740614175797,
0.011583990417420864,
-0.018749553710222244,
-0.02903848886489868,
0.007435475941747427,
0.020399222150444984,
0.010532792657613754,
0.02642257884144783,
-0.058420516550540924,
0.0189936812967062,
0.009626639075577259,
0.010092206299304962,
0.0020022161770612,
-0.0019439931493252516,
-0.007751755882054567,
0.014808647334575653,
-0.019899534061551094,
0.026430418714880943,
0.005758327431976795,
0.03184688463807106,
0.09098075330257416,
0.006192467175424099,
0.005643473006784916,
-0.04727775231003761,
-0.047642916440963745,
0.01853141561150551,
0.04146889969706535,
0.01644650660455227,
-0.02724289707839489,
-0.06812327355146408,
-0.012265880592167377,
0.023577164858579636,
-0.029246971011161804,
0.03253215178847313,
0.010156523436307907,
0.026761388406157494,
-0.024119077250361443,
-0.016199801117181778,
-0.023149345070123672,
0.017649170011281967,
-0.04371282830834389,
-0.02262149751186371,
-0.019178641960024834,
-0.010417651385068893,
-0.025704074651002884,
0.01841004006564617,
0.02745344676077366,
0.04997699707746506,
0.03021513670682907,
0.005508631467819214,
-0.004151180386543274,
-0.006526795681566,
-0.0272497721016407,
-0.08862358331680298,
0.0028303188737481833,
0.018993046134710312,
-0.04089134559035301,
0.03224465623497963,
-0.013579300604760647,
0.01298736035823822,
0.017903629690408707,
0.018898263573646545,
-0.0014173011295497417,
-0.014312809333205223,
-0.06351878494024277,
0.039474405348300934,
0.04054803401231766,
-0.0010764262406155467,
0.037330932915210724,
0.0344674214720726,
-0.010005548596382141,
0.005147756543010473,
-0.0229131318628788,
0.003959063906222582,
-0.06263841688632965,
-0.0332397036254406,
-0.005139973014593124,
-0.020640335977077484,
-0.06699851900339127,
0.07229863852262497,
-0.019603164866566658,
0.006421373225748539,
0.011690717190504074,
-0.057772230356931686,
0.007440398447215557,
0.008268998004496098,
0.0027652878779917955,
0.05372275412082672,
-0.022991523146629333,
0.015131192281842232,
-0.010380369611084461,
-0.014313570223748684,
0.016351928934454918,
-0.0073074474930763245,
-0.02164210006594658,
0.04136081784963608,
-0.010939951986074448,
0.06770136952400208,
0.015492347069084644,
0.01859802007675171,
0.0005578179261647165,
-0.03640430420637131,
0.03389764949679375,
0.007821336388587952,
0.012436934746801853,
0.031234433874487877,
-0.02288854867219925,
-0.04152298346161842,
0.029500873759388924,
-0.011019924655556679,
0.010688294656574726,
-0.03534520044922829,
0.03571118041872978,
0.047758799046278,
0.0006002540467306972,
-0.07307935506105423,
-0.015549086965620518,
0.02306995540857315,
0.01233950350433588,
-0.003043352160602808,
-0.008446352556347847,
-0.008214481174945831,
-0.053505610674619675,
-0.03985515609383583,
-0.02495536394417286,
0.03152802586555481,
-0.01311679556965828,
0.0009636852191761136,
-0.0028305300511419773,
0.02833430841565132,
0.0154082290828228,
0.003630297724157572,
-0.021203257143497467,
-0.005979370791465044,
0.01935054548084736,
0.027834415435791016,
-0.006707711145281792,
0.038977157324552536,
-0.0032571223564445972,
-0.00787961483001709,
-0.047460414469242096,
0.009660417214035988,
0.0055017126724123955,
-0.018795518204569817,
-0.014310542494058609,
0.09662577509880066,
0.008141378872096539,
-0.012029002420604229,
-0.02388026937842369,
0.007238189689815044,
-0.044965486973524094,
0.04466276988387108,
-0.03339898958802223,
-0.010450341738760471,
0.01972845569252968,
-0.07942163944244385,
0.033352285623550415,
-0.021589817479252815,
0.008638862520456314,
0.00597313791513443,
0.024803711101412773,
-0.01824065111577511,
-0.000332676456309855,
-0.02598418854176998,
-0.043088119477033615,
0.03853317350149155,
-0.0173054002225399,
0.014114475809037685,
-0.004611974116414785,
-0.009590217843651772,
-0.035125602036714554,
-0.04347359761595726,
-0.040957510471343994,
-0.023522114381194115,
0.07013408839702606,
0.036162808537483215,
0.02305249124765396,
0.009823801927268505,
0.018573446199297905,
-0.019641408696770668,
-0.043756406754255295,
0.008435489609837532,
0.003878559684380889,
-0.006415253970772028,
0.016799412667751312,
-0.04124322161078453,
0.02277955412864685,
0.04555672034621239,
0.04076872020959854,
-0.004766526166349649,
0.04464375600218773,
0.00952322781085968,
0.04709243029356003,
0.03969617187976837,
0.01597735472023487,
-0.011877460405230522,
0.01406884379684925,
-0.04855579510331154,
0.016112100332975388,
0.023867573589086533,
0.022880738601088524,
0.03447455167770386,
0.030874086543917656,
0.03763456642627716,
-0.03936304524540901,
0.002457528840750456,
-0.04477474465966225,
-0.007803397718816996,
-0.023210005834698677,
0.03045998327434063,
-0.009907987900078297,
-0.006581381894648075,
0.02280127815902233,
-0.010978368110954762,
0.02909022383391857,
-0.0003664442920126021,
-0.06688525527715683,
-0.021342063322663307,
-0.05832767114043236,
0.009016952477395535,
0.04718470573425293,
0.007988308556377888,
-0.025074034929275513,
0.010230259038507938,
-0.04701385647058487,
-0.002766743768006563,
0.037647001445293427,
0.0627291351556778,
0.02296786569058895,
0.03704605624079704,
-0.03340490162372589,
0.008395692333579063,
-0.05619056522846222,
-0.006213457323610783,
0.1472034454345703,
0.0532456636428833,
0.00955805741250515,
-0.0384250171482563,
0.03176800534129143,
-0.0016441256739199162,
0.026880968362092972,
-0.029241714626550674,
0.01818319410085678,
-0.019511764869093895,
0.019737226888537407,
0.043421655893325806,
0.07410381734371185,
-0.013424744829535484,
-0.027296889573335648,
0.027572151273489,
-0.04331180825829506,
0.01587539166212082,
0.01345848012715578,
0.04118305817246437,
0.013224530965089798,
0.009710977785289288,
0.006249676924198866,
0.02903839573264122,
-0.005322495009750128,
-0.02626492828130722,
-0.032846588641405106,
-0.015496866777539253,
-0.005542964208871126,
-0.031233299523591995,
-0.05723925307393074,
-0.0003178599290549755,
0.006729577202349901,
-0.04602727293968201,
-0.01908760704100132,
0.012292057275772095,
0.01793653331696987,
-0.017442358657717705,
0.027556292712688446,
0.040560077875852585,
0.009057490155100822,
-0.008019951172173023,
0.009273692965507507,
0.01576957292854786,
0.0008267515222541988,
0.017359694465994835,
-0.00266485963948071,
0.05029325559735298,
-0.015493340790271759,
0.00822195690125227,
0.0018635396845638752,
-0.01752570830285549,
0.03168543800711632,
-0.05795614793896675,
-0.0007925250101834536,
-0.0009428101475350559,
-0.025272002443671227,
-0.030231304466724396,
-0.011951559223234653,
-0.01941126026213169,
0.02145879715681076,
0.04198621213436127,
0.013356445357203484,
0.004300949163734913,
0.012289125472307205,
-0.011868773959577084,
-0.02921322174370289,
0.040806517004966736,
0.0066727581433951855,
-0.008659160695970058,
-0.015910889953374863,
0.001218688441440463,
-0.04331570118665695,
0.0023722604382783175,
-0.009089539758861065,
0.018827492371201515,
0.02921074815094471,
0.023305604234337807,
0.015904705971479416,
-0.027902482077479362,
-0.06622347235679626,
0.011019818484783173,
-0.00009565339860273525,
0.0042829979211091995,
-0.01328843180090189,
0.012066868133842945,
0.024750037118792534,
0.02577698603272438,
-0.0059736319817602634,
-0.0006619071937166154,
0.02723618410527706,
0.050753891468048096,
0.014680124819278717,
-0.003056760411709547,
-0.008060699328780174,
0.01288234069943428,
-0.02376367524266243,
-0.011564858257770538,
-0.02735885977745056,
0.04029275104403496,
0.004848912358283997,
0.01648012176156044,
-0.00799263920634985,
0.036949679255485535,
-0.02224944718182087,
-0.006927526090294123,
0.030137600377202034,
-0.015413525514304638,
-0.004527476616203785,
0.03287915512919426,
0.030664224177598953,
-0.031070059165358543,
0.0020729422103613615,
-0.004119877703487873,
0.024375412613153458,
-0.03689469024538994,
0.009849817492067814,
-0.034981291741132736,
0.05244613066315651,
-0.004827127791941166,
0.014476919546723366,
-0.04812845587730408,
0.01234822440892458,
-0.04611807316541672,
-0.004594773054122925,
0.013379176147282124,
-0.0088403495028615,
0.011742470785975456,
0.023265888914465904,
-0.03053002431988716,
-0.055473364889621735,
0.02577061951160431,
0.019256163388490677,
-0.062517911195755,
0.002542321803048253,
0.013312635011970997,
0.01523654442280531,
-0.00840684026479721,
0.03537001833319664,
-0.038455780595541,
0.02829856611788273,
-0.02161276526749134,
-0.05160333588719368,
0.03337252885103226,
0.020069802179932594,
0.0207058172672987,
0.006078657228499651,
-0.021888257935643196,
-0.001543172518722713,
0.04042183235287666,
0.018365975469350815,
-0.008753353729844093,
-0.03317621722817421,
-0.02259794995188713,
0.02866329811513424,
0.007326597347855568,
0.02929006889462471,
-0.00024113785184454173,
0.009736243635416031,
0.04029463976621628,
0.006503012962639332,
-0.01373796071857214,
0.016050081700086594,
-0.02398492954671383,
-0.030305922031402588,
-0.01893131621181965,
-0.03300157189369202,
0.016815433278679848,
0.03197591379284859,
0.06555189937353134,
-0.06930519640445709,
0.0411607101559639,
0.017209457233548164,
-0.009191203862428665,
-0.11490356922149658,
-0.024228164926171303,
0.035123251378536224,
0.01311073824763298,
0.024882547557353973,
-0.0407121405005455,
0.04491395503282547,
0.013597669079899788,
-0.048500701785087585,
0.03314941003918648,
-0.020461084321141243,
0.014919235371053219,
-0.034203868359327316,
0.02797861397266388,
-0.03353777900338173,
0.003529726294800639,
0.04569118469953537,
0.036475446075201035,
-0.013133376836776733,
0.020480850711464882,
-0.02796378917992115,
-0.019687946885824203,
-0.01370586734265089,
0.02833634614944458,
-0.002124717691913247,
-0.0028666879516094923,
0.09582706540822983,
0.01439633872359991,
-0.013559676706790924,
0.035724036395549774,
0.013932731933891773,
-0.01351019274443388,
-0.03359723463654518,
-0.021074719727039337,
0.042731963098049164,
-0.00571181857958436,
0.025004670023918152,
-0.0067998799495399,
-0.01879343017935753,
-0.004905611742287874,
0.02697327919304371,
-0.004458016250282526,
-0.0040690479800105095,
0.01334893237799406,
0.0014150297502055764,
-0.04115796834230423,
0.025328241288661957,
0.003205682849511504,
-0.019636843353509903,
-0.006377277430146933,
0.013299388810992241,
0.024609610438346863,
0.0023349630646407604,
0.001155369565822184,
-0.020042408257722855,
-0.06325973570346832,
-0.021200938150286674,
0.031684767454862595,
-0.01945369318127632,
0.02548270672559738,
0.016249900683760643,
-0.027598503977060318,
-0.0175545085221529,
0.012233651243150234,
-0.04530768468976021,
0.010575964115560055,
-0.022769277915358543,
-0.004436457064002752,
-0.02888466790318489,
0.03105553798377514,
0.02863139472901821,
-0.04179733991622925,
-0.02860281988978386,
0.030526038259267807,
-0.007683191914111376,
-0.001105423434637487,
-0.02217136323451996,
-0.03599241003394127,
-0.011289883404970169,
-0.04015039652585983,
0.014991779811680317,
0.024793531745672226,
0.00041827422683127224,
-0.046062320470809937,
-0.03803228959441185,
0.00965714082121849,
0.004911104217171669,
0.06309618800878525,
-0.008623050525784492,
-0.027384554967284203,
0.04196065291762352,
-0.03645612299442291,
0.024920886382460594,
-0.05359744280576706,
0.027698716148734093,
0.015910593792796135,
-0.02640705741941929,
-0.0044000712223351,
-0.004254806321114302,
-0.015334457159042358,
0.028542714193463326,
0.058875683695077896,
-0.008395984768867493,
0.07923554629087448,
0.0031299598049372435,
-0.015034622512757778,
0.04618406668305397,
0.025806846097111702,
-0.010136589407920837,
0.02928086370229721,
0.015874644741415977,
0.04410663619637489,
0.047314196825027466,
0.002634929958730936,
-0.019481826573610306,
0.00614545401185751,
-0.022367913275957108,
-0.015785522758960724,
0.008550106547772884,
-0.024106169119477272,
0.021927060559391975,
-0.052528318017721176,
-0.04223437234759331,
0.017155496403574944,
-0.028530646115541458,
-0.023128710687160492,
0.04603271931409836,
-0.002907717600464821,
0.03391424939036369,
0.02196457050740719,
0.019217096269130707,
-0.016264306381344795,
-0.009607617743313313,
-0.01804175041615963,
0.05264677852392197,
0.03976086527109146,
0.0010277366964146495,
0.03870975598692894,
0.022995559498667717,
-0.03532388061285019,
-0.006368343252688646,
-0.035550422966480255,
0.040803346782922745,
-0.0748881846666336,
-0.021383345127105713,
-0.005218478385359049,
-0.004225794691592455,
0.017541954293847084,
0.04997262731194496,
-0.0166903268545866,
0.06479063630104065,
0.002562206005677581,
0.03907182440161705,
0.00810796394944191,
-0.01602725312113762,
-0.026546921581029892,
0.0794236809015274,
-0.0010916395112872124,
0.05712387338280678,
0.03885911405086517,
-0.009919854812324047,
-0.02812531217932701,
0.0023895541671663523,
0.010760351084172726,
-0.03083237260580063,
-0.001296165632084012,
-0.003477533580735326,
-0.025366127490997314,
0.012964784167706966,
-0.015683086588978767,
0.024577217176556587,
-0.03576234355568886,
0.039654020220041275,
0.03609069064259529,
0.04242775961756706,
-0.023727212101221085,
-0.043962426483631134,
-0.05028260126709938,
0.030308008193969727,
-0.054001133888959885,
0.01213663537055254,
0.02984665147960186,
0.005773909855633974,
-0.025959325954318047,
-0.032818958163261414
] |
<p>This is the known equation of air drag:</p>
<p>$$m{\bf a}=mg-\mathcal D=mg-b{\bf v}.$$</p>
<p>Considering this, is air drag equation in term of momentum still valid?</p>
<p>$$m{\bf v}=mv_g-b{\bf r}.$$</p> | 2,860 | [
-0.023352421820163727,
0.00041714328108355403,
-0.05004091560840607,
-0.000593568489421159,
0.023996926844120026,
-0.01154307834804058,
-0.052703335881233215,
-0.014795143157243729,
0.011983433738350868,
-0.013277396559715271,
0.02181946113705635,
0.046510908752679825,
0.05759024992585182,
0.0007963120588101447,
0.013707674108445644,
-0.017876284196972847,
-0.017098361626267433,
0.011002683080732822,
0.03919588774442673,
-0.0009116310975514352,
-0.02888212725520134,
0.00014049740275368094,
0.02697703056037426,
0.00468476302921772,
-0.0017045208951458335,
0.006417963653802872,
0.04555130749940872,
-0.009724884293973446,
0.012166946195065975,
0.03566472977399826,
-0.002332333941012621,
0.004184363409876823,
0.029216481372714043,
0.014039475470781326,
-0.008668282069265842,
0.015524857677519321,
-0.031802959740161896,
-0.022829433903098106,
-0.03037339076399803,
0.03538117930293083,
-0.02215859852731228,
-0.021429169923067093,
-0.010445121675729752,
0.04946710914373398,
-0.013425949960947037,
0.0491408109664917,
-0.0038133689668029547,
-0.011054101400077343,
0.042478423565626144,
-0.06690925359725952,
0.08521228283643723,
-0.005314130801707506,
0.054012734442949295,
0.03416639193892479,
-0.035484880208969116,
-0.0322725884616375,
0.062249891459941864,
0.08717039972543716,
-0.015156538225710392,
-0.0272113885730505,
0.014026924036443233,
-0.03490588068962097,
-0.004878654144704342,
-0.006689775735139847,
-0.016561543568968773,
0.024396944791078568,
-0.018334032967686653,
-0.009243633598089218,
0.0430179238319397,
0.018753090873360634,
0.029454823583364487,
0.010277067311108112,
0.041369084268808365,
-0.019493425264954567,
0.03667687997221947,
-0.01319943368434906,
0.03855292499065399,
0.0026767521630972624,
0.045462168753147125,
0.08880148828029633,
-0.021709753200411797,
0.021949006244540215,
0.02068239264190197,
0.018119679763913155,
0.032823752611875534,
-0.022013504058122635,
0.057105567306280136,
-0.0010827342048287392,
-0.024234820157289505,
-0.010136442258954048,
0.01516877580434084,
-0.03293944150209427,
0.032846152782440186,
-0.0023809673730283976,
0.004140048287808895,
0.012263720855116844,
-0.000223006252781488,
0.04062306135892868,
0.020539572462439537,
-0.02971254102885723,
0.010095912963151932,
-0.0031235769856721163,
0.03276952728629112,
0.06557849794626236,
-0.002419510157778859,
-0.0054646446369588375,
-0.027586882933974266,
-0.004422722849994898,
-0.026520369574427605,
-0.004725662991404533,
-0.044885192066431046,
0.008824428543448448,
-0.03571152314543724,
-0.04478941485285759,
0.01270847674459219,
-0.019892165437340736,
0.019699806347489357,
0.0005468580056913197,
0.06871837377548218,
0.07641519606113434,
0.0331139899790287,
-0.02023719809949398,
0.010396144352853298,
0.004865160211920738,
-0.052985336631536484,
0.017401499673724174,
0.01684701442718506,
-0.022017186507582664,
-0.05200441554188728,
0.0083408672362566,
-0.024716641753911972,
-0.011681153438985348,
0.012927776202559471,
-0.007089922670274973,
0.0328848697245121,
-0.035613469779491425,
-0.10593023896217346,
-0.05354814976453781,
0.009381810203194618,
-0.015843531116843224,
-0.01334427297115326,
-0.07842928171157837,
-0.01728292554616928,
-0.013291249051690102,
0.06999759376049042,
0.01320341695100069,
0.03884219005703926,
-0.008029136806726456,
0.049779076129198074,
-0.04651850834488869,
-0.01465432159602642,
-0.022518496960401535,
0.028596417978405952,
-0.04115734249353409,
-0.023107754066586494,
-0.0829550251364708,
0.03160955756902695,
0.03000536561012268,
-0.00820949301123619,
-0.02842686139047146,
0.05338442698121071,
-0.019907286390662193,
-0.005038544535636902,
-0.008635764010250568,
0.01353289745748043,
-0.022178377956151962,
0.019816357642412186,
0.04140960052609444,
0.018871480599045753,
0.030020220205187798,
0.03920198231935501,
0.030638312920928,
-0.002433883724734187,
-0.021981438621878624,
0.05264057591557503,
-0.012513203546404839,
-0.011661233380436897,
-0.04664984717965126,
0.010333487764000893,
-0.012043346650898457,
-0.0461387075483799,
-0.04057098552584648,
0.008146057836711407,
0.004752941895276308,
-0.002417059848085046,
0.05474291741847992,
0.0014338907785713673,
-0.001451632590033114,
-0.010614029131829739,
-0.03254580870270729,
-0.03770643472671509,
-0.09484881162643433,
0.03887098282575607,
-0.021001914516091347,
0.014979533851146698,
-0.005542256403714418,
0.0025251919869333506,
0.043588366359472275,
-0.02266073226928711,
-0.005851792637258768,
-0.0008901968831196427,
0.03447558730840683,
-0.005507820751518011,
0.009531337767839432,
-0.002097519813105464,
0.0370548740029335,
0.029839741066098213,
-0.00016172394680324942,
0.028733814135193825,
0.011834654025733471,
-0.04040741175413132,
-0.001648479956202209,
-0.034966252744197845,
0.011800886131823063,
0.020731527358293533,
-0.006720092613250017,
0.068852499127388,
0.0053353807888925076,
0.006543864496052265,
0.008844459429383278,
-0.0074648926965892315,
0.06600731611251831,
0.04242049157619476,
0.038207247853279114,
0.01114747580140829,
0.027377285063266754,
0.030003657564520836,
-0.005241795442998409,
0.016971789300441742,
-0.00808724295347929,
-0.026084724813699722,
-0.0035281458403915167,
0.026351619511842728,
0.01687708869576454,
-0.05613873153924942,
0.03836417943239212,
0.04786810651421547,
0.006063181906938553,
0.06858847290277481,
0.059812888503074646,
0.012243329547345638,
-0.07736828178167343,
0.019532136619091034,
0.04797481745481491,
0.007109725382179022,
0.021327998489141464,
0.007468588650226593,
0.04626797139644623,
0.022562464699149132,
-0.03749443218111992,
0.001584134646691382,
0.033090975135564804,
0.03792337700724602,
-0.026368223130702972,
-0.01898323744535446,
-0.037701211869716644,
0.06407686322927475,
-0.040440820157527924,
0.048704542219638824,
0.042194440960884094,
0.010076034814119339,
0.014237112365663052,
-0.015203569084405899,
-0.02891169860959053,
0.007918923161923885,
-0.0028995692264288664,
0.0022026922088116407,
-0.012685263529419899,
0.0349884107708931,
-0.022784901782870293,
0.003555380506440997,
-0.05518706887960434,
0.01379250455647707,
-0.03328246995806694,
-0.009934665635228157,
0.01894851215183735,
0.0010683229193091393,
0.052510377019643784,
0.015438629314303398,
-0.0386219285428524,
-0.017543088644742966,
-0.03436669707298279,
-0.028473343700170517,
0.004994499962776899,
-0.043615832924842834,
0.015849942341446877,
-0.034310463815927505,
-0.03582065925002098,
0.06555894017219543,
-0.007231066469103098,
0.012280598282814026,
0.0323614701628685,
-0.0002623455075081438,
-0.04835096374154091,
0.010029367171227932,
-0.034101925790309906,
-0.005177525337785482,
-0.014897073619067669,
-0.020914889872074127,
0.03818235546350479,
-0.009391838684678078,
-0.02098400890827179,
0.01960667595267296,
-0.029580118134617805,
-0.047292351722717285,
-0.006384826265275478,
-0.0049221096560359,
0.020909644663333893,
-0.03795911744236946,
0.029056139290332794,
0.0518421046435833,
-0.03814658150076866,
0.0014157947152853012,
-0.02352619171142578,
-0.037744950503110886,
0.017953429371118546,
-0.018511351197957993,
0.06062669679522514,
0.00473704282194376,
-0.06164376065135002,
0.08199049532413483,
0.031979650259017944,
-0.03779429569840431,
0.022038161754608154,
-0.046148862689733505,
-0.0025536275934427977,
-0.03886733576655388,
-0.03353874012827873,
0.029091935604810715,
0.00942325871437788,
0.015111793763935566,
0.01764603704214096,
0.004646585322916508,
0.012815747410058975,
0.002308803843334317,
-0.01436419878154993,
-0.018178733065724373,
0.032054491341114044,
-0.019980061799287796,
0.06558714807033539,
-0.008309070020914078,
-0.013961391523480415,
0.006686674430966377,
-0.02810906060039997,
0.07125639915466309,
0.02469024993479252,
-0.0654463842511177,
0.07503762096166611,
-0.03770141303539276,
0.019740696996450424,
-0.014500499702990055,
0.019613215699791908,
0.006176167167723179,
0.009663398377597332,
0.016056617721915245,
0.023298783227801323,
0.02967519499361515,
-0.001999134663492441,
0.012039565481245518,
0.0334307923913002,
0.04111894965171814,
-0.012678206898272038,
-0.03520835563540459,
-0.0034175957553088665,
-0.015088451094925404,
0.0303823072463274,
0.005855442490428686,
-0.029285375028848648,
0.02599002979695797,
0.028552958741784096,
0.03274872899055481,
0.0002969088964164257,
-0.0407622829079628,
0.03396258130669594,
-0.07293212413787842,
-0.0032112684566527605,
-0.018511146306991577,
0.03647686168551445,
-0.014646937139332294,
0.040818728506565094,
0.0033090400975197554,
0.029681043699383736,
0.023767903447151184,
0.0006808370817452669,
-0.08496089279651642,
0.01917976886034012,
-0.027330175042152405,
-0.03246649354696274,
-0.018630066886544228,
-0.02068115770816803,
-0.007563275750726461,
-0.030579520389437675,
-0.008530289866030216,
-0.003308864776045084,
-0.019841482862830162,
-0.05180688947439194,
0.00630610529333353,
-0.042135968804359436,
-0.03983042389154434,
0.029067983850836754,
0.03816291689872742,
0.029361672699451447,
-0.008509129285812378,
0.0261556264013052,
0.07842455804347992,
-0.03231610357761383,
-0.05453762412071228,
-0.03255821391940117,
0.004020893946290016,
-0.011242811568081379,
0.012805309146642685,
0.033594392240047455,
-0.0018892793450504541,
-0.03227436542510986,
0.004609462805092335,
0.023824164643883705,
0.03658725321292877,
-0.03754834458231926,
0.015450776554644108,
-0.046958714723587036,
-0.07234858721494675,
-0.0348723903298378,
0.014464004896581173,
0.0030120795127004385,
-0.006696369033306837,
0.008953097276389599,
0.015844520181417465,
0.016559038311243057,
-0.016254058107733727,
0.0763964131474495,
0.04910583421587944,
0.010723595507442951,
0.012509281747043133,
-0.0701582133769989,
0.04040465131402016,
-0.019709985703229904,
-0.054428551346063614,
0.023084700107574463,
0.015198154374957085,
-0.023262429982423782,
-0.005332819186151028,
0.03216201066970825,
0.04401813820004463,
-0.008919126354157925,
0.04854460805654526,
-0.001514064148068428,
0.010950873605906963,
0.029852934181690216,
0.003872224595397711,
-0.005173736717551947,
0.05287672206759453,
0.0011364197125658393,
0.03883103281259537,
-0.004600981716066599,
-0.06566933542490005,
0.004941190127283335,
0.04096480831503868,
0.03887869045138359,
-0.04627716541290283,
0.0014300363836809993,
-0.05754691734910011,
-0.020253686234354973,
0.05409311503171921,
-0.011126255616545677,
0.022147206589579582,
-0.03743257373571396,
0.01839541643857956,
0.02480606734752655,
-0.01285929698497057,
-0.0020987633615732193,
0.032113488763570786,
0.003598329145461321,
-0.06071670353412628,
-0.019393814727663994,
0.0015364846913143992,
0.020099861547350883,
0.03366227075457573,
0.019997231662273407,
0.0538875088095665,
0.007633669301867485,
-0.024156149476766586,
-0.032285626977682114,
0.004426832776516676,
-0.06354275345802307,
-0.07681722939014435,
-0.01032171305269003,
-0.00777497049421072,
0.00039296119939535856,
-0.002637903206050396,
-0.018710767850279808,
-0.06070772930979729,
0.04800849035382271,
-0.0195038802921772,
-0.0017283351626247168,
-0.0018018808914348483,
-0.03514932468533516,
0.013759690336883068,
0.020130164921283722,
-0.026897573843598366,
0.021152377128601074,
0.06292396038770676,
-0.016028273850679398,
-0.0074754152446985245,
0.006288318429142237,
0.019621247425675392,
-0.016246620565652847,
-0.006594447884708643,
-0.03468344733119011,
0.008892100304365158,
-0.007768277078866959,
0.03793972358107567,
0.004789724014699459,
0.029029974713921547,
0.010324766859412193,
-0.055180877447128296,
-0.014763528481125832,
-0.0020886226557195187,
0.016764380037784576,
-0.0365777388215065,
0.018774619325995445,
0.024166293442249298,
-0.010267572477459908,
-0.023139851167798042,
-0.005821868311613798,
0.023205304518342018,
0.015286901965737343,
0.022655179724097252,
-0.0014140061102807522,
-0.012535663321614265,
-0.0031366078183054924,
-0.015301894396543503,
-0.00216841883957386,
-0.04983590543270111,
0.05986832082271576,
-0.013089832849800587,
-0.024017710238695145,
0.021644577383995056,
-0.0626455694437027,
-0.03037574701011181,
0.033904507756233215,
0.028426695615053177,
0.021125268191099167,
-0.045313820242881775,
0.03995991870760918,
0.031830232590436935,
0.002830886049196124,
-0.04840456321835518,
-0.029308920726180077,
0.004095813725143671,
0.0057737925089895725,
-0.013334542512893677,
-0.03072994574904442,
-0.024271836504340172,
-0.047157421708106995,
-0.03838504105806351,
0.008549674414098263,
0.055240534245967865,
-0.0099519407376647,
-0.02891095168888569,
0.011678336188197136,
-0.010130017064511776,
0.032180093228816986,
-0.004383672494441271,
-0.02451672963798046,
0.004586954601109028,
-0.017586752772331238,
0.025863878428936005,
0.007386553101241589,
0.052443183958530426,
-0.006578520871698856,
0.033479709178209305,
0.01034651231020689,
-0.06009538099169731,
0.0623759925365448,
-0.0077714212238788605,
0.02543015405535698,
0.022201670333743095,
-0.019453123211860657,
0.01062141451984644,
-0.0057683298364281654,
0.042262934148311615,
-0.0012903789756819606,
0.030115151777863503,
-0.007397195789963007,
0.01135425828397274,
-0.031273677945137024,
0.010222344659268856,
0.030914580449461937,
-0.013501940295100212,
0.013628441840410233,
-0.004336146637797356,
0.06694168597459793,
-0.028428582474589348,
-0.012871582992374897,
0.011544465087354183,
0.0003416146500967443,
0.03461950272321701,
0.00902295671403408,
0.003806230379268527,
-0.009420624002814293,
0.015052000992000103,
-0.011447081342339516,
-0.0629776269197464,
-0.006448838394135237,
0.006204984150826931,
0.06902763992547989,
-0.038853131234645844,
0.04163127765059471,
-0.005779388826340437,
0.018298279494047165,
-0.005948800593614578,
-0.020612040534615517,
-0.014017224311828613,
0.011248106136918068,
-0.008557473309338093,
0.031354568898677826,
0.004746712744235992,
0.019328584894537926,
0.015445634722709656,
-0.014533495530486107,
0.02195855788886547,
0.0010119294747710228,
0.01515983883291483,
0.01089983806014061,
0.031797509640455246,
0.027988962829113007,
-0.030390974134206772,
0.05201221629977226,
-0.049913834780454636,
0.044168621301651,
-0.011473745107650757,
-0.0008591543883085251,
0.04147908091545105,
0.02746729366481304,
-0.029854532331228256,
-0.03831879794597626,
0.0003207652480341494,
-0.029308641329407692,
0.009410792961716652,
-0.0021962502505630255,
0.010676026344299316,
0.021828122437000275,
0.0058629014529287815,
0.0442185178399086,
0.018292702734470367,
0.044993624091148376,
-0.010884039103984833,
-0.02905825711786747,
-0.013314885087311268,
-0.03894660621881485,
-0.030443064868450165,
0.013395871967077255,
0.005583941005170345,
-0.021114375442266464,
-0.009547151625156403,
-0.015867898240685463,
0.023820606991648674,
-0.01861603744328022,
0.021517464891076088,
0.01207794900983572,
0.09855867177248001,
-0.0193305853754282,
-0.0027753307949751616,
-0.0001458008773624897,
0.01943052187561989,
0.10193923860788345,
0.030828064307570457,
0.04520749673247337,
-0.05770748108625412,
-0.02189774066209793,
-0.02541768178343773,
-0.013296481221914291,
-0.046287693083286285,
0.04476888105273247,
-0.01847241073846817,
0.010873009450733662,
0.00797770731151104,
0.058165326714515686,
-0.009788919240236282,
-0.0023475568741559982,
0.030860552564263344,
-0.02772511914372444,
-0.0588047131896019,
-0.023701326921582222,
0.009753578342497349,
-0.025654874742031097,
0.011484513059258461,
-0.0216276403516531,
0.005601954180747271,
0.005195586476475,
0.002744316356256604,
0.01860281080007553,
-0.02391471341252327,
0.011840593069791794,
-0.0018764656269922853,
-0.053522076457738876,
0.0015936041017994285,
0.002668465254828334,
0.01635679043829441,
-0.054922815412282944,
-0.032829608768224716,
0.011926960200071335,
-0.03327814117074013,
0.01786952093243599,
0.03544500097632408,
0.019345823675394058,
0.004324063193053007,
0.009981770999729633,
-0.007988427765667439,
-0.050745077431201935,
-0.017551979050040245,
-0.04010035842657089,
0.022424785420298576,
-0.027680866420269012,
0.03395619988441467,
0.009292319416999817,
0.004865435417741537,
-0.016420235857367516,
-0.08365090191364288,
-0.02524612471461296,
-0.006441344972699881,
0.05607910826802254,
-0.03671857342123985,
-0.029295677319169044,
-0.03722637519240379,
0.004401781130582094,
0.005745605565607548,
0.024922329932451248,
-0.02313847281038761,
-0.007067728787660599,
-0.01026223786175251,
0.0049739982932806015,
0.08006326109170914,
-0.0374281220138073,
-0.045338284224271774,
-0.028361385688185692,
-0.02379150688648224,
-0.02634175308048725,
-0.026197858154773712,
0.037869036197662354,
0.05619928613305092,
0.024940764531493187,
0.025237098336219788,
0.019284525886178017,
-0.03230882063508034,
-0.04920011758804321,
0.04675879329442978,
-0.01784895360469818,
-0.00591622618958354,
-0.009614436887204647,
-0.00916837714612484,
0.018782272934913635,
0.05691063776612282,
-0.017200946807861328,
-0.012587550096213818,
-0.004404240287840366,
0.013972112908959389,
0.010526456870138645,
-0.06099309027194977,
-0.06050414219498634,
0.008561638183891773,
-0.05286980792880058,
0.029163535684347153,
0.02476430870592594,
0.024126620963215828,
-0.016347631812095642,
0.006403438281267881,
-0.0425376258790493,
0.041860662400722504,
0.011188948526978493,
0.038210537284612656,
0.004978683777153492,
-0.034567397087812424,
0.0314447246491909,
0.002343171974644065,
0.013482924550771713,
-0.023797346279025078,
-0.010218107141554356,
-0.04681815207004547,
0.008154856972396374,
0.0008498479728586972,
-0.014237465336918831,
-0.022132525220513344,
0.0228477381169796,
-0.012474880553781986,
0.017376840114593506,
-0.05114642530679703,
-0.0055600618943572044,
-0.041020672768354416,
-0.0009670493309386075,
-0.01263935212045908,
-0.03410986438393593,
-0.0074176304042339325,
0.024942994117736816,
-0.07491544634103775,
0.04008358344435692,
0.02747347578406334,
0.034767407923936844,
-0.011190940625965595,
-0.02769182063639164,
-0.00640093581750989,
0.011560383252799511,
0.061577022075653076,
-0.018260153010487556,
-0.018341505900025368,
0.07101628929376602,
0.0034260626416653395,
-0.06627272069454193,
0.04717916622757912,
0.012038148008286953,
0.04042569547891617,
0.036656469106674194,
-0.018757473677396774,
-0.022839663550257683,
0.08083635568618774,
-0.004296399187296629,
0.03547834977507591,
0.006460173055529594,
-0.03992768004536629,
-0.006276524625718594,
-0.023826714605093002,
0.005336725153028965,
-0.010611744597554207,
-0.017877645790576935,
0.0354461744427681,
0.014679323881864548,
-0.0331992581486702,
-0.0010609679156914353,
0.04398873448371887,
-0.004626442212611437,
0.004670672118663788,
0.037498269230127335,
0.025579718872904778,
0.016063880175352097,
0.0480080172419548,
-0.011751975864171982,
-0.0009136342559941113,
0.01115935668349266,
0.0005523113068193197,
-0.10911104083061218,
-0.004531546961516142,
0.02240675501525402,
0.013272267766296864,
0.008220497518777847,
-0.07436206191778183,
0.017118219286203384,
0.014098946005105972,
-0.06350497156381607,
-0.0609920509159565,
-0.019946133717894554,
-0.012042813934385777,
-0.02518787607550621,
0.01039698626846075,
0.025885222479701042,
0.013584298081696033,
0.0011672187829390168,
0.015193182975053787,
0.019669843837618828,
0.0077295429073274136,
-0.011097609996795654,
-0.015729080885648727,
-0.021991610527038574,
0.005178972613066435,
-0.034208353608846664,
-0.011591783724725246,
0.03381814807653427,
-0.03693844750523567,
-0.01844274438917637,
0.02405906841158867,
0.007474025711417198,
0.050349969416856766,
-0.019100772216916084,
0.021387021988630295,
0.00094961206195876,
0.005990392062813044,
0.05358927696943283,
0.002670290879905224,
-0.02764906734228134,
0.026700181886553764,
-0.01893468014895916,
0.04148798808455467,
-0.032131828367710114,
-0.007598464377224445,
-0.02798006497323513,
-0.029177673161029816,
-0.05243683233857155,
0.03428293764591217,
-0.04258054122328758,
-0.034888528287410736,
-0.028367387130856514,
-0.012583071365952492,
-0.004572077188640833,
-0.030899357050657272,
0.000494890206027776,
-0.06099042668938637,
0.01193441916257143,
0.039920151233673096,
-0.04541290923953056,
-0.02094694972038269,
0.02813214436173439,
0.022916147485375404,
-0.018023304641246796,
0.021228179335594177,
-0.015348074026405811,
-0.01832512393593788,
-0.05432295426726341,
-0.0009973107371479273,
-0.006757248193025589,
-0.013642644509673119,
-0.0361514650285244,
-0.06305305659770966,
0.0037816453259438276,
0.023628918454051018,
0.04212404787540436,
0.027932582423090935,
0.02547324448823929,
-0.009713596664369106,
-0.030562125146389008,
-0.041568852961063385,
0.03003743663430214,
-0.0015286279376596212,
-0.02301514893770218,
-0.03282473608851433,
-0.022033097222447395,
0.037840817123651505,
-0.01934203878045082,
0.047881897538900375,
-0.025504574179649353,
-0.01070812065154314,
0.03982695937156677,
-0.0014123799046501517,
-0.005192234180867672,
-0.017636483535170555,
-0.013537445105612278,
-0.00006465216574724764,
-0.010564117692410946,
-0.01043574046343565,
-0.006368601229041815,
-0.021322261542081833,
0.022104833275079727,
0.015937646850943565,
0.017181290313601494,
0.029269220307469368,
-0.013619651086628437,
-0.014618470333516598,
0.0030738087370991707,
0.03973010554909706,
-0.03697444126009941,
0.06133222207427025,
0.01475963369011879,
-0.003363705473020673,
-0.000138821080327034,
-0.01432997826486826,
-0.006887045688927174,
0.04232550412416458,
-0.01135258749127388,
-0.020583197474479675,
-0.017487287521362305,
-0.014963761903345585,
0.024054644629359245,
-0.0541343092918396,
0.0031028566882014275,
0.011442145332694054,
-0.034840796142816544,
0.03453139215707779,
0.041301529854536057,
0.0229240320622921,
0.007559820078313351,
0.00719037838280201,
-0.0018612921703606844,
0.07482647150754929,
-0.03183164447546005,
-0.013786894269287586,
0.005923413671553135,
0.043780140578746796,
-0.004015018697828054,
-0.000029984434149810113,
0.031697869300842285,
-0.0030098760034888983,
0.0233222134411335,
0.042747095227241516,
0.013804874382913113,
-0.022508123889565468,
-0.02156979963183403,
0.0011027005966752768,
0.010778543539345264,
0.005313856061547995,
0.014067502692341805,
-0.022307278588414192,
0.0699770450592041,
-0.021012773737311363,
0.009875224903225899,
-0.002125411992892623,
0.0005033890483900905,
-0.012432846240699291,
0.03557758778333664,
-0.0013635711511597037,
0.011407677084207535,
0.012689320370554924,
-0.03678406402468681,
0.016239400953054428,
-0.0001425477967131883,
0.023243436589837074,
-0.005831646267324686,
0.0024605949874967337,
-0.02190604992210865,
0.006615802645683289,
-0.03292132169008255,
-0.019357232376933098,
-0.03694898262619972,
-0.03312743455171585,
0.015653250738978386,
0.01763974130153656,
0.02669456973671913,
-0.014622502028942108,
-0.0029860788490623236,
-0.015436715446412563,
0.09383683651685715,
-0.051064129918813705,
-0.015470055863261223,
-0.011657776311039925,
0.009461254812777042,
-0.01044213492423296,
-0.02838418446481228
] |
<p>I have created a simulation of <strong>one</strong> electron bouncing through a 3D mesh of molecules. The electron hopping is determined by a calculation of electron transfer rate using the Marcus equation (a result in units of $1/s$). In order to force the electron to reach one end of this 3D mesh I have applied a driving energy $dE$ (negative) to <strong>each</strong> molecule.</p>
<p>I am familiar with the electric field equation but I do not see how it applies to one electron
bouncing through many molecules. How do I go about calculating the electric field that I applied?</p> | 2,861 | [
-0.01091714296489954,
0.0004692423390224576,
0.013191675767302513,
-0.013389780186116695,
0.06149871274828911,
-0.011667749844491482,
-0.009518914856016636,
0.003762634703889489,
0.036068011075258255,
-0.027123814448714256,
0.08022496849298477,
0.05657205358147621,
0.09320249408483505,
0.010801888071000576,
0.012256545946002007,
-0.01638164184987545,
-0.01061659399420023,
-0.0008513092761859298,
-0.000772518222220242,
-0.02713373303413391,
0.01860150694847107,
0.0017835783073678613,
0.019405169412493706,
0.009577116928994656,
-0.021172577515244484,
0.03893820941448212,
0.054683584719896317,
-0.02420857734978199,
0.011375783942639828,
0.024891383945941925,
-0.040895070880651474,
-0.040232814848423004,
0.012243619188666344,
0.00600083265453577,
0.01302496436983347,
-0.001374954590573907,
-0.07047976553440094,
-0.061674565076828,
-0.01178395003080368,
-0.017297834157943726,
-0.03507320582866669,
-0.0004250285855960101,
-0.025447843596339226,
0.07190690189599991,
-0.01016880664974451,
-0.013548202812671661,
0.01255171000957489,
-0.006059869192540646,
0.03601731359958649,
-0.04405146464705467,
0.07641679793596268,
-0.028779011219739914,
0.08243773132562637,
0.025518354028463364,
0.0000032951138564385474,
-0.023976383730769157,
0.08957923203706741,
0.05299503356218338,
0.008303133770823479,
-0.027604199945926666,
0.013584545813500881,
-0.051495835185050964,
-0.008764928206801414,
-0.03518184274435043,
-0.03315797448158264,
0.06450837850570679,
-0.0037515247240662575,
-0.0441071055829525,
0.01724696159362793,
-0.006939312908798456,
0.008587652817368507,
0.01329759694635868,
0.03564617782831192,
-0.03387942537665367,
0.03271656110882759,
0.008914453908801079,
0.04151768237352371,
-0.00015161262126639485,
0.04805190861225128,
0.037642523646354675,
-0.04584910720586777,
0.003096356289461255,
0.028658339753746986,
0.03541489318013191,
-0.015018417499959469,
-0.026661964133381844,
0.060682252049446106,
-0.02077537588775158,
0.003863527439534664,
-0.04387018457055092,
-0.025574320927262306,
0.04312557354569435,
0.032224658876657486,
0.01263957004994154,
-0.019006257876753807,
0.029505426064133644,
0.023782769218087196,
0.06521152704954147,
-0.011336402967572212,
-0.016309168189764023,
-0.03952343016862869,
-0.027071664109826088,
0.007864770479500294,
0.04086915776133537,
0.005121284630149603,
0.008650828152894974,
-0.020064353942871094,
-0.0023254125844687223,
-0.009160876274108887,
-0.022576341405510902,
-0.02019360288977623,
0.029329698532819748,
0.004162323195487261,
0.0007724644965492189,
-0.01413631346076727,
-0.02526925876736641,
0.006282473914325237,
-0.03089897893369198,
0.009477296844124794,
0.05807765945792198,
0.02103610895574093,
-0.053527284413576126,
0.03465726599097252,
-0.0036405690480023623,
-0.05233338475227356,
0.0004929794231429696,
-0.0029906718991696835,
0.004549335688352585,
-0.004310747142881155,
0.003332731081172824,
0.0028479311149567366,
-0.040293872356414795,
0.018722428008913994,
-0.014934059232473373,
0.03055417351424694,
0.003985941875725985,
-0.08068177103996277,
-0.07333236932754517,
0.024316173046827316,
-0.0361664816737175,
0.027248673141002655,
-0.05853006988763809,
-0.029816413298249245,
0.049777038395404816,
0.06061369553208351,
0.017817331477999687,
-0.008617131039500237,
-0.00862886942923069,
0.024107858538627625,
0.015373957343399525,
-0.0015450261998921633,
-0.008545131422579288,
-0.034974873065948486,
-0.0015577569138258696,
0.019223585724830627,
-0.03579868748784065,
0.05516718700528145,
0.02040255069732666,
0.018801165744662285,
-0.0028972115833312273,
0.07416078448295593,
-0.008893132209777832,
-0.03269144892692566,
-0.023037269711494446,
0.02356739528477192,
-0.009471626952290535,
0.07735053449869156,
0.043486371636390686,
0.016262203454971313,
0.030612658709287643,
-0.013593019917607307,
0.02839023992419243,
-0.014206141233444214,
0.026814807206392288,
0.01911277323961258,
-0.059242118149995804,
-0.007911973632872105,
-0.029474234208464622,
0.03200338035821915,
-0.005104127340018749,
-0.020913662388920784,
-0.042330894619226456,
0.03574401140213013,
-0.010653529316186905,
0.010727770626544952,
-0.002875901758670807,
-0.01729181595146656,
0.0210511963814497,
-0.01848377101123333,
-0.017409630119800568,
-0.034533437341451645,
-0.04352220892906189,
0.05061483755707741,
0.03614151477813721,
0.004421679303050041,
0.0296026561409235,
0.006317525636404753,
0.032252855598926544,
-0.011948068626224995,
-0.01203328650444746,
-0.036575041711330414,
0.01591404341161251,
-0.00827548373490572,
-0.0001856860180851072,
0.033424217253923416,
0.04384950175881386,
0.04272717237472534,
0.003755761543288827,
0.0376158207654953,
-0.0037541757337749004,
-0.004131054040044546,
-0.01950792595744133,
-0.062165629118680954,
0.02052290551364422,
0.01644742488861084,
-0.014858092181384563,
0.005661389324814081,
0.004874580539762974,
0.0116987694054842,
0.043984804302453995,
-0.031612712889909744,
0.05101006478071213,
0.08729403465986252,
0.04800758510828018,
0.0008075886289589107,
0.03466399759054184,
-0.017268497496843338,
-0.016352171078324318,
0.023915717378258705,
-0.05242273211479187,
-0.024791350588202477,
0.01612822152674198,
0.04891781136393547,
0.005703060422092676,
-0.042477596551179886,
-0.024935508146882057,
0.04402659088373184,
-0.012361771427094936,
0.05341964215040207,
0.0325307697057724,
-0.05269625037908554,
-0.014253629371523857,
0.053386881947517395,
0.018145084381103516,
0.004875097889453173,
-0.006132844369858503,
-0.0030717297922819853,
0.024824049323797226,
0.021561743691563606,
-0.0002864644047804177,
0.0020635537803173065,
0.036775149405002594,
-0.04278136417269707,
-0.006817840971052647,
0.02772899903357029,
-0.04590393230319023,
0.018379464745521545,
-0.024646732956171036,
0.03098113089799881,
-0.0004851383564528078,
0.0034028571099042892,
0.029644953086972237,
-0.015556826256215572,
-0.024032143875956535,
0.05714741349220276,
-0.005397752393037081,
0.019652865827083588,
-0.014495590701699257,
0.016426481306552887,
-0.029787521809339523,
0.06603781133890152,
0.021520040929317474,
-0.028172321617603302,
-0.020490184426307678,
-0.014106208458542824,
0.006324496120214462,
0.04936143755912781,
0.03509027883410454,
-0.04524487257003784,
-0.05105958878993988,
-0.023490872234106064,
-0.027853948995471,
0.03368350490927696,
0.04771525040268898,
-0.015722226351499557,
-0.008563184179365635,
-0.04836491867899895,
-0.04660981521010399,
0.07014808058738708,
0.008670799434185028,
-0.05444766581058502,
0.037971675395965576,
-0.014762413688004017,
-0.022172436118125916,
-0.022499455139040947,
-0.04412837699055672,
0.006025978364050388,
-0.028354091569781303,
-0.02291874587535858,
0.044922612607479095,
0.008420737460255623,
-0.025784878060221672,
0.03114083595573902,
-0.03892287611961365,
-0.016777532175183296,
0.00022243097191676497,
-0.0016961407382041216,
0.013601847924292088,
-0.013395723886787891,
0.03577566519379616,
0.044237103313207626,
-0.024448322132229805,
-0.03859398141503334,
-0.037658244371414185,
-0.055112436413764954,
0.011602049693465233,
-0.0004973191535100341,
0.027570150792598724,
-0.005993631202727556,
-0.04739636555314064,
0.0602179579436779,
0.0013324525207281113,
-0.04318257048726082,
0.0015921314479783177,
-0.04868466779589653,
-0.04179903864860535,
-0.02380092814564705,
0.03156541287899017,
0.010510633699595928,
-0.007257829885929823,
0.003382680704817176,
0.005636950489133596,
0.02052994817495346,
0.059353433549404144,
-0.03085915930569172,
-0.005997378844767809,
0.03501322865486145,
-0.012535805813968182,
-0.015393255278468132,
0.0557200089097023,
0.0000670105146127753,
-0.040408652275800705,
0.06170269846916199,
-0.011919534765183926,
0.0058987815864384174,
0.05430351570248604,
-0.07007195800542831,
0.016850095242261887,
-0.005716846790164709,
-0.015223950147628784,
-0.012056565843522549,
0.010944842360913754,
0.02964717708528042,
-0.03684544935822487,
0.026651449501514435,
0.04277489706873894,
0.024765565991401672,
-0.040158987045288086,
-0.006736149545758963,
0.03769659250974655,
0.030764365568757057,
-0.013357611373066902,
-0.06197446584701538,
-0.00780309084802866,
0.01162254624068737,
-0.0054434253834187984,
-0.008621358312666416,
-0.03832051903009415,
0.02287203259766102,
0.029745105654001236,
0.04518985003232956,
0.018280794844031334,
-0.013168332166969776,
0.00024267556727863848,
-0.03627563640475273,
-0.004613477271050215,
-0.003706691786646843,
0.07063945382833481,
0.012530755251646042,
0.07951764762401581,
-0.01010305155068636,
0.025261787697672844,
0.012870503589510918,
0.007331399247050285,
-0.032474786043167114,
0.024250805377960205,
0.007847623899579048,
-0.0351167693734169,
-0.02489907667040825,
0.01581360585987568,
0.0005540145211853087,
-0.029393620789051056,
-0.005824798718094826,
0.0012804477009922266,
-0.017747247591614723,
-0.057041168212890625,
-0.00419804360717535,
-0.043214548379182816,
-0.010649544186890125,
-0.03740818053483963,
0.0542709156870842,
0.038656990975141525,
-0.028928915038704872,
-0.00504732970148325,
0.046954501420259476,
-0.017405249178409576,
-0.008869246579706669,
-0.041823700070381165,
-0.021417930722236633,
0.01943180523812771,
0.029122283682227135,
0.03294174000620842,
0.024489395320415497,
-0.0214440505951643,
-0.0026331290137022734,
-0.0008726873784326017,
0.0310091320425272,
0.01672949083149433,
-0.004919320810586214,
-0.03571149334311485,
-0.05103687942028046,
-0.0061655910685658455,
-0.017370834946632385,
0.047812607139348984,
-0.004436687100678682,
0.02765192836523056,
0.04540947824716568,
0.013304098509252071,
-0.03113948181271553,
0.025747278705239296,
0.03448179364204407,
0.03611437603831291,
-0.014861123636364937,
-0.04906861484050751,
-0.00042165396735072136,
-0.02835831604897976,
0.006240203510969877,
0.01942952163517475,
0.011601311154663563,
-0.006365015637129545,
0.016222817823290825,
0.01892765611410141,
0.0052666012197732925,
-0.015463842079043388,
-0.014909543097019196,
-0.031061135232448578,
0.031091157346963882,
-0.023200444877147675,
-0.02669391967356205,
0.014218665659427643,
-0.0013121368829160929,
-0.00028765873867087066,
-0.007354153785854578,
-0.018269764259457588,
-0.09087079763412476,
-0.05866499990224838,
0.030209321528673172,
0.007907122373580933,
-0.013516235165297985,
0.018324345350265503,
-0.0745151937007904,
0.0083665382117033,
0.01870162971317768,
-0.06894222646951675,
0.015309358015656471,
0.02778475731611252,
0.034630514681339264,
-0.026226012036204338,
-0.025388071313500404,
-0.04194901883602142,
0.04031948745250702,
0.014437785372138023,
0.03964915871620178,
-0.031761787831783295,
0.02174619399011135,
0.01135612279176712,
0.05237547680735588,
0.017274096608161926,
0.0703066736459732,
-0.016124706715345383,
-0.01826697215437889,
0.018667591735720634,
-0.004591984674334526,
-0.03887667506933212,
-0.07292301207780838,
0.04972372576594353,
-0.015843309462070465,
0.022920172661542892,
0.0520988404750824,
-0.07587315142154694,
0.001325942692346871,
0.015116006135940552,
0.0013066049432381988,
0.008208769373595715,
-0.026145387440919876,
-0.026325780898332596,
0.042774368077516556,
0.037833597511053085,
0.001692004851065576,
0.057754483073949814,
0.0014832440065219998,
-0.03218555450439453,
0.025536786764860153,
-0.027068432420492172,
0.03687587380409241,
-0.004406857769936323,
-0.01280166581273079,
-0.02134532481431961,
-0.027081070467829704,
-0.022214990109205246,
0.052178796380758286,
-0.042813729494810104,
0.04128459468483925,
-0.022312643006443977,
-0.038927823305130005,
-0.004082707222551107,
0.049242548644542694,
-0.0043975235894322395,
0.02563960663974285,
-0.01719914749264717,
0.018972566351294518,
-0.004516101907938719,
-0.050238825380802155,
-0.008655998855829239,
-0.0016034397995099425,
0.011249740608036518,
-0.017641965299844742,
-0.045179981738328934,
-0.003634203225374222,
-0.01467719953507185,
-0.004823192022740841,
-0.01856498047709465,
-0.07895054668188095,
0.02423824369907379,
-0.015211419202387333,
0.007634534500539303,
-0.03802236542105675,
-0.04615694656968117,
-0.015465311706066132,
0.03255421668291092,
0.0009176247986033559,
-0.011942110024392605,
-0.04255259782075882,
-0.011244717054069042,
-0.032967276871204376,
0.04228522628545761,
-0.07510344684123993,
-0.07351445406675339,
0.005254358984529972,
0.028794925659894943,
0.027086414396762848,
-0.053261298686265945,
-0.02466912753880024,
-0.02373347617685795,
-0.020048195496201515,
0.04692845791578293,
0.04062483459711075,
-0.0002522824506741017,
0.016689924523234367,
0.03785166144371033,
-0.0039739725179970264,
0.01146184466779232,
-0.011749064549803734,
0.01211804710328579,
0.03333349898457527,
-0.034130532294511795,
-0.000003906685833499068,
0.01785580813884735,
0.017812766134738922,
-0.028649916872382164,
-0.038415372371673584,
-0.02646530792117119,
0.002154569374397397,
0.03211795166134834,
-0.07152678817510605,
-0.009168535470962524,
0.008937367238104343,
0.028629785403609276,
-0.028060657903552055,
-0.028333691880106926,
0.02488723210990429,
-0.008724212646484375,
0.013044078834354877,
0.0013193035265430808,
-0.009172596968710423,
-0.0337517149746418,
0.001484552165493369,
0.012242715805768967,
0.028137201443314552,
0.024107301607728004,
-0.007380374241620302,
0.07243663817644119,
-0.017144175246357918,
0.0046607633121311665,
0.038538362830877304,
-0.02619648352265358,
0.037053242325782776,
-0.01826668530702591,
-0.03184725344181061,
0.02919636480510235,
0.03141111135482788,
0.0033338316716253757,
-0.033155977725982666,
-0.039385512471199036,
-0.008336128666996956,
0.05728992074728012,
-0.03644189238548279,
0.00297644454985857,
-0.006082877516746521,
0.012190543115139008,
-0.03201017901301384,
-0.007934953086078167,
-0.01319862436503172,
0.03349783271551132,
-0.0002954227093141526,
0.018971575424075127,
-0.00015695465845055878,
0.020478971302509308,
0.017414508387446404,
0.038496632128953934,
-0.010348312556743622,
0.022484472021460533,
-0.003903848584741354,
0.004023605026304722,
0.011775333434343338,
-0.011790058575570583,
-0.012187637388706207,
0.05413971096277237,
-0.03340153396129608,
0.05217424035072327,
-0.010951291769742966,
0.0006631699507124722,
0.058412257581949234,
0.01478113979101181,
0.006334824953228235,
-0.027172697708010674,
0.022619664669036865,
0.018839184194803238,
0.007099933456629515,
0.00818438921123743,
0.0010092152515426278,
0.004451533313840628,
0.0399845726788044,
0.01649128645658493,
0.003118564374744892,
0.0326649472117424,
-0.003957667388021946,
-0.023553257808089256,
0.005121080204844475,
-0.030833296477794647,
-0.03364257887005806,
0.06527514010667801,
0.03101346828043461,
0.00277287932112813,
0.018592556938529015,
0.0021849290933459997,
0.04567025974392891,
-0.0016465523513033986,
0.02997962385416031,
-0.008681422099471092,
0.0847405269742012,
0.021463779732584953,
0.022655876353383064,
-0.01021183654665947,
-0.012107611633837223,
0.10034829378128052,
0.06845814734697342,
0.022988827899098396,
-0.026741448789834976,
-0.028422340750694275,
-0.01947754994034767,
-0.012658475898206234,
-0.018600329756736755,
-0.018744785338640213,
-0.010133481584489346,
-0.012115870602428913,
-0.01295340433716774,
0.03732699528336525,
-0.002771113533526659,
0.03667809069156647,
0.019413333386182785,
-0.05063507705926895,
-0.041545141488313675,
0.01212223619222641,
-0.018142158165574074,
-0.013837401755154133,
-0.010123396292328835,
-0.04652850702404976,
0.07269208878278732,
-0.05267485976219177,
-0.005957512184977531,
-0.03256453573703766,
-0.012671221047639847,
0.08022375404834747,
0.0036380046512931585,
-0.03199464827775955,
0.0022068165708333254,
-0.04324135556817055,
-0.026278091594576836,
-0.017637280747294426,
0.00452931085601449,
0.04551691189408302,
0.003208872163668275,
0.04279826954007149,
0.03139423951506615,
-0.025739353150129318,
0.04304758831858635,
-0.006032873410731554,
0.02441197633743286,
-0.012541019357740879,
-0.007570904213935137,
-0.025117559358477592,
0.032504383474588394,
0.0027809268794953823,
0.012366977520287037,
0.004613358527421951,
0.03734370693564415,
0.029978731647133827,
-0.03700947016477585,
-0.03581729903817177,
-0.031317126005887985,
0.02217075042426586,
-0.007370964158326387,
0.018407555297017097,
-0.028609564527869225,
0.03641651198267937,
-0.014375338330864906,
-0.02818860486149788,
-0.0033086733892560005,
0.0028057198505848646,
0.024862632155418396,
-0.010595335625112057,
0.04788707196712494,
0.012144886888563633,
-0.03238368034362793,
-0.057765647768974304,
-0.05037659779191017,
-0.01706792041659355,
0.008053065277636051,
0.03611762449145317,
0.056189145892858505,
0.009752270765602589,
-0.021015506237745285,
0.008281162939965725,
-0.015927357599139214,
-0.09134092181921005,
0.004165606573224068,
-0.004727171268314123,
-0.029551221057772636,
0.01660144329071045,
-0.05057784542441368,
0.03664154186844826,
0.05099838972091675,
-0.009746572002768517,
0.04403872415423393,
0.015140705741941929,
-0.003207483561709523,
0.03087455779314041,
-0.04713255539536476,
-0.025473017245531082,
0.0011780019849538803,
-0.04939038306474686,
0.01748170144855976,
-0.040655992925167084,
0.04125814884901047,
-0.04018784314393997,
0.003643645439296961,
0.007446163333952427,
0.03535196930170059,
-0.028979064896702766,
-0.004135062452405691,
-0.024035120382905006,
-0.004604197572916746,
0.0012960148742422462,
0.012955661863088608,
0.0029106156434863806,
-0.055986709892749786,
-0.026348216459155083,
-0.0038036773912608624,
-0.008725157007575035,
0.008530644699931145,
0.011541258543729782,
-0.01862710528075695,
0.011043399572372437,
-0.008459952659904957,
-0.004340273328125477,
-0.01869935356080532,
0.017076212912797928,
-0.027058478444814682,
0.020503094419836998,
-0.03735730051994324,
-0.005026127677410841,
-0.02687414549291134,
0.001291976310312748,
-0.00902032945305109,
0.03290238603949547,
0.038445476442575455,
0.02774415910243988,
0.02489033341407776,
0.00281703588552773,
0.009835139848291874,
-0.04794863983988762,
0.057027123868465424,
-0.002955010160803795,
-0.006590218283236027,
0.03957183286547661,
-0.08122052997350693,
-0.013799351640045643,
0.0060967011377215385,
-0.017077326774597168,
0.02665422111749649,
0.04370029270648956,
-0.007912708446383476,
-0.02310197241604328,
0.04057084396481514,
-0.032935015857219696,
-0.014766658656299114,
0.016988031566143036,
-0.04866788908839226,
0.021871935576200485,
-0.005344085860997438,
-0.00365243898704648,
-0.006501509342342615,
0.028697090223431587,
0.04708956554532051,
0.006228226702660322,
-0.00650465814396739,
-0.016310565173625946,
0.0002721052442211658,
0.017703523859381676,
0.012188561260700226,
0.061053525656461716,
-0.007362531032413244,
0.021539976820349693,
0.08682664483785629,
-0.015293068252503872,
0.00022131824516691267,
-0.00045556167606264353,
0.016252800822257996,
-0.07067790627479553,
-0.0032722000032663345,
-0.011194010265171528,
-0.016190340742468834,
0.03475666418671608,
-0.045173440128564835,
0.0024676593020558357,
0.027739763259887695,
-0.08446597307920456,
0.008816002868115902,
-0.006516797933727503,
0.013825079426169395,
-0.025782786309719086,
-0.020146936178207397,
-0.0225646011531353,
-0.017249079421162605,
0.011528260074555874,
0.03908615931868553,
0.0009940702002495527,
-0.0035659559071063995,
0.005547991953790188,
-0.036061063408851624,
0.0006079724989831448,
0.06164221093058586,
0.007594598922878504,
0.007059118244796991,
0.021881988272070885,
-0.029581112787127495,
-0.05541795492172241,
0.0034571911673992872,
-0.0190055500715971,
-0.01490171067416668,
0.005248486064374447,
0.0032448165584355593,
-0.004236658103764057,
0.008771891705691814,
0.008432725444436073,
-0.03323560208082199,
0.004992458038032055,
-0.007850747555494308,
-0.0069306702353060246,
0.012797767296433449,
-0.018818458542227745,
-0.008736659772694111,
0.04221484810113907,
0.0021381904371082783,
-0.03774471953511238,
0.07344871759414673,
0.011042841710150242,
-0.03193928301334381,
-0.0037105565425008535,
0.011531244032084942,
0.039950497448444366,
-0.019651412963867188,
-0.012415983714163303,
-0.01101770345121622,
0.02346974052488804,
0.032119475305080414,
0.007242560386657715,
0.02295531891286373,
0.03088999353349209,
-0.04050782695412636,
-0.06950749456882477,
0.01065637543797493,
-0.018589239567518234,
-0.02877161279320717,
-0.07788216322660446,
0.0008618775755167007,
0.015414965339004993,
-0.021552277728915215,
-0.011967160739004612,
-0.027088643983006477,
-0.014212299138307571,
0.03491818532347679,
-0.01723080687224865,
-0.016583243384957314,
-0.026034170761704445,
-0.03185468539595604,
0.013984931632876396,
-0.05969490110874176,
0.021513797342777252,
0.004856413695961237,
-0.027707941830158234,
-0.01848866418004036,
-0.04106215387582779,
0.008313925005495548,
0.02415517345070839,
0.06270717084407806,
-0.020367611199617386,
-0.025195172056555748,
0.0007019296172074974,
0.01138593815267086,
0.02614409476518631,
-0.0696692243218422,
-0.01667206734418869,
0.008260227739810944,
-0.0009259654907509685,
-0.042550209909677505,
-0.007658202201128006,
-0.04290049523115158,
0.051175545901060104,
-0.023887643590569496,
0.007958660833537579,
0.0344536192715168,
-0.022028272971510887,
-0.031114527955651283,
0.016108820214867592,
-0.004022588487714529,
-0.008274795487523079,
0.06109675019979477,
-0.018838435411453247,
0.005244726315140724,
0.019036589190363884,
-0.008592142723500729,
-0.038970500230789185,
-0.00911166425794363,
-0.06116251274943352,
-0.021790292114019394,
-0.006624714937061071,
-0.007569802459329367,
0.02115236595273018,
-0.06781801581382751,
-0.008158310316503048,
0.020433858036994934,
-0.0506427176296711,
0.02574356272816658,
0.047182660549879074,
-0.004945659544318914,
0.030637020245194435,
0.022617623209953308,
0.0184981320053339,
-0.004057937301695347,
0.008559605106711388,
-0.019983693957328796,
0.055408671498298645,
0.02759537287056446,
0.0006436508847400546,
0.04157567769289017,
0.03118504397571087,
-0.0071310680359601974,
0.004591609816998243,
0.021679053083062172,
-0.011684976518154144,
0.002692613285034895,
0.018354881554841995,
0.014010765589773655,
0.003969376906752586,
-0.008957012556493282,
0.004686780273914337,
-0.011084776371717453,
0.07992512732744217,
-0.014012305997312069,
0.02838432975113392,
0.002764104399830103,
0.015527479350566864,
0.01282587368041277,
0.040737953037023544,
-0.023493515327572823,
0.06784284114837646,
-0.028985673561692238,
-0.000021123085389262997,
-0.03536919131875038,
-0.010049068368971348,
0.02840624563395977,
-0.014577138237655163,
0.00977878738194704,
0.03330808877944946,
-0.028976144269108772,
-0.013659220188856125,
-0.02091033011674881,
-0.03147111460566521,
-0.010765251703560352,
0.02616138942539692,
0.014035167172551155,
0.0009428043849766254,
0.015774767845869064,
0.005613251123577356,
0.018353044986724854,
0.0452943854033947,
-0.036856669932603836,
-0.03982197120785713,
0.005138302221894264,
0.005328814033418894,
-0.012501228600740433,
0.01361177209764719
] |
<p>I am interested in gravitational lensing caused by a cluster of galaxies (say it has a diameter of 1 Mpc and mass of $10^{12}$ solar masses). How close must a light travel as it passes by to be notably bent - if compared to a case where there would be much smaller object in a spot where is now a center of cluster, like one isolated galaxy?</p>
<p>I am trying to determine angle of deflection for a special case of gravitational potential and I have no feeling for the distances at which lens still has an effect on light.</p> | 2,862 | [
-0.02715233527123928,
-0.02117912285029888,
0.003485838882625103,
-0.03422315791249275,
0.0541134811937809,
0.036642324179410934,
-0.046089690178632736,
-0.03038846142590046,
-0.015088475309312344,
-0.03983532264828682,
0.021621711552143097,
0.057260774075984955,
0.061054814606904984,
-0.005299759097397327,
0.018372315913438797,
0.007572893984615803,
-0.01918604224920273,
-0.0024843942373991013,
0.00374962342903018,
-0.041823193430900574,
0.014812549576163292,
0.02087043598294258,
0.008623861707746983,
-0.014435378834605217,
-0.026556214317679405,
0.002383677288889885,
0.011853829026222229,
-0.017709193751215935,
0.020467514172196388,
0.03717649355530739,
0.006003592163324356,
-0.029625872150063515,
0.019238844513893127,
0.053117331117391586,
-0.014626030810177326,
0.010812085121870041,
-0.03417893871665001,
-0.027150727808475494,
-0.03414367511868477,
0.025549350306391716,
-0.05407583713531494,
-0.02126959152519703,
0.01691516675055027,
0.06704863905906677,
-0.020638231188058853,
-0.005513560026884079,
-0.007294097449630499,
0.016817867755889893,
0.05769186094403267,
-0.03774714842438698,
0.06418883055448532,
0.009358206763863564,
0.015809258446097374,
0.03215663507580757,
-0.021158363670110703,
0.0037273599300533533,
0.06630008667707443,
0.09120785444974899,
-0.03734225034713745,
-0.05702228471636772,
-0.04426974430680275,
-0.012824795208871365,
-0.005821140483021736,
-0.03616049513220787,
-0.007989855483174324,
0.01329681184142828,
-0.041670992970466614,
0.017832638695836067,
0.01777251623570919,
0.01689799129962921,
0.01266371738165617,
0.015495911240577698,
0.019388915970921516,
-0.0018555392744019628,
-0.021699797362089157,
-0.044218529015779495,
0.008640704676508904,
0.017011230811476707,
0.03841810300946236,
0.008105101995170116,
0.006712043657898903,
0.013011517003178596,
0.0467866025865078,
0.012010816484689713,
0.00018491568334866315,
-0.030499417334794998,
0.09017249196767807,
-0.02194267511367798,
-0.0017653591930866241,
0.019941193982958794,
-0.012907790951430798,
0.009518804028630257,
0.019741151481866837,
0.02074613608419895,
-0.013961409218609333,
0.05060870945453644,
-0.03247266635298729,
0.037954192608594894,
-0.0061379726976156235,
-0.014093699865043163,
-0.02376825176179409,
-0.001607597223483026,
-0.0015360695542767644,
0.06003837287425995,
0.0006289645098149776,
-0.048676345497369766,
-0.04609299078583717,
-0.0004708619089797139,
-0.03036491386592388,
0.012426001019775867,
-0.023375242948532104,
0.019426438957452774,
0.0021193670108914375,
-0.014049937948584557,
0.05528112128376961,
-0.029839951545000076,
-0.003812833921983838,
-0.0541992262005806,
0.07095616310834885,
0.035446424037218094,
0.051630813628435135,
-0.03109867125749588,
0.023791126906871796,
-0.08576652407646179,
-0.05034324526786804,
0.047568291425704956,
0.09664358198642731,
-0.012694040313363075,
-0.019330251961946487,
0.007322593592107296,
0.034148361533880234,
0.024225739762187004,
0.004244429524987936,
-0.0035213041119277477,
0.012663785368204117,
-0.027590245008468628,
-0.06593725085258484,
-0.04851164668798447,
0.013461345806717873,
0.019440561532974243,
0.0027847234159708023,
-0.03018258884549141,
0.017742177471518517,
0.04972043260931969,
0.0899854451417923,
0.0007344129262492061,
0.015210255980491638,
-0.00543619180098176,
0.06587143242359161,
-0.039282578974962234,
0.008789357729256153,
-0.002295843558385968,
-0.029425758868455887,
-0.0053572203032672405,
0.003636183449998498,
-0.08308953046798706,
-0.01259012520313263,
0.04031937196850777,
0.00869355071336031,
-0.046208374202251434,
0.07434764504432678,
-0.01783391833305359,
0.020352834835648537,
0.0057913269847631454,
0.0004890368436463177,
-0.03270197659730911,
0.06935684382915497,
0.015303591266274452,
-0.01221479568630457,
0.027486197650432587,
-0.017232652753591537,
0.026750192046165466,
-0.02463207021355629,
-0.0029391031712293625,
0.06709660589694977,
-0.028642628341913223,
0.006814587861299515,
-0.01818261295557022,
0.009885800071060658,
0.010612203739583492,
-0.0016040535410866141,
-0.018046865239739418,
-0.004206500947475433,
-0.013508780859410763,
-0.004808000288903713,
0.022018682211637497,
-0.002378906589001417,
0.022693216800689697,
0.014556830748915672,
-0.01918097585439682,
-0.013563752174377441,
-0.022554634138941765,
0.0008051836048252881,
0.011927958577871323,
0.017976660281419754,
0.030229244381189346,
0.008377308025956154,
0.007406709250062704,
0.015641340985894203,
-0.03904306888580322,
-0.019418608397245407,
0.04081444442272186,
-0.03249402716755867,
0.002621414139866829,
0.019290311262011528,
0.040319520980119705,
0.03316277265548706,
0.015904739499092102,
0.0022651643957942724,
-0.024187549948692322,
-0.009230267256498337,
0.014041133224964142,
-0.027189690619707108,
0.02041863277554512,
-0.01391575951129198,
0.027985505759716034,
0.0018789635505527258,
0.03342794254422188,
0.006052087526768446,
0.011542931199073792,
-0.018870308995246887,
0.07768304646015167,
0.040919624269008636,
0.01899724267423153,
0.01679922826588154,
0.03338423743844032,
-0.005633645690977573,
0.008971610106527805,
-0.025973567739129066,
-0.01970599964261055,
-0.07739587873220444,
-0.01912546530365944,
0.026902612298727036,
0.008854387328028679,
-0.02513321302831173,
0.019504494965076447,
0.05411047488451004,
0.02633478492498398,
0.017875580117106438,
-0.01567726954817772,
-0.035497888922691345,
-0.056860074400901794,
0.011221080087125301,
0.02536039613187313,
-0.009529193863272667,
-0.000650523288641125,
0.004297593608498573,
-0.017944995313882828,
0.015879711136221886,
-0.022886762395501137,
-0.013676534406840801,
0.028230486437678337,
0.008983820676803589,
0.026091784238815308,
-0.012565145269036293,
-0.005403473507612944,
0.08778351545333862,
0.01961969956755638,
-0.006411039270460606,
0.022785937413573265,
0.0019048169488087296,
0.0044248453341424465,
-0.03409166261553764,
-0.022197121754288673,
-0.000742103555239737,
0.026466190814971924,
-0.06505801528692245,
-0.031060578301548958,
0.014271627180278301,
-0.05966619402170181,
0.04723139479756355,
-0.013870702125132084,
0.026264553889632225,
-0.01802041195333004,
-0.009966201148927212,
0.026387082412838936,
0.05575324222445488,
0.006860392168164253,
-0.007406457327306271,
-0.021113257855176926,
0.012463361956179142,
-0.01385447382926941,
0.017221912741661072,
0.0017654692055657506,
-0.04878664389252663,
0.009642177261412144,
-0.01267734169960022,
-0.009483857080340385,
0.0226148534566164,
0.0017397215124219656,
-0.0006169805419631302,
0.018813783302903175,
0.03116421028971672,
-0.049888238310813904,
-0.002320788335055113,
-0.021299738436937332,
-0.013921954669058323,
-0.042599499225616455,
-0.0011473643826320767,
0.0006294895429164171,
0.024163706228137016,
-0.028739232569932938,
0.03627513721585274,
-0.04497787356376648,
-0.020346902310848236,
-0.03065086342394352,
0.002531337784603238,
0.012691627256572247,
-0.04327854886651039,
0.03902265802025795,
0.0027431887574493885,
-0.012406043708324432,
0.025314779952168465,
-0.04924159124493599,
-0.05447884649038315,
0.044318877160549164,
-0.011179845780134201,
0.02374120242893696,
-0.01600765436887741,
-0.012620065361261368,
0.07304921001195908,
0.029327355325222015,
-0.017397738993167877,
-0.038689859211444855,
0.011673729866743088,
-0.007565814070403576,
0.0090155228972435,
0.0069993603974580765,
0.016358820721507072,
0.010161411948502064,
0.01393063273280859,
0.034275323152542114,
0.03662445396184921,
0.03295121714472771,
-0.0024449783377349377,
-0.011429756879806519,
-0.004959804937243462,
-0.032387640327215195,
-0.02053122967481613,
0.019938001409173012,
0.023331940174102783,
-0.01211340818554163,
0.004475465044379234,
-0.02258147858083248,
0.020428376272320747,
-0.018257983028888702,
-0.039381206035614014,
0.03759931027889252,
-0.025053730234503746,
-0.014630350284278393,
0.013558698818087578,
0.039910268038511276,
0.000566343602258712,
0.000833318626973778,
0.040154580026865005,
0.013029072433710098,
0.05925600603222847,
-0.004665115382522345,
-0.030390610918402672,
0.01730608008801937,
0.03191410377621651,
0.018618162721395493,
-0.048319991677999496,
0.007826870307326317,
-0.02049444615840912,
0.009042487479746342,
-0.022456858307123184,
-0.04321771487593651,
0.03136176988482475,
0.048936981707811356,
0.01292152889072895,
-0.04149051383137703,
-0.01681867055594921,
0.025074420496821404,
-0.02943824976682663,
-0.012117688544094563,
-0.004888295661658049,
0.013159801252186298,
0.012746420688927174,
0.004388356581330299,
0.03846590593457222,
0.010581151582300663,
0.0174561720341444,
0.008472753688693047,
-0.06489816308021545,
0.01535092107951641,
-0.04094882309436798,
-0.031344953924417496,
-0.025609837844967842,
0.0024602783378213644,
-0.0347018837928772,
-0.01492038369178772,
0.032480645924806595,
-0.030082201585173607,
-0.013294241391122341,
-0.028346041217446327,
-0.0026369988918304443,
-0.01912783272564411,
-0.05347838252782822,
-0.021996136754751205,
0.042368337512016296,
0.018436100333929062,
-0.0025269866455346346,
0.03602290153503418,
0.00509382551535964,
-0.014945773407816887,
-0.030607327818870544,
0.0048369658179581165,
0.030255760997533798,
-0.028553053736686707,
0.04598398879170418,
0.028241658583283424,
0.008170639164745808,
-0.034838493913412094,
-0.0067027113400399685,
0.011696340516209602,
0.021309223026037216,
0.04435495287179947,
0.0012465681647881866,
-0.0049630627036094666,
-0.038992539048194885,
-0.022571498528122902,
0.0015117605216801167,
0.05166652053594589,
-0.04231114685535431,
0.009891645051538944,
0.0315229669213295,
-0.011836444027721882,
-0.028351521119475365,
0.012030215002596378,
0.02887413278222084,
0.028719808906316757,
-0.05480310320854187,
-0.06607314199209213,
-0.02348819561302662,
-0.010294205509126186,
0.02505055069923401,
0.05680450424551964,
-0.023294787853956223,
-0.007693219464272261,
0.024865267798304558,
0.007157305721193552,
0.010612507350742817,
-0.06329067796468735,
0.03844910115003586,
-0.02819768153131008,
-0.0116092124953866,
0.011493120342493057,
0.00027739800862036645,
0.028994781896471977,
0.046895191073417664,
0.08905389159917831,
0.002255713799968362,
0.019114991649985313,
-0.07119572162628174,
-0.013643761165440083,
0.03988514840602875,
0.03673116862773895,
-0.0107502406463027,
-0.02230759896337986,
-0.0364353284239769,
-0.03394132852554321,
0.053547587245702744,
-0.03492984548211098,
0.030356571078300476,
0.0051412382163107395,
-0.017886383458971977,
0.0010699942940846086,
0.009006617590785027,
-0.06761597096920013,
0.022636011242866516,
-0.0011597604025155306,
-0.024525558575987816,
-0.03504977002739906,
0.03169022873044014,
-0.007401255890727043,
-0.010514209978282452,
0.02391391061246395,
0.05591890215873718,
0.03663818910717964,
-0.010221514850854874,
0.02644275315105915,
0.006278779823333025,
0.0006824294687248766,
-0.06271717697381973,
0.024298908188939095,
0.008536341600120068,
-0.024922776967287064,
0.05879684165120125,
-0.006797662004828453,
0.013233809731900692,
0.05570550262928009,
0.01964179426431656,
0.0190157201141119,
0.0047192866913974285,
-0.022037848830223083,
0.0167604498565197,
0.03557520732283592,
-0.00883569847792387,
0.09323109686374664,
0.021019628271460533,
-0.022490251809358597,
0.018557006493210793,
-0.050189677625894547,
0.04402806609869003,
-0.02964492328464985,
-0.027649693191051483,
-0.0031547637190669775,
-0.00801040604710579,
-0.031212620437145233,
0.03969934210181236,
-0.018988020718097687,
0.016147848218679428,
0.04664967209100723,
-0.02691759541630745,
-0.01223029289394617,
0.06033896654844284,
0.016290035098791122,
0.0192558653652668,
0.0288382638245821,
0.028293859213590622,
0.009107003919780254,
-0.017455225810408592,
0.008255125023424625,
-0.03088492900133133,
0.01768306829035282,
-0.00786937028169632,
-0.03346164897084236,
-0.0029686002526432276,
-0.01836739480495453,
-0.003789059119299054,
0.0020916806533932686,
-0.03509783744812012,
0.05885525420308113,
-0.00783340074121952,
-0.001003166544251144,
0.0795775055885315,
-0.04952473193407059,
-0.027831511572003365,
0.016622235998511314,
-0.05588175356388092,
0.06310711801052094,
-0.03564343973994255,
-0.007241833955049515,
0.015576080419123173,
0.03755759447813034,
-0.07368768006563187,
-0.0058076512068510056,
0.010593682527542114,
-0.007978972047567368,
-0.018514515832066536,
-0.035048872232437134,
-0.005524834617972374,
-0.02404041774570942,
-0.037427838891744614,
-0.024190915748476982,
0.0362137071788311,
-0.039952363818883896,
-0.01224498450756073,
-0.024344254285097122,
-0.01006640587002039,
0.06676917523145676,
-0.00037504101055674255,
-0.027807587757706642,
0.027134930714964867,
-0.008979144506156445,
-0.007830190472304821,
0.01330781914293766,
0.06830527633428574,
-0.03865380585193634,
-0.03656609356403351,
-0.06695100665092468,
-0.03581496328115463,
0.023681052029132843,
-0.05362506955862045,
0.008093477226793766,
0.007507538888603449,
0.003454386256635189,
0.03152957186102867,
0.023710742592811584,
0.03714844956994057,
-0.041946232318878174,
-0.01579749770462513,
-0.03193449601531029,
-0.016964856535196304,
0.017060911282896996,
-0.07071725279092789,
0.07631324231624603,
0.03444754332304001,
-0.00001680254536040593,
-0.005887170787900686,
0.06695041060447693,
0.005098875146359205,
-0.026583388447761536,
0.023326771333813667,
-0.013866950757801533,
0.021497098729014397,
-0.045044898986816406,
0.007329508196562529,
0.04024611413478851,
0.008875354193150997,
-0.013592413626611233,
-0.035804182291030884,
-0.0035887311678379774,
-0.01719437912106514,
0.11897504329681396,
0.031138939782977104,
0.017453288659453392,
-0.006904049310833216,
-0.014951090328395367,
-0.011441566050052643,
-0.02240498550236225,
0.0035365717485547066,
0.020794197916984558,
0.01845362037420273,
0.04971173778176308,
-0.04922839626669884,
-0.012480377219617367,
0.0026950156316161156,
0.029434438794851303,
-0.05737484619021416,
0.005735870450735092,
0.005134812090545893,
0.021837284788489342,
0.0059520346112549305,
-0.011380346491932869,
-0.048913199454545975,
-0.00315178744494915,
-0.04877942427992821,
0.040216293185949326,
-0.027598438784480095,
-0.007904516533017159,
0.03370169550180435,
0.004552623722702265,
0.05136558786034584,
-0.03064296953380108,
-0.017500827088952065,
-0.029198700562119484,
-0.006159941665828228,
0.025912752375006676,
0.004673326388001442,
-0.02465890720486641,
0.04414113610982895,
0.030045218765735626,
0.02504229173064232,
0.02207132615149021,
-0.010556108318269253,
-0.07203677296638489,
-0.05301081761717796,
-0.010157071985304356,
-0.054531414061784744,
0.04161185771226883,
0.011896388605237007,
-0.03644824028015137,
0.031641386449337006,
-0.030505504459142685,
-0.0020493699703365564,
0.03817439824342728,
0.010507388971745968,
-0.01602363958954811,
0.055035922676324844,
-0.015117286704480648,
0.02502410113811493,
-0.037999726831912994,
-0.030339078977704048,
0.10697884857654572,
0.0422469861805439,
0.006256334483623505,
-0.04472118988633156,
0.009709395468235016,
-0.019484074786305428,
-0.023852186277508736,
-0.05323715880513191,
0.011806952767074108,
-0.0353153757750988,
0.002005677204579115,
0.036576319485902786,
0.05475312098860741,
0.005952202249318361,
-0.0363357812166214,
0.06342960894107819,
-0.005056128837168217,
-0.03493755683302879,
0.01764075644314289,
0.011453324928879738,
-0.018968431279063225,
-0.0023718972224742174,
-0.02793751284480095,
0.04174836724996567,
-0.042979754507541656,
0.021943453699350357,
-0.03623419627547264,
-0.032268375158309937,
-0.016256263479590416,
0.022138407453894615,
-0.03654662147164345,
-0.005946781020611525,
0.006664499640464783,
-0.07681439071893692,
-0.06732119619846344,
0.02124273031949997,
0.01068603154271841,
-0.03186832368373871,
0.012313244864344597,
0.05015856772661209,
-0.04605484381318092,
0.012724206782877445,
0.025163553655147552,
-0.03193782642483711,
-0.04232927784323692,
-0.016705669462680817,
-0.026983113959431648,
0.053508613258600235,
-0.010920753702521324,
0.009291370399296284,
0.02735794708132744,
0.0302073135972023,
0.02802950143814087,
-0.0514809675514698,
0.02280173823237419,
0.005850694607943296,
0.01550767570734024,
-0.01439318060874939,
-0.033404480665922165,
0.017814340069890022,
0.06427256017923355,
0.03501584753394127,
0.021231358870863914,
-0.02998596429824829,
0.01751920022070408,
-0.015075836330652237,
-0.016972659155726433,
0.06775637716054916,
-0.017877280712127686,
-0.023615064099431038,
-0.019488321617245674,
0.010031279176473618,
-0.011828039772808552,
0.015645267441868782,
0.02795673906803131,
-0.0018230946734547615,
-0.013110595755279064,
0.0204467810690403,
0.016307193785905838,
0.009564699605107307,
-0.0682041123509407,
0.008141993544995785,
-0.05036383494734764,
-0.032345667481422424,
-0.05126168578863144,
-0.004497176967561245,
0.06299817562103271,
0.01885191909968853,
0.026792306452989578,
-0.0035479539074003696,
-0.013990672305226326,
0.04987270012497902,
0.0070042735897004604,
-0.013671554625034332,
-0.02358414977788925,
0.01376782264560461,
-0.03153681382536888,
0.011018536984920502,
-0.0263932254165411,
0.04389993101358414,
0.016797248274087906,
-0.03470560163259506,
0.0022187891881912947,
-0.010221099480986595,
-0.02481710910797119,
0.00861349143087864,
0.001020036987029016,
0.004082607105374336,
-0.012441585771739483,
-0.0018828059546649456,
0.02290388010442257,
-0.01580747403204441,
-0.030392596498131752,
-0.03704594448208809,
-0.04358850046992302,
0.02917872741818428,
-0.01846419833600521,
-0.0019085669191554189,
0.020697275176644325,
-0.011398501694202423,
-0.018100155517458916,
-0.04280608519911766,
0.006349028553813696,
0.0019095864845439792,
0.011213366873562336,
-0.004177185706794262,
-0.013095948845148087,
0.013163411989808083,
0.03090840019285679,
-0.00677453400567174,
-0.047705911099910736,
0.012958874925971031,
-0.002329542301595211,
0.05188395082950592,
0.026037273928523064,
0.028619881719350815,
-0.029392225667834282,
0.06349898129701614,
0.004750649444758892,
-0.02641654759645462,
0.03371661156415939,
-0.027915656566619873,
-0.06473946571350098,
0.044714752584695816,
0.012715539894998074,
0.042803313583135605,
0.0031243807170540094,
-0.000503703486174345,
-0.025705574080348015,
0.06798145920038223,
0.025045890361070633,
-0.04117022454738617,
0.02057611010968685,
-0.03361036628484726,
0.020895276218652725,
-0.0007843122584745288,
0.015747208148241043,
-0.053764693439006805,
-0.031046733260154724,
0.009733392857015133,
0.014126562513411045,
-0.034725479781627655,
-0.00912690069526434,
0.007859141565859318,
-0.034248631447553635,
-0.020409075543284416,
-0.025004569441080093,
0.02022136189043522,
0.0003066106582991779,
0.029370371252298355,
-0.05389201641082764,
0.06291244924068451,
0.061267007142305374,
0.006362684536725283,
-0.09038528800010681,
-0.02002832479774952,
0.012714795768260956,
0.032709550112485886,
0.055900681763887405,
-0.07811756432056427,
0.012985940091311932,
-0.009742642752826214,
-0.06490715593099594,
0.014196579344570637,
-0.02850194461643696,
-0.04083053767681122,
-0.027911243960261345,
-0.020932553336024284,
0.0009767151204869151,
0.044468048959970474,
0.015454434789717197,
0.019049471244215965,
0.008525482378900051,
-0.0010392944095656276,
-0.028540659695863724,
0.00009709418372949585,
0.02252889983355999,
0.017066940665245056,
0.022832445800304413,
0.024486558511853218,
0.06765475124120712,
0.0022369942162185907,
-0.04320061206817627,
0.023027978837490082,
0.0037131865974515676,
-0.013552292250096798,
0.005681375972926617,
-0.009159435518085957,
0.0017526595620438457,
0.03785329312086105,
-0.005182314198464155,
-0.012397200800478458,
-0.004604799672961235,
0.0017639559227973223,
-0.010983308777213097,
0.01584852859377861,
-0.005355983041226864,
-0.0021614853758364916,
-0.013295629061758518,
-0.04861781746149063,
-0.02752779982984066,
0.010820982046425343,
0.0025260222610086203,
-0.03792710229754448,
-0.015085053630173206,
0.012473863549530506,
0.012511441484093666,
-0.029370678588747978,
0.03333858773112297,
-0.05976000800728798,
-0.010494708083570004,
0.037139151245355606,
0.006921772379428148,
-0.028647540137171745,
0.03250124305486679,
-0.014759674668312073,
-0.05695892125368118,
0.015384101308882236,
-0.017178641632199287,
-0.020536398515105247,
-0.03507349640130997,
-0.006821266375482082,
-0.0017678611911833286,
0.008928200230002403,
0.01948334276676178,
-0.007128797471523285,
-0.008547437377274036,
0.04487047716975212,
0.004368988797068596,
0.01685362122952938,
0.015658823773264885,
0.01190091110765934,
-0.025540681555867195,
-0.06267927587032318,
-0.008734415285289288,
0.004873096011579037,
0.030951453372836113,
-0.013139467686414719,
-0.03883608430624008,
-0.02014848217368126,
-0.013771148398518562,
0.0639890506863594,
0.007172854151576757,
-0.03513045608997345,
0.01703626476228237,
-0.03170192614197731,
-0.01875842548906803,
-0.05847496539354324,
0.0014059734530746937,
0.007088559679687023,
-0.014643187634646893,
-0.0017011627787724137,
-0.023311514407396317,
0.011195672675967216,
0.01853756792843342,
0.01363646611571312,
0.016082728281617165,
0.0013577858917415142,
-0.014787564054131508,
-0.03933663293719292,
0.05157230421900749,
0.01623982936143875,
0.02087140455842018,
0.06674358993768692,
0.026344753801822662,
-0.007070564664900303,
0.024435313418507576,
-0.02914036437869072,
-0.017216511070728302,
0.008729826658964157,
-0.04412583261728287,
-0.022651566192507744,
-0.011957326903939247,
-0.01033983938395977,
0.027015065774321556,
-0.03525504842400551,
-0.01763448305428028,
0.03715314343571663,
-0.02817869931459427,
0.008224989287555218,
0.03025767020881176,
-0.01728905364871025,
0.05176909640431404,
-0.0067903874441981316,
0.033774323761463165,
0.02526557631790638,
-0.015134668909013271,
0.023220598697662354,
0.021802334114909172,
0.02945941500365734,
0.03515223041176796,
-0.0005847351276315749,
-0.00830016192048788,
-0.0015008560148999095,
0.00156297255307436,
-0.03849039226770401,
0.03564463183283806,
-0.05848155543208122,
-0.006873888894915581,
0.039229247719049454,
0.0021781655959784985,
-0.017699986696243286,
0.03540773317217827,
0.02018621563911438,
0.06849568337202072,
-0.013991901651024818,
0.0051056803204119205,
-0.03363833576440811,
-0.03591812402009964,
0.004644370172172785,
0.01242377981543541,
0.006403190083801746,
0.058532845228910446,
-0.005677852313965559,
-0.01126576866954565,
0.013421210460364819,
-0.010223126038908958,
0.028607094660401344,
-0.028081990778446198,
0.003286309540271759,
0.004626687150448561,
-0.006192571949213743,
0.013745415024459362,
-0.015605519525706768,
-0.036673784255981445,
-0.003674241481348872,
0.028247347101569176,
0.047013912349939346,
0.020158326253294945,
0.025448095053434372,
0.021659012883901596,
-0.013221243396401405,
0.04084886237978935,
-0.0675177350640297,
-0.012376080267131329,
-0.027388911694288254,
0.0038246819749474525,
0.003734012134373188,
0.006455251947045326
] |
<p>I just started learning physics 3 days ago and am having trouble understanding what I am doing wrong. Can someone please explain my error(s)? Thanks!</p>
<p>We have a 1kg object on a plane at a 30 degree angle from horizontal. Force of friction is 1.5N. We are asked to calculate the net force. </p>
<p>I assume the object is moving along a line with negative slope (toward positive x and negative y quadrant). All vectors are as they would be interpreted in $\mathbb{R}^2$ Euclidean space. </p>
<p>I solved to get:</p>
<p>Force normal = [5.66, 9.8], I am assuming that the y component is 9.8N because otherwise the object would move vertically through the plane, right? I got to this assumption because I didn't understand how a vertical force, gravity, could cause motion at a non-vertical angle, so I assumed that the normal force must be pushing the object forward, rather than gravity pulling it forward.</p>
<ul>
<li>Force g = [0, -9.8]</li>
<li>Force friction = [-1.3, .75]</li>
</ul>
<p>adding to get</p>
<ul>
<li>Force net = [4.3, -.75]</li>
</ul>
<p>which is a 4.42N force acting at 30 degree angle.</p>
<p>The book I am using says the force should be 3.4N. The book rotates the the x,y axes by 30 degrees, I don't really like their way. I feel my main problem is not properly understanding the relationship between the normal force and gravity, and how it leads to motion at an angle.</p> | 2,863 | [
-0.024370279163122177,
0.0010521230287849903,
-0.03611350059509277,
0.046248145401477814,
0.034207284450531006,
0.015220445580780506,
-0.022409703582525253,
-0.02410978637635708,
0.013622717000544071,
-0.03704244643449783,
0.01507397647947073,
0.05897111818194389,
0.06907420605421066,
0.04729914665222168,
0.018417637795209885,
-0.0018490287475287914,
-0.044125646352767944,
-0.03669583052396774,
0.0016173799522221088,
-0.0270279198884964,
-0.018728332594037056,
0.027080433443188667,
0.024988990277051926,
-0.011833381839096546,
0.01578935980796814,
0.007563456427305937,
0.028539245948195457,
-0.02354896068572998,
0.029046542942523956,
0.04227140173316002,
0.0007543400279246271,
-0.04327203705906868,
0.008393565192818642,
0.003896065056324005,
-0.003361868904903531,
0.05106775462627411,
-0.01822185330092907,
-0.0031676727812737226,
-0.005096628796309233,
0.03130060434341431,
-0.023804552853107452,
0.012518892996013165,
-0.018328050151467323,
0.04861923307180405,
-0.03190270811319351,
0.05618886277079582,
0.025377118960022926,
0.01224080752581358,
0.06811633706092834,
-0.03302878141403198,
0.08974199742078781,
0.006299907807260752,
0.032198816537857056,
0.034445375204086304,
0.008489329367876053,
-0.046753667294979095,
0.050762102007865906,
0.05081782117486,
-0.007025052327662706,
-0.04753926768898964,
0.0025040474720299244,
-0.06525792926549911,
-0.04492725804448128,
-0.04648420587182045,
-0.014326509088277817,
0.03990888223052025,
-0.03014977090060711,
-0.043411023914813995,
0.03254784271121025,
0.011049049906432629,
0.036289624869823456,
0.029266804456710815,
0.014390825293958187,
-0.05288315564393997,
-0.03633261099457741,
-0.038632769137620926,
0.033180586993694305,
0.010421313345432281,
-0.005680677480995655,
0.04712766036391258,
-0.001755339908413589,
0.012001605704426765,
0.022941285744309425,
0.04122597724199295,
0.03564649075269699,
-0.042486269026994705,
0.09366552531719208,
-0.0008767504477873445,
0.01763003133237362,
0.01675877906382084,
0.0003057669964618981,
-0.008007760159671307,
0.019532183185219765,
0.02372479997575283,
-0.040273018181324005,
0.003071082988753915,
-0.010843073949217796,
0.0071545750834047794,
0.037097714841365814,
-0.03275950253009796,
-0.020776860415935516,
-0.039158161729574203,
0.01636028289794922,
0.06118263676762581,
0.002025770954787731,
0.00035000094794668257,
-0.025689836591482162,
0.019387511536478996,
-0.006613001227378845,
-0.029331473633646965,
-0.02284117415547371,
0.017487026751041412,
-0.043033212423324585,
-0.011465995572507381,
-0.00373974721878767,
-0.03182560205459595,
0.0016344340983778238,
0.01308419369161129,
0.02443001978099346,
0.0416276790201664,
0.04655752703547478,
-0.03542746603488922,
0.026251714676618576,
-0.029891101643443108,
-0.05661555379629135,
-0.00413181958720088,
0.03886035457253456,
-0.021774303168058395,
-0.003456492442637682,
0.026426395401358604,
-0.010125813074409962,
-0.007482679560780525,
0.009365071542561054,
-0.008584032766520977,
0.04699098318815231,
0.03993324190378189,
-0.08860500901937485,
-0.10402118414640427,
0.06353186815977097,
-0.007184920832514763,
0.013787157833576202,
-0.09373383969068527,
-0.011248425580561161,
0.0072436220943927765,
0.05252953991293907,
0.01080747228115797,
0.004544408060610294,
0.020228292793035507,
0.03712143003940582,
-0.02815122902393341,
-0.01589617133140564,
0.010483358055353165,
-0.007055574096739292,
-0.08053220063447952,
-0.0418221652507782,
-0.052232444286346436,
0.05184618756175041,
-0.006036046892404556,
0.01660545915365219,
-0.059167295694351196,
0.04078396037220955,
-0.04248197004199028,
0.015941347926855087,
0.017977720126509666,
-0.020043574273586273,
-0.046549830585718155,
0.05191303417086601,
0.014154440723359585,
0.014818602241575718,
0.0460815504193306,
0.015905290842056274,
0.03554889187216759,
-0.028022047132253647,
0.031314145773649216,
0.05903197079896927,
-0.006008666940033436,
0.009015983901917934,
-0.04162547364830971,
0.005767752416431904,
0.005923853255808353,
-0.0440581738948822,
-0.023061534389853477,
-0.012915699742734432,
-0.0004287371411919594,
-0.012850192375481129,
0.04389768838882446,
-0.015701454132795334,
-0.0006910809897817671,
-0.01486697793006897,
-0.018048256635665894,
-0.021427571773529053,
-0.07420449703931808,
0.04913830757141113,
-0.0017300534527748823,
-0.026774248108267784,
-0.010479633696377277,
0.025682460516691208,
0.03425763174891472,
-0.024800656363368034,
-0.02205721288919449,
0.00045389027218334377,
0.018447555601596832,
0.031307317316532135,
0.004630831070244312,
0.008461141027510166,
0.04309992492198944,
0.05853284150362015,
0.011219209991395473,
0.002315012738108635,
-0.04012160375714302,
0.018777713179588318,
-0.018116936087608337,
-0.026810703799128532,
-0.010713678784668446,
0.04460005834698677,
-0.002322148997336626,
0.02742593362927437,
0.016417518258094788,
-0.005939624272286892,
0.009563159197568893,
-0.030529754236340523,
0.06284120678901672,
0.0598728246986866,
0.00912520196288824,
-0.012711003422737122,
0.03696284070611,
-0.008590483106672764,
0.0014155341777950525,
0.004905996844172478,
0.005798028316348791,
-0.04826883599162102,
-0.00008024388807825744,
0.02212650142610073,
0.015216179192066193,
-0.04161914810538292,
0.00812048651278019,
0.05485310032963753,
0.0027807883452624083,
0.04324271157383919,
0.012509654276072979,
-0.00020581961143761873,
-0.03752213343977928,
0.011399601586163044,
0.03940558061003685,
0.01175695937126875,
0.005846762098371983,
0.0016086415853351355,
0.038423147052526474,
0.020498117431998253,
0.008282597176730633,
-0.04975355789065361,
0.05179929360747337,
-0.009367752820253372,
0.04042044281959534,
0.013255326077342033,
-0.009486958384513855,
0.05698631703853607,
0.008513253182172775,
-0.0074505931697785854,
0.029977019876241684,
0.00724812364205718,
0.0015188689576461911,
-0.017850125208497047,
0.012647236697375774,
0.03167986124753952,
0.012778573669493198,
-0.02254774607717991,
-0.0038130104076117277,
0.031462498009204865,
-0.03469957038760185,
0.02001032419502735,
-0.03496440872550011,
-0.01052818913012743,
-0.02256343886256218,
-0.0063296351581811905,
0.013804064132273197,
0.03161536529660225,
0.07337767630815506,
-0.022663071751594543,
-0.006987469736486673,
0.0215297881513834,
-0.027164191007614136,
-0.010814044624567032,
0.007444746792316437,
-0.03643488511443138,
-0.007386632263660431,
-0.05547093227505684,
-0.046702515333890915,
0.01853719912469387,
-0.002599853789433837,
0.01843942143023014,
0.0362229160964489,
-0.004551638849079609,
-0.025480369105935097,
-0.021838689222931862,
-0.044969506561756134,
0.0022202744148671627,
-0.0235736146569252,
-0.025208590552210808,
0.028532015159726143,
-0.03067183867096901,
0.025755297392606735,
0.053843043744564056,
-0.03319621458649635,
-0.026555614545941353,
-0.031745173037052155,
0.004311942029744387,
0.006276553962379694,
0.008602920919656754,
-0.026876825839281082,
-0.005918445065617561,
-0.031212307512760162,
0.019653983414173126,
-0.05400385707616806,
-0.03297804668545723,
-0.015859507024288177,
-0.0011440737871453166,
0.02236710861325264,
0.025303667411208153,
0.01013396866619587,
0.0752880647778511,
0.03577253222465515,
-0.03747718036174774,
-0.031427230685949326,
-0.0080250333994627,
-0.024340607225894928,
-0.07147049158811569,
0.00906316377222538,
0.026623833924531937,
-0.0032825942616909742,
0.013191540725529194,
-0.026978749781847,
0.0032455334439873695,
0.06851957738399506,
0.023885611444711685,
0.005293088965117931,
0.0012843201402574778,
-0.004790358245372772,
-0.026338806375861168,
0.07425687462091446,
0.01918160170316696,
-0.031327709555625916,
0.0028251877520233393,
0.007936088368296623,
0.03982357680797577,
0.010846692137420177,
-0.029895460233092308,
0.042519211769104004,
-0.007504930254071951,
0.0026285697240382433,
-0.0288247037678957,
0.03716807812452316,
0.009893599897623062,
-0.029877223074436188,
0.007125353440642357,
0.01824982278048992,
0.06972537189722061,
-0.02110266499221325,
0.0049082133919000626,
0.06585206836462021,
0.016039445996284485,
-0.02247285097837448,
-0.023297030478715897,
-0.008966753259301186,
-0.00018397056555841118,
0.03852717578411102,
-0.014616172760725021,
0.0014493371127173305,
0.00861381646245718,
0.020354686304926872,
0.006640033796429634,
0.01873091794550419,
-0.03949979692697525,
0.023293906822800636,
-0.043220385909080505,
0.006168703082948923,
0.010161451064050198,
0.027846964076161385,
-0.01684684492647648,
-0.00030144082847982645,
0.007102732080966234,
0.012451771646738052,
0.028666168451309204,
0.027156099677085876,
-0.08618271350860596,
0.057219624519348145,
-0.026264613494277,
-0.05244211480021477,
0.011662518605589867,
-0.03304668143391609,
-0.002409613225609064,
-0.020374111831188202,
0.026504745706915855,
0.037554048001766205,
-0.01648990996181965,
-0.040934886783361435,
0.00413365988060832,
-0.019101819023489952,
-0.015617113560438156,
0.003556807991117239,
-0.008700390346348286,
0.06083141639828682,
-0.030807552859187126,
-0.0072407228872179985,
0.06543277949094772,
-0.014203999191522598,
-0.030811697244644165,
-0.0049995495937764645,
0.0003355596272740513,
0.007829603739082813,
0.015323081985116005,
-0.007762601133435965,
0.03385848551988602,
0.04046803340315819,
0.007017022464424372,
-0.01571390964090824,
0.042316608130931854,
0.03835532069206238,
0.0049615465104579926,
-0.04540503770112991,
-0.07528308779001236,
-0.010873249731957912,
-0.022658174857497215,
0.051417089998722076,
0.005388601217418909,
-0.0076966360211372375,
0.04481431096792221,
0.00282863387838006,
-0.019243111833930016,
0.01040992233902216,
0.03638002648949623,
0.028846854344010353,
-0.022126158699393272,
-0.055474963039159775,
-0.013689897954463959,
-0.05180932581424713,
0.010420035570859909,
0.052803296595811844,
-0.010763532482087612,
-0.022937994450330734,
0.010257026180624962,
0.035571444779634476,
0.0047387718223035336,
-0.0007832137634977698,
0.03999393433332443,
-0.017565909773111343,
0.034263115376234055,
-0.020569464191794395,
-0.0089463135227561,
0.00474957562983036,
0.03998209908604622,
0.0394584983587265,
-0.02476350963115692,
-0.03559171035885811,
-0.0628962591290474,
-0.016805963590741158,
0.024123914539813995,
0.04507146775722504,
-0.025489790365099907,
-0.0027388117741793394,
-0.02259494550526142,
-0.022583186626434326,
0.033154960721731186,
-0.03334333375096321,
0.03795662894845009,
-0.025014059618115425,
-0.006585404742509127,
-0.014725039713084698,
-0.03555559739470482,
-0.059231050312519073,
-0.012675058096647263,
-0.047065507620573044,
0.028762251138687134,
-0.0069784140214324,
-0.05119723826646805,
0.01266296487301588,
0.004177447874099016,
0.02634202130138874,
0.05651026964187622,
-0.001824210281483829,
-0.04697795957326889,
0.02252841182053089,
-0.018405115231871605,
-0.02917567268013954,
-0.04460078477859497,
-0.006708591710776091,
0.00659120874479413,
0.004170568194240332,
0.0024572471156716347,
-0.001955212326720357,
-0.04130244255065918,
0.01631997898221016,
-0.007309980224817991,
-0.024326832965016365,
-0.010672538541257381,
-0.05023907870054245,
0.034160565584897995,
0.026680590584874153,
-0.024560604244470596,
0.03681866452097893,
0.010157493874430656,
-0.04139702022075653,
0.022153647616505623,
-0.06165222078561783,
0.03304579108953476,
0.015096438117325306,
0.008894740603864193,
-0.04604064300656319,
-0.01345459558069706,
0.028504321351647377,
0.03718159720301628,
0.013985743746161461,
0.033014655113220215,
-0.04458392411470413,
-0.02727191522717476,
-0.009787228889763355,
0.030521318316459656,
-0.003565475344657898,
0.01878192462027073,
0.04379245638847351,
-0.0017235275590792298,
0.01216208841651678,
-0.007393004838377237,
0.000688586791511625,
0.0001759465376380831,
-0.002899148967117071,
0.02701861970126629,
-0.006396092940121889,
0.0009960628813132644,
0.0007931584841571748,
-0.056078314781188965,
-0.007650809362530708,
-0.09104333072900772,
0.026357024908065796,
-0.014728469774127007,
0.0016588745638728142,
0.031661663204431534,
-0.03652601316571236,
-0.01802164502441883,
-0.004009169992059469,
0.02476534992456436,
0.0173377376049757,
-0.043818194419145584,
0.002476923866197467,
0.002327670343220234,
0.06438284367322922,
-0.010139350779354572,
-0.04848775267601013,
-0.003909222781658173,
-0.01572679542005062,
-0.024846024811267853,
-0.020448196679353714,
-0.014250172302126884,
-0.008310780860483646,
-0.028771793469786644,
0.01867598108947277,
0.0525648333132267,
-0.04943182319402695,
-0.0002633790427353233,
0.020650634542107582,
0.00825864914804697,
0.07094230502843857,
-0.03303809463977814,
-0.015723176300525665,
0.00885366927832365,
0.007002699188888073,
-0.05243060365319252,
-0.010778148658573627,
0.05364958941936493,
-0.03626963868737221,
-0.022984787821769714,
0.02674800343811512,
-0.009080340154469013,
0.04025961831212044,
-0.016256950795650482,
0.03344462811946869,
0.03309183567762375,
0.021718023344874382,
-0.031031807884573936,
-0.01818760111927986,
0.03344162181019783,
0.007855415344238281,
0.012297828681766987,
0.00345336995087564,
0.01798146404325962,
-0.016374604776501656,
-0.0668884739279747,
0.0421392060816288,
-0.012592649087309837,
0.043020084500312805,
0.011631795205175877,
0.07333400845527649,
-0.03253456577658653,
0.002610868774354458,
-0.0043797786347568035,
-0.024951720610260963,
0.040019817650318146,
0.03289448842406273,
-0.019777754321694374,
0.02952587977051735,
0.0074192071333527565,
-0.035313162952661514,
-0.05157669633626938,
-0.06450188159942627,
0.0249804574996233,
0.05734550207853317,
-0.02823413535952568,
0.06990958750247955,
0.03287380561232567,
-0.0005314690642990172,
-0.011235589161515236,
0.007762486115098,
-0.011010599322617054,
-0.010057209990918636,
0.02031036466360092,
0.013829801231622696,
0.006287482101470232,
-0.00539441779255867,
0.009164146147668362,
0.009523361921310425,
0.013144231401383877,
-0.004946362692862749,
0.021519295871257782,
-0.004717029631137848,
0.016101239249110222,
0.014355095103383064,
-0.048845257610082626,
0.021006900817155838,
-0.014557098969817162,
0.0793474093079567,
-0.019931919872760773,
-0.051866594702005386,
0.02414865791797638,
0.021472947672009468,
-0.03185432404279709,
-0.03699763864278793,
-0.01200659666210413,
-0.020882554352283478,
-0.03753497451543808,
0.017626332119107246,
-0.009624128229916096,
-0.012689797207713127,
0.027211207896471024,
0.062156062573194504,
0.0022567184641957283,
0.04849379137158394,
-0.01147489808499813,
-0.06123794987797737,
-0.008917647413909435,
-0.0368572473526001,
-0.02312505804002285,
0.03842012584209442,
-0.006145933642983437,
-0.04400721564888954,
0.028542449697852135,
-0.044518228620290756,
0.023925719782710075,
0.03418617323040962,
0.039699677377939224,
-0.010089771822094917,
0.08363822102546692,
-0.017309555783867836,
-0.00481957383453846,
-0.01962270401418209,
-0.00038857123581692576,
0.12951715290546417,
0.04461122676730156,
-0.006331908516585827,
-0.05679304525256157,
0.014407964423298836,
-0.020935798063874245,
-0.017216311767697334,
0.0011920630931854248,
0.015219051390886307,
0.0021100162994116545,
0.01161828450858593,
0.03346060961484909,
0.015902770683169365,
0.0010517373448237777,
-0.011209259741008282,
0.032233450561761856,
-0.04920569434762001,
-0.047511931508779526,
-0.00476616807281971,
0.0024968667421489954,
-0.01583201251924038,
-0.009043839760124683,
-0.02921716310083866,
0.03794440999627113,
-0.049048926681280136,
-0.02602134272456169,
-0.04090454801917076,
-0.023599155247211456,
0.04969051852822304,
-0.017362510785460472,
-0.07922539114952087,
0.007782734464854002,
-0.03788962587714195,
-0.045584507286548615,
-0.01969177834689617,
0.04629245400428772,
0.039484068751335144,
-0.002241780050098896,
0.015641914680600166,
0.027176637202501297,
-0.013937967829406261,
0.016658013686537743,
0.024715606123209,
-0.02937912940979004,
-0.04262090474367142,
-0.023657847195863724,
-0.0191333070397377,
0.058313459157943726,
-0.013500489294528961,
0.02846408635377884,
0.006235111504793167,
0.025869209319353104,
-0.0006817615358158946,
-0.05598486214876175,
0.02842738665640354,
-0.016674313694238663,
0.06557901203632355,
-0.0035613304935395718,
-0.022655218839645386,
-0.009076077491044998,
0.000038825055526103824,
0.037429291754961014,
0.008049173280596733,
0.034086912870407104,
0.0004888350376859307,
0.023390695452690125,
0.0015140800969675183,
0.058945417404174805,
-0.028153561055660248,
-0.003448827425017953,
-0.011223946698009968,
0.005495252087712288,
-0.03336319327354431,
-0.021023187786340714,
0.01421662699431181,
0.04904390498995781,
-0.0031894545536488295,
-0.04302031174302101,
-0.037775151431560516,
-0.026841621845960617,
-0.051186732947826385,
0.0163700133562088,
-0.0362936332821846,
-0.008492494001984596,
-0.010610894300043583,
-0.014463121071457863,
0.011745903640985489,
0.01114485040307045,
0.026922063902020454,
-0.0029753497801721096,
0.010869497433304787,
0.016811830922961235,
0.02086399681866169,
-0.0305581446737051,
-0.03783422335982323,
0.013294607400894165,
-0.02298315428197384,
-0.0031262929551303387,
0.018710579723119736,
0.023961778730154037,
0.03603523224592209,
-0.002075508004054427,
0.02092846669256687,
0.03164480999112129,
0.012782064266502857,
-0.006185927428305149,
0.012180031277239323,
-0.04485122859477997,
0.003507878864184022,
0.024768885225057602,
0.0117039754986763,
-0.06723449379205704,
-0.01316933985799551,
-0.032468199729919434,
-0.05545594170689583,
0.018230445683002472,
0.06439683586359024,
-0.012482890859246254,
-0.0020802447106689215,
-0.024012872949242592,
0.044008661061525345,
-0.02063862793147564,
-0.00830736942589283,
-0.02885264717042446,
-0.023199113085865974,
0.011138218455016613,
0.0054622432217001915,
-0.06630629301071167,
0.03229350224137306,
0.007887725718319416,
-0.0008469937602058053,
0.013912901282310486,
0.0254715234041214,
0.02880368009209633,
-0.00540695758536458,
-0.003911635372787714,
-0.023329289630055428,
0.04568934068083763,
-0.030607806518673897,
-0.037104349583387375,
0.03403108939528465,
-0.024556543678045273,
-0.028068147599697113,
0.03180064633488655,
0.015216462314128876,
0.041915811598300934,
0.01149737648665905,
-0.02214331179857254,
0.011929629370570183,
0.07252538949251175,
-0.023739585652947426,
0.01626349799335003,
-0.025370066985487938,
-0.01637434959411621,
-0.031557898968458176,
-0.02558242157101631,
-0.013132570311427116,
-0.017881859093904495,
0.044187359511852264,
0.046168021857738495,
-0.0014406820992007852,
-0.007203797809779644,
-0.0004297757113818079,
0.024086497724056244,
0.016810031607747078,
-0.028012758120894432,
0.0460200160741806,
0.01637260615825653,
0.024251621216535568,
0.02024361863732338,
-0.028997277840971947,
0.017325405031442642,
-0.002709565218538046,
0.04077405482530594,
-0.07492314279079437,
-0.03205538168549538,
0.0010424666106700897,
-0.014692150056362152,
0.06657052040100098,
-0.08101574331521988,
-0.02530628629028797,
0.016368472948670387,
-0.028188670054078102,
-0.007966031320393085,
-0.027674080803990364,
-0.026732604950666428,
0.0016893591964617372,
-0.003992727492004633,
0.04847725108265877,
0.014194557443261147,
-0.008477694354951382,
0.05048580840229988,
0.03325207158923149,
-0.010582995600998402,
-0.013176270760595798,
-0.03640313073992729,
0.01837996207177639,
0.03753676638007164,
0.0011621565790846944,
-0.010165315121412277,
0.0034825503826141357,
0.021588966250419617,
-0.0378304198384285,
0.031841523945331573,
-0.03459008038043976,
0.005403739400207996,
0.01924976147711277,
0.024557122960686684,
-0.028822479769587517,
0.011712088249623775,
0.017582498490810394,
0.01750405691564083,
-0.025396153330802917,
0.02661043591797352,
0.032464709132909775,
0.057166870683431625,
-0.005578859243541956,
-0.0018803441198542714,
0.007840978913009167,
-0.034432608634233475,
-0.024496236816048622,
0.015101968310773373,
-0.03700096905231476,
0.029115309938788414,
0.005507431458681822,
-0.014152061194181442,
0.004586257506161928,
-0.07156852632761002,
-0.011411450803279877,
-0.01872921921312809,
-0.01031413208693266,
0.0563611201941967,
-0.008216699585318565,
-0.004536920692771673,
0.002021423541009426,
0.012428087182343006,
-0.008884373120963573,
-0.0131228594109416,
-0.011360871605575085,
0.030239367857575417,
-0.0638047531247139,
0.004560817498713732,
-0.012544876895844936,
-0.049780119210481644,
0.0043879239819943905,
-0.014845003373920918,
-0.05396851897239685,
0.03647003322839737,
0.030266210436820984,
-0.004982001148164272,
-0.014051958918571472,
-0.03480828180909157,
-0.021540751680731773,
-0.07849990576505661,
0.03549693524837494,
0.033411722630262375,
-0.046560075134038925,
-0.033899348229169846,
0.017789892852306366,
-0.003415449522435665,
0.018313802778720856,
0.054445430636405945,
-0.02546285279095173,
-0.011471830308437347,
-0.014235622249543667,
0.022698817774653435,
0.009293577633798122,
-0.04345465451478958,
0.010302712209522724,
-0.01833464950323105,
-0.03192548081278801,
0.03217078745365143,
-0.001089898287318647,
-0.027307258918881416,
-0.0025098088663071394,
-0.0007837676093913615,
0.016916286200284958,
0.0272815003991127,
-0.01539094839245081,
-0.025031747296452522,
0.022788437083363533,
-0.0030643681529909372,
-0.00252177519723773,
0.045741599053144455,
0.0049158004112541676,
-0.003621317446231842,
0.051027823239564896,
-0.03569486737251282,
-0.04370317608118057,
0.02581462636590004,
-0.03247027099132538,
-0.013842196203768253,
-0.03396940976381302,
-0.0015362813137471676,
0.0314408540725708,
-0.09431035071611404,
-0.007274952717125416,
0.031210551038384438,
-0.0005645159399136901,
0.007104882970452309,
0.04280989617109299,
0.03326665982604027,
0.0417979396879673,
-0.0316382460296154,
0.03181273117661476,
0.02096068114042282,
0.007232896983623505,
0.02311035804450512,
0.002980791497975588,
0.016275418922305107,
-0.015569530427455902,
-0.017309721559286118,
0.04544805735349655,
-0.004546613898128271,
0.023429561406373978,
0.00847052875906229,
0.053750015795230865,
0.0062729716300964355,
0.004889372270554304,
-0.004678959958255291,
0.021032122895121574,
-0.004254245664924383,
0.042740706354379654,
0.007166912313550711,
0.034921351820230484,
-0.029698384925723076,
0.05104132369160652,
0.017847271636128426,
-0.008526784367859364,
-0.02204059064388275,
0.029604662209749222,
0.012932104989886284,
0.0403364822268486,
-0.00014459375233855098,
-0.03373413905501366,
-0.009640973061323166,
-0.005012765992432833,
0.018424415960907936,
0.008767422288656235,
-0.00730943726375699,
-0.010004552081227303,
0.008851601742208004,
-0.008571847341954708,
-0.03158748149871826,
-0.016142750158905983,
-0.034180350601673126,
0.014588728547096252,
0.009365319274365902,
-0.012306131422519684,
-0.042323362082242966,
0.026480862870812416,
-0.01583249866962433,
0.06350196897983551,
-0.07031898945569992,
-0.04594850540161133,
-0.01772323250770569,
0.029427355155348778,
0.007419451139867306,
-0.004224611911922693
] |
<p>In quantum mechanical systems which have classical counterparts, we can typically recover classical mechanics by letting $\hbar \rightarrow 0$. Is recovering Einstein's field equations (conceptually) that simple in string theory?</p> | 59 | [
0.002603314584121108,
-0.03958069905638695,
0.012219211086630821,
-0.0410957895219326,
0.008659228682518005,
0.0030589879024773836,
-0.04734841734170914,
0.0028125338722020388,
-0.0037021422758698463,
-0.010027187876403332,
0.016694385558366776,
-0.017121734097599983,
0.03603033348917961,
-0.01041963417083025,
0.023737607523798943,
0.012440118938684464,
-0.0023502742405980825,
0.0005148818017914891,
-0.012060693465173244,
-0.03443100303411484,
0.013086619786918163,
0.04245707765221596,
0.0015597561141476035,
0.030742112547159195,
-0.012900512665510178,
-0.018136458471417427,
0.019787179306149483,
0.014053843915462494,
0.013693705201148987,
0.07747334241867065,
0.016218610107898712,
0.004227654077112675,
0.015403999015688896,
0.06084907427430153,
0.007936977781355381,
-0.01323216687887907,
-0.009089328348636627,
-0.012702614068984985,
0.006291345693171024,
-0.03488239645957947,
-0.0402420237660408,
-0.02350146323442459,
-0.03019477054476738,
0.05526784807443619,
-0.001256219344213605,
0.02261069044470787,
-0.01655333861708641,
-0.007669670507311821,
0.039610087871551514,
-0.07588786631822586,
0.07581990957260132,
-0.005858537275344133,
0.015981517732143402,
0.03421469032764435,
-0.04195350036025047,
-0.03894413635134697,
0.08907570689916611,
0.046632662415504456,
0.021659323945641518,
-0.06847938895225525,
-0.07046599686145782,
-0.009356047958135605,
-0.010397564619779587,
-0.024205798283219337,
-0.03729511797428131,
0.057409171015024185,
0.003784437431022525,
0.00007675124652450904,
0.01545686461031437,
-0.010951533913612366,
-0.03092001937329769,
0.02326183393597603,
0.06542999297380447,
0.008489616215229034,
0.024088021367788315,
-0.01540763583034277,
-0.008783753030002117,
-0.02597472071647644,
0.017779968678951263,
0.049800027161836624,
-0.01127102691680193,
0.0013157121138647199,
0.04409860819578171,
0.020263655111193657,
0.01381573174148798,
-0.012364908121526241,
0.06685640662908554,
-0.015038615092635155,
0.024900292977690697,
0.0392005555331707,
-0.00920125748962164,
-0.0021341457031667233,
0.02705802395939827,
-0.01775592751801014,
-0.04499833285808563,
0.036880578845739365,
0.03138531744480133,
0.0701037123799324,
0.010748734697699547,
-0.02465970441699028,
-0.015083729289472103,
-0.03204099088907242,
0.00487210787832737,
0.06663954257965088,
0.008774559944868088,
0.0014488196466118097,
-0.03358463570475578,
0.019922727718949318,
-0.050775106996297836,
-0.008461989462375641,
-0.014146975241601467,
0.024828549474477768,
-0.034016236662864685,
-0.04145188629627228,
0.03247826546430588,
-0.021488314494490623,
-0.013004379346966743,
-0.04448461905121803,
0.08238175511360168,
0.06977637857198715,
0.0312923789024353,
-0.017306722700595856,
0.012677188031375408,
-0.012332324869930744,
-0.03273129090666771,
-0.029062101617455482,
0.028403302654623985,
-0.011837905272841454,
-0.057909224182367325,
-0.012362699024379253,
-0.012574145570397377,
-0.03209693357348442,
0.025950273498892784,
0.04058104753494263,
0.03438295051455498,
-0.031645096838474274,
-0.07993268966674805,
-0.05816039815545082,
0.006540194153785706,
-0.013094211928546429,
-0.0117649519816041,
-0.05425325408577919,
0.0035561327822506428,
0.01917727291584015,
0.061852872371673584,
0.008125425316393375,
0.006362125743180513,
0.04775786027312279,
0.03546221926808357,
-0.01820787973701954,
-0.014862319454550743,
-0.03665180504322052,
-0.002940500620752573,
-0.024155505001544952,
-0.013310299254953861,
-0.06998065859079361,
0.044676877558231354,
0.05229280889034271,
-0.008533740416169167,
0.0115809952840209,
0.07625933736562729,
-0.018898766487836838,
0.0039438712410628796,
0.02023133635520935,
-0.011612954549491405,
-0.004682173486799002,
0.03979939967393875,
0.005180275999009609,
-0.001463676686398685,
0.043170683085918427,
0.004098054952919483,
0.026359569281339645,
0.0480416938662529,
0.012684639543294907,
0.006763641256839037,
-0.0751991719007492,
-0.012630101293325424,
0.05089700594544411,
0.016278937458992004,
0.014771416783332825,
-0.009320384822785854,
-0.011241483502089977,
0.021952422335743904,
0.012271874584257603,
0.005599419120699167,
0.030179964378476143,
-0.02104625105857849,
-0.005593460984528065,
-0.023364804685115814,
-0.031111527234315872,
0.020225638523697853,
-0.061525896191596985,
0.0064154574647545815,
0.009925352409482002,
0.017353016883134842,
0.016758641228079796,
0.03338242694735527,
0.00960547849535942,
-0.025322671979665756,
-0.028046436607837677,
0.026934126392006874,
0.04782719537615776,
0.0015753324842080474,
-0.01538651529699564,
0.012258951552212238,
0.02713068574666977,
0.05803684890270233,
-0.01794779859483242,
0.06291916966438293,
-0.01081797108054161,
-0.06509674340486526,
0.01087198220193386,
-0.019624991342425346,
0.013340615667402744,
-0.025936946272850037,
0.020862119272351265,
0.03033379092812538,
-0.06905460357666016,
-0.013655007816851139,
0.05007178708910942,
-0.04065470024943352,
0.04676894098520279,
0.016012582927942276,
0.01835477724671364,
0.004738659597933292,
0.033749986439943314,
-0.010388374328613281,
0.0216190367937088,
0.028635352849960327,
-0.03542432188987732,
-0.041230108588933945,
-0.020830128341913223,
0.038268253207206726,
0.057654935866594315,
-0.028618698939681053,
0.040233220905065536,
0.05037682130932808,
0.012391118332743645,
0.006093968171626329,
0.022034956142306328,
-0.021531017497181892,
0.006684174761176109,
0.04861532151699066,
-0.009202075190842152,
0.012144838459789753,
0.017189892008900642,
0.04115915670990944,
0.018023168668150902,
-0.029203617945313454,
-0.004335188772529364,
-0.018165115267038345,
0.02605031244456768,
-0.0018590028630569577,
-0.003500664606690407,
0.008034261874854565,
-0.050385329872369766,
0.040393486618995667,
-0.032676465809345245,
0.04263997822999954,
0.02445119619369507,
-0.02618328481912613,
-0.0007602139376103878,
-0.025756943970918655,
0.010222450830042362,
0.0021089769434183836,
-0.023524900898337364,
-0.01817719079554081,
-0.0163966603577137,
0.0288113821297884,
-0.04829009249806404,
-0.02221035584807396,
-0.028298435732722282,
-0.010416933335363865,
-0.001810575369745493,
0.040885597467422485,
0.03147723153233528,
0.004414010792970657,
0.03551992028951645,
-0.03942108154296875,
-0.02878115139901638,
0.04274772107601166,
-0.004686271771788597,
-0.0014524949947372079,
0.025513319298624992,
-0.019915791228413582,
0.020439736545085907,
-0.04491887241601944,
-0.030975008383393288,
0.024291137233376503,
0.0011150393402203918,
0.04322890192270279,
-0.007460577879101038,
-0.0304098017513752,
-0.016079382970929146,
-0.03328021615743637,
-0.03519270569086075,
0.023767992854118347,
-0.022202013060450554,
0.0175703726708889,
0.04912067577242851,
0.0008632085518911481,
0.010681653395295143,
-0.0039534554816782475,
-0.013412299565970898,
-0.08526945114135742,
-0.01464258786290884,
0.015214765444397926,
0.04158172383904457,
-0.04679213836789131,
0.035777583718299866,
0.018516389653086662,
-0.08821915835142136,
-0.010253595188260078,
-0.07013030350208282,
-0.05089086294174194,
0.03136711195111275,
0.020582396537065506,
0.01188401784747839,
0.015405744314193726,
-0.04037941247224808,
0.07055952399969101,
-0.014593084342777729,
-0.029992705211043358,
0.004892023280262947,
-0.011959569528698921,
0.006525071337819099,
0.004846521653234959,
-0.0219303909689188,
0.00046647986164316535,
-0.020794393494725227,
0.01472062524408102,
0.024912405759096146,
0.014029481448233128,
0.0488346628844738,
0.01982705481350422,
-0.04131077975034714,
-0.009421727620065212,
0.0056304773315787315,
0.037543490529060364,
0.018790222704410553,
-0.014092883095145226,
-0.007548023015260696,
0.012667045928537846,
0.0227146465331316,
0.01989538036286831,
0.010774104855954647,
-0.04303717985749245,
0.053502559661865234,
0.033450741320848465,
-0.005792245734483004,
0.0013909353874623775,
0.007893642410635948,
-0.017683029174804688,
0.0020960415713489056,
0.0032825397793203592,
0.01665768027305603,
0.02515106089413166,
-0.009518622420728207,
-0.006118025165051222,
-0.0041900393553078175,
0.032885607331991196,
-0.04867655038833618,
-0.016380775719881058,
0.018156331032514572,
-0.035468608140945435,
0.019289007410407066,
-0.00999113917350769,
0.012602857314050198,
0.027906669303774834,
0.0530843548476696,
0.011188503354787827,
-0.007003276143223047,
-0.04018893092870712,
0.009012140333652496,
-0.07515746355056763,
-0.013709740713238716,
0.0018181263003498316,
0.024097904562950134,
0.004071598872542381,
0.04814669489860535,
0.007095967419445515,
0.03376208618283272,
0.006002260837703943,
0.02086685411632061,
-0.058888450264930725,
0.004029176663607359,
-0.05955237150192261,
-0.00900575052946806,
-0.012784969061613083,
0.01757858134806156,
0.023661090061068535,
-0.0236754659563303,
-0.03190133348107338,
-0.05025612190365791,
-0.008262939751148224,
-0.04451518878340721,
-0.0037877156864851713,
-0.04504027217626572,
-0.0735667422413826,
-0.0004241201968397945,
0.02985752932727337,
0.06659843772649765,
-0.0020618289709091187,
0.0027754404582083225,
0.060787368565797806,
-0.01969093456864357,
-0.02147495560348034,
-0.008415876887738705,
0.020716652274131775,
-0.013117709197103977,
0.04758301004767418,
0.055245064198970795,
0.022554870694875717,
-0.011633834801614285,
0.008178805001080036,
0.028844166547060013,
0.06970883160829544,
0.00010996664059348404,
0.003212703624740243,
0.008952939882874489,
-0.04537513107061386,
-0.02295912429690361,
-0.026361022144556046,
0.0688631534576416,
-0.033144619315862656,
-0.01901962235569954,
0.03156569227576256,
0.006202823482453823,
-0.009837889112532139,
0.019908860325813293,
0.057256247848272324,
-0.01186826266348362,
-0.027784936130046844,
-0.06373342871665955,
-0.0017951452173292637,
-0.04284060746431351,
0.005156874191015959,
0.015846136957406998,
-0.040678977966308594,
-0.03200089558959007,
0.012282346375286579,
0.039156779646873474,
0.037144582718610764,
-0.02890555001795292,
-0.015956861898303032,
0.0005300197517499328,
0.017988691106438637,
-0.013063540682196617,
0.028918875381350517,
0.02067689597606659,
0.05386306345462799,
0.04203736037015915,
-0.005252596456557512,
-0.006239496171474457,
-0.0916106328368187,
0.0017770420527085662,
-0.009560336358845234,
0.03452769294381142,
0.018402550369501114,
-0.024494744837284088,
-0.08172551542520523,
-0.033021993935108185,
0.05082463473081589,
-0.002169710583984852,
-0.0035257504787296057,
-0.007027582265436649,
-0.0015429522609338164,
0.02491729147732258,
-0.00023473240435123444,
-0.002673964248970151,
0.04939670115709305,
-0.016298191621899605,
-0.009569751098752022,
-0.016913989558815956,
0.03826058283448219,
-0.01961803436279297,
0.046340107917785645,
-0.003030098509043455,
0.02921098656952381,
0.04067693278193474,
0.015842294320464134,
-0.010952155105769634,
0.005988135933876038,
-0.057026684284210205,
-0.07498130202293396,
0.009605512954294682,
-0.022674493491649628,
-0.024972595274448395,
0.01982920989394188,
-0.001997580984607339,
-0.020703205838799477,
0.01438806764781475,
-0.02404068596661091,
0.028485851362347603,
0.029421163722872734,
-0.052859045565128326,
0.003921872936189175,
-0.0020068709272891283,
0.024418499320745468,
0.029779359698295593,
0.02932373248040676,
0.0017593189841136336,
-0.02905469946563244,
-0.021348707377910614,
0.040855772793293,
-0.043824583292007446,
-0.00023344704823102802,
-0.0381154902279377,
-0.022758277133107185,
-0.04123827442526817,
0.03059392049908638,
-0.027821121737360954,
0.017908191308379173,
0.02101881615817547,
-0.03745037317276001,
-0.014746337197721004,
-0.006596221122890711,
-0.006532105151563883,
-0.008523466065526009,
-0.015849299728870392,
0.017715008929371834,
-0.0180209930986166,
-0.02424418367445469,
-0.0012544613564386964,
0.017187509685754776,
0.008458319120109081,
0.02292707934975624,
0.006687088869512081,
0.037842877209186554,
-0.0110920500010252,
-0.01164320670068264,
0.015612030401825905,
-0.04404717683792114,
0.032994672656059265,
-0.015011679381132126,
-0.043391454964876175,
0.0043751634657382965,
-0.0447331964969635,
0.008790533058345318,
-0.02821037732064724,
-0.0010903525399044156,
0.002389592817053199,
-0.03963392600417137,
-0.002599102910608053,
0.027417752891778946,
0.016101589426398277,
-0.06440718472003937,
-0.05285912752151489,
0.020734569057822227,
0.028752168640494347,
-0.01153062004595995,
-0.01930522546172142,
0.03085939958691597,
-0.04106435552239418,
0.004168294370174408,
-0.02596515417098999,
0.07418897747993469,
-0.004282435402274132,
0.00017866541747935116,
0.007992181926965714,
0.029026342555880547,
-0.004461345262825489,
-0.005203560460358858,
-0.004618480335921049,
0.01882863976061344,
-0.02856675535440445,
0.0067259157076478004,
-0.018251953646540642,
0.04981613531708717,
-0.0012940565356984735,
-0.009859053418040276,
-0.030054889619350433,
-0.029527632519602776,
-0.009707178920507431,
0.028355661779642105,
0.017087526619434357,
0.048524267971515656,
0.027303265407681465,
-0.017371326684951782,
-0.007085986435413361,
0.009124742820858955,
-0.011582080274820328,
0.05197688192129135,
-0.029026485979557037,
-0.00016130905714817345,
0.0031016601715236902,
-0.0018219886114820838,
0.030869388952851295,
-0.005240992642939091,
-0.030961014330387115,
-0.005064583849161863,
0.08029400557279587,
0.003988603129982948,
-0.04103124514222145,
0.023684101179242134,
-0.016305435448884964,
0.009866385720670223,
0.0012536488939076662,
0.008906517177820206,
0.020780378952622414,
0.0045014675706624985,
-0.021547818556427956,
-0.07346451282501221,
-0.015973547473549843,
-0.006357345264405012,
0.06938174366950989,
-0.008678645826876163,
0.054270267486572266,
0.008818870410323143,
0.016005920246243477,
0.0221543125808239,
-0.02105707861483097,
-0.002543516457080841,
0.03236084058880806,
0.006248455960303545,
0.03215021267533302,
-0.015087367966771126,
0.01970827206969261,
0.03609931841492653,
0.02553272247314453,
-0.03302474319934845,
0.0043738060630857944,
0.008940067142248154,
0.006075214594602585,
0.008779124356806278,
-0.015605922788381577,
-0.04275258630514145,
0.02963731810450554,
-0.03234153240919113,
0.042806338518857956,
0.010297819040715694,
-0.024204181507229805,
0.05580965057015419,
0.018310392275452614,
0.008162925951182842,
0.01857004314661026,
-0.03278058394789696,
-0.027513770386576653,
0.042705636471509933,
0.004105960950255394,
0.047882914543151855,
0.010324225760996342,
0.010321104899048805,
0.021057579666376114,
0.014388651587069035,
0.04724772274494171,
0.027280168607831,
-0.06847409904003143,
-0.012823075987398624,
-0.055560942739248276,
-0.03866863623261452,
0.08350623399019241,
0.0498759001493454,
-0.0049890680238604546,
0.034276269376277924,
-0.01481033768504858,
0.03622589632868767,
0.008108565583825111,
0.056713636964559555,
-0.02937311865389347,
0.037093065679073334,
-0.006499779876321554,
-0.009431703016161919,
-0.014928620308637619,
0.016505882143974304,
0.12259752303361893,
0.07082259654998779,
0.02234247699379921,
-0.08052688837051392,
0.0007345259655267,
-0.04598325490951538,
-0.014757617376744747,
-0.04832670837640762,
0.03982806205749512,
0.0010057283798232675,
-0.022048138082027435,
-0.016164524480700493,
0.04734988138079643,
0.010914943180978298,
-0.03141138702630997,
0.06524212658405304,
-0.05982860177755356,
-0.016502106562256813,
-0.014317205175757408,
0.021319160237908363,
0.0009557800367474556,
0.034057021141052246,
-0.022664159536361694,
-0.004758210387080908,
-0.03027200512588024,
0.026006024330854416,
-0.031012529507279396,
-0.055200282484292984,
-0.0030971516389399767,
-0.021566957235336304,
-0.026552779600024223,
0.030349042266607285,
0.03142007812857628,
-0.008016197942197323,
-0.034457772970199585,
0.016362452879548073,
0.015177248977124691,
0.022762717679142952,
0.009062044322490692,
0.013910696841776371,
0.0030333080794662237,
0.024407705292105675,
-0.008047659881412983,
0.026740141212940216,
-0.03665276989340782,
0.0017626567278057337,
-0.013626784086227417,
0.055213045328855515,
-0.017679190263152122,
0.02669743075966835,
-0.014778327196836472,
-0.04739713668823242,
0.013929236680269241,
-0.029356293380260468,
0.007941437885165215,
0.024087633937597275,
0.02873717062175274,
-0.0227148849517107,
-0.011722812429070473,
-0.0179204773157835,
0.032238032668828964,
0.00164596491958946,
0.013861117884516716,
-0.008594594895839691,
-0.013435454107820988,
0.01761133037507534,
0.017662255093455315,
0.021084222942590714,
-0.037138987332582474,
-0.03062414936721325,
-0.02465367130935192,
-0.04227566346526146,
-0.0364840067923069,
-0.006701517850160599,
0.02683510072529316,
0.030953118577599525,
0.03891007974743843,
0.011552684009075165,
0.001917557674460113,
-0.019242823123931885,
-0.06009817123413086,
0.03493094444274902,
-0.03184507414698601,
-0.02381671965122223,
-0.04753629490733147,
0.012175804004073143,
0.02135658636689186,
0.05833256244659424,
0.009210772812366486,
0.00777992932125926,
-0.0053789932280778885,
-0.010902623645961285,
0.031373899430036545,
-0.023023594170808792,
0.00897053349763155,
-0.010292229242622852,
-0.029257940128445625,
-0.019282380118966103,
-0.02324424497783184,
0.01701359450817108,
0.014921513386070728,
0.030701763927936554,
-0.027915986254811287,
0.07011570036411285,
-0.027982857078313828,
0.027398020029067993,
0.03597308322787285,
-0.0341031514108181,
0.024335218593478203,
0.0062623354606330395,
0.03787858039140701,
-0.03410227224230766,
-0.040730927139520645,
0.004598615691065788,
0.014228465035557747,
0.0029842813964933157,
0.032922182232141495,
-0.042166274040937424,
0.02344951592385769,
-0.0010476676980033517,
0.012585073709487915,
-0.044832974672317505,
-0.008258659392595291,
-0.04382500797510147,
0.04567831754684448,
0.01514372881501913,
-0.052759312093257904,
-0.007767136674374342,
0.03406261280179024,
-0.0032721194438636303,
-0.05544378235936165,
0.022508056834340096,
0.04834362491965294,
-0.015215497463941574,
0.0020057535730302334,
0.024752235040068626,
0.0004617447266355157,
0.007256228942424059,
0.004230803344398737,
-0.051861755549907684,
0.009815292432904243,
-0.058928340673446655,
-0.03798193484544754,
0.027226345613598824,
-0.013235402293503284,
0.039154596626758575,
0.05667652189731598,
-0.05091932415962219,
-0.023018071427941322,
0.030577221885323524,
-0.028959788382053375,
-0.0004478788760025054,
0.053130242973566055,
-0.042013347148895264,
-0.006133296061307192,
0.009593733586370945,
0.006566615309566259,
0.001895243301987648,
-0.012611635029315948,
0.028327101841568947,
-0.006865051109343767,
0.007821585051715374,
-0.00810543168336153,
0.05321802198886871,
0.002256871899589896,
0.01092258095741272,
0.01868126355111599,
0.014312966726720333,
-0.0025720198173075914,
0.06281676143407822,
-0.027939191088080406,
0.031813956797122955,
0.030067645013332367,
0.0481598936021328,
-0.09741207212209702,
-0.0026720240712165833,
0.01961018703877926,
0.01776042766869068,
0.0430154949426651,
-0.028448613360524178,
0.0069958060048520565,
0.018844906240701675,
-0.05785725265741348,
0.05737655609846115,
-0.03525776043534279,
-0.0307117011398077,
-0.00572672626003623,
-0.023571694269776344,
-0.004914472810924053,
0.034165866672992706,
0.054656896740198135,
0.04593032971024513,
-0.016483737155795097,
-0.004458077717572451,
0.025620171800255775,
0.012617837637662888,
-0.006925813853740692,
0.02911425195634365,
-0.006927473470568657,
-0.024370230734348297,
0.05503542348742485,
-0.019130120053887367,
-0.05618632212281227,
0.004256529733538628,
0.03305748105049133,
-0.020725786685943604,
-0.00788577739149332,
0.00486405286937952,
0.03082035481929779,
0.005199203733354807,
0.015603393316268921,
-0.058739420026540756,
-0.0338863730430603,
0.004784749820828438,
-0.0031513518188148737,
0.014125418849289417,
-0.05126647651195526,
0.020911119878292084,
-0.0034129598643630743,
-0.04836343228816986,
-0.05210529640316963,
0.043892230838537216,
-0.002664637053385377,
-0.027174538001418114,
-0.020309308543801308,
-0.00179600331466645,
-0.019039174541831017,
0.008560086600482464,
0.003520852653309703,
-0.052579306066036224,
0.019498057663440704,
0.007252194453030825,
-0.01158053707331419,
-0.04653460159897804,
0.024795399978756905,
-0.03225264698266983,
-0.03203536942601204,
0.022067870944738388,
-0.003632197855040431,
-0.006928924471139908,
-0.05525832623243332,
0.010908180847764015,
0.014267166145145893,
0.0380781814455986,
-0.0010473259026184678,
-0.0853600949048996,
0.030195051804184914,
0.042477983981370926,
0.0027661623898893595,
0.014012365601956844,
-0.0271286740899086,
-0.04504967853426933,
-0.03587963804602623,
-0.08148997277021408,
0.004009842406958342,
-0.007864091545343399,
0.017810000106692314,
-0.024195708334445953,
-0.00266566826030612,
0.0003393715887796134,
-0.0028130689170211554,
0.03630558028817177,
-0.04054727405309677,
-0.0038617600221186876,
-0.0008979726117104292,
-0.005525101907551289,
0.013557800091803074,
-0.021176565438508987,
-0.006803175900131464,
-0.01026398129761219,
-0.0205916166305542,
-0.013125495053827763,
-0.0018829813925549388,
-0.014519833028316498,
0.04278872534632683,
0.02233051508665085,
-0.00841538980603218,
0.014003075659275055,
-0.0023717363364994526,
-0.025070803239941597,
0.04120267927646637,
-0.010622353293001652,
-0.027550337836146355,
0.06059896573424339,
-0.007111989893019199,
0.009698338806629181,
0.057516396045684814,
-0.011863961815834045,
0.012229527346789837,
0.008651933632791042,
-0.02717604488134384,
-0.05028827488422394,
-0.003649539779871702,
0.017137808725237846,
-0.001434901962056756,
-0.011581883765757084,
-0.003928199410438538,
0.048047855496406555,
-0.03684467822313309,
-0.009568743407726288,
0.04294464364647865,
-0.057227570563554764,
0.01916043646633625,
0.002287822775542736,
0.014543815515935421,
0.07148026674985886,
0.0006778058013878763,
0.018037855625152588,
0.04521380364894867,
0.0406600646674633,
0.005081149749457836,
0.01716308668255806,
0.019634926691651344,
-0.02186622843146324,
-0.0002346138790016994,
0.0018489768262952566,
0.04419698193669319,
-0.03826089948415756,
-0.032644856721162796,
-0.003990199416875839,
-0.018842874094843864,
0.014985127374529839,
0.0011837953934445977,
-0.02620312198996544,
0.07638466358184814,
-0.005972736515104771,
0.015413040295243263,
-0.0028901014011353254,
-0.0019071914721280336,
-0.01598959043622017,
-0.0009496076963841915,
-0.013733310624957085,
0.02552981674671173,
-0.00003169289630022831,
-0.015302381478250027,
-0.03382217139005661,
-0.0016737355617806315,
0.01564175821840763,
-0.0417315773665905,
-0.02367723546922207,
0.014931170269846916,
-0.019523316994309425,
0.009062808007001877,
-0.043369684368371964,
-0.02968832477927208,
-0.029194602742791176,
0.003088992089033127,
-0.005465880036354065,
0.03274306282401085,
-0.04328523203730583,
0.021121997386217117,
-0.038646798580884933,
0.029976297169923782,
-0.06673683226108551,
0.02002769522368908,
-0.014644225127995014,
0.006419050041586161,
-0.010486357845366001,
-0.03708011284470558
] |
<p>This is really a basic question whose answer I guess may have to do with the way we construct Feynman rules and diagrams. The question is: Suppose I have been given a two-point function (found in some other ways, say for example some gauge/gravity duality or some symmetry in the theory). How can we construct the Lagrangian of that theory from there?</p>
<p>Is there a general rule for that? Can you give me a reference?</p> | 2,864 | [
0.017741430550813675,
0.006340815220028162,
-0.013199505396187305,
-0.00820955727249384,
-0.006677801720798016,
0.037293385714292526,
-0.009221430867910385,
-0.027990972623229027,
0.00470000971108675,
-0.03491552546620369,
0.0042868731543421745,
0.0040952106937766075,
0.0737563893198967,
0.003923260141164064,
0.028737878426909447,
0.012256763875484467,
0.014155765064060688,
-0.0071489945985376835,
-0.00872876774519682,
-0.02655094489455223,
0.006080274935811758,
-0.012453695759177208,
-0.004158105235546827,
-0.014697006903588772,
-0.016183821484446526,
0.0076004271395504475,
0.027869362384080887,
0.040764980018138885,
-0.002772580599412322,
0.09007275104522705,
0.009529118426144123,
-0.045049868524074554,
0.025695936754345894,
0.02676883526146412,
0.017004236578941345,
0.013568774797022343,
-0.049950011074543,
-0.026011303067207336,
0.010795514099299908,
-0.011034716852009296,
-0.028160354122519493,
-0.004465381149202585,
-0.023846814408898354,
0.06790763884782791,
-0.029474860057234764,
0.01943512074649334,
0.004824399948120117,
-0.026508042588829994,
0.0846179649233818,
-0.059476304799318314,
0.05863603577017784,
0.031618017703294754,
0.01593257300555706,
0.037796083837747574,
-0.011824424378573895,
-0.016521185636520386,
0.06114938110113144,
0.044602230191230774,
0.0008629190851934254,
-0.05278930813074112,
-0.06954611092805862,
-0.044013991951942444,
0.000050346701755188406,
-0.03163078799843788,
-0.015820316970348358,
-0.0004978118231520057,
0.030563127249479294,
0.0008509759791195393,
0.013800135813653469,
-0.020583072677254677,
-0.011046145111322403,
-0.002000856911763549,
0.057094868272542953,
-0.007284844759851694,
0.008486722595989704,
0.007162272930145264,
0.0583481602370739,
-0.0024483066517859697,
0.015681682154536247,
0.026650501415133476,
-0.00029416620964184403,
0.05820546671748161,
0.05336447432637215,
0.021756073459982872,
0.005324476398527622,
-0.022819869220256805,
0.05955274775624275,
0.014177133329212666,
-0.000483968760818243,
0.027405092492699623,
-0.056636400520801544,
-0.013508234173059464,
0.06764855235815048,
-0.0315118208527565,
-0.018035123124718666,
0.013724482618272305,
0.008833063766360283,
0.048955753445625305,
0.016383174806833267,
-0.01669900119304657,
-0.009625365026295185,
-0.025148849934339523,
-0.012431550770998001,
0.06655354052782059,
-0.010304853320121765,
-0.008686433546245098,
-0.0071773589588701725,
0.014184604398906231,
-0.007666369434446096,
0.0034557876642793417,
-0.03699614480137825,
0.03573209047317505,
-0.018711119890213013,
0.0071652778424322605,
0.03016548790037632,
-0.010907954536378384,
0.0034452080726623535,
-0.008582196198403835,
0.08720114827156067,
0.04433075711131096,
0.06060626357793808,
-0.009675731882452965,
0.04451664909720421,
-0.02312435209751129,
-0.033657822757959366,
0.01094994880259037,
0.025843314826488495,
0.011019148863852024,
0.017140155658125877,
0.003581095254048705,
0.027080820873379707,
-0.015114686451852322,
-0.01212549302726984,
0.04267966002225876,
0.034663762897253036,
-0.0236111581325531,
-0.07765775918960571,
-0.05579883232712746,
-0.001005028374493122,
-0.0019275522790849209,
-0.007600503508001566,
-0.03687262162566185,
-0.000954728398937732,
0.019553113728761673,
0.08004304766654968,
-0.005531870294362307,
0.010294712148606777,
-0.020491067320108414,
0.02402830496430397,
-0.013945821672677994,
-0.0073381466791033745,
-0.022307831794023514,
-0.014925887808203697,
-0.05297403782606125,
-0.03011476993560791,
-0.055347833782434464,
0.03557293862104416,
0.007246736902743578,
-0.011868846602737904,
-0.04563268646597862,
0.1392190307378769,
-0.05657237023115158,
0.021214284002780914,
-0.022879499942064285,
0.0010655951919034123,
-0.005832625087350607,
0.06238529458642006,
0.017549598589539528,
-0.023541061207652092,
0.04664459824562073,
-0.011714963242411613,
0.01053249929100275,
0.01047042291611433,
0.026428554207086563,
0.04468709975481033,
-0.01891050674021244,
-0.05439852923154831,
-0.0018126298673450947,
0.030195018276572227,
0.0017718733288347721,
-0.017988044768571854,
-0.025993583723902702,
-0.0032889414578676224,
-0.0034984389785677195,
-0.025240445509552956,
0.023507485166192055,
0.01636255718767643,
0.002055143238976598,
-0.019659534096717834,
-0.05375535413622856,
-0.013386004604399204,
-0.055536117404699326,
-0.02602287381887436,
-0.0005244688945822418,
-0.007669142913073301,
0.04189589247107506,
0.01737314835190773,
-0.00916582066565752,
-0.03901248425245285,
-0.0708375796675682,
-0.004368775058537722,
0.03654801845550537,
0.01503508910536766,
0.010843095369637012,
0.01091060508042574,
0.02644883655011654,
0.05209880322217941,
0.015758778899908066,
0.06117863953113556,
-0.05356130748987198,
-0.006114883814007044,
0.009935515001416206,
-0.012624803930521011,
0.02574850805103779,
-0.011224674060940742,
0.022438114508986473,
-0.023183505982160568,
0.029403632506728172,
-0.012660430744290352,
0.03606822341680527,
-0.06987590342760086,
0.06863035261631012,
0.07649285346269608,
-0.0006399480043910444,
-0.030331242829561234,
0.027824852615594864,
-0.024140549823641777,
0.010053671896457672,
0.015875011682510376,
-0.03520834818482399,
-0.016222767531871796,
0.0001919939531944692,
0.03680061921477318,
0.021682489663362503,
-0.02659202180802822,
0.008626553229987621,
0.030309701338410378,
0.005546713713556528,
0.0094014722853899,
0.04446673393249512,
-0.07331809401512146,
-0.01483586709946394,
0.01618312858045101,
0.020792564377188683,
-0.000030825569410808384,
-0.0020730746909976006,
0.028494643047451973,
0.03869855776429176,
-0.030179107561707497,
0.025143299251794815,
-0.03803073242306709,
0.05724867433309555,
-0.019927598536014557,
-0.0029437860939651728,
0.009548861533403397,
-0.019317513331770897,
0.05819080024957657,
-0.035438891500234604,
0.044084470719099045,
0.015476995147764683,
-0.010239566676318645,
-0.03173058107495308,
-0.021740911528468132,
-0.004873346071690321,
0.029564645141363144,
-0.014892930164933205,
-0.052110712975263596,
0.01798231527209282,
0.028217723593115807,
-0.014504829421639442,
-0.005814549047499895,
-0.015423468314111233,
-0.002026319969445467,
-0.018343282863497734,
0.012792562134563923,
-0.0027216083835810423,
-0.027726752683520317,
0.038330793380737305,
-0.007945350371301174,
-0.05978308990597725,
-0.001853692694567144,
-0.025581127032637596,
0.03991212695837021,
0.04395526647567749,
-0.016850706189870834,
0.018850691616535187,
-0.06487781554460526,
-0.009208200499415398,
0.04095248505473137,
-0.005158404819667339,
0.04382145404815674,
-0.019733518362045288,
-0.017672337591648102,
-0.03145367652177811,
-0.008165388368070126,
-0.023311059921979904,
0.02164149284362793,
-0.004805953707545996,
-0.025319626554846764,
0.02179715782403946,
0.034514788538217545,
-0.036848217248916626,
0.003776917466893792,
-0.018987298011779785,
-0.035055011510849,
-0.01977216824889183,
0.03410221263766289,
0.0034024915657937527,
-0.05770336836576462,
0.017504706978797913,
0.01450060959905386,
-0.02732977084815502,
0.03657542169094086,
-0.04182935133576393,
-0.022400515154004097,
0.017578894272446632,
-0.004264120943844318,
-0.004128028638660908,
-0.012942485511302948,
-0.05595090612769127,
0.09329742938280106,
0.03939186409115791,
-0.03948405012488365,
-0.01910969614982605,
-0.023680156096816063,
0.011674284003674984,
-0.019135314971208572,
0.026131168007850647,
0.025596430525183678,
-0.020710231736302376,
0.05577977001667023,
0.03865344077348709,
-0.009221903048455715,
0.011801561340689659,
0.0036459267139434814,
0.015306117944419384,
-0.022831140086054802,
0.03417413681745529,
-0.008703476749360561,
0.03744397684931755,
0.01576775126159191,
-0.04378504306077957,
0.021172385662794113,
0.003675700630992651,
0.027237704023718834,
0.00995573215186596,
-0.027853677049279213,
0.041499827057123184,
0.017026958987116814,
-0.0039999461732804775,
-0.032948561012744904,
0.034679584205150604,
-0.0011794018791988492,
-0.03498784452676773,
0.012989424169063568,
0.02200341783463955,
0.00842191930860281,
-0.03010113164782524,
-0.01620578207075596,
0.031958870589733124,
0.06060604006052017,
-0.03726634383201599,
-0.04913720861077309,
-0.016513898968696594,
0.01119917817413807,
0.03017888404428959,
-0.008397844620049,
-0.04406028985977173,
0.039556749165058136,
0.02368580736219883,
0.006489500869065523,
-0.0008058648090809584,
-0.032880257815122604,
0.01142417173832655,
-0.05178976058959961,
-0.00014460526290349662,
0.0394367054104805,
0.048615604639053345,
-0.009515062905848026,
0.03608496114611626,
0.012765699997544289,
0.007682251278311014,
-0.007749936543405056,
0.0029142675921320915,
-0.06223045662045479,
0.061610300093889236,
-0.03290025517344475,
-0.02053796872496605,
-0.0005379499052651227,
-0.011250356212258339,
0.03510937839746475,
-0.023881640285253525,
-0.04119173809885979,
-0.017629560083150864,
-0.01798737607896328,
-0.01617218181490898,
0.010084347799420357,
-0.06182347610592842,
-0.04815753921866417,
-0.04049943387508392,
0.03909377381205559,
0.05075182393193245,
-0.0214834026992321,
-0.018721096217632294,
0.02674388699233532,
-0.006946837063878775,
-0.008537979796528816,
0.0018717319471761584,
0.03748440369963646,
0.02376806177198887,
0.011593104340136051,
0.011976465582847595,
0.02457199990749359,
0.007353933993726969,
0.02362050674855709,
0.0048742047511041164,
0.06457389891147614,
0.03317102789878845,
-0.01658931002020836,
-0.00884261354804039,
-0.018677959218621254,
-0.013709367252886295,
-0.014990516006946564,
0.08064791560173035,
0.024244073778390884,
0.008469391614198685,
0.04634591564536095,
0.03393544629216194,
-0.024846335873007774,
0.024624792858958244,
0.06843561679124832,
0.02498054876923561,
-0.0248783640563488,
-0.06330090761184692,
0.012905565090477467,
0.028718506917357445,
-0.003878682618960738,
-0.013400129973888397,
0.0007290957146324217,
-0.03218770772218704,
0.014988633804023266,
0.010847523808479309,
0.0008839030633680522,
-0.028364652767777443,
-0.007819069549441338,
-0.004627030808478594,
0.041459690779447556,
0.0206000879406929,
0.0024381016846746206,
0.009919049218297005,
0.04452288895845413,
0.0431329682469368,
0.03776830434799194,
-0.021761136129498482,
-0.05161438509821892,
-0.005015573464334011,
0.02209368906915188,
0.011270971968770027,
0.008635935373604298,
-0.0074600582011044025,
-0.048310671001672745,
-0.026697566732764244,
0.0747876986861229,
-0.014443841762840748,
0.006323112640529871,
-0.009411751292645931,
0.0070602805353701115,
0.009931436739861965,
0.010149233043193817,
-0.04213409498333931,
0.02548704482614994,
-0.019955238327383995,
0.0343724824488163,
-0.03694237768650055,
0.01555841974914074,
-0.020635148510336876,
0.040316518396139145,
0.030546065419912338,
0.0676775649189949,
0.0401545949280262,
-0.003946434240788221,
-0.04678741842508316,
0.013868763111531734,
-0.024068398401141167,
-0.06172587722539902,
-0.031671252101659775,
0.03419474512338638,
0.0037080098409205675,
0.009523298591375351,
-0.007115865126252174,
-0.025955483317375183,
-0.009280236437916756,
-0.03875984624028206,
-0.014908039942383766,
0.061928890645504,
-0.0273516234010458,
0.005574014037847519,
0.03978024050593376,
0.016109755262732506,
0.05765838921070099,
0.040667757391929626,
-0.008478488773107529,
-0.014980647712945938,
-0.028326911851763725,
0.024229442700743675,
0.004248207435011864,
0.010969256982207298,
-0.0353475920855999,
0.0010754773393273354,
-0.0239909365773201,
-0.0025225498247891665,
-0.021808354184031487,
0.014703178778290749,
0.011400597169995308,
-0.058878302574157715,
-0.028731144964694977,
0.039759330451488495,
0.025250667706131935,
-0.018773473799228668,
0.008038138039410114,
0.04520280659198761,
0.01757456362247467,
-0.027232596650719643,
-0.007024336606264114,
-0.0196290984749794,
-0.012897410430014133,
-0.002242572605609894,
-0.015001855790615082,
0.04574165865778923,
-0.014241521246731281,
-0.017955968156456947,
0.0002735392772592604,
-0.06620912998914719,
0.04250246658921242,
-0.0015033819945529103,
-0.026036957278847694,
0.004968380555510521,
-0.052876751869916916,
-0.0456395260989666,
-0.013154256157577038,
0.01227352861315012,
0.02311534993350506,
-0.0641537755727768,
0.022803857922554016,
-0.01090096216648817,
-0.0006429430213756859,
-0.07298039644956589,
-0.04094056040048599,
0.015209141187369823,
0.00012940011220052838,
-0.024917293339967728,
-0.009974685497581959,
0.0025301706045866013,
-0.04819253087043762,
-0.02179756574332714,
-0.016190562397241592,
0.07082640379667282,
0.003255911637097597,
-0.019884470850229263,
0.0018755820346996188,
0.0029280614107847214,
0.024066660553216934,
-0.00747448205947876,
-0.008330137468874454,
0.004073877353221178,
-0.02959766611456871,
0.008178390562534332,
0.00798820797353983,
0.01593203656375408,
-0.012565616518259048,
0.0217206459492445,
-0.011541659012436867,
-0.014471346512436867,
0.014558502472937107,
-0.04553865268826485,
0.01687006652355194,
0.03305046260356903,
0.04214353859424591,
-0.0041010333225131035,
-0.032105278223752975,
-0.02044103480875492,
-0.019313201308250427,
0.022309988737106323,
-0.01955871656537056,
0.015329988673329353,
0.0139260059222579,
-0.019065052270889282,
0.021276315674185753,
-0.009642488323152065,
0.02418562024831772,
0.012700154446065426,
0.010758054442703724,
0.01050386019051075,
-0.040834423154592514,
0.06196250766515732,
-0.017152249813079834,
-0.01778974011540413,
0.010057085193693638,
0.03299503028392792,
-0.0011291942792013288,
0.0038037614431232214,
-0.042461637407541275,
-0.005696580745279789,
-0.015528631396591663,
0.00535696791484952,
0.05532651022076607,
-0.02398327738046646,
0.049706656485795975,
0.023313969373703003,
0.011423459276556969,
0.0001270780776394531,
-0.017486676573753357,
-0.024594377726316452,
-0.05151636153459549,
0.0066230688244104385,
0.0616808719933033,
-0.036582767963409424,
-0.027431724593043327,
0.03467082977294922,
0.025217577815055847,
-0.02989840880036354,
0.04013921692967415,
0.003898363560438156,
0.01667162775993347,
0.02179093100130558,
-0.003654421539977193,
-0.033486299216747284,
0.01732100360095501,
-0.005096600390970707,
0.04299037158489227,
-0.0048746466636657715,
-0.06138024851679802,
0.02963537536561489,
-0.008592850528657436,
0.008844485506415367,
-0.008353020995855331,
-0.05706873908638954,
-0.041740842163562775,
0.019626321271061897,
0.032689061015844345,
0.02556188963353634,
0.026476455852389336,
0.03264564648270607,
0.033767007291316986,
-0.0157697182148695,
0.01862027309834957,
-0.0083821015432477,
-0.05588230490684509,
-0.031038768589496613,
-0.05389551818370819,
-0.0855567455291748,
0.04454035684466362,
0.002937563695013523,
-0.037611834704875946,
0.006168234162032604,
0.005655032582581043,
0.010637852363288403,
-0.014733854681253433,
0.0477742962539196,
-0.037808872759342194,
0.06544936448335648,
0.010103088803589344,
0.0032911028247326612,
-0.008800117298960686,
-0.015247649513185024,
0.08871445804834366,
0.06070425733923912,
0.0014571960782632232,
-0.13776005804538727,
0.026536008343100548,
-0.02970471791923046,
-0.000571256794501096,
-0.03693089634180069,
0.08312356472015381,
0.0020716425497084856,
0.0008603865862824023,
-0.0040373061783611774,
0.08097842335700989,
-0.013515923172235489,
-0.005274759605526924,
0.09264422208070755,
-0.01557832583785057,
-0.047619014978408813,
0.008181245997548103,
0.052113424986600876,
-0.028011221438646317,
-0.006643947679549456,
-0.010636611841619015,
-0.0027951286174356937,
0.006236883345991373,
0.034542981535196304,
0.03401283547282219,
-0.06370870769023895,
0.033451903611421585,
-0.0012856711400672793,
-0.013155044987797737,
-0.017981261014938354,
0.013805464841425419,
-0.022112585604190826,
-0.05364392697811127,
-0.028350867331027985,
-0.0004036522877868265,
-0.018262919038534164,
0.005968792364001274,
0.03974105417728424,
0.02833435870707035,
0.04925323277711868,
-0.001307023107074201,
0.002495009917765856,
-0.017712630331516266,
-0.0258027371019125,
-0.03334182873368263,
0.02837092988193035,
-0.019493483006954193,
0.0037751635536551476,
0.0124351866543293,
0.01875850185751915,
0.029840994626283646,
-0.016627004370093346,
0.002160297241061926,
0.0013176646316424012,
0.04368817061185837,
-0.013970728032290936,
0.005248009227216244,
-0.014237215742468834,
0.029843606054782867,
-0.03325586020946503,
0.009871489368379116,
-0.01697254739701748,
-0.003151085926219821,
-0.0052478802390396595,
-0.004756184294819832,
0.008916418999433517,
0.009790758602321148,
-0.029970621690154076,
-0.03874499723315239,
-0.058209843933582306,
-0.02989180199801922,
-0.00388406403362751,
0.02491786703467369,
0.014572263695299625,
0.012450279667973518,
-0.020172178745269775,
0.008720248006284237,
-0.018832700327038765,
-0.05046602711081505,
-0.011386213824152946,
-0.03501862287521362,
0.005692501086741686,
-0.003871518187224865,
0.02196916937828064,
0.015412778593599796,
0.07713211327791214,
0.008774228394031525,
-0.03093821555376053,
0.004206586163491011,
-0.006515210494399071,
0.016298366710543633,
-0.07582465559244156,
-0.019456490874290466,
-0.0005974545492790639,
-0.04039585962891579,
-0.050469718873500824,
-0.033554524183273315,
0.001207868685014546,
0.010558373294770718,
0.017550339922308922,
-0.007640572730451822,
0.026887284591794014,
-0.01780843548476696,
0.008121871389448643,
0.006366621237248182,
-0.00752226822078228,
0.008250385522842407,
0.030654234811663628,
-0.0045221177861094475,
-0.04928058385848999,
-0.058103982359170914,
0.02315562404692173,
-0.015933720394968987,
-0.0030350026208907366,
0.02910243719816208,
-0.05741726607084274,
0.005471766460686922,
-0.020559735596179962,
0.0014762119390070438,
-0.031071186065673828,
0.039301175624132156,
-0.055525220930576324,
0.035602595657110214,
-0.03261261805891991,
-0.014380262233316898,
-0.018854884430766106,
0.021408025175333023,
-0.03538135066628456,
-0.006332329474389553,
0.00017430909792892635,
0.021711915731430054,
-0.005809959024190903,
-0.014943000860512257,
0.018098343163728714,
-0.027878612279891968,
0.02563789300620556,
0.02691582776606083,
-0.013804841786623001,
-0.01076807826757431,
-0.03184150159358978,
-0.04254206642508507,
0.018867308273911476,
0.011151839978992939,
0.03034878894686699,
0.0308686476200819,
-0.015730667859315872,
0.012311264872550964,
0.015712333843111992,
-0.01788848266005516,
-0.033144041895866394,
0.005731222685426474,
-0.037751540541648865,
-0.010497760027647018,
-0.015217393636703491,
0.022076865658164024,
0.005125741474330425,
0.01974286325275898,
-0.00730123370885849,
-0.01530326809734106,
-0.023280810564756393,
-0.031119199469685555,
-0.000533430720679462,
0.007167160511016846,
0.04236811399459839,
0.018351120874285698,
-0.016095897182822227,
0.002226702170446515,
0.07013830542564392,
-0.017915235832333565,
0.007087730336934328,
0.010751510038971901,
0.0022822825703769922,
-0.08044908195734024,
-0.02543666400015354,
-0.0012600022600963712,
-0.024052763357758522,
0.05529848858714104,
-0.04127490520477295,
0.02216881513595581,
0.004689378198236227,
-0.03231341764330864,
0.014891458675265312,
-0.020479032769799232,
0.002826175419613719,
-0.0033980910666286945,
-0.011294063180685043,
-0.01577356457710266,
0.06952275335788727,
0.04199613630771637,
0.037467993795871735,
-0.001820485107600689,
-0.02159453183412552,
0.014419900253415108,
-0.018958302214741707,
-0.022691424936056137,
0.012128487229347229,
0.003824862651526928,
-0.0184875950217247,
0.07110996544361115,
-0.023120207712054253,
-0.051555365324020386,
0.019506994634866714,
-0.02394750528037548,
-0.0005510865012183785,
-0.0021896713878959417,
-0.02092035487294197,
0.019450528547167778,
0.013856271281838417,
0.003175638383254409,
-0.009317259304225445,
-0.013478637672960758,
0.02219833806157112,
0.02032363973557949,
-0.0005808787536807358,
-0.04912745952606201,
0.006884837988764048,
0.004263343755155802,
-0.019170917570590973,
-0.027844863012433052,
0.07352827489376068,
-0.01477660983800888,
-0.04388515278697014,
-0.0025167108979076147,
0.0005310047999955714,
0.04085468128323555,
-0.006198052782565355,
0.03802937641739845,
-0.04700067639350891,
0.018570274114608765,
0.04938283562660217,
0.0024709426797926426,
-0.014456341974437237,
0.039225704967975616,
-0.02546708658337593,
-0.043109212070703506,
0.03762275353074074,
0.015964949503540993,
-0.011769396252930164,
-0.09500839561223984,
0.00809995736926794,
0.009684356860816479,
-0.025190580636262894,
-0.002746966201812029,
-0.05696694925427437,
-0.007839150726795197,
0.020436115562915802,
0.020359482616186142,
0.024990059435367584,
0.00782534759491682,
-0.01616734080016613,
0.033202458173036575,
-0.07292253524065018,
0.035857800394296646,
0.013926192186772823,
0.01937108486890793,
-0.01850649155676365,
-0.019271787256002426,
0.01109278853982687,
0.005414473824203014,
0.033158328384160995,
-0.024090934544801712,
-0.016554709523916245,
-0.00926322303712368,
0.020567819476127625,
0.0005478931707330048,
-0.0023159023839980364,
-0.01606590673327446,
-0.012041137553751469,
0.002985043916851282,
-0.016700446605682373,
0.02288062870502472,
0.007252052891999483,
0.044199347496032715,
0.027719315141439438,
0.0065225702710449696,
0.021089833229780197,
-0.006485213525593281,
-0.05913693457841873,
0.02475774846971035,
0.010326261632144451,
0.002946386346593499,
0.03319980576634407,
-0.00559933390468359,
-0.002222298411652446,
0.044373441487550735,
-0.021403703838586807,
-0.02428273856639862,
0.020451311022043228,
-0.047134850174188614,
-0.033698488026857376,
-0.01851264387369156,
-0.008200917392969131,
0.01882416568696499,
-0.07347854971885681,
-0.001990735763683915,
0.03595058619976044,
0.01788240857422352,
-0.02222537063062191,
0.03969426080584526,
0.011914622969925404,
0.007098683156073093,
0.016156457364559174,
0.00313694030046463,
0.016069432720541954,
0.006893487647175789,
0.011766183190047741,
0.01987822726368904,
0.05790049955248833,
-0.0017452910542488098,
0.048491355031728745,
0.029892412945628166,
-0.004126703832298517,
0.022804560139775276,
-0.020247071981430054,
0.04770329222083092,
-0.03828155994415283,
0.019393401220440865,
-0.00009053883695742115,
-0.023872386664152145,
0.018772006034851074,
-0.0167787317186594,
-0.05097077041864395,
0.07339851558208466,
-0.03046584501862526,
0.001612905994988978,
-0.022259501740336418,
0.025239307433366776,
-0.015028310008347034,
0.012643362395465374,
0.028589585795998573,
0.1029643714427948,
0.007777147926390171,
-0.01774933747947216,
-0.024291768670082092,
-0.009226564317941666,
-0.009099718183279037,
-0.02679501101374626,
0.031673163175582886,
-0.0031951298005878925,
-0.006447122897952795,
-0.02782241627573967,
-0.005303116515278816,
-0.04283279925584793,
-0.014319008216261864,
-0.004690641537308693,
0.050348587334156036,
0.020521940663456917,
-0.00397517392411828,
-0.014707619324326515,
-0.03221606835722923,
0.0621124766767025,
-0.0822591707110405,
-0.024782778695225716,
-0.02331666275858879,
0.02905653603374958,
-0.02006727270781994,
0.005265995394438505
] |
<p>Here's an example to describe the issue</p>
<p>Supossed a high power laser (eg a 100 kW laser, ie, electromagnetic weapons)
is fired to a target, then it will receive energy and move.
(and likely to burn or explode, but that's not the point)</p>
<p>My question is, statting that photons have no mass</p>
<p>Would the laser transmitter get a kickback/recoil like in a "normal" gun?</p> | 2,865 | [
0.004660771228373051,
-0.023313989862799644,
-0.005649746395647526,
-0.040048032999038696,
0.033766455948352814,
0.029070621356368065,
-0.03347024321556091,
-0.021879009902477264,
0.02110883593559265,
-0.027111386880278587,
0.026541270315647125,
0.026553140953183174,
0.05900057032704353,
0.010127942077815533,
0.006172114983201027,
0.017227377742528915,
-0.007778009865432978,
-0.01279475912451744,
0.012446795590221882,
-0.058565881103277206,
-0.0038106536958366632,
0.020743828266859055,
0.014278767630457878,
-0.007447382435202599,
-0.027969524264335632,
0.030900411307811737,
0.016938725486397743,
-0.026387091726064682,
0.018880464136600494,
0.03751785680651665,
0.026125214993953705,
-0.017235541716217995,
-0.030330443754792213,
0.04268934950232506,
0.0012048910139128566,
0.026822807267308235,
-0.069459930062294,
-0.04823920130729675,
0.01724560186266899,
-0.009593556635081768,
-0.01868552342057228,
0.00966374296694994,
0.02236405946314335,
0.041244566440582275,
-0.06045287847518921,
0.0004176987276878208,
-0.02160593308508396,
-0.0007076974143274128,
0.05560564622282982,
-0.06316615641117096,
0.054046135395765305,
0.0054373242892324924,
0.05415887385606766,
0.013059674762189388,
-0.040001243352890015,
-0.0023423938546329737,
0.07593987882137299,
0.05241180583834648,
-0.01659126579761505,
-0.06159773841500282,
0.013746158219873905,
-0.011421735398471355,
-0.02134072035551071,
-0.018854785710573196,
0.0027794328052550554,
0.036452315747737885,
-0.027143768966197968,
-0.027639184147119522,
0.05093507096171379,
0.050346583127975464,
-0.020559510216116905,
-0.0010494632879272103,
-0.0013053956208750606,
-0.00752869900316,
0.0037375162355601788,
-0.008585480973124504,
0.029544759541749954,
0.03383946046233177,
0.03737640753388405,
0.021131059154868126,
-0.02428116463124752,
-0.01795332506299019,
0.01918283849954605,
0.048802923411130905,
0.01766206882894039,
-0.020756179466843605,
0.06157399341464043,
0.01100212149322033,
0.0044286614283919334,
0.027764365077018738,
-0.005682198330760002,
0.02224917523562908,
0.016105538234114647,
-0.0014683572808280587,
-0.022646602243185043,
0.021973561495542526,
0.000941745936870575,
0.07606250792741776,
0.01206272467970848,
-0.022157592698931694,
0.04293084144592285,
0.013487637974321842,
0.04949045553803444,
0.04467615485191345,
0.028337007388472557,
-0.050951942801475525,
-0.02046157605946064,
0.03362472727894783,
-0.04901786893606186,
-0.0000566073831578251,
-0.05064611881971359,
0.040398694574832916,
0.03939824923872948,
-0.022409968078136444,
0.04315345361828804,
-0.05033286660909653,
0.016554800793528557,
-0.03623446822166443,
0.0354032889008522,
0.04523015394806862,
0.025136319920420647,
-0.03860972076654434,
0.029704637825489044,
-0.02779177762567997,
-0.02884054183959961,
-0.0015567364171147346,
0.03553295508027077,
-0.008147897198796272,
-0.05515308305621147,
0.005668472498655319,
-0.02570764720439911,
-0.025598492473363876,
0.01915939524769783,
-0.029924441128969193,
0.03205789625644684,
-0.03621168062090874,
-0.08034104108810425,
-0.045067574828863144,
0.020878134295344353,
-0.0026459807995706797,
-0.037584252655506134,
-0.0679650828242302,
-0.030509361997246742,
0.016882820054888725,
0.09267722815275192,
0.0027345160488039255,
-0.013177069835364819,
0.00955988373607397,
0.0709419772028923,
-0.019648144021630287,
0.0023255751002579927,
0.008556459099054337,
0.007457669358700514,
-0.026841137558221817,
0.010314351879060268,
-0.061020951718091965,
0.013647963292896748,
0.0023756360169500113,
-0.015512346290051937,
-0.007964865304529667,
-0.01716182567179203,
-0.021618371829390526,
0.010258577764034271,
0.013752955012023449,
-0.0012308737495914102,
-0.029442865401506424,
0.08424471318721771,
0.03525586798787117,
-0.03843636065721512,
0.027286773547530174,
0.003723187604919076,
0.018109604716300964,
-0.010547068901360035,
0.0022139125503599644,
0.04486925154924393,
-0.043223440647125244,
-0.017947107553482056,
-0.0240242388099432,
0.024666668847203255,
0.010787242092192173,
-0.023189209401607513,
-0.03366878628730774,
-0.007437156978994608,
0.048249632120132446,
0.012847479432821274,
0.026594683527946472,
0.0018587002996355295,
0.028019843623042107,
0.000563805631827563,
-0.028152167797088623,
0.008183932863175869,
-0.06278006732463837,
0.07168301194906235,
0.008483189158141613,
-0.018747549504041672,
-0.009975800290703773,
0.005985854659229517,
0.0023223210591822863,
-0.01811901479959488,
-0.01729758270084858,
-0.001102196634747088,
0.01776949316263199,
-0.007178087718784809,
-0.0013365268241614103,
0.021679069846868515,
0.06549301743507385,
0.026004500687122345,
0.023008376359939575,
0.013276755809783936,
0.01185827236622572,
-0.0408271923661232,
0.0018497633282095194,
0.002449420979246497,
0.028671570122241974,
0.009063559584319592,
0.02011878229677677,
-0.010318093001842499,
-0.04115587845444679,
0.005476540420204401,
0.020081155002117157,
-0.02445535734295845,
0.08755069226026535,
0.056610461324453354,
-0.029081260785460472,
-0.0027972273528575897,
0.03803979977965355,
-0.003979590255767107,
-0.015712358057498932,
0.002492553321644664,
-0.04386705160140991,
-0.06038244068622589,
0.02156880311667919,
-0.026937609538435936,
-0.011209314689040184,
-0.06466883420944214,
0.04190335050225258,
0.052479177713394165,
0.03268461301922798,
0.043464429676532745,
0.0012608264805749059,
-0.04484311118721962,
-0.052569471299648285,
0.04560443386435509,
0.030295269563794136,
-0.007869199849665165,
0.008913867175579071,
0.04128013923764229,
0.018876701593399048,
-0.027105942368507385,
0.037661969661712646,
0.008690699003636837,
0.023566316813230515,
-0.01623569242656231,
0.0002744965604506433,
-0.01081913523375988,
-0.04376301169395447,
0.05584872514009476,
-0.034083042293787,
0.011003252118825912,
0.015177606604993343,
-0.032285891473293304,
-0.001574242953211069,
-0.03431278094649315,
-0.010638277046382427,
-0.04199035093188286,
0.01660189963877201,
-0.01838580332696438,
-0.014394041150808334,
0.0232715904712677,
-0.03195326402783394,
-0.014975417405366898,
0.005651324987411499,
0.013785046525299549,
-0.035879723727703094,
-0.018331825733184814,
0.044146109372377396,
0.009687894955277443,
0.01444240938872099,
-0.048041656613349915,
-0.05819712579250336,
-0.012356797233223915,
-0.04671423137187958,
-0.014989841729402542,
-0.005773412063717842,
-0.026493189856410027,
-0.014956013299524784,
-0.03329656645655632,
-0.05048857629299164,
0.048584893345832825,
-0.0066655888222157955,
0.03778551518917084,
0.025942690670490265,
-0.05402591452002525,
-0.05347519740462303,
0.00861009769141674,
-0.013171922415494919,
-0.019323593005537987,
-0.005673880223184824,
0.015700247138738632,
0.054567478597164154,
0.004396534990519285,
-0.01698317937552929,
-0.04612619802355766,
-0.014629073441028595,
-0.02503364346921444,
-0.032857004553079605,
-0.019911974668502808,
-0.00853862427175045,
-0.04343397170305252,
0.030114926397800446,
0.00587508687749505,
-0.052964065223932266,
0.028476940467953682,
-0.052063800394535065,
-0.032960664480924606,
0.027441419661045074,
0.007422974798828363,
0.0393151119351387,
0.02596411481499672,
-0.0035179031547158957,
0.061551544815301895,
0.020336095243692398,
-0.01523255929350853,
0.0027065041940659285,
-0.01973380148410797,
0.008801225572824478,
-0.018361473456025124,
-0.005764644593000412,
-0.004562075715512037,
0.016531992703676224,
0.016846144571900368,
0.044110413640737534,
0.0011716494336724281,
0.006065848283469677,
-0.007991855032742023,
-0.027901818975806236,
0.00867087859660387,
0.0139359962195158,
-0.005696543026715517,
0.07064255326986313,
0.03564991429448128,
-0.055410102009773254,
0.048824869096279144,
-0.00569735374301672,
0.014242937788367271,
-0.012220068834722042,
-0.028190886601805687,
0.052221085876226425,
0.034382421523332596,
-0.03196115419268608,
-0.015421589836478233,
0.06070442125201225,
-0.04857603460550308,
0.012344414368271828,
-0.0021449411287903786,
0.0441242940723896,
0.06761526316404343,
0.005639773327857256,
0.0018070871010422707,
-0.02309430204331875,
0.05512256175279617,
0.007853101938962936,
-0.017297763377428055,
0.031012266874313354,
-0.024217261001467705,
-0.022209854796528816,
0.006324154324829578,
-0.006173867266625166,
0.06047333404421806,
0.017550216987729073,
0.03579067811369896,
0.030622579157352448,
0.009301980957388878,
-0.02861449494957924,
-0.03432473912835121,
0.00873201247304678,
0.008675011806190014,
0.04005439206957817,
0.0023216179106384516,
0.029403042048215866,
0.04019410163164139,
0.029173128306865692,
0.012365400791168213,
-0.015266463160514832,
-0.07705524563789368,
0.0007766085909679532,
-0.021405404433608055,
-0.034310683608055115,
-0.003383667441084981,
0.0019208523444831371,
-0.049159564077854156,
-0.023137757554650307,
-0.030404092743992805,
-0.0035478619392961264,
-0.027601683512330055,
-0.05309951677918434,
-0.008071834221482277,
-0.02974708192050457,
-0.047348495572805405,
-0.008703978732228279,
-0.013138691894710064,
0.015666641294956207,
-0.01727479323744774,
-0.01604233868420124,
-0.003930276725441217,
-0.02116578258574009,
0.012645715847611427,
-0.012567614205181599,
0.005333136301487684,
-0.01027993019670248,
0.035974983125925064,
0.055859725922346115,
0.019916610792279243,
-0.027423448860645294,
0.029836155474185944,
0.007371067069470882,
0.04708890616893768,
0.024829106405377388,
-0.03385866433382034,
-0.03827818110585213,
-0.03396819531917572,
-0.022112270817160606,
0.012470896355807781,
0.05635066330432892,
0.007708445657044649,
-0.0037694855127483606,
-0.009657775983214378,
-0.013426309451460838,
0.029279978945851326,
0.015234722755849361,
0.04455672204494476,
0.01942478120326996,
-0.014967773109674454,
-0.04699486866593361,
0.05566852167248726,
-0.01961594633758068,
-0.0059834690764546394,
-0.0056357113644480705,
0.0063643683679401875,
-0.0028065748047083616,
0.022817032411694527,
0.0032534601632505655,
0.01701873354613781,
-0.014476338401436806,
-0.005203623790293932,
-0.0011858480283990502,
0.00778277637436986,
-0.011068122461438179,
0.00851907953619957,
0.008536804467439651,
0.021901696920394897,
0.02503913827240467,
0.014650893397629261,
0.011886577121913433,
-0.11296121776103973,
0.015011273324489594,
0.03819362446665764,
0.0413406677544117,
-0.009000795893371105,
-0.02281748503446579,
-0.027182884514331818,
-0.005603081546723843,
0.027409285306930542,
-0.033561356365680695,
0.045495644211769104,
-0.02762175351381302,
-0.004046372137963772,
0.015768038108944893,
-0.013047097250819206,
-0.008331059478223324,
-0.001583149190992117,
-0.01772947795689106,
-0.004427656996995211,
-0.025073982775211334,
-0.012682256288826466,
0.028202982619404793,
0.015663892030715942,
0.028824420645833015,
0.04314092919230461,
-0.00794081762433052,
-0.028504159301519394,
0.004435378592461348,
0.0271653700619936,
0.005127560347318649,
-0.08940339833498001,
0.02243015542626381,
0.01169566810131073,
-0.035893846303224564,
0.045379072427749634,
-0.015429859980940819,
-0.03921591490507126,
0.01536841131746769,
0.017919782549142838,
-0.019524434581398964,
-0.03523336723446846,
-0.03533581644296646,
-0.03606116399168968,
0.0387176051735878,
-0.010942460037767887,
0.025906987488269806,
0.07318343222141266,
-0.031976982951164246,
0.016125032678246498,
-0.02643199823796749,
0.030993856489658356,
-0.03962935134768486,
-0.018371552228927612,
-0.059216853231191635,
0.025169525295495987,
-0.04038975387811661,
0.06715857982635498,
-0.01096729002892971,
-0.014548046514391899,
0.05380601808428764,
-0.0006812195060774684,
0.00420765858143568,
0.020711056888103485,
-0.034371502697467804,
0.020931217819452286,
-0.08523774892091751,
0.05232638120651245,
-0.04055096209049225,
-0.0007423590868711472,
0.007999132387340069,
0.028493845835328102,
-0.003174601821228862,
0.01932946965098381,
-0.0005161979934200644,
0.0013525641988962889,
-0.047721218317747116,
-0.0023204730823636055,
0.020342227071523666,
-0.05237067863345146,
0.06834942102432251,
0.02309291437268257,
-0.013209314085543156,
-0.0060259015299379826,
-0.043874386698007584,
-0.037668101489543915,
-0.007398536428809166,
-0.003332314547151327,
0.039266180247068405,
-0.0432552732527256,
0.03728855401277542,
-0.029742825776338577,
-0.006134122610092163,
-0.044972922652959824,
-0.03943805396556854,
0.018759578466415405,
-0.002217960311099887,
0.03591153025627136,
-0.001605506637133658,
0.016900992020964622,
-0.05220509320497513,
-0.013520894572138786,
-0.0014791846042498946,
0.012681511230766773,
-0.023185184225440025,
0.0062090069986879826,
0.031375087797641754,
-0.04922647774219513,
0.04180214926600456,
-0.012276194989681244,
-0.05455708131194115,
0.04797004163265228,
0.009316431358456612,
-0.03542143851518631,
-0.029575010761618614,
0.055753543972969055,
-0.028598416596651077,
-0.04472111165523529,
-0.018893089145421982,
0.0014228575164452195,
0.029276786372065544,
-0.010548197664320469,
-0.012863928452134132,
0.013483209535479546,
0.00011522576824063435,
0.0192423015832901,
-0.024175958707928658,
0.016467886045575142,
-0.001466949936002493,
0.019996410235762596,
-0.005868297535926104,
0.000900828861631453,
-0.03831314295530319,
-0.03557337448000908,
0.06245673820376396,
0.02893931046128273,
0.0293908528983593,
0.014458301477134228,
0.04773188754916191,
0.011699452996253967,
0.007364347577095032,
0.030227603390812874,
0.00013628360466100276,
0.029489977285265923,
-0.02824685536324978,
0.004949960391968489,
0.0061510829254984856,
-0.007185485679656267,
-0.006477151997387409,
-0.033928804099559784,
-0.02753561921417713,
-0.0010465328814461827,
0.08020161837339401,
-0.026992781087756157,
0.061583567410707474,
-0.01686309278011322,
-0.003221758408471942,
0.009529359638690948,
-0.013932816684246063,
-0.014959448017179966,
0.007420949172228575,
0.019679969176650047,
0.006232716143131256,
-0.012741606682538986,
0.002620929852128029,
0.043852221220731735,
0.04808705300092697,
0.005607497878372669,
0.0325179398059845,
0.004392096307128668,
0.033566154539585114,
0.0042755561880767345,
-0.029838960617780685,
-0.03539043292403221,
0.02064349688589573,
-0.06617990136146545,
0.017402883619070053,
0.0013324088649824262,
-0.0016246564919129014,
0.01784558780491352,
-0.005906020291149616,
0.01049425546079874,
-0.02498869225382805,
-0.018265139311552048,
-0.057424385100603104,
0.05531683564186096,
-0.015261366032063961,
0.025416087359189987,
0.0109651368111372,
0.020922210067510605,
0.027229662984609604,
-0.013268396258354187,
0.0345781184732914,
0.0032877495978027582,
-0.0699649453163147,
-0.048762496560811996,
-0.02496728114783764,
-0.04999638348817825,
0.055992767214775085,
-0.019144462421536446,
-0.0004980824305675924,
0.014471425674855709,
-0.025618689134716988,
0.026760093867778778,
0.031446125358343124,
0.04710041731595993,
-0.0014603255549445748,
0.06347940117120743,
-0.0022827910725027323,
0.004769319202750921,
-0.014405325055122375,
0.04989209026098251,
0.08565417677164078,
0.020962202921509743,
0.028211962431669235,
-0.016192227602005005,
0.005071014631539583,
-0.03824051469564438,
0.030785655602812767,
-0.005219628103077412,
0.03452513739466667,
-0.036060038954019547,
0.019018543884158134,
0.026543742045760155,
-0.013139884918928146,
-0.01995074562728405,
0.019526734948158264,
0.015674060210585594,
-0.028903890401124954,
-0.035864606499671936,
0.03617521747946739,
0.005050090607255697,
0.0053671495988965034,
0.0531887412071228,
-0.018937356770038605,
0.03119628131389618,
-0.02176399528980255,
-0.011564393527805805,
-0.0033810841850936413,
-0.037120271474123,
0.01194941159337759,
0.040939126163721085,
-0.04140675812959671,
-0.036409977823495865,
0.00604646559804678,
-0.019485456869006157,
-0.039962414652109146,
0.0360974483191967,
0.0028496331069618464,
-0.001929445075802505,
-0.023523101583123207,
0.005420461297035217,
0.03102297894656658,
0.003321930533275008,
0.0017503901617601514,
0.015430226922035217,
-0.06417037546634674,
0.013911225832998753,
-0.01577839069068432,
0.05072193220257759,
-0.012485290877521038,
0.010160304605960846,
0.002772760344669223,
0.008843699470162392,
0.032155901193618774,
-0.05472610518336296,
-0.018558263778686523,
-0.002571204910054803,
0.011681968346238136,
0.0032939466182142496,
-0.013051715679466724,
-0.0004354120173957199,
0.0318165123462677,
-0.00016346934717148542,
0.010510072112083435,
-0.02451772801578045,
0.046803995966911316,
-0.003378276014700532,
-0.022062592208385468,
0.033064089715480804,
-0.020224427804350853,
-0.0521632544696331,
0.005493899341672659,
0.001611044630408287,
-0.04385248199105263,
-0.0362214632332325,
-0.0011856521014124155,
0.04307965561747551,
0.01924522966146469,
0.025149239227175713,
-0.0006354693323373795,
-0.0316028967499733,
-0.10270903259515762,
0.06218207627534866,
-0.03186178579926491,
-0.030410870909690857,
-0.001796059776097536,
-0.005655422806739807,
0.04467932879924774,
0.04231339693069458,
-0.017237193882465363,
-0.022687796503305435,
-0.006167634855955839,
0.020306279882788658,
0.025534208863973618,
-0.03276240825653076,
-0.010007836855947971,
0.05563416704535484,
-0.00864019151777029,
-0.005178061313927174,
-0.018381547182798386,
0.0050961608067154884,
0.03553396835923195,
-0.01049010083079338,
0.016495665535330772,
0.010892645455896854,
-0.04505851864814758,
-0.027221569791436195,
0.018886853009462357,
0.001778353238478303,
0.0020385554526001215,
0.019289422780275345,
0.027322368696331978,
-0.0017094692448154092,
-0.03800227865576744,
-0.02334979735314846,
-0.03778059780597687,
-0.019447147846221924,
0.04229440167546272,
-0.008403454907238483,
0.011855599470436573,
-0.021073227748274803,
0.0054016136564314365,
-0.013488320633769035,
-0.01956114172935486,
-0.04953461512923241,
0.005337490700185299,
-0.0007864285726100206,
-0.0077760000713169575,
-0.030764859169721603,
0.01904892921447754,
-0.04650750011205673,
-0.02294754795730114,
0.009153936058282852,
0.04945477843284607,
-0.005150787066668272,
0.025760672986507416,
-0.02203071117401123,
0.015298143960535526,
0.04046733304858208,
-0.0035665794275701046,
0.027149111032485962,
0.029328996315598488,
-0.03362872079014778,
-0.02516334317624569,
0.03457384184002876,
-0.055816132575273514,
0.03854857012629509,
0.02874317765235901,
-0.003295690519735217,
-0.026248950511217117,
0.08640821278095245,
0.023807229474186897,
0.00027832918567582965,
0.022032590582966805,
-0.06968917697668076,
0.020982377231121063,
0.0644531100988388,
0.02234197035431862,
-0.03319335728883743,
-0.031146908178925514,
0.03339540213346481,
0.025888776406645775,
-0.008976306766271591,
0.015283908694982529,
0.04480354115366936,
0.009022913873195648,
-0.024264464154839516,
-0.004087856970727444,
-0.002818963024765253,
-0.012245558202266693,
0.047957103699445724,
-0.040232837200164795,
-0.004306256305426359,
-0.007140959147363901,
0.005058040376752615,
-0.14615017175674438,
-0.005373187363147736,
0.002739868126809597,
0.006663436070084572,
0.018089182674884796,
-0.04921286925673485,
0.011007864028215408,
0.03740648552775383,
-0.09590525180101395,
-0.018743574619293213,
-0.03370429575443268,
-0.03525696322321892,
-0.05581570044159889,
0.03316430374979973,
-0.03313519060611725,
0.030380435287952423,
0.008721507154405117,
0.02935425192117691,
0.005402592476457357,
0.007960821501910686,
0.0029916311614215374,
0.008877442218363285,
-0.02678067795932293,
0.026037853211164474,
-0.013875486329197884,
0.01773371547460556,
0.04753010347485542,
-0.015720941126346588,
-0.005904756486415863,
0.04674452915787697,
0.011858319863677025,
0.05565590783953667,
0.0007088893325999379,
0.0318831205368042,
0.033303506672382355,
0.015480571426451206,
0.0027582852635532618,
0.005325669888406992,
-0.0013202570844441652,
0.01121885422617197,
0.044287048280239105,
0.025162221863865852,
-0.025348026305437088,
0.053769614547491074,
0.015343891456723213,
-0.03681843727827072,
-0.0034021539613604546,
0.02278878726065159,
-0.024926647543907166,
-0.03309011459350586,
-0.016412364318966866,
0.03011118806898594,
-0.009718614630401134,
-0.03730800375342369,
0.01545393280684948,
-0.08427758514881134,
-0.010424052365124226,
0.013463132083415985,
0.010955040343105793,
0.002882471075281501,
-0.017832927405834198,
-0.013784300535917282,
-0.01806034706532955,
0.003295476548373699,
0.017760002985596657,
-0.005128468852490187,
-0.05134699121117592,
0.00387753639370203,
0.0004985238774679601,
-0.000007539364105468849,
0.001406495226547122,
-0.05993102490901947,
-0.010693460702896118,
0.046549033373594284,
-0.013661949895322323,
0.01520937867462635,
0.026400411501526833,
0.0037259182427078485,
-0.03272342309355736,
-0.09006472676992416,
0.0012942022876814008,
0.008256228640675545,
0.022217396646738052,
-0.06808073073625565,
-0.03435865789651871,
0.024889709427952766,
0.008843248710036278,
0.026950685307383537,
-0.008295511826872826,
-0.027432722970843315,
0.06692837178707123,
-0.045535702258348465,
-0.023685764521360397,
-0.027674345299601555,
-0.011523264460265636,
-0.018809206783771515,
-0.02811439335346222,
-0.03385839983820915,
-0.008302212692797184,
-0.009669559076428413,
0.014208424836397171,
0.05965892970561981,
0.007860819809138775,
-0.015848243609070778,
-0.05415619909763336,
-0.05236189812421799,
0.036162130534648895,
0.020377377048134804,
0.014408084563910961,
0.05081991106271744,
0.017845014110207558,
0.02235240489244461,
0.02509722299873829,
-0.016522346064448357,
-0.033655762672424316,
0.013821208849549294,
-0.007467096671462059,
0.007829447276890278,
-0.029187649488449097,
0.008579587563872337,
0.033660683780908585,
-0.02487228438258171,
0.01257123053073883,
0.045973025262355804,
-0.026243001222610474,
0.028366809710860252,
0.057508911937475204,
0.00817619077861309,
0.03517717495560646,
0.013969107531011105,
0.05633179843425751,
0.0356890931725502,
0.015620894730091095,
-0.009092438034713268,
0.03524050489068031,
-0.005281116813421249,
0.00839131511747837,
0.017646469175815582,
0.030222240835428238,
-0.037048760801553726,
-0.01948687434196472,
0.0029536020010709763,
0.022547053173184395,
-0.007031301502138376,
0.015109340660274029,
0.020713258534669876,
0.030014118179678917,
-0.009549515321850777,
0.02721085026860237,
0.010103493928909302,
0.048665404319763184,
-0.005129477474838495,
0.02275426685810089,
-0.01739465445280075,
-0.014277378097176552,
0.005583508871495724,
0.018865302205085754,
-0.015914296731352806,
0.05796884000301361,
0.026900436729192734,
0.0015736795030534267,
-0.0389985516667366,
-0.004463477525860071,
0.04147758707404137,
-0.04501465708017349,
0.019354237243533134,
-0.03353840857744217,
-0.013322737999260426,
-0.016517342999577522,
-0.035542525351047516,
0.019224906340241432,
-0.016583027318120003,
-0.016790499910712242,
0.020561687648296356,
0.022014137357473373,
0.009013082832098007,
-0.02592174895107746,
-0.026461729779839516,
0.04106149822473526,
-0.04724440351128578,
0.02288607694208622,
-0.018315834924578667,
0.03820778802037239,
-0.0012410683557391167,
-0.005241804756224155
] |
<p>Suppose there's a radioactive material and a 1/2 quantum probability of detecting it by a Geiger counter. This puts the system in a superposition. Also suppose you are in the same room, and the walls of the room are perfectly decoherence-proof. You observe the Geiger counter and get a definite result. Either it had gone off, or it hadn't. The Copenhagen interpretation tells you the decay or nondecay only became real when it was measured, and the result reached you. Your friend is waiting outside the room. After a very long delay, you open the door, and he observes whether or not you had seen the Geiger counter go off.</p>
<p>He then has the nerve to tell you </p>
<blockquote>
<p>There is only one observer, and that's me, not you. You are nothing more than a dull bound state of electrons and protons. Before the door opened, you never had the property of knowing whether the Geiger counter went off. Only when the door opened did you acquire that property.</p>
</blockquote>
<p>Unnerving, but you reason, your friend is just like you. Both of you are humans and made up of a bound state of electrons and protons. What applies to you ought to apply to him and vice versa. Or are you special and inherently different from him?</p>
<p>You object that you remember very distinctly whether or not you heard the Geiger counter go off. He counters</p>
<blockquote>
<p>Your memory of having known whether or not the Geiger counter went off only came into being when the door opened. Just because you have that memory now does not mean it was real before the door opened. </p>
</blockquote>
<p>You object that applying the Copenhagen interpretation to yourself tells you you did have a definite knowledge before the door opened. He counters</p>
<blockquote>
<p>It's a meaningless question whether or not you knew the state of the Geiger counter before the door opened and I measured you because there is no way in principle for me to find out. There is no inconsistency here.</p>
</blockquote>
<p>Don't all observers have to agree? Both of you agree on your current memory of having had a definite state and that is observable.</p>
<p>Did you have a definite knowledge of the state of the Geiger counter before the door opened? Change the story a little. You haven't opened the door yet, but you know your friend is waiting outside. Do you have a definite knowledge now? You think you do, but does that make it so?</p>
<p>After some further reflection, you realize the present you is a different observer from your past selves. How definite was the past?</p> | 2,866 | [
-0.005649765953421593,
-0.019490014761686325,
0.04773250222206116,
-0.05752446502447128,
0.015452932566404343,
0.006030670367181301,
0.0019715423695743084,
0.0068701282143592834,
-0.01124703697860241,
-0.0131243159994483,
0.07309985905885696,
-0.00009873107774183154,
0.04565153643488884,
0.05641560256481171,
-0.011028502136468887,
0.007266687694936991,
0.03040151484310627,
-0.030249377712607384,
-0.021315334364771843,
-0.02217303030192852,
-0.013532133772969246,
0.024586547166109085,
-0.002420235425233841,
0.008827878162264824,
-0.03343766927719116,
0.03207472711801529,
0.029268383979797363,
-0.025541430339217186,
0.010374052450060844,
0.06716245412826538,
-0.046734876930713654,
-0.04104752838611603,
-0.0018796423682942986,
0.0017560651758685708,
0.02515261620283127,
0.03666452690958977,
0.002594071440398693,
0.008489766158163548,
0.022495580837130547,
0.020796019583940506,
0.0014432452153414488,
0.005258854478597641,
0.0256937425583601,
0.042659323662519455,
-0.0484548881649971,
-0.015147016383707523,
0.004829859361052513,
-0.010216187685728073,
0.040411487221717834,
-0.03110458329319954,
0.053807519376277924,
-0.012344790622591972,
0.025062937289476395,
0.0407177172601223,
-0.0050005535595119,
0.013745216652750969,
0.06184305250644684,
0.056602124124765396,
0.002395656891167164,
-0.030121609568595886,
-0.025227049365639687,
-0.038476694375276566,
-0.009403245523571968,
-0.013994377106428146,
0.006603866349905729,
0.007580352947115898,
0.015308080241084099,
-0.03533671051263809,
0.005087682045996189,
-0.011021156795322895,
0.031003287062048912,
-0.011832397431135178,
0.03557777777314186,
-0.0064012412913143635,
0.03810720518231392,
-0.006217669229954481,
-0.025773053988814354,
0.012973420321941376,
0.0332515686750412,
0.023938588798046112,
-0.002209902973845601,
-0.014084137044847012,
0.04951484501361847,
0.008186562918126583,
0.025613896548748016,
-0.023723913356661797,
0.04643525183200836,
-0.015643496066331863,
0.01926683448255062,
0.04381865635514259,
0.027976306155323982,
0.009024645201861858,
0.017877455800771713,
-0.007309596985578537,
0.013903104700148106,
0.02589261531829834,
0.0062061091884970665,
0.07032030820846558,
-0.004636586643755436,
0.031706422567367554,
-0.020230645313858986,
-0.040124375373125076,
0.005524275358766317,
0.05852461978793144,
0.007632112596184015,
0.010777805931866169,
-0.02480211853981018,
0.032017916440963745,
0.001161876949481666,
-0.031266793608665466,
-0.009922456927597523,
0.0393049493432045,
0.011769946664571762,
0.023201391100883484,
-0.014405653811991215,
-0.003204809268936515,
-0.01804519258439541,
-0.02259456180036068,
0.09504561871290207,
0.02686231955885887,
0.022038765251636505,
0.0014297665329650044,
-0.04523590952157974,
-0.056660573929548264,
-0.062186919152736664,
-0.021589534357190132,
0.01702100969851017,
-0.018414238467812538,
-0.02740323171019554,
0.018964476883411407,
0.014409582130610943,
-0.009891231544315815,
0.016804367303848267,
-0.009599393233656883,
0.0441247932612896,
-0.011226150207221508,
-0.09770224243402481,
-0.0716736912727356,
0.022233834490180016,
0.017643075436353683,
-0.018455006182193756,
-0.06956743448972702,
0.021480511873960495,
0.04166589677333832,
0.0655127465724945,
-0.006840904243290424,
-0.011189023032784462,
0.01603838987648487,
-0.020275777205824852,
-0.004055869299918413,
-0.0161217600107193,
-0.011411642655730247,
-0.008584507741034031,
-0.029655881226062775,
-0.030438262969255447,
-0.015214650891721249,
0.02016454190015793,
0.03610731288790703,
-0.011015065014362335,
0.030527843162417412,
0.04472666233778,
-0.028181292116642,
-0.0047801220789551735,
-0.017292924225330353,
-0.02746117115020752,
-0.05318302661180496,
0.0689377561211586,
0.03941161558032036,
-0.012994647026062012,
0.03986089676618576,
0.050139956176280975,
0.02006314881145954,
-0.03476954996585846,
0.001773000811226666,
0.0049151284620165825,
-0.04765399545431137,
-0.01718284748494625,
0.01342206634581089,
-0.021889805793762207,
-0.01821923442184925,
-0.03805326670408249,
0.003928309306502342,
-0.03463384509086609,
-0.0036129746586084366,
-0.0015115635469555855,
-0.004703878425061703,
0.022747091948986053,
0.007165522314608097,
-0.015370216220617294,
-0.042009834200143814,
-0.03514547273516655,
-0.06777782738208771,
-0.02600797824561596,
-0.004952885676175356,
-0.04082106426358223,
0.01761540025472641,
0.005276860669255257,
-0.008369226939976215,
-0.03205228969454765,
-0.04447375610470772,
-0.021331705152988434,
0.015750542283058167,
0.03988306224346161,
0.01601373963057995,
0.016268976032733917,
0.047611914575099945,
0.0367574468255043,
0.0009831557981669903,
0.044299859553575516,
-0.006512949243187904,
-0.011896844953298569,
0.04103444144129753,
-0.01129656471312046,
0.015239086002111435,
0.019492799416184425,
0.05898594111204147,
0.005485316272825003,
-0.016360588371753693,
0.016675662249326706,
0.012941469438374043,
-0.053747132420539856,
0.03142428770661354,
0.003343365853652358,
0.0035104695707559586,
-0.03590639680624008,
0.022810308262705803,
0.04460277780890465,
-0.028418347239494324,
-0.004194625187665224,
-0.023313380777835846,
-0.026482919231057167,
-0.02174636535346508,
-0.0004725659091491252,
0.02166156657040119,
0.006738518364727497,
0.004405010491609573,
-0.017328770831227303,
0.05498166382312775,
-0.0055770715698599815,
-0.009073354303836823,
0.008237913250923157,
-0.0078189792111516,
-0.01452995277941227,
-0.020118530839681625,
0.010964238084852695,
-0.006198601797223091,
0.014478957280516624,
-0.009869995526969433,
0.036007389426231384,
-0.04583706334233284,
-0.012348972260951996,
-0.009248792193830013,
-0.015650495886802673,
0.0059318942949175835,
0.014997828751802444,
-0.04070420190691948,
-0.007381266448646784,
0.024948233738541603,
0.004574399907141924,
0.001639199093915522,
-0.03328738734126091,
-0.013987727463245392,
-0.06217658892273903,
-0.024597253650426865,
-0.0056649474427104,
0.014088455587625504,
-0.03383518010377884,
-0.006563121452927589,
0.04086441919207573,
-0.020793883129954338,
0.004016028717160225,
0.003758372738957405,
-0.009988285601139069,
0.016115838661789894,
-0.006753318477421999,
-0.008633491583168507,
0.014974349178373814,
0.0367853157222271,
-0.03931874781847,
-0.05661599338054657,
-0.04257733374834061,
0.0006662815576419234,
0.02675183117389679,
-0.005272906739264727,
-0.04519561305642128,
0.03753657639026642,
-0.0057539488188922405,
-0.015053920447826385,
0.018530353903770447,
0.037323370575904846,
-0.010102501139044762,
0.04093814641237259,
-0.02830955944955349,
-0.0396137498319149,
-0.03292594105005264,
-0.04227276146411896,
-0.04246160387992859,
-0.02514616958796978,
-0.004497239366173744,
0.06339740753173828,
-0.002881990047171712,
-0.061975911259651184,
-0.0014220280572772026,
-0.05498054251074791,
-0.07356010377407074,
0.012398087419569492,
-0.029759321361780167,
-0.004001704975962639,
-0.022989727556705475,
-0.0015115748392418027,
-0.016905441880226135,
-0.028144413605332375,
-0.03715483844280243,
-0.033729828894138336,
-0.0957898199558258,
0.03777146339416504,
0.01839265786111355,
0.028057364746928215,
-0.015309970825910568,
0.04963831603527069,
0.09173771739006042,
0.04431444779038429,
0.002450366737321019,
-0.023129280656576157,
0.022767966613173485,
0.004544634837657213,
-0.02536308765411377,
0.0033861789852380753,
0.02532126009464264,
-0.019888265058398247,
0.016902144998311996,
-0.020123807713389397,
0.061827853322029114,
-0.016629420220851898,
-0.008832824416458607,
-0.00768714863806963,
0.030702287331223488,
0.05969591066241264,
0.013081454671919346,
0.05741215869784355,
0.015477503649890423,
-0.059908024966716766,
-0.010922476649284363,
-0.018697714433073997,
0.004883219487965107,
0.02771253138780594,
-0.028361976146697998,
0.06543337553739548,
0.01910492591559887,
0.029366672039031982,
-0.03229488432407379,
0.03742103651165962,
-0.030527297407388687,
-0.0353936105966568,
0.014172116294503212,
-0.018128065392374992,
0.011567531153559685,
0.023786207661032677,
0.019382406026124954,
0.04832173511385918,
0.046788401901721954,
0.005320437718182802,
-0.03398900479078293,
0.006633835844695568,
0.0055075278505682945,
0.020461728796362877,
-0.0055468278005719185,
-0.028452638536691666,
0.03993107005953789,
0.02732926607131958,
0.0033716214820742607,
0.009868819266557693,
-0.044305220246315,
-0.07055455446243286,
-0.04687873646616936,
0.0135722067207098,
0.017834240570664406,
0.05446452647447586,
0.0012641166104003787,
0.05406060442328453,
0.010727441869676113,
0.003359704278409481,
-0.02478177845478058,
-0.006189507432281971,
-0.08583461493253708,
-0.01837822049856186,
-0.03374864161014557,
-0.001499641453847289,
0.007715498562902212,
-0.008172594010829926,
0.017274457961320877,
-0.013569985516369343,
-0.03061164915561676,
-0.00079578987788409,
0.01968935877084732,
-0.06755664944648743,
0.012913381680846214,
0.003335395362228155,
-0.03362732380628586,
-0.021780846640467644,
0.04921386390924454,
0.03826739266514778,
0.01349013950675726,
0.02128458581864834,
0.030816610902547836,
-0.04500788450241089,
0.04780079796910286,
0.008488437160849571,
0.011518814601004124,
0.06055818125605583,
0.012019953690469265,
0.036180347204208374,
0.021342745050787926,
-0.03399060666561127,
0.011805828660726547,
0.032633520662784576,
0.040099143981933594,
0.0037576162721961737,
-0.032139018177986145,
0.0011689492966979742,
-0.028917061164975166,
-0.0349249467253685,
-0.005729732569307089,
0.058272525668144226,
-0.007596341893076897,
0.008892824873328209,
-0.01165839470922947,
0.025850888341665268,
0.005191265605390072,
0.04543953761458397,
0.010527703911066055,
0.0008390226284973323,
-0.027810396626591682,
-0.01633349619805813,
0.010314497165381908,
-0.024427292868494987,
-0.003716907696798444,
-0.021576542407274246,
0.010778114199638367,
0.007780993357300758,
-0.010679356753826141,
-0.022272514179348946,
0.02706713043153286,
-0.0021028548944741488,
0.009339244104921818,
-0.044443197548389435,
-0.004285306204110384,
-0.013542801141738892,
0.03197922930121422,
0.043120551854372025,
-0.0036042218562215567,
0.009063394740223885,
0.0278884656727314,
-0.000024981038222904317,
-0.04472804069519043,
-0.011355802416801453,
0.03998371958732605,
0.0631270781159401,
-0.007729014381766319,
-0.016779383644461632,
-0.023264354094862938,
-0.03896384686231613,
0.0750131905078888,
0.009892595931887627,
0.038922231644392014,
-0.028649840503931046,
0.005830844864249229,
-0.019589990377426147,
-0.07537752389907837,
0.012583120726048946,
0.013289845548570156,
0.008699913509190083,
0.017771277576684952,
-0.009584463201463223,
-0.0030579245649278164,
-0.00854963343590498,
-0.012944716960191727,
-0.0021647089160978794,
0.03767343983054161,
-0.02130650356411934,
0.04063978046178818,
0.0010886176023632288,
-0.0024663282092660666,
-0.0137564055621624,
-0.04315084591507912,
0.032550033181905746,
-0.009611166082322598,
-0.016946151852607727,
0.01201134268194437,
-0.01188813615590334,
-0.05959668755531311,
0.008634081110358238,
-0.04563067480921745,
-0.005204707849770784,
0.029921889305114746,
-0.05595219135284424,
0.07200811058282852,
-0.0034034457057714462,
0.013787731528282166,
0.03868322819471359,
0.037478551268577576,
-0.020364636555314064,
0.007865102961659431,
-0.018223056569695473,
-0.000795253727119416,
-0.018715914338827133,
0.03468676656484604,
-0.04343665763735771,
0.02136116847395897,
-0.03870074823498726,
0.03355316445231438,
-0.01481805369257927,
0.02673526108264923,
0.04674527421593666,
-0.02353307418525219,
0.01425187662243843,
-0.01545768603682518,
0.009812995791435242,
0.007135904394090176,
-0.05391236022114754,
-0.02135736308991909,
-0.00965888425707817,
-0.009356256574392319,
0.010852114297449589,
-0.0076864659786224365,
-0.0011828026035800576,
0.03347444161772728,
-0.020760495215654373,
0.02224319614470005,
-0.040935564786195755,
-0.039426613599061966,
0.024716002866625786,
-0.06351135671138763,
0.016548695042729378,
-0.028416335582733154,
-0.027003144845366478,
0.016577275469899178,
-0.011166210286319256,
-0.036578305065631866,
0.01983514055609703,
-0.0026732885744422674,
0.0052843885496258736,
-0.038425397127866745,
0.017786618322134018,
0.022558458149433136,
-0.02680343948304653,
-0.08800146728754044,
0.0006942662876099348,
-0.006558606401085854,
0.022860443219542503,
-0.0046298508532345295,
-0.04267082363367081,
0.025003768503665924,
-0.007219168357551098,
-0.03791995346546173,
-0.02505131997168064,
0.01226742658764124,
0.009561479091644287,
-0.003553583286702633,
0.02278882823884487,
0.03590325638651848,
0.03601131960749626,
-0.0018838932737708092,
-0.01929572783410549,
-0.05049940571188927,
0.009839855134487152,
-0.02017086371779442,
-0.012057718820869923,
0.007845733314752579,
-0.0028707580640912056,
-0.05058784410357475,
-0.004284986294806004,
0.004754436668008566,
-0.003955008462071419,
-0.02555384300649166,
-0.009088932536542416,
0.03478453308343887,
-0.008748301304876804,
-0.02477233111858368,
-0.03577910736203194,
-0.02121158502995968,
0.018712786957621574,
0.02978629432618618,
-0.0026146601885557175,
0.057867567986249924,
-0.004583088215440512,
-0.05841044336557388,
0.004890084266662598,
0.03847992420196533,
-0.020159801468253136,
-0.009594791568815708,
0.02687467262148857,
0.009555263444781303,
0.010504433885216713,
0.007740698754787445,
0.009191636927425861,
0.0013716634130105376,
-0.039646655321121216,
0.017846912145614624,
0.018879977986216545,
-0.0025717755779623985,
-0.026552576571702957,
0.02526991069316864,
-0.05410299450159073,
-0.0028817951679229736,
0.03958584740757942,
0.032441359013319016,
0.03213811293244362,
0.025711432099342346,
-0.03636609762907028,
-0.022619208320975304,
-0.01898077130317688,
-0.006474943365901709,
0.012474138289690018,
0.017825905233621597,
0.055966973304748535,
-0.043089210987091064,
-0.005334228742867708,
0.049331337213516235,
0.04890161380171776,
-0.03143998235464096,
0.015067447908222675,
0.017330024391412735,
0.022637274116277695,
0.0314791165292263,
-0.018168529495596886,
-0.019417492672801018,
0.023957710713148117,
-0.05289995297789574,
0.020555410534143448,
0.0030525908805429935,
0.00627866992726922,
0.007560746278613806,
-0.018476994708180428,
0.0010762113379314542,
-0.05279026925563812,
-0.03311911225318909,
-0.0929974764585495,
0.000060082540585426614,
0.02558867074549198,
0.026964809745550156,
0.007480890955775976,
-0.0031218479853123426,
0.020353015512228012,
0.00998996663838625,
0.01284164097160101,
-0.016047736629843712,
-0.07519850134849548,
-0.03396683186292648,
-0.015740998089313507,
-0.019938481971621513,
0.062213148921728134,
-0.027596360072493553,
-0.020882336422801018,
0.020434658974409103,
-0.03135006129741669,
0.049573346972465515,
0.04714009910821915,
0.01949208416044712,
-0.033224087208509445,
0.03360694274306297,
-0.017584040760993958,
0.05824596807360649,
-0.013921776786446571,
0.03528902307152748,
0.12629087269306183,
0.04321322590112686,
-0.004307045601308346,
-0.02320157177746296,
-0.027511216700077057,
0.02663727104663849,
0.04741144925355911,
0.01677359826862812,
0.03489779680967331,
-0.006776649504899979,
-0.03482837975025177,
0.020275024697184563,
0.04674656689167023,
0.048598513007164,
0.0033474082592874765,
0.011968709528446198,
-0.04179169237613678,
-0.04785071685910225,
-0.01935919001698494,
0.01657511107623577,
-0.003972760401666164,
-0.0040682642720639706,
0.010500325821340084,
0.022860705852508545,
-0.025112293660640717,
0.016043592244386673,
0.004423818551003933,
-0.019525934010744095,
-0.0051393061876297,
0.02954299934208393,
-0.007078773342072964,
0.04387447237968445,
-0.005005658138543367,
-0.016806110739707947,
-0.002824423834681511,
0.02926621586084366,
0.05494585260748863,
0.005031022243201733,
0.03138585388660431,
0.038585513830184937,
0.003471225034445524,
-0.031721267849206924,
-0.018626270815730095,
0.030914774164557457,
-0.04829933121800423,
-0.00616886280477047,
-0.01352114137262106,
0.06081761047244072,
0.0067566814832389355,
-0.04336380958557129,
0.015286429785192013,
-0.018977325409650803,
0.03360339254140854,
-0.06562348455190659,
-0.04382750764489174,
0.018878737464547157,
0.016002854332327843,
-0.026299158111214638,
-0.029660770669579506,
0.028754597529768944,
0.0228610560297966,
-0.02233821712434292,
-0.010191352106630802,
0.0036213784478604794,
-0.017163481563329697,
-0.02813546732068062,
-0.028614455834031105,
0.015869660302996635,
0.004288610070943832,
0.03472377732396126,
-0.04040710628032684,
-0.009209806099534035,
-0.03276384621858597,
-0.04309668019413948,
0.020214863121509552,
0.02867639809846878,
0.06950438767671585,
-0.028269385918974876,
0.01749092899262905,
-0.019223805516958237,
-0.02278931252658367,
0.056210946291685104,
-0.019932886585593224,
0.0018594113644212484,
-0.011191530153155327,
0.011791911907494068,
0.027678489685058594,
0.03909903019666672,
-0.0012347368756309152,
-0.009867693297564983,
0.05174476280808449,
0.059154585003852844,
0.02361178584396839,
-0.005418785847723484,
-0.02291915938258171,
0.030507849529385567,
-0.05563495680689812,
0.0027998031582683325,
-0.01938292384147644,
-0.008977413177490234,
0.01917538046836853,
-0.010944666340947151,
0.015347985550761223,
0.0392363965511322,
-0.028509270399808884,
-0.007262145634740591,
0.01587420515716076,
-0.001981144305318594,
-0.03979172557592392,
0.053248122334480286,
0.05324287712574005,
0.006736823823302984,
-0.03190603852272034,
-0.051632560789585114,
0.02108108438551426,
0.011239740997552872,
0.023304495960474014,
-0.019373120740056038,
-0.025821825489401817,
0.0010058898478746414,
0.03413794934749603,
0.008547945879399776,
-0.017059989273548126,
-0.032825421541929245,
-0.0064410255290567875,
-0.005935056135058403,
-0.0162606593221426,
-0.03525051474571228,
0.022212281823158264,
0.029286369681358337,
-0.030796987935900688,
0.023577457293868065,
0.00032086449209600687,
-0.0630023181438446,
-0.018271099776029587,
-0.013912061229348183,
-0.01779286377131939,
0.012788362801074982,
0.0017740416806191206,
-0.01408225018531084,
0.006591416895389557,
-0.020599354058504105,
-0.03710263594985008,
0.03505364805459976,
0.02792183868587017,
0.017259465530514717,
0.05453498661518097,
-0.029380807653069496,
-0.0005264772335067391,
0.02987268753349781,
-0.05463486164808273,
-0.019938115030527115,
0.001599827199243009,
-0.0018939393339678645,
0.0038105871062725782,
0.013576681725680828,
0.0325748547911644,
0.002418114570900798,
-0.027186494320631027,
0.031216494739055634,
0.0031116758473217487,
0.025736862793564796,
0.022957464680075645,
-0.02947053126990795,
-0.01231375802308321,
-0.042174775153398514,
0.007260381244122982,
0.0018121052999049425,
0.012023369781672955,
0.038906946778297424,
-0.06135644018650055,
0.0339384600520134,
0.01627597026526928,
0.01980089396238327,
-0.07889746874570847,
-0.013159257359802723,
0.007423112168908119,
0.01655326597392559,
0.04288434237241745,
-0.01614827662706375,
0.027577543631196022,
0.0257266815751791,
-0.08826765418052673,
-0.01764492318034172,
-0.00038415074232034385,
-0.025744648650288582,
-0.02395186759531498,
0.01938067190349102,
-0.0463387593626976,
0.05965476855635643,
0.004801559261977673,
0.07202636450529099,
-0.006096065044403076,
0.058376070111989975,
0.018157348036766052,
-0.036698080599308014,
-0.05887198820710182,
0.006065879948437214,
0.004513452760875225,
-0.003465555841103196,
0.03550948202610016,
-0.0586177296936512,
0.014241608791053295,
0.029114270582795143,
-0.019385263323783875,
-0.010325965471565723,
-0.04245540872216225,
0.06598472595214844,
0.019336389377713203,
0.031116841360926628,
0.011201047338545322,
0.009772801771759987,
0.02045593224465847,
-0.0011212325189262629,
0.01265170332044363,
0.010358459316194057,
0.030778728425502777,
-0.042228925973176956,
0.008109696209430695,
-0.014603856950998306,
-0.05843561887741089,
-0.006358760874718428,
0.008681485429406166,
-0.0032588602043688297,
-0.018128972500562668,
0.048263926059007645,
-0.016323771327733994,
0.0014782175421714783,
-0.005903363693505526,
-0.013800126500427723,
-0.020386334508657455,
0.07159982621669769,
0.04614726081490517,
-0.03582334518432617,
0.023696208372712135,
-0.06991761177778244,
-0.03047848679125309,
0.041933219879865646,
0.026242949068546295,
-0.013919916935265064,
-0.02722342312335968,
-0.04767777398228645,
0.004605303518474102,
0.037790168076753616,
0.025381704792380333,
-0.04794525355100632,
-0.04783949628472328,
0.0058449250645935535,
-0.015571621246635914,
0.04016700014472008,
-0.057637736201286316,
-0.05685349926352501,
-0.0012185464147478342,
-0.0861973911523819,
0.03263356164097786,
0.026171715930104256,
0.02499985508620739,
-0.09087051451206207,
0.004560461733490229,
0.0021025047171860933,
0.02229774184525013,
0.06152581796050072,
0.01067549828439951,
-0.0062376512214541435,
0.019504673779010773,
-0.016883183270692825,
0.018119197338819504,
-0.04724331945180893,
0.01916801556944847,
-0.019502388313412666,
-0.007984882220625877,
0.000041672505176393315,
0.012094655074179173,
-0.03704211115837097,
0.02240501530468464,
0.04388609156012535,
-0.01784592866897583,
-0.0034745323937386274,
-0.016330121085047722,
-0.01277576107531786,
0.07259273529052734,
-0.010351572185754776,
-0.0014337125467136502,
0.01698533445596695,
0.012096581980586052,
0.06397408992052078,
0.0748867318034172,
-0.022638272494077682,
-0.08026205003261566,
0.019250420853495598,
0.012734354473650455,
-0.01603304222226143,
0.011329338885843754,
0.0010426563676446676,
0.0017089622560888529,
0.003341861767694354,
0.007985941134393215,
0.021649658679962158,
-0.04332016408443451,
0.013522779569029808,
0.06676577031612396,
0.010030170902609825,
0.05205964669585228,
0.005696370266377926,
0.03616935759782791,
-0.019227327778935432,
0.018199872225522995,
0.025534072890877724,
0.04364825040102005,
0.021549412980675697,
-0.007693206891417503,
0.04759128764271736,
0.045086007565259933,
0.011506692506372929,
0.03026462532579899,
0.0027557064313441515,
0.043916355818510056,
-0.02401137165725231,
0.011814209632575512,
0.04762893542647362,
-0.033586081117391586,
-0.0155118303373456,
0.0541832372546196,
-0.0032188654877245426,
0.06751814484596252,
-0.02229554019868374,
-0.007800612598657608,
-0.01502164639532566,
0.023077048361301422,
-0.011996922083199024,
-0.005779351107776165,
0.07609125226736069,
0.02814377285540104,
-0.039656754583120346,
-0.015328255482017994,
-0.03966677561402321,
-0.01719430834054947,
-0.01168237067759037,
-0.05730126053094864,
-0.004622663836926222,
0.019649315625429153,
-0.013015802018344402,
0.002916505094617605,
-0.01003170758485794,
-0.02073509618639946,
-0.0016103325178846717,
0.038767218589782715,
0.00033887234167195857,
0.004066490568220615,
-0.032100025564432144,
-0.062102075666189194,
-0.032645534723997116,
0.042450401932001114,
-0.05429965630173683,
0.001682729460299015,
-0.031838104128837585,
0.05663697421550751,
-0.029342977330088615,
-0.016323795542120934
] |
<p>Let us consider Bloch wave function solutions for a particle confined to a 2D square lattice with a potential of the form
$V=V(x) + V(y)$
(that is, one that can be factorized).</p>
<p>In this case we can factorize the Hamiltonian to
$\hat{H} = \hat{H}_x + \hat{H}_y$
and the band spectrum structure (the energy dispersion for states) can be presented as
$E( \vec{q}) = E_x(q_x) + E_y(q_y)$. </p>
<p>One-dimensional dispersion spectrum has gaps between the bands for quasimomentum values of $q_{x} = n \frac{\pi}{a}$, here $n$ is integer. It means that the energy gaps between the bands are situated at the quasimomentum border values of $q_{x,y} = n \frac{\pi}{a}$.</p>
<p>Am I correct?
Is it a specific case of some general principle regarding the positions of band gaps I need to know about? What can be said about the band gap positions generally?</p> | 2,867 | [
0.01793295331299305,
0.010658185929059982,
0.028807442635297775,
-0.05549982562661171,
0.027072051540017128,
0.005576785188168287,
-0.03165172412991524,
-0.05570743978023529,
0.03559277206659317,
-0.03942212462425232,
0.03116205520927906,
-0.012673022225499153,
0.05636758729815483,
0.01087890099734068,
0.008732061833143234,
0.016430407762527466,
-0.012838379479944706,
-0.05662916600704193,
-0.02426210045814514,
-0.02761724963784218,
-0.00855307374149561,
0.05426335334777832,
-0.01873777247965336,
0.003714170539751649,
-0.0053347148932516575,
0.026410449296236038,
-0.0040440731681883335,
0.03220720961689949,
0.029847072437405586,
0.03955196216702461,
-0.019024694338440895,
-0.026159949600696564,
0.005981286522001028,
0.031026747077703476,
-0.00944508146494627,
-0.011733784340322018,
-0.058612264692783356,
-0.06684477627277374,
-0.0010081699583679438,
0.041079387068748474,
-0.027157966047525406,
-0.033365774899721146,
0.009398705326020718,
0.033278658986091614,
-0.005206550471484661,
-0.010791322216391563,
0.032838113605976105,
-0.02831757441163063,
0.042764853686094284,
-0.06088588014245033,
0.06150851026177406,
0.010792339220643044,
0.04173268377780914,
0.009474632330238819,
-0.0035847893450409174,
-0.0014820694923400879,
0.02923540584743023,
0.06564213335514069,
-0.01881871186196804,
-0.02437072992324829,
-0.027761727571487427,
-0.02363666519522667,
-0.005742248147726059,
-0.006436931435018778,
-0.025775687769055367,
-0.004389339126646519,
-0.021938513964414597,
-0.06780754774808884,
0.001397806336171925,
-0.030955124646425247,
-0.015046253800392151,
0.0178242027759552,
0.031804408878088,
-0.08949849009513855,
0.035098373889923096,
-0.026123488321900368,
0.001879839226603508,
0.03572244197130203,
0.0009968641679733992,
0.0024400793481618166,
-0.02455700933933258,
0.011564990505576134,
0.037537939846515656,
0.013398420996963978,
-0.016051243990659714,
-0.037500254809856415,
0.04114748165011406,
-0.0645231157541275,
-0.0005026562139391899,
0.029273968189954758,
-0.01385683286935091,
0.013993536122143269,
0.07449664175510406,
-0.009940210729837418,
-0.03623223677277565,
-0.012608584947884083,
0.02561759203672409,
0.029524238780140877,
0.0141428392380476,
-0.04628922417759895,
-0.003444705856963992,
-0.013635484501719475,
0.03639449179172516,
0.05657380074262619,
-0.040794193744659424,
-0.0019299052655696869,
-0.03168657794594765,
0.04512621834874153,
0.010395999997854233,
0.004184921737760305,
-0.05622917786240578,
0.02495753765106201,
-0.028367845341563225,
0.008418490178883076,
0.016447575762867928,
0.005556673277169466,
-0.01379123330116272,
-0.005816287361085415,
0.03208335489034653,
0.08085022121667862,
-0.005265119951218367,
-0.007351899519562721,
0.031243497505784035,
-0.02084198407828808,
-0.07813476026058197,
-0.00378558156080544,
0.04215206578373909,
0.025073952972888947,
-0.07851503789424896,
0.009637992829084396,
0.03564196825027466,
0.003032814245671034,
0.018008116632699966,
-0.009601075202226639,
0.04252508282661438,
-0.00002631792813190259,
-0.10262085497379303,
-0.06200188398361206,
0.046207819133996964,
-0.03423769399523735,
-0.008335567079484463,
-0.05249590426683426,
-0.005844754166901112,
0.0008252095431089401,
0.07559188455343246,
-0.0038375083822757006,
0.022331658750772476,
-0.023121222853660583,
0.03419291600584984,
0.029683174565434456,
-0.019033310934901237,
-0.02130245417356491,
0.014093110337853432,
-0.059030044823884964,
-0.01866971142590046,
-0.011379417963325977,
0.033856071531772614,
0.023920318111777306,
0.021915415301918983,
-0.014110522344708443,
0.10163990408182144,
0.0020881779491901398,
-0.028397588059306145,
0.0056827859953045845,
-0.03214825689792633,
-0.027315709739923477,
0.04932134598493576,
-0.002759285271167755,
0.03252791613340378,
0.02606148086488247,
0.010168232023715973,
-0.008161013014614582,
-0.004800811875611544,
0.03566765412688255,
0.0030792513862252235,
-0.004939615726470947,
-0.028870336711406708,
-0.040097545832395554,
0.024866623803973198,
0.020531469956040382,
-0.04638929292559624,
-0.05543854087591171,
0.008839098736643791,
0.033689677715301514,
0.008816264569759369,
0.051526669412851334,
-0.003517103148624301,
0.0032511730678379536,
0.0060235061682760715,
-0.04004021733999252,
-0.024639977142214775,
-0.07008162140846252,
0.041527148336172104,
0.006624413188546896,
0.007409248501062393,
0.04100394994020462,
-0.0021670216228812933,
-0.012836990877985954,
0.009395071305334568,
-0.003716071369126439,
-0.01529808808118105,
-0.003998645581305027,
0.006161428987979889,
-0.03759054094552994,
0.034287985414266586,
0.01728680729866028,
0.015871446579694748,
0.013744969852268696,
0.05801485851407051,
-0.03488221392035484,
-0.03317773714661598,
-0.0007863740320317447,
-0.048701126128435135,
0.048213426023721695,
0.0030140255112200975,
0.013089667074382305,
-0.0029946696013212204,
-0.026659991592168808,
-0.029286758974194527,
0.021218471229076385,
-0.04292149096727371,
0.07529869675636292,
0.03607224300503731,
0.00931412260979414,
-0.0061959573067724705,
0.03658295050263405,
0.030082957819104195,
0.00573061965405941,
-0.015103534795343876,
-0.0689433142542839,
-0.04738501086831093,
-0.004237383604049683,
0.023687640205025673,
0.006833809427917004,
-0.0325419120490551,
0.015793191269040108,
0.024122057482600212,
0.02718200534582138,
0.04689953103661537,
0.007428782992064953,
-0.04913480207324028,
0.010012626647949219,
0.03521593660116196,
0.0395679697394371,
0.0044343192130327225,
-0.005280965939164162,
-0.014218957163393497,
0.032230548560619354,
0.010729338973760605,
-0.014884836971759796,
0.01287865824997425,
0.04126971215009689,
-0.005811857525259256,
-0.01692419871687889,
-0.0061101363971829414,
-0.03914643079042435,
0.026804529130458832,
-0.014860670082271099,
0.033513519912958145,
0.04086872562766075,
-0.01795892044901848,
0.0019165067933499813,
-0.03898220881819725,
-0.026431618258357048,
0.03940786421298981,
-0.009906504303216934,
-0.060501810163259506,
0.0015617419267073274,
0.01617986522614956,
-0.019581716507673264,
-0.0003790453774854541,
-0.04009474441409111,
-0.009489256888628006,
0.024986660107970238,
-0.011850793845951557,
0.038910213857889175,
0.01644347980618477,
0.05996878445148468,
-0.0665188804268837,
-0.009050772525370121,
-0.0014454529155045748,
-0.020846089348196983,
0.021366829052567482,
0.021555280312895775,
0.015825673937797546,
0.005938988644629717,
-0.08231902867555618,
0.004989891778677702,
0.004375557415187359,
0.005483519285917282,
-0.02974601462483406,
-0.026120441034436226,
0.010401759296655655,
-0.039469607174396515,
0.026931701228022575,
-0.003662296338006854,
0.0017153517110273242,
-0.030358176678419113,
-0.03896186128258705,
0.014599203132092953,
0.005610353779047728,
-0.035020407289266586,
-0.01733391173183918,
-0.001397482119500637,
-0.02634488418698311,
-0.03686000779271126,
-0.0008950529736466706,
0.015605916269123554,
-0.012308100238442421,
0.035654760897159576,
0.03341354802250862,
-0.013556653633713722,
0.002380519872531295,
-0.039259038865566254,
-0.03805282339453697,
-0.021647250279784203,
-0.0020501127000898123,
0.029199790209531784,
-0.01066832710057497,
0.0008424041443504393,
0.09958311915397644,
0.009158669039607048,
-0.021860165521502495,
0.017144061625003815,
-0.028157759457826614,
0.01784759946167469,
0.011471188627183437,
0.028943074867129326,
0.0580439567565918,
0.01358845829963684,
0.03291924297809601,
-0.009813550859689713,
0.05306526646018028,
0.06245725601911545,
-0.02098102681338787,
-0.030915552750229836,
0.029836121946573257,
0.04329463467001915,
0.001161548076197505,
0.04164861515164375,
-0.0008298116736114025,
0.008685090579092503,
0.03794775530695915,
-0.024414291605353355,
0.011504960246384144,
0.04380074515938759,
-0.08822671324014664,
0.016723299399018288,
-0.03303181380033493,
0.0042699468322098255,
-0.020402636379003525,
0.04603444039821625,
0.026666322723031044,
-0.014023846946656704,
0.011952466331422329,
0.021622680127620697,
0.021840084344148636,
0.0006175335147418082,
-0.009822354651987553,
0.038763705641031265,
0.026066195219755173,
-0.01320192962884903,
-0.006252606399357319,
0.02021700143814087,
-0.00737044308334589,
0.045176755636930466,
-0.036233142018318176,
-0.025487888604402542,
0.018326876685023308,
0.056688595563173294,
0.020780574530363083,
-0.044921860098838806,
-0.054586008191108704,
-0.008689581416547298,
-0.041403878480196,
-0.057076595723629,
-0.005253157578408718,
0.06005238741636276,
-0.005499133374541998,
0.024325553327798843,
0.029671313241124153,
0.03372548893094063,
0.02423664554953575,
0.008721679449081421,
-0.0657273679971695,
-0.04348091781139374,
-0.0013817845610901713,
0.03423776850104332,
-0.027340110391378403,
0.006057773716747761,
0.018397504463791847,
0.013544274494051933,
-0.04920731112360954,
0.0008589816861785948,
-0.007173009682446718,
-0.06334852427244186,
0.02861919440329075,
-0.03795688599348068,
-0.05040564760565758,
-0.04238142445683479,
0.012527555227279663,
0.016218259930610657,
-0.01725016161799431,
0.01635489985346794,
0.032379407435655594,
-0.0184231735765934,
0.043929573148489,
-0.01175500638782978,
0.016176722943782806,
0.041169147938489914,
0.06120654195547104,
0.03104984574019909,
0.025679193437099457,
-0.005275965202599764,
-0.030902711674571037,
-0.015120593830943108,
0.05042649433016777,
-0.011726855300366879,
0.00210114405490458,
0.03771909326314926,
-0.012447621673345566,
0.0047089168801903725,
-0.014894670806825161,
0.03600894287228584,
-0.0314529649913311,
0.0356266126036644,
0.04770014062523842,
0.00709415040910244,
-0.03551821783185005,
0.026235992088913918,
0.023827344179153442,
0.03840243071317673,
0.009105455130338669,
-0.06705662608146667,
-0.02886299416422844,
-0.01992872729897499,
0.01827230304479599,
-0.013955682516098022,
-0.040186651051044464,
-0.014559418894350529,
0.04441557079553604,
0.028980253264307976,
0.04059077054262161,
-0.03637808933854103,
0.005633086431771517,
-0.025081776082515717,
0.031054921448230743,
-0.01914588175714016,
-0.0028434470295906067,
0.015298768877983093,
-0.02276802994310856,
0.01919366978108883,
0.003813582705333829,
0.015025739558041096,
-0.05943833664059639,
-0.0184466689825058,
0.01792246289551258,
0.05069088190793991,
0.026825880631804466,
-0.011918903328478336,
-0.04110897332429886,
-0.010436256416141987,
0.03324666991829872,
-0.002845695475116372,
0.0261149313300848,
-0.008769483305513859,
-0.015604078769683838,
-0.043538037687540054,
-0.05855686590075493,
-0.018091266974806786,
-0.013023138977587223,
0.036237623542547226,
0.03491675853729248,
-0.03248637169599533,
-0.03488334268331528,
-0.047915153205394745,
0.012535493820905685,
0.030598584562540054,
0.03877919912338257,
0.005300183314830065,
-0.001031384919770062,
0.006985077168792486,
0.007759780157357454,
-0.01754228211939335,
-0.09289085865020752,
0.006920364685356617,
0.02164672128856182,
0.047807417809963226,
0.032548800110816956,
-0.024156637489795685,
-0.074912890791893,
0.020600467920303345,
0.01632181741297245,
-0.009030197747051716,
0.03838365525007248,
0.003830061061307788,
0.0680915117263794,
0.03116442821919918,
0.004369320347905159,
0.0427926629781723,
0.017135536298155785,
0.017076820135116577,
-0.031253404915332794,
-0.04220786690711975,
0.025475438684225082,
-0.008050828240811825,
-0.0009815229568630457,
-0.025888482108712196,
-0.012347419746220112,
-0.022126054391264915,
0.026913031935691833,
-0.006984887178987265,
0.02199622243642807,
0.0021760081872344017,
-0.057884763926267624,
-0.006384280044585466,
0.02794617973268032,
-0.023241376504302025,
0.006450371816754341,
-0.007994075305759907,
0.027314703911542892,
0.019004257395863533,
0.010391728952527046,
-0.005181253422051668,
-0.005894905421882868,
0.01611739583313465,
0.028370235115289688,
0.009082590229809284,
0.006811168976128101,
-0.045575693249702454,
0.01193782314658165,
-0.015845678746700287,
-0.06676150113344193,
0.05242820456624031,
-0.031609226018190384,
-0.017606504261493683,
-0.04182140529155731,
-0.050752148032188416,
-0.04521931707859039,
0.009886208921670914,
-0.01890352927148342,
-0.017821967601776123,
-0.017299102619290352,
0.018334554508328438,
0.018961133435368538,
-0.007487440016120672,
-0.10386011004447937,
-0.023867184296250343,
0.004480155184864998,
0.016300546005368233,
-0.033518701791763306,
-0.021993715316057205,
0.006189121399074793,
-0.010934203863143921,
-0.005620467942208052,
0.03602667525410652,
0.005467796232551336,
-0.023326750844717026,
-0.018410971388220787,
0.0015541203320026398,
0.025497304275631905,
0.07400955259799957,
0.004431290086358786,
-0.013193733058869839,
0.0114877475425601,
-0.020472699776291847,
0.022257931530475616,
0.005469230934977531,
0.01894230954349041,
-0.04620489850640297,
-0.012050984427332878,
-0.013965382240712643,
0.020826151594519615,
0.07114032655954361,
-0.008274107240140438,
-0.038540326058864594,
0.04249127581715584,
0.02071218192577362,
0.029789863154292107,
-0.013106631115078926,
0.0099929329007864,
-0.032520540058612823,
0.007965737953782082,
0.008212137967348099,
0.002412038389593363,
-0.053440745919942856,
-0.020362261682748795,
0.01442064717411995,
-0.018803194165229797,
0.015833528712391853,
0.018207665532827377,
0.10065280646085739,
-0.012851759791374207,
0.015428993850946426,
0.03849988058209419,
-0.03521895036101341,
0.02228834666311741,
-0.005697045475244522,
0.014910363592207432,
-0.004508991725742817,
0.0346282534301281,
-0.03495140001177788,
-0.08461050689220428,
-0.06393079459667206,
0.029988782480359077,
0.03157962113618851,
0.0058638728223741055,
0.04110250994563103,
-0.0011701611801981926,
-0.02801857516169548,
-0.012210643850266933,
-0.0025223689153790474,
-0.003024608828127384,
0.009146262891590595,
-0.012108060531318188,
0.052513886243104935,
-0.06140221655368805,
-0.008687094785273075,
0.02387942187488079,
0.034792594611644745,
0.003746498143300414,
0.0036353450268507004,
0.04190277308225632,
0.00033517004339955747,
0.01619352027773857,
-0.02573304995894432,
-0.013852913863956928,
0.033655181527137756,
-0.018600881099700928,
0.010674710385501385,
0.02277480810880661,
-0.020730625838041306,
0.06760094314813614,
0.04926669970154762,
0.02737533301115036,
-0.05527087301015854,
-0.03486481308937073,
-0.01064478512853384,
0.03590479865670204,
0.003543353406712413,
0.017372915521264076,
0.017217615619301796,
-0.00327854510396719,
0.00420911842957139,
0.006319751031696796,
0.013855291530489922,
0.018337517976760864,
-0.03237571567296982,
-0.006260603200644255,
-0.010825606063008308,
-0.03247280418872833,
-0.014320790767669678,
-0.027074722573161125,
-0.033019840717315674,
0.030956124886870384,
-0.04245813563466072,
0.01873508095741272,
-0.01670919544994831,
0.01658596470952034,
-0.018557734787464142,
0.07303592562675476,
0.03165142983198166,
-0.000028221144020790234,
0.014299982227385044,
0.045133814215660095,
0.11325675994157791,
0.07080302387475967,
0.03096717782318592,
-0.06557926535606384,
0.013897135853767395,
0.013510352931916714,
-0.017190802842378616,
-0.013742940500378609,
-0.02391676791012287,
-0.008522212505340576,
-0.0009383252472616732,
-0.021870803087949753,
0.06916338950395584,
0.004266086500138044,
0.019398661330342293,
0.013855925761163235,
-0.03902639076113701,
-0.03161034360527992,
0.023974470794200897,
0.00445398548617959,
-0.010156958363950253,
0.0031512966379523277,
-0.0067839049734175205,
0.0064209746196866035,
-0.007979273796081543,
0.002497089095413685,
-0.03046756237745285,
-0.0315508097410202,
0.02194151096045971,
-0.005939778406172991,
-0.037675660103559494,
0.013521135784685612,
0.022057978436350822,
-0.019418425858020782,
-0.012645285576581955,
0.00504316808655858,
0.02763943374156952,
-0.002849535783752799,
0.015316670760512352,
0.03193824365735054,
-0.003227375680580735,
0.007073839195072651,
0.03037024475634098,
-0.000496066058985889,
-0.02413656935095787,
-0.03515571728348732,
-0.005803605075925589,
0.012155089527368546,
-0.03069743886590004,
-0.011207436211407185,
0.019133903086185455,
-0.018859924748539925,
-0.02396450750529766,
-0.024204730987548828,
0.012992552481591702,
-0.016559068113565445,
0.034294307231903076,
-0.0031907446682453156,
0.004603125620633364,
-0.00577196991071105,
-0.0006142221391201019,
-0.005342851858586073,
0.0072137583047151566,
-0.02039647288620472,
-0.03521821275353432,
0.01587175391614437,
0.010365838184952736,
0.06141107901930809,
-0.013090319000184536,
0.0033123944886028767,
0.0016073437873274088,
-0.03249269351363182,
-0.058521125465631485,
-0.06437056511640549,
0.005670857150107622,
0.02055167779326439,
0.04649103060364723,
-0.005211397539824247,
-0.007903553545475006,
-0.020320216193795204,
-0.08634014427661896,
-0.019761590287089348,
-0.01592511311173439,
-0.01331547275185585,
-0.011455737054347992,
0.015197359025478363,
0.011301902122795582,
0.04674389958381653,
-0.038746871054172516,
-0.008365007117390633,
-0.021771881729364395,
0.02965330146253109,
0.011654633097350597,
-0.021488629281520844,
-0.04682900011539459,
-0.016262231394648552,
-0.043837517499923706,
0.01288576889783144,
-0.012179660610854626,
0.005649276543408632,
0.013160818256437778,
-0.007177595980465412,
0.025089342147111893,
0.0587596520781517,
-0.035937562584877014,
-0.010912355035543442,
-0.016072353348135948,
-0.05693627521395683,
0.005941400770097971,
0.045731671154499054,
0.027189331129193306,
-0.037680912762880325,
-0.0312664695084095,
0.007736926898360252,
-0.004781213589012623,
0.012185296975076199,
0.008547789417207241,
-0.03704465180635452,
-0.02019498310983181,
0.011091751977801323,
-0.021098870784044266,
-0.035169120877981186,
-0.012371083721518517,
-0.012306584976613522,
0.036109473556280136,
0.034206632524728775,
-0.012912418693304062,
-0.012076177634298801,
-0.006553146988153458,
-0.035732049494981766,
0.014305634424090385,
0.036038514226675034,
0.05626210570335388,
-0.009117732755839825,
0.020909734070301056,
0.020452061668038368,
0.0029182597063481808,
0.05531453341245651,
-0.006903527304530144,
-0.019211459904909134,
-0.0014369499403983355,
-0.0263743344694376,
-0.038120146840810776,
0.0302149448543787,
-0.01070292480289936,
0.012514366768300533,
0.0253587756305933,
0.03175275772809982,
-0.014892480336129665,
0.04277915880084038,
-0.026756415143609047,
0.0028351866640150547,
0.02554643712937832,
-0.0199032723903656,
-0.0010077301412820816,
-0.043847933411598206,
0.0035163196735084057,
-0.00038796020089648664,
0.0024485010653734207,
0.019163213670253754,
0.01155223697423935,
0.006799630355089903,
0.005666373763233423,
0.008480305783450603,
-0.02561023086309433,
0.024682380259037018,
0.030049124732613564,
0.002025600289925933,
0.021649200469255447,
0.07217010855674744,
-0.02255687303841114,
0.029049599543213844,
0.016089003533124924,
0.013185220770537853,
-0.04054294526576996,
-0.03369489312171936,
0.05040459334850311,
0.03134498745203018,
0.053046274930238724,
-0.029588965699076653,
-0.002980390563607216,
0.02904476784169674,
-0.05978143960237503,
0.022794803604483604,
-0.02787618897855282,
-0.0003879691066686064,
-0.02294478565454483,
0.012324905954301357,
-0.05115976929664612,
0.011071070097386837,
0.019344935193657875,
0.0021287021227180958,
-0.015746476128697395,
0.00548949558287859,
-0.005789958871901035,
-0.03397030010819435,
0.038538858294487,
0.02522420510649681,
-0.012199865654110909,
-0.03083275444805622,
0.09996557980775833,
0.013537507504224777,
-0.026399334892630577,
-0.02176925726234913,
0.005474762991070747,
-0.03862408548593521,
0.01518620178103447,
-0.0034846256021410227,
-0.04185640439391136,
0.046824123710393906,
0.008402198553085327,
0.023444507271051407,
-0.009466638788580894,
-0.012160839512944221,
0.002606343710795045,
0.02631555125117302,
0.008516822010278702,
-0.0020099778193980455,
0.04730236157774925,
-0.02168029546737671,
0.01270871888846159,
0.04099320247769356,
0.012785004451870918,
0.00437933811917901,
0.04132388159632683,
0.007889309898018837,
0.03754322603344917,
-0.042532917112112045,
0.016820689663290977,
-0.03141738101840019,
-0.026149077340960503,
0.011572455987334251,
0.015261436812579632,
-0.017880259081721306,
-0.01731555536389351,
-0.004236259032040834,
-0.08076940476894379,
0.026483427733182907,
0.028821291401982307,
-0.04364616051316261,
-0.017496591433882713,
-0.005117554217576981,
0.02075190469622612,
-0.0020663936156779528,
0.00963790062814951,
-0.0356011725962162,
-0.01845395565032959,
0.011230762116611004,
-0.0069254739210009575,
0.0024525008630007505,
-0.04679111763834953,
-0.03595462441444397,
-0.03336278721690178,
-0.0448598675429821,
0.02695472724735737,
0.02423148602247238,
-0.020524589344859123,
0.017501194030046463,
0.0004096371994819492,
0.013065007515251637,
0.03103909082710743,
0.07315745204687119,
-0.017871607095003128,
-0.009193799458444118,
0.02131960727274418,
-0.047401584684848785,
0.028766853734850883,
-0.0040929582901299,
0.006502010393887758,
0.008564174175262451,
0.019536027684807777,
0.018224241212010384,
0.02731575258076191,
-0.0528978668153286,
0.020382899791002274,
0.025855373591184616,
-0.00900309905409813,
-0.00751098059117794,
-0.031306784600019455,
-0.006658775731921196,
0.05808930844068527,
0.015745943412184715,
-0.012606969103217125,
0.07297112792730331,
0.01819763146340847,
0.002242974704131484,
0.02339537814259529,
-0.03906062990427017,
-0.07070287317037582,
0.0027151494286954403,
-0.04227278754115105,
-0.023638762533664703,
0.024328701198101044,
-0.0026542942505329847,
0.05567854270339012,
-0.051619283854961395,
0.003119598375633359,
0.052157990634441376,
-0.03748733550310135,
-0.013766041956841946,
0.025475723668932915,
0.03054761327803135,
0.02676355466246605,
-0.020091088488698006,
-0.01748271845281124,
0.05775707587599754,
0.016616780310869217,
-0.007440422661602497,
0.0525178499519825,
0.016703203320503235,
0.04776529222726822,
0.03558273985981941,
0.012791807763278484,
-0.003104223171249032,
0.013555138371884823,
0.0020632341038435698,
0.0017327021341770887,
-0.02550407499074936,
0.01835068129003048,
0.0255318321287632,
-0.01578221470117569,
-0.021811774000525475,
0.006415409501641989,
-0.029627254232764244,
0.10834891349077225,
-0.031419239938259125,
0.024832699447870255,
-0.045072007924318314,
-0.01721372827887535,
-0.03241618722677231,
0.007161219138652086,
-0.009685701690614223,
0.06305516511201859,
-0.008721677586436272,
-0.03618432953953743,
-0.01559538021683693,
0.0030864847358316183,
0.01958090253174305,
-0.054494522511959076,
0.010668803937733173,
-0.009222186170518398,
0.006673647556453943,
-0.012425465509295464,
-0.01770593412220478,
-0.02106439135968685,
0.037055183202028275,
0.031812191009521484,
0.04819796606898308,
0.02914697863161564,
0.00014386617112904787,
0.01367221213877201,
-0.03598751500248909,
0.06256897002458572,
-0.04534592479467392,
-0.007043680641800165,
-0.02272236905992031,
-0.016163581982254982,
-0.00576925091445446,
-0.004604604560881853
] |
<p>How many virtual gravitons do the sun and earth exchange in one year?<br>
What are their wavelengths?</p> | 2,868 | [
0.007557949051260948,
-0.03755217418074608,
-0.029274113476276398,
-0.04207213222980499,
0.020930936560034752,
0.021341631188988686,
-0.03365045040845871,
-0.03133891895413399,
0.004029499366879463,
0.0038163543213158846,
0.07415253669023514,
0.03459380939602852,
0.029933040961623192,
0.022977683693170547,
-0.020077195018529892,
0.0023262149188667536,
0.009789950214326382,
0.023164166137576103,
-0.017387449741363525,
-0.025357063859701157,
-0.005927738733589649,
0.0017920129466801882,
0.01336281094700098,
-0.0022762189619243145,
-0.046221472322940826,
-0.007426069583743811,
0.04696270823478699,
-0.0007075908361002803,
0.016550274565815926,
0.06300961971282959,
0.019937308505177498,
0.004479937721043825,
0.01073681190609932,
0.05036597326397896,
0.01611386612057686,
-0.005743099842220545,
-0.027364803478121758,
-0.03128156065940857,
-0.011827072128653526,
0.0221584253013134,
-0.02879396080970764,
-0.026641324162483215,
-0.03298650681972504,
0.0504305325448513,
-0.004964344669133425,
-0.010637343861162663,
0.041062191128730774,
0.012694548815488815,
0.07833544164896011,
-0.06355755031108856,
0.08296459913253784,
0.013243366032838821,
0.04338992014527321,
-0.02686375193297863,
-0.031018516048789024,
0.006968238390982151,
0.0541447252035141,
0.05658335983753204,
0.009774377569556236,
-0.033407919108867645,
-0.04216863960027695,
0.0014177224365994334,
-0.015303146094083786,
-0.02057831548154354,
-0.03644724562764168,
0.04434515908360481,
0.01580824889242649,
-0.0103139104321599,
0.015301530249416828,
0.010577075183391571,
-0.003010455286130309,
-0.01749029941856861,
0.014306210912764072,
0.0039612953551113605,
0.01892153173685074,
-0.016947917640209198,
0.005709507968276739,
0.019548067823052406,
0.03842592239379883,
0.05397030711174011,
-0.05831313133239746,
0.01236299704760313,
0.008239476941525936,
-0.02039283514022827,
0.04677877947688103,
-0.00845395028591156,
0.07897230982780457,
0.0039365943521261215,
-0.041204798966646194,
0.05094009265303612,
-0.01777651719748974,
-0.01276846881955862,
0.04257664456963539,
-0.007126715034246445,
-0.052161864936351776,
-0.01066980417817831,
0.01900762878358364,
0.020416971296072006,
0.004180557560175657,
-0.03518439456820488,
0.01313741598278284,
-0.02366531826555729,
0.008620609529316425,
0.0925159901380539,
-0.0003528990491759032,
-0.023295613005757332,
-0.03665115311741829,
-0.01805243268609047,
-0.01528201811015606,
-0.0045172953978180885,
-0.02294822409749031,
-0.04685799777507782,
-0.0175764262676239,
-0.00005658151349052787,
0.027716975659132004,
-0.02098185382783413,
0.008633301593363285,
-0.0189104825258255,
0.07575932145118713,
0.03968164697289467,
0.05268483608961105,
0.0048247748054564,
0.020701413974165916,
-0.020525449886918068,
-0.03250971436500549,
0.01883126236498356,
0.014931673184037209,
0.013725434429943562,
-0.026092208921909332,
0.0028624809347093105,
0.021911390125751495,
-0.013784791342914104,
-0.009931344538927078,
-0.04841543734073639,
0.002339310711249709,
-0.005233800504356623,
-0.0792434811592102,
-0.07100584357976913,
0.06741442531347275,
-0.02619997225701809,
-0.023053908720612526,
-0.04679211601614952,
0.003192055504769087,
0.016658689826726913,
0.07689211517572403,
0.013243496417999268,
0.00561373308300972,
0.011996684595942497,
0.06388529390096664,
0.002388631459325552,
-0.022161882370710373,
0.028911501169204712,
-0.014888769946992397,
-0.0052184052765369415,
-0.006380949169397354,
-0.04421510919928551,
0.009928284212946892,
0.0595410019159317,
0.028993282467126846,
0.027068041265010834,
0.09587697684764862,
-0.006785233970731497,
0.005321480333805084,
0.044697925448417664,
-0.00008001882815733552,
-0.04756336659193039,
0.05153973773121834,
0.008093982003629208,
-0.036767859011888504,
0.05089271441102028,
-0.015463258139789104,
0.013064955361187458,
0.04230089485645294,
0.00047947559505701065,
0.014502243138849735,
0.0015539041487500072,
0.0037058922462165356,
0.007969265803694725,
0.009918677620589733,
-0.015021233819425106,
-0.02937818132340908,
-0.041083626449108124,
-0.004934566095471382,
0.011258462443947792,
0.013054536655545235,
0.047263599932193756,
-0.016515089198946953,
-0.00821740087121725,
-0.02533661015331745,
-0.036606572568416595,
0.0035304119810462,
-0.012971973046660423,
-0.00810425914824009,
0.04489856958389282,
0.024230727925896645,
-0.031143132597208023,
0.017626451328396797,
0.009546108543872833,
-0.016784843057394028,
-0.05198907479643822,
0.00848148763179779,
0.05584452301263809,
0.026399699971079826,
0.01622137241065502,
0.006554211489856243,
0.08193924278020859,
0.04113608971238136,
-0.01803537644445896,
0.008475633338093758,
-0.001674832310527563,
-0.027643615379929543,
0.0038400108460336924,
-0.012647678144276142,
0.06157606095075607,
-0.01831040345132351,
0.009772960096597672,
-0.0041136229410767555,
0.004869460128247738,
-0.017426015809178352,
0.0296067725867033,
-0.024200817570090294,
0.049322351813316345,
0.052482761442661285,
0.005374422296881676,
-0.003559838281944394,
0.05798134580254555,
-0.00042575798579491675,
0.03861990198493004,
0.011791853234171867,
-0.005572741385549307,
-0.055535223335027695,
-0.025044118985533714,
0.016329865902662277,
0.040818944573402405,
0.028544677421450615,
0.02273453213274479,
0.03007766790688038,
0.07680252939462662,
0.008761085569858551,
0.02664203755557537,
-0.015780413523316383,
-0.009105556644499302,
0.02880401723086834,
-0.0003240072401240468,
0.01732005551457405,
0.024235209450125694,
0.04490204155445099,
0.038471024483442307,
-0.030430978164076805,
-0.015449953265488148,
-0.03285808116197586,
0.015555706806480885,
-0.022600369527935982,
-0.022976724430918694,
-0.012863398529589176,
-0.01602080650627613,
0.016861140727996826,
-0.03680553287267685,
-0.022720247507095337,
0.027150044217705727,
-0.012459220364689827,
-0.03840236738324165,
0.004774723667651415,
0.0039539458230137825,
0.01858072355389595,
-0.009034888818860054,
-0.019814686849713326,
-0.0042819613590836525,
0.0523538663983345,
-0.05328501760959625,
0.015200872905552387,
-0.025036249309778214,
-0.01907624863088131,
0.009537468664348125,
-0.004735447932034731,
0.01213966403156519,
0.04531988874077797,
0.04213647171854973,
-0.01067410595715046,
-0.033346716314554214,
0.05368204787373543,
-0.045560017228126526,
-0.01341601088643074,
0.008970944210886955,
-0.015287905931472778,
0.08039020001888275,
-0.01821281388401985,
-0.05040682479739189,
0.03139127418398857,
-0.019606785848736763,
-0.020252546295523643,
0.05112062767148018,
-0.023654840886592865,
-0.048512473702430725,
-0.016907459124922752,
-0.0064122420735657215,
-0.0015030932845547795,
-0.04699789732694626,
0.02799946442246437,
0.003811287460848689,
-0.009478675201535225,
-0.045139145106077194,
-0.047081295400857925,
-0.021367020905017853,
-0.03337865322828293,
0.00035297032445669174,
-0.00823584757745266,
-0.004141123499721289,
-0.06573522090911865,
-0.02152121253311634,
-0.0055957455188035965,
-0.03243177756667137,
0.026539530605077744,
-0.06418118625879288,
-0.03606666997075081,
0.010641314089298248,
-0.021569425240159035,
0.023370232433080673,
-0.00930811371654272,
-0.03135594353079796,
0.05043855309486389,
0.03348349407315254,
0.030704881995916367,
0.017764609307050705,
-0.028043290600180626,
0.00030687201069667935,
-0.009218153543770313,
0.07225635647773743,
0.002818097360432148,
0.01191728189587593,
0.015372447669506073,
0.04560193791985512,
0.0074729775078594685,
0.004668149631470442,
0.02812998555600643,
-0.020562108606100082,
-0.000029156180971767753,
-0.02810332551598549,
-0.005100678652524948,
0.0764867514371872,
0.013528452254831791,
-0.016893258318305016,
0.011747884564101696,
0.0035457913763821125,
0.016937853768467903,
-0.0036329738795757294,
-0.040249910205602646,
0.08950857073068619,
0.03273170068860054,
0.028301002457737923,
0.005795791279524565,
0.05201241001486778,
0.053948089480400085,
0.005627857521176338,
-0.013927304185926914,
0.003540352452546358,
0.021355953067541122,
-0.006323585752397776,
-0.014914966188371181,
0.027283232659101486,
0.03826061263680458,
-0.023970618844032288,
-0.013290442526340485,
-0.03086196444928646,
0.027391882613301277,
-0.0007842917693778872,
-0.02724769152700901,
0.006185516715049744,
0.023171398788690567,
0.05631246417760849,
0.012284329161047935,
0.004224143456667662,
-0.03276956453919411,
-0.054777681827545166,
-0.059876419603824615,
-0.019369367510080338,
-0.0021838152315467596,
0.00916353426873684,
0.009360992349684238,
0.028459133580327034,
0.012818831950426102,
0.014343418180942535,
0.011872387491166592,
-0.004909717943519354,
-0.04467799887061119,
0.010915029793977737,
-0.039552319794893265,
0.0086813447996974,
-0.01614603027701378,
-0.028035417199134827,
-0.024781443178653717,
0.0030176504515111446,
-0.04065098613500595,
-0.040564123541116714,
-0.023878511041402817,
-0.036121781915426254,
0.007939613424241543,
-0.03724108263850212,
-0.06084718182682991,
-0.0017074866918846965,
0.011317376047372818,
0.03863805904984474,
0.008748535998165607,
0.009496712125837803,
0.033674418926239014,
-0.03669319674372673,
0.006609814241528511,
0.003942978102713823,
0.023979371413588524,
-0.015472907572984695,
0.012297583743929863,
0.0020929696038365364,
0.01883910410106182,
-0.06070616841316223,
-0.020182054489850998,
0.014860473573207855,
0.01803237944841385,
0.01638513244688511,
-0.017320241779088974,
-0.025046968832612038,
-0.053344160318374634,
-0.008302592672407627,
0.018572907894849777,
0.058274686336517334,
-0.010186733677983284,
0.04170994460582733,
0.07074780762195587,
-0.021116720512509346,
-0.014084841124713421,
0.055678267031908035,
0.0483749583363533,
-0.03330221772193909,
-0.046364929527044296,
0.006669121794402599,
-0.030960427597165108,
0.005585856270045042,
0.02955746464431286,
0.005099849309772253,
-0.0160171277821064,
-0.009120570495724678,
-0.006103215739130974,
0.0015622173668816686,
0.021382981911301613,
-0.05335940420627594,
0.02790403552353382,
0.002713800873607397,
0.014149744994938374,
-0.041267234832048416,
-0.0011717306915670633,
-0.02009618654847145,
0.07203454524278641,
0.05218897759914398,
-0.0077377487905323505,
-0.02060156688094139,
-0.10965463519096375,
-0.002148901578038931,
0.05119291692972183,
0.04732678458094597,
-0.005918361712247133,
-0.02838541567325592,
-0.055949438363313675,
-0.019406359642744064,
0.02588527835905552,
-0.025059422478079796,
-0.02077408693730831,
-0.004156344570219517,
-0.010547216050326824,
-0.015039938502013683,
-0.02696591429412365,
0.009534002281725407,
0.029803622514009476,
-0.03200780227780342,
0.002806704258546233,
-0.03323009982705116,
-0.004438827279955149,
-0.018192242830991745,
0.07369010895490646,
0.035718441009521484,
0.046057652682065964,
0.03687125816941261,
0.008852759376168251,
-0.01503803115338087,
-0.016778727993369102,
-0.0559130534529686,
-0.05973893776535988,
-0.004655714612454176,
0.04589679464697838,
-0.02583770826458931,
0.08355781435966492,
-0.018154630437493324,
-0.0407005213201046,
-0.012140181846916676,
0.017313454300165176,
0.028065791353583336,
-0.010039863176643848,
-0.06335119903087616,
0.016714509576559067,
0.008471198379993439,
0.024846768006682396,
0.05326257273554802,
0.011813993565738201,
-0.02549516223371029,
-0.0036744256503880024,
-0.024475397542119026,
0.04662042856216431,
-0.036903396248817444,
-0.023642918094992638,
0.058568522334098816,
-0.02565501071512699,
-0.055530041456222534,
0.005354982800781727,
-0.011459503322839737,
0.002405979437753558,
-0.00302136386744678,
-0.060952309519052505,
-0.023423727601766586,
0.032293036580085754,
0.022504426538944244,
0.011382999829947948,
0.02658815123140812,
0.0012531433021649718,
-0.016527095809578896,
0.03985960781574249,
0.019613873213529587,
-0.001173529657535255,
0.0037859610747545958,
-0.01230565644800663,
-0.0043340581469237804,
-0.005357637070119381,
-0.02489987574517727,
0.016610994935035706,
-0.0050394064746797085,
-0.04361717030405998,
0.03963429480791092,
-0.004085156135261059,
0.001159223960712552,
0.04779597744345665,
-0.023013178259134293,
-0.03862296789884567,
-0.0249542985111475,
-0.032724469900131226,
0.04036173224449158,
-0.03271649405360222,
0.04625587537884712,
0.031693119555711746,
0.020561544224619865,
-0.05625179782509804,
-0.0022449817042797804,
0.021704431623220444,
0.0408630445599556,
-0.01637336239218712,
0.0025094246957451105,
0.019982624799013138,
-0.06110609322786331,
0.004618456587195396,
-0.03382138907909393,
0.03186452016234398,
-0.022522181272506714,
0.009913492016494274,
-0.03564760833978653,
0.0352957509458065,
0.04575998708605766,
-0.012711532413959503,
0.028218628838658333,
0.007515695411711931,
0.004669333342462778,
-0.013145211152732372,
-0.020079487934708595,
0.032673824578523636,
-0.04133166745305061,
-0.043489791452884674,
0.006634881254285574,
-0.04109317809343338,
-0.018833661451935768,
-0.04450973868370056,
-0.002167740371078253,
0.05750545859336853,
0.008060291409492493,
-0.034246332943439484,
0.002243588911369443,
0.04055749252438545,
-0.047676123678684235,
0.012093731202185154,
-0.03711795061826706,
-0.0015687873819842935,
-0.013372176326811314,
-0.018060879781842232,
0.010287045501172543,
-0.005303769838064909,
-0.0022616011556237936,
-0.0024721643421798944,
0.047094136476516724,
0.027776500210165977,
-0.03294133022427559,
0.008396699093282223,
-0.0039514582604169846,
-0.018130194395780563,
-0.04112262278795242,
0.02355095185339451,
-0.0020461769308894873,
-0.03761322796344757,
-0.01802578568458557,
-0.0644550770521164,
-0.02554643340408802,
0.011122091673314571,
0.08033305406570435,
-0.0053442055359482765,
0.04424763470888138,
-0.0066837891936302185,
0.014929662458598614,
0.008288745768368244,
-0.061090148985385895,
-0.00162977515719831,
0.02555268630385399,
0.024675944820046425,
-0.01886071264743805,
-0.04069952294230461,
-0.0004137843498028815,
-0.002785213990136981,
0.01938832364976406,
0.01578076183795929,
0.03876253217458725,
0.011018597520887852,
0.0008353612502105534,
0.000502679671626538,
-0.05607800930738449,
-0.051934946328401566,
0.02321610599756241,
-0.031970687210559845,
0.02442563883960247,
0.026751253753900528,
0.005055987276136875,
0.04207969456911087,
0.0014955970691516995,
0.023034600540995598,
0.004084211308509111,
-0.05139455944299698,
-0.027716532349586487,
0.030587531626224518,
0.04110986739397049,
0.0034670603927224874,
0.014636789448559284,
0.0021733599714934826,
0.02188032865524292,
0.00970468856394291,
-0.02218298614025116,
0.0033277994953095913,
-0.09548633545637131,
-0.019228607416152954,
-0.03433407098054886,
-0.07272972166538239,
0.05670484900474548,
0.021291116252541542,
-0.05971376597881317,
-0.0044255913235247135,
0.0015819011023268104,
0.018978284671902657,
-0.012363048270344734,
0.022402815520763397,
-0.024637693539261818,
0.0662316158413887,
-0.03786449134349823,
0.009271498769521713,
-0.04109910503029823,
-0.005583277437835932,
0.13390739262104034,
0.0505949892103672,
-0.009251109324395657,
-0.04936595633625984,
0.008483655750751495,
0.006818103604018688,
-0.00025416756398044527,
-0.0337531641125679,
-0.0002719759941101074,
-0.015419878996908665,
0.010938340798020363,
-0.0002138580457540229,
0.028839509934186935,
-0.021986033767461777,
-0.0426810085773468,
0.031071925535798073,
0.0026180429849773645,
-0.028410863131284714,
-0.02425334043800831,
0.022004203870892525,
0.021911628544330597,
0.016006121411919594,
-0.062387775629758835,
0.026468155905604362,
-0.04341202229261398,
-0.0024848070461302996,
-0.01730002462863922,
-0.03500085324048996,
0.04192057624459267,
-0.00227929325774312,
-0.02929062768816948,
0.025762168690562248,
0.023708956316113472,
-0.001240996178239584,
-0.0018967535579577088,
0.02887597307562828,
0.05362376943230629,
-0.03544527664780617,
0.030085710808634758,
0.06988640129566193,
-0.028865832835435867,
-0.007551688235253096,
-0.015324064530432224,
0.019603349268436432,
-0.031801506876945496,
-0.022529236972332,
-0.002335482742637396,
0.03457322344183922,
-0.00992554146796465,
-0.02294290065765381,
0.006996687036007643,
-0.03317620977759361,
-0.02329259365797043,
-0.02895364910364151,
-0.0037896272260695696,
0.002611625473946333,
0.0347195602953434,
-0.044134873896837234,
-0.006336213555186987,
-0.01081974059343338,
0.022407591342926025,
-0.03979027643799782,
0.021669959649443626,
-0.005633402615785599,
0.008963122963905334,
-0.005714622791856527,
-0.00029613295919261873,
0.04939039424061775,
0.007990228943526745,
-0.0330246277153492,
-0.03419364243745804,
-0.05682288855314255,
-0.016053318977355957,
-0.02806420810520649,
0.0049280705861747265,
0.037506915628910065,
0.03665582835674286,
-0.007928977720439434,
-0.030059879645705223,
-0.019717637449502945,
-0.028286444023251534,
0.037825990468263626,
-0.012816756963729858,
-0.02301761507987976,
-0.024926310405135155,
0.013897215016186237,
0.008678875863552094,
-0.0016271269414573908,
-0.011032321490347385,
0.06297318637371063,
-0.013921167701482773,
0.01333703100681305,
0.026322713121771812,
-0.020158840343356133,
-0.004203180782496929,
0.0038785163778811693,
-0.007904758676886559,
-0.05495646223425865,
-0.026806622743606567,
0.049827851355075836,
0.013213732279837132,
-0.027042556554079056,
0.0034324589651077986,
0.021846964955329895,
-0.04017309099435806,
0.0025525677483528852,
0.031868841499090195,
-0.018873725086450577,
-0.0020164435263723135,
0.030788037925958633,
-0.030925465747714043,
-0.050622377544641495,
-0.030664745718240738,
-0.02845233865082264,
-0.013042477890849113,
0.017848383635282516,
0.049568016082048416,
-0.05444278568029404,
0.07479006797075272,
0.025973685085773468,
0.01666702702641487,
-0.04007922485470772,
0.009767876006662846,
-0.03541605547070503,
0.01810436137020588,
-0.025057237595319748,
-0.051201626658439636,
0.010470656678080559,
0.017994042485952377,
-0.039428576827049255,
-0.01802831143140793,
0.03876985237002373,
0.010945438407361507,
0.019304323941469193,
-0.005366092082113028,
0.020786212757229805,
-0.025016630068421364,
0.01650538295507431,
0.0006672792369499803,
-0.06988196074962616,
0.039965301752090454,
-0.04764866828918457,
0.0024386895820498466,
0.04218689352273941,
-0.018519338220357895,
0.06673683226108551,
0.0190158411860466,
-0.043671783059835434,
0.031691260635852814,
0.07177712023258209,
-0.03149450570344925,
-0.014529853127896786,
-0.028061682358384132,
-0.026510139927268028,
0.0014456266071647406,
0.009909490123391151,
-0.013398793525993824,
0.026336761191487312,
-0.0036841724067926407,
0.01615975983440876,
0.005856058094650507,
0.023655829951167107,
0.021174635738134384,
-0.028836455196142197,
-0.036949027329683304,
-0.001510709524154663,
0.03896069899201393,
0.005247576627880335,
0.0012278727954253554,
0.042514629662036896,
-0.014863125048577785,
0.02997872419655323,
0.02355569787323475,
-0.01673492044210434,
-0.0682515799999237,
-0.021107157692313194,
-0.004266637843102217,
0.01985871233046055,
0.04723771661520004,
-0.04369325563311577,
0.031026268377900124,
0.02106938324868679,
-0.05410269275307655,
0.058152761310338974,
-0.011341385543346405,
-0.005526185967028141,
-0.007828673347830772,
0.003898667637258768,
-0.002811178332194686,
0.02605179138481617,
0.01345297321677208,
0.038447070866823196,
-0.03608177974820137,
-0.002048047725111246,
-0.015113342553377151,
-0.06617139279842377,
-0.024809731170535088,
0.010136519558727741,
-0.0002710013941396028,
0.024250244721770287,
0.053040508180856705,
-0.009360304102301598,
-0.016593001782894135,
0.04490897059440613,
-0.01996169611811638,
0.02940801903605461,
-0.015173438936471939,
-0.007760917767882347,
0.040589187294244766,
0.05263591930270195,
0.009252422489225864,
-0.003654703963547945,
-0.01133783534169197,
-0.010967436246573925,
0.0036060367710888386,
0.04198092967271805,
0.0003130188852082938,
0.021269574761390686,
0.022506192326545715,
-0.027818769216537476,
-0.006872078869491816,
0.005239445250481367,
-0.0023947686422616243,
-0.01326804794371128,
-0.000007492535132769262,
-0.019759634509682655,
0.0026182779110968113,
-0.015689464285969734,
-0.030277051031589508,
-0.016212649643421173,
0.0017156322719529271,
0.03238796442747116,
0.013369040563702583,
-0.021197162568569183,
0.010753498412668705,
-0.007306696381419897,
-0.005805187858641148,
0.006384288426488638,
0.01631290279328823,
0.016336755827069283,
0.003448196453973651,
0.018211951479315758,
0.00808157678693533,
0.021554773673415184,
0.02418721839785576,
-0.021493474021553993,
-0.04316982626914978,
-0.0022199591621756554,
0.0003177127509843558,
0.02058960497379303,
-0.049373265355825424,
-0.03497717157006264,
-0.016496621072292328,
-0.03153274953365326,
0.02050011418759823,
0.04259653761982918,
-0.016710802912712097,
-0.03909720480442047,
-0.03351176157593727,
-0.01695888862013817,
0.011627806350588799,
0.021930383518338203,
0.019632311537861824,
-0.0341453030705452,
0.00584259070456028,
-0.0241856686770916,
0.030492598190903664,
-0.05665510520339012,
0.016315646469593048,
-0.011312797665596008,
-0.029760124161839485,
-0.010803735814988613,
-0.015862619504332542,
-0.015090434812009335,
0.0032821556087583303,
0.02223108895123005,
-0.03973279148340225,
0.028414089232683182,
0.04569745808839798,
-0.016496285796165466,
0.05172159522771835,
-0.004392125643789768,
0.017118996009230614,
0.04647696763277054,
0.02475658245384693,
0.030599603429436684,
0.015270870178937912,
-0.017075784504413605,
-0.010016138665378094,
-0.0035023789387196302,
-0.028541095554828644,
-0.01725594326853752,
0.016718920320272446,
0.0009458122658543289,
0.0007758663850836456,
-0.0616333931684494,
-0.0077988398261368275,
0.06609607487916946,
-0.016568457707762718,
-0.01571018062531948,
0.04466114938259125,
-0.004297759849578142,
0.023413274437189102,
0.037454064935445786,
0.011110617779195309,
0.022167406976222992,
0.006223942618817091,
0.01397794485092163,
0.06157480552792549,
-0.010754690505564213,
-0.004400409758090973,
0.0027286740951240063,
0.02013336308300495,
-0.0000727677033864893,
0.016115199774503708,
0.03583971783518791,
0.01866167224943638,
-0.023434512317180634,
-0.014562839642167091,
0.02059190161526203,
0.03220647946000099,
0.00741116376593709,
0.024218248203396797,
-0.027449695393443108,
0.08930005878210068,
-0.0824868381023407,
0.010462560690939426,
-0.0029336391016840935,
-0.008723005652427673,
-0.0034434024710208178,
0.03086533397436142,
-0.016119206324219704,
0.03694302588701248,
-0.023222526535391808,
0.00009167350799543783,
-0.033167414367198944,
0.010951686650514603,
0.002742036711424589,
-0.0901162177324295,
0.05868139490485191,
0.018062543123960495,
0.002675062045454979,
0.03126692399382591,
-0.012723054736852646,
-0.010101876221597195,
-0.028997208923101425,
0.023220926523208618,
0.030076459050178528,
0.0032344250939786434,
-0.02645047940313816,
0.021667635068297386,
-0.026444673538208008,
0.0037075530271977186,
-0.04381508380174637,
-0.02105597034096718,
-0.034745264798402786,
0.030383164063096046,
-0.031871821731328964,
-0.023369336500763893
] |
<p>A typical problem in quantum mechanics is to calculate the spectrum that corresponds to a given potential. </p>
<ol>
<li>Is there a one to one correspondence between the potential and its spectrum? </li>
<li>If the answer to the previous question is yes, then given the spectrum, is there a systematic way to calculate the corresponding potential?</li>
</ol> | 2,869 | [
0.002604022389277816,
-0.004515757318586111,
0.01699993386864662,
-0.0099669573828578,
0.028277698904275894,
-0.0004837572341784835,
-0.013157852925360203,
-0.0178639218211174,
0.03998459875583649,
-0.023590655997395515,
0.048429880291223526,
0.011468704789876938,
0.05798888951539993,
0.005335896275937557,
0.014551862142980099,
0.03600072115659714,
-0.010191301815211773,
0.004188756458461285,
-0.01240102294832468,
-0.0460546538233757,
0.012339121662080288,
0.026528501883149147,
0.015967171639204025,
0.010828246362507343,
-0.018629370257258415,
0.04476573318243027,
0.021126016974449158,
-0.010073347948491573,
0.025598477572202682,
0.062430862337350845,
-0.03177950903773308,
-0.011672337539494038,
0.02963968552649021,
0.05311956629157066,
0.02548292651772499,
-0.01177874393761158,
-0.027313629165291786,
-0.03228436037898064,
-0.015353155322372913,
0.020365290343761444,
-0.031231630593538284,
-0.04628218337893486,
0.01566411182284355,
0.06360173225402832,
-0.02422516420483589,
0.007678728085011244,
-0.06720730662345886,
-0.015240238979458809,
0.010256309062242508,
-0.04234330728650093,
0.06285197287797928,
0.00018191827984992415,
0.03438727557659149,
0.007881342433393002,
-0.03946041315793991,
0.012692290358245373,
0.06711487472057343,
0.07329075038433075,
0.021898970007896423,
-0.03142642229795456,
-0.0464923195540905,
-0.008624030277132988,
-0.015083870850503445,
-0.007897541858255863,
-0.03332863748073578,
-0.002054500626400113,
-0.006430920213460922,
-0.025828024372458458,
0.025643283501267433,
-0.0145303625613451,
-0.014703454449772835,
0.04568897932767868,
0.01832209713757038,
-0.03175290673971176,
0.031974609941244125,
-0.026864124462008476,
-0.003801552578806877,
0.03916524350643158,
0.03909188136458397,
0.0026181736029684544,
-0.007583612110465765,
0.027453700080513954,
0.01911265403032303,
0.014871825464069843,
0.01900879107415676,
-0.014619244262576103,
0.04590209946036339,
-0.042957376688718796,
0.0037194995675235987,
0.022751040756702423,
0.007765613496303558,
0.033911820501089096,
0.034550316631793976,
-0.02929512970149517,
0.006088966503739357,
0.030062910169363022,
-0.009068570099771023,
0.03769170865416527,
0.008255768567323685,
-0.05300956219434738,
-0.003796132979914546,
-0.023232297971844673,
0.009626383893191814,
0.0481349378824234,
-0.01375436969101429,
0.007102670148015022,
-0.00873001292347908,
-0.0008386812405660748,
0.019656917080283165,
-0.0028863868210464716,
-0.018429983407258987,
0.04184870049357414,
0.011869036592543125,
0.036801114678382874,
0.007273050490766764,
0.009596950374543667,
-0.011052158661186695,
-0.011448406614363194,
0.0414346382021904,
0.044383805245161057,
0.01175694726407528,
-0.03975354880094528,
0.015358546748757362,
-0.05744895711541176,
-0.026671526953577995,
-0.0095292329788208,
0.030169658362865448,
0.007780530024319887,
-0.05238652974367142,
0.020626787096261978,
0.02677304297685623,
-0.02307175286114216,
0.004337873309850693,
0.01099740993231535,
0.017071375623345375,
-0.02544379234313965,
-0.10409820824861526,
-0.06492764502763748,
0.008716562762856483,
-0.005995644256472588,
-0.048166461288928986,
-0.0478048138320446,
-0.025216076523065567,
0.03355121985077858,
0.08025647699832916,
0.016498953104019165,
0.023683086037635803,
0.023626364767551422,
0.0137949138879776,
0.010778816416859627,
0.024098217487335205,
-0.030864503234624863,
0.018183942884206772,
-0.025828324258327484,
-0.012244367972016335,
-0.02588987722992897,
0.009265808388590813,
0.009309900924563408,
0.006516413763165474,
-0.004799527581781149,
0.060122016817331314,
-0.01459342148154974,
-0.02599945291876793,
0.01880059204995632,
0.03854973986744881,
-0.022232165560126305,
0.07036742568016052,
0.019415827468037605,
-0.038000717759132385,
0.01620863750576973,
-0.034919559955596924,
0.004041177686303854,
0.0005921099800616503,
0.025680195540189743,
0.050258759409189224,
-0.038337647914886475,
-0.02205670066177845,
-0.03923174366354942,
0.022541938349604607,
-0.030543839558959007,
-0.0011688863160088658,
-0.026827210560441017,
-0.028498923406004906,
0.043817825615406036,
0.037166379392147064,
0.02655300684273243,
0.012954901903867722,
-0.0029879158828407526,
-0.0012992547126486897,
-0.03424413129687309,
0.006440893746912479,
-0.046054162085056305,
0.03020673617720604,
-0.001782222418114543,
-0.029065756127238274,
0.05726703628897667,
0.032479628920555115,
0.019272062927484512,
-0.01525071356445551,
-0.03243182599544525,
-0.0009631274733692408,
0.014469129033386707,
-0.00800239946693182,
-0.00410103052854538,
0.015410554595291615,
0.06829966604709625,
0.048801764845848083,
-0.020181497558951378,
0.04521776735782623,
-0.061423160135746,
-0.06255701929330826,
-0.02336101233959198,
-0.005534483585506678,
0.0579526461660862,
0.027710329741239548,
0.03956626355648041,
-0.016050156205892563,
-0.03270012140274048,
-0.01606537029147148,
0.027567021548748016,
-0.052298132330179214,
0.04809121787548065,
0.04097966477274895,
-0.010162665508687496,
-0.015093900263309479,
0.0546695850789547,
0.03617588430643082,
0.013629632070660591,
0.034086406230926514,
-0.06292359530925751,
-0.030585184693336487,
-0.009000799618661404,
0.01502467691898346,
0.05867357179522514,
-0.04639802128076553,
0.0011890589958056808,
0.029016459360718727,
0.03801876679062843,
0.02531467191874981,
0.007929433137178421,
-0.06889230757951736,
-0.0296026524156332,
0.023231681436300278,
-0.02006102167069912,
0.022196413949131966,
0.00020490417955443263,
0.0013432392152026296,
0.026394613087177277,
0.004078440833836794,
-0.023263461887836456,
-0.016347788274288177,
0.043881312012672424,
-0.028003016486763954,
0.01675790548324585,
0.0331839881837368,
-0.03409046307206154,
0.024266375228762627,
-0.04106442630290985,
0.04356284439563751,
-0.0037003797478973866,
-0.06658211350440979,
-0.005946111399680376,
0.01710359752178192,
-0.029787806794047356,
0.017197521403431892,
-0.02278047986328602,
-0.02686580829322338,
0.02055767923593521,
0.03515409305691719,
-0.02641163021326065,
0.012929433025419712,
-0.011582529172301292,
-0.02790667675435543,
0.005914348643273115,
0.01329820603132248,
0.04543091729283333,
-0.004202172625809908,
0.028470339253544807,
-0.049285437911748886,
-0.038447581231594086,
0.02673579566180706,
-0.02510090172290802,
-0.03145560249686241,
0.0393214225769043,
-0.03670746833086014,
0.020355291664600372,
-0.05121423676609993,
-0.02759353443980217,
0.007005403749644756,
0.006673495750874281,
0.0012834143126383424,
0.01975698210299015,
0.019383270293474197,
-0.04438125714659691,
-0.0022824197076261044,
-0.01664363220334053,
0.014478456228971481,
-0.04849984496831894,
0.018805144354701042,
0.038753949105739594,
-0.01298749353736639,
-0.044645681977272034,
0.01017784234136343,
-0.023090453818440437,
-0.04213825240731239,
-0.03703179582953453,
0.0021051340736448765,
0.018299072980880737,
-0.00893449131399393,
0.02510850504040718,
0.02796502783894539,
-0.037314292043447495,
-0.007438319269567728,
-0.04927949234843254,
-0.04463539272546768,
0.018476806581020355,
0.012978538870811462,
0.03325831890106201,
0.03376331925392151,
0.012360009364783764,
0.08634310215711594,
-0.003017713315784931,
-0.022892199456691742,
-0.02055288292467594,
-0.001832164591178298,
0.018123723566532135,
0.003688076976686716,
0.013040869496762753,
0.030373280867934227,
-0.030189836397767067,
0.0264055747538805,
0.019709285348653793,
0.02685130201280117,
0.02801445871591568,
0.020933285355567932,
-0.010134109295904636,
0.016006415709853172,
0.004861555993556976,
0.014096713624894619,
0.03614388778805733,
-0.03190482407808304,
-0.011239351704716682,
0.02132880873978138,
-0.011795305646955967,
0.010354000143706799,
0.036389872431755066,
-0.022824637591838837,
0.034944213926792145,
-0.00002392289934505243,
0.013597911223769188,
-0.023929355666041374,
0.0485711470246315,
-0.0027710008434951305,
-0.0023652331437915564,
0.00028689493774436414,
0.0516049899160862,
0.049549221992492676,
0.012072290293872356,
-0.0016553603345528245,
0.055471211671829224,
0.03500250726938248,
-0.04145555570721626,
-0.04809367284178734,
0.009823733009397984,
-0.028096679598093033,
0.010493495501577854,
-0.03714009001851082,
-0.06606712192296982,
0.012145332992076874,
0.027960894629359245,
0.037855472415685654,
-0.039851102977991104,
-0.06427840143442154,
-0.01572299562394619,
-0.05340833216905594,
-0.02522966079413891,
-0.040745846927165985,
0.05066061019897461,
-0.021483775228261948,
0.05810776352882385,
0.0004446528328116983,
0.011943372897803783,
0.03519943356513977,
0.026056528091430664,
-0.06834056973457336,
0.01679197885096073,
-0.022975051775574684,
0.025698861107230186,
-0.027200287207961082,
-0.006379976402968168,
0.00829373486340046,
-0.04698960483074188,
-0.02252710610628128,
0.0038913569878786802,
-0.027153946459293365,
-0.03774663805961609,
0.012275547720491886,
-0.03753224387764931,
-0.05674266442656517,
-0.02431626059114933,
0.023762177675962448,
0.028462769463658333,
-0.014143596403300762,
0.011081362143158913,
0.027429718524217606,
-0.00922816526144743,
0.005181664600968361,
-0.021225858479738235,
0.0358639694750309,
-0.013600037433207035,
0.054598692804574966,
0.015013184398412704,
0.038400620222091675,
-0.01637437753379345,
0.0007468739058822393,
-0.03255445882678032,
0.06262198835611343,
0.015970274806022644,
-0.06165947765111923,
0.004778315778821707,
-0.03436514735221863,
0.02254978008568287,
-0.00507249915972352,
0.08026713132858276,
-0.029238833114504814,
0.021036604419350624,
0.022247683256864548,
0.005276359152048826,
-0.0355444997549057,
0.03215799480676651,
0.07370715588331223,
0.0458686463534832,
-0.023666182532906532,
-0.009570913389325142,
0.022672172635793686,
-0.016467222943902016,
0.026339435949921608,
0.000994145404547453,
0.000931893358938396,
-0.00818695593625307,
0.034244947135448456,
0.015364205464720726,
0.03788912668824196,
-0.027969056740403175,
-0.03743843734264374,
-0.009489345364272594,
0.023421406745910645,
-0.021831030026078224,
-0.005495668854564428,
0.030863208696246147,
0.01686207577586174,
0.047682374715805054,
-0.004498875699937344,
0.009943746961653233,
-0.08244719356298447,
-0.025782663375139236,
0.02991189807653427,
0.01929374411702156,
-0.0015369525644928217,
-0.014684849418699741,
-0.042308203876018524,
-0.015141037292778492,
0.07552642375230789,
-0.016047198325395584,
0.03008638322353363,
-0.004424537066370249,
-0.005473301280289888,
0.003750342410057783,
-0.04026506468653679,
-0.00802757777273655,
0.024358056485652924,
0.010866629891097546,
0.0014954237267374992,
-0.018825965002179146,
0.007635262794792652,
-0.05893847346305847,
0.0176334660500288,
0.02664608135819435,
0.06319832056760788,
0.012232325971126556,
0.003283961908891797,
-0.01632603257894516,
0.02159724198281765,
-0.008623257279396057,
-0.04916417598724365,
-0.015336976386606693,
0.01976521499454975,
-0.01793830469250679,
0.009679541923105717,
-0.026072286069393158,
-0.05271197855472565,
0.03330075740814209,
-0.01752394624054432,
-0.004968507215380669,
0.01786743849515915,
-0.002717052586376667,
0.03642546385526657,
0.07015552371740341,
0.016831833869218826,
0.055139247328042984,
0.040213633328676224,
-0.005167179740965366,
-0.011784191243350506,
-0.027989283204078674,
0.02846399135887623,
-0.029788322746753693,
-0.019534889608621597,
0.005683015566319227,
0.014303890988230705,
-0.03429337590932846,
0.01767726056277752,
-0.0072291516698896885,
0.009997985325753689,
0.01564350724220276,
-0.009183057583868504,
-0.06388445198535919,
0.01248316839337349,
-0.04149923473596573,
-0.014851759187877178,
0.006641278974711895,
0.04596279188990593,
0.024668090045452118,
-0.03271562233567238,
0.010646054521203041,
0.001587019069120288,
0.002097210381180048,
0.029144421219825745,
-0.028654377907514572,
0.05205874517560005,
-0.04592067748308182,
0.018950842320919037,
0.02828780934214592,
-0.07849633693695068,
0.03615366667509079,
-0.025289155542850494,
0.005661281757056713,
0.03711080551147461,
-0.07439686357975006,
-0.0560729019343853,
0.0393194854259491,
0.016204865649342537,
-0.023648682981729507,
-0.028118155896663666,
0.03004380688071251,
0.028264926746487617,
0.00893297791481018,
-0.07486289739608765,
0.019451038911938667,
-0.0039037454407662153,
0.046929165720939636,
-0.004424829967319965,
-0.04103865846991539,
-0.00708665931597352,
0.0038834274746477604,
0.008875305764377117,
0.01280509028583765,
0.006167438812553883,
0.021800240501761436,
-0.044895440340042114,
0.009108409285545349,
0.024105120450258255,
0.05733712762594223,
-0.023885102942585945,
0.006076077930629253,
0.01823345199227333,
-0.03436879441142082,
-0.002448305254802108,
0.005292734131217003,
0.05601479858160019,
-0.027539974078536034,
-0.04678323119878769,
-0.02935425564646721,
0.0047430912964046,
0.0659254938364029,
-0.02026945725083351,
-0.01344440970569849,
0.025284675881266594,
0.01867459900677204,
-0.009614607319235802,
-0.030801404267549515,
-0.013634116388857365,
0.016486845910549164,
0.037156056612730026,
-0.004984254948794842,
-0.0013856957666575909,
-0.023047251626849174,
-0.05065912380814552,
0.001376402098685503,
-0.014679373241961002,
-0.011895237490534782,
0.05000230669975281,
0.05171008035540581,
-0.02148122526705265,
-0.005040911491960287,
0.021450987085700035,
0.00429626414552331,
-0.012538994662463665,
-0.0560753233730793,
0.03705526515841484,
0.00796777568757534,
0.014215607196092606,
-0.014277218841016293,
-0.07803446799516678,
-0.02873840555548668,
0.017684055492281914,
0.02927239052951336,
0.005468548741191626,
0.059500016272068024,
0.016133805736899376,
0.018707236275076866,
-0.0076464200392365456,
-0.005562609992921352,
0.0017448818543925881,
-0.028199080377817154,
0.019740482792258263,
0.05261409655213356,
-0.05526873469352722,
0.01993701048195362,
0.016911383718252182,
0.016537189483642578,
-0.030963895842432976,
-0.010281872004270554,
0.029405739158391953,
0.02633802406489849,
0.03349045664072037,
-0.00809407513588667,
-0.019196629524230957,
0.041378673166036606,
-0.010256113484501839,
0.039683468639850616,
0.002768338192254305,
-0.021720750257372856,
0.03364672511816025,
0.011832011863589287,
0.00018191382696386427,
-0.02815842814743519,
-0.008997024036943913,
-0.01844657212495804,
0.05385761708021164,
-0.00007531805022154003,
0.04038381949067116,
0.02236919105052948,
0.01962394081056118,
0.009549741633236408,
-0.007237368728965521,
0.007735412567853928,
0.0042481208220124245,
-0.05459747463464737,
-0.01647016778588295,
-0.037219539284706116,
-0.07864182442426682,
0.00977469515055418,
-0.004238078370690346,
-0.022316206246614456,
0.025168851017951965,
-0.04235796257853508,
0.020576372742652893,
-0.012808503583073616,
0.04101552814245224,
-0.03194807097315788,
0.043318718671798706,
0.014988098293542862,
0.02251514606177807,
0.010508141480386257,
0.023499300703406334,
0.09866779297590256,
0.07938417792320251,
0.026928892359137535,
-0.0660722479224205,
-0.01492411270737648,
-0.018379129469394684,
-0.041036322712898254,
0.012321092188358307,
0.023353533819317818,
-0.009855619631707668,
-0.012853847816586494,
-0.038451578468084335,
0.03947990760207176,
-0.01785091869533062,
0.022588081657886505,
0.03396764397621155,
-0.04357822239398956,
-0.013559455052018166,
0.016309062018990517,
-0.004963055718690157,
0.0006622343207709491,
0.03169259801506996,
-0.017542490735650063,
0.015394280664622784,
-0.054537173360586166,
0.012524093501269817,
-0.04553444683551788,
-0.029128551483154297,
0.00973543245345354,
-0.014700662344694138,
-0.013992375694215298,
0.0015543779591098428,
0.020838119089603424,
-0.015511560253798962,
-0.011295109055936337,
0.067791648209095,
0.024033857509493828,
0.00044916372280567884,
-0.011774337850511074,
0.037305913865566254,
0.007874567061662674,
0.024331094697117805,
-0.0075826505199074745,
-0.007653037551790476,
-0.02637624740600586,
-0.005683605559170246,
-0.030715707689523697,
-0.001774091855622828,
-0.015539395622909069,
0.01262434758245945,
-0.010926255024969578,
-0.013733341358602047,
0.002694568829610944,
-0.03436632454395294,
-0.020162776112556458,
0.0071832528337836266,
0.03834187984466553,
-0.029329679906368256,
-0.01602579839527607,
-0.05132688581943512,
0.013192513026297092,
-0.012171278707683086,
0.02016477845609188,
-0.023538358509540558,
-0.024055324494838715,
0.019639840349555016,
0.020942453294992447,
0.05048877373337746,
0.0037097465246915817,
-0.020656762644648552,
-0.012390883639454842,
-0.028378302231431007,
-0.052709829062223434,
-0.07331294566392899,
0.006901005748659372,
0.02288280799984932,
0.05013562738895416,
0.023338275030255318,
0.0007456369348801672,
-0.02639978937804699,
-0.12509067356586456,
0.010444584302604198,
-0.012073020450770855,
-0.014052595011889935,
-0.014753916300833225,
-0.016822824254631996,
0.0389399491250515,
0.07317757606506348,
-0.024419477209448814,
0.010487556457519531,
0.009078864008188248,
0.006221790332347155,
0.05128588527441025,
-0.01932487264275551,
-0.018592407926917076,
0.028283631429076195,
-0.041028015315532684,
0.05997062101960182,
-0.010147473774850368,
0.009370191022753716,
-0.015032497234642506,
0.02596951276063919,
-0.01029659528285265,
0.06661932170391083,
-0.0387512743473053,
0.025423040613532066,
-0.03268410265445709,
-0.015674961730837822,
-0.02661893703043461,
-0.003957771696150303,
0.032704517245292664,
-0.04875567927956581,
-0.028303148224949837,
-0.03788061439990997,
0.002770345890894532,
0.04238944873213768,
0.00637309905141592,
-0.0559818297624588,
0.0012330359313637018,
-0.004159324336796999,
0.031127972528338432,
-0.06386233121156693,
-0.02607675828039646,
-0.038771744817495346,
0.03759900853037834,
0.011576908640563488,
-0.01594105176627636,
0.0077512990683317184,
0.01665644720196724,
-0.03186400607228279,
-0.01585434377193451,
0.02827139012515545,
0.020635079592466354,
-0.02007087506353855,
-0.0011473457561805844,
0.006224599666893482,
-0.01800062321126461,
0.07537338137626648,
-0.02236168459057808,
0.00001841900848376099,
0.02075459435582161,
-0.05840019881725311,
-0.013595744967460632,
0.029440823942422867,
-0.03328397497534752,
0.04243774339556694,
0.03313136845827103,
0.016334770247340202,
0.005371657200157642,
-0.0028217078652232885,
-0.03818933665752411,
0.0008394774631597102,
0.0090278135612607,
-0.011292781680822372,
0.03245409578084946,
0.0001306037447648123,
0.01894696243107319,
0.018152505159378052,
-0.013565280474722385,
-0.008744126185774803,
-0.012011771090328693,
0.0008956266683526337,
-0.01025093998759985,
0.0013925274834036827,
-0.006799871567636728,
0.04968899488449097,
0.026649102568626404,
-0.006771827582269907,
0.016426613554358482,
0.0481778122484684,
-0.037117063999176025,
0.03297319635748863,
0.054591335356235504,
-0.0044812727719545364,
-0.07290428876876831,
-0.027482695877552032,
0.0035337565932422876,
-0.01933368295431137,
0.025108035653829575,
-0.05637168884277344,
0.0031204442493617535,
0.02160969190299511,
-0.07536729425191879,
0.03852725028991699,
-0.0002634114061947912,
0.006381424143910408,
-0.001062779570929706,
0.029761480167508125,
-0.066202811896801,
0.028911525383591652,
0.036911435425281525,
0.02807275950908661,
-0.018057702109217644,
0.005148201249539852,
0.025143345817923546,
0.0020153194200247526,
-0.018573306500911713,
-0.0005746824899688363,
-0.017954247072339058,
-0.013271557167172432,
0.0532694049179554,
-0.05966614931821823,
-0.02377544343471527,
0.024444472044706345,
-0.022363580763339996,
-0.013645733706653118,
-0.017674358561635017,
0.003231084905564785,
0.0005163068417459726,
0.02455570548772812,
0.029848814010620117,
-0.012524975463747978,
-0.028598640114068985,
0.02902885153889656,
0.03105122782289982,
0.033782534301280975,
-0.0280599445104599,
-0.00974300317466259,
0.0206685159355402,
-0.04316188395023346,
-0.0210067480802536,
0.02910899929702282,
0.013244114816188812,
-0.012632045894861221,
-0.023241592571139336,
0.001636807806789875,
-0.005782329477369785,
0.002124055987223983,
0.01319496612995863,
-0.061237309128046036,
-0.01033187098801136,
0.04804380238056183,
0.007952829822897911,
0.006312408484518528,
0.010642466135323048,
-0.03119347244501114,
-0.06979180872440338,
0.05951584503054619,
0.029596125707030296,
-0.0653136819601059,
-0.029817942529916763,
-0.002286160597577691,
0.04003868252038956,
-0.0009043561294674873,
0.012287739664316177,
-0.05073726549744606,
-0.03176309913396835,
0.0186671931296587,
-0.03312618285417557,
0.033515021204948425,
-0.020996807143092155,
-0.014271751046180725,
-0.041060734540224075,
-0.049374114722013474,
0.027875060215592384,
0.00572300935164094,
-0.038311392068862915,
-0.022614669054746628,
-0.041161615401506424,
0.02639594115316868,
-0.008641478605568409,
0.04629907011985779,
-0.0363086499273777,
-0.04601819068193436,
0.0053011346608400345,
-0.03118251822888851,
0.036189161241054535,
-0.010722818784415722,
-0.025111021474003792,
0.0021764368284493685,
-0.01834845170378685,
0.007104204501956701,
0.009554470889270306,
-0.03778349608182907,
0.040085531771183014,
0.00581653555855155,
-0.0004759593866765499,
-0.013928049243986607,
-0.005020285490900278,
-0.01819721609354019,
0.07403497397899628,
0.00728234089910984,
-0.007451559882611036,
0.05847243592143059,
0.019590124487876892,
0.005266841500997543,
0.020584961399435997,
-0.01787484623491764,
-0.03501351177692413,
0.009706530719995499,
-0.06770341843366623,
-0.03369981795549393,
0.02369704470038414,
0.009444675408303738,
0.01640358939766884,
-0.028817854821681976,
-0.03235567361116409,
0.042689867317676544,
-0.001384827890433371,
-0.03163359314203262,
0.0482049398124218,
-0.01874006912112236,
0.030453020706772804,
0.025527162477374077,
0.01972223073244095,
0.031330764293670654,
0.008760376833379269,
-0.00014148368791211396,
0.033301252871751785,
0.04177776351571083,
-0.007288421504199505,
0.019436579197645187,
0.03479064628481865,
0.000178965026861988,
-0.003727364121004939,
0.02759186550974846,
0.018684476613998413,
-0.05124741792678833,
-0.004222113639116287,
0.053994759917259216,
0.008731751702725887,
-0.024820251390337944,
-0.013126191683113575,
-0.04590382054448128,
0.07804375141859055,
-0.020700840279459953,
0.006185762584209442,
-0.057158008217811584,
0.02872125431895256,
-0.02024546079337597,
0.022107934579253197,
0.01083742082118988,
0.009224175475537777,
-0.011149710044264793,
-0.022042129188776016,
-0.03162231668829918,
0.03401894122362137,
-0.004209587350487709,
-0.0801679790019989,
-0.00033070973586291075,
0.004557013511657715,
0.0017595919780433178,
-0.035950612276792526,
0.007130843121558428,
0.0003873668028973043,
-0.0002955813251901418,
0.01632450893521309,
0.07902549207210541,
0.005040301941335201,
0.010985818691551685,
0.014244035817682743,
-0.020087145268917084,
0.028402594849467278,
-0.06175800785422325,
-0.021686499938368797,
-0.027851412072777748,
0.02684927172958851,
-0.014631480909883976,
-0.0031863574404269457
] |
<p>A mass spring system is in equilibrium. If I pull on the load by $x$ meters, the energy stored in the spring is (this is what is given in my book):</p>
<p>$$E=\frac12kx^2 $$</p>
<p>However, doesn't the load lose gravitational potential energy as it moves down? Where would this energy go? By conservation law, shouldn't the energy equation be:
$$E_{stored}= \frac12kx^2 + mgx$$</p>
<p>In short, where does the loss of gravitational potential energy (mgx) of the load get transferred to if it is not stored in the spring?</p>
<p>(Referring to a vertical mass spring system)</p>
<p>The picture in my mind:
<img src="http://i.stack.imgur.com/OdVee.png" alt="enter image description here"></p> | 2,870 | [
-0.0593605563044548,
-0.006645547691732645,
-0.04351384937763214,
-0.0026695807464420795,
-0.012127847410738468,
0.029914112761616707,
-0.024656927213072777,
-0.025575460866093636,
0.013569248840212822,
-0.02218957059085369,
-0.003781738691031933,
0.028967974707484245,
0.05448257550597191,
0.017224060371518135,
0.03101072646677494,
-0.0005065309233032167,
-0.03297021985054016,
-0.011634130030870438,
0.011529769748449326,
-0.05083374306559563,
-0.03248874470591545,
-0.011355833150446415,
0.0030518067069351673,
-0.008320343680679798,
-0.02633272297680378,
0.011297040618956089,
0.03869807347655296,
-0.035078100860118866,
0.025056127458810806,
0.05497441440820694,
0.016224423423409462,
-0.04750168323516846,
-0.026383506134152412,
0.04608282446861267,
-0.019509317353367805,
0.018628083169460297,
-0.046976763755083084,
-0.023375965654850006,
-0.0087894257158041,
0.024143552407622337,
-0.030335726216435432,
-0.00006947274232516065,
-0.00591248506680131,
0.04839947819709778,
-0.02797004207968712,
0.0022046826779842377,
0.023772984743118286,
0.002476850990206003,
0.042958445847034454,
-0.03144625201821327,
0.0388360433280468,
0.010317192412912846,
0.026327816769480705,
0.04194088652729988,
-0.01867375336587429,
-0.018596485257148743,
0.04004089534282684,
0.04759502410888672,
-0.015739211812615395,
-0.05140051245689392,
0.0020618431735783815,
-0.056368496268987656,
-0.02530803345143795,
-0.022324103862047195,
0.006690626498311758,
0.02642611227929592,
0.03192407637834549,
0.022298987954854965,
0.07436241954565048,
-0.008709433488547802,
0.0032749713864177465,
0.026060422882437706,
0.027387095615267754,
-0.02551128901541233,
0.0006623088847845793,
-0.01929643005132675,
0.04779678210616112,
0.04323294013738632,
0.037881817668676376,
0.01778184249997139,
-0.02187689021229744,
0.007649742066860199,
0.033509425818920135,
0.07122904062271118,
0.006864312570542097,
-0.01093570701777935,
0.04534418135881424,
0.02529842033982277,
0.03583872318267822,
0.027661925181746483,
0.036605075001716614,
0.030270474031567574,
-0.032699257135391235,
-0.026972472667694092,
-0.006881306413561106,
0.05371945723891258,
0.009011069312691689,
0.03523465245962143,
-0.001232817186973989,
-0.014140590094029903,
0.012747351080179214,
0.004555066581815481,
0.03318977355957031,
0.05021810531616211,
0.024501090869307518,
-0.03635900467634201,
-0.010374639183282852,
0.0005217156722210348,
-0.0031102076172828674,
0.00473523186519742,
-0.08289386332035065,
-0.024127932265400887,
0.011591569520533085,
-0.00902518816292286,
0.03650280088186264,
-0.05545487254858017,
-0.003817404853180051,
-0.02701377123594284,
0.03919820487499237,
0.01467577088624239,
0.017901979386806488,
-0.033852286636829376,
0.036430854350328445,
-0.0259114820510149,
-0.06853190809488297,
0.008150613866746426,
0.027169303968548775,
-0.00990857183933258,
-0.05473966524004936,
0.009635739028453827,
0.022066103294491768,
0.0006611812277697027,
-0.013876608572900295,
-0.006151734851300716,
0.04979526251554489,
0.013815970160067081,
-0.09602963924407959,
-0.032332099974155426,
0.026788752526044846,
-0.008714862167835236,
-0.005163191817700863,
-0.07774204760789871,
-0.028565730899572372,
0.02346956357359886,
0.038270387798547745,
0.01919359341263771,
-0.00794974248856306,
-0.005392311606556177,
0.02479548193514347,
0.02446715161204338,
0.023139100521802902,
-0.026781154796481133,
0.005867892410606146,
-0.031175535172224045,
-0.005421766545623541,
-0.061589885503053665,
0.02401966042816639,
0.04278259351849556,
0.00549367954954505,
-0.028187846764922142,
0.024704931303858757,
-0.008725996129214764,
-0.0015654427697882056,
-0.020871030166745186,
-0.014770392328500748,
-0.02300529181957245,
0.04711362347006798,
0.0009367788443341851,
-0.0058578010648489,
0.007588626816868782,
0.025197885930538177,
0.026788992807269096,
-0.03519026190042496,
0.02031339332461357,
0.010913711041212082,
-0.024127356708049774,
0.0019208356970921159,
-0.05416877195239067,
0.014884700067341328,
0.006321766879409552,
-0.039973899722099304,
-0.0702672079205513,
0.025925414636731148,
-0.006021074950695038,
-0.0032396104652434587,
0.03955275937914848,
0.00377453351393342,
-0.010386131703853607,
-0.0063763889484107494,
0.0075972131453454494,
-0.013296179473400116,
-0.052466005086898804,
0.07302409410476685,
-0.013219350948929787,
0.014416919089853764,
-0.010847066529095173,
0.019106125459074974,
0.04209130257368088,
-0.056249797344207764,
0.003717562183737755,
0.01019862201064825,
-0.012103770859539509,
-0.03470049798488617,
-0.01007200125604868,
0.00019940838683396578,
0.041536327451467514,
0.05421367660164833,
0.041595254093408585,
-0.01042676530778408,
0.00035782845225185156,
-0.013797827064990997,
0.003249816130846739,
-0.022790901362895966,
0.030624888837337494,
-0.015092618763446808,
-0.01671646162867546,
-0.008835877291858196,
-0.0203215591609478,
-0.0003049130318686366,
0.004409405868500471,
-0.004800819326192141,
0.05581727251410484,
0.0647597387433052,
-0.028815729543566704,
0.004548224620521069,
0.035207271575927734,
-0.022906934842467308,
0.06460320949554443,
-0.0363948717713356,
-0.022408945485949516,
-0.02641272358596325,
-0.022713761776685715,
-0.001876562600955367,
0.03998992592096329,
-0.020818736404180527,
0.015423839911818504,
0.0290097463876009,
0.003114597871899605,
0.011563979089260101,
0.004858008585870266,
0.02434687316417694,
-0.056532684713602066,
0.04561612010002136,
0.027307361364364624,
-0.00018220633501186967,
0.030011767521500587,
0.018519345670938492,
0.022718004882335663,
-0.007094403263181448,
-0.033961545675992966,
0.014341142028570175,
0.040523286908864975,
-0.001116053550504148,
0.0489150770008564,
-0.007243321277201176,
-0.03125683218240738,
0.03733124956488609,
-0.01579921506345272,
0.03896713629364967,
0.02770911157131195,
-0.010220120660960674,
0.016568616032600403,
-0.05548345670104027,
-0.035147152841091156,
-0.0035319810267537832,
0.021621400490403175,
-0.016685795038938522,
-0.038284122943878174,
0.016370488330721855,
-0.023197714239358902,
0.030367650091648102,
-0.008518910966813564,
-0.014281222596764565,
0.008626560680568218,
-0.01327996701002121,
0.025407034903764725,
-0.009475503116846085,
-0.013680594973266125,
-0.04356375336647034,
-0.018516143783926964,
-0.013594545423984528,
-0.05894012749195099,
-0.01711614616215229,
0.010548694059252739,
-0.03660981357097626,
-0.007371184881776571,
-0.04126674681901932,
-0.007081911899149418,
0.06393799930810928,
0.013994050212204456,
0.003158142324537039,
0.02873213216662407,
0.004866981413215399,
-0.02678508497774601,
-0.0016544994432479143,
-0.009969471953809261,
-0.02433401346206665,
-0.00043679092777892947,
-0.007471041288226843,
0.07149431109428406,
-0.013252722099423409,
-0.014145849272608757,
0.03142629563808441,
-0.0560363344848156,
-0.07023617625236511,
-0.01316784042865038,
0.016122600063681602,
0.0458499900996685,
-0.010443922132253647,
0.04279368370771408,
-0.010111338458955288,
-0.048814404755830765,
-0.015041756443679333,
-0.0460675023496151,
-0.03994696959853172,
-0.006187233608216047,
-0.020152153447270393,
0.04240768402814865,
0.0012040561996400356,
-0.0280352421104908,
0.11020305752754211,
0.02703157067298889,
-0.032678235322237015,
0.01942499354481697,
-0.024250933900475502,
0.01529571320861578,
-0.019842905923724174,
-0.01491540390998125,
0.0023569611366838217,
0.0017786946846172214,
0.0021535365376621485,
0.0014355122111737728,
0.03297756612300873,
0.025511864572763443,
-0.0031715785153210163,
-0.015287847258150578,
-0.007934896275401115,
0.0008870036108419299,
0.010438619181513786,
0.026592327281832695,
0.009634803049266338,
0.005016386043280363,
0.003243840066716075,
-0.0014318424509838223,
0.05327199399471283,
-0.02031426876783371,
-0.07021430879831314,
0.08778683841228485,
-0.026839951053261757,
-0.012033961713314056,
-0.04378858208656311,
0.033187560737133026,
0.019385581836104393,
-0.0012314867926761508,
0.02363104559481144,
0.009684843011200428,
0.06450505554676056,
0.002009583869948983,
0.004996138159185648,
0.021454956382513046,
0.06129034236073494,
-0.01778298430144787,
-0.027936801314353943,
0.0035207364708185196,
0.002434964058920741,
0.04538210481405258,
0.021297527477145195,
0.006882811430841684,
0.010034979321062565,
0.02209669165313244,
0.031161673367023468,
0.011430762708187103,
-0.061939969658851624,
-0.03528360649943352,
-0.05143631249666214,
-0.019982101395726204,
0.005656118504703045,
0.016583340242505074,
0.011585366912186146,
0.06275714188814163,
0.018313517794013023,
0.04140172898769379,
0.04342273995280266,
0.022013437002897263,
-0.08623695373535156,
0.02363112010061741,
-0.031157365068793297,
0.012031271122395992,
0.024574413895606995,
0.030083155259490013,
0.004142262041568756,
-0.025695685297250748,
-0.02824677899479866,
-0.00018813896167557687,
0.02305814065039158,
-0.055502813309431076,
-0.032430846244096756,
-0.036084484308958054,
-0.022462505847215652,
-0.019069047644734383,
0.0225294828414917,
0.02211037650704384,
-0.051501672714948654,
0.014467857778072357,
0.057985905557870865,
-0.02628934197127819,
-0.018282786011695862,
-0.0290854349732399,
-0.02107974700629711,
0.01008999440819025,
-0.013521376065909863,
0.04515867307782173,
0.03945043310523033,
0.0170281995087862,
-0.0053504835814237595,
0.014145029708743095,
0.0364910252392292,
-0.003159601241350174,
0.002890831558033824,
0.006377063225954771,
-0.04546967148780823,
-0.02424704283475876,
-0.006688285619020462,
0.056055016815662384,
-0.017259672284126282,
0.009552616626024246,
-0.0022080764174461365,
0.0017317632446065545,
0.0006175268208608031,
0.09701365977525711,
0.05639591068029404,
0.03748147562146187,
0.01720365136861801,
-0.0518878735601902,
-0.003921769559383392,
-0.05513345077633858,
-0.023239608854055405,
0.022610602900385857,
-0.034333933144807816,
-0.037800926715135574,
-0.013148853555321693,
0.01740754023194313,
0.04913496598601341,
0.03223684802651405,
0.008798675611615181,
0.010241479612886906,
0.028915274888277054,
0.0033213915303349495,
-0.022554878145456314,
0.042368266731500626,
-0.0014138069236651063,
0.05676167830824852,
0.014623149298131466,
0.027429165318608284,
-0.09135115146636963,
-0.0421781949698925,
0.03430183604359627,
0.005982319358736277,
-0.010007434524595737,
-0.004541890695691109,
-0.04456595703959465,
-0.051597073674201965,
0.014806381426751614,
-0.023407353088259697,
0.04789842292666435,
0.004841491114348173,
0.04030230641365051,
-0.007072008680552244,
-0.05187474191188812,
-0.019237609580159187,
-0.010847244411706924,
-0.03812958300113678,
0.025372039526700974,
-0.00008291073027066886,
0.015119116753339767,
0.009696447290480137,
0.020575951784849167,
-0.0046874540857970715,
0.03642529994249344,
0.01918712630867958,
-0.0010871822014451027,
-0.014940557070076466,
-0.014735174365341663,
-0.02177746221423149,
-0.07276738435029984,
-0.022874142974615097,
-0.004217837005853653,
-0.030075259506702423,
0.03915360942482948,
-0.03405998274683952,
-0.07501191645860672,
0.01914924755692482,
0.02381526492536068,
0.00005800621147500351,
0.007727982010692358,
-0.03725283592939377,
0.011796879582107067,
0.05874967202544212,
-0.0008664772030897439,
0.048101700842380524,
0.006988877896219492,
-0.028788769617676735,
0.010832549072802067,
0.01745048724114895,
0.03012627176940441,
-0.06582710146903992,
-0.007650841027498245,
-0.03561260551214218,
0.03284638747572899,
-0.043572038412094116,
0.031122827902436256,
0.019334902986884117,
0.03618636354804039,
-0.019343459978699684,
-0.03640052676200867,
-0.01040175836533308,
0.024357272312045097,
0.016322193667292595,
0.01847759447991848,
0.0025052381679415703,
0.0003721925022546202,
-0.0382387638092041,
-0.0022948086261749268,
-0.022868257015943527,
0.023322204127907753,
-0.041485924273729324,
-0.011828749440610409,
-0.008880557492375374,
-0.004390230402350426,
-0.014832841232419014,
-0.00857518520206213,
0.0033827587030828,
-0.01943708397448063,
0.035616256296634674,
0.0052678934298455715,
0.014096670784056187,
0.05008883774280548,
-0.04063007980585098,
-0.04469285160303116,
0.004890181589871645,
-0.00900778267532587,
-0.01068138051778078,
-0.01650320738554001,
0.019060416147112846,
0.0347742885351181,
0.04382394254207611,
-0.0559103786945343,
-0.04888160154223442,
0.014152590185403824,
-0.004212889354676008,
-0.023723259568214417,
0.007490592077374458,
-0.0199714507907629,
-0.013725364580750465,
-0.01802835986018181,
0.005472258199006319,
-0.010972290299832821,
-0.02782999910414219,
0.041505128145217896,
0.039725493639707565,
0.03448598459362984,
0.06343229115009308,
0.007539079058915377,
-0.008687102235853672,
0.025642836466431618,
0.013018330559134483,
-0.04840004816651344,
-0.03889030963182449,
0.061080947518348694,
0.0013672452187165618,
-0.00014205077604856342,
0.003442497691139579,
-0.04063357412815094,
0.04018976911902428,
-0.020639844238758087,
-0.012988784350454807,
0.03414037078619003,
0.005626987665891647,
-0.0027102569583803415,
-0.01087233331054449,
0.03404824808239937,
-0.009875327348709106,
0.048458755016326904,
-0.015312215313315392,
-0.019574925303459167,
-0.02491435781121254,
-0.0325683131814003,
0.009150764904916286,
-0.005510347429662943,
-0.007058544084429741,
-0.0032551013864576817,
0.06874580681324005,
-0.041045110672712326,
0.008678539656102657,
0.037842921912670135,
0.002260226756334305,
0.03790169581770897,
0.0008777033071964979,
0.026490455493330956,
0.004037482663989067,
0.004872920922935009,
-0.03129301965236664,
-0.04214714840054512,
-0.05472548305988312,
0.005292837042361498,
0.0601109080016613,
-0.03790507838129997,
0.031380053609609604,
0.012075632810592651,
0.009316111914813519,
0.03103160485625267,
-0.029050372540950775,
0.02308972179889679,
0.02604593336582184,
-0.004733182489871979,
0.012884830124676228,
-0.023497892543673515,
0.019074425101280212,
0.012244567275047302,
0.029109857976436615,
-0.028361329808831215,
-0.006493633147329092,
0.00819064024835825,
0.024582916870713234,
0.012968272902071476,
-0.02099066600203514,
-0.04725725203752518,
0.003149570431560278,
-0.008224993012845516,
0.07366600632667542,
-0.00604755524545908,
-0.05020836740732193,
0.06051298603415489,
0.0296128261834383,
0.014911575242877007,
-0.0777011439204216,
-0.006418372038751841,
-0.04500564932823181,
0.007058634422719479,
-0.008185897022485733,
-0.001399561995640397,
-0.016791757196187973,
0.03741201013326645,
0.00862422026693821,
-0.00817959289997816,
0.03795134276151657,
-0.015775220468640327,
-0.057814821600914,
-0.03274892643094063,
-0.033980660140514374,
-0.054177384823560715,
0.013942554593086243,
-0.00719832070171833,
-0.00504386518150568,
0.02609880082309246,
-0.05111530423164368,
0.00891061034053564,
0.015961986035108566,
0.01459607481956482,
-0.016283005475997925,
0.07635502517223358,
-0.015800047665834427,
0.007955601438879967,
-0.025206364691257477,
0.018337368965148926,
0.1132391095161438,
0.044477954506874084,
0.02510344423353672,
-0.04130049794912338,
0.0005861087120138109,
-0.004054384306073189,
-0.014863824471831322,
-0.03556562215089798,
-0.007873864844441414,
0.005919978022575378,
0.005486232694238424,
-0.001232312759384513,
0.05902092158794403,
-0.05348750576376915,
-0.06298184394836426,
0.06428644061088562,
-0.01704942248761654,
-0.016897350549697876,
0.019089365378022194,
0.01612797938287258,
-0.05577099695801735,
0.024478673934936523,
-0.009646358899772167,
0.01982123963534832,
-0.010051853954792023,
0.0112073989585042,
-0.016587717458605766,
-0.061367496848106384,
-0.0005253844428807497,
0.012114894576370716,
-0.01163291372358799,
0.013383094221353531,
-0.020840125158429146,
-0.04144266992807388,
0.0006133080460131168,
0.024152154102921486,
0.04228690639138222,
-0.0044989269226789474,
0.01835009455680847,
0.053693342953920364,
0.005303319077938795,
-0.004911730065941811,
0.020775362849235535,
0.003891568398103118,
-0.0325370654463768,
0.008767927065491676,
-0.028920505195856094,
0.07894442230463028,
-0.027466366067528725,
0.0057365745306015015,
0.02760343812406063,
-0.01788034848868847,
0.010560181923210621,
-0.036681920289993286,
-0.014445286244153976,
-0.01992599107325077,
0.014631892554461956,
-0.007009692490100861,
-0.006629680283367634,
-0.024332480505108833,
-0.011862271465361118,
0.02451762929558754,
0.006537123583257198,
-0.014930755831301212,
-0.01689314842224121,
0.0050592548213899136,
0.00020829166169278324,
0.026036091148853302,
-0.01080282498151064,
-0.013495359569787979,
-0.02021287940442562,
-0.02043059468269348,
-0.004637924488633871,
-0.020117633044719696,
-0.0004730460641440004,
0.025415126234292984,
0.0063337464816868305,
0.02333216555416584,
0.00485203368589282,
-0.03401608765125275,
-0.03051065467298031,
0.04909827932715416,
0.019397292286157608,
-0.02646603435277939,
-0.03448385000228882,
0.03070846013724804,
-0.002161721233278513,
0.07649342715740204,
0.031101996079087257,
0.0025280683767050505,
-0.024200499057769775,
0.0006465505575761199,
0.009385889396071434,
-0.040658656507730484,
-0.008054496720433235,
0.028801223263144493,
-0.050528526306152344,
-0.01352013647556305,
-0.03937719762325287,
-0.002195011591538787,
0.019140208140015602,
0.05792374163866043,
0.006853988394141197,
0.029533909633755684,
-0.00023007008712738752,
0.017924197018146515,
0.006379809230566025,
-0.02107807621359825,
0.0039116679690778255,
0.007975549437105656,
-0.004431063309311867,
-0.017958158627152443,
-0.0023437654599547386,
0.0034350589849054813,
-0.00894988514482975,
-0.017794299870729446,
0.03875456750392914,
-0.03491963818669319,
0.044384073466062546,
-0.0441070981323719,
0.052239976823329926,
-0.06152734532952309,
-0.011721014976501465,
-0.03134210780262947,
-0.019414998590946198,
0.045727238059043884,
-0.024224385619163513,
-0.04084734246134758,
0.03106464445590973,
-0.015980223193764687,
-0.018637025728821754,
0.009927709586918354,
0.03970586881041527,
0.005787204951047897,
-0.008063264191150665,
0.04324425756931305,
-0.024055887013673782,
0.06903810799121857,
-0.011652816087007523,
-0.012029378674924374,
0.058794934302568436,
0.011536418460309505,
-0.008917318657040596,
0.00962082389742136,
-0.010909059084951878,
0.03199389576911926,
0.015953123569488525,
-0.02812916599214077,
-0.03554655611515045,
0.04343375191092491,
-0.009776958264410496,
0.03808394819498062,
-0.023355672135949135,
-0.055873751640319824,
-0.024209190160036087,
-0.005171956028789282,
-0.024401845410466194,
-0.05018512159585953,
0.010070886462926865,
0.043855857104063034,
0.01741218753159046,
-0.02676151506602764,
-0.05812661349773407,
0.011552651412785053,
0.01119703333824873,
-0.030194565653800964,
0.02486119605600834,
0.025831546634435654,
0.00920093897730112,
0.06071518734097481,
-0.036931268870830536,
0.005908644758164883,
0.007266890723258257,
-0.018314151093363762,
-0.09931478649377823,
-0.02680768072605133,
-0.007882077246904373,
0.009199737571179867,
0.02824401669204235,
-0.009901151992380619,
-0.019918696954846382,
0.033949099481105804,
-0.07681038230657578,
0.01615999825298786,
-0.037609320133924484,
-0.013804076239466667,
0.0045251804403960705,
-0.02319549210369587,
0.020565401762723923,
0.026291104033589363,
0.022107791155576706,
0.06201321259140968,
-0.0058267368003726006,
0.006401266437023878,
0.02097264491021633,
-0.005251515656709671,
-0.01328450907021761,
0.03250137344002724,
-0.0337597094476223,
0.024192465469241142,
0.09292507916688919,
-0.02457042783498764,
-0.037885647267103195,
0.030562017112970352,
-0.02426011674106121,
-0.008957624435424805,
0.02321779914200306,
-0.0034474150743335485,
-0.02207515947520733,
0.0689159408211708,
0.010235108435153961,
-0.007045497186481953,
0.009965593926608562,
0.014735442586243153,
0.03154677525162697,
0.011445444077253342,
-0.01819421909749508,
0.018623173236846924,
-0.0146164046600461,
-0.049864936619997025,
-0.045688435435295105,
0.03701420873403549,
-0.05633917078375816,
0.019066788256168365,
0.0017470305319875479,
-0.004566479939967394,
0.003740121377632022,
-0.019731074571609497,
-0.025447886437177658,
-0.01956368237733841,
0.005560011137276888,
0.05494023486971855,
-0.017255079001188278,
0.02601189911365509,
0.030156249180436134,
0.05110263451933861,
-0.021095460280776024,
0.009792711585760117,
0.019364237785339355,
-0.037899523973464966,
-0.06212170422077179,
0.008429808542132378,
-0.017433878034353256,
-0.02215414121747017,
-0.021586237475275993,
-0.04964995011687279,
-0.04538645222783089,
0.03696177899837494,
0.04388973116874695,
0.011402894742786884,
-0.022712893784046173,
-0.06471344828605652,
-0.022700808942317963,
-0.07414979487657547,
-0.012756851501762867,
-0.0006464411853812635,
-0.04841583967208862,
-0.017166193574666977,
-0.003274807007983327,
-0.002296632621437311,
-0.010726523585617542,
0.05483192205429077,
-0.021036390215158463,
-0.012754812836647034,
0.01766403764486313,
-0.036502107977867126,
0.049961429089307785,
-0.03786173462867737,
0.014078032225370407,
-0.006363262888044119,
-0.012578845024108887,
0.03453059121966362,
0.022447260096669197,
-0.003049529856070876,
0.036453645676374435,
0.02877085842192173,
-0.03626101464033127,
0.0035773636773228645,
-0.018214724957942963,
-0.014007254503667355,
0.0377645343542099,
0.004960248246788979,
-0.012295217253267765,
0.10448986291885376,
-0.010877224616706371,
0.002883083885535598,
0.009625778533518314,
-0.042435172945261,
-0.03986029326915741,
0.028004584833979607,
-0.04469458386301994,
0.013550925068557262,
-0.028918124735355377,
0.008921816945075989,
0.03731568530201912,
-0.026832353323698044,
-0.0034843417815864086,
0.05710042640566826,
-0.03286542743444443,
-0.03540683165192604,
0.02691113017499447,
0.022990994155406952,
0.038742274045944214,
0.03326769918203354,
0.059739548712968826,
0.00387996481731534,
0.00997774675488472,
0.05010460689663887,
0.03292855992913246,
0.04211314022541046,
-0.03497523441910744,
-0.039170607924461365,
0.02061125449836254,
0.00038766112993471324,
0.012847897596657276,
0.0065922061912715435,
0.03130688518285751,
-0.07089339196681976,
-0.043756164610385895,
0.03893695026636124,
0.022221801802515984,
-0.007840439677238464,
0.001313037471845746,
-0.017158886417746544,
0.03661724179983139,
-0.033141568303108215,
-0.017606262117624283,
-0.02189168520271778,
0.03514694795012474,
0.003247603541240096,
-0.007356217596679926,
-0.015981100499629974,
-0.00020262850739527494,
0.02989484928548336,
0.005155513994395733,
-0.02505877986550331,
0.013850084505975246,
0.0038660268764942884,
0.020738517865538597,
0.023529136553406715,
0.02048061601817608,
-0.02174139767885208,
0.019469669088721275,
0.007322333753108978,
-0.0451362319290638,
-0.033535245805978775,
0.06624706834554672,
0.055862944573163986,
0.021262889727950096,
-0.008335724472999573,
0.0002964026643894613,
-0.003517370205372572,
0.0416506864130497,
-0.031147466972470284,
-0.019129280000925064,
0.00008398904174100608,
0.008839717134833336,
0.05143320932984352,
-0.012068565934896469
] |
<p>I was wondering what voltage or current, if any, would be produced if the basic magnet through a copper coil experiment had the poles rotated 90 degrees so north and south faced the top/bottom of the coil rather than the entry/exit points?</p>
<p>The attached image has a basic illustration of this.</p>
<p>Thanks</p>
<p><img src="http://i.stack.imgur.com/YUv75.jpg" alt="enter image description here"></p> | 2,871 | [
-0.05026400461792946,
-0.015989389270544052,
-0.017955997958779335,
-0.0033638454042375088,
0.030719202011823654,
0.030773606151342392,
-0.04469316452741623,
0.0024525406770408154,
0.02372477762401104,
-0.042325906455516815,
0.03904756158590317,
0.05950219929218292,
0.06394919753074646,
0.03057592734694481,
0.01050182618200779,
-0.0016474449075758457,
-0.0022247096057981253,
0.016487544402480125,
0.0055947196669876575,
-0.014264078810811043,
-0.008888677693903446,
0.007518889382481575,
-0.0031810333020985126,
0.024550143629312515,
-0.022088566794991493,
0.022986866533756256,
0.074070505797863,
0.01583953946828842,
-0.005144194699823856,
0.04238716512918472,
0.002544351387768984,
-0.05885252729058266,
0.01374648604542017,
0.005282431375235319,
0.002056034514680505,
-0.011890005320310593,
-0.012808500789105892,
-0.058021001517772675,
-0.014619462192058563,
0.018825573846697807,
0.007744060829281807,
0.012681791558861732,
0.0047226822935044765,
0.05553162470459938,
-0.004537939094007015,
-0.013424728997051716,
-0.01662275567650795,
0.01980331353843212,
0.03933989629149437,
-0.051658570766448975,
0.04916895925998688,
-0.017123844474554062,
0.013920871540904045,
0.0028781495057046413,
0.03344479948282242,
0.0004577379731927067,
0.07273319363594055,
0.032797180116176605,
0.003094256389886141,
-0.06164875999093056,
-0.012712564319372177,
-0.03268153592944145,
-0.015565257519483566,
-0.0497889444231987,
-0.06034829467535019,
0.01771392859518528,
-0.008932911790907383,
0.0025498769246041775,
0.036763809621334076,
0.010174298658967018,
0.012993850745260715,
0.01781882904469967,
0.01662839762866497,
-0.011610462330281734,
-0.002115747658535838,
-0.032481275498867035,
0.014183100312948227,
0.027531065046787262,
0.003569647204130888,
0.011299129575490952,
-0.06177140399813652,
0.005401309113949537,
0.021004166454076767,
0.05379939079284668,
0.010067268274724483,
0.006289269309490919,
0.04210684821009636,
-0.012098561972379684,
0.02417854033410549,
0.04113540053367615,
0.030094798654317856,
0.018788950517773628,
0.018711358308792114,
-0.008366450667381287,
-0.03598159924149513,
0.0023850740399211645,
0.008629719726741314,
0.05477391555905342,
-0.0022151335142552853,
-0.02105681039392948,
-0.0022007892839610577,
0.020786672830581665,
-0.008224490098655224,
0.07563339918851852,
0.03157050535082817,
-0.025056777521967888,
0.020021287724375725,
0.024526484310626984,
-0.00398951256647706,
-0.007340146694332361,
-0.042391661554574966,
0.03230768069624901,
0.018015112727880478,
-0.0013028280809521675,
-0.0003163152141496539,
-0.0569685623049736,
-0.027405062690377235,
-0.04469139873981476,
0.028580807149410248,
-0.001193248201161623,
0.05909406393766403,
-0.012593159452080727,
0.0333457812666893,
-0.018522683531045914,
-0.0448932871222496,
-0.02303943783044815,
0.011514732614159584,
0.0042012338526546955,
0.004527904558926821,
0.05048643425107002,
-0.005326459184288979,
-0.03472503647208214,
0.002051320858299732,
-0.004482241813093424,
0.04284725338220596,
0.007631103042513132,
-0.08095008134841919,
-0.07308772206306458,
0.002787813078612089,
-0.01640288718044758,
0.02578294277191162,
-0.08681360632181168,
-0.013091346248984337,
0.046006254851818085,
0.058112602680921555,
-0.02528475597500801,
-0.02297343499958515,
-0.012425191700458527,
0.03663930669426918,
0.027347296476364136,
0.02351417765021324,
0.0007893505971878767,
-0.010689892806112766,
-0.054886773228645325,
-0.034020401537418365,
-0.02593705616891384,
0.023220254108309746,
0.025637226179242134,
-0.0002487684250809252,
-0.02571137249469757,
0.032889578491449356,
-0.042514868080616,
0.053103648126125336,
0.006159291137009859,
-0.031442202627658844,
-0.006345943547785282,
0.08057928830385208,
-0.01803034543991089,
-0.017302662134170532,
0.01341016311198473,
-0.026036420837044716,
0.03810862451791763,
-0.00018595722212921828,
0.005800121463835239,
0.060763053596019745,
-0.060076937079429626,
-0.013082453049719334,
-0.011444374918937683,
0.06929254531860352,
-0.01131376251578331,
-0.033543821424245834,
-0.0394858792424202,
0.002009846270084381,
0.0017884090775623918,
-0.006525047123432159,
0.09074285626411438,
-0.03090883232653141,
-0.039674144238233566,
0.014542683959007263,
-0.02386273257434368,
-0.018772989511489868,
-0.010240770876407623,
0.04973772168159485,
-0.03082241490483284,
-0.02270631678402424,
0.0000847009796416387,
0.030278673395514488,
0.04350003972649574,
-0.011309899389743805,
-0.02688661590218544,
0.014842918142676353,
0.014953128062188625,
-0.004488701932132244,
0.010578466579318047,
0.00042512689833529294,
0.04720562696456909,
0.05857725068926811,
-0.026378104463219643,
0.019462741911411285,
-0.026448892429471016,
-0.00859599094837904,
-0.04031594470143318,
-0.02622024342417717,
-0.013934269547462463,
0.06521036475896835,
-0.010723316110670567,
-0.00417184317484498,
0.031036987900733948,
0.0065294187515974045,
0.025875866413116455,
0.010530246421694756,
0.09152673929929733,
0.047202568501234055,
0.0016847532242536545,
0.05096922442317009,
0.04226890951395035,
0.037225231528282166,
0.015868334099650383,
-0.004852364305406809,
-0.00450116815045476,
-0.04668605327606201,
0.03500436246395111,
0.0718049705028534,
-0.015808112919330597,
-0.06085929647088051,
0.03799683600664139,
-0.006963922176510096,
0.02493646927177906,
0.010926355607807636,
0.04760805889964104,
-0.005001679994165897,
-0.03798985853791237,
-0.02151821181178093,
0.023722847923636436,
-0.009070550091564655,
-0.0026214970275759697,
0.05632716789841652,
0.04167050123214722,
0.00942628737539053,
0.04274755343794823,
-0.04553665220737457,
0.03920038789510727,
-0.015333336777985096,
0.02740209549665451,
-0.0014385584509000182,
-0.017972450703382492,
0.04354231804609299,
-0.016672490164637566,
0.011876988224685192,
0.014002367854118347,
-0.01455364003777504,
0.026897571980953217,
-0.005997328087687492,
0.048177383840084076,
0.002022658009082079,
0.010173697024583817,
0.004561943933367729,
-0.02921963669359684,
0.02086745575070381,
-0.03493031859397888,
0.005647437181323767,
-0.012538060545921326,
0.03014427050948143,
-0.006250742822885513,
0.006049072835594416,
0.022020768374204636,
0.017063764855265617,
0.020220637321472168,
-0.02657333016395569,
-0.06254222244024277,
-0.012028791010379791,
-0.006498965434730053,
0.011036811396479607,
0.06145009025931358,
-0.05245591700077057,
0.025902196764945984,
-0.04037883132696152,
-0.004062747582793236,
0.029053790494799614,
0.025699103251099586,
0.003445285838097334,
0.031172653660178185,
-0.004925667308270931,
-0.048328474164009094,
-0.026322316378355026,
-0.0031011069659143686,
0.028710221871733665,
-0.04432104900479317,
-0.012438368983566761,
0.056596338748931885,
-0.0047018155455589294,
-0.010791908949613571,
0.04325398430228233,
-0.039582110941410065,
-0.03718388080596924,
0.018639832735061646,
0.026679836213588715,
0.05462108552455902,
-0.029333505779504776,
0.04578090086579323,
0.021114874631166458,
-0.04368416219949722,
-0.0191473588347435,
-0.0404391810297966,
-0.04882445186376572,
-0.007309791166335344,
-0.0105820307508111,
0.012497763149440289,
-0.004423264879733324,
-0.024773338809609413,
0.05827464163303375,
0.005342430900782347,
-0.062197793275117874,
-0.04715489223599434,
-0.033164553344249725,
-0.024054210633039474,
-0.029258262366056442,
0.013229100033640862,
0.038660384714603424,
-0.03886324539780617,
0.0010490324348211288,
-0.009108180180191994,
0.0009324142592959106,
0.0071341497823596,
0.060262154787778854,
0.006348356604576111,
0.0242925938218832,
0.0007952957530505955,
-0.007663289550691843,
0.039070840924978256,
-0.013869266957044601,
-0.030211009085178375,
-0.01531209610402584,
0.01413814164698124,
0.029648996889591217,
0.04932929202914238,
-0.02734377607703209,
0.08250569552183151,
-0.027051936835050583,
0.027026807889342308,
-0.032704710960388184,
0.011368519626557827,
0.0007873259019106627,
0.0274923425167799,
-0.052381932735443115,
0.024800462648272514,
0.05990183353424072,
-0.023940930142998695,
-0.02905907668173313,
0.020372984930872917,
0.027305375784635544,
0.000015954590708133765,
-0.04513749107718468,
-0.02413584105670452,
-0.010361417196691036,
0.039414238184690475,
-0.005700451321899891,
0.0029264348559081554,
0.008258025161921978,
0.039432622492313385,
0.020303824916481972,
0.037813302129507065,
-0.0335700623691082,
-0.0022591950837522745,
-0.04751075059175491,
0.0020843236707150936,
-0.04637341946363449,
0.012147663161158562,
0.009060215204954147,
0.04044371098279953,
0.02875494956970215,
-0.011010813526809216,
0.0021408717148005962,
0.004489387385547161,
-0.0831112340092659,
0.040459807962179184,
-0.027549119666218758,
-0.00845717266201973,
0.010645674541592598,
-0.005631711799651384,
-0.015446772798895836,
-0.022323286160826683,
0.012770521454513073,
0.006944280583411455,
-0.01751302182674408,
-0.044597115367650986,
0.013339835219085217,
0.022102465853095055,
-0.007747747469693422,
-0.009192888624966145,
0.058907024562358856,
0.015055688098073006,
-0.04627878963947296,
0.017834724858403206,
-0.009867618791759014,
-0.039060600101947784,
0.0031492055859416723,
-0.023711983114480972,
0.00781378522515297,
-0.017625240609049797,
0.057396773248910904,
0.028051920235157013,
-0.013571403920650482,
-0.05554039403796196,
0.0011094344081357121,
0.016080468893051147,
0.04802612587809563,
0.008653922937810421,
-0.02241097204387188,
-0.039967264980077744,
-0.06349437683820724,
-0.04377834498882294,
0.014592200517654419,
0.037315502762794495,
0.004729097243398428,
0.01179587747901678,
0.022838585078716278,
-0.011866712011396885,
0.010148565284907818,
0.019505415111780167,
0.060019172728061676,
0.01664130762219429,
-0.014500821940600872,
-0.03579193726181984,
-0.04407966136932373,
-0.029635099694132805,
-0.04333612695336342,
0.0006987052620388567,
-0.009057841263711452,
-0.011787188239395618,
-0.03201780840754509,
0.023939816281199455,
0.013340780511498451,
-0.007375457789748907,
0.01853041723370552,
0.011319179087877274,
0.06640153378248215,
-0.013752416707575321,
0.006829177029430866,
0.022864961996674538,
-0.01189300138503313,
0.06258123368024826,
-0.013162218034267426,
-0.03488542139530182,
-0.09514884650707245,
-0.02442002296447754,
0.02263685315847397,
0.026261117309331894,
0.0016265504527837038,
-0.017747698351740837,
-0.03722524270415306,
0.016856051981449127,
0.0334329716861248,
-0.03438271954655647,
0.049680788069963455,
0.001198979327455163,
0.006386663299053907,
-0.017516737803816795,
-0.03263816982507706,
-0.0538330115377903,
0.00967118889093399,
-0.014442116022109985,
0.01903175190091133,
-0.024984870105981827,
-0.02672412432730198,
0.029045598581433296,
0.005285970401018858,
0.05744507536292076,
0.029057247564196587,
0.014728597365319729,
0.03729639947414398,
0.005832056049257517,
0.039842452853918076,
-0.034235402941703796,
-0.07739030569791794,
0.01993609592318535,
0.006154710426926613,
0.009467336349189281,
0.03976869583129883,
0.006054914556443691,
-0.03850589692592621,
-0.00022190305753611028,
0.00857003964483738,
0.04315793514251709,
0.0054351286962628365,
-0.013179700821638107,
0.03624448552727699,
0.03148053213953972,
0.004002862144261599,
0.04859406128525734,
-0.0059216381050646305,
0.008758642710745335,
0.010781392455101013,
0.006148854736238718,
0.028553955256938934,
0.002471765736117959,
0.011122127063572407,
-0.04157192260026932,
0.044206537306308746,
0.0032297209836542606,
0.05183103308081627,
-0.04995321109890938,
0.016616929322481155,
-0.0567987821996212,
-0.023426668718457222,
-0.009300862438976765,
-0.016824226826429367,
0.015217543579638004,
-0.04763847589492798,
-0.001307969563640654,
-0.004380888771265745,
-0.00455342186614871,
-0.04582935944199562,
0.005739908665418625,
-0.0454678051173687,
0.007758065592497587,
-0.017045915126800537,
-0.04789773002266884,
-0.014928811229765415,
-0.013731587678194046,
0.005929761100560427,
0.011048202402889729,
-0.039641499519348145,
0.0439908392727375,
-0.038037221878767014,
-0.03177403658628464,
0.01869083195924759,
-0.0551934652030468,
-0.00685484055429697,
0.07038934528827667,
-0.027277149260044098,
0.01643967628479004,
-0.03343107923865318,
0.0007689831545576453,
0.024861952289938927,
0.014654984697699547,
-0.011917904019355774,
-0.0763082206249237,
0.03369907662272453,
0.0018213416915386915,
0.005632586777210236,
0.028372889384627342,
-0.06857907772064209,
-0.011862051673233509,
-0.03278960660099983,
-0.013246237300336361,
0.03419163450598717,
-0.04061843082308769,
0.01874401979148388,
0.010083071887493134,
-0.002205249387770891,
0.09119745343923569,
0.015239601954817772,
-0.024024073034524918,
0.03439569100737572,
-0.03595345839858055,
-0.030626602470874786,
-0.010983425192534924,
0.03228364884853363,
-0.014102652668952942,
-0.049788787961006165,
0.009921944700181484,
-0.013027927838265896,
0.06341911852359772,
-0.013123951852321625,
-0.009713997133076191,
0.02572517842054367,
0.017153682187199593,
-0.006402280647307634,
-0.020537838339805603,
0.008592098020017147,
-0.016114987432956696,
-0.01069644931703806,
-0.023478470742702484,
-0.01673678122460842,
-0.044031836092472076,
-0.02665359154343605,
-0.0025206219870597124,
0.02081870660185814,
-0.02442704327404499,
-0.026935042813420296,
0.07469462603330612,
0.013077059760689735,
-0.05271288380026817,
-0.008869492448866367,
-0.024440880864858627,
0.006268321070820093,
0.02587479166686535,
0.045808855444192886,
0.03275822103023529,
-0.010456342250108719,
-0.038605697453022,
-0.022602537646889687,
-0.03160465508699417,
-0.004305012058466673,
0.09341508895158768,
0.01475529931485653,
0.06993123888969421,
0.0064003425650298595,
0.0036172440741211176,
-0.023873133584856987,
-0.024599576368927956,
0.007597793824970722,
0.025830693542957306,
0.010919414460659027,
0.03319459408521652,
0.009256497956812382,
0.003013703739270568,
0.02339331991970539,
0.03200634941458702,
-0.020364124327898026,
0.03270382806658745,
0.03776386007666588,
0.03276921436190605,
0.03114349953830242,
0.04508001729846001,
-0.0373484306037426,
0.014666860923171043,
-0.05439057573676109,
0.0369013212621212,
-0.031651079654693604,
-0.018658462911844254,
0.038115084171295166,
-0.016603970900177956,
0.010887600481510162,
-0.028820253908634186,
-0.018698252737522125,
-0.03586054593324661,
-0.022358480840921402,
0.008039720356464386,
-0.00017219346773345023,
-0.032599590718746185,
0.046095769852399826,
0.04299419745802879,
0.014901949092745781,
0.016394926235079765,
-0.014798000454902649,
-0.10358767211437225,
-0.034032486379146576,
-0.011023225262761116,
-0.05884532630443573,
0.05432768538594246,
0.01153783593326807,
-0.006621720269322395,
0.015289396978914738,
-0.00719376839697361,
0.02457570657134056,
0.03834826126694679,
0.027744313701987267,
0.00023797560425009578,
0.09050318598747253,
-0.0020884389523416758,
0.01685524918138981,
-0.03986366465687752,
0.02028004080057144,
0.11480410397052765,
0.021185442805290222,
0.01991078443825245,
-0.057272378355264664,
0.029451915994286537,
-0.04362288862466812,
-0.0016643613344058394,
0.018628956750035286,
0.018482543528079987,
-0.002171542029827833,
0.002498036716133356,
0.02602991834282875,
0.023261649534106255,
-0.018813161179423332,
0.0019076159223914146,
0.036077968776226044,
-0.0020890790037810802,
-0.02501203678548336,
-0.013280126266181469,
-0.00638872105628252,
-0.0194711796939373,
-0.00970082450658083,
-0.053018078207969666,
0.017869221046566963,
-0.047326140105724335,
-0.02772304229438305,
0.0048558348789811134,
-0.04320146143436432,
0.052458055317401886,
0.007351543754339218,
-0.019666636362671852,
0.03617270663380623,
-0.0008877255022525787,
-0.00226099556311965,
-0.08484643697738647,
0.018588241189718246,
0.04636017978191376,
0.0106813320890069,
0.012847048230469227,
0.03882082924246788,
0.026490429416298866,
0.007225439418107271,
0.034542880952358246,
0.0395805686712265,
-0.0419376976788044,
0.015839410945773125,
-0.02062063105404377,
0.056517861783504486,
0.004266004543751478,
-0.004961276892572641,
-0.03822866827249527,
0.026890477165579796,
0.03702192381024361,
-0.020134489983320236,
-0.010218159295618534,
-0.0050740912556648254,
0.012010134756565094,
0.021598663181066513,
0.002435171278193593,
-0.04269993677735329,
0.0243903286755085,
-0.025350525975227356,
0.023847617208957672,
-0.01006398256868124,
-0.024361999705433846,
-0.011234026402235031,
0.054189253598451614,
0.07054048776626587,
0.006570068653672934,
-0.03708618879318237,
-0.03894303739070892,
-0.008174438029527664,
-0.01907915249466896,
0.025181803852319717,
0.029910124838352203,
0.006902304477989674,
0.013861597515642643,
-0.01831832341849804,
-0.043394897133111954,
0.01084752008318901,
-0.03007831983268261,
0.00910878088325262,
0.020604591816663742,
-0.010353831574320793,
0.008932876400649548,
0.004703283775597811,
0.03439559042453766,
0.015762541443109512,
-0.05990089476108551,
0.01487954705953598,
0.018975384533405304,
0.03478117659687996,
0.034429971128702164,
-0.012702153995633125,
-0.03577062860131264,
0.029170172289013863,
-0.05972636863589287,
-0.03304339945316315,
-0.021834874525666237,
0.06782810389995575,
0.026003779843449593,
0.016843773424625397,
-0.011738876812160015,
0.02836052142083645,
-0.009875750169157982,
-0.027488628402352333,
0.0004255219246260822,
-0.04852405562996864,
-0.012035122141242027,
-0.01443901564925909,
-0.013950229622423649,
-0.034243106842041016,
-0.04114815592765808,
-0.0017278034938499331,
0.0010430634720250964,
0.037295568734407425,
0.02651817724108696,
-0.03496778383851051,
-0.00928633101284504,
-0.03217204287648201,
0.015018227510154247,
-0.013766615651547909,
-0.02786792628467083,
-0.0306153055280447,
-0.011099116876721382,
0.033465251326560974,
0.006828847341239452,
0.01159096322953701,
0.015105757862329483,
0.006161340977996588,
0.014122487045824528,
0.03472068905830383,
0.029947685077786446,
0.01492445357143879,
-0.0011192013043910265,
0.010539080016314983,
0.019228767603635788,
0.037409570068120956,
-0.02304675430059433,
-0.05199366435408592,
0.0620872862637043,
-0.03434370458126068,
-0.0234444048255682,
0.013809442520141602,
-0.006896886974573135,
0.022039130330085754,
0.021508220583200455,
-0.01810670644044876,
-0.00798267312347889,
0.06703917682170868,
-0.0011697732843458652,
-0.013945420272648335,
0.005692277103662491,
-0.011021433398127556,
0.018431656062602997,
-0.01966334879398346,
-0.015359175391495228,
-0.02413768321275711,
-0.00045680595212616026,
0.016621889546513557,
0.0022196813952177763,
-0.018924133852124214,
-0.015415113419294357,
-0.006834637839347124,
0.01232469268143177,
-0.028650769963860512,
0.010412115603685379,
-0.04064787179231644,
-0.011022593826055527,
0.008699470199644566,
-0.0523916557431221,
0.022245271131396294,
-0.031660690903663635,
0.009231485426425934,
-0.05448705703020096,
-0.008946617133915424,
0.0285500455647707,
-0.021541504189372063,
0.012400470674037933,
-0.051880985498428345,
0.006523745600134134,
0.06809021532535553,
-0.061721332371234894,
0.003716042498126626,
0.020514024421572685,
-0.03894810378551483,
-0.018612220883369446,
-0.03897591307759285,
0.012079932726919651,
0.04055710509419441,
-0.01520582102239132,
0.04559052363038063,
0.015854420140385628,
-0.02032245695590973,
-0.01606679894030094,
-0.048115286976099014,
-0.009810670278966427,
0.017731988802552223,
0.00019862230692524463,
-0.00867528561502695,
0.036419909447431564,
-0.022165535017848015,
-0.05483388528227806,
0.04769979789853096,
-0.023376889526844025,
0.00320197525434196,
0.00919302273541689,
0.02187306061387062,
0.006308871321380138,
0.04257558658719063,
-0.003037629183381796,
0.01674322411417961,
-0.01252342015504837,
0.008536930195987225,
0.02720966562628746,
0.024592051282525063,
-0.019980233162641525,
0.011478631757199764,
0.014394349418580532,
-0.003398468252271414,
-0.018603021278977394,
0.005687662400305271,
-0.06547602266073227,
-0.005613925401121378,
-0.0077375685796141624,
-0.022620942443609238,
0.010338803753256798,
-0.037206996232271194,
0.0031043679919093847,
-0.030748581513762474,
-0.022894952446222305,
0.011112873442471027,
-0.01552618108689785,
0.029348403215408325,
0.00944021251052618,
0.0005166126065887511,
-0.029875891283154488,
0.001319381408393383,
-0.007459551561623812,
-0.025921335443854332,
-0.045859042555093765,
-0.00442919647321105,
-0.0034328706096857786,
0.004140330478549004,
0.025421161204576492,
-0.05437806621193886,
-0.012229934334754944,
0.034466713666915894,
-0.00881274975836277,
0.04306655749678612,
0.03486495465040207,
-0.07294616848230362,
-0.008963885717093945,
-0.06309933215379715,
0.03300561383366585,
-0.03217441216111183,
-0.024036437273025513,
-0.04136641323566437,
-0.015172320418059826,
-0.016050465404987335,
-0.01747475005686283,
0.045196909457445145,
0.03137463703751564,
-0.012965555302798748,
0.03107394464313984,
-0.023041892796754837,
0.06505443155765533,
-0.07538321614265442,
0.03436487540602684,
0.008922399021685123,
-0.007171483710408211,
0.025919411331415176,
-0.026519279927015305,
-0.025310350582003593,
0.024075843393802643,
-0.007092343643307686,
-0.0017545718001201749,
-0.013187560252845287,
-0.031111638993024826,
-0.03435009717941284,
0.019208651036024094,
0.0006453811656683683,
-0.009746653959155083,
0.05836157128214836,
-0.0331311896443367,
0.006712202914059162,
-0.011546258814632893,
-0.01577916368842125,
-0.03263453021645546,
0.03119993954896927,
-0.006642940454185009,
-0.007485315669327974,
-0.024069001898169518,
-0.004168045241385698,
0.029783014208078384,
-0.039135996252298355,
-0.03148568421602249,
0.023490222170948982,
-0.05927876755595207,
-0.003951907157897949,
0.04403163492679596,
0.01402999646961689,
0.0021086710039526224,
-0.03458574041724205,
0.03964480757713318,
0.03624635189771652,
0.005745995324105024,
0.015009909868240356,
0.05240875482559204,
-0.006517223082482815,
0.0070022353902459145,
-0.010749525390565395,
0.03853793814778328,
0.009923436678946018,
0.0297704990953207,
0.02234974317252636,
0.020363233983516693,
-0.011421005241572857,
-0.03356768935918808,
0.007794014643877745,
-0.021904516965150833,
0.03046930767595768,
0.009697968140244484,
-0.01942414976656437,
0.05874190852046013,
-0.03583310544490814,
0.010227316059172153,
-0.0478426031768322,
0.0047196256928145885,
-0.007054649759083986,
0.003766334615647793,
0.019663130864501,
0.015749288722872734,
-0.01955695077776909,
-0.027435043826699257,
0.007932416163384914,
-0.014133172109723091,
0.07016219943761826,
-0.016162414103746414,
0.022351320832967758,
-0.04185108467936516,
-0.01618669554591179,
-0.010271567851305008,
-0.017904948443174362,
-0.04532260075211525,
-0.030324852094054222,
0.029679762199521065,
0.01539398543536663,
0.041640132665634155,
-0.009331878274679184,
-0.012820790521800518,
-0.0024131392128765583,
0.03970067575573921,
-0.05625564232468605,
-0.02981218323111534,
-0.010271153412759304,
0.035722412168979645,
0.016315260902047157,
0.0242485161870718
] |
<p><img src="http://i.stack.imgur.com/crCx4.png" alt="enter image description here"></p>
<p>The spectrum of a filament has been given before, the left one having the lowest temperature, the middle with a medium temperature and the right one with the highest. My question is this: Why does the region of yellow light on the left have a small range of spectrum while the red and green ones both have a large range? </p>
<p>Also, why the temperature increasing results in the shrinking of red and green region and the expansion of yellow region? It seems strange that the continous wavelenth has different pattern.</p> | 2,872 | [
-0.02531130239367485,
-0.053777217864990234,
0.02325204759836197,
-0.0383203960955143,
0.039676252752542496,
0.007429509423673153,
-0.03238372877240181,
-0.037105266004800797,
0.0076738521456718445,
-0.029669499024748802,
0.06954480707645416,
0.027458997443318367,
0.02767615020275116,
0.001467740279622376,
0.038739025592803955,
0.010482733137905598,
0.023136265575885773,
0.013504489324986935,
-0.030750082805752754,
-0.0007015023147687316,
-0.009172337129712105,
0.014327598735690117,
0.006004638969898224,
0.010758728720247746,
-0.06557896733283997,
0.026001615449786186,
0.04491857439279556,
0.04910893738269806,
0.040458064526319504,
0.050537656992673874,
-0.05209789797663689,
-0.007313898764550686,
-0.007151004392653704,
0.010829907841980457,
0.03275793790817261,
-0.02132423408329487,
-0.028958814218640327,
-0.010530068539083004,
0.019694393500685692,
0.014638022519648075,
-0.012419983744621277,
-0.028026212006807327,
-0.023839373141527176,
0.02359492890536785,
-0.009069787338376045,
-0.011932121589779854,
-0.020783040672540665,
-0.00838457327336073,
0.06755447387695312,
-0.0517287477850914,
0.05143105983734131,
-0.021626122295856476,
0.03468387946486473,
0.062403056770563126,
0.00019688368774950504,
0.014734841883182526,
0.05805761367082596,
0.07318595051765442,
-0.048013925552368164,
-0.020192893221974373,
0.024366304278373718,
0.013260099105536938,
-0.014613493345677853,
0.018616288900375366,
-0.00040884639020077884,
0.01441262848675251,
0.008286511525511742,
-0.03437523543834686,
0.012109695933759212,
0.008356457576155663,
0.007961992174386978,
-0.008450510911643505,
0.02295510098338127,
-0.036118462681770325,
0.03748618811368942,
-0.029178932309150696,
-0.0012192598078399897,
0.05133228749036789,
0.02590324357151985,
0.03253137692809105,
0.006191008258610964,
0.0022972626611590385,
-0.022679047659039497,
-0.03392414003610611,
-0.009749077260494232,
-0.012725412845611572,
0.06920956820249557,
-0.030850810930132866,
0.022888032719492912,
0.013992480002343655,
0.0070207733660936356,
0.04058271273970604,
0.03130652382969856,
0.023906711488962173,
-0.015205329284071922,
0.009064219892024994,
0.020753217861056328,
0.023723116144537926,
-0.010396802797913551,
-0.024538492783904076,
0.012912007980048656,
-0.004824631381779909,
0.038395851850509644,
0.05464812368154526,
-0.0073951613157987595,
-0.012636985629796982,
-0.04415171220898628,
-0.02706395462155342,
0.012340964749455452,
-0.0021250967402011156,
-0.02884479984641075,
0.004259208217263222,
-0.001571296015754342,
-0.007585721090435982,
-0.01684175431728363,
-0.0246236901730299,
0.04839296266436577,
0.007687035016715527,
0.09339579194784164,
0.054060596972703934,
-0.021279994398355484,
-0.011995888315141201,
0.025381164625287056,
0.006742968689650297,
-0.048948194831609726,
0.026074839755892754,
0.007306423503905535,
-0.012462032027542591,
-0.011928321793675423,
0.04801049456000328,
-0.018967894837260246,
0.0037410741206258535,
-0.0007094808970578015,
-0.021062448620796204,
-0.004426622297614813,
-0.004561364185065031,
-0.10041313618421555,
-0.014511392451822758,
0.04245325177907944,
-0.0178437028080225,
-0.008774771355092525,
-0.03328193351626396,
-0.0009828261099755764,
0.04529822990298271,
0.09104932844638824,
-0.016216902062296867,
0.012130864895880222,
-0.027048148214817047,
0.05943557620048523,
-0.016601981595158577,
-0.0005936968955211341,
0.013340361416339874,
0.005836774129420519,
-0.01801486127078533,
-0.017712028697133064,
-0.05518776923418045,
-0.008609483018517494,
0.04213780164718628,
0.0036081529688090086,
0.008417293429374695,
0.0514020137488842,
0.0030252241995185614,
0.012714986689388752,
-0.005026592873036861,
0.02344433218240738,
-0.007981794886291027,
0.08624830842018127,
-0.017769116908311844,
-0.018212001770734787,
0.06642013788223267,
-0.019033290445804596,
0.02028479613363743,
-0.008957929909229279,
-0.005638090893626213,
0.038337040692567825,
0.002425946993753314,
0.00045389015576802194,
0.01048514898866415,
0.013473927043378353,
0.011817052029073238,
-0.055080268532037735,
-0.03184802085161209,
-0.009209702722728252,
0.03227916359901428,
0.03444729745388031,
0.07179254293441772,
0.008062283508479595,
-0.045788586139678955,
0.047004785388708115,
-0.061458490788936615,
0.007092256564646959,
-0.019572429358959198,
0.007361824624240398,
-0.008927445858716965,
-0.030483322218060493,
0.011102652177214622,
0.0284226443618536,
0.02570311352610588,
0.02071773074567318,
-0.01653907634317875,
0.006938905455172062,
0.027267422527074814,
0.010109558701515198,
0.0159525815397501,
0.038789257407188416,
0.0721360519528389,
-0.009495291858911514,
-0.009348605759441853,
0.01891344040632248,
-0.07193785160779953,
-0.01721758395433426,
0.01724974811077118,
-0.020718710497021675,
0.026072639971971512,
-0.007849798537790775,
0.010970167815685272,
0.01506015844643116,
0.03727864846587181,
-0.011295060627162457,
0.019180357456207275,
-0.0182363111525774,
0.045404139906167984,
0.04954008385539055,
-0.024060677736997604,
-0.018560802564024925,
0.029390953481197357,
0.001293390174396336,
0.03347058594226837,
-0.0013987628044560552,
-0.05552496016025543,
-0.07240448892116547,
0.002290870063006878,
0.007175829261541367,
0.05579930543899536,
-0.03160438314080238,
0.011214615777134895,
0.04181157425045967,
0.023940686136484146,
0.038432445377111435,
0.013372083194553852,
-0.011117622256278992,
-0.01669742353260517,
0.01582445576786995,
0.03291703015565872,
0.00546242156997323,
-0.010041208937764168,
0.00044305925257503986,
0.017808277159929276,
0.027401525527238846,
-0.04248931631445885,
-0.027025775983929634,
0.05574566498398781,
-0.0030733125749975443,
0.01037752814590931,
-0.013557067140936852,
0.03166275471448898,
0.027778547257184982,
-0.04358843341469765,
0.03190538287162781,
0.03607878088951111,
-0.014266383834183216,
0.021039627492427826,
-0.024337535724043846,
-0.03916070610284805,
0.005319464020431042,
0.03443737328052521,
-0.017567111179232597,
-0.028736785054206848,
0.017932983115315437,
-0.05297491326928139,
0.003997983876615763,
-0.034626372158527374,
-0.002952139126136899,
-0.06045427918434143,
-0.009699306450784206,
0.04325931891798973,
0.027679158374667168,
0.03961852192878723,
-0.07444239407777786,
-0.02033822052180767,
-0.010919882915914059,
-0.007281423080712557,
0.008919701911509037,
0.014434470795094967,
-0.008759946562349796,
-0.0013323232997208834,
0.012114973738789558,
-0.03291492536664009,
0.008326147682964802,
0.006952385418117046,
-0.010992180556058884,
-0.012793515808880329,
-0.033920180052518845,
-0.07662083953619003,
-0.03159893676638603,
0.006044330075383186,
0.033407360315322876,
-0.005013525951653719,
-0.03160141780972481,
0.07815885543823242,
-0.033339403569698334,
-0.03626193106174469,
0.02581971324980259,
-0.06588249653577805,
-0.015039327554404736,
-0.029856408014893532,
-0.004353586584329605,
0.016244791448116302,
-0.0020752300042659044,
0.03707970306277275,
0.021807653829455376,
0.009750775061547756,
0.0000827885523904115,
-0.0323917493224144,
-0.017745288088917732,
-0.018875306472182274,
-0.025262244045734406,
0.016548817977309227,
-0.038295283913612366,
0.018364286050200462,
0.04768557474017143,
0.05254040285944939,
0.011204487644135952,
-0.05315803736448288,
0.004747638013213873,
-0.07648415118455887,
-0.054539818316698074,
0.05019499734044075,
0.0556831993162632,
-0.03492950648069382,
0.02690030448138714,
0.049498412758111954,
0.04912036284804344,
0.07612919062376022,
0.013586296699941158,
-0.026671551167964935,
0.015850450843572617,
0.007248712237924337,
-0.03328680619597435,
0.05292583256959915,
0.011812900193035603,
0.02689843624830246,
-0.0007598451338708401,
0.006919522769749165,
0.03890525549650192,
0.032691411674022675,
-0.06362149864435196,
0.030885692685842514,
0.0107744624838233,
0.010567144490778446,
-0.03157174214720726,
0.05140824243426323,
0.01740078814327717,
-0.0047201900742948055,
-0.039610110223293304,
0.014051451347768307,
0.044070661067962646,
-0.03299986571073532,
-0.021582024171948433,
0.03575639799237251,
0.006501353811472654,
-0.016194691881537437,
-0.0073310136795043945,
-0.0027089864015579224,
-0.0464983768761158,
0.035722073167562485,
-0.015874654054641724,
-0.057066623121500015,
0.04646239057183266,
0.028922561556100845,
0.020913563668727875,
-0.00017290006508119404,
-0.04110054671764374,
0.0003449998330324888,
-0.04999899864196777,
-0.030568264424800873,
-0.013171618804335594,
0.08143826574087143,
0.0004032185534015298,
0.06118900328874588,
0.04155786335468292,
0.06569939851760864,
0.04657275974750519,
0.014097737148404121,
-0.13080129027366638,
0.034770723432302475,
-0.024461591616272926,
0.013747869990766048,
-0.053699199110269547,
-0.0015812625642865896,
-0.011632775887846947,
-0.011960185132920742,
-0.016345316544175148,
0.0045023104175925255,
0.013666639104485512,
-0.05634439364075661,
0.012112963013350964,
-0.017530694603919983,
-0.021303780376911163,
-0.04395260661840439,
0.04514558985829353,
0.045426130294799805,
-0.003177381819114089,
0.031862374395132065,
0.014647619798779488,
-0.026843568310141563,
0.018743624910712242,
-0.03047606721520424,
0.021270323544740677,
0.022281143814325333,
0.023651178926229477,
0.00612990278750658,
0.026692626997828484,
-0.014009120874106884,
-0.01607319340109825,
0.01636919006705284,
0.026332134380936623,
-0.01894720084965229,
-0.041535262018442154,
0.0015241436194628477,
-0.025149254128336906,
-0.016484936699271202,
-0.013617237098515034,
0.04830104857683182,
0.0037136494647711515,
-0.001163231790997088,
0.024554559960961342,
-0.03408975899219513,
-0.025091292336583138,
0.020113997161388397,
0.0032814813312143087,
-0.02059829793870449,
-0.007345602381974459,
-0.027460087090730667,
0.0022005399223417044,
-0.04352058470249176,
0.02833537757396698,
0.0050452882423996925,
-0.014328069053590298,
-0.008034291677176952,
-0.017323678359389305,
0.05196677893400192,
-0.0006729423184879124,
-0.0013147750869393349,
-0.025883058086037636,
-0.0074029345996677876,
0.013424690812826157,
-0.038538847118616104,
-0.01973053812980652,
0.00682354811578989,
0.020602798089385033,
0.02636033482849598,
-0.023933371528983116,
0.0012261979281902313,
-0.05447779968380928,
-0.044145990163087845,
0.0022344114258885384,
-0.009230590425431728,
-0.005445210263133049,
-0.02840179018676281,
-0.08307337015867233,
-0.0219374168664217,
0.03090444765985012,
-0.036456238478422165,
0.07285749912261963,
0.008355787955224514,
0.0015816079685464501,
-0.026072923094034195,
-0.013045201078057289,
-0.01364735048264265,
0.026204215362668037,
0.004416571464389563,
0.020579740405082703,
-0.02543507143855095,
-0.001048073172569275,
0.000027000305635738187,
0.0011972524225711823,
0.028674019500613213,
0.03771904855966568,
-0.01471030805259943,
-0.0059873429127037525,
0.0203318502753973,
0.001313636195845902,
-0.006618219427764416,
-0.08451113104820251,
-0.028011169284582138,
0.021085189655423164,
0.0015005780151113868,
0.03212227299809456,
-0.04665360972285271,
-0.019175902009010315,
0.020307494327425957,
0.018768684938549995,
-0.019667383283376694,
-0.0003636640321929008,
-0.015746058896183968,
0.027273477986454964,
0.028461139649152756,
-0.011254891753196716,
0.03469148278236389,
0.013531966134905815,
0.018764672800898552,
-0.014151438139379025,
-0.006253957748413086,
0.0536343939602375,
-0.034738536924123764,
-0.017436018213629723,
-0.012446769513189793,
-0.007740034721791744,
-0.03134327754378319,
0.06880617141723633,
-0.008145245723426342,
0.009260767139494419,
-0.026245655491948128,
-0.014493233524262905,
0.029445409774780273,
0.02245718613266945,
-0.0045431931503117085,
0.01568804867565632,
0.0008107151952572167,
0.03876039758324623,
-0.005961060989648104,
-0.01236195769160986,
0.03518854081630707,
-0.026676777750253677,
-0.021686334162950516,
0.04314722493290901,
-0.004483877215534449,
0.0569889135658741,
-0.04145488515496254,
-0.004656471777707338,
-0.03160668909549713,
-0.03949734568595886,
0.042125094681978226,
0.023979976773262024,
0.03424989804625511,
0.039497215300798416,
-0.05864667892456055,
-0.0004281605069991201,
-0.02829734794795513,
-0.024807536974549294,
0.006775396876037121,
-0.012054627761244774,
0.05336577817797661,
0.019019704312086105,
-0.016518646851181984,
-0.07000955939292908,
-0.04103396460413933,
-0.019360806792974472,
0.023227231577038765,
-0.038206811994314194,
-0.021729759871959686,
-0.009985506534576416,
-0.01441540103405714,
-0.013390825130045414,
-0.0068555595353245735,
-0.003793006530031562,
0.0014802842633798718,
-0.010577975772321224,
0.02868940494954586,
-0.006788119673728943,
0.03722100332379341,
0.0000953952330746688,
-0.020342126488685608,
0.02329440787434578,
-0.020691312849521637,
-0.035000815987586975,
-0.00029535804060287774,
0.038639891892671585,
-0.014146259054541588,
-0.06548110395669937,
-0.00235168868675828,
0.025660496205091476,
0.0226199459284544,
0.004794329404830933,
-0.013370496220886707,
0.020018188282847404,
0.07174165546894073,
-0.009650283493101597,
-0.02505013532936573,
0.005494092591106892,
-0.0238312017172575,
-0.013119340874254704,
-0.0008516426896676421,
-0.010483969934284687,
-0.021155012771487236,
-0.044239453971385956,
-0.004243222065269947,
0.0008332263096235693,
-0.01082981564104557,
0.01858924888074398,
0.07878537476062775,
-0.039340488612651825,
0.0138047831133008,
-0.00016133193275891244,
0.011794374324381351,
-0.0125092389062047,
-0.02125917188823223,
-0.0029047185089439154,
0.04005999118089676,
0.042012281715869904,
-0.029771100729703903,
-0.030169988051056862,
-0.041274990886449814,
0.018493378534913063,
0.0655902698636055,
-0.012699967250227928,
0.055500056594610214,
0.01758846454322338,
-0.0269254669547081,
0.0367036871612072,
-0.02844437211751938,
-0.013455369509756565,
-0.025624407455325127,
-0.0018812358612194657,
0.0014131558127701283,
-0.05162257328629494,
-0.02040257677435875,
0.02146628499031067,
0.03550045192241669,
-0.037883028388023376,
0.016963742673397064,
0.05099048838019371,
0.027581337839365005,
-0.024916937574744225,
0.0060429200530052185,
-0.04649396613240242,
0.038317084312438965,
0.00669934181496501,
0.06639925390481949,
0.01172517891973257,
0.044762738049030304,
0.045537497848272324,
0.012244517914950848,
-0.006334897596389055,
-0.047973863780498505,
0.007292208727449179,
-0.04952603206038475,
-0.009425090625882149,
0.0015339476522058249,
0.008603068068623543,
0.029995732009410858,
0.0075074550695717335,
0.022741233929991722,
0.03628666698932648,
0.02111392840743065,
-0.028719333931803703,
-0.0003033769316971302,
-0.014653646387159824,
-0.026699816808104515,
-0.07616250962018967,
0.07378514856100082,
-0.0251343734562397,
-0.041314300149679184,
0.019650299102067947,
-0.04092730954289436,
0.004051504656672478,
0.009976867586374283,
0.016088517382740974,
-0.0017541676061227918,
0.03814329579472542,
0.013537979684770107,
0.022808685898780823,
0.02457902766764164,
0.028354523703455925,
0.12155553698539734,
0.05714278295636177,
-0.024039799347519875,
-0.06996116042137146,
0.0019535908941179514,
-0.0007056401227600873,
-0.03398063778877258,
-0.0233367457985878,
0.025804797187447548,
-0.023676658049225807,
0.030468640848994255,
0.02817661315202713,
0.03766193613409996,
0.007109165191650391,
0.018511969596147537,
0.023230712860822678,
-0.023469792678952217,
-0.014246326871216297,
0.026897327974438667,
-0.02391769550740719,
-0.03145381435751915,
0.048751939088106155,
-0.05795789137482643,
0.0348057858645916,
-0.029442762956023216,
0.014773605391383171,
-0.023642582818865776,
-0.0608750581741333,
0.03332482650876045,
0.0015758747467771173,
-0.034318313002586365,
0.009625528939068317,
0.020078936591744423,
-0.007714151404798031,
-0.03411151468753815,
0.018204668536782265,
0.010317175649106503,
-0.012510469183325768,
0.009661541320383549,
-0.007787835318595171,
0.02524695359170437,
-0.01873304881155491,
0.014144179411232471,
0.028694521635770798,
-0.004309037234634161,
-0.022695448249578476,
-0.014798073098063469,
0.01640528440475464,
0.01654035970568657,
-0.008409019559621811,
0.01814858429133892,
0.02875758893787861,
-0.0144688431173563,
-0.05632336810231209,
-0.017746776342391968,
0.022576604038476944,
0.014730949886143208,
-0.0305243618786335,
-0.021318208426237106,
-0.05254191532731056,
-0.008758515119552612,
-0.01802433654665947,
-0.006116480566561222,
0.012928714975714684,
-0.008262892253696918,
-0.008918565697968006,
0.021170182153582573,
0.07733345031738281,
-0.0014274850254878402,
0.006467364262789488,
-0.021558253094553947,
0.007568941917270422,
0.0025815609842538834,
-0.01545546855777502,
0.017741160467267036,
0.02802765555679798,
0.013981097377836704,
0.02679396979510784,
-0.03893031179904938,
-0.010306242853403091,
-0.06512557715177536,
0.011435950174927711,
0.04102064296603203,
-0.023940160870552063,
-0.0036316465120762587,
-0.022063838317990303,
0.03782983124256134,
0.0153119508177042,
0.0007781891035847366,
-0.009869431145489216,
0.004980039317160845,
0.01347026415169239,
0.035251010209321976,
-0.05899975821375847,
-0.02592150866985321,
0.042970094829797745,
-0.039307571947574615,
-0.0027980864979326725,
-0.018339216709136963,
0.07558534294366837,
0.014353676699101925,
-0.015270193107426167,
0.025957388803362846,
0.023507941514253616,
-0.06744550168514252,
-0.04652225226163864,
-0.002269154414534569,
-0.01090172864496708,
0.03488635644316673,
0.009489546529948711,
-0.040287844836711884,
-0.027811087667942047,
-0.018908170983195305,
-0.002209567464888096,
-0.015426923520863056,
0.033650826662778854,
0.04232703149318695,
0.0019817061256617308,
0.003056848421692848,
-0.014612113125622272,
-0.005184593144804239,
-0.04658646881580353,
-0.057522792369127274,
-0.08126208931207657,
0.020595885813236237,
-0.03394259512424469,
-0.0008079581311903894,
-0.029806850478053093,
0.047861404716968536,
-0.029099788516759872,
-0.040954094380140305,
0.04618392884731293,
0.018863702192902565,
0.0071908640675246716,
-0.03350294381380081,
-0.013207321986556053,
-0.01612197794020176,
0.04698553681373596,
-0.008757696487009525,
-0.0609603114426136,
0.021012749522924423,
-0.012282016687095165,
-0.01139895711094141,
0.0064014592207968235,
0.011602162383496761,
0.02891281060874462,
0.026951780542731285,
-0.001170699018985033,
0.03428702428936958,
0.052968237549066544,
0.010351364500820637,
-0.028947902843356133,
0.005983409937471151,
-0.03482041135430336,
0.06519553810358047,
-0.00792680587619543,
-0.02581646852195263,
-0.0046529569663107395,
0.026082364842295647,
0.03329059109091759,
0.05154366046190262,
-0.0012149275280535221,
-0.03914622589945793,
-0.02967682108283043,
-0.039295732975006104,
0.027136990800499916,
0.026955867186188698,
0.013703998178243637,
0.06096847355365753,
0.012111173011362553,
-0.02301691100001335,
0.014967037364840508,
0.015298426151275635,
-0.00021649652626365423,
-0.08777014166116714,
0.014583265408873558,
0.010051806457340717,
-0.023247776553034782,
0.007029139436781406,
-0.05415665730834007,
0.0026787498500198126,
0.009837071411311626,
-0.04160762205719948,
-0.0056726993061602116,
-0.022402390837669373,
-0.017585208639502525,
-0.05871902406215668,
-0.004265626892447472,
-0.03404538333415985,
0.06705674529075623,
0.046797845512628555,
0.03937763348221779,
0.022763950750231743,
-0.0035563979763537645,
-0.03092462196946144,
-0.013779966160655022,
-0.006053007207810879,
0.0608784444630146,
0.0034008852671831846,
-0.00047714594984427094,
0.04118749499320984,
-0.030778957530856133,
-0.003737089689821005,
0.020262841135263443,
-0.0249516312032938,
0.02125438116490841,
0.024398645386099815,
-0.012787917628884315,
-0.02926071360707283,
0.012199818156659603,
0.0024331281892955303,
-0.036774396896362305,
-0.034802455455064774,
-0.012768076732754707,
0.017961015924811363,
-0.009072923101484776,
0.00375756504945457,
-0.015592099167406559,
0.049775876104831696,
-0.04353717342019081,
-0.0017167468322440982,
0.027427010238170624,
0.016363440081477165,
-0.012504744343459606,
0.04056393727660179,
0.009825382381677628,
0.009398956783115864,
-0.03313064202666283,
0.008932188153266907,
-0.02015729993581772,
-0.012575366534292698,
0.01333665568381548,
0.040857456624507904,
-0.001371287740767002,
-0.01994541846215725,
-0.0067279404029250145,
-0.0354006364941597,
0.015523265115916729,
0.005561948753893375,
-0.012050977908074856,
0.022245077416300774,
0.0038492907769978046,
0.018695110455155373,
0.009545938111841679,
-0.019915033131837845,
-0.014062871225178242,
-0.03942076861858368,
0.03529477119445801,
-0.033861663192510605,
-0.008222234435379505,
-0.015481391921639442,
-0.05523638427257538,
-0.04981687292456627,
-0.07743086665868759,
0.027069929987192154,
-0.06010929122567177,
-0.027591228485107422,
-0.05926508828997612,
-0.01185021735727787,
-0.03392386808991432,
0.07865305244922638,
0.019019804894924164,
0.016950679942965508,
-0.017623556777834892,
-0.015018542297184467,
0.023157872259616852,
0.03771163150668144,
-0.04358062893152237,
0.007500724866986275,
-0.016709478572010994,
-0.0012619022745639086,
0.002138499403372407,
-0.015982991084456444,
-0.016253972426056862,
0.037503525614738464,
-0.0009315379429608583,
-0.0066259149461984634,
0.007703232578933239,
0.0003839530691038817,
-0.004096521530300379,
0.02950327843427658,
0.0026958438102155924,
-0.041959743946790695,
0.07728703320026398,
-0.01844252459704876,
0.01631038822233677,
0.0349271260201931,
0.017133712768554688,
-0.032620809972286224,
0.006965871900320053,
-0.040023986250162125,
-0.027726875618100166,
0.02877364680171013,
0.004660942126065493,
0.028041506186127663,
-0.06512399017810822,
0.008366561494767666,
0.0030332040041685104,
-0.031219659373164177,
-0.03951454162597656,
0.04053954407572746,
0.0042196884751319885,
0.010247688740491867,
-0.043333977460861206,
0.01895940862596035,
0.011954634450376034,
0.005676536355167627,
-0.008351144380867481,
0.06278648972511292,
-0.009807148016989231,
0.02196200005710125,
0.037143636494874954,
-0.01713029481470585,
-0.002295718528330326,
-0.005287093576043844,
-0.01995023339986801,
0.01077400054782629,
-0.01663946732878685,
0.015841446816921234,
0.022718505933880806,
-0.019453076645731926,
0.0007327686762437224,
0.035061925649642944,
0.00292504602111876,
0.048831187188625336,
-0.047608084976673126,
0.030381813645362854,
-0.010652313940227032,
-0.008693484589457512,
-0.024757366627454758,
0.02704164758324623,
0.018925294280052185,
0.01902661845088005,
0.012016566470265388,
0.0012580221518874168,
-0.0069345044903457165,
0.00700517650693655,
0.03741448000073433,
-0.044649433344602585,
-0.01931092143058777,
-0.021223092451691628,
-0.025927819311618805,
0.015486696735024452,
-0.010831741616129875,
-0.020236724987626076,
0.003120332956314087,
0.029264580458402634,
0.03507806360721588,
-0.00786024983972311,
0.024761971086263657,
-0.012846561148762703,
-0.04065878689289093,
0.05379077047109604,
-0.04155348241329193,
-0.025523779913783073,
-0.026078375056385994,
0.003665622090920806,
0.01674616150557995,
-0.0456504188477993
] |
<p>I was thinking about an apparently simple question about quantum mechanics, if I am looking at a quantum system described by a Hilbert space $\cal{H}$ under what hypothesis can I define A and B as subsystems whose union gives the full former system and decompose $\cal{H} = \cal{H_A}\otimes \cal{H_B}$. The other way, it is evident, if I join two quantum systems, their state will evolve in the tensorial products of the two, and the states are factorizable if there is no quantum correlation. But starting with the first joined system, I am puzzled by the meaning of this decomposition.</p>
<p>Thank you. And sorry if that question is a no brainer, it's just not that evident to me. =)</p> | 2,873 | [
-0.004715481773018837,
0.0202067568898201,
0.007466140203177929,
-0.04031330347061157,
-0.011083588004112244,
0.025000326335430145,
-0.03631811961531639,
-0.019158998504281044,
0.05167700722813606,
-0.03523916378617287,
0.0034645497798919678,
0.002327391877770424,
0.04977649077773094,
-0.005338009912520647,
0.01038425788283348,
-0.0022566195111721754,
-0.014365577138960361,
-0.013489264994859695,
-0.020017271861433983,
-0.0074898479506373405,
0.02347913570702076,
0.018228257074952126,
0.013668336905539036,
-0.02742273174226284,
0.017019592225551605,
0.03820985183119774,
-0.016348324716091156,
-0.010560785420238972,
0.05369734764099121,
0.09475778043270111,
-0.009810011833906174,
-0.061241596937179565,
0.00537160923704505,
0.03785375878214836,
-0.01688811369240284,
-0.04622211679816246,
-0.050232816487550735,
-0.010550327599048615,
0.004658601246774197,
-0.0039695436134934425,
-0.050890203565359116,
-0.038774725049734116,
-0.02570827305316925,
0.05336212366819382,
-0.030231701210141182,
0.025243297219276428,
-0.0036743159871548414,
-0.03631861135363579,
-0.0022056950256228447,
-0.05285642668604851,
0.046445392072200775,
0.018684687092900276,
0.02770438976585865,
0.004648448433727026,
-0.0007668719626963139,
0.02780214510858059,
0.05251762643456459,
0.07393520325422287,
0.017032023519277573,
-0.04557729884982109,
-0.04172240570187569,
-0.047096867114305496,
-0.0035196689423173666,
-0.00681619206443429,
-0.03949074447154999,
0.04674966260790825,
-0.007903587073087692,
-0.016478177160024643,
0.010510028339922428,
-0.010932325385510921,
0.003920834977179766,
0.008629209361970425,
0.05489109829068184,
-0.05006556212902069,
0.014253555797040462,
-0.03650935739278793,
0.023408567532896996,
0.0008833637111820281,
0.021803678944706917,
0.02806820161640644,
0.012024728581309319,
-0.0025811903178691864,
0.0068781254813075066,
0.0019147918792441487,
0.00536862388253212,
-0.01796041987836361,
0.056790731847286224,
-0.020137006416916847,
-0.002942025428637862,
0.024972066283226013,
-0.023298354819417,
0.020882051438093185,
0.03161689266562462,
0.019049182534217834,
-0.02695605717599392,
0.010337953455746174,
-0.009375105611979961,
0.03390926122665405,
0.02214382216334343,
-0.041157353669404984,
-0.009083269163966179,
-0.025188958272337914,
0.004301527515053749,
0.056103162467479706,
0.008471153676509857,
0.02290351502597332,
-0.024077793583273888,
0.059498708695173264,
-0.01573735475540161,
-0.009408943355083466,
-0.03309790790081024,
0.04324117675423622,
0.006926445756107569,
0.05918479338288307,
-0.0033228446263819933,
-0.053945090621709824,
0.002029054332524538,
-0.022077161818742752,
0.0638662800192833,
0.07497427612543106,
0.05514170229434967,
-0.026893630623817444,
0.013034692034125328,
-0.012282711453735828,
-0.07117874175310135,
0.024549053981900215,
0.024209266528487206,
0.0009414967498742044,
-0.04668384790420532,
0.024967333301901817,
0.010714702308177948,
-0.03531649708747864,
0.058624040335416794,
0.015173275023698807,
0.004257665015757084,
-0.050615597516298294,
-0.12503688037395477,
-0.059811897575855255,
0.04211738333106041,
-0.003521762089803815,
-0.02292441762983799,
-0.06056470423936844,
0.05056345835328102,
0.0342099592089653,
0.08012630045413971,
-0.015049570240080357,
0.0281805582344532,
0.008511166088283062,
0.021219104528427124,
0.027931900694966316,
0.007257027085870504,
-0.06927862763404846,
-0.007330730557441711,
-0.027410514652729034,
0.004648582544177771,
-0.05058109387755394,
0.017707273364067078,
0.04837413132190704,
-0.017300032079219818,
-0.011913085356354713,
0.06594026833772659,
-0.0010001615155488253,
-0.007579087279736996,
0.04099074751138687,
0.019876454025506973,
-0.006356137804687023,
0.04371677339076996,
-0.017583072185516357,
0.010314743965864182,
0.06596792489290237,
0.018260078504681587,
-0.004159051459282637,
0.019536234438419342,
0.057219915091991425,
-0.00700502609834075,
-0.0036721201613545418,
-0.0038065544795244932,
-0.011660668067634106,
0.005961866118013859,
-0.01612144336104393,
-0.02692508138716221,
-0.03133968636393547,
-0.03996795043349266,
0.020177993923425674,
0.029172176495194435,
0.011217809282243252,
0.02449117600917816,
-0.0424078069627285,
0.008669817820191383,
-0.05008024349808693,
-0.020294802263379097,
-0.09164827316999435,
-0.026237603276968002,
0.0027837331872433424,
-0.03332038223743439,
0.05921611934900284,
0.017288880422711372,
0.0082884905859828,
-0.02718670666217804,
-0.048284877091646194,
-0.028475012630224228,
0.021287841722369194,
-0.020881177857518196,
-0.01812279038131237,
0.0695202648639679,
0.036070968955755234,
0.05136338993906975,
0.0069512310437858105,
0.03130201995372772,
-0.030134234577417374,
-0.026952117681503296,
0.013306020759046078,
0.011950509622693062,
0.013146307319402695,
-0.03761924058198929,
0.0004996301140636206,
-0.0082019604742527,
-0.03333419933915138,
-0.010326487943530083,
0.018009627237915993,
-0.07766503840684891,
0.05855070427060127,
0.02261485531926155,
0.01314756739884615,
0.009993207640945911,
0.05255384370684624,
0.02818382903933525,
0.006588709075003862,
-0.011755996383726597,
-0.02004322223365307,
-0.023988621309399605,
0.029773712158203125,
0.057216890156269073,
0.02748212218284607,
-0.03424781560897827,
0.035080961883068085,
0.015535223297774792,
0.029317332431674004,
0.019781818613409996,
0.01257831696420908,
-0.04799344763159752,
0.014455294236540794,
-0.008366682566702366,
-0.014414031058549881,
0.008842090144753456,
0.00899242889136076,
-0.013187695294618607,
-0.008286705240607262,
0.014299105852842331,
0.027023356407880783,
-0.02568986639380455,
0.061393074691295624,
-0.010016083717346191,
0.04229956865310669,
-0.011873873881995678,
-0.03294156491756439,
0.01569638028740883,
-0.03949587419629097,
0.02377508580684662,
-0.002188401762396097,
0.0036733103916049004,
-0.0150675093755126,
-0.02272968739271164,
-0.05398869141936302,
0.011093057692050934,
0.006623311433941126,
-0.03034030832350254,
0.004402324091643095,
0.015518100932240486,
-0.03595307841897011,
0.010591146536171436,
-0.0100697111338377,
0.012604610994458199,
-0.03397206589579582,
-0.025575309991836548,
0.03798157721757889,
0.00008774753951001912,
0.047646697610616684,
-0.06700804829597473,
-0.030921129509806633,
-0.00933501124382019,
-0.027011249214410782,
0.03324556723237038,
-0.0021152060944586992,
-0.04982501640915871,
0.04842359945178032,
-0.03891817107796669,
-0.017431776970624924,
0.007044221740216017,
-0.02504010684788227,
0.014259951189160347,
-0.016747498884797096,
-0.02295692265033722,
-0.06293942779302597,
-0.03974173963069916,
-0.018130751326680183,
0.025271911174058914,
-0.03494354337453842,
0.03565606474876404,
0.03613656759262085,
-0.017629312351346016,
-0.03883054479956627,
-0.03261898085474968,
-0.019790709018707275,
-0.04681388661265373,
-0.011908021755516529,
-0.037830859422683716,
0.0181904099881649,
-0.018124276772141457,
0.016319457441568375,
0.03517884761095047,
-0.06962482631206512,
-0.01747128553688526,
-0.0513872392475605,
-0.06864961236715317,
0.009108848869800568,
0.026820911094546318,
0.0315481573343277,
0.0132523188367486,
-0.030950095504522324,
0.0648031011223793,
-0.008792737498879433,
-0.03534974157810211,
-0.00492978235706687,
0.026359371840953827,
-0.0003615404129959643,
-0.016761867329478264,
0.025537576526403427,
0.010712620802223682,
0.005170094780623913,
0.060499731451272964,
0.02229190617799759,
0.04314124956727028,
0.04283561930060387,
0.010953254997730255,
-0.007905314676463604,
0.02240636572241783,
0.04320603609085083,
0.029669122770428658,
0.00643132533878088,
0.008214665576815605,
-0.02780737914144993,
-0.0032509032171219587,
-0.017911281436681747,
0.017667772248387337,
0.017828719690442085,
-0.011980862356722355,
0.012348449788987637,
0.01343121100217104,
0.00941524188965559,
-0.007520686369389296,
0.010089150629937649,
-0.041678279638290405,
-0.006084413733333349,
0.01355366688221693,
0.0416061133146286,
0.0018667688127607107,
-0.0315520204603672,
0.023825479671359062,
0.042559266090393066,
0.007420557085424662,
-0.06376414746046066,
-0.004805692937225103,
-0.0027969677466899157,
-0.0026308810338377953,
0.02913035824894905,
0.012316832318902016,
-0.029633566737174988,
0.04740026220679283,
-0.00204645493067801,
0.03244560956954956,
-0.015317444689571857,
-0.0399160273373127,
-0.038338955491781235,
-0.03899533674120903,
-0.006387624889612198,
0.02305707335472107,
0.03325271233916283,
0.0007673383806832135,
0.04419272392988205,
-0.0006856960244476795,
0.008407941088080406,
0.005575727205723524,
0.0003488078946247697,
-0.06701775640249252,
0.014799616299569607,
-0.024961328133940697,
-0.0065294126980006695,
-0.001322246971540153,
-0.02433248981833458,
0.03482220694422722,
-0.02478857710957527,
-0.0602945014834404,
-0.029705828055739403,
-0.014177929610013962,
-0.05656636133790016,
0.013737158849835396,
-0.04279424250125885,
-0.05149190500378609,
-0.01590738072991371,
0.0025364502798765898,
0.014752239920198917,
0.01773136295378208,
0.03066665306687355,
0.04136768728494644,
-0.024733083322644234,
0.010477399453520775,
-0.001551501452922821,
0.02415560930967331,
0.019814155995845795,
0.01862333156168461,
0.02084854617714882,
0.03170092776417732,
-0.00043857377022504807,
0.01860610581934452,
0.013030694797635078,
0.10153985023498535,
-0.011088180355727673,
0.006931421346962452,
0.029751712456345558,
0.006460415665060282,
-0.04214911162853241,
-0.009602023288607597,
0.07371296733617783,
0.015484753996133804,
-0.005687264259904623,
0.007309775799512863,
0.05383801460266113,
-0.010426283814013004,
0.018825016915798187,
0.0662619099020958,
-0.0013961122604086995,
-0.023100627586245537,
-0.009617092087864876,
-0.017903268337249756,
-0.029299892485141754,
-0.0017178971320390701,
0.012317045591771603,
-0.005089279264211655,
-0.011044694110751152,
0.017049267888069153,
0.0386820062994957,
0.017623160034418106,
-0.024918025359511375,
0.012111182324588299,
-0.01491360180079937,
-0.005048679653555155,
-0.0018472366500645876,
-0.02667405642569065,
-0.008253267034888268,
0.04577390477061272,
0.029488060623407364,
0.011112404987215996,
0.018181810155510902,
-0.059757668524980545,
0.008632797747850418,
0.026017019525170326,
0.026207812130451202,
-0.00785268284380436,
-0.0016798203578218818,
-0.03365815430879593,
-0.071326844394207,
0.05283517763018608,
-0.0007195929647423327,
0.04344519227743149,
-0.012577188201248646,
-0.027992304414510727,
-0.026270832866430283,
-0.006657288409769535,
-0.0050545441918075085,
0.03531011566519737,
0.03179286792874336,
0.03538361191749573,
-0.010325394570827484,
0.0008940265979617834,
-0.030651818960905075,
0.01215285249054432,
0.0299641415476799,
0.04718310013413429,
0.005329570267349482,
-0.04805156961083412,
-0.017756352201104164,
0.04194251447916031,
0.020943040028214455,
-0.06775092333555222,
0.027278471738100052,
0.021543389186263084,
-0.03886724263429642,
0.03246873989701271,
-0.04385901615023613,
-0.037375036627054214,
0.020416023209691048,
-0.0007709097117185593,
0.013970728032290936,
0.03734273463487625,
-0.007175665348768234,
0.09850052744150162,
0.028275681659579277,
0.002132212510332465,
0.0543193444609642,
0.0023811471182852983,
-0.013668173924088478,
-0.013820495456457138,
-0.03505885601043701,
0.038139745593070984,
-0.05648420378565788,
0.02783116325736046,
-0.04276665672659874,
0.011160881258547306,
-0.011460000649094582,
0.024974960833787918,
-0.007837054319679737,
0.008091419003903866,
-0.004120627883821726,
-0.047626037150621414,
-0.018208367750048637,
-0.001997991232201457,
-0.040617723017930984,
-0.005409643054008484,
0.00605050241574645,
0.03879113122820854,
0.005490316543728113,
-0.04299754276871681,
-0.005319439340382814,
-0.006319217383861542,
0.01684739999473095,
0.027163371443748474,
-0.02582252025604248,
0.05165328085422516,
-0.052485741674900055,
0.0003151775454171002,
0.04116837680339813,
-0.017756810411810875,
-0.008533996529877186,
-0.03514983132481575,
0.02235424518585205,
0.031301505863666534,
-0.04992998391389847,
-0.03363002836704254,
-0.021522758528590202,
-0.0063334256410598755,
0.02009417861700058,
-0.054438356310129166,
0.01265429612249136,
-0.000038282065361272544,
-0.014565449208021164,
-0.0667891651391983,
-0.044505972415208817,
0.0025419017765671015,
0.027056455612182617,
-0.009680924005806446,
-0.05750814825296402,
0.03266734629869461,
-0.03848375752568245,
-0.004369702190160751,
-0.032799169421195984,
0.03869006037712097,
-0.05241921916604042,
0.006942796055227518,
0.007472092751413584,
0.0062283724546432495,
0.05815038084983826,
0.01797926053404808,
0.02831915020942688,
0.013863367959856987,
0.012514068745076656,
0.00550125353038311,
0.026005832478404045,
0.02489471435546875,
-0.02203870378434658,
-0.0025065343361347914,
-0.03605085238814354,
-0.010076398961246014,
0.0399397537112236,
-0.02706904523074627,
-0.000040396436816081405,
-0.008663308806717396,
0.03105786256492138,
0.014798217453062534,
0.0030127670615911484,
0.01569720171391964,
0.010158276185393333,
0.03383074700832367,
0.021086949855089188,
0.02267281711101532,
0.017041362822055817,
-0.06412870436906815,
0.0054992795921862125,
-0.010813992470502853,
-0.009717294946312904,
0.022257614880800247,
0.021013621240854263,
0.012264021672308445,
-0.0026552898343652487,
0.04960993677377701,
-0.023878270760178566,
0.016279278323054314,
0.013880444690585136,
0.020644448697566986,
0.030304040759801865,
0.005445891059935093,
-0.03239881619811058,
-0.05542884021997452,
-0.059087786823511124,
-0.0019430574029684067,
0.03911953791975975,
-0.02983962930738926,
0.026424232870340347,
0.04886293783783913,
0.00015769712626934052,
0.016455762088298798,
-0.02307741530239582,
-0.012711569666862488,
0.031871188431978226,
0.004267499316483736,
0.026413803920149803,
-0.042322270572185516,
-0.019026149064302444,
0.04250869154930115,
0.05591887980699539,
-0.023291418328881264,
0.01684049516916275,
0.030526870861649513,
0.03371328487992287,
0.017642267048358917,
-0.019082333892583847,
-0.05802403762936592,
0.028836671262979507,
-0.061051689088344574,
-0.010401892475783825,
-0.03284376487135887,
-0.0031033919658511877,
0.03730201721191406,
0.041376952081918716,
0.006216586567461491,
-0.08323868364095688,
-0.027106475085020065,
-0.04562005400657654,
0.027047675102949142,
0.0036382016260176897,
0.023409180343151093,
0.025026654824614525,
0.03271744027733803,
0.03454923629760742,
0.010646591894328594,
0.012182156555354595,
0.01162426732480526,
-0.07366516441106796,
-0.030259696766734123,
-0.045154351741075516,
-0.016670912504196167,
0.02699391171336174,
-0.026565244421362877,
-0.01734096370637417,
0.0209435373544693,
-0.03840474784374237,
0.006632979493588209,
-0.024747559800744057,
0.05303800851106644,
-0.013751313090324402,
0.04360579326748848,
0.016743352636694908,
0.011259797029197216,
-0.002255325671285391,
-0.0019164812983945012,
0.09441310167312622,
0.04278935119509697,
0.010861828923225403,
-0.04849924147129059,
0.029064685106277466,
0.0045810420997440815,
-0.014939204789698124,
0.0007772186654619873,
0.028945039957761765,
0.03437484800815582,
0.028709398582577705,
0.003320028306916356,
0.03665204718708992,
0.022770671173930168,
-0.0033505395986139774,
0.053899962455034256,
-0.05168887972831726,
-0.04706456884741783,
-0.01161032821983099,
0.025936907157301903,
-0.020044175907969475,
-0.005776140373200178,
-0.05941995605826378,
-0.021867934614419937,
-0.010000527836382389,
0.011113759130239487,
-0.023873906582593918,
-0.006224534474313259,
0.018988775089383125,
0.0053611034527421,
-0.02919725701212883,
0.019664624705910683,
0.01982005499303341,
-0.00009946944192051888,
-0.04741628095507622,
0.015263267792761326,
0.0331529937684536,
-0.014103233814239502,
0.01845763809978962,
0.014447623863816261,
0.04362078011035919,
0.010513014160096645,
0.0031000955495983362,
0.0016446833033114672,
-0.04353948310017586,
0.009259814396500587,
-0.022847604006528854,
0.07353461533784866,
-0.028949834406375885,
-0.010879217647016048,
-0.009860525839030743,
-0.026469793170690536,
0.013959132134914398,
-0.024286514148116112,
0.014560990035533905,
-0.004302303772419691,
0.02946637012064457,
-0.01364410761743784,
-0.006902498658746481,
-0.03457949683070183,
0.016444405540823936,
-0.009802787564694881,
0.03759763389825821,
-0.0034080781042575836,
-0.007903936319053173,
0.015533327125012875,
0.017091747373342514,
0.032129064202308655,
0.012332472018897533,
-0.013263748027384281,
-0.025334948673844337,
0.006694963667541742,
-0.0124069107696414,
-0.008933509700000286,
0.0298868790268898,
0.00440563028678298,
0.08705973625183105,
0.0004903158987872303,
-0.012940849177539349,
-0.008411138318479061,
-0.04689643904566765,
0.022504566237330437,
0.0005337089532986283,
-0.03869813308119774,
-0.014398652128875256,
-0.010061296634376049,
0.029969563707709312,
0.07237164676189423,
-0.024869482964277267,
-0.006382534746080637,
0.014316163957118988,
0.012325696647167206,
0.0604667142033577,
-0.028020726516842842,
0.023806065320968628,
0.003606948535889387,
-0.0025287577882409096,
-0.02180391550064087,
-0.04329271987080574,
0.029178481549024582,
0.004497057758271694,
0.016546674072742462,
-0.01424663607031107,
0.026440128684043884,
0.0003873988171108067,
0.0062352498061954975,
0.025269078090786934,
-0.006955787539482117,
0.0054689268581569195,
-0.004421878140419722,
0.03592522814869881,
-0.02020415849983692,
-0.01637141965329647,
-0.0045470441691577435,
0.023747701197862625,
0.02688828855752945,
0.015094093047082424,
-0.017976807430386543,
-0.0021087045315653086,
0.007920968346297741,
0.05087106302380562,
-0.015536133199930191,
-0.009083185344934464,
-0.05002303794026375,
-0.003993004560470581,
0.06020302698016167,
-0.0018711354350671172,
0.0051451995968818665,
0.028281118720769882,
-0.00185679632704705,
-0.05544256046414375,
0.04370551556348801,
0.040305331349372864,
-0.04946586489677429,
-0.033814456313848495,
0.003608216531574726,
0.00155131914652884,
0.03191153705120087,
-0.005692166741937399,
-0.012290023267269135,
0.042191773653030396,
-0.03618073835968971,
-0.03056216612458229,
0.021200744435191154,
-0.012149762362241745,
0.0696033239364624,
0.04430258646607399,
-0.04198082908987999,
-0.04198954999446869,
0.02740928716957569,
-0.01996723748743534,
0.03369898349046707,
0.012125341221690178,
-0.013516687788069248,
-0.015026644803583622,
-0.005172774661332369,
-0.013342412188649178,
0.010493911802768707,
-0.012840339913964272,
0.01022628415375948,
0.025299888104200363,
0.01824159547686577,
0.0023342156782746315,
0.0017592724179849029,
0.029344694688916206,
0.04245602339506149,
0.012132718227803707,
0.0019236447988077998,
0.01581544429063797,
0.06158211827278137,
-0.03408243507146835,
0.037177711725234985,
0.061442285776138306,
0.030981963500380516,
-0.08863126486539841,
-0.045637451112270355,
0.004187877289950848,
-0.01840006373822689,
0.03188847005367279,
-0.057356271892786026,
-0.016436349600553513,
0.02766384929418564,
-0.06730394065380096,
0.03631008416414261,
-0.032135747373104095,
-0.029621083289384842,
-0.051492515951395035,
-0.00838914979249239,
-0.04247761890292168,
0.07038171589374542,
0.0038430183194577694,
0.022948840633034706,
0.022604946047067642,
0.010469372384250164,
-0.012371622025966644,
-0.02856455370783806,
-0.03147340565919876,
-0.02107296511530876,
-0.02087501250207424,
-0.028706252574920654,
0.10448379814624786,
-0.022061733528971672,
-0.05873671919107437,
0.018811579793691635,
-0.04631739854812622,
-0.021573616191744804,
-0.03394648805260658,
-0.005400745198130608,
0.03611508011817932,
0.004271985497325659,
0.006778671406209469,
-0.040506161749362946,
-0.0029409416019916534,
0.04300722852349281,
0.03251098841428757,
0.02278713509440422,
-0.0021642125211656094,
-0.014293491840362549,
0.021611029282212257,
-0.0277455635368824,
-0.051206838339567184,
0.016650281846523285,
0.020857924595475197,
-0.008419406600296497,
-0.008608868345618248,
-0.010754873976111412,
0.01564844511449337,
-0.007116112392395735,
0.014352541416883469,
-0.03496559336781502,
-0.02413499355316162,
0.042898621410131454,
0.007005845196545124,
-0.027859479188919067,
-0.011778230778872967,
-0.045964669436216354,
-0.03389667347073555,
0.03587967902421951,
0.012540649622678757,
0.010683740489184856,
-0.04863600432872772,
-0.016555197536945343,
0.00042838850640691817,
-0.012216360308229923,
-0.02228603884577751,
-0.04549693316221237,
-0.03976577892899513,
0.051097430288791656,
-0.012658706866204739,
0.046924203634262085,
-0.02464897185564041,
-0.06386436522006989,
-0.04024256765842438,
-0.053600143641233444,
0.020964154973626137,
0.03258613497018814,
-0.0018939418951049447,
-0.028363680467009544,
-0.011713575571775436,
-0.01746748387813568,
-0.004510956350713968,
0.03762558847665787,
-0.0027299197390675545,
-0.008622976951301098,
0.005533806513994932,
-0.005715634673833847,
0.04108220711350441,
-0.010991385206580162,
0.009254487231373787,
-0.03280247375369072,
0.006264443043619394,
0.001415991224348545,
-0.0013380920281633735,
-0.005181613843888044,
0.007036341354250908,
0.03151347115635872,
0.007705748081207275,
-0.009517358615994453,
-0.0265903789550066,
-0.019614191725850105,
0.059006910771131516,
-0.009688224643468857,
0.006126584485173225,
0.06499718129634857,
0.0008408846915699542,
0.013208418153226376,
0.04015662521123886,
-0.018095290288329124,
-0.04488058760762215,
-0.00013946286344435066,
-0.01027612667530775,
-0.011870176531374454,
-0.00009685221448307857,
0.01101712603121996,
0.011478538624942303,
-0.011936190538108349,
-0.014596025459468365,
0.03527304157614708,
-0.03329581394791603,
0.008712231181561947,
0.03611915931105614,
-0.002285524969920516,
0.019092950969934464,
-0.01899193599820137,
0.013208662159740925,
0.03305061534047127,
-0.007814407348632812,
0.008092382922768593,
0.036524172872304916,
0.03658432886004448,
0.005824234802275896,
0.0004536641063168645,
0.0045644789934158325,
-0.02214300073683262,
0.03039051778614521,
-0.00094288942636922,
0.053371794521808624,
-0.06436747312545776,
0.01050676591694355,
0.01063205674290657,
-0.029125967994332314,
0.016938628628849983,
-0.013324364088475704,
-0.01268893200904131,
0.09091250598430634,
-0.021748343482613564,
-0.005912648048251867,
-0.0219517033547163,
0.0376509428024292,
-0.04488333687186241,
0.0047294022515416145,
0.03138844668865204,
0.05028727650642395,
-0.016727764159440994,
-0.015174318104982376,
-0.04782471805810928,
-0.017237404361367226,
-0.025937413796782494,
-0.03361497074365616,
0.012664099223911762,
0.0007448605028912425,
-0.011634412221610546,
-0.026317281648516655,
0.001727811060845852,
0.0010844491189345717,
-0.04630785062909126,
0.03667730465531349,
0.05468374490737915,
0.014540721662342548,
-0.03837982937693596,
-0.003277459181845188,
-0.03781947121024132,
0.026709718629717827,
-0.0400436632335186,
-0.0017695544520393014,
-0.02378378063440323,
0.025924919173121452,
0.013755382038652897,
0.014874721877276897
] |
<p>What I mean is, the nuclear chain reactions take microseconds for every generation and that is the reason that nuclear weapons exist. Because in nuclear reactors the reaction rate is much slower thus it can be controlled and prevent it from exploding.
So my question here is about the speed of matter-antimatter reaction. Just imagine we have a kilogram of antimatter, is the annihilation speed enough to make it usable as a weapon ?</p> | 2,874 | [
-0.011940174736082554,
-0.05592083930969238,
-0.03501388803124428,
-0.03332109749317169,
0.07163738459348679,
-0.028686190024018288,
-0.03175351023674011,
-0.05144002288579941,
-0.014359451830387115,
-0.0061949556693434715,
0.03032473288476467,
0.025144308805465698,
0.06643293797969818,
-0.005733796861022711,
0.00032042659586295485,
0.01577501744031906,
-0.007816086523234844,
-0.05041671544313431,
0.0087543074041605,
-0.03256282955408096,
0.0239606574177742,
-0.039791177958250046,
0.008030346594750881,
0.00375291402451694,
-0.014064415358006954,
0.045869749039411545,
0.03660193085670471,
0.016310645267367363,
0.008213475346565247,
0.029771968722343445,
0.03837853670120239,
-0.053450461477041245,
0.044664058834314346,
0.05105868726968765,
0.03221800923347473,
-0.005316270049661398,
-0.02414763905107975,
-0.06203437224030495,
-0.01244609896093607,
0.032043833285570145,
-0.017711879685521126,
-0.03500472381711006,
0.016929155215620995,
0.03630566969513893,
-0.0289856418967247,
0.029252711683511734,
-0.028217947110533714,
-0.02415713109076023,
0.05457521602511406,
-0.04048663377761841,
0.05895151197910309,
0.01791435480117798,
0.03790314495563507,
-0.014993344433605671,
0.0007355959387496114,
-0.01202439796179533,
0.08211550861597061,
0.06811435520648956,
-0.027309948578476906,
-0.031154723837971687,
-0.0035866941325366497,
-0.000811944657471031,
-0.007283036597073078,
-0.010555790737271309,
-0.030096707865595818,
0.029890427365899086,
-0.018283454701304436,
-0.02176775224506855,
0.021809415891766548,
0.027774978429079056,
0.013509153388440609,
-0.002308268565684557,
0.035032108426094055,
0.02300754375755787,
-0.038034942001104355,
-0.033350296318531036,
0.02403436042368412,
-0.011058734729886055,
0.020159661769866943,
0.09460865706205368,
-0.018776526674628258,
0.03409062325954437,
0.0010067600524052978,
0.0489291250705719,
0.009883778169751167,
0.00892234779894352,
0.06646689027547836,
-0.01675053872168064,
0.005377089139074087,
0.01969539374113083,
-0.035190265625715256,
0.0027452881913632154,
0.0275759045034647,
0.021911129355430603,
-0.027520256116986275,
0.047374624758958817,
0.005951636470854282,
0.060405511409044266,
0.006897320970892906,
0.01063804142177105,
0.04290981963276863,
-0.018456635996699333,
0.029150836169719696,
0.04760809987783432,
0.05060650780797005,
-0.032443344593048096,
-0.05617331713438034,
0.038557276129722595,
-0.03191210702061653,
0.005091220140457153,
-0.05135321989655495,
-0.00938425213098526,
0.004887595307081938,
-0.027330441400408745,
0.01700420118868351,
-0.022709719836711884,
-0.00995153933763504,
-0.017507197335362434,
0.0822543203830719,
0.05761642009019852,
0.019751092419028282,
-0.011759474873542786,
0.02348174899816513,
-0.022332319989800453,
-0.03991338238120079,
-0.01213880069553852,
0.020413406193256378,
-0.028928957879543304,
-0.014090577140450478,
0.014892886392772198,
-0.0027655509766191244,
-0.014795472845435143,
0.014291707426309586,
-0.03501510247588158,
0.0769200474023819,
-0.03324701264500618,
-0.08729833364486694,
-0.09013905376195908,
0.013242261484265327,
-0.0276211928576231,
-0.03356659784913063,
-0.08095341175794601,
-0.016243893653154373,
0.010677454993128777,
0.02860231138765812,
0.006318872328847647,
-0.040874630212783813,
-0.008267143741250038,
0.02356668747961521,
0.03371274471282959,
-0.03839339315891266,
-0.019190581515431404,
0.04883413389325142,
-0.06114218011498451,
-0.007968309335410595,
-0.06465412676334381,
0.027517884969711304,
0.039188940078020096,
-0.0015599103644490242,
-0.01797396130859852,
0.017959242686629295,
-0.028661612421274185,
0.0035603265278041363,
-0.0010393599513918161,
-0.01031871885061264,
-0.027909688651561737,
0.0750938430428505,
0.033984433859586716,
-0.010442395694553852,
0.028266724199056625,
0.039103709161281586,
0.04024761915206909,
0.022414078935980797,
0.013115541078150272,
0.0534786581993103,
-0.03438537195324898,
-0.012380871921777725,
-0.011881721206009388,
-0.013549589551985264,
0.004852833691984415,
-0.03446429222822189,
-0.016345951706171036,
-0.03174251690506935,
0.034839045256376266,
0.03744489327073097,
0.05187089741230011,
-0.03109428845345974,
0.013921651057898998,
-0.002244361210614443,
-0.06481728702783585,
-0.03415066376328468,
-0.051707491278648376,
0.04624509811401367,
0.0016283183358609676,
-0.01208497304469347,
-0.0026533687487244606,
0.02469017170369625,
0.019757330417633057,
-0.0319407694041729,
-0.026322541758418083,
-0.028160857036709785,
0.0272284634411335,
-0.023231159895658493,
-0.011585689149796963,
0.02295907400548458,
0.04832931235432625,
-0.0030704219825565815,
-0.03393879160284996,
0.04393654316663742,
0.00512460945174098,
-0.03617018461227417,
-0.009967535734176636,
-0.040403813123703,
-0.00010797348659252748,
0.019472753629088402,
-0.012723519466817379,
0.031109526753425598,
-0.011827192269265652,
0.01021173782646656,
0.038379158824682236,
-0.01085912436246872,
0.10834337770938873,
-0.0024624792858958244,
0.0006193793960846961,
-0.03457768261432648,
0.013713674619793892,
0.04405045136809349,
0.0024413950741291046,
0.0002915138902608305,
-0.05090147256851196,
-0.06344679743051529,
-0.007477800827473402,
0.0033981299493461847,
0.03363864868879318,
-0.035300809890031815,
0.003743403125554323,
0.02210427261888981,
0.0292315986007452,
0.06648040562868118,
0.004373984411358833,
-0.0046259998343884945,
-0.03698958456516266,
0.002884659683331847,
0.022809471935033798,
-0.02611677721142769,
0.015308191999793053,
0.036658868193626404,
0.009672174230217934,
-0.012432941235601902,
0.0018608678365126252,
-0.01062571071088314,
0.021515021100640297,
-0.027208629995584488,
-0.019536450505256653,
0.0024845092557370663,
-0.06412191689014435,
0.011124893091619015,
-0.026287071406841278,
0.013822456821799278,
0.011601213365793228,
-0.011498920619487762,
0.030848778784275055,
-0.014828856103122234,
-0.011589748784899712,
0.010993336327373981,
-0.021985800936818123,
-0.0034499710891395807,
-0.024493180215358734,
0.032706260681152344,
-0.010113302618265152,
0.003959381487220526,
0.013607400469481945,
0.01152945775538683,
-0.02091338485479355,
0.015211948193609715,
0.032625675201416016,
-0.0017336936434730887,
0.04577615112066269,
-0.016787851229310036,
-0.049537595361471176,
0.0026767998933792114,
-0.036820486187934875,
0.0020974159706383944,
-0.010122265666723251,
-0.0390554815530777,
0.009545979090034962,
-0.02873934432864189,
-0.05178951099514961,
0.03878231719136238,
-0.03522203490138054,
0.007652243599295616,
0.024925580248236656,
-0.034670475870370865,
-0.07039824873209,
0.0029283883050084114,
-0.023108329623937607,
0.015758946537971497,
-0.010836060158908367,
0.019531937316060066,
0.014635995030403137,
-0.012131059542298317,
-0.03582824766635895,
-0.02200852520763874,
-0.03811044618487358,
-0.03562255948781967,
-0.006852876860648394,
-0.020258653908967972,
0.03183344379067421,
-0.04269206151366234,
0.0339476652443409,
0.06645593792200089,
-0.06226184964179993,
0.008092090487480164,
-0.026272861286997795,
-0.030831830576062202,
0.05309326946735382,
-0.005646296311169863,
0.055830296128988266,
-0.005810450296849012,
-0.02665822207927704,
0.0685461238026619,
0.06410731375217438,
-0.027039989829063416,
0.009738663211464882,
-0.010013832710683346,
0.012329168617725372,
-0.012912782840430737,
0.024209637194871902,
0.015638241544365883,
0.002723096637055278,
0.018724149093031883,
0.009475179016590118,
0.027677588164806366,
0.023374302312731743,
-0.03576093539595604,
-0.03218856826424599,
-0.0051624588668346405,
0.014270714484155178,
0.03663782775402069,
0.02522251196205616,
0.006232134066522121,
-0.0469844676554203,
0.0360848531126976,
0.008266272954642773,
0.06890909373760223,
-0.010572673752903938,
-0.017089692875742912,
0.041055694222450256,
0.01731863059103489,
0.0033832078333944082,
-0.0106201795861125,
0.025700757279992104,
-0.032443635165691376,
0.002784255426377058,
0.029340142384171486,
0.042470067739486694,
0.040492136031389236,
0.01861393079161644,
0.027003230527043343,
0.0006338874809443951,
0.04379870742559433,
-0.0008934788056649268,
-0.006277219858020544,
0.021769514307379723,
-0.010155584663152695,
0.005743250250816345,
-0.0026054929476231337,
0.010689247399568558,
0.0185238104313612,
0.021029045805335045,
-0.003710635006427765,
-0.0019978689961135387,
-0.006473919842392206,
0.010629541240632534,
-0.09264495968818665,
0.0010586660355329514,
0.006654619239270687,
0.030550416558980942,
0.0011406325502321124,
0.06249450519680977,
0.026944227516651154,
-0.004715038929134607,
-0.009817328304052353,
-0.03451218456029892,
-0.05952683836221695,
0.03998946398496628,
-0.05473799630999565,
-0.05221789702773094,
-0.006925499066710472,
-0.024410609155893326,
-0.022965043783187866,
-0.011606017127633095,
-0.03855038061738014,
0.0003998778120148927,
-0.011308101005852222,
-0.04645409807562828,
0.016101336106657982,
-0.04109858721494675,
-0.020224973559379578,
-0.014724387787282467,
0.0036052989307790995,
0.02083187736570835,
0.005900281015783548,
0.008633943274617195,
0.02023966610431671,
-0.06702999770641327,
-0.0035977421794086695,
-0.007843953557312489,
-0.016717152670025826,
-0.009883958846330643,
0.05880562216043472,
0.051611222326755524,
0.0047700549475848675,
-0.0438791923224926,
0.017475906759500504,
0.02509395033121109,
0.028694696724414825,
0.00919713731855154,
0.01233351044356823,
-0.03394496440887451,
-0.06706399470567703,
-0.030240582302212715,
0.03351379185914993,
0.02203625626862049,
-0.010219627991318703,
-0.009481234475970268,
0.0028003426268696785,
0.025670547038316727,
0.0006573916180059314,
0.026933427900075912,
0.09175078570842743,
-0.0183520819991827,
-0.007749723736196756,
-0.07122795283794403,
-0.015477687120437622,
-0.023062074556946754,
0.005101726856082678,
0.03136925771832466,
-0.014569617807865143,
-0.029851729050278664,
0.009969528764486313,
0.015123626217246056,
0.03579115495085716,
-0.0569402240216732,
0.008042783476412296,
-0.02840733900666237,
0.0009752626647241414,
0.021846851333975792,
-0.004465860314667225,
0.025089776143431664,
0.01600930653512478,
0.01486967969685793,
0.02030138671398163,
0.016273735091090202,
-0.08294392377138138,
-0.00045884671271778643,
0.02837652899324894,
0.04159313440322876,
-0.04809816554188728,
-0.021681055426597595,
-0.07796311378479004,
-0.03232773020863533,
0.08365292847156525,
-0.00437822425737977,
0.04671071842312813,
-0.009149969555437565,
-0.03258240967988968,
0.00005105120726511814,
-0.01168164610862732,
0.005409653298556805,
0.022067736834287643,
0.005465636029839516,
-0.04414762556552887,
-0.009483702480793,
0.006822121795266867,
0.003416140330955386,
-0.019515806809067726,
0.02954154461622238,
0.041458722203969955,
0.02541590854525566,
0.003234782023355365,
0.02060379832983017,
0.021674908697605133,
-0.0014246378559619188,
-0.029826102778315544,
0.013705349527299404,
0.0008148152264766395,
-0.030941162258386612,
0.021191194653511047,
-0.03487961366772652,
-0.024815112352371216,
0.028073156252503395,
0.010711455717682838,
-0.01795032061636448,
-0.03477545455098152,
-0.04389980807900429,
0.013036047108471394,
0.026065589860081673,
-0.03158341348171234,
0.0078300004824996,
0.0628952905535698,
-0.006884640082716942,
0.006942935287952423,
-0.028422296047210693,
0.02906336821615696,
-0.020477809011936188,
0.014969008974730968,
0.0021895302925258875,
0.01425184216350317,
-0.023351410403847694,
0.03363420069217682,
-0.03368285298347473,
-0.004850149620324373,
-0.006544407457113266,
-0.01965407282114029,
0.0031766495667397976,
0.028458300977945328,
0.015884291380643845,
-0.0028415352571755648,
0.002314353361725807,
-0.00772716524079442,
-0.04462002217769623,
-0.018824223428964615,
0.01742062345147133,
0.009183417074382305,
0.00909674447029829,
0.02498907595872879,
-0.007634934037923813,
0.008703886531293392,
-0.02692105434834957,
-0.04025239869952202,
0.03017609938979149,
-0.03641071543097496,
0.0328238345682621,
0.010007943026721478,
-0.025421880185604095,
0.009093694388866425,
-0.09007339179515839,
-0.018897073343396187,
0.018556533381342888,
-0.008677536621689796,
0.05582413822412491,
-0.028215644881129265,
0.06552433967590332,
-0.021741706877946854,
0.019436361268162727,
-0.09520579129457474,
-0.043857309967279434,
0.022204125300049782,
-0.02271832711994648,
-0.003823756007477641,
-0.04843166843056679,
0.005921705160290003,
-0.028102071955800056,
0.0008145688334479928,
0.0014944486320018768,
0.0715591162443161,
-0.018526315689086914,
-0.04877455160021782,
0.025761641561985016,
-0.005515044555068016,
0.05099094286561012,
0.0157304797321558,
-0.031700413674116135,
0.003964731469750404,
0.0004577959480229765,
0.011399737559258938,
0.01080375351011753,
0.07325011491775513,
-0.017341047525405884,
-0.029414094984531403,
0.01655598171055317,
-0.010677889920771122,
0.038010988384485245,
-0.03680122643709183,
-0.010967399924993515,
0.03527575358748436,
0.034466084092855453,
0.016621645539999008,
0.002844659611582756,
0.017473740503191948,
-0.012887636199593544,
0.00695400033146143,
-0.02025379240512848,
-0.01101301982998848,
-0.03522538021206856,
-0.025610223412513733,
0.036017920821905136,
0.02495878003537655,
0.004393869079649448,
0.009644368663430214,
0.04574497044086456,
-0.005039413459599018,
0.013067803345620632,
-0.005171450320631266,
-0.03008001483976841,
0.05172246694564819,
-0.0427771620452404,
-0.018651826307177544,
0.01270175352692604,
-0.013996437191963196,
0.022171301767230034,
-0.0047603813000023365,
-0.025876743718981743,
-0.014695190824568272,
0.04080342501401901,
-0.04557114094495773,
0.033947285264730453,
-0.01582649163901806,
0.04706505686044693,
-0.024342114105820656,
-0.03888363018631935,
-0.010068717412650585,
-0.0010946022812277079,
0.02014448679983616,
-0.0032332781702280045,
-0.0042848410084843636,
0.015736490488052368,
0.04573669284582138,
0.028686096891760826,
-0.0020992420613765717,
0.03143055737018585,
0.019252022728323936,
0.0006213434389792383,
0.011121991090476513,
-0.0046434784308075905,
-0.03133548051118851,
0.02171866036951542,
-0.05014839023351669,
0.028564412146806717,
-0.025845371186733246,
-0.02554350718855858,
0.017908750101923943,
-0.0250846017152071,
0.011733753606677055,
-0.03007114678621292,
-0.01903265155851841,
-0.009832808747887611,
-0.006101836916059256,
0.011869734153151512,
0.0030711512081325054,
0.00042778579518198967,
0.005994328297674656,
0.029945889487862587,
0.0329224057495594,
0.028071237727999687,
-0.011475932784378529,
-0.07975375652313232,
-0.03828277066349983,
-0.044375624507665634,
-0.048639822751283646,
0.008425622247159481,
-0.01130619551986456,
-0.03240161016583443,
0.015122565440833569,
-0.03543597459793091,
0.037724170833826065,
-0.005326284095644951,
0.014596540480852127,
-0.0093060452491045,
0.07827690988779068,
0.004412203561514616,
0.028500957414507866,
0.026544077321887016,
0.058349452912807465,
0.09360042214393616,
0.006649903487414122,
-0.03438028320670128,
-0.03780166432261467,
0.02337491139769554,
-0.029129890725016594,
0.00404849648475647,
-0.02692890167236328,
0.006838534958660603,
-0.005537327844649553,
-0.009630993939936161,
0.03821231424808502,
0.039501141756772995,
0.004243038594722748,
0.023248296231031418,
0.03217928856611252,
-0.007332710083574057,
-0.04393027350306511,
0.015447098761796951,
0.0120535958558321,
-0.00569423520937562,
0.026807766407728195,
-0.021935157477855682,
0.027661453932523727,
-0.008406319655478,
0.006871040444821119,
0.01729864999651909,
0.01629682444036007,
0.006342362612485886,
0.020703932270407677,
-0.03639046847820282,
-0.005877206567674875,
0.011924980208277702,
-0.0364714115858078,
-0.010687233880162239,
0.0010315318359062076,
0.027268201112747192,
0.0007011718116700649,
-0.005799375008791685,
0.054363466799259186,
0.02133212611079216,
0.017895588651299477,
0.016592683270573616,
0.007345786318182945,
-0.06615020334720612,
-0.018312741070985794,
-0.017254440113902092,
0.0002607980277389288,
-0.00005300963675836101,
0.023114079609513283,
0.019182289019227028,
0.018141970038414,
0.02761184424161911,
-0.007686259690672159,
-0.013676639646291733,
0.016914399340748787,
0.013591843657195568,
-0.030147871002554893,
0.0029120075050741434,
-0.035451747477054596,
0.01894363947212696,
-0.02973851002752781,
0.05004792660474777,
-0.034402817487716675,
0.02183040976524353,
0.010517618618905544,
0.006501591298729181,
-0.0026809091214090586,
-0.03484141081571579,
-0.03362010791897774,
0.003305616555735469,
0.015932776033878326,
-0.03306953236460686,
0.008120044134557247,
0.07591425627470016,
0.032928161323070526,
0.017741309478878975,
0.03870706632733345,
-0.025819087401032448,
-0.03433486446738243,
-0.05353516712784767,
0.060732707381248474,
-0.03586094453930855,
-0.019273260608315468,
0.009442958049476147,
-0.008296644315123558,
0.035239215940237045,
0.02500441111624241,
-0.044534556567668915,
0.00958850234746933,
-0.029165906831622124,
0.01456691324710846,
0.028594883158802986,
-0.016665300354361534,
-0.0012762641999870539,
0.0011450278107076883,
-0.016521461308002472,
0.023024220019578934,
-0.03080223873257637,
0.03097778558731079,
0.060484156012535095,
-0.013564308173954487,
0.0052908482030034065,
0.025706389918923378,
0.0022080037742853165,
0.011289139278233051,
0.011318814940750599,
-0.026489607989788055,
-0.022534219548106194,
-0.00664180563762784,
0.024214239791035652,
-0.005753892939537764,
-0.02627544105052948,
-0.04282168298959732,
0.008356350474059582,
-0.005888012703508139,
0.009827894158661366,
-0.018860166892409325,
0.029232501983642578,
-0.009983216412365437,
-0.03450622037053108,
-0.025775272399187088,
0.010606286115944386,
-0.04723631590604782,
-0.006621456705033779,
-0.004686824511736631,
-0.0162839125841856,
0.007554915267974138,
0.0517512746155262,
-0.021460751071572304,
0.011569160968065262,
-0.0006177091272547841,
0.03795508295297623,
-0.023453909903764725,
-0.011040070094168186,
0.025565046817064285,
0.011949530802667141,
0.08495767414569855,
-0.034371450543403625,
0.012078113853931427,
0.040601834654808044,
-0.04962138459086418,
-0.04857104644179344,
0.06731300801038742,
-0.024630624800920486,
0.03244677186012268,
0.03057902678847313,
-0.017182018607854843,
-0.017187032848596573,
0.0898841992020607,
-0.020179297775030136,
0.014398750849068165,
0.04604076221585274,
-0.003117014653980732,
-0.04262304678559303,
0.024678321555256844,
-0.024620909243822098,
-0.0065926541574299335,
0.00021706518600694835,
0.025327298790216446,
0.004797621164470911,
-0.033839937299489975,
0.03254672512412071,
-0.03725568577647209,
-0.02165934629738331,
0.01370469480752945,
0.019691117107868195,
-0.011221883818507195,
0.041176483035087585,
0.05125321075320244,
-0.02511022426187992,
0.03784468024969101,
0.004163636360317469,
0.004605400376021862,
-0.10516662150621414,
0.008840233087539673,
-0.0023438686039298773,
-0.0031652043107897043,
0.017943264916539192,
-0.03974907472729683,
0.021213624626398087,
0.03908959776163101,
-0.039520829916000366,
-0.0014922141563147306,
-0.06400544941425323,
-0.048575226217508316,
-0.05833479017019272,
-0.016430635005235672,
-0.002435367088764906,
0.05799819901585579,
0.021479658782482147,
0.05175113305449486,
0.05995532125234604,
0.009958968497812748,
-0.03745044767856598,
-0.015076999552547932,
0.0024347598664462566,
0.015416807495057583,
-0.013195374049246311,
-0.004383258055895567,
0.05190523713827133,
-0.03772728517651558,
0.009473067708313465,
0.038649335503578186,
-0.030654218047857285,
0.012511198408901691,
0.014372706413269043,
0.05187615752220154,
0.021249208599328995,
0.006587481591850519,
0.013098516501486301,
-0.02687894180417061,
0.006026802584528923,
0.06133776158094406,
-0.011678945273160934,
0.003413959639146924,
-0.015986500307917595,
0.024582821875810623,
0.00636599725112319,
-0.015177477151155472,
-0.004125446546822786,
0.008071874268352985,
0.0051240501925349236,
-0.05915910378098488,
0.0012077991850674152,
0.02767825312912464,
0.02772369049489498,
-0.03905660659074783,
-0.010709850117564201,
-0.02353428490459919,
-0.007928265258669853,
0.018171263858675957,
0.006441435776650906,
-0.0021206114906817675,
-0.002816425170749426,
-0.0437370203435421,
-0.023418806493282318,
-0.012317010201513767,
-0.0014450115850195289,
0.0018208082765340805,
-0.02903728000819683,
-0.015504945069551468,
0.02001221477985382,
0.045424290001392365,
-0.007781826891005039,
-0.03432517126202583,
-0.010176494717597961,
0.06518574804067612,
0.002113534603267908,
0.043205924332141876,
-0.002967589069157839,
-0.019841477274894714,
-0.02862863801419735,
-0.030994698405265808,
0.0038436539471149445,
-0.020149696618318558,
0.04118134081363678,
-0.04734865576028824,
-0.013225951232016087,
0.005604540463536978,
-0.02731030248105526,
0.03797074034810066,
-0.045285411179065704,
-0.007289163302630186,
0.026204507797956467,
-0.009527708403766155,
-0.016049370169639587,
-0.03124101832509041,
-0.022323427721858025,
-0.03385807201266289,
-0.05625586584210396,
-0.04800884425640106,
-0.009205378592014313,
-0.01652621477842331,
0.019908051937818527,
0.015194378793239594,
0.0009399546543136239,
-0.03841765597462654,
-0.00427769822999835,
-0.02585114724934101,
0.0523180291056633,
-0.0012917066924273968,
0.008338351733982563,
0.04631241783499718,
-0.0013190164463594556,
0.012464548461139202,
0.03910166770219803,
0.0005434385384432971,
-0.059792060405015945,
0.013944598846137524,
-0.00928723718971014,
0.046736299991607666,
-0.004701714497059584,
-0.040718913078308105,
0.01740756630897522,
-0.04961247742176056,
0.002831702120602131,
0.028687434270977974,
-0.040638189762830734,
0.0023403200320899487,
0.038192104548215866,
0.033049967139959335,
0.057511813938617706,
-0.003305021207779646,
0.03805919736623764,
0.03372422605752945,
0.06236632168292999,
-0.02941107377409935,
0.045110877603292465,
-0.005349759943783283,
0.022603550925850868,
0.03748537600040436,
-0.00023114895157050341,
-0.006933551747351885,
0.019304201006889343,
0.029372984543442726,
0.03108757548034191,
0.008260737173259258,
-0.03342839330434799,
0.006957645993679762,
-0.058845385909080505,
0.04585817828774452,
0.0688367635011673,
-0.015408998355269432,
0.0777585357427597,
-0.017942318692803383,
0.02318952977657318,
0.014388179406523705,
-0.016411181539297104,
-0.041839614510536194,
0.0075558628886938095,
-0.005033313296735287,
0.032481707632541656,
-0.024390334263443947,
-0.015032665804028511,
0.0192791186273098,
0.013530035503208637,
0.04859156906604767,
-0.05495825782418251,
0.013021964579820633,
-0.01306699588894844,
-0.013125956989824772,
-0.022464245557785034,
-0.02328135445713997,
-0.03711903095245361,
-0.013897719793021679,
0.015104175545275211,
0.03578678146004677,
0.013499952852725983,
0.00308269658125937,
-0.025645136833190918,
0.009730222634971142,
0.047293536365032196,
-0.052540816366672516,
-0.006877245381474495,
-0.04167475551366806,
-0.0012483166065067053,
-0.01747286505997181,
0.003846031380817294
] |
<p>I apologize if I am missing something obvious, but I am in my first class with tensors and I am still learning the notation. I am running into a problem with the transformation of the transformation of the four-tensor for electromagnetism that is given by</p>
<p>$$
F^{\mu \nu} =
\left[
\matrix
{
0 & - \cal{E}_x/c & - \cal{E}_y /c & - \cal{E}_z /c \\
\cal{E}_x/c & 0 & -B_z & B_y \\
\cal{E}_y/c & B_z & 0 & -B_x \\
\cal{E}_z/c & -B_y & B_x & 0
}
\right]
$$</p>
<p>And the Lorentz transformation of this tensor is given by</p>
<p>$$
F^{' \mu \nu} = \sum\limits^3_{\alpha, \beta = 0}{\Lambda^\mu_\alpha \Lambda^\nu_\beta F^{\alpha \beta}}
$$</p>
<p>From what I understand, this is just a single sum and $\alpha = \beta$ over every iteration; however, by this $F^{00} = F^{11} = F^{22} = F^{33} = 0$, so the transformation of any element would result in a zero.</p>
<p>Where have I gone wrong here?</p> | 2,875 | [
-0.026412244886159897,
0.00980946235358715,
-0.021633712574839592,
0.0001535118935862556,
0.06726375222206116,
0.0247572623193264,
-0.038925591856241226,
-0.031734269112348557,
-0.0002249120152555406,
-0.008627001196146011,
0.04054135084152222,
0.009441121481359005,
0.07091972976922989,
0.012992003001272678,
0.038107339292764664,
-0.016918683424592018,
-0.026155909523367882,
0.0024396684020757675,
-0.023497076705098152,
-0.036189187318086624,
0.0014877052744850516,
0.016451027244329453,
-0.022869817912578583,
-0.0005558601696975529,
-0.009939093142747879,
0.02716519497334957,
0.005536062177270651,
-0.01691289059817791,
0.012145062908530235,
0.041470788419246674,
0.00026654466637410223,
-0.0405212864279747,
0.013349849730730057,
0.011486141942441463,
0.019496038556098938,
-0.0009926942875608802,
-0.03864070773124695,
-0.04867953434586525,
0.0024990043602883816,
0.00029042409732937813,
-0.032261740416288376,
-0.02770700864493847,
-0.014587273821234703,
0.0446697399020195,
-0.011577439494431019,
-0.009836101904511452,
0.02287408895790577,
0.02817094512283802,
0.0600176602602005,
-0.02773439511656761,
0.10124897211790085,
0.03144162520766258,
0.031983520835638046,
0.0066691250540316105,
-0.02544298581779003,
-0.03711388632655144,
0.04812623932957649,
0.03164289891719818,
0.04522630199790001,
-0.025450274348258972,
-0.016611285507678986,
-0.04740993678569794,
0.0039791446179151535,
-0.02618437260389328,
-0.03894077613949776,
0.050011370331048965,
-0.00835060328245163,
0.00554405665025115,
0.050864290446043015,
-0.017608221620321274,
-0.006156971212476492,
0.029880112037062645,
0.03059452399611473,
-0.01814933493733406,
0.005573144182562828,
-0.0008002641261555254,
0.018848927691578865,
0.046986665576696396,
0.05693991854786873,
0.026038561016321182,
-0.05722967907786369,
0.021157072857022285,
0.008667988702654839,
0.0075267706997692585,
-0.013717924244701862,
-0.03594261035323143,
0.06385190784931183,
-0.006760442163795233,
0.03212573379278183,
0.013828307390213013,
0.021737443283200264,
-0.011438796296715736,
0.043191805481910706,
0.015485778450965881,
-0.021609805524349213,
0.02817559242248535,
0.01855350285768509,
0.030022338032722473,
0.017118051648139954,
-0.02323812060058117,
0.007825749926269054,
-0.011368577368557453,
0.022785110399127007,
0.010679278522729874,
0.016722122207283974,
0.03650630638003349,
-0.07349956035614014,
-0.006933108437806368,
0.008038127794861794,
-0.04425765201449394,
-0.015479305759072304,
0.0005816130433231592,
-0.03395698219537735,
0.0013842785265296698,
0.030735203996300697,
-0.04746643453836441,
0.005020303186029196,
0.002017418621107936,
0.027019275352358818,
0.04040775075554848,
0.014420886524021626,
0.0008025236311368644,
0.046554990112781525,
-0.008657009340822697,
-0.10110007971525192,
0.007320346310734749,
0.014097197912633419,
-0.01624741032719612,
-0.025943465530872345,
0.027468500658869743,
-0.0072587658651173115,
-0.04551888257265091,
-0.01161595806479454,
-0.014740105718374252,
0.00007159652159316465,
-0.00619080476462841,
-0.050396550446748734,
-0.07017223536968231,
0.021664941683411598,
-0.01987227238714695,
-0.013140073977410793,
-0.08280832320451736,
-0.02015509642660618,
0.02749471366405487,
0.08009321242570877,
0.0006836116081103683,
0.01690920628607273,
-0.024421732872724533,
0.04619475454092026,
0.005092173349112272,
0.025694219395518303,
0.01131665613502264,
-0.06327763944864273,
-0.00048934540245682,
-0.0020394136663526297,
-0.03447231277823448,
0.010679262690246105,
0.010439390316605568,
0.0031219031661748886,
0.014074588194489479,
0.06405268609523773,
0.03575142100453377,
0.03217577934265137,
0.048934485763311386,
0.014569061808288097,
-0.022341527044773102,
0.05292583629488945,
0.02774536795914173,
0.053214628249406815,
0.023715967312455177,
-0.00424573477357626,
0.015869395807385445,
-0.023388054221868515,
0.04925353825092316,
0.06805704534053802,
-0.031316522508859634,
-0.029172392562031746,
-0.017714429646730423,
0.008713452145457268,
-0.027578314766287804,
-0.0439985953271389,
-0.04434196650981903,
0.006138337776064873,
0.007276508957147598,
-0.012667332775890827,
0.049005232751369476,
-0.018800795078277588,
-0.034779809415340424,
0.02246849238872528,
-0.03933555260300636,
-0.006745764520019293,
-0.04829607158899307,
0.019983839243650436,
0.03109787590801716,
-0.044704098254442215,
0.04737208038568497,
-0.013586346991360188,
0.03595290705561638,
0.003236433258280158,
-0.012142110615968704,
-0.016544368118047714,
0.0056429049000144005,
0.007454735692590475,
0.015480916947126389,
0.006157268304377794,
0.03252171352505684,
0.04718097671866417,
-0.011016304604709148,
0.03533053770661354,
-0.01109138410538435,
0.021777423098683357,
-0.026340540498495102,
0.005399048328399658,
0.003361600684002042,
0.006806043442338705,
0.02869528904557228,
-0.01937253028154373,
-0.0057989200577139854,
-0.021016927435994148,
0.013027713634073734,
-0.032941918820142746,
0.04753797873854637,
0.06668324023485184,
-0.0017001666128635406,
0.027924668043851852,
0.04160064831376076,
0.012717527337372303,
0.044012270867824554,
0.002002575434744358,
-0.03462236374616623,
-0.03706907853484154,
0.030610080808401108,
-0.014040541835129261,
0.006427984684705734,
-0.03756595030426979,
-0.008989100344479084,
0.051890067756175995,
0.01445806585252285,
0.009515293873846531,
0.04271625727415085,
0.003976824227720499,
-0.00793401151895523,
-0.009815752506256104,
0.0028596511110663414,
0.02857607789337635,
-0.007918366231024265,
0.006577728316187859,
-0.008278696797788143,
0.029287153854966164,
0.006021432112902403,
0.0025462426710873842,
0.02444460801780224,
-0.0003055680135730654,
-0.011264108121395111,
-0.021049739792943,
0.009635952301323414,
0.019185489043593407,
-0.015528744086623192,
0.032469939440488815,
0.07408738136291504,
0.035990167409181595,
-0.02590065263211727,
-0.006912177428603172,
0.018267005681991577,
-0.014166837558150291,
-0.025349397212266922,
0.0470125712454319,
0.0068218945525586605,
0.018886668607592583,
-0.02474847622215748,
0.00904766097664833,
0.031414151191711426,
-0.021400289610028267,
-0.023331478238105774,
0.031047673895955086,
0.00010305661999154836,
0.03517301753163338,
0.0029473176691681147,
-0.040150899440050125,
-0.02199511043727398,
-0.006020643748342991,
0.024464767426252365,
0.04271118715405464,
0.02944912202656269,
-0.07175017148256302,
0.012882874347269535,
-0.06063621863722801,
-0.03118729218840599,
0.025269629433751106,
0.0029282765462994576,
-0.02811012603342533,
0.015339946374297142,
0.0004880246124230325,
-0.02760506607592106,
-0.020676925778388977,
0.015614143572747707,
-0.001647016266360879,
-0.030584441497921944,
0.029601983726024628,
0.08436287194490433,
0.00024295637558680028,
-0.013745563104748726,
0.0020101256668567657,
-0.012938572093844414,
-0.039584457874298096,
-0.00492217019200325,
-0.03770465403795242,
-0.019961584359407425,
0.006174453534185886,
0.028278550133109093,
0.027323616668581963,
0.012119011022150517,
-0.0047080665826797485,
-0.06523679941892624,
-0.040252942591905594,
-0.03126198798418045,
-0.0012838407419621944,
0.022658150643110275,
-0.006653741467744112,
-0.03706498444080353,
0.06095254048705101,
0.054466571658849716,
-0.02908533439040184,
-0.01768163964152336,
0.03919810801744461,
0.007433731574565172,
-0.06823115050792694,
-0.009730166755616665,
0.034048374742269516,
-0.01939774490892887,
-0.0015133046545088291,
0.00933933537453413,
0.02667061984539032,
0.05435242876410484,
0.03225257992744446,
-0.0005562940496020019,
0.005128795746713877,
0.007157756015658379,
0.005380419548600912,
0.054509956389665604,
0.029690928757190704,
0.025953559204936028,
0.03832920268177986,
0.01667788252234459,
0.04303295165300369,
0.023685114458203316,
-0.044143300503492355,
0.0027744555845856667,
0.015469787642359734,
0.01207597367465496,
-0.021686427295207977,
0.03731142356991768,
0.001342094736173749,
-0.021097825840115547,
-0.02465108595788479,
0.009019547142088413,
0.02717052586376667,
-0.06921585649251938,
0.011692769825458527,
0.0404774434864521,
0.006108493078500032,
-0.052945125848054886,
-0.02439369261264801,
-0.02283596619963646,
-0.02881954051554203,
0.014563025906682014,
-0.007177919615060091,
-0.0033979760482907295,
0.03738942742347717,
0.053482040762901306,
0.05246671289205551,
-0.02078898996114731,
-0.024847541004419327,
-0.013161134906113148,
-0.04690961167216301,
-0.020217979326844215,
-0.029492070898413658,
0.04055598005652428,
0.04557974636554718,
0.013495584949851036,
0.028101323172450066,
0.020999707281589508,
-0.0028148647397756577,
-0.014340760186314583,
-0.09890136867761612,
0.04725254699587822,
0.004273710306733847,
-0.024759158492088318,
-0.020988695323467255,
0.005434960592538118,
0.01709616743028164,
-0.026453502476215363,
-0.02161969058215618,
-0.035276852548122406,
-0.005814951378852129,
-0.026638280600309372,
0.010731241665780544,
-0.023345062509179115,
-0.01081045251339674,
-0.02527928352355957,
0.042218830436468124,
0.016520684584975243,
-0.008725828491151333,
-0.0037798164412379265,
0.0189250148832798,
-0.02955438941717148,
0.019189834594726562,
-0.02827310562133789,
0.05055408552289009,
0.024324284866452217,
-0.0051703788340091705,
0.00523812510073185,
0.00629202276468277,
-0.03870123252272606,
-0.00903596542775631,
-0.0006679900106973946,
0.045198697596788406,
0.02203625626862049,
-0.02623050846159458,
-0.010144826024770737,
-0.03718745708465576,
-0.03804522380232811,
-0.012892159633338451,
0.05781951919198036,
0.04051384702324867,
0.02698454074561596,
0.03116241842508316,
0.024749862030148506,
0.0030972734093666077,
0.0477212630212307,
0.08361372351646423,
-0.01173974946141243,
-0.0296150054782629,
-0.05215312913060188,
0.006287779193371534,
-0.015916233882308006,
0.0009619028423912823,
0.005222307983785868,
-0.006857424974441528,
-0.0019753440283238888,
-0.07350552827119827,
0.018828395754098892,
-0.019380910322070122,
0.027130180969834328,
0.030539827421307564,
0.011992945335805416,
-0.007626767735928297,
0.014651230536401272,
0.013683860190212727,
0.002305401489138603,
0.02601650357246399,
0.04607710614800453,
-0.004658008459955454,
-0.033573608845472336,
-0.03022347204387188,
-0.012061871588230133,
-0.018167423084378242,
0.046289414167404175,
-0.011379171162843704,
0.015551312826573849,
-0.04247255623340607,
-0.04158031940460205,
0.04589454457163811,
-0.07158879935741425,
0.05282909795641899,
0.008845629170536995,
0.007644931320101023,
-0.02250995673239231,
-0.016320059075951576,
-0.03520170599222183,
0.04625312611460686,
0.014360180124640465,
0.058966975659132004,
-0.03858121484518051,
0.021204069256782532,
-0.007017224095761776,
0.006600314285606146,
-0.002297587925568223,
0.019163426011800766,
-0.02049236372113228,
-0.0008622388704679906,
0.0038593553472310305,
0.04259756579995155,
-0.03323984146118164,
-0.08865117281675339,
-0.01297068689018488,
-0.0055649057030677795,
-0.008609195239841938,
0.00963281188160181,
-0.021022671833634377,
-0.06976905465126038,
0.044997330754995346,
0.004722300451248884,
-0.0077435849234461784,
-0.0046457513235509396,
-0.059837888926267624,
0.04181237518787384,
-0.004680757410824299,
0.026522694155573845,
0.043385401368141174,
0.018338259309530258,
-0.035960614681243896,
0.025393769145011902,
-0.02860167808830738,
-0.006160504650324583,
-0.006376806180924177,
0.04477035999298096,
-0.007810103241354227,
0.040357328951358795,
-0.0027623947244137526,
0.07262467592954636,
-0.051301900297403336,
0.014870318584144115,
-0.02321963757276535,
0.02659754641354084,
0.013146228156983852,
0.004150427412241697,
-0.01990521512925625,
-0.001953881699591875,
-0.0006789166945964098,
-0.021842002868652344,
-0.041583579033613205,
-0.03629055619239807,
0.046388886868953705,
-0.028507910668849945,
-0.0065407101064920425,
0.025026198476552963,
-0.002263979520648718,
0.01859193854033947,
0.005076163914054632,
0.01388612762093544,
-0.00016301039431709796,
-0.10049726068973541,
0.028488889336586,
-0.019136056303977966,
-0.043925851583480835,
0.0017728855600580573,
0.0066206487827003,
-0.041359301656484604,
-0.017000757157802582,
-0.00436603045091033,
0.018969900906085968,
-0.029320845380425453,
-0.02640087902545929,
0.03176484629511833,
0.016248997300863266,
-0.0538419634103775,
-0.0714343711733818,
0.018389182165265083,
0.008608527481555939,
0.001907610916532576,
-0.0005302426288835704,
-0.0033716598991304636,
-0.0259492639452219,
-0.03863191604614258,
0.002542642178013921,
0.052050139755010605,
-0.030121149495244026,
-0.029493143782019615,
0.021422026678919792,
0.041484419256448746,
0.07876846194267273,
0.002953046467155218,
-0.02060270495712757,
0.021423257887363434,
-0.015210948884487152,
-0.03585880622267723,
-0.00020556348317768425,
0.04560057446360588,
-0.011553428135812283,
-0.04852941259741783,
0.01916911080479622,
-0.01322061289101839,
0.022199705243110657,
-0.0028791348449885845,
0.0032683545723557472,
0.020618092268705368,
0.04738374799489975,
-0.0027541923336684704,
-0.012075300328433514,
0.012162632308900356,
0.026477690786123276,
-0.007062594406306744,
-0.03432649374008179,
-0.009332127869129181,
-0.02394627034664154,
-0.056081514805555344,
0.031983502209186554,
-0.01470853015780449,
0.0028760831337422132,
-0.007157552987337112,
0.08949898928403854,
-0.01030742283910513,
0.006147906184196472,
0.00023178133415058255,
-0.026423390954732895,
-0.007655951660126448,
0.06180167198181152,
-0.0034319960977882147,
0.013950314372777939,
-0.010707502253353596,
-0.02552340179681778,
-0.01871829479932785,
-0.053250882774591446,
0.07810769230127335,
0.10092860460281372,
-0.02825131081044674,
0.04807780683040619,
0.06165817007422447,
0.012027165852487087,
0.015560658648610115,
0.004631932824850082,
-0.008406720124185085,
0.04086536914110184,
-0.021275291219353676,
0.026442354544997215,
0.009736068546772003,
-0.03159027919173241,
0.024114537984132767,
0.008299585431814194,
-0.011530579067766666,
-0.010108882561326027,
-0.003225943772122264,
0.03037755936384201,
-0.01066084485501051,
0.001950511708855629,
-0.06762173771858215,
0.01954009383916855,
-0.02613762393593788,
0.041592419147491455,
0.012822658754885197,
-0.017175132408738136,
0.052121058106422424,
0.015903888270258904,
0.012812627479434013,
-0.029905512928962708,
-0.03971362113952637,
-0.04246581345796585,
-0.008468052372336388,
0.045556534081697464,
-0.0029254078399389982,
-0.006738442461937666,
-0.005637709982693195,
0.08550706505775452,
-0.0004402844060678035,
0.0443209744989872,
-0.02319442667067051,
-0.04585912823677063,
-0.01617869921028614,
-0.04030636325478554,
-0.046523381024599075,
0.061337072402238846,
-0.004552578087896109,
-0.012077663093805313,
-0.004161343444138765,
-0.03251882269978523,
0.029687613248825073,
0.032370101660490036,
0.033052075654268265,
-0.03155311569571495,
0.024545585736632347,
-0.003459966043010354,
-0.007826936431229115,
-0.010218612849712372,
-0.014266513288021088,
0.11833114176988602,
0.0684560090303421,
0.04209287464618683,
-0.04324667528271675,
0.008950458839535713,
-0.019448192790150642,
-0.029138263314962387,
-0.036656297743320465,
0.04173647612333298,
-0.038046639412641525,
0.0387868694961071,
-0.018898211419582367,
0.0650964006781578,
0.006738724187016487,
-0.002674838062375784,
0.024949604645371437,
-0.03082241117954254,
-0.011462993919849396,
0.025031760334968567,
0.05298294126987457,
0.004996212664991617,
-0.004598097410053015,
-0.08160053938627243,
0.017731696367263794,
-0.06704612076282501,
0.030552895739674568,
-0.052516765892505646,
-0.006616597529500723,
0.007580616511404514,
-0.0044787246733903885,
-0.02735079638659954,
0.030542047694325447,
0.011198977008461952,
-0.0272578876465559,
-0.006270209327340126,
0.042018719017505646,
0.04167637601494789,
0.0012699045473709702,
0.004781476687639952,
0.05129782482981682,
0.008239347487688065,
0.010421770624816418,
0.03743676841259003,
0.014796081930398941,
-0.017850778996944427,
0.015985703095793724,
-0.043519891798496246,
0.06776571273803711,
-0.04382223263382912,
-0.007088769227266312,
0.01577444188296795,
0.019495520740747452,
-0.006592584773898125,
-0.08312313258647919,
0.0212879478931427,
-0.014849935658276081,
0.022078819572925568,
-0.006410952657461166,
0.019434675574302673,
-0.009577794000506401,
0.03147157281637192,
-0.008564479649066925,
-0.0473930649459362,
-0.012642930261790752,
0.010515292175114155,
-0.023695651441812515,
0.006173374596983194,
0.033021386712789536,
0.00681950431317091,
0.0030829000752419233,
-0.02579815872013569,
-0.028341801837086678,
-0.01980612985789776,
-0.008303250186145306,
-0.008629919029772282,
-0.0015324729029089212,
0.0361117385327816,
-0.028581995517015457,
-0.036523252725601196,
-0.018814928829669952,
-0.06826985627412796,
-0.003303173230960965,
0.03892907127737999,
-0.006322239059954882,
-0.016889657825231552,
-0.022825637832283974,
-0.010790806263685226,
0.0699601098895073,
-0.04206617549061775,
-0.016199391335248947,
0.011655143462121487,
0.01605529710650444,
0.01969676837325096,
-0.03282313793897629,
-0.02537175454199314,
0.002647257409989834,
-0.022206341847777367,
0.0170297771692276,
-0.02460511587560177,
0.026648614555597305,
0.037305641919374466,
0.00591877568513155,
0.0023414911702275276,
0.06556221097707748,
-0.011021937243640423,
-0.025010965764522552,
0.008862930350005627,
-0.02117335982620716,
0.027089232578873634,
0.034139715135097504,
0.015502889640629292,
-0.06336838006973267,
0.0048211426474153996,
-0.04839378222823143,
-0.02268369309604168,
0.018405798822641373,
0.020926158875226974,
-0.03541167452931404,
-0.007217406760901213,
-0.041491564363241196,
0.022544125095009804,
-0.04026971384882927,
0.025823654606938362,
-0.020184369757771492,
0.01488522533327341,
0.015567632392048836,
-0.04009582847356796,
-0.02746177278459072,
0.02977924235165119,
-0.027561170980334282,
-0.024581216275691986,
0.048259835690259933,
0.021637674421072006,
0.008687468245625496,
-0.01467675156891346,
-0.00405462458729744,
0.02645014598965645,
0.034599680453538895,
0.012678293511271477,
-0.01227939035743475,
0.02170543558895588,
0.003986757714301348,
-0.03354699909687042,
0.028836067765951157,
0.02855384349822998,
0.030624156817793846,
0.029183432459831238,
0.006796014495193958,
-0.02342263236641884,
0.06678027659654617,
-0.014869138598442078,
-0.0001980953966267407,
-0.021058721467852592,
-0.045903753489255905,
-0.00163253431674093,
0.015049307607114315,
-0.006446687504649162,
0.001706770621240139,
0.007825559005141258,
-0.031263019889593124,
0.01350045669823885,
-0.008758727461099625,
0.016490010544657707,
-0.00872068665921688,
-0.001634631073102355,
-0.013234477490186691,
0.010873530991375446,
0.032708846032619476,
-0.011804768815636635,
0.07106661051511765,
0.007560732774436474,
-0.001773068681359291,
-0.0060069444589316845,
0.0171967763453722,
-0.06874338537454605,
-0.01732022315263748,
0.01955592632293701,
0.008635183796286583,
0.05211811885237694,
-0.04960065335035324,
0.026856541633605957,
0.051695626229047775,
-0.015588989481329918,
0.0020870028529316187,
-0.023792188614606857,
-0.034125916659832,
0.005595045629888773,
-0.02745114266872406,
0.015620716847479343,
0.03920116648077965,
0.04584023728966713,
0.04442417994141579,
0.0069023859687149525,
0.009968714788556099,
-0.018317649140954018,
-0.03090369701385498,
-0.026763545349240303,
0.036445252597332,
0.005892415996640921,
-0.003359288675710559,
0.015346914529800415,
0.0352594368159771,
-0.037973616272211075,
0.00961883645504713,
-0.03887350857257843,
-0.02724405936896801,
0.017026754096150398,
0.03372708708047867,
0.04016156122088432,
0.06596776843070984,
0.02762794867157936,
0.003291603410616517,
0.00864811334758997,
-0.003729043761268258,
0.0266234390437603,
0.014452814124524593,
-0.023199087008833885,
-0.006504106801003218,
0.03005613200366497,
-0.04095645621418953,
-0.04074513539671898,
-0.006157853174954653,
-0.033376969397068024,
-0.025538984686136246,
-0.024528689682483673,
-0.02026296593248844,
-0.02442045323550701,
-0.043882105499506,
-0.031905706971883774,
-0.04406721517443657,
-0.019109783694148064,
0.04332742840051651,
0.022544855251908302,
0.009157290682196617,
0.010873400606215,
0.006851088721305132,
-0.010774746537208557,
-0.006715178489685059,
0.011454419232904911,
-0.020804692059755325,
-0.03354465588927269,
0.010650412179529667,
0.0003442798915784806,
-0.034011706709861755,
0.020208340138196945,
-0.03871794417500496,
-0.06159456819295883,
0.0007728681666776538,
0.011677480302751064,
-0.01274295523762703,
-0.020404651761054993,
-0.03935965523123741,
0.01976897194981575,
-0.06440772861242294,
0.005712591577321291,
-0.01805579662322998,
-0.034715697169303894,
0.002383600454777479,
-0.009125130251049995,
-0.032330065965652466,
0.037126027047634125,
0.06332465261220932,
-0.04018780216574669,
0.006432913243770599,
-0.013503766618669033,
0.015200333669781685,
0.031058458611369133,
-0.05413525924086571,
0.03141546621918678,
0.039548128843307495,
-0.005490306299179792,
0.0225161574780941,
0.004297174047678709,
-0.011505281552672386,
0.006204513367265463,
-0.0005495951627381146,
0.01620885357260704,
0.010855298489332199,
-0.02774428203701973,
-0.024472244083881378,
0.002705868799239397,
-0.0073674339801073074,
-0.04291480779647827,
0.012467731721699238,
0.0053918748162686825,
-0.0192070621997118,
0.017469046637415886,
-0.03788100183010101,
-0.0782499760389328,
0.000012629844604816753,
-0.0398736335337162,
-0.006249154917895794,
-0.033467549830675125,
-0.006608587224036455,
0.03269660472869873,
-0.03541679307818413,
0.011300013400614262,
0.036083292216062546,
-0.01938123255968094,
-0.01588211953639984,
0.051523543894290924,
-0.040240075439214706,
0.009620501659810543,
0.00585484504699707,
0.009105773642659187,
0.003513930831104517,
-0.03307531774044037,
0.006124594714492559,
0.03547392040491104,
0.008510300889611244,
-0.01689213514328003,
0.005116524640470743,
0.023591235280036926,
-0.04021253436803818,
-0.025460168719291687,
0.00026967693702317774,
0.024754324927926064,
-0.01782875880599022,
-0.015041210688650608,
0.05074870586395264,
0.016221908852458,
-0.022521760314702988,
-0.019842665642499924,
-0.01782243140041828,
0.03890136629343033,
-0.06541213393211365,
0.05642131343483925,
-0.025856155902147293,
-0.007231453433632851,
-0.01083693839609623,
0.04615822061896324,
-0.016724757850170135,
0.05632251873612404,
-0.02387266419827938,
-0.02395228110253811,
-0.06828945130109787,
-0.04917028546333313,
0.0644281655550003,
-0.05437195673584938,
-0.03356531634926796,
0.001945228548720479,
-0.011921294964849949,
0.038672078400850296,
-0.005621803924441338,
-0.027127154171466827,
-0.03550216183066368,
0.016453351825475693,
-0.011528553441166878,
-0.0027394206263124943,
-0.036597173660993576,
-0.028513751924037933,
-0.05283357948064804,
0.028877820819616318,
0.0048594363033771515,
-0.011115911416709423,
-0.008688031695783138,
0.03610225394368172,
0.01462562195956707,
0.0073889996856451035
] |
<p>It's my understanding that Earth's core is hot and molten because of the high pressure from gravity compressing the planet's mass towards the center. How does this heat reconcile with thermodynamics, meaning, would it be possible for all the heat to bleed away into space through infrared radiation etc., such that the Earth eventually had about the same mass in about the same configuration, but was instead cold at the core? Or would it always be the case that as long as the planet holds together, it will be hot at the center due to gravity?</p>
<p>How are these two processes reconciled, meaning, why would there eventually be a "heat death" of the universe so long as there is gravity making masses come together into a form that causes local hot spots (or in larger cases, new suns)? Wouldn't the planet have to fly apart to get much colder, and why would it do that? Is it possible for the mass to stay together while all the energy dissipates (ie temperature eventually goes to zero K)?</p>
<p>[I'm not a physicist, so if I'm way off the rails, please help me understand what's really going on.]</p> | 2,876 | [
-0.016521375626325607,
-0.023030610755085945,
0.00007871341949794441,
-0.01878642849624157,
0.02513178624212742,
0.014330919831991196,
-0.019580943509936333,
-0.038295041769742966,
0.0008534406661055982,
-0.054675955325365067,
-0.013670113869011402,
0.02362695150077343,
0.007808184716850519,
-0.0020628799684345722,
0.03344959020614624,
-0.02030106820166111,
-0.0022824553307145834,
-0.043646104633808136,
0.009433476254343987,
-0.02142234705388546,
-0.014980083331465721,
0.010064126923680305,
-0.010244001634418964,
0.01628740318119526,
-0.05950169637799263,
0.02735193818807602,
0.004560950677841902,
0.017005767673254013,
0.03517182171344757,
0.0691155269742012,
0.021501688286662102,
-0.017197923734784126,
-0.015554429963231087,
0.043647900223731995,
0.03796568140387535,
-0.0025286651216447353,
-0.024002699181437492,
-0.030491363257169724,
-0.043761588633060455,
0.05567999929189682,
-0.046106889843940735,
-0.02722448669373989,
-0.039297595620155334,
0.026185177266597748,
-0.034226834774017334,
-0.006725568324327469,
0.02096458151936531,
-0.018895627930760384,
0.031135715544223785,
-0.05945182964205742,
0.03683830052614212,
-0.009501286782324314,
0.024549009278416634,
0.03332801163196564,
-0.00026608703774400055,
0.00888563971966505,
0.09242795407772064,
0.08450300991535187,
0.014908745884895325,
-0.04774601012468338,
-0.034131575375795364,
0.033682577311992645,
-0.014580165967345238,
-0.011115134693682194,
-0.010113170370459557,
0.06884785741567612,
-0.0051041762344539165,
-0.021525537595152855,
0.028715956956148148,
0.025602057576179504,
0.024464452639222145,
0.01113514881581068,
0.033657100051641464,
-0.021834906190633774,
0.007972669787704945,
-0.02970690093934536,
0.027568692341446877,
0.002989699598401785,
0.03553157299757004,
0.03374667093157768,
-0.015450961887836456,
0.0015025542816147208,
0.022854728624224663,
0.03932848200201988,
0.010274308733642101,
0.04804113879799843,
0.06177534908056259,
-0.00857485830783844,
0.006126951891928911,
0.03646089881658554,
0.0015865314053371549,
0.013460975140333176,
0.021017391234636307,
-0.02478092722594738,
-0.027924669906497,
0.009698045440018177,
-0.013930447399616241,
0.04151955991983414,
0.0017409423599019647,
-0.007006214000284672,
0.03356434032320976,
0.01976667158305645,
0.015798186883330345,
0.05547355115413666,
0.042761821299791336,
-0.017504876479506493,
-0.05631104111671448,
-0.004615023732185364,
0.012728880159556866,
-0.030155489221215248,
-0.05556457117199898,
0.0010303225135430694,
-0.015930160880088806,
-0.03312313184142113,
0.022766118869185448,
-0.03246957063674927,
0.02223895490169525,
-0.041955091059207916,
0.03049725480377674,
0.03165580332279205,
0.022326001897454262,
0.002847242634743452,
0.04068342596292496,
-0.04207717254757881,
-0.04989853873848915,
0.03652578964829445,
0.0490468367934227,
-0.014902929775416851,
-0.04913274943828583,
0.028871579095721245,
-0.03233673796057701,
-0.02224920690059662,
-0.023289872333407402,
-0.029611552134156227,
0.04681985825300217,
-0.022174881771206856,
-0.06008158624172211,
-0.045119062066078186,
0.05923101678490639,
-0.021282538771629333,
-0.04544096440076828,
-0.05241190642118454,
0.024994540959596634,
-0.0012061798479408026,
0.09607702493667603,
-0.002311598975211382,
-0.014613077044487,
-0.021783707663416862,
0.06595797091722488,
0.015999609604477882,
-0.020680628716945648,
-0.028535418212413788,
0.007150879129767418,
-0.05044145882129669,
-0.015344141982495785,
-0.07231952250003815,
0.01227017305791378,
0.023703845217823982,
0.002296128775924444,
-0.03639230504631996,
0.029042838141322136,
-0.009385150857269764,
0.005931091494858265,
0.029629318043589592,
-0.018327366560697556,
-0.012082592584192753,
0.11237375438213348,
0.0293696578592062,
-0.011232447810471058,
0.05323188751935959,
0.051106903702020645,
0.023543955758213997,
0.022581949830055237,
0.04004361480474472,
0.000990802189335227,
-0.030144907534122467,
0.012967395596206188,
-0.04372725263237953,
0.00394471874460578,
0.0032912692986428738,
-0.046533748507499695,
-0.011380665935575962,
0.007468545809388161,
-0.007105342578142881,
0.02058805525302887,
0.07636351883411407,
0.002152422210201621,
-0.03970380127429962,
0.0244955662637949,
-0.026834486052393913,
0.0007270144997164607,
-0.061120565980672836,
0.012242758646607399,
-0.012065344490110874,
0.01250420417636633,
-0.015163525007665157,
0.043187547475099564,
0.052177321165800095,
-0.03693755343556404,
-0.026276906952261925,
0.016774578019976616,
0.02877676673233509,
-0.0006368828471750021,
0.014256591908633709,
0.02324223890900612,
0.0844968631863594,
0.04889891296625137,
0.00181194010656327,
-0.0003255319024901837,
-0.006841651163995266,
-0.04783853515982628,
-0.013871588744223118,
-0.014567405916750431,
0.029619907960295677,
-0.012487352825701237,
-0.008411147631704807,
0.005964804440736771,
0.026013078168034554,
0.01199386827647686,
-0.013546952977776527,
-0.02017066814005375,
0.10707929730415344,
-0.00966085959225893,
0.010156359523534775,
-0.02423109859228134,
0.061693500727415085,
0.006550380494445562,
0.002897387370467186,
-0.023372184485197067,
-0.011062519624829292,
-0.07671186327934265,
0.010998470708727837,
0.04050289839506149,
0.014110107906162739,
-0.020380331203341484,
0.019217917695641518,
0.03902159631252289,
0.06649512052536011,
0.01560122612863779,
-0.013608957640826702,
-0.017702292650938034,
0.0088665671646595,
0.014972135424613953,
-0.02226627804338932,
0.03150247037410736,
0.04940032586455345,
0.019516192376613617,
0.03050597757101059,
0.00171545404009521,
-0.005361285991966724,
-0.03030778467655182,
0.03898700699210167,
0.013286035507917404,
0.01559960376471281,
-0.015974808484315872,
-0.01330566219985485,
0.01925523765385151,
-0.009523274376988411,
0.022077713161706924,
-0.0021700765937566757,
0.004488952457904816,
0.0027769028674811125,
-0.08411669731140137,
-0.03316715732216835,
-0.0032811155542731285,
0.024178534746170044,
-0.009592924267053604,
0.0006039642612449825,
0.022772928699851036,
-0.03889113664627075,
-0.0007778312428854406,
0.0017049001762643456,
-0.01032299268990755,
-0.05638616159558296,
-0.013556710444390774,
0.0063672554679214954,
-0.02126927860081196,
0.02107281982898712,
-0.03761058300733566,
-0.034901656210422516,
-0.03738865628838539,
-0.036667779088020325,
-0.015573561191558838,
0.031162813305854797,
-0.04887628182768822,
-0.00391383795067668,
0.0008548086043447256,
-0.01815187558531761,
0.04278793931007385,
0.01977359689772129,
0.053984384983778,
0.01366308331489563,
-0.0032279021106660366,
-0.062465786933898926,
0.011419408954679966,
-0.004473199602216482,
0.01447824202477932,
-0.024387026205658913,
0.045471228659152985,
0.06363227218389511,
-0.06812620162963867,
-0.02092690020799637,
0.01425138022750616,
-0.07480040192604065,
-0.02850073017179966,
-0.03045990690588951,
-0.0034964282531291246,
0.0301691684871912,
-0.012301933020353317,
0.02671085298061371,
0.05168154090642929,
-0.07343434542417526,
-0.02002709172666073,
-0.029357587918639183,
-0.030344678089022636,
0.027114976197481155,
-0.026190688833594322,
0.022993721067905426,
-0.01663825288414955,
-0.04180159047245979,
0.03583222255110741,
0.03890594094991684,
0.006654202938079834,
-0.008187212981283665,
0.02768721990287304,
-0.006045064888894558,
0.004238350782543421,
0.03643454238772392,
-0.015103574842214584,
0.005901950877159834,
-0.017647428438067436,
0.04043637216091156,
0.02945423685014248,
0.02838287129998207,
0.0010310503421351314,
-0.028955668210983276,
0.018626512959599495,
-0.008345014415681362,
0.028470801189541817,
0.019738061353564262,
-0.009161069057881832,
-0.007607618812471628,
0.03455642983317375,
-0.021724533289670944,
0.05009256303310394,
0.024920176714658737,
-0.06024598330259323,
0.019568100571632385,
0.007064593490213156,
0.013525081798434258,
-0.06312475353479385,
0.03972355276346207,
-0.008835278451442719,
0.0013657583622261882,
0.020258797332644463,
0.03133879229426384,
0.08454286307096481,
0.012171315029263496,
-0.020804589614272118,
0.0038447347469627857,
0.04080604389309883,
-0.0046564508229494095,
-0.016707155853509903,
0.009569942951202393,
0.00007269473280757666,
0.021636411547660828,
0.009018316864967346,
0.01003293041139841,
0.035987336188554764,
0.02392669953405857,
0.0339801199734211,
0.00012165719090262428,
-0.022551298141479492,
-0.006192729342728853,
-0.07409092783927917,
-0.013954647816717625,
-0.001286108628846705,
0.054170992225408554,
0.015879612416028976,
0.0414445586502552,
0.04992194101214409,
0.0325174406170845,
0.038211822509765625,
0.024595314636826515,
-0.10571299493312836,
0.020116368308663368,
-0.052441634237766266,
-0.013408149592578411,
-0.016146985813975334,
0.0200762078166008,
-0.006502453703433275,
-0.041707418859004974,
-0.01698850840330124,
-0.0007318920688703656,
0.0008802875527180731,
-0.053053952753543854,
-0.010606828145682812,
-0.035401489585638046,
-0.039516840130090714,
-0.018488967791199684,
0.02894682250916958,
0.07042167335748672,
-0.02402356080710888,
0.03634701669216156,
0.02727498859167099,
-0.015174994245171547,
-0.00504132779315114,
-0.023674312978982925,
0.01985616236925125,
0.01170972641557455,
0.012686440721154213,
-0.0011947804596275091,
0.02782847359776497,
-0.006595945917069912,
0.0026614200323820114,
0.04983898252248764,
0.037926096469163895,
-0.024232788011431694,
-0.011946925893425941,
-0.023401977494359016,
-0.03893238678574562,
-0.01598348282277584,
0.021962905302643776,
0.021047061309218407,
-0.02012954279780388,
0.026402007788419724,
0.010028315708041191,
0.010915223509073257,
-0.005082698073238134,
0.04698563739657402,
0.047144319862127304,
-0.03585056588053703,
-0.04538962244987488,
-0.018491551280021667,
-0.03786791115999222,
-0.05349797382950783,
0.00868535041809082,
0.021261995658278465,
-0.003165441332384944,
-0.03948158770799637,
0.0015449424972757697,
0.00878114439547062,
0.005630127619951963,
-0.00047967920545488596,
-0.04724675789475441,
0.02060220018029213,
0.06307685375213623,
-0.013345087878406048,
-0.007305431645363569,
0.030109234154224396,
0.014207259751856327,
0.05509521812200546,
-0.007197158876806498,
0.01602412760257721,
-0.05911407619714737,
0.001851264969445765,
0.037074316293001175,
0.030563252046704292,
0.003411632962524891,
-0.020238665863871574,
-0.06683614104986191,
-0.05371303856372833,
0.032046105712652206,
-0.010627263225615025,
0.056657370179891586,
0.0034821159206330776,
-0.012071503326296806,
0.005027827341109514,
-0.04090617597103119,
0.010521613992750645,
0.017767779529094696,
-0.023235805332660675,
0.040427111089229584,
-0.010405360721051693,
-0.004506508354097605,
-0.0183430053293705,
-0.0028800261206924915,
0.02546110562980175,
0.009659088216722012,
0.016916316002607346,
0.004469301085919142,
-0.007594542112201452,
0.037968654185533524,
-0.014885269105434418,
-0.08289115130901337,
-0.049639761447906494,
-0.011969970539212227,
-0.04479547217488289,
0.04243076965212822,
-0.04002273455262184,
-0.06133449450135231,
0.047219015657901764,
0.04214633256196976,
-0.034074652940034866,
0.010304832831025124,
-0.04088345542550087,
0.04906994849443436,
0.0013524085516110063,
0.005170377437025309,
0.04950811713933945,
0.023271258920431137,
-0.021425411105155945,
-0.01538961660116911,
-0.03863131254911423,
0.03197409212589264,
-0.045331597328186035,
-0.004441443365067244,
-0.014850582927465439,
0.009762615896761417,
-0.020191919058561325,
0.012419412843883038,
-0.0009967513615265489,
-0.010342917405068874,
-0.01945684477686882,
-0.026442820206284523,
0.019195115193724632,
0.0024802887346595526,
0.027700772508978844,
0.03510689735412598,
0.02406005561351776,
0.054262708872556686,
-0.013011819683015347,
-0.032258521765470505,
0.025278333574533463,
0.00008902583795133978,
-0.01651802845299244,
0.011984524317085743,
-0.03892838954925537,
0.022319110110402107,
-0.031134871765971184,
-0.011441702954471111,
0.018129095435142517,
-0.01990363933146,
0.07079797238111496,
-0.010622596368193626,
0.041208427399396896,
0.05915690213441849,
-0.05617868900299072,
-0.004574826452881098,
-0.0419032946228981,
-0.028816452249884605,
0.03211646527051926,
-0.024169063195586205,
0.02589469775557518,
0.00819103978574276,
0.012128271162509918,
-0.08798642456531525,
-0.040810417383909225,
0.027912426739931107,
0.019248344004154205,
-0.02296619489789009,
-0.050054121762514114,
0.0035729422233998775,
-0.04166374355554581,
-0.042490772902965546,
-0.004897712729871273,
0.02796361781656742,
0.0033099062275141478,
0.0017226648051291704,
-0.0055835917592048645,
0.02610192634165287,
0.027765581384301186,
-0.024904577061533928,
-0.026685280725359917,
-0.004901927895843983,
0.010684196837246418,
-0.01571234129369259,
-0.026761552318930626,
0.0751723200082779,
-0.026124300435185432,
-0.024919839575886726,
-0.0067300619557499886,
-0.005220977123826742,
0.017563646659255028,
0.01015307754278183,
-0.02024843916296959,
0.043694764375686646,
0.02168109454214573,
0.012274122796952724,
-0.02232111617922783,
0.06312045454978943,
-0.0047871628776192665,
-0.0025301179848611355,
-0.010088080540299416,
-0.016889816150069237,
0.012432538904249668,
-0.0618910938501358,
0.04523422196507454,
-0.04241899028420448,
0.017309032380580902,
0.018939686939120293,
0.057712581008672714,
0.020932679995894432,
-0.008027045987546444,
0.00495678698644042,
-0.02278304658830166,
0.033312514424324036,
-0.009574315510690212,
-0.005957482848316431,
-0.0014548746403306723,
0.007742216344922781,
-0.03839140757918358,
-0.011438901536166668,
-0.018132098019123077,
0.008795767091214657,
0.06727790832519531,
-0.033298976719379425,
0.03385608270764351,
0.03208097815513611,
-0.01643606834113598,
0.02092692255973816,
-0.03143185377120972,
0.003293786197900772,
0.016301918774843216,
-0.009003634564578533,
0.0185104813426733,
-0.027818389236927032,
-0.027011269703507423,
0.05920489504933357,
0.03434659168124199,
-0.04257126897573471,
0.037581998854875565,
-0.0011875047348439693,
0.000030160423193592578,
0.0321095734834671,
-0.0011472110636532307,
-0.019353637471795082,
0.014217407442629337,
-0.04143460839986801,
0.043300971388816833,
0.027920259162783623,
-0.018730614334344864,
0.0008789574494585395,
0.023863233625888824,
0.006479750387370586,
-0.03374022617936134,
-0.04414171725511551,
-0.055599525570869446,
0.022480856627225876,
0.00478708278387785,
0.01266464777290821,
0.009223980829119682,
0.026222819462418556,
0.010902853682637215,
0.0032007384579628706,
-0.029353700578212738,
0.004713185131549835,
-0.058598946779966354,
-0.021574946120381355,
-0.027441764250397682,
-0.05773212015628815,
0.03153379261493683,
-0.017668601125478745,
-0.020938953384757042,
-0.0077852047979831696,
-0.016201157122850418,
-0.008828598074615002,
0.0044664437882602215,
0.04125426709651947,
-0.017677875235676765,
0.05557485669851303,
-0.00781338196247816,
-0.01012501772493124,
-0.01269268523901701,
0.008754965849220753,
0.09780363738536835,
0.03680609166622162,
0.013896727003157139,
-0.04921967163681984,
0.031200550496578217,
-0.02570764161646366,
-0.015721922740340233,
-0.016730299219489098,
0.002133650006726384,
-0.0024664460215717554,
0.049776408821344376,
0.04223877191543579,
0.0493476465344429,
0.0038694075774401426,
-0.03782080486416817,
0.05757138878107071,
-0.019069209694862366,
-0.007368292193859816,
0.014080244116485119,
0.0008615257684141397,
-0.028441227972507477,
0.005401532631367445,
-0.049290578812360764,
0.0031133785378187895,
-0.03294486179947853,
-0.0024449555203318596,
-0.05204471945762634,
-0.01602153852581978,
0.0156550332903862,
0.01661844179034233,
-0.06878119707107544,
0.0012076367856934667,
-0.012370220385491848,
-0.04222032055258751,
-0.014089878648519516,
0.010930135846138,
0.024787353351712227,
-0.01047410536557436,
0.009757242165505886,
0.005166321061551571,
-0.0023250181693583727,
0.02819361351430416,
0.008331025950610638,
-0.00040003593312576413,
-0.0156545490026474,
-0.00550784170627594,
-0.024353057146072388,
0.045202694833278656,
-0.02045038528740406,
0.0013763909228146076,
0.021941106766462326,
0.004174317233264446,
0.022035611793398857,
0.002542399801313877,
0.04009467363357544,
-0.00850250106304884,
0.04248570278286934,
-0.02266394905745983,
-0.04095536842942238,
0.004434756003320217,
0.02274101972579956,
0.013597775250673294,
0.01493735983967781,
0.002951163100078702,
0.012138458900153637,
-0.001301446813158691,
-0.029190249741077423,
0.040491435676813126,
-0.02243076078593731,
0.0008360081119462848,
-0.040621332824230194,
-0.014438648708164692,
-0.03358939290046692,
-0.010774971917271614,
0.023397261276841164,
0.018489906564354897,
0.015696000307798386,
-0.004990855231881142,
0.006961749400943518,
-0.034222185611724854,
0.0023213124368339777,
0.058497104793787,
-0.025140728801488876,
-0.03521530330181122,
0.0007585767307318747,
0.0043565575033426285,
0.02171400561928749,
0.03348364308476448,
-0.0178744588047266,
-0.0326133593916893,
0.0030960054136812687,
0.01548166386783123,
0.020283669233322144,
-0.032374415546655655,
0.0001585210266057402,
0.0047210524789988995,
-0.0439666323363781,
-0.014662610366940498,
-0.0001293066015932709,
0.014899865724146366,
0.039356302469968796,
0.017005324363708496,
0.015961406752467155,
0.00968175008893013,
-0.00566525012254715,
0.012767881155014038,
0.0005621894961223006,
-0.012695401906967163,
-0.017758218571543694,
0.00859337393194437,
-0.01971694640815258,
0.008980178274214268,
-0.027082188054919243,
-0.015038223005831242,
-0.008764484897255898,
-0.0008976187091320753,
0.03192999213933945,
-0.05112605169415474,
0.05491382256150246,
-0.015433713793754578,
0.03958721086382866,
-0.046111367642879486,
0.003572141518816352,
-0.07430700957775116,
-0.037473611533641815,
0.015626579523086548,
-0.020721711218357086,
0.0038085549604147673,
0.034557994455099106,
-0.014453853480517864,
-0.05658778175711632,
0.02581525593996048,
0.00028294697403907776,
-0.005060087889432907,
-0.004385244566947222,
0.018747704103589058,
-0.02468835934996605,
0.06442200392484665,
-0.01858631893992424,
-0.024141591042280197,
0.02815728820860386,
-0.029148630797863007,
-0.05518726631999016,
0.0386066772043705,
-0.011454269289970398,
0.013650709763169289,
0.018296634778380394,
-0.011318476870656013,
-0.05159251019358635,
0.07418269664049149,
-0.004926073364913464,
-0.008481479249894619,
-0.0037865792401134968,
0.006628321949392557,
-0.015688123181462288,
0.047373153269290924,
0.0325612835586071,
-0.050717778503894806,
-0.012436400167644024,
0.03358763828873634,
0.022198911756277084,
-0.023067008703947067,
0.004764193203300238,
-0.011236224323511124,
-0.05276939272880554,
0.001567162573337555,
0.022236863151192665,
0.012939165346324444,
0.02636745572090149,
0.045853808522224426,
-0.06027806177735329,
0.01846730336546898,
0.047845225781202316,
0.008334341458976269,
-0.08785635232925415,
-0.006327987182885408,
-0.01882408745586872,
-0.01891200616955757,
0.007029957138001919,
-0.030371593311429024,
-0.00796500127762556,
0.011061993427574635,
-0.0536051020026207,
0.01932763308286667,
-0.025721456855535507,
-0.015751821920275688,
-0.02652136981487274,
0.01686989888548851,
-0.013521352782845497,
0.042026713490486145,
0.04729674383997917,
0.040703725069761276,
-0.009826429188251495,
0.01002082135528326,
-0.030972054228186607,
-0.0009080064482986927,
-0.007924262434244156,
0.018839873373508453,
-0.020544428378343582,
0.047413043677806854,
0.048967551440000534,
-0.01396089419722557,
-0.02221458964049816,
0.011382566764950752,
-0.046814098954200745,
0.00666810804978013,
0.012658671475946903,
-0.006342863664031029,
-0.02870195172727108,
-0.0010983337415382266,
0.00629919720813632,
-0.01764664612710476,
0.01662534289062023,
0.029776111245155334,
0.024915024638175964,
0.03307729586958885,
-0.007545061409473419,
0.02114114724099636,
0.030898967757821083,
-0.05872056633234024,
0.004868838936090469,
0.027014127001166344,
-0.023636162281036377,
0.026691071689128876,
0.012740856036543846,
0.029847076162695885,
0.03753942996263504,
-0.012780433520674706,
-0.0022772550582885742,
-0.062427014112472534,
-0.021209480240941048,
-0.004206362180411816,
0.01551247388124466,
0.023897992447018623,
0.024200614541769028,
0.027589434757828712,
0.020867478102445602,
-0.01181143056601286,
0.006092757452279329,
-0.017476821318268776,
-0.023807045072317123,
-0.01314763817936182,
-0.007784941233694553,
-0.03734259307384491,
-0.03249042108654976,
-0.060636505484580994,
-0.05161529406905174,
0.04161209613084793,
0.03818652406334877,
0.056385673582553864,
-0.022666048258543015,
-0.06321882456541061,
-0.034849219024181366,
-0.0469738245010376,
0.006387015804648399,
-0.04374205321073532,
0.0257103331387043,
-0.044373299926519394,
-0.016155539080500603,
-0.01863177679479122,
0.008328328840434551,
0.02765628881752491,
-0.0025027294177562,
0.03646749258041382,
0.01945413649082184,
-0.035405099391937256,
0.04786321520805359,
-0.06468626111745834,
0.008815539069473743,
-0.0018412926001474261,
-0.040853578597307205,
0.005661499220877886,
-0.02205747365951538,
0.006009738426655531,
-0.004658575635403395,
0.04824136570096016,
-0.02909545786678791,
0.04248756915330887,
0.011019785888493061,
-0.01664993166923523,
0.062054798007011414,
-0.01129982527345419,
-0.0021510510705411434,
0.07023674994707108,
-0.028943650424480438,
0.003111507510766387,
0.05857722833752632,
-0.005875959526747465,
-0.030312851071357727,
0.038050491362810135,
-0.009253953583538532,
0.0009340995457023382,
-0.025250403210520744,
-0.031020715832710266,
0.028382642194628716,
-0.03708226978778839,
0.02684354968369007,
0.03457840904593468,
-0.0295406486839056,
0.001679089036770165,
0.022149058058857918,
-0.0038063658867031336,
0.03525692969560623,
-0.022053826600313187,
-0.03127589076757431,
0.008211899548768997,
0.025559639558196068,
-0.004859242122620344,
0.03612884506583214,
0.03384839743375778,
0.011862043291330338,
0.014812445268034935,
-0.011888530105352402,
0.012572186067700386,
0.013299049809575081,
-0.023756487295031548,
0.022885968908667564,
-0.09517037123441696,
-0.039075594395399094,
0.019344761967658997,
-0.011993199586868286,
0.027925368398427963,
0.02187461219727993,
-0.0073675308376550674,
0.0760563313961029,
0.011273491196334362,
0.000056879594922065735,
-0.007342368829995394,
-0.033154964447021484,
-0.0018220804631710052,
0.02009216509759426,
0.009778250008821487,
0.054739318788051605,
0.0006159125478006899,
-0.009668630547821522,
-0.011596922762691975,
0.02542022429406643,
0.044761430472135544,
-0.002274142811074853,
0.020239489153027534,
-0.013685369864106178,
-0.014563463628292084,
-0.018071187660098076,
-0.008244650438427925,
-0.021809034049510956,
-0.04342862591147423,
0.030782563611865044,
0.042996909469366074,
0.01563975401222706,
0.023375893011689186,
-0.015929777175188065,
-0.03165877237915993,
0.032530542463064194,
-0.05149764195084572,
-0.030259693041443825,
-0.014486145228147507,
0.048878367990255356,
-0.016421981155872345,
-0.00356591516174376
] |
<p>I've studied something so I'm able to explain better what I'm thinking about.</p>
<p>'t Hooft duality states:</p>
<p>In a gauge theory with fields in the adjoint representation in presence of a mass gap only the following alternatives are allowed:</p>
<p>1 Magnetic condensation and electric confinement</p>
<p>2 Electric condensation and magnetic confinement.</p>
<p>I've also learnt that the object of electric nature are the ones that are affected by gauge transformation while the magnetic ones are not.
Moreover, but I'm not so sure of that, magnetic objects in an electric theory can be admitted only as singularities (such as Dirac delta) in analogy to the Meissner effect in which the magnetic field can penetrate a superconductor only via tiny tubes.</p>
<p>So I would appreciate if someone would give me a better insight of this characterization of electric and magnetic objects since they have been presented to me only as facts to accept.</p>
<p>Thank you in advance.</p>
<p>The previous, less clear, version of my question was:</p>
<p>Approaching the study of QCD, I've read about the 't Hooft duality that is similar to the Meissner effect for superconductors: magnetic condensation implies electric confinement and vice versa.
At first I'm not sure about what is magnetic and what is electric in QCD. Then I would appreciate if someone could give me a formal description of this phenomenon, cause I've only found this naive description.
Thanks.</p> | 2,877 | [
-0.01915661245584488,
0.003379889763891697,
0.034464046359062195,
-0.047143884003162384,
0.040298547595739365,
0.034418560564517975,
-0.017371416091918945,
-0.01084682997316122,
0.024538088589906693,
-0.019375424832105637,
0.02141493372619152,
-0.000364802370313555,
0.059161700308322906,
0.008636130951344967,
0.011899985373020172,
-0.0030867946334183216,
-0.013052238151431084,
-0.01676155813038349,
0.023435942828655243,
-0.027465855702757835,
0.009526676498353481,
0.03512011468410492,
0.02187454141676426,
0.013324135914444923,
-0.02118467167019844,
0.012593633495271206,
-0.004287270829081535,
0.05262986570596695,
0.006083051674067974,
0.050378959625959396,
-0.007644697558134794,
-0.040840499103069305,
0.01211669109761715,
0.021191412582993507,
-0.006010973826050758,
0.013597090728580952,
-0.03258061036467552,
-0.03175836801528931,
-0.021485595032572746,
-0.007237359415739775,
-0.014820750802755356,
-0.043996427208185196,
-0.017263060435652733,
0.034208714962005615,
-0.007332825567573309,
-0.027550112456083298,
-0.004490421153604984,
-0.017212536185979843,
0.05961345508694649,
-0.0811789333820343,
0.07054053246974945,
0.008769156411290169,
0.049025584012269974,
0.03393327072262764,
-0.0032238815911114216,
-0.018955396488308907,
0.048680633306503296,
0.059931788593530655,
-0.03035348653793335,
-0.06199037283658981,
-0.03256618604063988,
-0.04108329489827156,
0.011252274736762047,
-0.02943318337202072,
-0.035703521221876144,
0.044837165623903275,
0.0003721565008163452,
-0.024580735713243484,
0.003908014856278896,
0.010006336495280266,
0.010788915678858757,
0.0016992527525871992,
-0.005188332870602608,
-0.004076491110026836,
0.04480873793363571,
-0.016659332439303398,
0.006049454677850008,
0.030310753732919693,
0.03092271275818348,
0.03296626731753349,
-0.03142617642879486,
0.03536660224199295,
0.010930250398814678,
0.014487138949334621,
0.009764675982296467,
-0.008322067558765411,
0.06207619979977608,
-0.03471419960260391,
-0.012073644436895847,
0.02904398925602436,
-0.03368530049920082,
-0.021783845499157906,
0.016653014346957207,
-0.0375463142991066,
-0.05237213894724846,
0.013407719321548939,
0.020281946286559105,
0.04083395376801491,
-0.03571108728647232,
-0.02227712981402874,
-0.009740076959133148,
0.025678981095552444,
0.028829488903284073,
0.06397132575511932,
0.00825068075209856,
-0.008244507946074009,
-0.034561801701784134,
-0.0008708162349648774,
0.001638007932342589,
-0.018532749265432358,
-0.04607493802905083,
-0.010891372337937355,
0.007555160205811262,
-0.008770674467086792,
-0.004737728275358677,
-0.023278970271348953,
-0.016659576445817947,
-0.02043684385716915,
0.0493088997900486,
0.09201385825872421,
0.0424136146903038,
-0.053727541118860245,
0.025940407067537308,
-0.03751170635223389,
-0.09889870882034302,
-0.029012979939579964,
0.0390436016023159,
0.034509576857089996,
-0.003372688079252839,
0.018952906131744385,
-0.04154590889811516,
-0.030832037329673767,
-0.008867745287716389,
-0.024428118020296097,
0.027484672144055367,
-0.03385769575834274,
-0.091493621468544,
-0.03346150368452072,
0.015440613031387329,
0.024304531514644623,
-0.04147611930966377,
-0.05752977728843689,
-0.007317344658076763,
0.017151538282632828,
0.06324921548366547,
0.02262176014482975,
0.0019248613389208913,
0.011969526298344135,
0.054327212274074554,
0.04332241415977478,
-0.03622063249349594,
-0.027501679956912994,
-0.03619580343365669,
-0.040349964052438736,
0.002236619358882308,
-0.052687812596559525,
0.012122591026127338,
0.027204612269997597,
-0.00793327298015356,
0.0059220013208687305,
0.09214246273040771,
-0.06056259199976921,
-0.02857374958693981,
0.038556575775146484,
0.006475979462265968,
-0.0426589734852314,
0.09829284995794296,
0.016425400972366333,
0.03144201263785362,
0.06260626018047333,
0.00906743761152029,
0.009853898547589779,
0.028133517131209373,
0.0495416633784771,
0.027736904099583626,
-0.016583096235990524,
-0.028789442032575607,
-0.01820147968828678,
-0.0048690615221858025,
-0.003071532817557454,
-0.06458523124456406,
-0.04850442335009575,
-0.008023416623473167,
-0.019161880016326904,
0.0054931738413870335,
0.034656822681427,
-0.010854389518499374,
-0.05869637429714203,
0.00265372171998024,
-0.06800082325935364,
-0.02675331011414528,
-0.070292629301548,
0.015599081292748451,
-0.03673827648162842,
-0.009465092793107033,
0.02995907887816429,
0.006315353326499462,
0.009794428013265133,
-0.06690274924039841,
-0.03474622219800949,
0.014341440983116627,
0.037472084164619446,
-0.00016345336916856468,
-0.018630122765898705,
0.0026172264479100704,
-0.016871407628059387,
0.014248741790652275,
-0.03391518443822861,
0.04259226471185684,
-0.023656796663999557,
-0.05861516296863556,
-0.0016222704434767365,
-0.02798936516046524,
0.016332747414708138,
0.004543845541775227,
0.01459614560008049,
0.02677297592163086,
0.0142503147944808,
-0.014769332483410835,
0.04494914412498474,
-0.014924437738955021,
0.07448597997426987,
0.02896321564912796,
-0.01771136000752449,
-0.007953088730573654,
0.04845283925533295,
0.007678480353206396,
-0.007613011170178652,
-0.04310718551278114,
-0.021540744230151176,
-0.030768563970923424,
0.031522106379270554,
0.03501268848776817,
0.01980624534189701,
-0.03523525968194008,
0.05196493864059448,
0.01615467108786106,
0.03563804179430008,
0.03229964151978493,
0.030928291380405426,
-0.034275222569704056,
0.011726940050721169,
0.0261333417147398,
0.007334696128964424,
-0.006578750442713499,
-0.014221489429473877,
0.024643827229738235,
0.016388220712542534,
0.027950255200266838,
0.0029037247877568007,
-0.043371327221393585,
0.08811686933040619,
-0.031868599355220795,
0.025287598371505737,
0.0005718875909224153,
-0.030715445056557655,
0.0433630533516407,
-0.006272754166275263,
0.020780406892299652,
-0.01635563373565674,
-0.02843490242958069,
0.033493414521217346,
-0.005259764846414328,
0.01214255578815937,
0.006186397280544043,
-0.012514871545135975,
-0.01355347502976656,
0.0017785317031666636,
-0.006964870262891054,
-0.014210748486220837,
0.009143891744315624,
0.011507242918014526,
-0.001772079849615693,
-0.003245145780965686,
0.02722109854221344,
0.02848000079393387,
-0.002788623096421361,
0.04307849705219269,
-0.012478787451982498,
-0.050921130925416946,
-0.002784449141472578,
-0.03855438157916069,
0.04006002098321915,
0.07182332128286362,
-0.026899373158812523,
0.015837298706173897,
-0.09592395275831223,
-0.003159173531457782,
0.04748428240418434,
-0.00896177813410759,
0.0077737318351864815,
-0.02836989425122738,
-0.025723477825522423,
-0.04389933496713638,
0.01916573755443096,
0.010466102510690689,
0.0015656279865652323,
0.0029304930940270424,
-0.016922421753406525,
0.050969019532203674,
0.023706354200839996,
-0.017147377133369446,
0.005658833775669336,
-0.02189158834517002,
-0.020701004192233086,
-0.022730372846126556,
-0.026136208325624466,
0.00036779025685973465,
-0.02715594880282879,
0.058972492814064026,
-0.0013430218677967787,
-0.05563148111104965,
-0.02895238995552063,
-0.0434299074113369,
0.009947567246854305,
0.015472488477826118,
-0.0010706994216889143,
0.0048370822332799435,
-0.02030349336564541,
-0.06790739297866821,
0.05929040536284447,
0.004320934880524874,
-0.03922388702630997,
-0.004187001846730709,
-0.012152263894677162,
-0.040953945368528366,
-0.005915679037570953,
0.023588877171278,
0.042571548372507095,
-0.02357080951333046,
-0.01784605346620083,
0.03307522460818291,
0.03849625959992409,
-0.04561502858996391,
0.0019878025632351637,
-0.03285646066069603,
0.028041401877999306,
-0.00569175835698843,
0.0032728014048188925,
0.06634534150362015,
-0.0008320219349116087,
-0.026504667475819588,
0.007345941849052906,
0.0032892904710024595,
0.02040443755686283,
0.01910603605210781,
-0.04344986379146576,
0.03836508095264435,
0.002359007252380252,
0.015941940248012543,
-0.010914994403719902,
0.06717302650213242,
-0.01920485869050026,
-0.047159746289253235,
0.0072006843984127045,
0.009569255635142326,
0.022076012566685677,
-0.03624318912625313,
-0.029722947627305984,
0.027837317436933517,
0.049223657697439194,
-0.04767100512981415,
-0.018799511715769768,
-0.023285944014787674,
-0.010944669134914875,
0.01798136904835701,
-0.03900405392050743,
-0.019502434879541397,
0.034186482429504395,
0.04280402511358261,
0.027870435267686844,
-0.011300806887447834,
-0.019683944061398506,
0.008592438884079456,
-0.04728899151086807,
0.025058764964342117,
0.056258879601955414,
0.06796520203351974,
0.030237140133976936,
0.030896978452801704,
0.022404899820685387,
0.013741099275648594,
-0.0014649982331320643,
-0.023385487496852875,
-0.12083509564399719,
-0.0053628236055374146,
-0.002462714910507202,
0.015783363953232765,
-0.02174166403710842,
-0.022152816876769066,
-0.014838946983218193,
-0.004428332671523094,
-0.053448595106601715,
-0.039125628769397736,
-0.006446222309023142,
-0.04767328500747681,
0.038569919764995575,
-0.05825603008270264,
-0.013574725016951561,
-0.024218440055847168,
0.02660035900771618,
0.04173748940229416,
-0.04604930803179741,
0.009749255143105984,
-0.016358420252799988,
-0.05325419455766678,
-0.00968616921454668,
0.0168614499270916,
0.02767750807106495,
0.013054321520030499,
0.014213194139301777,
0.03013468161225319,
0.020118599757552147,
-0.004916423466056585,
-0.003631344297900796,
0.033296678215265274,
0.048016488552093506,
-0.023600615561008453,
-0.027640439569950104,
0.005127612967044115,
-0.048923395574092865,
-0.017245939001441002,
-0.030117271468043327,
0.07994256913661957,
0.026270931586623192,
0.00829725619405508,
0.030422287061810493,
0.026498770341277122,
-0.0008428338915109634,
0.047525372356176376,
0.05178814381361008,
0.03307969123125076,
-0.049059849232435226,
-0.07160830497741699,
0.011147772893309593,
-0.015950758010149002,
0.011890172958374023,
0.02182120643556118,
-0.019135452806949615,
-0.024685844779014587,
0.0032225940376520157,
0.0004566158459056169,
-0.027902569621801376,
-0.015010537579655647,
-0.010512588545680046,
0.020154006779193878,
-0.0030296137556433678,
-0.014151766896247864,
0.005460643675178289,
0.010028524324297905,
0.03367214277386665,
0.038472019135951996,
-0.0008205033955164254,
0.006057039834558964,
-0.09425012022256851,
-0.002486513927578926,
0.06497065722942352,
0.02115378901362419,
0.0050834366120398045,
-0.009239261969923973,
-0.04435042291879654,
0.0070240693166852,
0.059571027755737305,
-0.03556596860289574,
0.0027447917964309454,
-0.01848386600613594,
-0.016376623883843422,
-0.014424554072320461,
-0.016711870208382607,
0.009743832051753998,
0.013730174861848354,
-0.0027131831739097834,
0.025417255237698555,
-0.01329145859926939,
-0.008614861406385899,
-0.005697679705917835,
0.043965648859739304,
0.008079280145466328,
0.006773334927856922,
0.028602834790945053,
0.020038872957229614,
-0.007523363456130028,
0.004524705000221729,
0.006165105849504471,
-0.0800638347864151,
0.018732309341430664,
0.009265728294849396,
0.0025836455170065165,
0.06261247396469116,
-0.017436794936656952,
-0.010031143203377724,
-0.01570681668817997,
-0.004218784626573324,
-0.018326548859477043,
-0.018285339698195457,
-0.029406270012259483,
0.04781205207109451,
0.02936120331287384,
-0.022493446245789528,
0.023001130670309067,
-0.017701251432299614,
0.005097051616758108,
-0.003263944759964943,
-0.013413823209702969,
0.029788082465529442,
0.013899208046495914,
-0.017198780551552773,
-0.03992638364434242,
0.005932046566158533,
-0.05375434458255768,
0.06804269552230835,
-0.049585580825805664,
0.023208854719996452,
-0.005411540158092976,
-0.04491489753127098,
-0.006785852834582329,
0.01043232623487711,
-0.01842287927865982,
-0.05128325894474983,
-0.008948123082518578,
0.007492123171687126,
0.007620051968842745,
-0.019548509269952774,
0.019716326147317886,
-0.01516844891011715,
0.0015746583230793476,
-0.001948493649251759,
-0.03267906606197357,
0.010628001764416695,
0.014837204478681087,
-0.009641273878514767,
0.021801289170980453,
-0.042484384030103683,
0.03844422847032547,
-0.05790184810757637,
-0.02261488139629364,
-0.0010578836081549525,
-0.04448770731687546,
-0.01008251216262579,
0.010792954824864864,
-0.013973793014883995,
0.001306853722780943,
-0.06583607196807861,
0.01913253590464592,
0.02342659793794155,
-0.021284980699419975,
-0.07313136011362076,
-0.07211093604564667,
0.00018573086708784103,
0.01468669157475233,
-0.015806863084435463,
-0.003669419791549444,
-0.0020255898125469685,
-0.008807151578366756,
-0.04545769840478897,
0.009987596422433853,
0.049424055963754654,
-0.05247063189744949,
0.008127487264573574,
0.03830306977033615,
0.054714616388082504,
0.0418732576072216,
-0.01071046944707632,
-0.037337563931941986,
0.0006118818419054151,
-0.03201042488217354,
0.013667617924511433,
-0.00006358818791341037,
0.018543891608715057,
-0.00927688553929329,
-0.046354591846466064,
-0.0148833729326725,
-0.025881623849272728,
0.030659470707178116,
-0.010826841928064823,
0.01410978939384222,
0.03971173241734505,
0.024398960173130035,
0.01618226245045662,
-0.01811264455318451,
-0.013526967726647854,
0.02308797650039196,
0.014240611344575882,
-0.016661904752254486,
-0.005089537240564823,
0.0007965512340888381,
-0.023837050423026085,
0.03442833572626114,
-0.002950866473838687,
0.002536500571295619,
0.006155301351100206,
0.051780518144369125,
-0.00331547437235713,
-0.01648804172873497,
0.044042278081178665,
-0.06259226053953171,
-0.006922166794538498,
0.004545306321233511,
0.01482036616653204,
0.02546917460858822,
0.0005316563765518367,
-0.004459706600755453,
-0.002312703523784876,
-0.02437032014131546,
-0.01713274046778679,
0.034579306840896606,
0.0031837185379117727,
0.02610485814511776,
0.004075929056853056,
0.014190388843417168,
-0.00020314898574724793,
-0.030475670471787453,
-0.009361818432807922,
0.015644963830709457,
-0.013106250204145908,
0.03739267960190773,
-0.0346309132874012,
-0.029245203360915184,
0.041598666459321976,
0.06614130735397339,
-0.05031050741672516,
0.002208418445661664,
0.05809539183974266,
0.04986016824841499,
0.04835408553481102,
-0.010058463551104069,
-0.0525457002222538,
0.06072326377034187,
-0.05014455318450928,
0.023415081202983856,
0.013817050494253635,
0.008870336227118969,
0.01565936952829361,
0.01865207776427269,
0.06181133911013603,
0.004937365185469389,
-0.04229883477091789,
-0.0211784690618515,
0.0518246665596962,
0.0072153289802372456,
-0.0022143160458654165,
0.006696436554193497,
0.010113521479070187,
0.033423688262701035,
0.011010303162038326,
-0.00914522260427475,
0.03524300456047058,
-0.07053620368242264,
-0.01943865604698658,
-0.019453203305602074,
-0.04656495153903961,
0.062441181391477585,
-0.021951016038656235,
-0.010874759405851364,
-0.00951647199690342,
-0.019394708797335625,
0.02356104366481304,
0.015166866593062878,
0.008151650428771973,
-0.026742851361632347,
0.04328088462352753,
-0.006337399128824472,
0.009057390503585339,
-0.03294902667403221,
0.01819378137588501,
0.10169800370931625,
0.04939669743180275,
0.0337386429309845,
-0.08484890311956406,
0.031598806381225586,
0.0035216521937400103,
0.04563106596469879,
-0.04153946787118912,
0.02009511925280094,
0.009653226472437382,
0.003628362901508808,
-0.0056021548807621,
0.07217887789011002,
0.007687648758292198,
0.010471387766301632,
0.06542058289051056,
-0.02795102261006832,
-0.03064841404557228,
-0.008682341314852238,
0.05071472004055977,
-0.024782074615359306,
0.011575445532798767,
-0.058879490941762924,
0.019107213243842125,
-0.006159577518701553,
0.039778001606464386,
-0.027647968381643295,
-0.04370063543319702,
0.044209856539964676,
0.0075915963388979435,
-0.0472770519554615,
0.010805658996105194,
-0.014394411817193031,
0.004220929462462664,
-0.0319480299949646,
-0.018054621294140816,
0.0031601248774677515,
0.03974828124046326,
0.020660454407334328,
0.009452467784285545,
0.011357717216014862,
-0.025986863300204277,
0.014957611449062824,
0.04692733660340309,
-0.05012328177690506,
-0.026557590812444687,
-0.03236142545938492,
0.05247974395751953,
-0.02923409268260002,
-0.010605883784592152,
0.02999422885477543,
0.014971058815717697,
0.02618531323969364,
-0.02981051243841648,
-0.01944122090935707,
-0.03921598941087723,
-0.001192232477478683,
-0.008116587065160275,
0.0011983391596004367,
-0.009346794337034225,
0.05182616785168648,
-0.00647260807454586,
0.016640830785036087,
-0.02931557036936283,
-0.0031624024268239737,
0.04013030603528023,
0.02683175355195999,
0.04202824458479881,
-0.002209175145253539,
0.017896875739097595,
-0.0492081455886364,
-0.004221620038151741,
0.009850279428064823,
-0.009142807684838772,
0.016225328668951988,
-0.0031537190079689026,
0.029953032732009888,
0.0003772054042201489,
-0.008170997723937035,
-0.004752918146550655,
-0.03565762937068939,
0.03509964793920517,
0.016308987513184547,
-0.02366221323609352,
-0.000572792487218976,
0.010695183649659157,
0.018398692831397057,
0.0734519511461258,
-0.03641977161169052,
-0.006543941795825958,
-0.016910584643483162,
0.02622050978243351,
0.0027837471570819616,
-0.011475824750959873,
-0.01790139265358448,
0.012846838682889938,
-0.05971922352910042,
0.008384856395423412,
-0.023035500198602676,
0.018685566261410713,
0.00025882211048156023,
0.01478579267859459,
0.010095246136188507,
0.027225971221923828,
-0.000007612334684381494,
0.014258523471653461,
0.0325976237654686,
-0.044876594096422195,
-0.020042024552822113,
0.006528188940137625,
-0.030657567083835602,
-0.027264568954706192,
-0.043480999767780304,
0.004513431806117296,
0.0011762573849409819,
-0.012006989680230618,
0.0014626088086515665,
0.00954781286418438,
0.0008130493224598467,
-0.018616104498505592,
0.03493652865290642,
-0.020412590354681015,
0.002855312777683139,
-0.05209372565150261,
0.01836184412240982,
0.010910333134233952,
0.0010620164684951305,
0.010185189545154572,
0.015730593353509903,
-0.04615097865462303,
-0.011975276283919811,
-0.031183447688817978,
0.01787761226296425,
-0.022682832553982735,
0.022144611924886703,
0.02450288087129593,
0.018695048987865448,
0.05017843469977379,
-0.021005377173423767,
-0.00913330353796482,
0.020936844870448112,
-0.04861391708254814,
-0.02732972428202629,
0.006752266548573971,
-0.012720354832708836,
0.022021569311618805,
0.02915746346116066,
-0.003412574762478471,
-0.01852913200855255,
0.06780511140823364,
-0.009414524771273136,
0.003557140938937664,
-0.017223455011844635,
-0.03871119022369385,
-0.023434076458215714,
-0.034528616815805435,
0.014377220533788204,
0.006431786343455315,
-0.0054567004553973675,
0.007544927764683962,
0.021625837311148643,
0.015146246179938316,
-0.023812539875507355,
-0.020778093487024307,
0.026798823848366737,
0.021206097677350044,
0.005606789141893387,
0.01587713323533535,
-0.006882829591631889,
0.06675390154123306,
-0.050722476094961166,
0.002120075048878789,
0.0033314337488263845,
0.03397005423903465,
-0.09881043434143066,
0.01035885326564312,
0.019762219861149788,
-0.0288556981831789,
0.03666193038225174,
-0.0317813977599144,
-0.0037477274890989065,
0.027285104617476463,
-0.025158917531371117,
-0.0003373634535819292,
-0.02047031559050083,
-0.02476438134908676,
-0.03455675393342972,
-0.009106184355914593,
-0.013804936781525612,
0.07038990408182144,
0.04996510222554207,
0.009228961542248726,
-0.009926127269864082,
-0.003873998299241066,
-0.015250529162585735,
-0.01802072487771511,
-0.03213348984718323,
0.02978787012398243,
-0.0040660579688847065,
-0.03880995884537697,
0.09190430492162704,
-0.01935211755335331,
-0.0376502126455307,
0.0537734217941761,
0.022567035630345345,
-0.014128042384982109,
0.007718666456639767,
0.00696305837482214,
0.008893056772649288,
0.03138880059123039,
0.004512269515544176,
0.01908743940293789,
-0.006687917280942202,
0.009477921761572361,
0.029515691101551056,
0.042688094079494476,
-0.01060839556157589,
-0.001411391538567841,
0.018629707396030426,
-0.030609676614403725,
0.02008056826889515,
0.03280889242887497,
-0.03302711620926857,
-0.022158125415444374,
-0.003946481738239527,
0.022898375988006592,
0.03695317730307579,
-0.006732259411364794,
0.018578313291072845,
-0.031154850497841835,
-0.030529748648405075,
0.022793613374233246,
0.03571167215704918,
0.032106295228004456,
0.059369172900915146,
-0.0008689445094205439,
-0.03849463164806366,
0.029587119817733765,
0.027606401592493057,
-0.025447849184274673,
-0.03819957748055458,
-0.005221558269113302,
-0.0019466226221993566,
0.013680717907845974,
0.014780226163566113,
-0.05646182596683502,
-0.005825194995850325,
0.045692674815654755,
0.011682840064167976,
0.018078867346048355,
-0.02633211947977543,
-0.019875403493642807,
-0.0006405246094800532,
-0.03400668501853943,
0.0406201109290123,
-0.015107710845768452,
0.006963256746530533,
0.0006266845157369971,
-0.013120802119374275,
-0.003811889560893178,
0.024935977533459663,
0.061861466616392136,
0.028134355321526527,
-0.02431204542517662,
0.022132357582449913,
-0.017469258978962898,
0.033887919038534164,
-0.019968809559941292,
-0.0056323278695344925,
-0.0019182552350685,
-0.010912103578448296,
0.03373515233397484,
-0.006398617289960384,
-0.0143390242010355,
0.05824026092886925,
0.04754742607474327,
0.010882645845413208,
0.02995661273598671,
-0.00937737338244915,
-0.06029105931520462,
0.04614231362938881,
-0.01198670081794262,
0.0018929248908534646,
0.044990964233875275,
-0.026858584955334663,
-0.008085671812295914,
0.016079479828476906,
-0.0059091998264193535,
-0.025911692529916763,
0.03879052773118019,
-0.009972412139177322,
0.01557125709950924,
-0.028439773246645927,
-0.034908682107925415,
0.03577730059623718,
-0.02372795343399048,
0.012425773777067661,
0.02886028029024601,
-0.015797290951013565,
-0.01169445551931858,
0.07290656119585037,
0.027384312823414803,
0.043955136090517044,
-0.017739174887537956,
-0.020865434780716896,
0.013633672147989273,
0.012372183613479137,
0.004422221798449755,
0.010917055420577526,
0.0615730844438076,
0.03927871584892273,
-0.02342134714126587,
0.0278953667730093,
-0.002562470966950059,
0.022165026515722275,
-0.005365979857742786,
0.0073514352552592754,
-0.014815889298915863,
-0.036268383264541626,
0.03273877128958702,
0.007079836912453175,
0.01542832050472498,
0.012427685782313347,
-0.04277466610074043,
0.08415468037128448,
-0.035780277103185654,
0.003027138765901327,
-0.017399197444319725,
-0.006055760197341442,
0.005447919946163893,
-0.0013582258252426982,
0.007168920245021582,
0.07325352728366852,
0.00206468696705997,
-0.00012887046614196151,
-0.013280880637466908,
-0.03900701180100441,
0.01049690693616867,
-0.031128717586398125,
0.03455241397023201,
-0.01573404110968113,
-0.03238431364297867,
-0.021774688735604286,
-0.009480180218815804,
-0.03161650151014328,
-0.001064092037267983,
0.014152919873595238,
0.040745414793491364,
0.015399353578686714,
-0.012777515687048435,
-0.03814044967293739,
-0.019254015758633614,
0.0547066293656826,
-0.04228632152080536,
-0.028901943936944008,
-0.005137650296092033,
0.016962232068181038,
0.00012903613969683647,
0.006577407009899616
] |
<p>There was a reason why I constantly failed physics at school and university, and that reason was, apart from the fact I was immensely lazy, that I mentally refused to "believe" more advanced stuff until I understand the fundamentals (which I, eventually, never did).</p>
<p>As such, one of the most fundamental things in physics that I still don't understand (a year after dropping out from the university) is <strong>the concept of <a href="http://en.wikipedia.org/wiki/Field_%28physics%29">field</a></strong>. No one cared to explain what a field <em>actually is</em>, they just used to throw in a bunch of formulas and everyone was content. The school textbook definition for a field (electromagnetic in this particular case, but they were similar), as I remember it, goes like:</p>
<blockquote>
<p>An electromagnetic field is a special kind of substance by which charged moving particles or physical bodies with a magnetic moment interact.</p>
</blockquote>
<p><em>A special kind of substance</em>, are they for real? This sounds like the authors themselves didn't quite understand what a field is so they decided to throw in a bunch of buzzwords to make it sounds right. I'm fine with the second half but <em>a special kind of substance</em> really bugs me, so I'd like to focus on that.</p>
<h3>Is a field <em>material</em>?</h3>
<p>Apparently, it isn't. It doesn't consist of particles like my laptop or even the light. </p>
<p>If it isn't material, <strong>is it <em>real</em> or is it just <em>a concept that helps to explain our observations</em></strong>? While this is prone to speculations, I think we can agree that in scope of this discussion particles actually do exist and laws of physics don't (the latter are nothing but human ideas so I suspect Universe doesn't "know" a thing about them, at least if we're talking raw matter and don't take it on metalevel where human knowledge, being a part of the Universe, makes the Universe contain laws of physics). Any laws are only a product of human thinking while the stars are likely to exist without us homo sapiens messing around. Or am I wrong here too? I hope you already see why I hate physics.</p>
<h3>Is a field <em>not material but still real</em>?</h3>
<p>Can something "not touchable" by definition be considered part of our Universe by physicians? I used to imagine that a "snapshot" of our Universe in time would contain information about each particle and its position, and this would've been enough to "de<a href="http://en.wikipedia.org/wiki/Serialization">seralize</a>" it but I guess my programmer metaphors are largely off the track. (Oh, and I know that the uncertainty principle makes such (de)serialization impossible — I only mean that I thought the Universe can be "defined" as the set of all material objects in it). Is such assumption false?</p>
<p>At this point, if fields indeed are <em>not</em> material but <em>are</em> part of the Universe, I don't really see how they are different from <a href="http://en.wikipedia.org/wiki/Hindu_deities">the whole Hindu pantheon</a> except for perhaps a more geeky flavor.</p>
<p>When I talked about this with the teacher who helped me to prepare for the exams (which I did pass, by the way, it was before I dropped out), she said to me that, if I wanted hardcore definitions,</p>
<blockquote>
<p>a field is a function that returns a value for a point in space.</p>
</blockquote>
<p>Now this finally makes a hell lot of sense to me but I still don't understand how mathematical functions can be a part of the Universe and shape the reality.</p>
<p>I'm afraid the question will seem ambiguous and get closed but I had a really hard time trying to shape my confusion into sentences, and I will highly appreciate if someone clears it up, suggests a link or confirms that there is no definitive answer to my question.</p> | 558 | [
-0.03271252661943436,
-0.017797483131289482,
0.028888145461678505,
-0.05631844699382782,
0.06305312365293503,
0.025808509439229965,
0.0025054870638996363,
-0.023156460374593735,
0.003431560005992651,
-0.010754830203950405,
0.05315259471535683,
0.037932250648736954,
0.056948620826005936,
0.03245072811841965,
0.02091822773218155,
0.02526303008198738,
0.04112225025892258,
0.012403229251503944,
-0.03500252962112427,
-0.04015854373574257,
-0.0015020458959043026,
0.005795700941234827,
-0.07439486682415009,
0.05661242455244064,
-0.012240210548043251,
0.014834573492407799,
0.0040593999437987804,
0.006890653166919947,
-0.021439649164676666,
0.019912974908947945,
-0.0041994438506662846,
-0.03426016494631767,
-0.017849182710051537,
-0.05353256314992905,
0.07014577090740204,
0.0170446690171957,
-0.015144800767302513,
-0.03601684421300888,
0.020956555381417274,
0.009266488254070282,
-0.004576034843921661,
-0.006575861945748329,
-0.01711903139948845,
0.029457924887537956,
-0.06699367612600327,
0.013627092353999615,
0.010735875926911831,
-0.0032352320849895477,
0.07062160223722458,
-0.04578880965709686,
0.024760160595178604,
-0.01870007812976837,
0.04337923228740692,
0.03884775564074516,
-0.013344277627766132,
-0.05239078029990196,
0.05706404149532318,
0.023393284529447556,
-0.003073457395657897,
-0.0761609598994255,
-0.006226109806448221,
0.006951221264898777,
-0.011092150583863258,
-0.024246718734502792,
-0.040085356682538986,
0.05281567573547363,
-0.024591516703367233,
-0.030439773574471474,
0.04794719070196152,
0.021865155547857285,
0.02057022787630558,
0.03180055692791939,
0.02209802344441414,
0.010218664072453976,
0.008194944821298122,
-0.03952379524707794,
-0.022356532514095306,
0.0037232080940157175,
0.024377858266234398,
0.042884740978479385,
-0.02588558942079544,
-0.0012741846730932593,
0.008586442098021507,
0.0186235923320055,
0.008862590417265892,
0.0013182067777961493,
0.07683008164167404,
0.007439710665494204,
-0.0229287538677454,
0.016856791451573372,
-0.019658971577882767,
0.01678706519305706,
0.04326754808425903,
0.016824712976813316,
-0.028254294767975807,
0.02263408526778221,
0.01947101764380932,
0.02104276232421398,
-0.018642563372850418,
0.01939995214343071,
0.0021300374064594507,
0.01775652915239334,
0.033065930008888245,
0.06175262853503227,
0.029158564284443855,
-0.056018032133579254,
-0.018781349062919617,
0.010920017026364803,
-0.05087998881936073,
-0.006236379034817219,
0.003130622673779726,
-0.004955466836690903,
0.034364644438028336,
-0.0047059995122253895,
0.015646567568182945,
-0.015373129397630692,
0.026861293241381645,
-0.018353117629885674,
0.06104201078414917,
0.07563748955726624,
0.04160585254430771,
-0.045596644282341,
0.003538835095241666,
-0.03443393483757973,
-0.06936577707529068,
-0.0041919793002307415,
0.036764610558748245,
0.017733605578541756,
-0.03723176196217537,
0.014779984019696712,
-0.02046198397874832,
0.030731944367289543,
0.004031839314848185,
0.010269520804286003,
0.02605743147432804,
-0.0033195067662745714,
-0.10676956921815872,
-0.05777018144726753,
0.031340789049863815,
0.011303110979497433,
-0.04133368283510208,
-0.03486352786421776,
0.007265310734510422,
0.04104169085621834,
0.06945058703422546,
0.006711538415402174,
-0.02078254148364067,
-0.026512017473578453,
0.043638285249471664,
0.018298029899597168,
-0.02040424384176731,
-0.0010259175905957818,
-0.01685292087495327,
-0.0009254598408006132,
-0.014464674517512321,
-0.02215271256864071,
0.02359052002429962,
0.0180558729916811,
0.01851581409573555,
-0.0012420741841197014,
0.07151049375534058,
-0.05001121014356613,
0.004099451471120119,
0.048159025609493256,
-0.048479046672582626,
-0.026628991588950157,
0.055460136383771896,
0.013314124196767807,
0.028212295845150948,
0.04039405286312103,
0.006202009506523609,
0.027027299627661705,
0.01706859841942787,
0.013371189124882221,
0.01981649547815323,
-0.059573862701654434,
-0.020679647102952003,
-0.03676199913024902,
-0.01998686045408249,
-0.006308440584689379,
-0.08269432187080383,
-0.022434908896684647,
-0.0170959010720253,
0.035975970327854156,
-0.03782586008310318,
0.02974741719663143,
0.011130615137517452,
-0.02384886145591736,
0.010309955105185509,
-0.012234640307724476,
-0.023045707494020462,
-0.031993988901376724,
0.010266060009598732,
-0.03799552470445633,
-0.016306022182106972,
0.0014569307677447796,
-0.017643442377448082,
-0.02507738582789898,
-0.043690022081136703,
-0.037448152899742126,
0.015041929669678211,
0.041456159204244614,
-0.0021154587157070637,
0.00915680080652237,
0.0071840244345366955,
0.0427217110991478,
-0.0035606296733021736,
0.031685780733823776,
0.01112380437552929,
-0.0260623712092638,
-0.04915771260857582,
-0.0011840630322694778,
-0.0024433578364551067,
0.04491889476776123,
0.013516182079911232,
-0.010730713605880737,
0.01721612550318241,
-0.023323502391576767,
-0.013931939378380775,
0.023925866931676865,
-0.046473488211631775,
0.08005276322364807,
-0.01015919353812933,
-0.009189740754663944,
-0.011579923331737518,
0.08029681444168091,
-0.0046536000445485115,
0.0023065214045345783,
-0.0009130240068770945,
-0.010452168062329292,
-0.06931115686893463,
-0.02810843102633953,
0.06494796276092529,
0.013069119304418564,
-0.0011629584478214383,
0.02774702198803425,
-0.0253222044557333,
0.044694069772958755,
0.029136966913938522,
0.010653975419700146,
-0.03272084519267082,
-0.0720435157418251,
0.03113197721540928,
-0.014604409225285053,
-0.007117035798728466,
0.06875811517238617,
-0.004021783825010061,
0.02538735419511795,
0.007156550418585539,
-0.005990995559841394,
0.025381209328770638,
0.03950152546167374,
0.002117475960403681,
-0.0026181109715253115,
0.014678338542580605,
-0.055889029055833817,
0.022514551877975464,
-0.022159477695822716,
0.005744886118918657,
0.008536809124052525,
-0.000633668270893395,
-0.006134822499006987,
-0.06098589301109314,
0.018094981089234352,
0.01252633798867464,
0.014007940888404846,
-0.008482322096824646,
-0.023955877870321274,
0.034811411052942276,
-0.022771764546632767,
-0.016873979941010475,
0.0051489658653736115,
-0.010269716382026672,
-0.0040073636919260025,
-0.025191329419612885,
-0.027497952803969383,
0.010591276921331882,
0.04640908166766167,
-0.0012629893608391285,
0.016482915729284286,
-0.004164434038102627,
-0.03070511668920517,
-0.007910753600299358,
0.028298068791627884,
-0.04079177975654602,
0.004226592369377613,
-0.0014763737563043833,
-0.04498209431767464,
0.05129618942737579,
-0.001434688689187169,
-0.016242006793618202,
0.039887480437755585,
-0.003905834397301078,
-0.03632180020213127,
-0.007853889837861061,
-0.01466738898307085,
-0.006316800136119127,
-0.024959830567240715,
0.004124673083424568,
0.04449237138032913,
-0.029600463807582855,
-0.0180888082832098,
-0.008955397643148899,
0.007542209699749947,
-0.017907273024320602,
-0.02781589701771736,
0.004489626735448837,
0.004756366368383169,
-0.008471175096929073,
0.003862893907353282,
0.02073279768228531,
-0.027533870190382004,
0.0019905257504433393,
-0.03756103664636612,
-0.026129024103283882,
-0.01594953052699566,
-0.027699099853634834,
0.020474471151828766,
0.012532836757600307,
-0.03009701706469059,
0.09044577181339264,
0.033310338854789734,
-0.040572572499513626,
-0.015716129913926125,
-0.013111615553498268,
-0.0007039632764644921,
-0.05103187635540962,
0.01889246515929699,
0.01819073036313057,
-0.006129567977041006,
-0.005865686107426882,
-0.009106500074267387,
0.015694381669163704,
-0.01318575069308281,
0.024450769647955894,
-0.013396126218140125,
0.01622472144663334,
-0.015107210725545883,
0.002312548691406846,
0.048579081892967224,
0.020402388647198677,
-0.038159385323524475,
0.027969688177108765,
-0.026508484035730362,
0.03881174325942993,
0.024456799030303955,
-0.04518377035856247,
0.05422937124967575,
0.0023507268633693457,
0.015439372509717941,
-0.026474827900528908,
0.05898100137710571,
-0.013145942240953445,
-0.05411244556307793,
0.01543179340660572,
-0.002996006514877081,
0.00428052106872201,
0.02236577868461609,
0.016858981922268867,
0.04970942810177803,
0.061954330652952194,
-0.0548030249774456,
-0.009200050495564938,
-0.019106663763523102,
0.02891518920660019,
-0.011461627669632435,
-0.041719164699316025,
-0.008276093751192093,
0.06566189229488373,
0.04487837851047516,
0.024733643978834152,
0.000861575361341238,
0.011417540721595287,
-0.03677869588136673,
-0.0471842922270298,
-0.005567630287259817,
-0.004493515472859144,
0.024758005514740944,
0.00805477611720562,
0.04490507021546364,
-0.009312016889452934,
0.02924478054046631,
0.011208746582269669,
-0.013042041100561619,
-0.09083076566457748,
-0.02025449462234974,
-0.012053177691996098,
-0.0019443226046860218,
-0.024198776111006737,
0.010163952596485615,
-0.04197606444358826,
-0.01400822028517723,
-0.007336446084082127,
-0.030558571219444275,
-0.01834290288388729,
-0.0347537100315094,
0.017132094129920006,
-0.05462168902158737,
-0.008697636425495148,
-0.020335525274276733,
0.009068149141967297,
0.05937330052256584,
-0.015469180420041084,
0.003707659663632512,
0.0009407640318386257,
-0.03434734046459198,
0.009616754949092865,
-0.022231217473745346,
-0.011995356529951096,
0.06214747950434685,
0.0025500664487481117,
-0.017834912985563278,
0.016703901812434196,
-0.03005579672753811,
-0.015249083749949932,
0.03207838162779808,
0.031166642904281616,
0.009164832532405853,
-0.0008591111982241273,
-0.03658647835254669,
-0.0409931056201458,
-0.016402898356318474,
0.013674065470695496,
0.0625825822353363,
0.002109516877681017,
0.013402260839939117,
0.003823979524895549,
-0.000020807601686101407,
-0.024125535041093826,
0.03566339239478111,
0.023386167362332344,
-0.018310142681002617,
0.0011520913103595376,
-0.02364232763648033,
-0.0007476586615666747,
-0.030880630016326904,
0.005849842447787523,
-0.007004742976278067,
0.011883405037224293,
-0.010088392533361912,
-0.0223329309374094,
0.016459915786981583,
0.019991716369986534,
-0.028468532487750053,
0.02763662487268448,
-0.04254363477230072,
-0.05545702576637268,
-0.02414558455348015,
-0.016853351145982742,
-0.0038080571684986353,
0.07732833176851273,
0.07784190028905869,
0.016430413350462914,
-0.013384523801505566,
-0.07977110147476196,
-0.041011735796928406,
0.04549892991781235,
0.029333481565117836,
0.015880873426795006,
-0.0062686363235116005,
-0.03961857035756111,
-0.019847549498081207,
0.007901844568550587,
-0.04952895641326904,
0.013989417813718319,
-0.009545647539198399,
0.02494274638593197,
-0.02378981187939644,
-0.07105547934770584,
-0.03045591153204441,
0.016366321593523026,
-0.024911487475037575,
0.023981694132089615,
0.006541500333696604,
-0.0050133634358644485,
-0.02313762903213501,
0.02928972989320755,
0.0013806938659399748,
0.005431891418993473,
-0.009523492306470871,
-0.020780416205525398,
-0.01081838645040989,
-0.034461382776498795,
-0.04557750001549721,
-0.10190951824188232,
0.0008875186904333532,
0.011812896467745304,
-0.01520401518791914,
0.03733132779598236,
-0.055767569690942764,
-0.07502523809671402,
0.01845819316804409,
-0.005733088590204716,
0.02666146121919155,
0.0066231414675712585,
-0.07132351398468018,
0.04337342828512192,
0.036101046949625015,
0.026030074805021286,
0.03343059495091438,
0.026280593127012253,
-0.021434178575873375,
0.04234267771244049,
-0.0060760932974517345,
0.008599505759775639,
-0.01888355240225792,
0.022380908951163292,
-0.03939425200223923,
-0.011219793930649757,
-0.056205932050943375,
0.053713224828243256,
0.005653562489897013,
-0.011741597205400467,
-0.020370956510305405,
-0.05193810164928436,
-0.02414841391146183,
-0.011653370223939419,
-0.005789905320852995,
-0.025799810886383057,
-0.03186674043536186,
0.013371193781495094,
-0.00931406207382679,
-0.008812560699880123,
0.01757212169468403,
-0.002300720661878586,
0.014505044557154179,
0.05018220841884613,
-0.011200860142707825,
0.017161233350634575,
-0.027964681386947632,
-0.03536524251103401,
0.007407482247799635,
-0.06129532679915428,
0.08559548854827881,
-0.044458433985710144,
0.006014614831656218,
-0.019270949065685272,
-0.03889501467347145,
-0.0565984807908535,
0.00908871740102768,
-0.0015374207869172096,
0.013773773796856403,
-0.004424560349434614,
-0.026668351143598557,
0.009900620207190514,
0.00848979502916336,
-0.024904634803533554,
-0.04839520901441574,
0.01090331468731165,
0.022739870473742485,
-0.051962025463581085,
0.0018745578126981854,
-0.00905071571469307,
-0.007975650019943714,
-0.059366095811128616,
0.04545978829264641,
0.030228981748223305,
-0.06771010160446167,
0.004329818766564131,
0.04391667991876602,
0.018118465319275856,
0.0381513275206089,
-0.008442099206149578,
-0.010607191361486912,
0.007016155403107405,
0.02902335301041603,
0.013239632360637188,
-0.02688477747142315,
0.042991071939468384,
-0.011826378293335438,
-0.018466003239154816,
-0.01665792241692543,
0.03622997924685478,
0.03426951915025711,
-0.015944868326187134,
0.00029169503250159323,
0.0754929706454277,
-0.0056737372651696205,
-0.05262592434883118,
-0.03225927799940109,
0.04982035234570503,
0.02952473983168602,
0.03370120748877525,
-0.027341192588210106,
0.0026654256507754326,
-0.004075171891599894,
-0.03200548142194748,
0.05838022753596306,
0.005742822308093309,
0.04726693406701088,
-0.005235573276877403,
0.022218264639377594,
-0.028560224920511246,
-0.013391523621976376,
0.04274299740791321,
-0.005823158659040928,
0.0022598402574658394,
-0.002486432669684291,
0.009261131286621094,
0.038237378001213074,
0.012904711067676544,
-0.0048361485823988914,
0.007182636763900518,
-0.025097256526350975,
-0.0028156053740531206,
0.015660878270864487,
0.00277115311473608,
0.0069468882866203785,
0.027881363406777382,
-0.04787302762269974,
-0.022967517375946045,
-0.029064463451504707,
-0.035916104912757874,
0.03143947198987007,
0.0018938812427222729,
0.022560209035873413,
-0.032531458884477615,
0.02987639047205448,
0.03403555974364281,
0.047174371778964996,
-0.06186826899647713,
0.004714810289442539,
0.043018411844968796,
0.023298267275094986,
0.029746584594249725,
-0.005827819462865591,
-0.04657759517431259,
0.05973431468009949,
-0.044843655079603195,
0.01042888592928648,
0.020557021722197533,
-0.0000894042823347263,
0.027636991813778877,
0.0039217229932546616,
0.015154196880757809,
-0.03920302167534828,
-0.031297218054533005,
-0.0480344258248806,
-0.024827050045132637,
0.016512105241417885,
-0.009379344061017036,
0.012475055642426014,
-0.009892159141600132,
0.01213163323700428,
-0.0006886907503940165,
0.000034886441426351666,
0.021469872444868088,
-0.055542152374982834,
-0.0008176098926924169,
-0.03970596566796303,
-0.012634290382266045,
0.05076880380511284,
-0.004728360567241907,
-0.03069460205733776,
0.03344759717583656,
-0.041871342808008194,
0.05017400532960892,
0.024328837171196938,
0.01982920430600643,
-0.04663410782814026,
-0.020805787295103073,
-0.02916976809501648,
0.006683822255581617,
-0.03705992549657822,
-0.010168728418648243,
0.13880477845668793,
0.03735696151852608,
0.04690071567893028,
-0.015725944191217422,
-0.0014716797741129994,
-0.027364064007997513,
0.0338812880218029,
-0.007781424093991518,
-0.0074599250219762325,
-0.06575991213321686,
0.02644493617117405,
-0.002211329760029912,
0.04810728877782822,
0.013482531532645226,
0.01858086884021759,
0.005977736786007881,
-0.02967669442296028,
-0.02187323197722435,
-0.020619848743081093,
0.021084727719426155,
-0.0070371245965361595,
0.00004131537571083754,
-0.02564803883433342,
0.018746066838502884,
0.011100411415100098,
-0.003938139416277409,
-0.012397072277963161,
-0.006408396642655134,
0.04011611267924309,
-0.0036741429939866066,
-0.04936259612441063,
0.015044271014630795,
0.0029954647179692984,
-0.011200884357094765,
-0.01861586607992649,
0.025551116093993187,
0.08796128630638123,
0.02722165547311306,
-0.012186331674456596,
0.012101639062166214,
0.03315025568008423,
-0.0004141154058743268,
0.01815224252641201,
0.03243425115942955,
-0.020183661952614784,
-0.01981416903436184,
-0.04134005680680275,
0.04412082955241203,
-0.023049740120768547,
-0.007797324098646641,
0.029078587889671326,
-0.01500704512000084,
0.021746566519141197,
-0.027873661369085312,
-0.010481302626430988,
-0.010062512941658497,
0.021909143775701523,
-0.019321754574775696,
-0.007444321643561125,
-0.0005415246123448014,
0.04336504265666008,
0.022899948060512543,
0.0020281935576349497,
-0.0019375139381736517,
-0.0016941039357334375,
0.02075309306383133,
0.004810932092368603,
0.019877463579177856,
0.007000291720032692,
-0.005915636196732521,
-0.013693127781152725,
0.0031685761641710997,
-0.013810630887746811,
0.013784030452370644,
-0.0033548239152878523,
0.024213504046201706,
0.016095895320177078,
-0.009592532180249691,
0.007642308250069618,
-0.04510927572846413,
-0.03324338048696518,
0.05075683817267418,
-0.003093186067417264,
-0.0026449207216501236,
-0.01383447926491499,
-0.025010189041495323,
-0.029312431812286377,
0.04650101065635681,
0.011483278125524521,
0.013135166838765144,
0.01541624404489994,
0.05198555439710617,
0.008035064674913883,
-0.014405368827283382,
-0.017646202817559242,
-0.009432647377252579,
-0.04517922177910805,
0.02780204825103283,
0.00831883680075407,
0.026095550507307053,
0.031470444053411484,
-0.019221818074584007,
0.0185564998537302,
0.00852278247475624,
-0.0068342904560267925,
0.0021747543942183256,
0.06651075184345245,
-0.005329387728124857,
-0.0016838267911225557,
0.050206299871206284,
0.015352500602602959,
-0.008477853611111641,
-0.021946467459201813,
-0.027870848774909973,
-0.017889337614178658,
-0.008056324906647205,
0.06285308301448822,
-0.025920502841472626,
0.004681187216192484,
0.025331171229481697,
0.02102968469262123,
-0.018051577731966972,
0.019433865323662758,
-0.061744607985019684,
0.010495753958821297,
0.016819240525364876,
-0.025921033695340157,
-0.04529653117060661,
0.04389319196343422,
-0.015001757070422173,
0.016169356182217598,
0.020688962191343307,
-0.018386075273156166,
-0.03489956632256508,
-0.0356881357729435,
-0.01695382222533226,
0.005305400118231773,
0.027231881394982338,
-0.01125486008822918,
-0.012154830619692802,
0.02346653677523136,
-0.015220828354358673,
-0.04859858751296997,
0.03109031170606613,
-0.0019884584471583366,
0.020142866298556328,
0.021438339725136757,
-0.005400398746132851,
0.009967966936528683,
0.06463002413511276,
-0.0030941003933548927,
-0.0026564046274870634,
-0.013163819909095764,
-0.02893543615937233,
-0.0020705026108771563,
-0.03411800414323807,
0.007740465458482504,
0.028888395056128502,
0.001327664009295404,
0.029734864830970764,
0.007203646004199982,
0.023159796372056007,
-0.002600607229396701,
-0.002803954528644681,
-0.021901484578847885,
-0.011058147996664047,
0.002325965790078044,
0.02924438938498497,
0.012145829387009144,
0.024096151813864708,
-0.02002009190618992,
0.013595151714980602,
0.0035578650422394276,
0.019315125420689583,
-0.12373163551092148,
-0.013579812832176685,
0.011843502521514893,
0.0185508094727993,
0.021302510052919388,
-0.03755997121334076,
-0.006207618862390518,
0.036600541323423386,
-0.06851229816675186,
0.0008609652286395431,
-0.01780707575380802,
-0.012711512856185436,
-0.010120564140379429,
-0.0016571400919929147,
-0.02390286698937416,
0.014358049258589745,
0.016347933560609818,
0.05806034430861473,
-0.029040329158306122,
0.044839948415756226,
-0.006232068873941898,
-0.04045914486050606,
-0.04026509448885918,
0.03741515055298805,
-0.033124469220638275,
0.007163026835769415,
0.08301333338022232,
-0.01921902969479561,
0.0054162247106432915,
0.031238654628396034,
0.0036618749145418406,
-0.0029715700075030327,
-0.008168434724211693,
0.020375141873955727,
0.007613181136548519,
0.02721613459289074,
0.00520008709281683,
-0.020329393446445465,
0.018151134252548218,
0.0003154745209030807,
0.011210571974515915,
0.053420212119817734,
0.015795275568962097,
-0.012964260764420033,
0.04647960886359215,
-0.02200358547270298,
-0.003577271942049265,
0.011888732202351093,
-0.022131728008389473,
0.03235544264316559,
-0.021631548181176186,
0.04838235303759575,
0.015508540906012058,
-0.02506164461374283,
-0.018828071653842926,
-0.06944764405488968,
-0.014803971163928509,
0.04928356409072876,
0.019312666729092598,
-0.029497189447283745,
0.04777896776795387,
-0.02388795092701912,
0.012770025990903378,
-0.019334405660629272,
0.007241625338792801,
0.012358675710856915,
-0.00818326324224472,
0.006472340319305658,
0.05778878554701805,
0.031795717775821686,
0.012112828902900219,
-0.03668619319796562,
-0.04151904955506325,
0.000991742592304945,
0.04080064594745636,
0.013228019699454308,
-0.01911342702805996,
-0.04465414211153984,
0.026856891810894012,
-0.09753420203924179,
0.0501217246055603,
0.017873700708150864,
-0.014143036678433418,
-0.05094156041741371,
-0.05064594745635986,
0.023196715861558914,
0.02932848408818245,
0.036723267287015915,
0.008511964231729507,
-0.017197025939822197,
0.03148572891950607,
-0.0013941858196631074,
0.037792883813381195,
-0.054142408072948456,
0.012919416651129723,
0.011653659865260124,
0.0036292204167693853,
0.033442530781030655,
0.027067968621850014,
0.005073627922683954,
-0.0030559843871742487,
0.03260982409119606,
-0.008630959317088127,
0.01831468753516674,
-0.002346472814679146,
-0.019946245476603508,
0.022565243765711784,
-0.010903079062700272,
-0.03166373446583748,
0.057763248682022095,
-0.032354626804590225,
0.003986801486462355,
0.031590383499860764,
-0.03155801072716713,
-0.011096067726612091,
-0.00608075549826026,
-0.032307080924510956,
0.016633950173854828,
0.007326327729970217,
-0.03733883798122406,
0.007152504753321409,
-0.04744692146778107,
-0.020794041454792023,
0.0598151870071888,
0.01855400577187538,
-0.02269035577774048,
0.04097520187497139,
-0.0016208977904170752,
0.04317334294319153,
0.034781333059072495,
0.01603727415204048,
0.024849804118275642,
-0.0344935767352581,
-0.02765272557735443,
0.06065152958035469,
0.051957521587610245,
0.026791954413056374,
0.00872694980353117,
0.04044888913631439,
-0.001178717240691185,
-0.024232132360339165,
-0.000363710307283327,
0.02406574785709381,
-0.023188650608062744,
-0.008565139025449753,
-0.02129366435110569,
0.004027603659778833,
0.014151590876281261,
0.036490872502326965,
-0.006027122028172016,
0.10854791104793549,
-0.023024333640933037,
-0.013447698205709457,
-0.002601241460070014,
0.05968325212597847,
0.026940535753965378,
0.054213326424360275,
0.014317425899207592,
0.028101665899157524,
0.007787645794451237,
-0.024226082488894463,
-0.06635653227567673,
0.008222179487347603,
0.02259640209376812,
-0.04489246755838394,
-0.012962354347109795,
0.02352178283035755,
0.009441091679036617,
-0.007660640403628349,
0.0037742245476692915,
-0.018950331956148148,
-0.01207008771598339,
0.045200418680906296,
-0.023122638463974,
-0.008406681939959526,
-0.04953897371888161,
0.011736465618014336,
-0.03813464567065239,
0.032697953283786774,
-0.05765461549162865,
0.056645382195711136,
-0.030109630897641182,
0.051187582314014435,
-0.0220471378415823,
-0.04573215916752815
] |
<p>Assuming I rotate a disk, I want to know how long it takes to completely stop, and the number of revolutions it made since I removed my fingers off the disk.</p>
<p>Lets say a DVD I rotate with my fingers. I only know the radians per second (velocity) of the last moment I touched the disc.</p>
<p>Can you guys tell me where to start?</p>
<p>Im trying to implement this on an iPhone app. So it would be nice if you mention <strong>equations</strong>. It should not be exact. </p> | 2,878 | [
-0.016865771263837814,
-0.03931119665503502,
-0.024195514619350433,
0.0034506209194660187,
0.013832601718604565,
-0.042301543056964874,
-0.026149937883019447,
0.006013020873069763,
-0.02338775247335434,
0.020965754985809326,
0.025735754519701004,
0.06399160623550415,
0.0164035614579916,
0.030703172087669373,
0.008244886063039303,
-0.006951170042157173,
-0.01780424825847149,
-0.009446936659514904,
-0.019223561510443687,
-0.037736449390649796,
-0.029017241671681404,
-0.019551143050193787,
0.00671034911647439,
0.00018075409752782434,
-0.05347702279686928,
0.0021781206596642733,
0.04710353538393974,
-0.014548618346452713,
-0.02018655836582184,
0.054130665957927704,
-0.0390748493373394,
-0.01940212771296501,
0.019217487424612045,
0.0437895767390728,
0.027894074097275734,
0.0354299433529377,
-0.06125406548380852,
-0.00656363507732749,
-0.04091738536953926,
0.00730202766135335,
-0.03473272547125816,
0.04001247510313988,
-0.0048384591937065125,
0.047435738146305084,
0.006347832269966602,
0.03613102063536644,
-0.03680034726858139,
0.004569040611386299,
0.048266537487506866,
-0.041987571865320206,
0.07835628092288971,
-0.018684757873415947,
0.07483915239572525,
-0.017185326665639877,
-0.00015526295464951545,
0.010661995969712734,
0.0639675110578537,
0.03298893943428993,
-0.025025473907589912,
-0.049417220056056976,
-0.017473647370934486,
-0.0054695578292012215,
0.016920441761612892,
-0.0644247829914093,
-0.02452768199145794,
0.02349032275378704,
-0.02004171907901764,
-0.019319986924529076,
0.05024956166744232,
0.003261246019974351,
0.008218144066631794,
0.017338715493679047,
0.06646719574928284,
-0.005102220922708511,
0.0024290953297168016,
-0.061288267374038696,
0.008051537908613682,
0.00787364225834608,
0.03618450090289116,
0.05975078418850899,
-0.04028933867812157,
0.008527382276952267,
0.01810939982533455,
0.052748192101716995,
0.034912966191768646,
-0.014920439571142197,
0.07461334019899368,
0.013430221006274223,
0.014374437741935253,
0.013271237723529339,
0.02741377428174019,
-0.011016438715159893,
0.012128418311476707,
0.02453567646443844,
-0.016164619475603104,
0.02769191563129425,
0.01856129802763462,
0.029083019122481346,
0.010806403122842312,
-0.028352970257401466,
0.00781053164973855,
-0.025444993749260902,
0.02953866310417652,
0.03822191059589386,
-0.03643709421157837,
-0.006215521600097418,
-0.007532909046858549,
-0.010251188650727272,
-0.02876845933496952,
-0.005067658144980669,
-0.015248489566147327,
0.007446715142577887,
0.006134341470897198,
0.009394604712724686,
-0.009230577386915684,
0.007566285785287619,
-0.021030783653259277,
-0.028574462980031967,
0.035445041954517365,
0.04975185915827751,
0.06920560449361801,
-0.05084593966603279,
-0.019463621079921722,
-0.06181032210588455,
-0.035530321300029755,
0.02781400829553604,
0.027292972430586815,
-0.0001639110705582425,
-0.03855705261230469,
0.01953200064599514,
-0.017579765990376472,
-0.03349855914711952,
0.033520154654979706,
-0.022578248754143715,
0.03234637901186943,
-0.029994327574968338,
-0.06337866187095642,
-0.05176287889480591,
0.038343023508787155,
-0.015375856310129166,
-0.03822462260723114,
-0.07001131772994995,
0.013475005514919758,
0.01844174601137638,
0.04638415202498436,
0.0039957864210009575,
0.008332447148859501,
0.008022382855415344,
0.011268970556557178,
-0.03613660857081413,
-0.034379445016384125,
-0.031749848276376724,
0.0033509358763694763,
-0.009338686242699623,
-0.017119338735938072,
-0.043697211891412735,
0.02669375389814377,
0.04924972355365753,
-0.00007542425009887666,
-0.015246630646288395,
0.01774308644235134,
-0.02682488225400448,
-0.00008951089694164693,
0.05757193639874458,
-0.011068170890212059,
-0.07303522527217865,
0.10198468714952469,
0.012031985446810722,
0.027100417762994766,
0.007065030746161938,
0.015994731336832047,
0.03521357476711273,
-0.008969735354185104,
0.011996487155556679,
0.07659507542848587,
0.008867324329912663,
-0.005536350887268782,
0.02605564147233963,
-0.02055293880403042,
-0.0003654755710158497,
-0.04298112541437149,
-0.03699328005313873,
0.003124027047306299,
-0.017248399555683136,
-0.024119701236486435,
0.03470584377646446,
-0.011476985178887844,
-0.01357230544090271,
-0.0408376008272171,
-0.024506086483597755,
0.01696937531232834,
-0.050294868648052216,
0.03040437586605549,
0.013188539072871208,
-0.021339109167456627,
-0.0020276398863643408,
0.014576650224626064,
0.040153153240680695,
-0.010264422744512558,
-0.03668668493628502,
-0.03483486920595169,
0.025406695902347565,
-0.021392904222011566,
-0.026425696909427643,
-0.032365571707487106,
0.061567410826683044,
0.05462612584233284,
-0.02013525366783142,
0.023614786565303802,
0.00038609214243479073,
-0.006084533873945475,
-0.020173843950033188,
-0.049832042306661606,
-0.03493497520685196,
0.036362744867801666,
-0.00994387548416853,
0.016524484381079674,
0.0283507090061903,
0.020291386172175407,
-0.009570421651005745,
0.008366133086383343,
0.04941130802035332,
0.052193742245435715,
0.022778665646910667,
0.04040517285466194,
0.007558336481451988,
-0.015317149460315704,
-0.020862631499767303,
-0.004524989984929562,
-0.05592186003923416,
-0.007768675219267607,
0.014417000114917755,
0.021884270012378693,
0.03455008566379547,
-0.032165706157684326,
-0.009433609433472157,
0.06549835205078125,
0.03827716037631035,
0.038595281541347504,
0.028049346059560776,
0.005037630908191204,
-0.0021175735164433718,
0.00030817705555818975,
0.0012773167109116912,
-0.04941777139902115,
0.03557053580880165,
0.006706851068884134,
0.029057325795292854,
0.003973889630287886,
0.031865477561950684,
-0.047872141003608704,
0.03873204439878464,
0.03750557452440262,
0.02662326954305172,
0.023963792249560356,
-0.05013304948806763,
0.04064296558499336,
-0.00958004780113697,
-0.014518423937261105,
0.01188159640878439,
-0.0043318686075508595,
0.004846876487135887,
-0.00153892464004457,
0.027666384354233742,
0.032915253192186356,
0.0027385293506085873,
-0.012762215919792652,
-0.01788175292313099,
0.03315019607543945,
-0.01642661914229393,
0.015051337890326977,
-0.022455692291259766,
0.014365294948220253,
-0.038801249116659164,
0.01997542195022106,
0.023370981216430664,
0.02321893908083439,
0.02152922749519348,
0.02119779959321022,
-0.024081941694021225,
-0.0020381049253046513,
-0.057454388588666916,
-0.007199634797871113,
0.016096554696559906,
-0.06334672123193741,
0.011387592181563377,
0.005400131922215223,
-0.03719500079751015,
0.055038854479789734,
-0.0020102292764931917,
-0.014871244318783283,
0.02064093016088009,
-0.012259410694241524,
-0.06728681921958923,
-0.0028731543570756912,
-0.005285406019538641,
0.010730794630944729,
-0.03372551500797272,
0.007387478370219469,
0.015485736541450024,
-0.0102707389742136,
-0.05016930028796196,
0.07641924172639847,
-0.05470786243677139,
-0.0435265488922596,
-0.010193108581006527,
0.020922129973769188,
0.049923546612262726,
-0.028825897723436356,
-0.01813790574669838,
0.009500937536358833,
0.004969281610101461,
0.006589375436306,
-0.09076951444149017,
-0.03409341350197792,
0.02532804012298584,
0.03570491448044777,
0.06854095309972763,
0.007675632368773222,
0.0040959566831588745,
0.08345296233892441,
0.0037688687443733215,
-0.035399388521909714,
-0.016942275688052177,
0.005991633981466293,
-0.006924533285200596,
-0.008746723644435406,
-0.04413743317127228,
-0.03977864980697632,
-0.04911348968744278,
-0.0024588238447904587,
-0.0321020781993866,
-0.007974464446306229,
0.04094046726822853,
-0.004121808800846338,
0.024061575531959534,
-0.011182653717696667,
0.002928131725639105,
-0.007304884027689695,
0.023101480677723885,
0.02667056769132614,
-0.04193425551056862,
0.012340635061264038,
-0.02000468224287033,
0.06395767629146576,
0.029989663511514664,
-0.060919806361198425,
-0.0008913982310332358,
-0.034071922302246094,
-0.025403382256627083,
0.02046046406030655,
0.021745558828115463,
-0.019082579761743546,
-0.02506004460155964,
-0.0018408194882795215,
0.05075296014547348,
0.044267043471336365,
0.006973624229431152,
-0.007132702507078648,
0.02263486199080944,
0.04242915287613869,
-0.014221777208149433,
-0.024769902229309082,
-0.029395630583167076,
0.003399872686713934,
0.025285637006163597,
-0.0607752799987793,
0.018869608640670776,
0.04144762456417084,
0.020796019583940506,
0.03908033296465874,
0.010598106309771538,
-0.037919722497463226,
-0.013854739256203175,
-0.07690539956092834,
0.00821742694824934,
0.0035221001598984003,
0.07527851313352585,
-0.00043241449748165905,
0.07078760862350464,
0.00436396012082696,
-0.0020050853490829468,
0.006125828251242638,
-0.0007078431081026793,
-0.06582621484994888,
0.07248266041278839,
-0.03687117248773575,
-0.047140032052993774,
0.01882408745586872,
0.031696029007434845,
0.03614289313554764,
-0.035672951489686966,
0.012223673984408379,
-0.002338834572583437,
-0.016285423189401627,
-0.05973709374666214,
-0.01265956275165081,
-0.03005947358906269,
0.008700319565832615,
0.00126600859221071,
0.014311079867184162,
0.042068056762218475,
-0.003640256356447935,
0.011930062435567379,
0.052202388644218445,
-0.02614751085639,
0.02428288944065571,
-0.017658637836575508,
-0.05564320832490921,
-0.040171485394239426,
0.028592994436621666,
0.03907714784145355,
-0.0004287196497898549,
0.008633372373878956,
0.00816061906516552,
-0.024820413440465927,
0.03824187070131302,
0.013679579831659794,
0.023227255791425705,
-0.030568204820156097,
-0.07867450267076492,
0.01204193476587534,
0.0099524836987257,
0.05255106836557388,
-0.02267259545624256,
0.005212693940848112,
0.0212569497525692,
0.004221509210765362,
-0.03219985589385033,
0.059524402022361755,
0.07312849164009094,
0.010000260546803474,
-0.018296683207154274,
-0.054089926183223724,
0.00252326182089746,
0.008244416676461697,
-0.0069060176610946655,
0.01598956808447838,
0.02481391280889511,
-0.007744479924440384,
-0.005180336069315672,
0.02733965404331684,
0.00809639971703291,
-0.02915172092616558,
0.05194155499339104,
-0.028762878850102425,
0.031159549951553345,
-0.019860852509737015,
0.0030354394111782312,
0.015288975089788437,
0.05206407979130745,
0.011163490824401379,
-0.026583310216665268,
0.0062266867607831955,
-0.0805269107222557,
-0.01427636481821537,
0.023817988112568855,
0.04115770384669304,
-0.011130871251225471,
0.007541711907833815,
-0.03951122239232063,
-0.027475403621792793,
0.02167384885251522,
-0.048525262624025345,
0.026239410042762756,
-0.015544602647423744,
0.002486461540684104,
-0.00022695079678669572,
-0.03229847922921181,
-0.028616013005375862,
0.05339270457625389,
-0.0010290048085153103,
0.001635656924918294,
-0.029058726504445076,
-0.0116474824026227,
-0.030555283650755882,
0.011734865605831146,
0.012960225343704224,
0.031129617244005203,
-0.0014060941757634282,
-0.009132116101682186,
0.016893506050109863,
-0.004055977798998356,
-0.031750600785017014,
-0.039225708693265915,
0.020974714308977127,
-0.009453305043280125,
0.0016215769574046135,
0.04214601218700409,
-0.01973111741244793,
-0.03382624313235283,
0.03493748977780342,
0.01707330532371998,
-0.010470842011272907,
-0.011258224956691265,
-0.054790135473012924,
0.010823494754731655,
0.022869206964969635,
0.003133272286504507,
0.02186140976846218,
0.02199927344918251,
-0.004881680011749268,
-0.0005642786272801459,
0.007808641996234655,
0.005556871648877859,
0.007631361950188875,
-0.016761554405093193,
-0.04788396507501602,
-0.014111275784671307,
-0.06538569927215576,
0.05586007982492447,
-0.002868111478164792,
0.023553047329187393,
-0.011134752072393894,
-0.010617202147841454,
-0.002383514540269971,
0.023597683757543564,
0.007772370707243681,
-0.008451420813798904,
0.005740566644817591,
0.001547978725284338,
0.0012417745310813189,
-0.03244300186634064,
-0.00010136199853150174,
0.02836182340979576,
0.027287933975458145,
0.0339508131146431,
0.009992223232984543,
0.001751387258991599,
-0.03832244873046875,
-0.06578170508146286,
0.014677117578685284,
-0.044320303946733475,
0.027805116027593613,
-0.05160454288125038,
0.004886367823928595,
0.04544341191649437,
-0.060480233281850815,
0.0036515439860522747,
0.007036599330604076,
-0.023924442008137703,
0.034109342843294144,
-0.044452909380197525,
0.02276313118636608,
0.018813606351614,
-0.008254507556557655,
-0.020433442667126656,
-0.0741095319390297,
0.0505436547100544,
-0.005862257443368435,
-0.022706812247633934,
-0.04100735858082771,
0.013010772876441479,
-0.03944586589932442,
-0.025137439370155334,
-0.003602958284318447,
0.0005767616094090044,
-0.015742769464850426,
-0.012164524756371975,
0.05563656985759735,
-0.02309401147067547,
0.06128973886370659,
-0.0064846184104681015,
-0.0232625100761652,
0.00609619589522481,
0.023587429895997047,
-0.050590090453624725,
0.02171655185520649,
0.046313509345054626,
-0.012853587046265602,
-0.03537740185856819,
-0.0016379310982301831,
-0.012090195901691914,
0.027286548167467117,
-0.005509679205715656,
0.028800789266824722,
-0.02163379080593586,
-0.002995323156937957,
-0.002194387372583151,
-0.03672895208001137,
0.018912645056843758,
-0.0015913607785478234,
-0.010287188924849033,
-0.010795462876558304,
-0.02351153828203678,
-0.02312246896326542,
-0.014706493355333805,
0.009183075278997421,
0.026156319305300713,
0.008219066075980663,
0.0023492714390158653,
0.014280450530350208,
-0.015767764300107956,
0.01675538718700409,
0.030878445133566856,
0.016603432595729828,
0.01900395378470421,
-0.006329501047730446,
-0.04562445729970932,
0.027232058346271515,
-0.009541473351418972,
-0.04309838265180588,
-0.02894601598381996,
-0.040401555597782135,
-0.02160724066197872,
0.07127942889928818,
-0.03006226196885109,
0.05274609476327896,
0.017103902995586395,
-0.003861132310703397,
-0.008878184482455254,
0.0432840920984745,
-0.0015948989894241095,
0.015422615222632885,
0.026789385825395584,
0.0361059308052063,
0.013389097526669502,
0.024501841515302658,
-0.0007588223088532686,
0.018974855542182922,
-0.015890909358859062,
0.02983248047530651,
0.000815716979559511,
-0.019617559388279915,
0.03986525163054466,
-0.023496735841035843,
-0.022740844637155533,
0.025995684787631035,
-0.0431903600692749,
0.055089231580495834,
-0.0011701027397066355,
-0.014900421723723412,
0.018548525869846344,
0.002792474115267396,
0.0021481497678905725,
-0.04134499654173851,
0.0036705518141388893,
-0.03794894739985466,
-0.019078213721513748,
0.01469589862972498,
0.01689864695072174,
0.007326064631342888,
0.0018798552919179201,
0.039099015295505524,
0.009931768290698528,
0.04168049618601799,
-0.0042035868391394615,
-0.04581432044506073,
-0.015518954023718834,
-0.03146444261074066,
-0.06338276714086533,
0.05554434284567833,
0.02956114523112774,
-0.02915806882083416,
0.006332967430353165,
0.00968114659190178,
0.009258084930479527,
0.04312331601977348,
0.039448000490665436,
0.02806892991065979,
0.09316490590572357,
0.01750602014362812,
-0.020979445427656174,
-0.0511397048830986,
0.010180574841797352,
0.10287987440824509,
0.04642592370510101,
0.008649568073451519,
-0.02130570448935032,
0.02014469914138317,
-0.023057445883750916,
-0.001189510221593082,
-0.04157296195626259,
0.04927168786525726,
-0.011587409302592278,
0.006822885945439339,
0.03683001175522804,
0.01269581913948059,
-0.02146650291979313,
0.00759933702647686,
0.007640467491000891,
-0.0033688959665596485,
-0.005953779444098473,
0.0179799422621727,
0.006117474287748337,
-0.013105298392474651,
-0.00580997671931982,
-0.052674125880002975,
0.02355504035949707,
-0.04322988912463188,
-0.05740431323647499,
-0.018365999683737755,
-0.033270079642534256,
0.01283838227391243,
0.01453004777431488,
-0.056103743612766266,
0.030001597478985786,
0.03336922824382782,
-0.024471336975693703,
-0.027899540960788727,
0.007814289070665836,
0.014752417802810669,
0.020807433873414993,
0.007990902289748192,
0.06104587763547897,
-0.01285699661821127,
0.0015571159310638905,
0.016138214617967606,
-0.0042426735162734985,
-0.0315554141998291,
-0.016160031780600548,
-0.04661574587225914,
0.01996050402522087,
0.010607629083096981,
0.028216319158673286,
-0.009907820262014866,
-0.014900597743690014,
-0.012547689490020275,
-0.05555582046508789,
-0.020214559510350227,
0.022737372666597366,
0.022670559585094452,
-0.032664909958839417,
-0.03449027240276337,
0.0033027660101652145,
0.020572800189256668,
0.015917325392365456,
0.025258906185626984,
0.003764011664316058,
-0.033276017755270004,
-0.008561637252569199,
0.004602034576237202,
0.03918799012899399,
-0.06504975259304047,
-0.004117738455533981,
0.023839807137846947,
-0.017573006451129913,
-0.01191712636500597,
0.02781703881919384,
0.03742603585124016,
0.008326830342411995,
-0.0009367838501930237,
-0.02499857358634472,
-0.032729633152484894,
-0.032428618520498276,
-0.030923083424568176,
0.03620528429746628,
-0.001897171139717102,
-0.023242969065904617,
0.0017431942978873849,
-0.010071064345538616,
0.034815188497304916,
0.025796271860599518,
-0.0007565237465314567,
0.02240845002233982,
-0.011084436438977718,
0.05536403879523277,
0.04512936994433403,
-0.019885580986738205,
-0.018285376951098442,
0.024230869486927986,
-0.05328904092311859,
0.0428878478705883,
-0.032001249492168427,
0.0708305686712265,
0.03982141241431236,
0.00030253425939008594,
-0.0036644134670495987,
0.02462131157517433,
-0.03158802166581154,
0.001918858615681529,
-0.013794606551527977,
-0.06983169913291931,
-0.054094839841127396,
0.026400486007332802,
-0.015464826487004757,
-0.04820994287729263,
-0.014898188412189484,
-0.02975471504032612,
-0.0022642696276307106,
-0.03150387108325958,
0.02412342093884945,
-0.011653812602162361,
0.04802148789167404,
-0.058010973036289215,
0.026381032541394234,
-0.00715745659545064,
0.020856032148003578,
-0.05111659690737724,
0.020648708567023277,
0.01869557797908783,
0.013550096191465855,
0.02431723102927208,
0.014231633394956589,
0.005633399356156588,
-0.02680438943207264,
0.013268397189676762,
0.010151932947337627,
0.038074277341365814,
0.018294185400009155,
0.005019873380661011,
-0.017523333430290222,
0.007729345466941595,
-0.026444489136338234,
-0.02681749314069748,
0.04050520062446594,
-0.06842420250177383,
-0.020319070667028427,
0.01661093346774578,
-0.03415171056985855,
0.04221424460411072,
0.03655952960252762,
-0.024343250319361687,
0.007470102980732918,
0.041448451578617096,
-0.007945367135107517,
-0.03160107508301735,
-0.005936515983194113,
-0.0009733567130751908,
0.00395700940862298,
0.01990905962884426,
0.01994442753493786,
-0.039795972406864166,
-0.024838728830218315,
0.017240693792700768,
0.01893274299800396,
-0.01305259857326746,
0.020205967128276825,
0.019658159464597702,
0.0167466402053833,
-0.01268000714480877,
0.025335950776934624,
0.007371910847723484,
0.03387350216507912,
0.02417420782148838,
-0.04224628210067749,
0.023403747007250786,
-0.005986530799418688,
0.01214210782200098,
-0.0753476694226265,
-0.00973421148955822,
0.009123342111706734,
0.0298953615128994,
0.04698804020881653,
-0.06258802860975266,
-0.01376513671129942,
0.05408415570855141,
-0.0579042062163353,
-0.017790120095014572,
-0.044824231415987015,
0.00796809047460556,
-0.011416715569794178,
-0.009300815872848034,
0.03486737981438637,
0.0018315145280212164,
0.009963423013687134,
0.02135085128247738,
0.03562481701374054,
0.022905893623828888,
-0.03310655802488327,
-0.020189132541418076,
0.01656787283718586,
0.012248954735696316,
-0.026651980355381966,
-0.034604765474796295,
0.04774602875113487,
-0.03344086930155754,
-0.003048732876777649,
0.015761861577630043,
-0.04887256398797035,
0.05373208224773407,
-0.007749403826892376,
0.01177551131695509,
0.003566471394151449,
0.0016205187421292067,
-0.0016680147964507341,
-0.029688159003853798,
-0.01703469827771187,
0.031439438462257385,
-0.03821149468421936,
0.04940350726246834,
-0.05723768100142479,
0.027385378256440163,
0.04855974391102791,
-0.020495351403951645,
-0.03782941773533821,
0.03874429315328598,
0.0037342621944844723,
0.010336015373468399,
0.010303191840648651,
0.03203262388706207,
0.0052486867643892765,
-0.0555192194879055,
-0.02471819333732128,
-0.030422506853938103,
0.025107940658926964,
0.022684644907712936,
-0.05914163962006569,
-0.021971624344587326,
0.007045992184430361,
0.004807805176824331,
-0.026579277589917183,
-0.0031159401405602694,
-0.0027789874002337456,
-0.011669237166643143,
-0.07702451199293137,
0.003196733770892024,
0.016077732667326927,
-0.008684264495968819,
-0.0032767904922366142,
0.00025565517717041075,
-0.029013516381382942,
0.053056031465530396,
0.04432591423392296,
-0.01590080000460148,
0.02271665260195732,
-0.024377398192882538,
-0.001410754630342126,
-0.054362282156944275,
0.0101860286667943,
0.025994794443249702,
-0.028508268296718597,
-0.04280524328351021,
-0.0394500307738781,
0.014431033283472061,
0.007022903300821781,
0.06671183556318283,
-0.0038437561597675085,
-0.03333207964897156,
0.010524091310799122,
-0.02174929529428482,
0.01849152334034443,
-0.033870629966259,
-0.025782950222492218,
-0.04902341216802597,
-0.016492843627929688,
-0.001388567266985774,
-0.004582542460411787,
-0.03881199657917023,
-0.024130910634994507,
0.019987473264336586,
0.009760255925357342,
0.025207674130797386,
-0.009914654307067394,
-0.022465571761131287,
0.045810069888830185,
-0.0016383874462917447,
0.020177414640784264,
0.06415008753538132,
0.0003707777359522879,
0.0011188472853973508,
0.03580939397215843,
-0.02042866125702858,
-0.0374116450548172,
0.0761285275220871,
-0.03705089911818504,
0.0047623952850699425,
-0.03404557704925537,
-0.011244736611843109,
0.03943495824933052,
-0.03674810379743576,
-0.015348601154983044,
0.026173852384090424,
-0.011359188705682755,
0.0194792952388525,
0.01781509630382061,
0.011570422910153866,
0.048061709851026535,
-0.02395077794790268,
0.028485294431447983,
0.06780903041362762,
-0.04585306718945503,
0.013441982679069042,
0.06157337874174118,
0.01292008999735117,
-0.00991824921220541,
0.005622066091746092,
0.004799064248800278,
-0.001280241529457271,
0.041347142308950424,
0.003503217129036784,
0.07369905710220337,
0.031944338232278824,
-0.0322704091668129,
-0.026697605848312378,
-0.02365706115961075,
0.00246004993095994,
0.04907242953777313,
-0.016639571636915207,
0.04975804686546326,
-0.010610437951982021,
0.018311576917767525,
-0.04895329847931862,
-0.00820894818753004,
-0.04758991673588753,
0.009200705215334892,
0.01882653683423996,
0.02571370266377926,
-0.025271613150835037,
0.027839617803692818,
-0.014302310533821583,
0.006927319802343845,
0.056083232164382935,
-0.011656921356916428,
0.049533575773239136,
0.03950752690434456,
0.004110041074454784,
0.004619069397449493,
-0.03954611346125603,
-0.015588786453008652,
-0.02443060278892517,
0.030980195850133896,
0.041396964341402054,
0.007848004810512066,
0.021295128390192986,
0.0012392365606501698,
0.024189628660678864,
0.02787698246538639,
-0.09844131767749786,
-0.01640075258910656,
-0.0154426796361804,
0.06411579996347427,
0.003768127178773284,
0.019147168844938278
] |
<p>I'm trying to understand a particular case of gauge theories, namely discrete spaces on which a group G can act transitively, with a gauge group H which is discrete as well.</p>
<p>From what I've already read about continuous and discrete gauge theory (I can provide the necessary references if needed*), it seems that the full gauge transformation group will be the semidirect product of G by H. However I'm unable to prove it...</p>
<p>Can someone point me to the proof of this fact ?</p>
<p>Any help greatly appreciated !</p>
<p>*Edit :
The bottom of page 2 in this reference describes this kind of thing without giving any proof : <a href="http://arxiv.org/pdf/1106.2759">http://arxiv.org/pdf/1106.2759</a></p> | 2,879 | [
0.0008638869621790946,
-0.009217697195708752,
0.01965140551328659,
-0.028292465955018997,
0.022673843428492546,
0.044863708317279816,
-0.036956433206796646,
0.0018045272445306182,
0.014168601483106613,
-0.030260609462857246,
0.032577481120824814,
-0.03055363893508911,
0.07353735715150833,
0.029775165021419525,
-0.004174793139100075,
0.00526070361956954,
-0.05425313860177994,
-0.007610976230353117,
-0.0005763821536675096,
-0.03903066739439964,
-0.024259544909000397,
0.04661228507757187,
-0.017072420567274094,
-0.006759383715689182,
0.0051128072664141655,
-0.027256663888692856,
-0.011330857872962952,
0.033839307725429535,
0.014847622253000736,
0.06776243448257446,
-0.011572671122848988,
-0.033206526190042496,
-0.00797557458281517,
0.02477666549384594,
-0.03246614336967468,
0.0005099248955957592,
-0.036550674587488174,
0.003702467540279031,
-0.00024495652178302407,
-0.02088514156639576,
-0.06636510789394379,
0.0019832777325063944,
-0.036670297384262085,
0.051156483590602875,
0.013341539539396763,
0.05483746528625488,
-0.03148657828569412,
0.02731061726808548,
0.06863848865032196,
-0.046665530651807785,
0.10257746279239655,
0.00562226353213191,
0.008366459049284458,
-0.0005842130049131811,
0.0038010776042938232,
0.009616315364837646,
0.05859517306089401,
0.05378732085227966,
-0.030404379591345787,
-0.022303249686956406,
-0.02324545755982399,
-0.09705543518066406,
-0.012804290279746056,
-0.04514452815055847,
-0.048417989164590836,
0.0014283218188211322,
0.013039331883192062,
-0.02730134129524231,
-0.012358803302049637,
-0.011378200724720955,
-0.011827108450233936,
-0.011584599502384663,
0.03752288967370987,
-0.02854357659816742,
0.035214126110076904,
0.014166866429150105,
0.03274375572800636,
-0.001942681148648262,
0.03730649873614311,
0.019106274470686913,
-0.049025390297174454,
0.046937841922044754,
0.010337339714169502,
0.018085647374391556,
0.008792281150817871,
-0.039578404277563095,
0.032435908913612366,
0.030632706359028816,
0.017008217051625252,
0.04589877650141716,
-0.026231208816170692,
-0.028793910518288612,
0.022847788408398628,
0.00226982613094151,
-0.04535742476582527,
0.05629987269639969,
0.023160135373473167,
0.03439616784453392,
-0.012857063673436642,
-0.034469686448574066,
-0.026740510016679764,
-0.03410334140062332,
-0.00809287466108799,
0.06257487088441849,
-0.025494743138551712,
0.047301001846790314,
-0.026201097294688225,
-0.01152168307453394,
-0.019150322303175926,
0.002331898547708988,
-0.03157636150717735,
-0.009396101348102093,
-0.011452230624854565,
-0.013943091966211796,
-0.0208569448441267,
-0.02543053589761257,
-0.040369488298892975,
-0.007222435902804136,
0.0750698372721672,
0.06577340513467789,
0.060118936002254486,
-0.022238722071051598,
0.006968598812818527,
-0.050255369395017624,
-0.06432532519102097,
0.017565863206982613,
0.02803228795528412,
0.007716458756476641,
-0.031612709164619446,
0.015561379492282867,
0.009945379570126534,
-0.03291293606162071,
-0.002328531350940466,
-0.00554664758965373,
0.035680972039699554,
-0.04387325420975685,
-0.10131632536649704,
-0.019419752061367035,
0.030310027301311493,
0.037196043878793716,
0.017173264175653458,
-0.05516883358359337,
0.01980726420879364,
0.03453671187162399,
0.0980619490146637,
-0.01820574514567852,
0.04660702869296074,
0.006857011467218399,
-0.006757230963557959,
0.0178613793104887,
0.008616674691438675,
-0.014459466561675072,
-0.0023605190217494965,
-0.05464117228984833,
-0.0035177182871848345,
-0.009443679824471474,
0.03957081958651543,
0.02967139333486557,
-0.013086155988276005,
-0.012669393792748451,
0.0831928700208664,
0.0002478869864717126,
-0.037515584379434586,
0.04703829064965248,
0.0021193798165768385,
0.009655261412262917,
0.03373914211988449,
0.012061523273587227,
-0.003873213194310665,
0.023031000047922134,
0.017440764233469963,
0.02071671187877655,
0.0446334108710289,
0.0671587884426117,
0.029306545853614807,
-0.012062087655067444,
-0.021981650963425636,
-0.024091850966215134,
-0.013526448979973793,
-0.03465687856078148,
0.02154991775751114,
-0.030071306973695755,
-0.037095922976732254,
0.022106217220425606,
-0.002874797908589244,
0.008343352004885674,
-0.011989087797701359,
-0.004996117204427719,
0.011663324199616909,
-0.0602254681289196,
-0.027227267622947693,
-0.0540974885225296,
-0.01225660927593708,
0.009352817200124264,
-0.011654314585030079,
0.03102383390069008,
0.012675349600613117,
0.006564919836819172,
-0.021172504872083664,
-0.05310157686471939,
-0.01798054948449135,
-0.013794643804430962,
-0.000654322502668947,
0.0023277520667761564,
0.037597477436065674,
0.031156159937381744,
0.07524660229682922,
0.0037681637331843376,
0.014193215407431126,
-0.0018819826655089855,
-0.008903189562261105,
0.038362208753824234,
-0.0012050456134602427,
0.02596738003194332,
-0.04819134622812271,
-0.010602796450257301,
0.028288833796977997,
0.0299200601875782,
-0.05150214582681656,
0.038157280534505844,
-0.04704791307449341,
0.05278322473168373,
0.09716099500656128,
0.0035073067992925644,
-0.022637639194726944,
-0.0023197419941425323,
0.014258517883718014,
0.012840544804930687,
-0.00667713163420558,
-0.028993254527449608,
-0.02154206857085228,
-0.00195531384088099,
0.043326325714588165,
0.018060775473713875,
0.005517479497939348,
-0.0013197623193264008,
0.001808728906325996,
0.06540736556053162,
0.015282963402569294,
0.021121541038155556,
-0.007854250259697437,
-0.007725751027464867,
0.004045124631375074,
0.0032833556178957224,
0.020483748987317085,
-0.015095285139977932,
0.011602051556110382,
-0.0052964105270802975,
0.027498884126544,
0.013727319426834583,
-0.026762446388602257,
0.05325651168823242,
-0.035155344754457474,
0.010530521161854267,
0.02876635268330574,
-0.003916620742529631,
0.053540755063295364,
-0.014319096691906452,
0.02334883250296116,
0.02051638998091221,
-0.03422314301133156,
0.03945225849747658,
-0.02021813578903675,
-0.02516048029065132,
0.0001954461185960099,
0.006788140162825584,
-0.007361073978245258,
-0.010354318656027317,
0.016273321583867073,
-0.03854867070913315,
0.001258599222637713,
-0.026950042694807053,
-0.0021840280387550592,
-0.02617216296494007,
-0.019580012187361717,
0.009683003649115562,
0.04615918546915054,
0.043377336114645004,
-0.04726241156458855,
-0.007141913753002882,
0.022397583350539207,
-0.039159201085567474,
0.039141155779361725,
0.023538785055279732,
-0.01999334990978241,
0.005507076624780893,
-0.06827342510223389,
-0.0234275721013546,
0.03743249177932739,
-0.019817974418401718,
-0.00573216937482357,
0.004888614173978567,
-0.011051164008677006,
-0.043442294001579285,
0.004745809361338615,
-0.03311964124441147,
0.028121646493673325,
-0.02369631826877594,
0.020418480038642883,
0.03123006410896778,
0.054710566997528076,
-0.07597201317548752,
-0.02263333648443222,
-0.003553225426003337,
0.010158516466617584,
-0.013168232515454292,
-0.013983337208628654,
-0.01237435545772314,
-0.032018326222896576,
0.062359608709812164,
0.005016552284359932,
-0.03381875157356262,
-0.005872749723494053,
-0.052155595272779465,
-0.02613975666463375,
-0.013883508741855621,
0.027959028258919716,
0.03832749277353287,
-0.003540125908330083,
-0.049823421984910965,
0.0569448322057724,
0.04816730320453644,
-0.061360083520412445,
-0.006635815370827913,
-0.0019142184173688293,
-0.017453491687774658,
-0.018597641959786415,
0.030002925544977188,
0.018559370189905167,
0.0051446957513689995,
0.008799122646450996,
0.034797582775354385,
0.032490186393260956,
0.02560473419725895,
-0.005456858314573765,
-0.05135578662157059,
-0.001687989803031087,
0.03217102587223053,
0.028819464147090912,
0.037187349051237106,
0.010487452149391174,
-0.03311147913336754,
-0.02562898024916649,
-0.013531588949263096,
-0.005181568209081888,
0.008113161660730839,
-0.038509633392095566,
0.036172155290842056,
0.00590973487123847,
0.0001589198800502345,
-0.02876712754368782,
0.043612003326416016,
-0.003122451016679406,
-0.05424005910754204,
0.03105526976287365,
0.043699465692043304,
0.020394518971443176,
-0.025549262762069702,
-0.018868420273065567,
0.02131701447069645,
0.04412342607975006,
-0.04893305152654648,
-0.013594317249953747,
-0.007108722347766161,
-0.02557576261460781,
0.06835848093032837,
-0.01621638610959053,
-0.00029478123178705573,
0.00857930351048708,
0.04378882423043251,
0.03559757024049759,
-0.004743106663227081,
-0.05733415484428406,
0.008294141851365566,
-0.03168700262904167,
0.022297093644738197,
0.03652185946702957,
0.045375991612672806,
-0.01874275878071785,
0.04625876247882843,
0.00512335728853941,
0.021463168784976006,
-0.004483534023165703,
-0.0029584113508462906,
-0.058998990803956985,
0.017140377312898636,
0.0052156890742480755,
0.0027406506706029177,
0.016303332522511482,
-0.01979089342057705,
0.00967324711382389,
0.020736390724778175,
-0.07350989431142807,
-0.03034786693751812,
-0.008607463911175728,
-0.05526673421263695,
-0.006022659130394459,
-0.06556908786296844,
-0.014488773420453072,
-0.012759329751133919,
0.017673704773187637,
0.05730593949556351,
-0.023491637781262398,
0.019364673644304276,
0.023196659982204437,
-0.037503693252801895,
0.015390889719128609,
-0.005507885944098234,
0.03350922837853432,
0.036162860691547394,
0.034342821687459946,
0.022079098969697952,
0.01214405708014965,
-0.007193116936832666,
0.0020541369449347258,
-0.01367890927940607,
0.03872086480259895,
-0.01191659364849329,
-0.026388047263026237,
-0.000148980543599464,
-0.055321477353572845,
-0.016290558502078056,
0.022230325266718864,
0.06440345197916031,
-0.006019491236656904,
-0.001947618555277586,
0.06977102160453796,
0.010371402837336063,
-0.016155028715729713,
0.017760679125785828,
0.041061822324991226,
-0.004151253029704094,
-0.05997953936457634,
-0.020027589052915573,
-0.01533032301813364,
0.013726156204938889,
-0.017261890694499016,
-0.003971905447542667,
-0.020701169967651367,
0.007592968642711639,
-0.00000733565639166045,
0.005013658665120602,
0.026530981063842773,
-0.01677965186536312,
0.008624752052128315,
0.025022219866514206,
0.0034731917548924685,
0.014178019016981125,
-0.010738732293248177,
0.015394100919365883,
0.06633039563894272,
0.06784428656101227,
0.0033388615120202303,
-0.015156744979321957,
-0.09074543416500092,
0.008673946373164654,
0.02474140375852585,
0.05753137543797493,
0.024224594235420227,
-0.006759861949831247,
-0.027859153226017952,
-0.021639766171574593,
0.04837348684668541,
-0.023498864844441414,
-0.0019625527784228325,
0.0009869885398074985,
-0.02509176917374134,
-0.02689197286963463,
-0.04723363369703293,
-0.0024221071507781744,
0.05284350737929344,
-0.008584579452872276,
0.015362066216766834,
-0.011806270107626915,
-0.0339970700442791,
-0.020322522148489952,
0.01710669696331024,
-0.007119093555957079,
0.028791597113013268,
0.021609021350741386,
0.03276709094643593,
0.008999072946608067,
0.05856063589453697,
-0.006975122261792421,
-0.03885474056005478,
0.03434889391064644,
0.06910190731287003,
0.005661004222929478,
0.07781943678855896,
-0.021150708198547363,
-0.023135151714086533,
0.03596753627061844,
-0.014776960015296936,
-0.007307492196559906,
-0.012944798916578293,
-0.03935570642352104,
0.018357548862695694,
0.04360189661383629,
-0.02087193913757801,
-0.004243758041411638,
0.03418890759348869,
-0.0006556846783496439,
-0.02708437480032444,
-0.0010070246644318104,
0.01787145622074604,
-0.03884655982255936,
0.019722215831279755,
0.02870772033929825,
0.007946235127747059,
-0.03093225695192814,
0.03841087222099304,
-0.014580021612346172,
0.02226117253303528,
-0.0006722668185830116,
-0.009663982316851616,
0.0027616978622972965,
0.006894107908010483,
-0.01573282666504383,
-0.006138081196695566,
-0.012746203690767288,
0.04930606856942177,
0.05037757009267807,
-0.020300425589084625,
0.04142915457487106,
-0.016527434810996056,
-0.0021870392374694347,
0.003482100088149309,
-0.015345895662903786,
-0.0228846687823534,
-0.03158407285809517,
-0.009262500330805779,
-0.0008206677157431841,
-0.024849161505699158,
0.0012590688420459628,
-0.022378351539373398,
-0.013245814479887486,
0.01886831969022751,
-0.04541228711605072,
-0.034593574702739716,
-0.017986411228775978,
-0.017435386776924133,
0.00714468490332365,
0.005939990747720003,
0.010022025555372238,
0.05061772093176842,
0.019125742837786674,
-0.08242465555667877,
-0.06130479276180267,
0.024822164326906204,
0.0038650864735245705,
-0.044255856424570084,
-0.051956988871097565,
0.0030461428686976433,
-0.06261862814426422,
-0.022249756380915642,
0.01989045925438404,
0.016595609486103058,
-0.04708635434508324,
0.015489093959331512,
0.00979059748351574,
0.04235255718231201,
0.05994303151965141,
0.005159659311175346,
-0.02245287038385868,
0.008377647958695889,
0.017550183460116386,
-0.013711058534681797,
0.007967373356223106,
-0.0004301582230255008,
-0.025995301082730293,
-0.0136719373986125,
0.005073123145848513,
-0.038503311574459076,
0.010288654826581478,
-0.04881787672638893,
-0.0007920642383396626,
0.04412315413355827,
-0.011398132890462875,
0.022397058084607124,
-0.04198230430483818,
-0.017160290852189064,
0.015057563781738281,
-0.007611067034304142,
-0.053337737917900085,
0.023454243317246437,
-0.022143376991152763,
-0.02589239925146103,
0.052574943751096725,
-0.00574647169560194,
0.015432209707796574,
0.003845660714432597,
0.022466719150543213,
-0.011966405436396599,
0.015547514893114567,
0.06891614943742752,
-0.047983262687921524,
-0.00609739450737834,
-0.04453309252858162,
0.029417743906378746,
0.035808540880680084,
-0.042111750692129135,
-0.06143394857645035,
-0.017225736752152443,
-0.02007407508790493,
0.0169416181743145,
0.0404307097196579,
-0.014560172334313393,
0.038318853825330734,
0.003599608549848199,
0.0007047094404697418,
-0.02666288986802101,
0.004258687142282724,
-0.0002876449725590646,
0.017706170678138733,
0.029324473813176155,
0.025951480492949486,
-0.03694754093885422,
-0.006558715365827084,
-0.002460743999108672,
0.02439292147755623,
-0.050466448068618774,
0.0027471999637782574,
0.019831910729408264,
0.007478602230548859,
0.011955360881984234,
-0.005234008654952049,
-0.003786007408052683,
0.04244929552078247,
-0.0493345744907856,
0.02871226705610752,
-0.01544808130711317,
0.043414611369371414,
0.006975338328629732,
0.03606446087360382,
0.024225519970059395,
-0.004324381239712238,
-0.04229779168963432,
-0.04777134209871292,
0.009274933487176895,
0.018037250265479088,
0.007858529686927795,
0.03680672124028206,
0.0053739724680781364,
0.044920291751623154,
-0.017754022032022476,
0.039593201130628586,
-0.01536822970956564,
-0.007809232454746962,
-0.03320201113820076,
-0.015864256769418716,
-0.02659868821501732,
0.03677734360098839,
-0.008826399222016335,
0.004247805569320917,
-0.04345398023724556,
-0.02660105936229229,
-0.006699013989418745,
0.015574208460748196,
0.03389393165707588,
0.029251359403133392,
0.0626225396990776,
0.0022495463490486145,
0.026654118672013283,
0.003916093613952398,
-0.021485285833477974,
0.11708556860685349,
0.030495470389723778,
0.013131959363818169,
-0.06577659398317337,
0.04452819004654884,
-0.012272210791707039,
0.033705923706293106,
-0.046176135540008545,
0.032478660345077515,
0.009917883202433586,
-0.03226924315094948,
0.024937426671385765,
0.04694988578557968,
-0.0038160919211804867,
-0.020314713940024376,
0.03488616645336151,
-0.03257014974951744,
-0.05654013156890869,
-0.00602923147380352,
0.028189728036522865,
-0.02324741706252098,
-0.015971273183822632,
-0.06443726271390915,
0.00558063667267561,
-0.014688029885292053,
0.007927101105451584,
-0.0354909747838974,
-0.004323424305766821,
0.009817956946790218,
0.053962934762239456,
-0.0470077320933342,
-0.0050005619414150715,
-0.029562024399638176,
-0.0304799173027277,
-0.05150154232978821,
-0.015252196229994297,
0.0010707497131079435,
0.025434639304876328,
0.030816039070487022,
0.04410712048411369,
-0.0009180502966046333,
0.016312746331095695,
0.004597253166139126,
0.025977501645684242,
-0.05607261508703232,
-0.0026084426790475845,
-0.032609716057777405,
0.0411655493080616,
-0.01628413423895836,
0.011412516236305237,
0.03487714007496834,
-0.010906979441642761,
-0.002660589525476098,
-0.04362361878156662,
-0.022756991907954216,
-0.015045558102428913,
0.011430530808866024,
-0.012188202701508999,
-0.005979101173579693,
0.033016614615917206,
0.027190539985895157,
-0.01771043799817562,
-0.015284279361367226,
-0.0417543388903141,
-0.03377038240432739,
-0.01799536868929863,
-0.007115530781447887,
0.018107200041413307,
0.0014462651452049613,
-0.032990604639053345,
-0.02298317290842533,
0.011373051442205906,
0.0015295532066375017,
0.007840588688850403,
-0.0024734330363571644,
0.007838912308216095,
0.07003491371870041,
0.017269317060709,
0.011048532091081142,
-0.00857757218182087,
-0.05229587107896805,
0.016815155744552612,
-0.0038581700064241886,
-0.045247845351696014,
-0.02023123949766159,
0.018749089911580086,
0.006245734170079231,
0.04475005716085434,
-0.03014807030558586,
-0.01319120917469263,
-0.017855625599622726,
0.013634509406983852,
0.036359094083309174,
-0.021928958594799042,
-0.002117875497788191,
0.021280165761709213,
-0.019752386957406998,
0.01248387061059475,
0.022690219804644585,
0.055304501205682755,
0.035418976098299026,
0.018193185329437256,
0.012491616420447826,
0.030852746218442917,
0.022721707820892334,
0.029361167922616005,
0.01884305104613304,
-0.0506722517311573,
0.023917026817798615,
0.012861049734055996,
-0.004438269883394241,
-0.06471029669046402,
-0.054260872304439545,
-0.0010044891387224197,
0.03311295434832573,
-0.0041606230661273,
-0.01250538695603609,
-0.024978768080472946,
-0.0233040489256382,
-0.034167587757110596,
0.045003194361925125,
-0.02933310531079769,
-0.005430562887340784,
-0.01826285384595394,
0.004289731848984957,
-0.019618410617113113,
0.015071621164679527,
-0.007687048986554146,
-0.00006343256973195821,
-0.008826084434986115,
-0.04653528332710266,
0.06310543417930603,
0.013494552113115788,
-0.02892831154167652,
-0.020998507738113403,
0.009510891512036324,
0.008554767817258835,
0.028402548283338547,
0.012159883975982666,
-0.03483632206916809,
0.005002752412110567,
-0.014668052084743977,
0.0007575703784823418,
0.024683816358447075,
-0.017132189124822617,
0.0434439554810524,
0.0026965371798723936,
-0.02233964204788208,
-0.02673349156975746,
0.04075419902801514,
-0.005376723594963551,
0.009289663285017014,
-0.02901802398264408,
-0.004307129420340061,
-0.007165206130594015,
-0.04426028952002525,
0.0377207025885582,
-0.009638539515435696,
-0.008544259704649448,
-0.002411389257758856,
-0.016817178577184677,
-0.012968335300683975,
0.0007121957023628056,
-0.02459714561700821,
-0.025572633370757103,
0.025133084505796432,
0.027049804106354713,
0.008379298262298107,
-0.00484097097069025,
0.031524308025836945,
-0.03940455615520477,
-0.0030867201276123524,
0.008899182081222534,
-0.010607942938804626,
-0.09636111557483673,
-0.006809995509684086,
0.06279376894235611,
0.011566704139113426,
0.04330170154571533,
-0.06198887154459953,
-0.0029937070794403553,
0.05747572332620621,
-0.08956729620695114,
0.00017218568245880306,
-0.028832873329520226,
-0.04824469983577728,
-0.04911908134818077,
-0.018910089507699013,
-0.01246658619493246,
0.06390195339918137,
0.05418460816144943,
0.05340471491217613,
0.0022253766655921936,
0.005229262635111809,
-0.02932903729379177,
-0.013159730471670628,
-0.022086650133132935,
0.000593010219745338,
0.03737877309322357,
-0.021788490936160088,
0.05948175489902496,
-0.02751137875020504,
-0.026247898116707802,
0.022002238780260086,
-0.00013621585094369948,
0.006075114477425814,
-0.005544408690184355,
0.019915027543902397,
0.04191203787922859,
0.023878803476691246,
0.04272701218724251,
0.020238742232322693,
0.010386955924332142,
0.002254362218081951,
0.01737530156970024,
0.01525215432047844,
-0.05869555100798607,
0.0003394886734895408,
0.00263554067350924,
-0.020938752219080925,
-0.03524903208017349,
0.016643451526761055,
-0.009752134792506695,
-0.03901290521025658,
0.020267436280846596,
-0.018832584843039513,
-0.006162358447909355,
0.025253605097532272,
-0.005697345826774836,
-0.052123408764600754,
-0.038076721131801605,
0.022646676748991013,
-0.015205198898911476,
0.020486781373620033,
0.025314871221780777,
-0.007696574088186026,
-0.018219763413071632,
0.030802935361862183,
0.031388286501169205,
-0.0015896643744781613,
-0.05650226026773453,
0.019926555454730988,
-0.015375207178294659,
0.00021428242325782776,
0.026997510343790054,
-0.009154977276921272,
-0.03519509732723236,
0.022719942033290863,
-0.005455571226775646,
0.044056277722120285,
-0.051726873964071274,
-0.01643691025674343,
-0.006789386738091707,
-0.058517493307590485,
0.03458187356591225,
0.027904046699404716,
-0.02024119719862938,
-0.025393370538949966,
-0.00595832709223032,
-0.014757455326616764,
-0.003858408657833934,
0.0795927569270134,
-0.0031324385199695826,
0.015833862125873566,
0.017964644357562065,
0.0053859613835811615,
0.029114343225955963,
-0.026720693334937096,
-0.02553384192287922,
-0.026854444295167923,
-0.033029504120349884,
0.012836840003728867,
-0.005169855430722237,
-0.011912389658391476,
0.035966068506240845,
-0.003355366410687566,
-0.015729455277323723,
0.024801861494779587,
-0.03497638180851936,
-0.07596367597579956,
0.04082171246409416,
-0.002088158391416073,
0.004936703946441412,
0.07322577387094498,
-0.03445420041680336,
-0.01035004947334528,
0.02987709827721119,
-0.002282594097778201,
-0.029202060773968697,
0.009471814148128033,
-0.030116135254502296,
0.04533606022596359,
-0.013381256721913815,
0.0023857092019170523,
0.028711838647723198,
-0.0058194370940327644,
0.006164120510220528,
0.03516274318099022,
-0.029422929510474205,
-0.0072096423245966434,
0.05651750788092613,
0.0221962109208107,
0.04644589126110077,
0.009759122505784035,
0.011432511731982231,
0.030352814123034477,
0.017336852848529816,
0.03667408600449562,
0.05100530385971069,
0.013954940252006054,
-0.018147064372897148,
-0.02527691051363945,
0.02085786871612072,
-0.028490077704191208,
0.019648147746920586,
0.0250807236880064,
0.030293475836515427,
-0.04366156458854675,
0.021371686831116676,
0.013955581933259964,
-0.04718729108572006,
0.005446809343993664,
0.04950735718011856,
-0.04322492703795433,
0.07537209987640381,
-0.036602314561605453,
0.035736776888370514,
-0.01602538488805294,
0.00942252203822136,
-0.005659088026732206,
0.04644988849759102,
0.025638537481427193,
0.03080194629728794,
-0.045024074614048004,
-0.0034885418135672808,
-0.003149285214021802,
-0.04869691655039787,
-0.015643978491425514,
-0.02372795343399048,
0.04904431477189064,
0.008311339654028416,
-0.019603809341788292,
0.022291840985417366,
-0.03780747205018997,
-0.004962610546499491,
-0.044805996119976044,
0.00022406836797017604,
0.060808636248111725,
0.02380390092730522,
-0.0037092657294124365,
-0.028091369196772575,
-0.037326544523239136,
0.057491060346364975,
-0.01551089622080326,
-0.012835035100579262,
-0.06159720569849014,
-0.014279487542808056,
-0.0064362166449427605,
0.010644548572599888
] |
<p>I am not exactly sure how the physics work here. If we take a car tow rope, which is manufactured for towing a 3500 kg car and we actually start towing such a car on this rope, what force do we really apply to the rope?</p>
<p>Could the same rope <strong>safely</strong> withhold an adult person (100 kg) hanging on it?</p> | 2,880 | [
-0.034794893115758896,
-0.010103694163262844,
0.01998615451157093,
-0.014096928760409355,
0.006984579376876354,
-0.02076464146375656,
-0.02674204856157303,
-0.023132607340812683,
0.01573515683412552,
-0.03141263127326965,
0.05218334123492241,
0.0847349539399147,
0.008158954791724682,
0.03601564094424248,
0.03218390792608261,
0.027290452271699905,
0.004375253338366747,
-0.005789615213871002,
0.016756976023316383,
-0.021029643714427948,
-0.04436957836151123,
0.009941157884895802,
0.011120980605483055,
0.0005356882466003299,
-0.017601484432816505,
-0.012463708408176899,
0.047685056924819946,
0.000489192723762244,
0.017867734655737877,
0.059223778545856476,
-0.011796876788139343,
-0.03953457623720169,
0.014103563502430916,
0.009081379510462284,
0.02119455859065056,
0.03487062081694603,
-0.07201921194791794,
-0.002365343738347292,
-0.0025443285703659058,
0.0035892059095203876,
-0.0276887658983469,
-0.028629841282963753,
0.007626005448400974,
0.0871116891503334,
-0.034556131809949875,
0.051950208842754364,
-0.026338225230574608,
-0.04304038733243942,
0.07925747334957123,
-0.04705743119120598,
0.056090451776981354,
-0.008753153495490551,
0.05023984983563423,
0.03405812382698059,
0.005020671524107456,
-0.03395998105406761,
0.05148598551750183,
0.023386381566524506,
-0.03982310742139816,
-0.07491724193096161,
-0.025790231302380562,
-0.019220020622015,
-0.04666052758693695,
-0.02868773229420185,
0.0077359601855278015,
0.00659499317407608,
-0.02259727753698826,
-0.052997853606939316,
0.03748172149062157,
0.006900998298078775,
0.00400583865121007,
-0.0030059264972805977,
0.03738997504115105,
-0.039323482662439346,
0.018127553164958954,
-0.006369350478053093,
0.017806947231292725,
0.023173030465841293,
0.03571346402168274,
0.046073995530605316,
-0.01323643047362566,
-0.016065366566181183,
0.052423346787691116,
0.07986076921224594,
0.02802714705467224,
-0.05421465262770653,
0.09033066034317017,
-0.015359022654592991,
0.028924887999892235,
0.014197682030498981,
-0.0013321336591616273,
0.003924389835447073,
0.01565493270754814,
-0.008156798779964447,
0.014000985771417618,
0.03892780840396881,
0.006754071917384863,
0.0621727779507637,
0.02800935134291649,
0.012233052402734756,
0.006346304435282946,
0.003644876182079315,
0.014388646930456161,
0.025515718385577202,
-0.01162110734730959,
-0.0065185436978936195,
0.012904356233775616,
0.0056530991569161415,
-0.018653634935617447,
-0.004226137418299913,
-0.03551432862877846,
-0.003162624314427376,
-0.0053114150650799274,
-0.041159406304359436,
-0.0004188748134765774,
-0.013703575357794762,
0.013743214309215546,
-0.002377887489274144,
0.035011887550354004,
0.014389969408512115,
0.027364607900381088,
-0.03376651182770729,
0.005797427613288164,
-0.04307877644896507,
-0.020647961646318436,
0.0018036005785688758,
0.039218969643116,
-0.002561152447015047,
-0.03763752430677414,
0.015496010892093182,
-0.000489543832372874,
-0.03892410919070244,
0.009508009999990463,
-0.0013274865923449397,
0.06452692300081253,
-0.018561221659183502,
-0.0949956402182579,
-0.056989289820194244,
0.01895873434841633,
-0.009598111733794212,
0.016078563407063484,
-0.051972683519124985,
0.020286157727241516,
0.017311042174696922,
0.05504823848605156,
-0.0012737400829792023,
0.05965762585401535,
0.02044343575835228,
-0.004602836910635233,
-0.041395194828510284,
0.008770066313445568,
-0.01457931101322174,
0.005365213844925165,
-0.03525494784116745,
-0.027527298778295517,
-0.10123205929994583,
0.058610785752534866,
0.03996177390217781,
0.02362547442317009,
-0.027494944632053375,
0.03292399272322655,
-0.023363642394542694,
0.006305927876383066,
0.0029210594948381186,
-0.016280630603432655,
-0.0033503274898976088,
0.07472611963748932,
-0.007895736955106258,
-0.0074720378033816814,
0.04624492675065994,
0.0015898122219368815,
0.03752168267965317,
0.03479520604014397,
0.00692075677216053,
0.016285564750432968,
-0.05314283445477486,
-0.008041172288358212,
-0.045082684606313705,
0.007126824464648962,
-0.02138049714267254,
-0.027698755264282227,
-0.039025016129016876,
0.004819531459361315,
0.03547416254878044,
-0.002807938726618886,
0.01804332248866558,
-0.008176829665899277,
-0.01414286345243454,
-0.0067830393090844154,
-0.013458321802318096,
-0.013512968085706234,
-0.03495262190699577,
0.023816199973225594,
-0.012712889350950718,
0.009037015028297901,
0.014710953459143639,
-0.029296880587935448,
0.04053099453449249,
-0.057192593812942505,
-0.007404219824820757,
-0.004600359592586756,
0.011730083264410496,
0.0006314468337222934,
0.05414314940571785,
0.028939003124833107,
0.05606430023908615,
0.06048760190606117,
0.042620085179805756,
0.01956573687493801,
-0.014726449735462666,
-0.08669223636388779,
-0.0036875370424240828,
-0.053144607692956924,
-0.004685886669903994,
0.027076736092567444,
0.008499408140778542,
0.031541626900434494,
-0.021227357909083366,
-0.010244222357869148,
0.032390352338552475,
-0.011922048404812813,
0.08071347326040268,
0.052064914256334305,
0.0244979877024889,
-0.006601046770811081,
0.03613793104887009,
-0.0037980785127729177,
-0.036298636347055435,
0.019685741513967514,
-0.036040328443050385,
-0.04421855881810188,
0.018778130412101746,
0.01967804506421089,
0.05106624960899353,
-0.03325635939836502,
0.02238740213215351,
0.019566114991903305,
0.04158569127321243,
0.05848376825451851,
0.03027537278831005,
-0.027394983917474747,
-0.03613773733377457,
0.05031903460621834,
0.02278539165854454,
-0.003325470257550478,
-0.02023334801197052,
-0.006290844641625881,
0.031882792711257935,
0.0042114462703466415,
-0.00981562864035368,
-0.027074351906776428,
0.0377575159072876,
-0.018954142928123474,
0.006684455554932356,
-0.01110909879207611,
-0.040006157010793686,
0.033689234405756,
-0.04921168088912964,
0.0034889166709035635,
0.011540485545992851,
-0.0027018780820071697,
-0.017345817759633064,
-0.024955475702881813,
-0.0031119121704250574,
0.03488028794527054,
0.016679028049111366,
-0.0382055938243866,
-0.015610316768288612,
0.03529566898941994,
-0.03212132677435875,
-0.0008110353955999017,
-0.004710416775196791,
-0.00016590920859016478,
-0.02066575549542904,
0.0058375815860927105,
0.0294547937810421,
-0.02938183955848217,
0.07311292737722397,
-0.003300354816019535,
-0.010531598702073097,
-0.0023244726471602917,
-0.025506069883704185,
-0.02797800302505493,
0.0019422853365540504,
-0.008678614161908627,
0.0073593431152403355,
-0.00773002952337265,
-0.023670310154557228,
0.08771117031574249,
-0.002481823554262519,
-0.009044765494763851,
0.02262323722243309,
-0.0012090540258213878,
-0.013501009903848171,
-0.02919914573431015,
-0.0018038160633295774,
0.030005227774381638,
-0.017311088740825653,
-0.04707280918955803,
0.04237646982073784,
0.014909232966601849,
0.007466938346624374,
0.02872217632830143,
-0.04814785718917847,
-0.017011839896440506,
0.024249596521258354,
0.025709060952067375,
-0.00641385605558753,
-0.01646336540579796,
-0.013174975290894508,
-0.011440466158092022,
-0.055415187031030655,
0.03423099219799042,
-0.07049670070409775,
-0.028390226885676384,
-0.0009146083611994982,
-0.000026896223062067293,
0.03663099184632301,
-0.014658593572676182,
-0.03352893516421318,
0.10237321257591248,
0.006280711852014065,
-0.029485175386071205,
-0.02245221473276615,
-0.07250328361988068,
-0.0483282171189785,
-0.01579582318663597,
0.005308339837938547,
0.024902164936065674,
-0.007760046981275082,
0.029813895002007484,
0.041422370821237564,
0.0036402493715286255,
0.016913626343011856,
0.03495430946350098,
-0.010710780508816242,
0.00023619268904440105,
-0.006878610234707594,
-0.017107512801885605,
0.0914427861571312,
0.014513170346617699,
-0.04851464554667473,
0.003338610753417015,
-0.008692413568496704,
0.065454863011837,
0.00024983315961435437,
-0.049810320138931274,
0.0731191635131836,
0.013721629977226257,
-0.00584263913333416,
0.00647369772195816,
0.07034139335155487,
-0.004801073111593723,
-0.018406156450510025,
0.015511547215282917,
-0.007306637242436409,
0.011198935098946095,
-0.04560824856162071,
-0.010343782603740692,
0.03150418400764465,
0.11403338611125946,
-0.036213669925928116,
-0.053469184786081314,
-0.003220299491658807,
0.00450361892580986,
0.018166394904255867,
-0.02784130908548832,
-0.04731563851237297,
-0.006950844544917345,
0.01258035097271204,
0.029012860730290413,
0.0028524724766612053,
-0.00413282448425889,
0.01291192602366209,
-0.06842395663261414,
-0.03866172209382057,
0.00015941215679049492,
0.025208188220858574,
-0.009963071905076504,
0.019261859357357025,
0.020964529365301132,
0.041591577231884,
0.004151389934122562,
0.04730377346277237,
-0.05557948723435402,
0.00003133101199637167,
-0.050819072872400284,
-0.04175080358982086,
-0.0064956727437675,
-0.04073205217719078,
-0.014294114895164967,
-0.03304099664092064,
0.005598606541752815,
-0.02876908890902996,
0.008479172363877296,
-0.049895621836185455,
-0.007997347973287106,
-0.031875308603048325,
-0.02417062409222126,
0.04090162739157677,
-0.014355798251926899,
0.025741299614310265,
-0.0065901014022529125,
0.03603833541274071,
0.031099651008844376,
-0.016771607100963593,
-0.00092600955395028,
-0.014825855381786823,
0.0006735082715749741,
-0.00029980429098941386,
0.01930994912981987,
0.0004917385522276163,
0.022395992651581764,
-0.01432353351265192,
-0.0035062783863395452,
-0.02212221920490265,
0.030429745092988014,
0.02171693556010723,
0.027317585423588753,
-0.04846585541963577,
-0.07720545679330826,
-0.03985246643424034,
-0.02204892225563526,
0.0024084090255200863,
-0.04444428160786629,
0.016277695074677467,
0.05387572571635246,
-0.009001419879496098,
-0.033229630440473557,
0.057261984795331955,
0.04748470336198807,
0.029203545302152634,
-0.027757642790675163,
-0.07114677131175995,
-0.010255246423184872,
0.009285856038331985,
-0.0230153389275074,
0.005143952555954456,
0.037350133061409,
-0.03153455629944801,
-0.003983129747211933,
0.04748629406094551,
0.023859743028879166,
-0.048285070806741714,
0.020100651308894157,
-0.0073357922956347466,
0.018270883709192276,
-0.02841133065521717,
0.034852493554353714,
0.04507870972156525,
0.014109738171100616,
0.047842346131801605,
0.011504372581839561,
0.002343820407986641,
-0.08417186886072159,
-0.02173672430217266,
0.032428205013275146,
0.012744280509650707,
-0.00004668818655773066,
0.022301236167550087,
-0.019770722836256027,
-0.029077665880322456,
0.056108519434928894,
-0.018753910437226295,
0.054665904492139816,
-0.024392826482653618,
0.035062480717897415,
0.01827983371913433,
-0.009061162360012531,
-0.015048615634441376,
0.013385817408561707,
-0.008089962415397167,
-0.007844218984246254,
-0.00542955007404089,
-0.010970355942845345,
0.02387980744242668,
0.03423835709691048,
0.03614077344536781,
0.017556052654981613,
0.024517223238945007,
-0.019396275281906128,
-0.006156612653285265,
0.003739041043445468,
-0.050968240946531296,
-0.06997278332710266,
0.017587807029485703,
0.006858952809125185,
-0.04459942504763603,
0.029693227261304855,
-0.031247427687048912,
-0.035172343254089355,
-0.024586714804172516,
-0.01986907422542572,
0.01601330377161503,
0.018936142325401306,
-0.03897110000252724,
0.01157207041978836,
0.024994641542434692,
0.012432939372956753,
0.02235119603574276,
0.060028355568647385,
-0.025029867887496948,
0.03190610557794571,
0.01180099043995142,
0.03410140797495842,
-0.0017977200914174318,
-0.001021800795570016,
-0.02422754094004631,
0.03208773955702782,
-0.054872628301382065,
0.011910568922758102,
0.01201334036886692,
0.006827416364103556,
-0.01610742136836052,
-0.012356195598840714,
-0.014085674658417702,
0.038408294320106506,
0.013803834095597267,
-0.008289692923426628,
-0.019121835008263588,
0.0021557724103331566,
-0.01324924174696207,
-0.03592192009091377,
0.008001407608389854,
0.023867420852184296,
0.04170532524585724,
0.008319556713104248,
-0.023975146934390068,
-0.006732520647346973,
-0.0140603082254529,
-0.010047107934951782,
0.0260132048279047,
-0.05241093039512634,
0.06421881914138794,
-0.04359684884548187,
0.055399321019649506,
-0.0052780876867473125,
-0.03947288170456886,
-0.003228585934266448,
0.005216443911194801,
-0.031172432005405426,
0.055651504546403885,
-0.009441609494388103,
0.05408552289009094,
0.01469422597438097,
0.00690881023183465,
0.004328284878283739,
-0.04963493347167969,
0.031771861016750336,
0.02182837948203087,
0.013731499202549458,
-0.01610836572945118,
0.02841937355697155,
-0.03492419421672821,
-0.018380388617515564,
-0.042692046612501144,
0.08102134615182877,
-0.0425216406583786,
0.038121093064546585,
-0.00018050150538329035,
-0.03520047664642334,
0.04902690649032593,
0.01783384568989277,
-0.01006969902664423,
0.008224140852689743,
-0.04216223582625389,
0.00011394558532629162,
0.004105762578547001,
0.01407264918088913,
-0.03508313000202179,
-0.0008992953808046877,
0.017858941107988358,
-0.0021928632631897926,
0.020053667947649956,
-0.023544572293758392,
0.026327036321163177,
0.04844558984041214,
0.02456912398338318,
0.029509397223591805,
0.004019584972411394,
0.041211649775505066,
0.014049068093299866,
0.030212653800845146,
-0.006891764234751463,
0.005225088447332382,
-0.023150548338890076,
-0.05403817445039749,
0.04490178823471069,
0.026854969561100006,
-0.010406465269625187,
0.023141508921980858,
0.06000730022788048,
-0.0018726367270573974,
-0.016956793144345284,
-0.019183961674571037,
0.023920400068163872,
0.044531550258398056,
0.0004622276173904538,
-0.0032782063353806734,
0.02890637330710888,
0.0023062413092702627,
-0.020013784989714622,
-0.023476695641875267,
-0.00995465274900198,
0.005030524916946888,
0.014308910816907883,
-0.04432223364710808,
0.058541543781757355,
0.013666008599102497,
-0.006374990567564964,
-0.009953735396265984,
0.008250031620264053,
-0.0030759256333112717,
0.001018906245008111,
-0.0038881043437868357,
-0.018514035269618034,
-0.020140543580055237,
0.026784058660268784,
0.03196248784661293,
0.01252052839845419,
0.0014847330749034882,
-0.010723595507442951,
0.012289384379982948,
0.01656656339764595,
0.03944103792309761,
-0.018158582970499992,
-0.010220872238278389,
0.018608534708619118,
-0.028145169839262962,
0.04368047043681145,
-0.024715416133403778,
-0.008613559417426586,
0.047946710139513016,
-0.006524684838950634,
0.02387956716120243,
-0.027690861374139786,
-0.009907441213726997,
-0.027350429445505142,
-0.0045644850470125675,
0.012962245382368565,
-0.01675950549542904,
0.023446811363101006,
-0.005312110297381878,
-0.011768638156354427,
0.024292968213558197,
0.015134544111788273,
-0.009932849556207657,
-0.025872662663459778,
-0.03326728940010071,
-0.013867867179214954,
-0.04331565648317337,
0.05839637294411659,
0.024701278656721115,
-0.054231125861406326,
0.03204038366675377,
-0.03622685745358467,
0.0020484563428908587,
0.026032159104943275,
0.01644115336239338,
-0.00915901642292738,
0.07827260345220566,
-0.01857868768274784,
0.021019725129008293,
-0.014605634845793247,
0.01791861467063427,
0.11696440726518631,
0.03221604600548744,
0.021160220727324486,
-0.02929041162133217,
-0.000928003282751888,
-0.03821871802210808,
-0.026036398485302925,
-0.029511190950870514,
0.019113246351480484,
0.034056637436151505,
0.01699872687458992,
0.007407771423459053,
0.02707226201891899,
-0.01754862070083618,
-0.03778500854969025,
0.03355513513088226,
-0.04234443977475166,
-0.0335090272128582,
-0.012412837706506252,
0.015738151967525482,
-0.03483464568853378,
-0.013018612749874592,
-0.03444061800837517,
0.011900641955435276,
0.008304765447974205,
0.001574724679812789,
-0.012091919779777527,
-0.013965655118227005,
0.037727680057287216,
-0.020637625828385353,
-0.05041665956377983,
-0.029414089396595955,
-0.0004080795624759048,
-0.016803041100502014,
-0.037904296070337296,
0.041672851890325546,
0.01822081208229065,
0.011968819424510002,
-0.04280843213200569,
0.018698319792747498,
0.010050979442894459,
-0.001287595252506435,
0.019832128658890724,
-0.005688074976205826,
-0.034104857593774796,
-0.007481852080672979,
-0.04114958271384239,
0.024989407509565353,
0.021257633343338966,
0.04341794177889824,
0.007142210379242897,
-0.018199753016233444,
0.02446005679666996,
-0.04781205579638481,
-0.011929139494895935,
0.0010840456234291196,
0.01935901865363121,
0.009031452238559723,
-0.02630288153886795,
-0.006781978998333216,
0.03758843243122101,
0.011711928993463516,
-0.003662612522020936,
0.04249783977866173,
-0.026497522369027138,
-0.01703551597893238,
-0.02644628845155239,
0.039886221289634705,
-0.023667966946959496,
-0.03394395858049393,
-0.04753021150827408,
-0.020776866003870964,
-0.04708859696984291,
0.022046677768230438,
-0.003481985302641988,
0.03162418678402901,
0.03939707949757576,
-0.0033570134546607733,
0.010196853429079056,
-0.03262809291481972,
-0.046443384140729904,
0.05292010307312012,
-0.02708427608013153,
-0.025028986856341362,
-0.037473637610673904,
-0.017058176919817924,
0.016748957335948944,
0.05287953093647957,
0.013872544281184673,
0.032973479479551315,
-0.014920760877430439,
0.030492430552840233,
-0.00199720892123878,
-0.03712215647101402,
-0.042586661875247955,
0.015420456416904926,
-0.06167863681912422,
0.010197912342846394,
0.0054229735396802425,
0.04880625009536743,
0.015365704894065857,
-0.022090092301368713,
-0.014237508177757263,
0.03108624741435051,
-0.011052699759602547,
0.02327059581875801,
0.033947303891181946,
-0.009480327367782593,
-0.02092886157333851,
0.026013897731900215,
-0.017809610813856125,
-0.03271346166729927,
-0.02164711058139801,
-0.02035955898463726,
-0.04051469266414642,
0.0036744470708072186,
0.020321395248174667,
0.004529980011284351,
-0.013184924609959126,
0.018426530063152313,
0.004187989514321089,
-0.040876276791095734,
-0.007869776338338852,
-0.040971335023641586,
-0.010110140778124332,
-0.02444440685212612,
-0.022339342162013054,
-0.06611122190952301,
0.008538509719073772,
-0.027770420536398888,
0.026614008471369743,
-0.011954010464251041,
-0.02666177786886692,
-0.04037032276391983,
-0.046461015939712524,
-0.03430383652448654,
-0.0009406149620190263,
0.008461718447506428,
-0.02548147179186344,
-0.05460411310195923,
0.06052224710583687,
-0.03811310604214668,
-0.019573740661144257,
0.008655993267893791,
-0.0034803682938218117,
0.041908200830221176,
0.0007781695458106697,
-0.00526852160692215,
-0.029908539727330208,
0.06928084045648575,
-0.040107253938913345,
-0.01573917642235756,
0.011325640603899956,
-0.021954040974378586,
-0.023509854450821877,
-0.03137475997209549,
-0.01409056968986988,
-0.015921058133244514,
-0.02942625619471073,
0.006487247068434954,
0.029666781425476074,
-0.009317786432802677,
0.008944248780608177,
0.022263111546635628,
0.026144273579120636,
-0.014576160348951817,
0.03511316701769829,
0.011149945668876171,
0.012092221528291702,
0.04587342217564583,
-0.021862151101231575,
0.003659657435491681,
-0.032943353056907654,
0.020157761871814728,
-0.0996139720082283,
-0.027097241953015327,
0.050041861832141876,
-0.012820758856832981,
0.05645096302032471,
-0.059190843254327774,
-0.010571938939392567,
0.00666561396792531,
-0.05578793212771416,
0.0010564684635028243,
-0.015361691825091839,
-0.014797034673392773,
-0.030607813969254494,
-0.0009530441602692008,
0.01482886541634798,
0.025943484157323837,
-0.007630689535290003,
0.044289860874414444,
0.00008514483488397673,
-0.02983759343624115,
0.016091464087367058,
-0.015277966856956482,
0.00628459919244051,
0.0527028888463974,
-0.010394171811640263,
0.045697279274463654,
0.07229345291852951,
-0.012332338839769363,
-0.010483380407094955,
0.02814543806016445,
-0.0049244100227952,
0.03306480869650841,
0.02337268367409706,
0.03559703007340431,
0.021146312355995178,
0.02342919632792473,
0.00881071574985981,
0.014998015016317368,
-0.00036253785947337747,
0.03383805230259895,
-0.02440681867301464,
0.023996271193027496,
-0.04842011258006096,
0.01936427131295204,
0.03726379573345184,
-0.06542512774467468,
-0.0056977407075464725,
0.03292127698659897,
-0.032367926090955734,
0.00982645433396101,
-0.015617482364177704,
-0.0017131430795416236,
-0.028229085728526115,
-0.0024272005539387465,
-0.022706052288413048,
-0.04921248182654381,
-0.011656556278467178,
0.04268259182572365,
-0.01540759950876236,
0.012132909148931503,
0.037062086164951324,
-0.02003420889377594,
0.008095145225524902,
-0.0012970271054655313,
-0.017973706126213074,
-0.010183985345065594,
-0.044517867267131805,
0.03529698774218559,
0.016027389094233513,
-0.0022048891987651587,
-0.01822054013609886,
-0.037772443145513535,
0.007633567787706852,
0.051864366978406906,
0.038013823330402374,
0.02669639326632023,
0.037371352314949036,
-0.02999425120651722,
0.02543032541871071,
-0.09418658912181854,
0.0478619709610939,
0.004276831168681383,
-0.03577694669365883,
-0.03284323588013649,
-0.017785146832466125,
0.017593540251255035,
-0.017711222171783447,
0.026108374819159508,
-0.0161354411393404,
-0.010779624804854393,
0.0015704958932474256,
-0.030460931360721588,
-0.017008783295750618,
0.006518498528748751,
0.0025614965707063675,
-0.005145134404301643,
-0.027163662016391754,
-0.023175982758402824,
0.027728665620088577,
-0.010033795610070229,
-0.006544623523950577,
0.02405920810997486,
0.02740374580025673,
0.020316412672400475,
-0.002938276855275035,
-0.03315897285938263,
0.029917357489466667,
-0.0004564684350043535,
-0.000440523202996701,
0.012999973259866238,
-0.04219147190451622,
0.034994419664144516,
0.04010728746652603,
-0.007054997608065605,
-0.04677257686853409,
0.042091891169548035,
-0.030750824138522148,
0.026479700580239296,
-0.020933356136083603,
-0.02935052290558815,
0.04662354290485382,
-0.032803039997816086,
0.009002582170069218,
0.037479646503925323,
-0.03172485902905464,
0.0008466708823107183,
0.03853268548846245,
0.06420591473579407,
-0.003564678831025958,
-0.015879321843385696,
-0.004987721797078848,
0.051817260682582855,
-0.028865795582532883,
0.003024421166628599,
0.0062460582703351974,
0.019012771546840668,
-0.0419454462826252,
-0.007300721947103739,
0.04297716170549393,
0.020452380180358887,
0.033555351197719574,
0.043119966983795166,
0.027424057945609093,
-0.0062667070887982845,
-0.027423560619354248,
-0.01328081451356411,
-0.005580818746238947,
0.024203309789299965,
0.02200816199183464,
-0.02792520821094513,
0.06053838133811951,
-0.023290148004889488,
0.004933956079185009,
0.021680399775505066,
0.011481761001050472,
-0.0075880964286625385,
-0.015172597952187061,
0.029049357399344444,
0.034799471497535706,
-0.024041350930929184,
-0.04081612452864647,
-0.0022109863348305225,
-0.0032295039854943752,
0.028109513223171234,
-0.010409954003989697,
0.016927208751440048,
-0.029178395867347717,
0.017184371128678322,
-0.03369530662894249,
-0.05659210681915283,
-0.03840598091483116,
-0.038872960954904556,
0.04351736977696419,
0.04076021537184715,
-0.011820659041404724,
-0.028985008597373962,
0.01204418670386076,
-0.029838692396879196,
0.06051746383309364,
-0.05602877959609032,
0.00040407737833447754,
-0.00703028030693531,
0.05065057426691055,
-0.02213638834655285,
-0.033240605145692825
] |
<p>I'm thinking about a project to tackle, and I'd like to make a simulation that allows the user to define a rope or chain of length L, pin it at arbitrary points r1, r2.... etc. and draw the resulting curve in real time.</p>
<p>Also, I'd like the user to be able to alter the field that the rope exists in, for example more complex vector fields than just a straight gravitational field. This is a bonus, however, and I'd like to get the basic example working.</p>
<p>Could you recommend some resources, preferably free/online, for me to learn the physics involved (I'm not exactly sure what to CALL this area of classical mechanics)? I learn through concepts and then math so a resource that is concept-heavy would be nice. </p>
<p>Thanks! </p> | 2,881 | [
-0.010390006937086582,
-0.008387279696762562,
-0.011763392016291618,
-0.02243145741522312,
0.005305713973939419,
0.004198255017399788,
-0.0019157488131895661,
-0.010522963479161263,
-0.0015502874739468098,
-0.030591217800974846,
0.03117610700428486,
0.08094058930873871,
0.031695395708084106,
0.04962445795536041,
0.013837328180670738,
0.000767146295402199,
0.018347445875406265,
-0.025427576154470444,
-0.00043586836545728147,
-0.04888016730546951,
-0.021353483200073242,
-0.027985304594039917,
0.022228054702281952,
-0.01050576101988554,
0.005032694432884455,
0.043188031762838364,
0.07013390213251114,
-0.02940501645207405,
0.011249072849750519,
0.07703713327646255,
-0.047556594014167786,
-0.011122068390250206,
-0.06804205477237701,
0.024215860292315483,
0.030096065253019333,
0.024286145344376564,
-0.07482101023197174,
-0.05929865688085556,
0.01762566901743412,
0.009189048781991005,
-0.025104112923145294,
-0.02058319002389908,
-0.04143852740526199,
0.054611917585134506,
-0.008268309757113457,
0.045865222811698914,
-0.029520248994231224,
-0.03993887081742287,
0.06431785225868225,
-0.024865416809916496,
0.05309334769845009,
0.0074721891433000565,
0.02342747151851654,
0.0025402288883924484,
0.01038904394954443,
-0.027260590344667435,
0.06681106984615326,
0.03985946625471115,
-0.017038386315107346,
-0.0626426488161087,
-0.005847826600074768,
-0.010996798053383827,
-0.02884792909026146,
-0.05251779407262802,
-0.013255174271762371,
0.021550070494413376,
0.022887451574206352,
-0.02466357871890068,
0.0413394495844841,
-0.015690192580223083,
-0.032045867294073105,
0.024608563631772995,
0.022848477587103844,
-0.022961711511015892,
-0.0068320464342832565,
-0.025394292548298836,
0.006463170982897282,
0.0012718185316771269,
0.024926839396357536,
0.04115293547511101,
-0.01247022207826376,
-0.0017730063991621137,
0.03343775123357773,
0.0621294341981411,
0.020097000524401665,
-0.04349939897656441,
0.06880506128072739,
0.016455166041851044,
-0.006235347129404545,
0.006418477278202772,
-0.00008986095053842291,
-0.01740865409374237,
0.01881873607635498,
0.007974786683917046,
-0.02693766914308071,
-0.02245742455124855,
-0.0030054536182433367,
0.02342098206281662,
0.04496517777442932,
0.003359717084094882,
0.007296601310372353,
-0.04606781527400017,
0.012585881166160107,
0.04377882182598114,
0.011473936960101128,
0.0066105094738304615,
0.032661568373441696,
-0.03091830015182495,
-0.018053242936730385,
-0.018314115703105927,
-0.020286522805690765,
-0.014017095789313316,
0.007646096870303154,
0.0035714777186512947,
-0.016703395172953606,
-0.07291371375322342,
0.0018238748889416456,
0.0047661662101745605,
0.03853549435734749,
0.043017130345106125,
0.05458610877394676,
-0.04480910673737526,
0.07823563367128372,
-0.0222576055675745,
-0.06274748593568802,
-0.015651391819119453,
0.02931736223399639,
-0.026536786928772926,
-0.03353652358055115,
0.021447759121656418,
0.018166083842515945,
-0.020376017317175865,
-0.0005461769760586321,
0.0035460737999528646,
0.0520012304186821,
-0.011046535335481167,
-0.1053946241736412,
-0.06794366985559464,
0.031408991664648056,
0.040793728083372116,
-0.008820710703730583,
-0.031213827431201935,
0.0283477995544672,
0.013118204660713673,
0.05161895975470543,
0.02205299399793148,
0.0017553709913045168,
-0.0026574810035526752,
0.027850495651364326,
-0.018207838758826256,
-0.011786754243075848,
0.009482336230576038,
-0.009598099626600742,
0.005860017612576485,
-0.03218245506286621,
-0.06560169905424118,
0.02643849141895771,
0.02838253602385521,
-0.0010061434004455805,
-0.034648213535547256,
0.049322932958602905,
-0.003376514185220003,
0.032371800392866135,
0.052382562309503555,
-0.039019614458084106,
-0.00853224191814661,
0.10327675938606262,
0.004109485074877739,
0.0030729463323950768,
0.02083313651382923,
-0.02144436538219452,
0.0266959797590971,
0.02671562321484089,
0.016208002343773842,
0.03541572019457817,
-0.04143255576491356,
-0.0012384109431877732,
0.024323606863617897,
0.0013879265170544386,
0.009159081615507603,
-0.017922591418027878,
-0.03600729629397392,
0.01748022995889187,
-0.010609334334731102,
-0.02193458192050457,
0.05944345146417618,
0.01579424738883972,
0.01661161705851555,
-0.013767676427960396,
-0.022502277046442032,
-0.010699370875954628,
-0.035767167806625366,
0.08120878040790558,
-0.00692686066031456,
-0.015464535914361477,
0.0072739156894385815,
0.041647277772426605,
0.022414296865463257,
-0.04971309006214142,
-0.04249855503439903,
-0.015346596017479897,
0.0304123368114233,
0.01463367324322462,
-0.004236866720020771,
-0.015331761911511421,
0.057334739714860916,
0.042091112583875656,
-0.002113949740305543,
0.0005865907296538353,
-0.014484700746834278,
-0.03719335049390793,
-0.01803906261920929,
-0.034019652754068375,
0.04794910177588463,
0.02201194316148758,
0.02872186340391636,
0.00952833704650402,
0.0008849350269883871,
-0.0034248405136168003,
0.019314059987664223,
-0.008876214735209942,
0.06268662959337234,
0.054278090596199036,
0.021318016573786736,
0.01991579309105873,
0.040031641721725464,
-0.020104406401515007,
0.014866971410810947,
0.019548172131180763,
-0.016131659969687462,
-0.0018337257206439972,
-0.0016173836775124073,
0.053357526659965515,
0.0423092283308506,
-0.04874828830361366,
-0.0055203731171786785,
0.05364746227860451,
0.04756084829568863,
0.04418228566646576,
0.03723205253481865,
-0.024941232055425644,
-0.038915906101465225,
0.009875020012259483,
0.0064514013938605785,
0.021428456529974937,
0.022139256820082664,
0.037650804966688156,
0.03997814282774925,
0.013401388190686703,
-0.013411488384008408,
-0.03628489747643471,
0.04204107075929642,
-0.028063662350177765,
0.002845157403498888,
0.010883117094635963,
-0.03502616286277771,
0.0402793325483799,
-0.02047189697623253,
0.00924826692789793,
0.012290437705814838,
-0.00017605937318876386,
-0.0184765737503767,
-0.005734396167099476,
-0.00990001019090414,
-0.006718811579048634,
0.00894816592335701,
-0.004810158628970385,
-0.014259728603065014,
0.03950788453221321,
-0.021083544939756393,
0.010187036357820034,
-0.010937768034636974,
-0.022267965599894524,
-0.06884673982858658,
0.017059195786714554,
-0.014623544178903103,
0.01199379749596119,
0.028892796486616135,
-0.034203436225652695,
-0.05466362461447716,
-0.000025444935090490617,
-0.025250975042581558,
0.02107226848602295,
0.036272644996643066,
-0.05223467946052551,
0.013738274574279785,
-0.022487644106149673,
-0.02629074640572071,
0.0771297737956047,
-0.0019769880454987288,
0.012902120128273964,
0.04194508120417595,
-0.014338917098939419,
-0.02456945739686489,
-0.034707311540842056,
-0.016336334869265556,
-0.0010490795830264688,
-0.0019741433206945658,
-0.004601412918418646,
0.026031291112303734,
-0.0044864085502922535,
-0.02785266935825348,
0.03848725184798241,
-0.08373293280601501,
-0.01412567961961031,
-0.031593453139066696,
0.0240464024245739,
0.023438939824700356,
0.0034028058871626854,
-0.018592439591884613,
0.02791382558643818,
-0.04304923489689827,
0.022302787750959396,
-0.03983113914728165,
-0.0634254664182663,
0.0010957407066598535,
-0.002840291475877166,
0.058076657354831696,
0.00015097403957042843,
-0.013081753626465797,
0.09039108455181122,
-0.0007282200385816395,
-0.03525989130139351,
-0.04330003261566162,
-0.0034167906269431114,
-0.00919921975582838,
-0.026952385902404785,
0.029751619324088097,
-0.006656994577497244,
-0.06027255579829216,
-0.012109236791729927,
0.0062252008356153965,
0.004617334343492985,
0.05624329298734665,
0.014329696074128151,
0.04275299608707428,
0.027714630588889122,
-0.027766847983002663,
-0.011012492701411247,
0.07875864952802658,
0.03650961071252823,
-0.07338304072618484,
0.008863773196935654,
-0.024965018033981323,
0.018098440021276474,
-0.01925952360033989,
-0.04378342255949974,
0.02768160030245781,
0.02287442423403263,
0.009049070067703724,
0.023739799857139587,
0.03618204966187477,
-0.026477929204702377,
-0.05181090906262398,
-0.010721785016357899,
0.041281361132860184,
0.01837312988936901,
-0.004175478592514992,
-0.012226483784615993,
0.02319464646279812,
0.05503681302070618,
-0.048979636281728745,
-0.004763494245707989,
0.010783175937831402,
0.007159416098147631,
0.05504321679472923,
-0.04781917482614517,
-0.026814941316843033,
0.0458979494869709,
0.017980389297008514,
0.03361733257770538,
-0.0019529861165210605,
-0.030817000195384026,
0.01885497011244297,
-0.05962760001420975,
-0.00003637060581240803,
-0.013212419115006924,
0.06635136902332306,
0.0006449762731790543,
0.06258679926395416,
-0.0072037274949252605,
0.048797283321619034,
0.019534023478627205,
0.03304975479841232,
-0.10479094088077545,
0.06904339045286179,
-0.03410504385828972,
-0.02406371384859085,
0.02102845534682274,
0.02963780239224434,
0.0019466474186629057,
-0.019421400502324104,
-0.03983213007450104,
0.0006828632322140038,
-0.004093704279512167,
-0.04547010362148285,
-0.014216828159987926,
-0.037647489458322525,
-0.04093635827302933,
-0.004697673488408327,
0.007184675894677639,
0.018423711881041527,
0.00037016894202679396,
0.04185738041996956,
0.047369517385959625,
-0.03431302309036255,
-0.005020058248192072,
0.009504707530140877,
0.004979229066520929,
0.010932362638413906,
0.028158918023109436,
0.02082507684826851,
0.032535307109355927,
-0.042279209941625595,
0.010228199884295464,
-0.02609400264918804,
0.05424833297729492,
0.019238555803894997,
0.0037782436702400446,
0.02251257374882698,
-0.07452855259180069,
-0.009508827701210976,
-0.01717652939260006,
0.03998145833611488,
-0.014119128696620464,
-0.0015850604977458715,
0.035701267421245575,
-0.00899763498455286,
-0.024588003754615784,
0.01041108462959528,
0.04077078774571419,
-0.001374988816678524,
-0.023997562006115913,
-0.027045080438256264,
-0.013172034174203873,
-0.016906172037124634,
0.00706876115873456,
-0.01193974819034338,
0.027671560645103455,
-0.0063115134835243225,
0.013153111562132835,
0.018944768235087395,
-0.0043233465403318405,
-0.003291996195912361,
-0.0011034185299649835,
-0.020639417693018913,
0.046361666172742844,
-0.005504702217876911,
0.010482393205165863,
0.05071975663304329,
0.0014113344950601459,
0.025618387386202812,
-0.006466531194746494,
-0.009341632016003132,
-0.09487506002187729,
-0.016499308869242668,
0.03692084550857544,
0.012530616484582424,
0.006453909911215305,
-0.014009037055075169,
-0.029988987371325493,
-0.02106415666639805,
0.07176041603088379,
-0.026385216042399406,
0.05044246464967728,
-0.01967674121260643,
0.006762130651623011,
-0.031238295137882233,
-0.013104673475027084,
-0.04389280453324318,
0.0274784117937088,
-0.06119505316019058,
0.025379184633493423,
-0.04198392108082771,
0.01857747882604599,
-0.022162580862641335,
0.059440433979034424,
-0.00010386560461483896,
0.05307142063975334,
-0.00027751742163673043,
-0.04402736574411392,
0.00020465625857468694,
0.015222380869090557,
-0.038366567343473434,
-0.06320623308420181,
-0.006730952765792608,
0.0037370852660387754,
-0.026473045349121094,
0.017201662063598633,
-0.01445680670440197,
-0.016666220501065254,
0.005076357629150152,
-0.033855509012937546,
0.022044170647859573,
0.018625471740961075,
-0.00012021581642329693,
0.012487399391829967,
0.049118880182504654,
0.03904353082180023,
0.022390194237232208,
0.04683704674243927,
-0.030687320977449417,
0.011767948046326637,
-0.01735744997859001,
0.035471994429826736,
0.03170733526349068,
-0.010936902835965157,
-0.0568980872631073,
0.003537491662427783,
-0.029866337776184082,
0.04264817759394646,
-0.007621864788234234,
0.004803369753062725,
-0.03699108958244324,
-0.015006953850388527,
-0.007350610103458166,
0.03995652124285698,
0.023104343563318253,
-0.01826740801334381,
-0.0018649096600711346,
-0.010017146356403828,
0.009356722235679626,
-0.014374361373484135,
0.005921610165387392,
0.02225547283887863,
-0.008525810204446316,
0.010167962871491909,
-0.012347958981990814,
-0.014320592395961285,
-0.03306436538696289,
-0.027830995619297028,
0.009562941268086433,
-0.0650205984711647,
0.07847970724105835,
0.015055608935654163,
0.02939523570239544,
0.020919661968946457,
-0.0539703406393528,
0.0014457865618169308,
-0.0008849296718835831,
-0.03661322593688965,
0.020042236894369125,
-0.02958633378148079,
0.0021961715538054705,
-0.047487810254096985,
0.00902717188000679,
-0.0034811547957360744,
-0.08366113901138306,
0.0158945731818676,
-0.012359322048723698,
-0.014835003763437271,
-0.018508926033973694,
0.024533720687031746,
-0.012108034454286098,
-0.011862857267260551,
0.00042834709165617824,
0.05102749913930893,
-0.04228436201810837,
-0.0161723829805851,
0.014614163897931576,
0.006230773404240608,
0.0250143650919199,
0.001986078917980194,
-0.004213536158204079,
-0.0026087388396263123,
-0.02353861555457115,
0.013039136305451393,
-0.00867109838873148,
0.058317020535469055,
-0.033532172441482544,
-0.015865357592701912,
-0.002051534131169319,
0.04592151939868927,
0.045683737844228745,
-0.010861199349164963,
0.023114806041121483,
0.019067851826548576,
0.025419039651751518,
-0.0032105022110044956,
-0.02366563491523266,
0.023433398455381393,
-0.0008710607653483748,
-0.010917787440121174,
-0.03212761878967285,
0.0138396630063653,
0.003694340121001005,
-0.0352279357612133,
0.014355825260281563,
0.016428910195827484,
0.01637984812259674,
0.011438409797847271,
0.05224662274122238,
-0.0068407561630010605,
-0.021191559731960297,
0.02519928477704525,
-0.012571784667670727,
0.02196107991039753,
-0.012391319498419762,
-0.02996847964823246,
0.03168376535177231,
0.0165837612003088,
-0.02551272325217724,
-0.06489776074886322,
-0.004036433063447475,
0.0039312830194830894,
0.08381245285272598,
0.0005899984971620142,
0.09716472774744034,
0.03368908911943436,
0.0027734844479709864,
0.0013808523071929812,
0.04101424664258957,
-0.04712267220020294,
-0.017002835869789124,
0.01608475111424923,
0.036229513585567474,
-0.03840266168117523,
-0.029684392735362053,
0.006522665731608868,
-0.0037879019510000944,
-0.013227579183876514,
0.02507837302982807,
0.011622373014688492,
0.03847163915634155,
0.02145150490105152,
-0.0041954233311116695,
-0.03370177373290062,
0.010979491285979748,
-0.0355832502245903,
0.07286287099123001,
0.0051349978893995285,
-0.03324723616242409,
0.04363540560007095,
0.020473318174481392,
0.0027053779922425747,
0.0029280739836394787,
0.0032803078647702932,
-0.018749454990029335,
0.0006714906776323915,
0.026609554886817932,
-0.030745821073651314,
-0.021155670285224915,
0.018962400034070015,
0.03982199355959892,
-0.028422195464372635,
0.017081856727600098,
-0.024009041488170624,
-0.06623153388500214,
-0.0181535966694355,
-0.05827111005783081,
-0.04292554035782814,
0.06658367067575455,
0.05241740122437477,
-0.03100847825407982,
0.03621888533234596,
0.005546573083847761,
0.015695255249738693,
0.014328718185424805,
0.027914199978113174,
-0.03363639861345291,
0.05518706142902374,
-0.046476952731609344,
0.010280050337314606,
-0.06108368933200836,
0.004728526808321476,
0.11486466974020004,
0.036609258502721786,
0.01224882435053587,
-0.05667201429605484,
-0.013723840937018394,
-0.017096932977437973,
0.01150226779282093,
-0.026323717087507248,
0.021657397970557213,
0.0017269112868234515,
-0.0024251937866210938,
-0.01606028713285923,
0.01620519533753395,
-0.011068121530115604,
0.011829948984086514,
0.08130998909473419,
-0.037247203290462494,
-0.03008711151778698,
-0.003162152599543333,
-0.046717047691345215,
-0.003089925507083535,
0.06442129611968994,
-0.05893491953611374,
0.016859980300068855,
-0.029784275218844414,
-0.016397587954998016,
-0.034123409539461136,
-0.03461950644850731,
0.05161239951848984,
-0.006447890307754278,
-0.04944559186697006,
-0.01045081578195095,
-0.004012912046164274,
-0.015948185697197914,
-0.023325514048337936,
0.0505051426589489,
0.045572679489851,
0.005711073521524668,
0.0031523832585662603,
0.04930318146944046,
0.0007519469363614917,
0.005214771255850792,
-0.006592522840946913,
-0.018785450607538223,
-0.03739762306213379,
0.02014152891933918,
-0.03755970671772957,
0.011788442730903625,
-0.02612612210214138,
0.025390341877937317,
-0.02530861459672451,
-0.010922502726316452,
0.023227201774716377,
-0.008883207105100155,
-0.012825487181544304,
-0.0028973219450563192,
0.03003454953432083,
-0.005209073424339294,
0.021525677293539047,
-0.016426589339971542,
0.015846479684114456,
-0.010349257849156857,
-0.014858067966997623,
-0.0002992945665027946,
-0.0357443168759346,
0.020772693678736687,
0.010186144150793552,
0.03329839929938316,
-0.02384374290704727,
-0.006619629450142384,
-0.01402954664081335,
-0.00010681893036235124,
-0.013902703300118446,
-0.0009812446078285575,
0.015526443719863892,
0.03856828808784485,
0.043070562183856964,
-0.01672334410250187,
-0.032796815037727356,
0.017209066078066826,
-0.041721176356077194,
0.03567556291818619,
-0.007857103832066059,
-0.0005562432925216854,
-0.01122781727463007,
-0.017452223226428032,
0.06722279638051987,
0.027845870703458786,
0.02786034345626831,
-0.008133549243211746,
-0.018504612147808075,
-0.008745275437831879,
0.028974389657378197,
-0.032720889896154404,
-0.009150480851531029,
0.012508057057857513,
-0.0344710499048233,
0.03250757232308388,
-0.03301661089062691,
0.03612099587917328,
0.006447162013500929,
0.029250433668494225,
-0.009776181541383266,
0.04669548198580742,
0.0006138362223282456,
0.014673169702291489,
0.009258296340703964,
-0.031016448512673378,
-0.007187413517385721,
0.00378495454788208,
0.013865928165614605,
-0.050730638206005096,
0.0018826364539563656,
0.0017156492685899138,
-0.04401589557528496,
-0.0242808535695076,
0.02740207128226757,
-0.014003336429595947,
0.020931899547576904,
-0.020481914281845093,
0.0022625522688031197,
-0.03340499848127365,
0.025994131341576576,
-0.0479312501847744,
-0.022058885544538498,
0.00587866548448801,
-0.00506379920989275,
-0.03580961376428604,
0.0016907298704609275,
-0.008592160418629646,
0.03220764547586441,
-0.008235626854002476,
-0.007825917564332485,
-0.004705720115453005,
-0.0035462621599435806,
-0.0019960070494562387,
0.017114998772740364,
0.036575011909008026,
-0.026836968958377838,
-0.03999578580260277,
0.006158639211207628,
-0.024861417710781097,
0.008133058436214924,
0.004445304162800312,
0.0022563564125448465,
0.02222466841340065,
0.031985729932785034,
-0.06210089102387428,
0.007803449872881174,
0.06806476414203644,
0.012577371671795845,
-0.021385034546256065,
-0.00976587925106287,
-0.02780601941049099,
0.00408840412274003,
-0.012385116890072823,
0.010522810742259026,
-0.049431849271059036,
-0.013713234104216099,
0.008281838148832321,
0.049802664667367935,
-0.028537355363368988,
-0.004956915508955717,
0.014661651104688644,
0.047605253756046295,
-0.02232302911579609,
0.026531333103775978,
-0.020919669419527054,
0.042396627366542816,
0.011985549703240395,
-0.04717865213751793,
0.004338413011282682,
0.029576217755675316,
0.028451094403862953,
-0.08389269560575485,
-0.0020278573501855135,
-0.023641562089323997,
-0.030971186235547066,
0.05947505682706833,
-0.05227447301149368,
-0.03642379119992256,
0.012203318066895008,
-0.06635480374097824,
-0.00698514562100172,
-0.015138588845729828,
-0.03734447807073593,
-0.024028602987527847,
-0.03059699945151806,
0.0027803664561361074,
0.01768927462399006,
0.008488202467560768,
0.028103476390242577,
-0.0010902704671025276,
-0.022332055494189262,
0.0029915403574705124,
0.013493247330188751,
-0.010843878611922264,
0.04588065296411514,
-0.02601458877325058,
-0.008243114687502384,
0.00988356489688158,
-0.013284578919410706,
-0.010861719958484173,
0.0028921947814524174,
-0.015197393484413624,
0.03278209641575813,
-0.012960733845829964,
0.009700505994260311,
-0.04502018168568611,
0.058988869190216064,
0.0009351700427941978,
-0.014048170298337936,
-0.01292743906378746,
-0.0076379235833883286,
0.011338956654071808,
0.01087667141109705,
-0.04252222925424576,
0.021779509261250496,
0.03079942613840103,
-0.044929470866918564,
-0.058643560856580734,
0.05216984823346138,
-0.009624956175684929,
0.029972439631819725,
-0.007207181304693222,
0.004728188272565603,
-0.010786847211420536,
-0.03248011693358421,
-0.039394985884428024,
-0.02189517579972744,
0.024654507637023926,
0.03795892745256424,
-0.016942236572504044,
-0.0023667088244110346,
0.004657463636249304,
-0.01931818388402462,
-0.005376966670155525,
-0.006704386323690414,
-0.005653977394104004,
0.014398067258298397,
-0.0661904513835907,
0.010777225717902184,
0.004732397850602865,
0.007817299105226994,
-0.002538445172831416,
-0.013219793327152729,
0.037222377955913544,
0.013226923532783985,
0.0379791185259819,
0.009824832901358604,
0.021699298173189163,
-0.02124480903148651,
0.004747994244098663,
-0.05168524384498596,
0.07836627960205078,
-0.003354027634486556,
-0.041353050619363785,
-0.0209657009691,
-0.019468039274215698,
0.012289125472307205,
0.023234868422150612,
0.019727673381567,
-0.06447803229093552,
-0.008889468386769295,
-0.00906456634402275,
0.026097392663359642,
0.01701689325273037,
-0.008485116995871067,
0.009108107537031174,
-0.02996687777340412,
-0.037851739674806595,
0.021202167496085167,
0.01192305888980627,
-0.02335108071565628,
-0.011876705102622509,
0.025509603321552277,
0.019765404984354973,
-0.0032133585773408413,
-0.03355751559138298,
-0.05521455407142639,
0.009103665128350258,
0.033962275832891464,
-0.00831640511751175,
0.03915553167462349,
-0.020414503291249275,
-0.010488447733223438,
-0.009173840284347534,
-0.018420007079839706,
-0.0072748539969325066,
0.05076809227466583,
-0.06643256545066833,
-0.010210613720119,
-0.028423665091395378,
-0.04507296904921532,
0.023705417290329933,
-0.058319393545389175,
0.029334530234336853,
0.013241586275398731,
-0.02226611226797104,
-0.0020064515992999077,
0.05531512200832367,
0.0183198694139719,
0.0213917288929224,
-0.01638931967318058,
0.020105257630348206,
0.03800548240542412,
-0.021363956853747368,
-0.008565463125705719,
0.0024122262839227915,
0.03637462109327316,
-0.028960859403014183,
-0.0038877015467733145,
0.05626610666513443,
-0.019193662330508232,
0.031041458249092102,
-0.01514874305576086,
0.02116687037050724,
-0.00851467065513134,
-0.006553226616233587,
0.022422080859541893,
-0.0009439688292331994,
0.016640640795230865,
0.015376302413642406,
-0.031801819801330566,
0.04732930660247803,
-0.0069115194492042065,
-0.006380573380738497,
-0.005156148690730333,
0.01773129403591156,
-0.013336846604943275,
-0.03297751024365425,
-0.009858506731688976,
0.04650953412055969,
-0.03058156743645668,
0.006483674049377441,
-0.019943926483392715,
-0.027885979041457176,
0.06588192284107208,
0.0002846818824764341,
0.05501321703195572,
0.01900813914835453,
-0.0044338153675198555,
0.04016483575105667,
-0.03495137393474579,
-0.018174344673752785,
-0.03188376873731613,
0.04351954162120819,
0.02135457843542099,
0.011398077011108398,
-0.04967772960662842,
0.01005304604768753,
-0.010876498185098171,
0.0255753081291914,
-0.07601059228181839,
-0.01658756285905838,
-0.0014009320875629783,
0.04312514141201973,
0.027262013405561447,
0.027286279946565628
] |
<p>I'm wondering if it would be possible to map out all the different types of molecules, atoms and nuclei and their energy levels on one page (even if in a generalised way)? But perhaps I'm referring to the periodic table here? Do representations differ according to whether one is looking at things from a Classical perspective or a Quantum perspective?</p>
<p>Apologies in advance for all the question marks! I'm generally interested in ways of visually conveying concepts- so would be curious to discover different approaches to the above.</p> | 2,882 | [
-0.0622253380715847,
-0.02195470593869686,
0.009901681914925575,
-0.007474386133253574,
0.02808862179517746,
0.00032228679629042745,
-0.02562219835817814,
-0.02918040193617344,
0.0007898520561866462,
-0.027377236634492874,
0.04861567169427872,
0.000025655104764155112,
0.048042379319667816,
-0.00897428672760725,
0.023097023367881775,
0.018101263791322708,
0.0010102660162374377,
-0.033154793083667755,
-0.022269094362854958,
-0.015446280129253864,
0.03413388505578041,
-0.006676057819277048,
0.007795940153300762,
0.017402587458491325,
0.02314171940088272,
0.04088212549686432,
0.004892678931355476,
-0.015471860766410828,
0.05138150602579117,
0.036731522530317307,
-0.02285413071513176,
-0.032392051070928574,
0.04681280255317688,
0.009586615487933159,
0.03447047621011734,
0.010514465160667896,
-0.014197239652276039,
-0.037886906415224075,
-0.054461006075143814,
0.01333367545157671,
-0.03694292530417442,
-0.026618678122758865,
-0.021817287430167198,
0.05396702140569687,
-0.034417737275362015,
0.050983231514692307,
-0.0014477809891104698,
-0.02529887668788433,
0.0013100869255140424,
-0.037296976894140244,
0.07984279841184616,
0.021410666406154633,
0.042047638446092606,
0.03728211671113968,
-0.010373462922871113,
-0.00502042006701231,
0.040837787091732025,
0.04434778168797493,
0.0018848462495952845,
-0.0498005747795105,
-0.026006454601883888,
0.009963931515812874,
0.030383192002773285,
-0.005742792505770922,
-0.03279326111078262,
0.02082952670753002,
-0.01024474948644638,
-0.052943211048841476,
0.03677918389439583,
0.02877599187195301,
-0.02180364541709423,
0.042141564190387726,
0.07322279363870621,
-0.010938338004052639,
0.004156687296926975,
-0.03645249083638191,
0.0423324815928936,
-0.02110631950199604,
0.03663165494799614,
0.025030797347426414,
-0.02345850318670273,
0.0065325903706252575,
0.0016794822877272964,
0.025353509932756424,
0.010036739520728588,
0.01942802593111992,
0.04329393431544304,
-0.0580100417137146,
-0.021690774708986282,
0.022665660828351974,
-0.006722950376570225,
0.004790183622390032,
0.05663060396909714,
0.02398565225303173,
-0.05108892545104027,
0.015243705362081528,
-0.006717463489621878,
0.03353223577141762,
0.019125310704112053,
0.003545529441908002,
0.040921490639448166,
0.01817612536251545,
0.01204485259950161,
0.0595255084335804,
0.0010251817293465137,
-0.0011598424753174186,
-0.02585558034479618,
0.008610416203737259,
0.001524003455415368,
0.018238471820950508,
-0.007932828739285469,
-0.0009328589658252895,
0.024995554238557816,
0.026563066989183426,
0.026144614443182945,
-0.027968475595116615,
0.0016751463990658522,
-0.02020053006708622,
0.05350080877542496,
0.08499059826135635,
0.016933444887399673,
-0.05616364628076553,
0.03682510182261467,
-0.0134566780179739,
-0.07568782567977905,
0.009611563757061958,
0.014804798178374767,
0.00733393058180809,
-0.026599735021591187,
-0.0002738579933065921,
-0.022298665717244148,
-0.001168608432635665,
0.0364835225045681,
-0.011420691385865211,
0.05357734113931656,
-0.0029159404803067446,
-0.09513969719409943,
-0.05283891409635544,
-0.030456986278295517,
-0.005935766268521547,
-0.015200971625745296,
-0.05771917477250099,
0.03418903052806854,
0.022235915064811707,
0.009791753254830837,
-0.008787562139332294,
-0.042980294674634933,
0.013997339643537998,
0.017576143145561218,
0.0018967688083648682,
-0.00926727894693613,
0.03501252830028534,
0.01768786832690239,
-0.0501825176179409,
0.02300858683884144,
-0.03881171718239784,
0.04697160795331001,
0.011894064955413342,
0.024826819077134132,
-0.025366736575961113,
0.04420984908938408,
-0.014922854490578175,
0.02987767569720745,
-0.010480535216629505,
0.023198317736387253,
-0.010346928611397743,
0.07055983692407608,
0.00820065289735794,
0.01670970395207405,
0.017822379246354103,
0.018926026299595833,
0.041809629648923874,
0.02177773416042328,
0.013239425607025623,
0.0394672192633152,
-0.029899749904870987,
-0.03978906571865082,
-0.012167427688837051,
0.020669732242822647,
-0.005897515919059515,
-0.04087305814027786,
-0.04733825847506523,
-0.020731577649712563,
0.022303078323602676,
0.022853603586554527,
0.02199883945286274,
-0.005061309784650803,
-0.04044928774237633,
-0.009127466939389706,
-0.04863468557596207,
0.024508561939001083,
-0.03601890802383423,
0.04197785630822182,
-0.05369419977068901,
-0.0002452876069582999,
0.05454688146710396,
0.019753918051719666,
-0.007276353891938925,
-0.019017191603779793,
-0.05904664844274521,
-0.01715850457549095,
0.029869602993130684,
-0.0029782780911773443,
-0.059101611375808716,
0.003571930807083845,
0.048571985214948654,
0.008888904005289078,
-0.0005666108918376267,
0.0020789809059351683,
-0.03531932085752487,
-0.03586560860276222,
-0.0020598028786480427,
-0.02021045610308647,
0.036957211792469025,
0.05409203842282295,
0.011476336047053337,
-0.047675229609012604,
0.03715633228421211,
-0.046515434980392456,
0.021491818130016327,
-0.020611878484487534,
0.09237205982208252,
0.01263274997472763,
-0.00012255054025445133,
-0.012012955732643604,
0.02658150903880596,
0.043541062623262405,
0.03741425275802612,
0.016132721677422523,
-0.024178948253393173,
-0.047533243894577026,
-0.018399950116872787,
0.01452027726918459,
0.05084452033042908,
-0.04333564266562462,
0.005034130997955799,
0.01738877408206463,
0.03977441415190697,
0.026970453560352325,
0.006425101775676012,
-0.042544618248939514,
-0.026191921904683113,
-0.026095561683177948,
0.01742643117904663,
0.0030552903190255165,
0.01040563452988863,
0.02366720512509346,
0.031656183302402496,
-0.002504609525203705,
-0.009592014364898205,
-0.0014577500987797976,
0.03216404467821121,
-0.03726743906736374,
0.0019607979338616133,
0.01019449345767498,
-0.02789553627371788,
0.05900825187563896,
-0.02760249935090542,
0.02844065986573696,
0.0027998490259051323,
-0.024755030870437622,
-0.03343275189399719,
-0.03125894442200661,
-0.022696740925312042,
0.00014645226474385709,
0.06466667354106903,
-0.03122442588210106,
0.0026335185393691063,
0.03459984064102173,
-0.04469424486160278,
0.05653484910726547,
-0.004579570610076189,
0.006265969481319189,
-0.012424906715750694,
0.028991851955652237,
0.04382307827472687,
-0.00917213037610054,
0.03531588241457939,
-0.055114828050136566,
-0.06296686083078384,
-0.017465541139245033,
-0.04204294830560684,
0.01344025693833828,
0.0074392142705619335,
-0.044601257890462875,
-0.00004011785858892836,
-0.04804382473230362,
-0.038379646837711334,
0.040505215525627136,
-0.02505185641348362,
-0.042685288935899734,
0.01361311785876751,
-0.028385784476995468,
-0.056646984070539474,
-0.014981507323682308,
-0.03033183515071869,
0.029657823964953423,
-0.0481085479259491,
0.005774093791842461,
0.021016264334321022,
-0.024431731551885605,
-0.013668944127857685,
-0.02466004528105259,
-0.029456734657287598,
-0.05520239844918251,
-0.007145542185753584,
0.025944512337446213,
-0.016575517132878304,
0.0072115566581487656,
-0.018918031826615334,
0.07817775756120682,
-0.05475778505206108,
-0.013962077908217907,
-0.04506167024374008,
-0.00878057535737753,
0.017784638330340385,
-0.0022890777327120304,
0.028644109144806862,
0.00040503303171135485,
0.0001911157014546916,
0.06267791241407394,
0.02087213285267353,
-0.08068402111530304,
-0.021248213946819305,
-0.02161163091659546,
0.005143512971699238,
-0.023876316845417023,
0.008457268588244915,
0.016085423529148102,
-0.020159928128123283,
0.019390376284718513,
0.0075230672955513,
0.02261982299387455,
0.024052375927567482,
0.005884154234081507,
-0.02949797734618187,
0.03662004694342613,
-0.0075311861000955105,
0.012833777815103531,
0.0304277241230011,
0.008411937393248081,
-0.05653493106365204,
0.0007369952509179711,
-0.04459057003259659,
0.04066337272524834,
0.03208843246102333,
-0.00646953983232379,
0.06326432526111603,
0.032208528369665146,
0.017926311120390892,
-0.02515621855854988,
-0.001232597278431058,
0.023357583209872246,
-0.022845808416604996,
-0.01739734224975109,
0.06687933951616287,
0.06822327524423599,
0.0012206140672788024,
-0.0008550749626010656,
0.05902731418609619,
0.04061199352145195,
-0.02653004229068756,
-0.0012413416989147663,
0.03877977654337883,
0.0018855134258046746,
0.020205961540341377,
-0.02380177192389965,
-0.012790419161319733,
0.02067931927740574,
0.02959503047168255,
0.035372115671634674,
0.03457619622349739,
-0.028780540451407433,
0.024901757016777992,
-0.06956328451633453,
-0.0493527390062809,
-0.007499628700315952,
0.03823450207710266,
0.006020025350153446,
0.051945921033620834,
0.0028640234377235174,
0.02261468768119812,
-0.007413950748741627,
0.008669493719935417,
-0.06567340344190598,
-0.0005644797347486019,
-0.015009771101176739,
0.012643923051655293,
-0.003839098382741213,
-0.017421118915081024,
-0.02140345610678196,
-0.03195734694600105,
-0.048828497529029846,
0.015879124402999878,
0.019467901438474655,
-0.039158109575510025,
0.002286608098074794,
-0.015544772148132324,
-0.02275589294731617,
-0.01731710135936737,
0.06129167973995209,
0.0073370193131268024,
-0.000277887680567801,
0.0037005613557994366,
0.021259300410747528,
-0.0338895358145237,
-0.019144494086503983,
-0.014157899655401707,
0.020478593185544014,
-0.014923769049346447,
0.023128880187869072,
0.008601964451372623,
0.04084686189889908,
-0.020990999415516853,
0.022979745641350746,
0.0008887936128303409,
0.06768576800823212,
-0.024958143010735512,
-0.03826117143034935,
0.024765947833657265,
-0.043955929577350616,
0.008601655252277851,
0.005250399466603994,
0.02718055434525013,
-0.021972736343741417,
0.02869546413421631,
-0.016237642616033554,
-0.0042149159125983715,
-0.04687361791729927,
0.02546197548508644,
0.03753519430756569,
-0.013724302873015404,
-0.01775326021015644,
-0.03436698764562607,
-0.03059454821050167,
-0.012885616160929203,
0.006412483751773834,
0.047591716051101685,
0.029222751036286354,
-0.029473012313246727,
0.023194458335638046,
0.002320040948688984,
0.038580041378736496,
-0.07171697914600372,
-0.0037430638913065195,
-0.013922549784183502,
-0.014193003997206688,
-0.014907540753483772,
-0.02045619860291481,
0.06914397329092026,
0.0033067648764699697,
0.039945654571056366,
-0.01356720644980669,
-0.02622389793395996,
-0.09987445920705795,
0.01342643890529871,
0.03270220384001732,
0.025591200217604637,
0.02974041923880577,
0.010010212659835815,
-0.026147659868001938,
-0.022211134433746338,
0.06910157203674316,
-0.008526151068508625,
0.007022308185696602,
-0.016465067863464355,
-0.0020083673298358917,
-0.005534387659281492,
-0.004160079639405012,
0.0521969310939312,
0.0038337050937116146,
0.005848982837051153,
-0.0068152290768921375,
-0.004878371022641659,
0.03018927201628685,
-0.022205499932169914,
0.03698953241109848,
0.017815252766013145,
0.028447328135371208,
0.009107350371778011,
0.0065999263897538185,
0.012498217634856701,
0.022424792870879173,
-0.02603408508002758,
-0.05302361771464348,
0.0013375217095017433,
0.01519468892365694,
-0.0020392807200551033,
0.057545680552721024,
-0.018421968445181847,
-0.06208239123225212,
0.027040977030992508,
-0.02337823435664177,
0.016001824289560318,
-0.01808672584593296,
-0.00965965073555708,
0.07178489863872528,
0.029999148100614548,
-0.016217075288295746,
0.037937309592962265,
0.07219148427248001,
-0.015521299093961716,
0.02317483350634575,
-0.02829117141664028,
0.023182783275842667,
-0.023237621411681175,
0.0079832524061203,
-0.06552498787641525,
-0.004013863392174244,
-0.026071494445204735,
0.0031144742388278246,
-0.01827223226428032,
0.011191489174962044,
0.013560058549046516,
-0.05919646471738815,
-0.027293719351291656,
0.0221842210739851,
0.007364933378994465,
-0.008722196333110332,
-0.004817572422325611,
0.030102495104074478,
-0.0026852597948163748,
-0.047844722867012024,
-0.013969996012747288,
-0.009976351633667946,
-0.008783265948295593,
-0.0185482669621706,
-0.009366188198328018,
0.01644553430378437,
-0.05537723749876022,
-0.01886756904423237,
0.03179328516125679,
-0.040923573076725006,
0.04228505492210388,
-0.032485801726579666,
0.03444265201687813,
0.03668804466724396,
-0.07530003041028976,
-0.044336725026369095,
0.047701381146907806,
-0.016079958528280258,
0.0016314368695020676,
0.00809446256607771,
0.004587922245264053,
-0.0024596804287284613,
-0.00981812085956335,
-0.04220808669924736,
-0.04416441544890404,
0.017309678718447685,
0.023299451917409897,
-0.024547496810555458,
-0.028018537908792496,
0.02410218119621277,
-0.0021908257622271776,
0.014690550044178963,
0.022165318951010704,
0.038996294140815735,
-0.015056712552905083,
-0.010578681714832783,
0.02215723879635334,
0.009521977044641972,
0.054258108139038086,
-0.0031872170511633158,
-0.04665560647845268,
-0.003617765149101615,
0.009707015007734299,
0.034208931028842926,
-0.027183691039681435,
0.012771901674568653,
-0.014476917684078217,
-0.00718754343688488,
-0.0065857707522809505,
0.0288532841950655,
0.06872622668743134,
-0.04793371260166168,
0.04186803847551346,
0.02536768466234207,
0.021583184599876404,
-0.010482684709131718,
-0.044563379138708115,
-0.0005132310325279832,
-0.04577707499265671,
0.031803131103515625,
-0.005065880715847015,
0.016938362270593643,
-0.006943472661077976,
-0.06831852346658707,
0.025031819939613342,
-0.02419155277311802,
-0.0141654834151268,
0.035873353481292725,
0.049691393971443176,
0.02464369498193264,
0.00002778083762677852,
0.046257343143224716,
-0.04795287922024727,
-0.007209685165435076,
-0.029628586024045944,
0.012446971610188484,
0.0199409332126379,
0.006611373275518417,
-0.0039754570461809635,
-0.05466851219534874,
-0.015430567786097527,
-0.009770451113581657,
0.03135930374264717,
0.025348849594593048,
0.03863232955336571,
0.0340992733836174,
0.01875249482691288,
0.007254696451127529,
-0.02090906724333763,
-0.02597319334745407,
-0.027433454990386963,
-0.004215181339532137,
0.06103001534938812,
-0.01119826827198267,
-0.0018776641227304935,
0.02577928826212883,
0.04148846119642258,
-0.010170039720833302,
0.04391937702894211,
0.041692767292261124,
0.014409206807613373,
0.019145529717206955,
-0.0007242849678732455,
-0.023467576131224632,
0.028055991977453232,
-0.028584327548742294,
0.04262814298272133,
-0.0015948850195854902,
-0.01977258361876011,
-0.004820658825337887,
0.02846994623541832,
-0.014550026506185532,
-0.025960836559534073,
-0.028361711651086807,
-0.03578304126858711,
0.05431537702679634,
0.019157979637384415,
0.027475161477923393,
-0.05278206616640091,
0.005545586347579956,
0.03358694165945053,
-0.05428905785083771,
-0.02887892723083496,
-0.00016022566705942154,
-0.05883326753973961,
-0.0218037199229002,
-0.02553093247115612,
-0.05356530100107193,
0.025824392214417458,
-0.0005623951437883079,
-0.026666559278964996,
0.006211941596120596,
0.0035147927701473236,
0.04734701290726662,
-0.030646756291389465,
0.03283185511827469,
-0.010201550088822842,
0.040565211325883865,
-0.006370208691805601,
0.0370369553565979,
0.024672284722328186,
0.021640533581376076,
0.1179506778717041,
0.041544005274772644,
0.011057247407734394,
-0.02953098528087139,
-0.014850822277367115,
-0.004072793293744326,
0.02070525661110878,
-0.013437304645776749,
0.03555600345134735,
-0.004668234381824732,
0.026539431884884834,
-0.04242207854986191,
0.07072873413562775,
0.019219495356082916,
0.04202849417924881,
0.061124298721551895,
-0.013974719680845737,
-0.005008873995393515,
-0.021799981594085693,
0.005453381221741438,
-0.020817261189222336,
0.02249353751540184,
-0.08244185894727707,
0.007935656234622002,
0.007132454309612513,
-0.007090200670063496,
-0.016568398103117943,
-0.016140183433890343,
0.04832169786095619,
0.00476157246157527,
-0.045107610523700714,
0.00878714956343174,
0.005960956681519747,
-0.0005301676574163139,
-0.011931825429201126,
0.005630290601402521,
0.0513814277946949,
0.026690442115068436,
-0.013713185675442219,
0.05066278204321861,
0.017742885276675224,
0.004658862017095089,
-0.02881394699215889,
-0.006830320693552494,
-0.00835071224719286,
-0.02032025158405304,
-0.03386818245053291,
0.015029896050691605,
-0.0712919533252716,
-0.025653699412941933,
-0.02319379895925522,
0.004810033366084099,
0.010319804772734642,
-0.03382588177919388,
-0.03744563087821007,
-0.0026902449317276478,
0.04038102179765701,
0.002029876224696636,
-0.022796526551246643,
-0.022667884826660156,
0.032370492815971375,
-0.03605636581778526,
0.025544434785842896,
-0.005644648801535368,
-0.019286535680294037,
0.022969594225287437,
-0.027999896556138992,
-0.0054013230837881565,
0.018652066588401794,
-0.0016679875552654266,
-0.024662958458065987,
0.001761195482686162,
-0.029920153319835663,
-0.07028032094240189,
0.019432833418250084,
0.06896795332431793,
0.03399151936173439,
0.017736215144395828,
-0.002519229194149375,
-0.011448321864008904,
-0.026012949645519257,
0.055808454751968384,
0.0035808810498565435,
-0.06158246472477913,
0.022053541615605354,
-0.001264359219931066,
0.05944780260324478,
0.008045723661780357,
-0.028188059106469154,
0.059400059282779694,
-0.0024843967985361814,
-0.02452128194272518,
0.0575646236538887,
-0.0412321500480175,
-0.001168769784271717,
0.02317764423787594,
-0.04410598799586296,
0.020821204409003258,
-0.01433010958135128,
0.02720174938440323,
0.01722608506679535,
-0.023393038660287857,
0.008327747695147991,
0.06327249109745026,
0.027297640219330788,
0.014479732140898705,
0.010883450508117676,
-0.05195828154683113,
0.015376637689769268,
-0.007207028567790985,
-0.015549211762845516,
-0.026747534051537514,
-0.010651757009327412,
-0.05226525664329529,
-0.011941834352910519,
-0.022422077134251595,
0.015091958455741405,
0.010998435318470001,
0.025958683341741562,
-0.0526110976934433,
0.00196500844322145,
0.0033972018864005804,
0.0034295597579330206,
-0.06156240776181221,
0.013380052521824837,
0.012443236075341702,
-0.04787221923470497,
-0.02891816757619381,
0.03247133269906044,
0.011131647042930126,
-0.018697647377848625,
0.027431732043623924,
0.021325286477804184,
-0.015878258273005486,
-0.012679166160523891,
0.004817410372197628,
-0.0032687687780708075,
0.04709811881184578,
-0.0163051076233387,
0.017585065215826035,
-0.004598118830472231,
0.003962962422519922,
-0.03572786971926689,
0.012781539931893349,
-0.04334123432636261,
0.017057104036211967,
0.04196209833025932,
-0.008597658947110176,
-0.031039541587233543,
0.07187493145465851,
-0.03338845074176788,
-0.0038390131667256355,
0.03956569358706474,
0.01136874035000801,
-0.030382443219423294,
-0.02171287126839161,
0.0011264580534771085,
-0.016831478103995323,
-0.03035021759569645,
0.02469116449356079,
0.01201866939663887,
0.05060423165559769,
-0.011292671784758568,
0.0033889689948409796,
-0.03509535640478134,
0.019468557089567184,
0.026222266256809235,
0.0017778852488845587,
0.04307771846652031,
0.016066664829850197,
-0.06436038762331009,
0.04430612549185753,
0.07615374028682709,
0.024993371218442917,
-0.04250146076083183,
-0.018721574917435646,
-0.005729368422180414,
-0.010496583767235279,
0.05340874567627907,
-0.055596236139535904,
0.029969599097967148,
0.023540465161204338,
-0.08802918344736099,
0.002329276641830802,
-0.030114034190773964,
-0.003606376238167286,
0.0037034761626273394,
-0.0025701026897877455,
-0.03034202754497528,
0.056827083230018616,
0.0056726885959506035,
0.07936280965805054,
0.019637322053313255,
0.0034521184861660004,
-0.002093251096084714,
0.004188270773738623,
-0.02196328714489937,
0.013065328821539879,
-0.019782613962888718,
-0.0377003438770771,
0.04911189153790474,
-0.03206754848361015,
-0.04017164930701256,
-0.01378405001014471,
-0.035428840667009354,
0.03665319085121155,
-0.005653978791087866,
-0.0069603463634848595,
0.005820461083203554,
0.018458789214491844,
0.008302540518343449,
-0.023084420710802078,
-0.05052576959133148,
0.00084702018648386,
0.008892092853784561,
0.004774231929332018,
-0.012738971970975399,
0.04443641006946564,
0.01302588451653719,
-0.0353754498064518,
-0.059764064848423004,
0.025963028892874718,
0.0016053796280175447,
0.0025601673405617476,
-0.03360975161194801,
-0.007455099374055862,
0.05228749290108681,
-0.025715477764606476,
-0.016611317172646523,
-0.04489767923951149,
0.007234910968691111,
0.0016448113601654768,
-0.007872296497225761,
0.03638692945241928,
0.01376929972320795,
-0.021109120920300484,
-0.03292755037546158,
-0.008128403685986996,
0.03540486842393875,
-0.010311610996723175,
-0.0478675402700901,
-0.009272057563066483,
0.04775266721844673,
0.026215068995952606,
0.039199523627758026,
-0.017991429194808006,
-0.05020071193575859,
0.012616444379091263,
0.012890158221125603,
0.024793973192572594,
0.005976479034870863,
-0.03827847167849541,
0.005214056931436062,
-0.02665083110332489,
0.04158477485179901,
-0.0024278739001601934,
0.006979672238230705,
-0.00914763193577528,
-0.0010678099934011698,
0.01508238073438406,
0.007895004004240036,
0.04529174417257309,
-0.030921312049031258,
0.0017917209770530462,
-0.02207012288272381,
0.005465885158628225,
0.021719615906476974,
-0.020389731973409653,
-0.014996119774878025,
-0.02918720245361328,
-0.03326767683029175,
0.007658783812075853,
-0.010164919309318066,
-0.028799675405025482,
0.015557656064629555,
0.0415375754237175,
-0.013988208025693893,
-0.013653751462697983,
-0.03816848248243332,
-0.02452172338962555,
0.03762560710310936,
0.022005712613463402,
-0.03412803262472153,
0.027266472578048706,
0.018927952274680138,
-0.016374649479985237,
0.033108603209257126,
-0.03232216462492943,
0.0008185539045371115,
0.02596123330295086,
-0.022572478279471397,
-0.04195438697934151,
-0.04448254778981209,
-0.017580972984433174,
0.02094838209450245,
-0.09078449010848999,
0.04488075524568558,
-0.004029181785881519,
-0.022572487592697144,
0.006507867481559515,
0.048118956387043,
0.0009742113761603832,
0.03562748804688454,
-0.00195306574460119,
0.009305967018008232,
0.034318238496780396,
-0.02819930575788021,
0.026198871433734894,
0.019383417442440987,
0.01088748499751091,
0.014972802251577377,
-0.003914442844688892,
0.011612005531787872,
-0.017359010875225067,
0.014283611439168453,
0.030728105455636978,
0.022529616951942444,
-0.011942616663873196,
0.019714144989848137,
0.035960182547569275,
0.023381954059004784,
0.0010442116763442755,
0.029265588149428368,
-0.016219088807702065,
0.07333272695541382,
-0.023624977096915245,
-0.009067810140550137,
-0.07441714406013489,
0.010916034691035748,
-0.027423175051808357,
0.02761247381567955,
0.011766483075916767,
0.03417737036943436,
-0.029844004660844803,
-0.010936731472611427,
-0.05875765532255173,
0.023489786311984062,
0.01321051549166441,
-0.04588368162512779,
0.02659689076244831,
-0.0395599901676178,
-0.025289928540587425,
0.009287609718739986,
0.02146090939640999,
-0.05054177716374397,
-0.022091075778007507,
0.03135573863983154,
0.02504538558423519,
0.012543164193630219,
-0.007597270887345076,
-0.004893402568995953,
-0.006833061575889587,
0.0309191532433033,
-0.04192700609564781,
-0.023216478526592255,
-0.05144994333386421,
0.007775054778903723,
-0.014053522609174252,
0.007210182957351208
] |
<p>I learned that as the earth rotates about its axis, the bodies on the earth also follow a circular path. In most books I read, they give the example of a person standing on a weight balance at the equator... and I did understand that. However, by doing the following calculation, I am seeing that the apparent weight at other points on the earth (apart from the poles) is the same</p>
<p>This is the picture on my mind:
<img src="http://i.stack.imgur.com/4C73k.png" alt="enter image description here"></p>
<p>At B,</p>
<p>$$W-N=m{\omega}^2 R$$</p>
<p>At A, a component of weight will provides the centripetal force to rotate around the circle with the radius $r$,
$$Wcos{\theta} - Ncos\theta =m{\omega}^2r $$
as $r=Rcos\theta$,
$$Wcos{\theta} - Ncos\theta =m{\omega}^2R\cos\theta$$</p>
<p>The equation eventually ends up as...
$$W - N =m{\omega}^2R $$</p>
<p>So from this, I think that the normal reaction force which is the apparent weight remains the same as to the apparent weight at the equator.</p>
<p>However the book states that the apparent weight varies along $A$ and $B$</p>
<p>Also, we assume that the earth is spherical.</p>
<p>I am really sorry for making the question so long. Could someone please tell me which part of my concept is wrong.</p> | 2,883 | [
-0.01343060564249754,
-0.05056176334619522,
-0.03383149579167366,
-0.005009487271308899,
0.04310409352183342,
-0.021617231890559196,
-0.012970667332410812,
-0.024993203580379486,
0.0026614833623170853,
-0.029421959072351456,
-0.023914316669106483,
0.03240320086479187,
0.04578116908669472,
-0.012287677265703678,
0.01978079229593277,
-0.034547384828329086,
-0.019966043531894684,
0.017830148339271545,
0.007713533006608486,
-0.016345249488949776,
0.0023041164968162775,
0.0016098098130896688,
0.008140931837260723,
-0.029129337519407272,
-0.009289201349020004,
-0.007122922223061323,
0.05161942169070244,
-0.02493487112224102,
0.02831127494573593,
0.06422542035579681,
-0.028629818931221962,
0.00015038806304801255,
-0.0012409541523084044,
0.015996435657143593,
0.028125949203968048,
0.015920767560601234,
-0.04203874617815018,
-0.022187331691384315,
-0.016460809856653214,
0.04399668425321579,
-0.030750947073101997,
-0.00897227879613638,
-0.016005273908376694,
0.04093152657151222,
-0.030807528644800186,
0.02180590108036995,
-0.01456536166369915,
0.03376412391662598,
0.06570816785097122,
-0.07630505412817001,
0.05251258984208107,
-0.011714690364897251,
0.031526386737823486,
0.016231035813689232,
0.035896964371204376,
-0.02586132474243641,
0.0641295537352562,
0.016310999169945717,
-0.0030933786183595657,
-0.03899253159761429,
-0.036468248814344406,
-0.0072746891528368,
-0.02326245605945587,
-0.03379293158650398,
0.025791402906179428,
-0.00650261715054512,
-0.03118639811873436,
-0.01087008137255907,
0.050020962953567505,
0.03672737255692482,
0.02327319234609604,
0.04024540260434151,
-0.00925321877002716,
-0.0032042493112385273,
-0.030333472415804863,
-0.0436217300593853,
0.014963776804506779,
0.014152699150145054,
0.02490999922156334,
0.003258449025452137,
-0.01990622468292713,
0.013867243193089962,
0.024564767256379128,
0.06444063037633896,
0.011911282315850258,
0.009403466247022152,
0.03487469628453255,
0.008662237785756588,
-0.013853286392986774,
0.02922649495303631,
0.01177030336111784,
0.015574175864458084,
-0.008976255543529987,
-0.06520425528287888,
-0.0074355523101985455,
0.03177010267972946,
0.00026565746520645916,
0.014679064974188805,
0.005355868488550186,
-0.008580470457673073,
0.006883612368255854,
-0.04137589409947395,
0.01700635626912117,
0.06942896544933319,
0.01211025845259428,
-0.01838015951216221,
-0.05953269079327583,
0.014405553229153156,
0.013636144809424877,
-0.04215387627482414,
-0.03981762006878853,
0.015383925288915634,
-0.004053208976984024,
-0.0006057306891307235,
-0.0009919063886627555,
-0.01026762742549181,
-0.011518196202814579,
-0.014121757820248604,
0.06502559036016464,
0.036014147102832794,
0.06091546639800072,
0.001081195194274187,
-0.004456154070794582,
-0.053797103464603424,
-0.02289331518113613,
0.0052728429436683655,
0.03009035438299179,
-0.0301540344953537,
-0.011716680601239204,
0.0014360669301822782,
0.0423792265355587,
-0.019614260643720627,
-0.009045722894370556,
0.031931836158037186,
0.022163860499858856,
0.025137804448604584,
-0.12348427623510361,
-0.030966393649578094,
0.034928735345602036,
-0.03786404803395271,
0.018439888954162598,
-0.053632527589797974,
-0.009027455002069473,
0.035741787403821945,
0.06656811386346817,
0.013211507350206375,
0.02044345811009407,
0.025964466854929924,
0.05622294172644615,
0.01563633419573307,
-0.01278191152960062,
-0.023671604692935944,
-0.010755244642496109,
-0.04750436171889305,
0.004584162030369043,
-0.07754530757665634,
0.031762052327394485,
0.027721501886844635,
0.03795863687992096,
-0.025818319991230965,
0.043478723615407944,
-0.022848350927233696,
-0.00284395064227283,
0.0071481564082205296,
0.016746265813708305,
-0.043055109679698944,
0.08229289203882217,
0.00952108670026064,
-0.03116747736930847,
0.018993103876709938,
0.03051331825554371,
0.047801755368709564,
-0.006369071081280708,
0.04432994872331619,
0.026877084746956825,
-0.04758165776729584,
0.011059348471462727,
-0.043392591178417206,
0.000733142951503396,
0.0272479560226202,
-0.03315061703324318,
-0.059081438928842545,
-0.019333835691213608,
-0.001029862673021853,
0.03232956677675247,
0.08173467218875885,
-0.01512934360653162,
-0.0030762795358896255,
-0.010126246139407158,
-0.03288441523909569,
0.022628365084528923,
-0.028748389333486557,
0.011660125106573105,
-0.0007131875609047711,
-0.0077812387607991695,
0.013282879255712032,
0.030070194974541664,
0.009535573422908783,
-0.007387024350464344,
0.0013534275349229574,
-0.01865250989794731,
0.06297610700130463,
-0.005736844148486853,
-0.015833735466003418,
0.020508721470832825,
0.03529965505003929,
0.022628894075751305,
0.0032594678923487663,
-0.00881313718855381,
-0.033626679331064224,
-0.010729233734309673,
0.0021688879933208227,
-0.029388148337602615,
0.016245895996689796,
0.0480811707675457,
-0.007685414515435696,
-0.03871744126081467,
0.013524667359888554,
0.015096698887646198,
0.06025455892086029,
-0.03326237574219704,
0.048227522522211075,
0.07697425782680511,
-0.022882938385009766,
0.025525270029902458,
0.08166930824518204,
0.04059760645031929,
0.011164329946041107,
-0.006510098930448294,
-0.008003787137567997,
-0.04854142665863037,
-0.008731937035918236,
0.022305356338620186,
-0.007140956819057465,
-0.05515284091234207,
0.012698940001428127,
0.03545194864273071,
0.06164714694023132,
0.022412775084376335,
-0.014690869487822056,
0.008788720704615116,
-0.05297204852104187,
0.003204053733497858,
0.006859879475086927,
0.01867590844631195,
0.026948194950819016,
0.0003324075660202652,
0.032193318009376526,
0.0004287563788238913,
-0.01828693598508835,
-0.0261218398809433,
0.026550475507974625,
-0.005925905890762806,
0.05043947324156761,
-0.024423297494649887,
0.016217032447457314,
0.06189827248454094,
-0.03732169419527054,
0.02287687174975872,
0.010460944846272469,
-0.013481217436492443,
-0.028971752151846886,
-0.04037770256400108,
-0.012253236025571823,
0.02472751773893833,
-0.01020977832376957,
-0.00881954375654459,
-0.010670823976397514,
0.018074098974466324,
-0.05107426270842552,
-0.037253908812999725,
-0.024488525465130806,
-0.0055577377788722515,
0.0020633996464312077,
0.01914905197918415,
0.0223386287689209,
0.0360431894659996,
0.02646726928651333,
0.018542127683758736,
-0.03155297040939331,
-0.03273308649659157,
-0.04357687011361122,
-0.005981049500405788,
0.022199317812919617,
-0.05058158561587334,
0.01998535916209221,
-0.03969419747591019,
-0.010002544149756432,
0.046401672065258026,
0.00677426066249609,
0.004491912201046944,
0.034129489213228226,
0.04253857582807541,
-0.030222661793231964,
-0.004117980599403381,
-0.020120834931731224,
-0.029517877846956253,
-0.030284160748124123,
-0.025711053982377052,
0.06165047734975815,
0.0070034051313996315,
0.02417837828397751,
0.01774814911186695,
-0.050668805837631226,
-0.06098461151123047,
0.005220147781074047,
0.005583463702350855,
-0.005446330644190311,
-0.03302808478474617,
0.0026133188512176275,
0.010435274802148342,
-0.012185164727270603,
-0.012473358772695065,
-0.05565262213349342,
-0.020142944529652596,
0.016338622197508812,
-0.030833275988698006,
0.04309516400098801,
0.006518781650811434,
-0.033211324363946915,
0.09500795602798462,
0.0028566012624651194,
-0.02935880422592163,
-0.021227696910500526,
0.023096928372979164,
0.005806054454296827,
-0.051705796271562576,
0.00005808121932204813,
0.051454100757837296,
-0.00617448752745986,
0.03087897039949894,
0.01735145039856434,
-0.03315189480781555,
0.018086036667227745,
0.014107029885053635,
-0.004854925908148289,
0.01018992718309164,
-0.004885002970695496,
-0.010498209856450558,
0.048387590795755386,
-0.01744665950536728,
-0.006984405219554901,
-0.013794168829917908,
-0.009748575277626514,
0.05542637035250664,
0.020324379205703735,
-0.056793197989463806,
0.02020643837749958,
-0.011098011396825314,
0.019268199801445007,
-0.02050555683672428,
0.04878326132893562,
0.019641505554318428,
-0.013670100830495358,
0.001486104796640575,
-0.011570706963539124,
0.08760005980730057,
-0.01163118053227663,
-0.039444684982299805,
0.04251013323664665,
0.041254863142967224,
0.0028568648267537355,
-0.03733663260936737,
-0.005682871211320162,
0.006634600926190615,
0.030888095498085022,
-0.032673709094524384,
-0.0008848612196743488,
0.017382360994815826,
0.029687345027923584,
0.009213973768055439,
0.021044986322522163,
-0.04411572590470314,
-0.01208262424916029,
-0.06697770953178406,
-0.03749527037143707,
-0.02194642834365368,
0.017899377271533012,
-0.023211225867271423,
0.018897319212555885,
0.005613615270704031,
-0.011545022949576378,
0.025404613465070724,
0.012109467759728432,
-0.0711946114897728,
0.021941544488072395,
-0.044166360050439835,
-0.015178423374891281,
0.03809530287981033,
-0.026372406631708145,
-0.01116750854998827,
0.011679026298224926,
0.01821797341108322,
-0.03590578958392143,
-0.006060193292796612,
-0.04373837634921074,
-0.0030958151910454035,
0.01691732555627823,
-0.025190692394971848,
-0.0054086861200630665,
0.01778338849544525,
0.013283995911478996,
-0.049097154289484024,
0.02025843784213066,
0.03112630918622017,
-0.03750425949692726,
0.009585985913872719,
-0.0642765536904335,
0.003377221990376711,
0.008559225127100945,
-0.011286916211247444,
0.028841977939009666,
0.008440785109996796,
-0.025344548746943474,
0.003589686006307602,
-0.025095149874687195,
-0.0027161629404872656,
0.020914295688271523,
0.012528332881629467,
-0.03078896924853325,
-0.058808136731386185,
-0.001283554476685822,
0.003001643344759941,
0.012961809523403645,
-0.004966765642166138,
0.0027027728501707315,
0.04297677427530289,
-0.018880074843764305,
0.03293508291244507,
0.029586080461740494,
0.03130201995372772,
-0.0030544844921678305,
-0.0038718709256500006,
-0.010328050702810287,
0.003887844504788518,
-0.03773169964551926,
0.008459980599582195,
0.041840244084596634,
-0.02435411512851715,
-0.01912105642259121,
-0.0037532243877649307,
0.06777971237897873,
0.040166936814785004,
0.01759006455540657,
0.04274970293045044,
0.0007547758868895471,
0.06512380391359329,
-0.0005653977277688682,
-0.01184991467744112,
0.014716306701302528,
0.0034523766953498125,
0.05899561196565628,
-0.00973789393901825,
-0.03981456160545349,
-0.048507511615753174,
-0.041293587535619736,
0.025087108835577965,
0.02051546424627304,
-0.02060854434967041,
-0.027875451371073723,
-0.037110213190317154,
0.006989419925957918,
0.06381046772003174,
-0.027275830507278442,
0.011386747471988201,
-0.012554333545267582,
0.01916772685945034,
-0.004516239278018475,
-0.01727360114455223,
-0.03505666181445122,
-0.027484683319926262,
-0.013909764587879181,
-0.0031473636627197266,
-0.01720704510807991,
0.01718519628047943,
-0.005588309373706579,
0.018317600712180138,
0.05545918270945549,
0.01160657498985529,
0.017253827303647995,
-0.029946597293019295,
-0.016578886657953262,
0.027079060673713684,
-0.02723068743944168,
-0.08087165653705597,
-0.03631715103983879,
0.024387961253523827,
-0.021895088255405426,
0.017458776012063026,
0.0004503048839978874,
-0.07729323953390121,
0.036762695759534836,
0.005458816885948181,
-0.004305179696530104,
-0.030592946335673332,
-0.03540767729282379,
0.04676637053489685,
0.026206109672784805,
-0.03306753188371658,
0.04379701614379883,
0.0024023496080189943,
-0.017962494865059853,
-0.019801003858447075,
-0.01508778054267168,
0.0007375962450169027,
-0.01819927617907524,
-0.02558436244726181,
-0.03623593971133232,
0.015836969017982483,
-0.04012886434793472,
-0.0012453057570382953,
0.01456117257475853,
-0.023603372275829315,
-0.050980452448129654,
-0.06692816317081451,
-0.01848524995148182,
-0.012438337318599224,
0.0031802933663129807,
0.03227854520082474,
0.027951406314969063,
0.007071612402796745,
0.02409818395972252,
-0.005141222383826971,
0.009802722372114658,
-0.030498677864670753,
-0.014696643687784672,
0.022103387862443924,
0.01864345744252205,
0.00923125259578228,
-0.03965349867939949,
-0.00513185141608119,
0.010211106389760971,
-0.08474747836589813,
0.054737746715545654,
-0.015037172473967075,
-0.00549291493371129,
0.04140036925673485,
-0.07506721466779709,
-0.034176237881183624,
0.004639442078769207,
-0.004235357977449894,
0.0001422883797204122,
-0.021494455635547638,
-0.028342436999082565,
0.07981447130441666,
0.025137759745121002,
-0.04256580024957657,
-0.055569883435964584,
0.027731528505682945,
-0.01879092864692211,
0.011030170135200024,
0.0010096571641042829,
-0.024850985035300255,
-0.007908978499472141,
-0.04128435254096985,
-0.005435154307633638,
0.05118178576231003,
-0.03938642889261246,
0.010563218034803867,
-0.011165138334035873,
0.042422086000442505,
0.07713533937931061,
-0.0017759749898687005,
-0.028133796527981758,
0.001249908935278654,
-0.013664902187883854,
-0.017687181010842323,
-0.006828015670180321,
0.10766350477933884,
-0.040627140551805496,
-0.03964623063802719,
-0.011687909252941608,
-0.025972051545977592,
0.050304487347602844,
0.003477624384686351,
-0.017234493046998978,
0.022944744676351547,
0.013185634277760983,
-0.01752004399895668,
-0.004867475479841232,
0.013081197626888752,
-0.002369183348491788,
0.0602438859641552,
-0.010937311686575413,
-0.002399008022621274,
-0.007158690597862005,
-0.030213909223675728,
0.004539842717349529,
0.002368899993598461,
-0.01658720336854458,
-0.004378531593829393,
0.08454111218452454,
-0.018967105075716972,
-0.03837036341428757,
-0.01987079158425331,
-0.03974044322967529,
0.02254839427769184,
0.030966198071837425,
-0.010531207546591759,
0.036082565784454346,
-0.003364715026691556,
-0.01577523723244667,
-0.017790207639336586,
-0.04088928550481796,
0.05070618912577629,
0.055526427924633026,
-0.0006346756708808243,
0.04565851390361786,
0.0327305905520916,
0.03755287453532219,
-0.01452881470322609,
-0.01057893130928278,
-0.012637373991310596,
-0.043797701597213745,
0.0039619700983166695,
0.06533686071634293,
-0.04638899117708206,
-0.017574071884155273,
0.03991425409913063,
0.048638831824064255,
-0.014883500523865223,
-0.02023780345916748,
0.011508975178003311,
0.020215798169374466,
-0.024105999618768692,
0.021683325991034508,
-0.02769871987402439,
0.016473209485411644,
0.004028647672384977,
0.047309450805187225,
0.021198097616434097,
-0.03562396764755249,
0.045008983463048935,
0.019557787105441093,
0.015637336298823357,
-0.019746867939829826,
-0.034161947667598724,
-0.007366107311099768,
-0.004214537795633078,
0.0022748473566025496,
-0.005497455596923828,
-0.04093560948967934,
-0.016778022050857544,
0.05015707388520241,
-0.008658437989652157,
0.005852841772139072,
-0.027261868119239807,
-0.07048862427473068,
-0.029193146154284477,
-0.01878269948065281,
-0.07272078096866608,
0.022156786173582077,
-0.03136688470840454,
-0.048092253506183624,
0.018846554681658745,
-0.04750371351838112,
0.027344588190317154,
0.029896313324570656,
0.01709139160811901,
-0.009621836245059967,
0.085397869348526,
-0.0502634234726429,
0.004159360192716122,
-0.002737349597737193,
-0.016595572233200073,
0.1256636083126068,
0.03204745054244995,
0.007535132579505444,
-0.03251997381448746,
0.010678990744054317,
-0.01470502745360136,
-0.02108224481344223,
-0.027812406420707703,
-0.010958055965602398,
-0.005887923762202263,
-0.0019072584109380841,
0.002996574155986309,
0.047831565141677856,
-0.01179671660065651,
-0.05210493505001068,
0.04685266688466072,
0.012636474333703518,
-0.04971396178007126,
-0.0007646378944627941,
0.0015225635142996907,
-0.038575898855924606,
-0.023276232182979584,
-0.008288784883916378,
0.047298770397901535,
-0.022983111441135406,
-0.0031927197705954313,
-0.033010996878147125,
-0.017327001318335533,
-0.021069467067718506,
-0.013536768965423107,
-0.07290913909673691,
0.021144308149814606,
-0.0006152759888209403,
-0.025010744109749794,
-0.02505376562476158,
0.06943628937005997,
0.028576476499438286,
-0.03919020667672157,
0.06569729000329971,
0.015270966105163097,
-0.0033254302106797695,
0.014885185286402702,
0.048749715089797974,
0.02802678942680359,
-0.035522110760211945,
0.016732417047023773,
-0.014693117700517178,
0.03089490346610546,
-0.017267072573304176,
-0.0038342138286679983,
0.04356406256556511,
-0.012109832838177681,
-0.009120863862335682,
-0.07047702372074127,
0.046211328357458115,
-0.012347103096544743,
0.002004580572247505,
-0.0021454114466905594,
-0.027174685150384903,
-0.0007788079674355686,
0.0031562766525894403,
0.028410756960511208,
0.01724383421242237,
0.034938011318445206,
-0.005897947121411562,
-0.01764608547091484,
-0.009582363069057465,
0.03805844113230705,
-0.026545165106654167,
0.004487719852477312,
-0.0153143759816885,
-0.010562900453805923,
-0.014645028859376907,
-0.006936326157301664,
0.003975893836468458,
-0.0041258083656430244,
0.011734058149158955,
-0.00505592068657279,
-0.013148434460163116,
-0.033395688980817795,
-0.03520236536860466,
0.005515655502676964,
-0.012198188342154026,
-0.04839828610420227,
-0.016858495771884918,
-0.006650113966315985,
0.003954439423978329,
0.017603421583771706,
-0.01243291050195694,
0.029393617063760757,
0.011961090378463268,
0.04900144785642624,
0.018595436587929726,
-0.047964632511138916,
-0.01974099688231945,
0.07143070548772812,
0.022674983367323875,
0.006886209361255169,
-0.010735034011304379,
0.02216123603284359,
0.039635952562093735,
0.018641667440533638,
-0.03953251987695694,
0.039020098745822906,
-0.025476427748799324,
0.01930154301226139,
-0.0020406071562319994,
-0.06342141330242157,
-0.0020897346548736095,
0.0227370485663414,
-0.030811838805675507,
-0.03464442119002342,
-0.002848454052582383,
-0.007510806899517775,
-0.03142769634723663,
-0.01649429462850094,
0.007782439235597849,
-0.020436089485883713,
0.03621169924736023,
-0.08542686700820923,
0.012909271754324436,
-0.04748759791254997,
0.011586295440793037,
-0.045733366161584854,
0.013539638370275497,
0.023627154529094696,
0.020059220492839813,
-0.020828526467084885,
0.03988485038280487,
-0.00930712092667818,
-0.008172173984348774,
0.01025035884231329,
-0.0029486841522157192,
0.016315042972564697,
0.03409687057137489,
0.007956856861710548,
-0.002912895055487752,
0.037870656698942184,
0.01711180806159973,
-0.027405666187405586,
0.04384482651948929,
-0.01919090561568737,
-0.040688082575798035,
0.042503613978624344,
-0.0188763327896595,
0.049531493335962296,
0.00499522453173995,
-0.0425746850669384,
0.012913929298520088,
0.06968320906162262,
-0.007697141729295254,
0.003703092224895954,
-0.0228789821267128,
-0.0014516207156702876,
-0.01073378510773182,
-0.005902260076254606,
0.028324391692876816,
-0.015064802952110767,
0.015693441033363342,
0.041241638362407684,
0.04618338495492935,
-0.04170975834131241,
-0.007339645177125931,
-0.00900848489254713,
-0.02745705097913742,
-0.0018348190933465958,
0.010441876947879791,
0.009881787933409214,
0.0029062086250633,
0.016712844371795654,
-0.03607983514666557,
0.013110583648085594,
-0.013908314518630505,
0.013856944628059864,
-0.03225405886769295,
-0.025049522519111633,
0.004628359340131283,
-0.02850375697016716,
0.05278311297297478,
-0.036098577082157135,
0.012374643236398697,
0.038205284625291824,
-0.08116849511861801,
-0.005243181250989437,
-0.03553015738725662,
-0.008866984397172928,
0.015425783582031727,
-0.007155522238463163,
0.016512379050254822,
0.017897265031933784,
0.015249825082719326,
0.04072514548897743,
0.04057382047176361,
0.00490313908085227,
0.00011533284850884229,
-0.057849954813718796,
0.040424272418022156,
0.04203246161341667,
-0.005339871160686016,
-0.034257370978593826,
0.04921280965209007,
-0.013266067951917648,
-0.05269410461187363,
0.05638930946588516,
-0.018817536532878876,
0.025265244767069817,
-0.0117667680606246,
0.0348341278731823,
0.0048308908008039,
0.035537946969270706,
0.00022888094827067107,
-0.017358550801873207,
-0.004772434942424297,
0.06852585822343826,
0.053605999797582626,
0.029650401324033737,
-0.03642917051911354,
-0.0026114708743989468,
0.009871537797152996,
-0.030356159433722496,
-0.021099131554365158,
0.009688267484307289,
-0.015230165794491768,
0.00947338342666626,
-0.008409370668232441,
0.01165931299328804,
0.020748749375343323,
-0.0271452609449625,
0.020946919918060303,
-0.040621984750032425,
0.01782218925654888,
0.006712993141263723,
-0.00919601321220398,
0.020684704184532166,
0.03356116637587547,
0.03481945022940636,
-0.0023854663595557213,
-0.012681758962571621,
-0.023128461092710495,
-0.05099700391292572,
-0.036986369639635086,
-0.014323104172945023,
0.008419626392424107,
-0.00024366639263462275,
-0.019047575071454048,
-0.03887372463941574,
-0.04133383184671402,
0.014196999371051788,
0.008321983739733696,
-0.01430396270006895,
0.009347383864223957,
-0.026411861181259155,
-0.013075407594442368,
-0.0695030689239502,
0.040553055703639984,
0.016973719000816345,
-0.032991912215948105,
-0.014785101637244225,
-0.054512638598680496,
-0.024087168276309967,
-0.0010571585735306144,
0.05676062032580376,
0.018433870747685432,
0.01151330303400755,
0.020024798810482025,
-0.015006802044808865,
-0.000011967184036620893,
-0.057957928627729416,
0.0314396396279335,
-0.007846503518521786,
-0.03905235975980759,
0.027708090841770172,
-0.019162412732839584,
0.029772965237498283,
0.002051242161542177,
-0.006578744854778051,
-0.01945863477885723,
0.05278210714459419,
0.009551231749355793,
0.012266000732779503,
0.05012622848153114,
-0.01726372353732586,
0.007333855610340834,
0.05488676577806473,
-0.020508170127868652,
0.0286521278321743,
0.04514941945672035,
-0.0441385954618454,
-0.012364468537271023,
0.07516487687826157,
-0.009964950382709503,
0.0004957053461112082,
-0.01213304977864027,
-0.006845024414360523,
0.02270195446908474,
-0.044141072779893875,
-0.026344845071434975,
0.030989496037364006,
0.0032865889370441437,
-0.004043714143335819,
0.010324490256607533,
0.021869564428925514,
0.03392075374722481,
0.03701195493340492,
0.011957787908613682,
0.027889005839824677,
-0.021189134567975998,
0.04172074422240257,
0.01104129757732153,
0.03570161387324333,
0.005079954396933317,
-0.009787729941308498,
0.035110145807266235,
0.013103080913424492,
0.07774802297353745,
-0.025470683351159096,
0.016893940046429634,
-0.027458906173706055,
-0.024625632911920547,
0.007877550087869167,
-0.025377552956342697,
0.020095504820346832,
0.021199416369199753,
0.014481902122497559,
0.06574025750160217,
-0.024126112461090088,
0.003257864387705922,
0.024241965264081955,
-0.00830218754708767,
-0.0008093229844234884,
0.008910712786018848,
0.0030779694207012653,
0.010022393427789211,
-0.006710827816277742,
-0.026832038536667824,
-0.006567683536559343,
-0.004354602657258511,
0.016072984784841537,
0.03250018507242203,
0.04897792637348175,
0.01146189495921135,
0.0073189628310501575,
0.0016935738967731595,
-0.017717385664582253,
-0.01934581808745861,
-0.007931995205581188,
0.06934972107410431,
0.023235294967889786,
0.060014545917510986,
-0.005593984853476286,
0.027779506519436836,
-0.0021339314989745617,
0.0375475212931633,
-0.07135725766420364,
-0.020703261718153954,
-0.00944035965949297,
0.03556448593735695,
0.03906898573040962,
-0.0487494133412838
] |
<p>In most of the field theory text they will start with lagrangian density for spin 1 and spin 1/2 particles. But i could find any text where this lagrangian density is derived from first principle. </p> | 2,884 | [
0.003401471534743905,
-0.014257421717047691,
0.023585939779877663,
-0.0024906049948185682,
0.013484594412147999,
0.0075438739731907845,
-0.032651569694280624,
-0.024746913462877274,
-0.003935273736715317,
-0.05687955021858215,
0.024024050682783127,
0.02699262462556362,
0.07469888776540756,
0.03322745859622955,
0.051238421350717545,
-0.003536536591127515,
0.008444217965006828,
0.003388446755707264,
-0.018784435465931892,
-0.028891852125525475,
0.027124330401420593,
0.013007013127207756,
0.02330709807574749,
-0.003894750028848648,
-0.020993150770664215,
0.023019608110189438,
-0.031088579446077347,
0.02055845782160759,
-0.0024057261180132627,
0.09246057271957397,
-0.0338188111782074,
-0.013083074241876602,
0.006747183855623007,
-0.0026747118681669235,
0.0462186262011528,
0.010797583498060703,
-0.003384833689779043,
-0.0657350942492485,
-0.009635299444198608,
-0.0077575212344527245,
-0.05144695192575455,
-0.03282499313354492,
-0.023234909400343895,
0.027018625289201736,
-0.029306070879101753,
0.031091419979929924,
0.029169129207730293,
-0.041984014213085175,
0.06111776828765869,
-0.06600771844387054,
0.05990520119667053,
0.026363516226410866,
0.02987745963037014,
0.025324147194623947,
0.0007663935539312661,
-0.002493815263733268,
0.06157355010509491,
0.04527122154831886,
0.03656646981835365,
-0.06579899042844772,
-0.060940563678741455,
-0.04164518788456917,
-0.007595503237098455,
-0.041434917598962784,
-0.01402956247329712,
0.024090662598609924,
0.010397952049970627,
-0.03868711739778519,
0.03663342446088791,
0.005757338833063841,
-0.0011827690759673715,
-0.007401688024401665,
0.04498056694865227,
-0.0049692546017467976,
-0.0019530748249962926,
0.019725479185581207,
0.01896665245294571,
-0.026052789762616158,
0.018602631986141205,
0.0016260100528597832,
0.012124712578952312,
0.03846172243356705,
0.03985944762825966,
0.021176373586058617,
-0.022466469556093216,
-0.008542193099856377,
0.0749000683426857,
0.007574672810733318,
-0.006421777419745922,
0.04752293601632118,
-0.03719658404588699,
-0.02175164222717285,
0.0478968508541584,
-0.0299343504011631,
-0.030026139691472054,
0.03854108229279518,
0.02201627381145954,
0.0666000097990036,
-0.004338967613875866,
-0.024638094007968903,
-0.0061669303104281425,
-0.029547221958637238,
0.003599744290113449,
0.05843878164887428,
0.014395751990377903,
-0.029516568407416344,
-0.05862663313746452,
0.036046355962753296,
-0.027972355484962463,
-0.014462013728916645,
-0.029314404353499413,
0.007768099661916494,
-0.03637099266052246,
-0.024171438068151474,
0.018731579184532166,
-0.015545961447060108,
-0.006877911742776632,
-0.0018676994368433952,
0.05706818774342537,
0.058527808636426926,
0.04756304994225502,
0.022246137261390686,
0.04042745381593704,
0.006843673065304756,
-0.054880280047655106,
0.0200420543551445,
0.0444336012005806,
-0.0040233139880001545,
-0.019597738981246948,
-0.000591671618167311,
0.00013760892034042627,
-0.01514459028840065,
0.007385013159364462,
0.027179449796676636,
0.03243120759725571,
-0.0008793711313046515,
-0.06635569781064987,
-0.03735196962952614,
0.0389801561832428,
-0.020212111994624138,
-0.00523774977773428,
-0.0344715379178524,
0.011900856159627438,
0.028405826538801193,
0.06955952942371368,
0.0019365249900147319,
0.05044886842370033,
-0.01634245179593563,
0.01472234632819891,
-0.00721843121573329,
-0.006689992733299732,
-0.04708436504006386,
0.01289424579590559,
-0.033286526799201965,
-0.008052020333707333,
-0.05148107931017876,
0.037744492292404175,
0.014011147432029247,
-0.01909511908888817,
-0.02472793683409691,
0.05652063712477684,
-0.007804612163454294,
0.03540630266070366,
0.027452880516648293,
-0.003252235474064946,
-0.009711633436381817,
0.06390614062547684,
-0.0006966840592212975,
0.01109743770211935,
0.029535450041294098,
-0.01274850219488144,
0.010807626880705357,
0.007304292172193527,
0.026190733537077904,
0.048662979155778885,
-0.040532201528549194,
-0.026389772072434425,
0.028777020052075386,
0.03398099169135094,
0.00027444108854979277,
-0.02833692915737629,
-0.0035270198713988066,
-0.016466908156871796,
0.019390545785427094,
-0.03307107463479042,
0.03218567743897438,
-0.009773422963917255,
-0.017416050657629967,
-0.014694576151669025,
-0.041289955377578735,
-0.0076134405098855495,
-0.06740377098321915,
-0.0230136439204216,
-0.030656838789582253,
0.001112840953283012,
0.06226816028356552,
0.026029370725154877,
0.031852129846811295,
-0.06152734160423279,
-0.05023191124200821,
-0.022792484611272812,
0.02110973931849003,
0.013667470775544643,
0.013436518609523773,
0.003745612921193242,
0.031615518033504486,
0.019265688955783844,
0.01081374753266573,
0.0206881333142519,
0.010216347873210907,
-0.026831183582544327,
0.002714623464271426,
-0.016509542241692543,
0.04560866206884384,
-0.007842550985515118,
0.021437006071209908,
-0.010502076707780361,
0.021905990317463875,
-0.01187461894005537,
0.009651178494095802,
-0.018872961401939392,
0.04498869553208351,
0.043141867965459824,
0.014299481175839901,
0.0068615498021245,
0.028212804347276688,
-0.013413611799478531,
-0.007849937304854393,
0.03500119596719742,
-0.025481849908828735,
-0.024945013225078583,
-0.005893365014344454,
0.0701068639755249,
0.05486290901899338,
-0.05215701833367348,
-0.02057383581995964,
0.06614745408296585,
0.01328916847705841,
0.036460064351558685,
0.03489040955901146,
-0.05626903101801872,
-0.08132921159267426,
0.0322527214884758,
0.023520953953266144,
-0.0050475881434977055,
-0.019126085564494133,
0.04431649297475815,
0.03272344917058945,
0.008638651110231876,
0.028993234038352966,
-0.06891817599534988,
0.02478085458278656,
-0.021074203774333,
0.005465035792440176,
0.01917065866291523,
-0.07360564917325974,
0.04554806277155876,
-0.03859272599220276,
0.05659687891602516,
-0.0051041413098573685,
-0.030443483963608742,
-0.04768051579594612,
-0.03227183222770691,
-0.03291734308004379,
0.02024046517908573,
-0.00192295853048563,
-0.05276999995112419,
0.009174675680696964,
0.039073504507541656,
-0.037641145288944244,
0.001085030846297741,
0.006387567147612572,
-0.03189120441675186,
-0.00885844137519598,
0.019436568021774292,
0.011766968294978142,
0.003987004514783621,
0.0037268437445163727,
-0.013505702838301659,
-0.007909233681857586,
0.021432099863886833,
-0.0021948651410639286,
0.034394655376672745,
0.041585542261600494,
-0.056697677820920944,
0.012008437886834145,
-0.07801122963428497,
-0.044392675161361694,
0.03980289399623871,
0.0036930383648723364,
0.0032633310183882713,
0.019563017413020134,
-0.012701553292572498,
-0.05747905746102333,
-0.006128166802227497,
-0.019781319424510002,
-0.016382312402129173,
-0.006236746907234192,
0.005723831709474325,
0.015411495231091976,
-0.012427662499248981,
-0.01289669331163168,
-0.01412141602486372,
-0.0432400219142437,
-0.026601586490869522,
-0.031382106244564056,
0.03403843566775322,
0.013466821052134037,
-0.03617287054657936,
0.008347894996404648,
0.05254427343606949,
-0.012576417997479439,
0.020090948790311813,
-0.04975702986121178,
-0.03906607627868652,
0.018010282889008522,
0.007345216348767281,
0.009295166470110416,
-0.013848956674337387,
-0.054224591702222824,
0.09230402857065201,
0.04228690639138222,
-0.04344438388943672,
-0.020763318985700607,
-0.0056054783053696156,
0.011808538809418678,
-0.012232300825417042,
0.021613318473100662,
-0.008130902424454689,
-0.00022643922420684248,
0.024194879457354546,
0.019888265058398247,
-0.009969357401132584,
0.0056539117358624935,
0.014931216835975647,
0.014011414721608162,
0.011111498810350895,
-0.019020387902855873,
-0.026283884420990944,
0.02582714520394802,
0.009930883534252644,
-0.011428694240748882,
0.030167153105139732,
0.004070229362696409,
0.058915723115205765,
-0.015780549496412277,
-0.020868616178631783,
0.06012449413537979,
0.008495504036545753,
-0.009947365149855614,
0.0002946245367638767,
0.03288113325834274,
0.0009774501668289304,
-0.037241335958242416,
0.026550397276878357,
0.0300897266715765,
-0.0018802660051733255,
0.009091834537684917,
-0.01328182127326727,
0.008713253773748875,
0.013887440785765648,
-0.0441330261528492,
-0.06048019230365753,
-0.0033933871891349554,
-0.025046590715646744,
0.04929807037115097,
-0.01955597847700119,
-0.01959136687219143,
0.04047039896249771,
0.01250526774674654,
0.014513797126710415,
-0.02173556759953499,
-0.044987864792346954,
0.032197121530771255,
-0.07432591915130615,
-0.00416426919400692,
0.02127271518111229,
0.0070204958319664,
0.0018560325261205435,
0.052719030529260635,
-0.020514026284217834,
0.016983693465590477,
0.026067813858389854,
0.011910458095371723,
-0.07689002901315689,
0.02478351816534996,
-0.04451127350330353,
-0.006173676811158657,
0.009953961707651615,
-0.028069451451301575,
0.005118733737617731,
-0.03918066248297691,
-0.013262028805911541,
-0.025378134101629257,
-0.010578623972833157,
-0.04706049710512161,
0.013093382120132446,
-0.031238598749041557,
-0.04537050798535347,
-0.046669185161590576,
0.05678210034966469,
0.02389886975288391,
-0.027028469368815422,
0.008496849797666073,
0.04013223573565483,
-0.023280130699276924,
-0.0072410823777318,
-0.02157069742679596,
0.02074090577661991,
0.005028551910072565,
-0.0032420107163488865,
0.04147098958492279,
-0.008221995085477829,
-0.0220955740660429,
0.0173636544495821,
0.011461598798632622,
0.08617489784955978,
0.006538891699165106,
-0.000757526489906013,
0.0036526620388031006,
-0.03907604515552521,
-0.027261795476078987,
0.01741941273212433,
0.047968219965696335,
-0.015875039622187614,
-0.02328510209918022,
0.03843596577644348,
0.002235240302979946,
0.01207217201590538,
0.034535687416791916,
0.03967239335179329,
0.007879392243921757,
-0.028777774423360825,
-0.03991886228322983,
0.015987059101462364,
0.007965704426169395,
0.014426367357373238,
0.019338475540280342,
0.007603221572935581,
-0.02335837297141552,
0.003346081357449293,
-0.011147602461278439,
0.024671370163559914,
-0.04697085916996002,
-0.0021293985191732645,
0.0034046273212879896,
0.017697719857096672,
0.011048859916627407,
-0.022996865212917328,
0.02215343900024891,
0.05024152621626854,
0.04470372572541237,
0.023758038878440857,
-0.00892286654561758,
-0.053141143172979355,
0.016346905380487442,
0.0383293479681015,
0.023201148957014084,
0.008918936364352703,
0.002558547304943204,
-0.03359590098261833,
-0.030034486204385757,
0.06995826214551926,
-0.011912815272808075,
0.012527734972536564,
0.002603469882160425,
-0.012027712538838387,
0.029416164383292198,
-0.020287035033106804,
-0.055052295327186584,
0.015206407755613327,
-0.021970143541693687,
-0.0052191042341291904,
-0.01120478194206953,
0.02831173874437809,
-0.03355366364121437,
0.02283550426363945,
0.00029856976470910013,
0.057346515357494354,
0.016544939950108528,
0.04307263717055321,
-0.03676220029592514,
0.04918985068798065,
-0.03617066890001297,
-0.07962273806333542,
-0.03744657710194588,
-0.0071373386308550835,
0.002841990441083908,
0.018000900745391846,
-0.013716179877519608,
-0.04755321890115738,
0.021919915452599525,
-0.012464531697332859,
-0.013240428641438484,
-0.009739372879266739,
-0.09296578168869019,
0.01854255422949791,
0.024886569008231163,
-0.005726812407374382,
0.0391579307615757,
0.01722164824604988,
-0.02687464840710163,
-0.013464583083987236,
-0.008636564947664738,
0.04060117155313492,
-0.01330962497740984,
0.01546225231140852,
-0.04277443513274193,
0.009763380512595177,
-0.016709111630916595,
0.006909829564392567,
-0.02847423404455185,
0.011065726168453693,
-0.013463489711284637,
-0.0475541315972805,
-0.04638596624135971,
0.01979701966047287,
0.015061278827488422,
-0.005206666886806488,
0.019830787554383278,
0.030136309564113617,
0.02147248573601246,
-0.0034407894127070904,
-0.002653205068781972,
-0.031324684619903564,
-0.004080992192029953,
0.01801254227757454,
0.013058986514806747,
0.04281018301844597,
-0.03848282992839813,
-0.020325643941760063,
0.004675319418311119,
-0.040261123329401016,
0.07498610019683838,
-0.00483471667394042,
-0.006433457136154175,
-0.008347893133759499,
-0.052570562809705734,
-0.06816577166318893,
0.03250214830040932,
0.016184261068701744,
0.048488009721040726,
-0.03972168639302254,
-0.018152635544538498,
-0.026605404913425446,
-0.009961828589439392,
-0.07362841814756393,
-0.018033025786280632,
0.005014797672629356,
-0.012267287820577621,
-0.03455369174480438,
-0.03771394118666649,
0.024687213823199272,
-0.014144920744001865,
-0.023280678316950798,
0.033229537308216095,
0.056689415127038956,
-0.00967648159712553,
0.010936498641967773,
0.0014836343470960855,
-0.0028442649636417627,
0.011078285984694958,
-0.015766534954309464,
-0.017901483923196793,
0.0014463170664384961,
-0.006047557108104229,
0.016912851482629776,
-0.02735818177461624,
0.024224212393164635,
-0.018414754420518875,
0.023819303140044212,
-0.030015459284186363,
-0.0012346860021352768,
0.04410167038440704,
-0.03815019130706787,
-0.00004532296588877216,
0.03190110996365547,
0.016011590138077736,
-0.017743641510605812,
-0.04726782068610191,
-0.03220979496836662,
-0.03547872602939606,
0.02870299108326435,
-0.029199760407209396,
-0.021231304854154587,
-0.04938720539212227,
-0.020369630306959152,
0.02583075687289238,
0.009674102067947388,
0.025101587176322937,
0.02586541138589382,
0.06869128346443176,
0.018534256145358086,
-0.030182259157299995,
0.049034859985113144,
-0.023496245965361595,
-0.024215014651417732,
0.03596087917685509,
0.027593640610575676,
0.014037908986210823,
0.014821684919297695,
-0.00876600667834282,
0.0032802752684801817,
-0.0011611999943852425,
-0.0025281624402850866,
0.06020648777484894,
0.008422735147178173,
0.020665790885686874,
0.02544000931084156,
-0.01233035046607256,
0.0072442591190338135,
0.018992573022842407,
-0.014557099901139736,
-0.0027891325298696756,
0.005087697878479958,
0.07213695347309113,
-0.03905582055449486,
-0.02480798028409481,
0.05252032354474068,
0.03155917674303055,
-0.03836007043719292,
0.04062527418136597,
-0.0014091000193729997,
0.014768670313060284,
0.011070512235164642,
0.007918527349829674,
-0.052827879786491394,
0.05195322260260582,
-0.01811095140874386,
0.030816422775387764,
-0.02041870914399624,
-0.05350925773382187,
0.04299575462937355,
-0.024902692064642906,
-0.003964562900364399,
-0.0018968982622027397,
-0.05545976012945175,
-0.005175328813493252,
0.030639316886663437,
0.037108585238456726,
-0.005340964067727327,
-0.01845957711338997,
0.034277208149433136,
0.04070137068629265,
-0.02185732126235962,
0.0142248859629035,
0.041490230709314346,
-0.026137813925743103,
-0.021869437769055367,
-0.06776208430528641,
-0.08197671175003052,
0.032040372490882874,
-0.010525595396757126,
-0.027262134477496147,
0.0019128338899463415,
-0.02213238552212715,
0.033197905868291855,
0.012751477770507336,
0.04206308722496033,
-0.0031711175106465816,
0.09306782484054565,
0.013248864561319351,
0.0312013179063797,
0.001897401874884963,
-0.012249980121850967,
0.13848444819450378,
0.08981428295373917,
0.025673190131783485,
-0.08487701416015625,
0.029010122641921043,
-0.03284868225455284,
0.02326079085469246,
-0.04159727692604065,
0.051142413169145584,
0.0005518004181794822,
-0.004196940455585718,
-0.011318949051201344,
0.07822604477405548,
0.00381045532412827,
-0.01650487259030342,
0.05166855826973915,
-0.005099450703710318,
-0.006314041558653116,
0.01284545473754406,
0.04772437736392021,
-0.006313700694590807,
-0.013210509903728962,
-0.02143433317542076,
0.0015964965568855405,
0.009211909025907516,
0.001860755030065775,
-0.01124543510377407,
-0.06763945519924164,
0.022191571071743965,
-0.02072509564459324,
-0.034181997179985046,
-0.02697259746491909,
-0.014051959849894047,
0.0103252362459898,
-0.037629202008247375,
-0.030858105048537254,
0.021775400266051292,
-0.009192798286676407,
0.03962358087301254,
0.03326315060257912,
0.024624072015285492,
0.0580625981092453,
0.033739469945430756,
0.04620100185275078,
-0.01699664816260338,
-0.000008427259672316723,
-0.015588250011205673,
0.06361375749111176,
-0.03499545902013779,
0.020767267793416977,
0.034343767911195755,
-0.010944669134914875,
0.008688926696777344,
-0.001664750394411385,
0.0013050835113972425,
-0.022434070706367493,
0.007122183218598366,
0.0013296665856614709,
0.0225534588098526,
-0.03313650190830231,
0.005299297161400318,
-0.03067142888903618,
0.019287923350930214,
-0.014795436523854733,
-0.010695227421820164,
-0.000142164746648632,
0.006078334525227547,
0.04567810520529747,
-0.014789316803216934,
-0.037429507821798325,
-0.016753938049077988,
-0.018683355301618576,
-0.05998345836997032,
-0.028865134343504906,
0.015027832239866257,
0.027850141748785973,
0.008856143802404404,
-0.009181784465909004,
-0.019624769687652588,
-0.001841637771576643,
-0.047959104180336,
0.01881144754588604,
-0.0186323169618845,
0.001051462721079588,
-0.001453765551559627,
0.0024710549041628838,
0.026892412453889847,
0.05681877210736275,
-0.02961069904267788,
-0.013119195587933064,
-0.018653493374586105,
0.0090177645906806,
0.0014578050468116999,
-0.021611148491501808,
0.03335686773061752,
-0.0013326517073437572,
-0.030507514253258705,
-0.003717997344210744,
-0.03365007042884827,
-0.015281915664672852,
0.019605819135904312,
0.02005280740559101,
0.010933121666312218,
0.013051589019596577,
-0.012023660354316235,
0.01207014825195074,
0.016453761607408524,
-0.025153864175081253,
-0.005576447118073702,
0.04025854170322418,
0.02234882116317749,
-0.0424400269985199,
-0.05721212923526764,
0.01834692992269993,
-0.005216538440436125,
-0.030985841527581215,
0.05004031956195831,
-0.03695089370012283,
-0.037340227514505386,
-0.03133013844490051,
0.004674582276493311,
-0.01567819155752659,
-0.006656618323177099,
-0.054466668516397476,
0.03703442960977554,
-0.013810737058520317,
0.005282520782202482,
-0.06308566778898239,
0.04003991186618805,
-0.00046959961764514446,
-0.003930227365344763,
-0.0019857659935951233,
-0.01878371275961399,
-0.029781075194478035,
0.02089698426425457,
0.048087917268276215,
0.005029010120779276,
0.03452300280332565,
0.008557799272239208,
-0.02277565188705921,
0.0021448852494359016,
-0.03543761372566223,
-0.07317852973937988,
0.03693980723619461,
-0.011776887811720371,
0.020832672715187073,
0.033052004873752594,
-0.009711972437798977,
-0.017381424084305763,
0.051777902990579605,
-0.014087628573179245,
-0.013741862960159779,
0.005408657714724541,
-0.030089009553194046,
-0.014938379637897015,
-0.02586280182003975,
0.028184950351715088,
-0.0027513541281223297,
-0.032432734966278076,
0.012819118797779083,
0.0031966520473361015,
-0.006816723383963108,
0.0133312763646245,
0.015328481793403625,
0.002887249458581209,
-0.006153437774628401,
0.015136165544390678,
-0.021715892478823662,
-0.014706853777170181,
0.02861720696091652,
-0.020513901486992836,
-0.001249716617166996,
-0.01086198166012764,
0.016663189977407455,
-0.07822710275650024,
-0.00784631259739399,
-0.013363592326641083,
0.022319594398140907,
0.07160822302103043,
-0.044551290571689606,
0.017430763691663742,
0.021873751655220985,
-0.06359788775444031,
0.023449881002306938,
0.015517909079790115,
-0.007205975707620382,
-0.02050759084522724,
0.01332381833344698,
-0.002528010867536068,
0.07004319876432419,
0.0027435303200036287,
0.056457288563251495,
0.005797822959721088,
0.006067120470106602,
-0.00439965957775712,
-0.021006247028708458,
-0.015598731115460396,
0.019795715808868408,
0.0011160612339153886,
0.006709603127092123,
0.07961438596248627,
0.00855571124702692,
-0.053032197058200836,
0.03900497034192085,
0.009301772341132164,
-0.014508301392197609,
-0.025189440697431564,
0.015109962783753872,
-0.019146814942359924,
0.018339021131396294,
-0.0022722750436514616,
-0.019383827224373817,
0.022345349192619324,
0.008048717863857746,
0.00879610050469637,
-0.0035314837004989386,
-0.02952413819730282,
0.02738060988485813,
0.02177436091005802,
-0.015942243859171867,
-0.04949583485722542,
0.05960807204246521,
-0.009631126187741756,
-0.020306618884205818,
-0.006425794679671526,
0.008878758177161217,
0.0025795146357268095,
-0.03462277352809906,
0.04514654353260994,
-0.06607524305582047,
0.022197742015123367,
-0.007753588259220123,
-0.03923898562788963,
-0.01020205020904541,
0.07167963683605194,
-0.012011487036943436,
0.007795355282723904,
0.04272562265396118,
0.023048432543873787,
-0.000678208889439702,
-0.05161713436245918,
0.000696419388987124,
0.03151160478591919,
-0.00846007652580738,
-0.010535412468016148,
-0.06556912511587143,
-0.009355753660202026,
0.026591883972287178,
-0.005986446514725685,
-0.017460927367210388,
0.014980025589466095,
-0.0017895306227728724,
0.030258620157837868,
-0.040664851665496826,
0.02562200278043747,
0.033403098583221436,
0.03418147563934326,
-0.022010819986462593,
-0.0167000200599432,
-0.005922917276620865,
-0.011779912747442722,
0.01746121048927307,
0.004791075363755226,
-0.000430481624789536,
0.017718810588121414,
0.003925319295376539,
0.004170241300016642,
-0.0433209203183651,
0.0008318186737596989,
-0.025749312713742256,
-0.05364859476685524,
-0.010190213099122047,
-0.0029451593291014433,
-0.01576927676796913,
0.0059179808013141155,
0.010870867408812046,
0.021032294258475304,
0.00695404876023531,
0.02545924484729767,
-0.035257622599601746,
0.06968469172716141,
0.013135964050889015,
0.008951161056756973,
0.0613618940114975,
-0.039719827473163605,
0.0019283515866845846,
0.05447343736886978,
-0.049309711903333664,
-0.023232847452163696,
0.004433365073055029,
-0.033799175173044205,
-0.0384574756026268,
-0.018321309238672256,
0.018107198178768158,
0.008896365761756897,
-0.06702399253845215,
0.006432956084609032,
0.028682641685009003,
-0.007114631123840809,
-0.028009971603751183,
0.037961218506097794,
-0.004440545570105314,
0.04522773250937462,
0.00838673859834671,
-0.011187889613211155,
0.03121737577021122,
-0.01383429579436779,
-0.004811398219317198,
0.04187967628240585,
0.009982582181692123,
-0.006574064493179321,
0.017182428389787674,
0.02448108419775963,
-0.03324988856911659,
0.028876541182398796,
0.011654041707515717,
0.05192669481039047,
-0.026160407811403275,
-0.013664906844496727,
0.013325684703886509,
-0.019037285819649696,
0.002514614723622799,
-0.01729026436805725,
-0.04172210767865181,
0.06310238689184189,
-0.02514585107564926,
0.0015415791422128677,
-0.020846610888838768,
-0.0049007548950612545,
-0.006429096218198538,
-0.011886972934007645,
0.03515656664967537,
0.0864487737417221,
-0.004509528633207083,
-0.014466478489339352,
-0.01725509949028492,
-0.014492511749267578,
0.00037302557029761374,
-0.06097336485981941,
0.008731706999242306,
0.0144805284217,
0.014164603315293789,
-0.005555066745728254,
-0.004550653975456953,
-0.028097879141569138,
-0.016774967312812805,
0.01529235951602459,
0.024266904219985008,
0.03042743168771267,
-0.04051993042230606,
-0.01557514164596796,
-0.02253476344048977,
0.08114378899335861,
-0.04354548081755638,
0.012041413225233555,
-0.03075151890516281,
0.01967322640120983,
-0.03636101260781288,
0.01385019812732935
] |
<p>If you stick a tissue to the bottom of a glass and immerse this glass fully (upside down) into a tumbler of water, then this tissue remains dry. Why is this so? / What conclusion would you draw from this?</p>
<p>a) Air occupies a definite volume.</p>
<p>b) Air has mass.</p>
<p>c) Both</p>
<p>Now, I think it should be both. Reason:</p>
<p>If air had a volume but zero mass (hypothetically speaking), then it will not exert any pressure, so therefore water would rise till it hits the tissue (pressure due to air is the reason water level is lower, right?)!</p>
<p>Also, we can say that if an object has zero mass, we can have 100 % compressibility for any definite volume.</p>
<p>Pls tell me if my approach is right? </p>
<p>PS: I am not in junior school, my sister is, and this is from her weekly test.</p> | 2,885 | [
-0.02000880055129528,
-0.04178028181195259,
-0.015120542608201504,
-0.027357544749975204,
0.029405472800135612,
-0.03363250941038132,
-0.005648354534059763,
-0.0048504788428545,
-0.006489017978310585,
0.0012167970417067409,
0.044773735105991364,
0.009592952206730843,
0.02320989780128002,
0.02386905997991562,
-0.012739799916744232,
-0.0011406035628169775,
-0.027453238144516945,
-0.022129196673631668,
0.014094887301325798,
-0.0009090907988138497,
-0.009656578302383423,
0.005287362728267908,
0.005632949993014336,
0.023504965007305145,
-0.01424427330493927,
0.05329865217208862,
-0.0016995146870613098,
-0.052775293588638306,
0.01906939595937729,
0.031019074842333794,
-0.028837284073233604,
-0.009176361374557018,
-0.015529370866715908,
-0.0052613429725170135,
0.03627576306462288,
0.00037342438008636236,
-0.015817224979400635,
0.011217505671083927,
-0.011545286513864994,
0.024573249742388725,
0.01574602723121643,
-0.027020787820219994,
-0.006688443943858147,
0.041709549725055695,
-0.023061132058501244,
0.04399688541889191,
0.018310364335775375,
-0.009111473336815834,
0.01933261938393116,
-0.07648245245218277,
0.036804020404815674,
0.020409228280186653,
0.05617766082286835,
0.052645690739154816,
0.02381940558552742,
-0.009577791206538677,
0.042402468621730804,
0.03559007868170738,
-0.061187420040369034,
-0.044640976935625076,
-0.006853082217276096,
-0.00041940799565054476,
-0.05659039691090584,
0.005169895477592945,
0.01474956888705492,
-0.00453034695237875,
-0.014928515069186687,
0.005912815220654011,
0.0512470006942749,
0.01277490146458149,
0.01062583364546299,
0.02279592491686344,
0.06001832336187363,
-0.016541942954063416,
0.02029307186603546,
0.001822187565267086,
0.041170649230480194,
0.032216593623161316,
0.0070733679458498955,
0.05523444712162018,
-0.009355828166007996,
0.0009595248266123235,
0.029689958319067955,
0.058047324419021606,
0.043020207434892654,
-0.028999699279665947,
0.05923866108059883,
0.02462482824921608,
0.03282671421766281,
0.06592540442943573,
0.024420160800218582,
-0.06642168760299683,
0.00490534445270896,
-0.01894194819033146,
0.01183162722736597,
0.002642605220898986,
-0.012698312290012836,
0.08508866280317307,
-0.012984581291675568,
-0.006350293755531311,
-0.045033346861600876,
0.041919633746147156,
0.0784514769911766,
0.08356884866952896,
0.0021061524748802185,
-0.03318993002176285,
-0.0451180562376976,
0.032370343804359436,
0.01841789297759533,
0.020501505583524704,
-0.003882751567289233,
0.029333975166082382,
-0.017136620357632637,
-0.04724368453025818,
0.018005874007940292,
-0.017799057066440582,
0.018872395157814026,
-0.016048463061451912,
0.04499144107103348,
0.006788995116949081,
0.055273059755563736,
-0.027850303798913956,
0.0035210379865020514,
-0.0021122030448168516,
-0.08336015790700912,
0.01547932531684637,
0.022791940718889236,
-0.0004561052774079144,
-0.03711818531155586,
0.05757402256131172,
-0.012506907805800438,
0.034997500479221344,
0.018618913367390633,
-0.0032359191682189703,
0.05602770298719406,
-0.01099491585046053,
-0.08637949824333191,
-0.04278464615345001,
0.06962652504444122,
0.014580379240214825,
-0.04473889619112015,
-0.06310857087373734,
-0.01946355774998665,
0.025209175422787666,
0.07295099645853043,
-0.022902632132172585,
0.03833552822470665,
-0.026170626282691956,
0.02207307144999504,
-0.001721033244393766,
0.019004585221409798,
-0.018076561391353607,
-0.0013880729675292969,
-0.06541534513235092,
-0.031180428341031075,
-0.05195664241909981,
0.01524385903030634,
0.05220672860741615,
0.0016124508110806346,
-0.04344344511628151,
0.0139020886272192,
-0.05165596306324005,
0.0041817110031843185,
-0.020308751612901688,
-0.01696983352303505,
-0.0418672114610672,
0.016785472631454468,
0.0022522038780152798,
0.006701563019305468,
0.013943984173238277,
0.0465332493185997,
0.018848994746804237,
-0.03223852813243866,
0.02014826610684395,
0.015115153975784779,
-0.010284674353897572,
-0.02601904608309269,
-0.06717357039451599,
0.030349312350153923,
0.03424052149057388,
-0.0270718801766634,
-0.0004907727707177401,
-0.0343768373131752,
0.0361565537750721,
0.014418868348002434,
0.012371101416647434,
0.009848450310528278,
-0.009228873066604137,
-0.0012461126316338778,
-0.07418088614940643,
-0.03395330160856247,
-0.06924358755350113,
0.047510143369436264,
-0.015521740540862083,
0.012616898864507675,
-0.007798046804964542,
0.01460550632327795,
0.037162888795137405,
-0.04655654728412628,
0.015207318589091301,
-0.009251182898879051,
-0.013090960681438446,
0.004249737598001957,
-0.000028858114092145115,
0.01989114284515381,
0.040872517973184586,
0.0285827424377203,
-0.03897149860858917,
-0.0361853688955307,
-0.02964847721159458,
0.018865758553147316,
0.0028398558497428894,
0.007882896810770035,
-0.00031480216421186924,
0.009028827771544456,
-0.015016388148069382,
0.043502289801836014,
0.00239999545738101,
-0.001499307807534933,
0.05322146415710449,
-0.03876069188117981,
0.07644136995077133,
0.05400891974568367,
0.010677405633032322,
0.023419827222824097,
0.007263830862939358,
0.03553932160139084,
0.0059968940913677216,
0.024382123723626137,
-0.016602257266640663,
-0.010768003761768341,
-0.011292661540210247,
-0.03562219813466072,
-0.00618034228682518,
-0.036938101053237915,
0.026231789961457253,
0.01802106760442257,
0.015473520383238792,
0.017689162865281105,
0.017205219715833664,
0.0171559676527977,
-0.04400157183408737,
-0.004013742785900831,
0.01597064547240734,
0.019935734570026398,
0.03022654540836811,
0.001417249208316207,
0.01952981762588024,
0.04853091016411781,
-0.012318694032728672,
-0.00043130063568241894,
0.022511452436447144,
0.024494122713804245,
0.032947998493909836,
0.00541266705840826,
-0.02623828500509262,
0.02218889445066452,
-0.05725354701280594,
0.013822522014379501,
0.03287753835320473,
-0.008478255942463875,
0.0004929050337523222,
-0.06884855031967163,
-0.023816486820578575,
-0.0032506403513252735,
0.03238874301314354,
0.016033386811614037,
-0.013045795261859894,
0.02650093287229538,
-0.0594591349363327,
-0.011929675936698914,
0.010368765331804752,
0.010302547365427017,
-0.022627349942922592,
0.034889962524175644,
0.051383111625909805,
0.02872392162680626,
0.0163789801299572,
-0.037235941737890244,
-0.004600872285664082,
-0.005289104301482439,
-0.017092611640691757,
0.00036917487159371376,
-0.009095750749111176,
-0.04032089561223984,
-0.003951062448322773,
-0.007019940763711929,
-0.02726590260863304,
0.04046160355210304,
0.007571653928607702,
-0.025018224492669106,
0.017159149050712585,
-0.011565362103283405,
-0.027993740513920784,
-0.015858428552746773,
-0.04817568510770798,
0.008468995802104473,
0.004589350428432226,
-0.006649610120803118,
0.044554855674505234,
-0.008810611441731453,
-0.020181678235530853,
0.01634492725133896,
-0.04455101117491722,
-0.05867870897054672,
-0.01845289207994938,
-0.0243866927921772,
0.018848203122615814,
-0.056294601410627365,
-0.0013423871714621782,
0.04146793857216835,
-0.02826704829931259,
-0.01709458976984024,
-0.04961782693862915,
-0.087721087038517,
0.013664936646819115,
0.020126286894083023,
0.05648910254240036,
0.021505163982510567,
-0.03999333083629608,
0.0861511379480362,
-0.027115799486637115,
-0.06541862338781357,
-0.007621803320944309,
-0.019161058589816093,
-0.017528509721159935,
-0.016355253756046295,
0.025080587714910507,
0.013166799210011959,
-0.04825055971741676,
0.012910653837025166,
0.051506198942661285,
0.039788007736206055,
-0.0014964676229283214,
0.012745311483740807,
-0.017530323937535286,
-0.02786853164434433,
0.043042536824941635,
-0.014546588063240051,
0.046005867421627045,
0.01453566923737526,
0.014606011100113392,
-0.0003447022754698992,
-0.0531468391418457,
0.04201563820242882,
0.029125599190592766,
-0.023489365354180336,
0.04775494337081909,
0.005230505019426346,
0.0002744974917732179,
-0.04565567895770073,
0.033229321241378784,
-0.02982700616121292,
-0.02850246988236904,
0.014785142615437508,
-0.030980395153164864,
0.01832827739417553,
0.017992207780480385,
-0.03245720639824867,
0.03710867837071419,
0.05344398319721222,
-0.019677147269248962,
-0.0403144396841526,
0.015875032171607018,
-0.006948776077479124,
0.056728944182395935,
-0.036408957093954086,
-0.0013545386027544737,
0.04189606010913849,
0.04143822565674782,
0.03430525213479996,
-0.03135696053504944,
-0.06382013857364655,
-0.010481280274689198,
-0.07322912663221359,
-0.0007018070900812745,
-0.005595328286290169,
0.03614947944879532,
-0.004065736196935177,
0.05972564220428467,
0.019255641847848892,
0.02165820635855198,
0.009664682671427727,
0.019930925220251083,
-0.07680867612361908,
-0.007381231524050236,
-0.009415965527296066,
0.02888547256588936,
0.025228846818208694,
-0.02284078486263752,
-0.005051795858889818,
-0.0486423596739769,
-0.02930613048374653,
-0.000035313314583618194,
0.0146837392821908,
-0.04763249680399895,
-0.001455559628084302,
-0.05929872393608093,
-0.009814061224460602,
-0.009571322239935398,
0.04452598839998245,
0.012834093533456326,
0.005700412672013044,
0.022107331082224846,
0.048249952495098114,
0.005240474361926317,
-0.01462942361831665,
-0.025247249752283096,
-0.009910770691931248,
0.03275543451309204,
0.04892662167549133,
0.02241782285273075,
0.001299045281484723,
-0.021912381052970886,
0.024398809298872948,
-0.00012471305672079325,
0.028868263587355614,
-0.04463587701320648,
-0.029551248997449875,
-0.035933900624513626,
-0.0115115437656641,
-0.026038676500320435,
-0.04247753694653511,
0.031652458012104034,
0.002920785453170538,
0.0005533230723813176,
0.003638677531853318,
-0.01771845482289791,
0.049318768084049225,
0.06761176139116287,
0.06029077246785164,
0.008120871149003506,
0.03527110815048218,
-0.03715086355805397,
0.024154547601938248,
-0.0566553957760334,
0.009524097666144371,
0.06691887229681015,
0.043791595846414566,
-0.03184683248400688,
-0.03852413594722748,
-0.0026926370337605476,
0.028093229979276657,
-0.0020860496442764997,
0.03220516815781593,
0.014639024622738361,
0.0015014950186014175,
-0.04822476580739021,
-0.015454249456524849,
0.04449399560689926,
0.017247099429368973,
0.0018405724549666047,
0.026308096945285797,
-0.021339161321520805,
-0.065920390188694,
-0.009236498735845089,
0.019146520644426346,
0.022951582446694374,
-0.008315691724419594,
0.03283931687474251,
-0.03266849368810654,
-0.0030680964700877666,
0.020737793296575546,
-0.04472588747739792,
-0.008848301135003567,
-0.041544340550899506,
0.008606231771409512,
-0.013488741591572762,
-0.005662676878273487,
-0.013923822902143002,
-0.0076837302185595036,
0.004893306642770767,
0.008191358298063278,
-0.006448490545153618,
-0.025152185931801796,
-0.04205264896154404,
0.001035215798765421,
-0.014448117464780807,
0.008805861696600914,
0.01204183790832758,
-0.01307598501443863,
-0.0025263181887567043,
-0.0003731196338776499,
-0.04297875240445137,
-0.04002290591597557,
0.022008856758475304,
-0.019919347018003464,
0.019493013620376587,
0.024868372827768326,
-0.019398966804146767,
-0.03920484334230423,
0.03964407742023468,
0.0006220059585757554,
-0.05816817283630371,
0.025319665670394897,
-0.04060598835349083,
0.005726337432861328,
-0.013279466889798641,
-0.014839786104857922,
0.0049383994191884995,
0.024028686806559563,
0.007893708534538746,
-0.03434278443455696,
-0.03127272427082062,
0.01444520615041256,
-0.04752759635448456,
-0.0007014009752310812,
-0.038560397922992706,
-0.00640504527837038,
-0.03921402618288994,
0.0015279256040230393,
0.026367980986833572,
0.024112828075885773,
-0.018392348662018776,
-0.04093663766980171,
0.008199471049010754,
0.023288210853934288,
0.025159159675240517,
-0.006275382824242115,
-0.00849172193557024,
-0.004041187930852175,
0.00198684842325747,
-0.022394828498363495,
0.015987912192940712,
0.01694043166935444,
-0.00020150633645243943,
0.03194626793265343,
0.026194965466856956,
0.05609453469514847,
0.010110846720635891,
-0.026910342276096344,
0.008517852984368801,
-0.05530581995844841,
0.03897877410054207,
-0.022012121975421906,
0.0009249509894289076,
0.004323518835008144,
-0.043464142829179764,
-0.008718663826584816,
0.009676370769739151,
0.0035021151416003704,
0.021910538896918297,
-0.042445696890354156,
0.006125128827989101,
0.04361385107040405,
0.001140174688771367,
-0.04845880717039108,
-0.06799943000078201,
0.03329839929938316,
0.03924311697483063,
-0.0186513252556324,
-0.030362337827682495,
0.021213458850979805,
-0.0272202230989933,
0.013782264664769173,
0.0008258896414190531,
0.04206874594092369,
-0.01186827290803194,
0.002313293283805251,
0.036972884088754654,
-0.006218572147190571,
0.06902380287647247,
-0.013993325643241405,
-0.018935946747660637,
-0.015440384857356548,
-0.007299421355128288,
-0.023623645305633545,
0.005467299837619066,
0.06370595842599869,
-0.024727026000618935,
-0.028759349137544632,
0.007198932580649853,
-0.035924941301345825,
0.05828484892845154,
0.022032538428902626,
0.000039690978155704215,
-0.006424728315323591,
0.0226158294826746,
-0.022007927298545837,
-0.02436515875160694,
0.023163873702287674,
-0.032276708632707596,
0.012325135990977287,
0.0004385598876979202,
-0.0027140856254845858,
-0.030357403680682182,
-0.050862379372119904,
0.013152921572327614,
-0.02730962447822094,
0.03295736387372017,
-0.01535691600292921,
0.09759089350700378,
-0.008651170879602432,
-0.026661692187190056,
0.026883384212851524,
-0.03496608883142471,
0.008486498147249222,
0.02428397536277771,
-0.037143729627132416,
0.006249158643186092,
0.01782241277396679,
-0.021047458052635193,
-0.020567642524838448,
-0.033401306718587875,
0.030903693288564682,
0.04420958086848259,
0.008404604159295559,
0.07326900959014893,
0.027121270075440407,
-0.018472379073500633,
0.0030994866974651814,
0.011798076331615448,
-0.008993814699351788,
0.024629877880215645,
-0.0031018236186355352,
0.008460402488708496,
-0.051755186170339584,
0.024267148226499557,
0.028288481757044792,
0.029093611985445023,
-0.004627244081348181,
0.03037242963910103,
0.06993495672941208,
0.01566654071211815,
0.01702423207461834,
-0.037068672478199005,
-0.01650850661098957,
0.026968879625201225,
-0.028405215591192245,
0.03215688467025757,
0.0003194230957888067,
0.014940838329494,
0.014720969833433628,
0.01521753054112196,
0.005208921618759632,
-0.0935167744755745,
-0.0038263299502432346,
-0.05037729814648628,
-0.009154549799859524,
-0.025550207123160362,
0.021594323217868805,
0.0031119673512876034,
-0.009110617451369762,
0.02262074127793312,
0.012280845083296299,
0.051599595695734024,
-0.029450954869389534,
-0.05059707909822464,
-0.01603229157626629,
-0.01534478459507227,
-0.024373603984713554,
0.009599009528756142,
-0.021591056138277054,
-0.026509586721658707,
-0.004552431404590607,
-0.02850213646888733,
0.04511093720793724,
0.02641845867037773,
0.03176030516624451,
-0.010508611798286438,
0.02641589567065239,
0.017515074461698532,
0.026112953200936317,
-0.01280867401510477,
0.048603981733322144,
0.12291703373193741,
0.049810077995061874,
0.037080202251672745,
-0.019732527434825897,
-0.018594659864902496,
-0.015575433149933815,
0.0015098346630111337,
-0.038912903517484665,
0.028365621343255043,
-0.0032345950603485107,
0.03395933285355568,
0.010347840376198292,
0.03935406357049942,
-0.012197023257613182,
0.013850950635969639,
0.015183273702859879,
-0.04715598747134209,
-0.04805898666381836,
-0.02257666550576687,
0.005401099566370249,
-0.009587455540895462,
0.02669541910290718,
-0.023028777912259102,
0.041151098906993866,
-0.00744533771649003,
-0.011591530404984951,
-0.019156131893396378,
-0.03294071927666664,
0.030493054538965225,
-0.0019413939444348216,
-0.05407241731882095,
0.024492429569363594,
0.010271250270307064,
-0.008302336558699608,
-0.09806197881698608,
0.010450760833919048,
0.014520113356411457,
-0.003558466676622629,
-0.008491011336445808,
0.026486368849873543,
-0.0029578539542853832,
0.001422256464138627,
0.04347531124949455,
0.05928438901901245,
-0.061110902577638626,
-0.0059905387461185455,
-0.03444061800837517,
0.057742729783058167,
-0.042670395225286484,
-0.015596622601151466,
0.014923974871635437,
-0.033781569451093674,
-0.0115186283364892,
-0.0384938083589077,
-0.06644246727228165,
0.031948406249284744,
0.060281187295913696,
-0.0025208282750099897,
-0.020026475191116333,
-0.0008934532525017858,
0.008424757979810238,
0.010872090235352516,
0.03986122086644173,
-0.02481645718216896,
0.012318615801632404,
-0.02846365049481392,
0.018202420324087143,
0.029105015099048615,
-0.030124353244900703,
0.021128641441464424,
0.0005823359824717045,
-0.017909079790115356,
-0.010801276192069054,
0.022192513570189476,
-0.0041318610310554504,
0.03496488928794861,
0.028323989361524582,
0.0036977340932935476,
-0.0013450148981064558,
-0.007914039306342602,
-0.002592714736238122,
0.024926722049713135,
-0.027725648134946823,
-0.021120883524417877,
-0.047889355570077896,
-0.005915945861488581,
-0.0317600853741169,
0.04795696958899498,
-0.03170744702219963,
-0.013416893780231476,
0.02532348409295082,
0.04229194298386574,
0.010523989796638489,
-0.034704387187957764,
-0.05530622601509094,
0.0006635527242906392,
-0.04117753729224205,
0.027343077585101128,
0.02356906235218048,
0.03261180594563484,
0.020347189158201218,
0.014368360862135887,
-0.003963203635066748,
0.04045918956398964,
-0.025692015886306763,
0.0160763431340456,
-0.03284060209989548,
-0.029208369553089142,
-0.023351777344942093,
0.030600901693105698,
0.012207291088998318,
-0.031070902943611145,
-0.045518916100263596,
-0.029202526435256004,
0.00003648214624263346,
-0.02992757223546505,
0.0008593956590630114,
0.01938149891793728,
0.020098881796002388,
-0.027586229145526886,
0.02951868250966072,
-0.007708883844316006,
0.012155533768236637,
-0.07007978111505508,
-0.01903429813683033,
0.061006490141153336,
0.005202186293900013,
-0.02061178907752037,
0.028291283175349236,
-0.07431024312973022,
-0.0075981272384524345,
0.0031115710735321045,
-0.0018720186781138182,
-0.017385311424732208,
-0.04139019548892975,
0.043468035757541656,
-0.011868169531226158,
0.029069410637021065,
0.001574144815094769,
-0.034991227090358734,
0.01332715805619955,
-0.03212476149201393,
-0.07016892731189728,
-0.004112520255148411,
0.0173097662627697,
0.01841459982097149,
0.026553921401500702,
0.003292002249509096,
-0.0193545650690794,
0.09841938316822052,
-0.019470756873488426,
0.0169843677431345,
-0.017854617908596992,
-0.061875954270362854,
-0.021242080256342888,
0.004703105892986059,
-0.006695143412798643,
-0.0011203550966456532,
-0.022749613970518112,
0.017796222120523453,
0.04943915084004402,
0.034880075603723526,
-0.0002918977988883853,
0.03532329946756363,
-0.01300120074301958,
-0.026207251474261284,
0.008075766265392303,
0.004217215348035097,
-0.00338440528139472,
0.061480309814214706,
-0.04135400056838989,
-0.00041482865344733,
0.005924765020608902,
-0.00915796309709549,
-0.07381423562765121,
0.0033054936211556196,
0.02294519916176796,
-0.017513440921902657,
0.014513134025037289,
-0.033517949283123016,
-0.012264260090887547,
0.05642783269286156,
-0.024605456739664078,
-0.008894510567188263,
-0.07300173491239548,
-0.0038580724503844976,
-0.045373085886240005,
-0.0006750720203854144,
-0.0326107032597065,
0.05774076655507088,
0.010431937873363495,
0.03257686272263527,
-0.010693282820284367,
0.005770357791334391,
-0.003950847312808037,
0.016650736331939697,
-0.006646508816629648,
0.035829007625579834,
-0.029164565727114677,
-0.0040229675360023975,
0.04134942218661308,
-0.010047733783721924,
-0.014143154956400394,
0.031286854296922684,
-0.05324562266469002,
0.03280366212129593,
0.015735605731606483,
-0.020314112305641174,
-0.019487207755446434,
0.005920561496168375,
0.003735607722774148,
0.011499179527163506,
-0.012719865888357162,
0.03930247947573662,
0.015313750132918358,
0.001548181870020926,
0.005928431171923876,
0.022640423849225044,
0.040358804166316986,
-0.034121256321668625,
-0.038206811994314194,
0.02165326289832592,
-0.009308945387601852,
0.017535381019115448,
0.029028361663222313,
-0.020671967417001724,
-0.002209113910794258,
0.0015509125078096986,
-0.03784602880477905,
-0.05427693948149681,
0.017419081181287766,
0.006427309475839138,
0.004996289033442736,
-0.053878214210271835,
0.009086607955396175,
0.002969493856653571,
0.0043694088235497475,
0.014096933417022228,
0.0006494668778032064,
-0.030873579904437065,
-0.003882134333252907,
-0.049623340368270874,
-0.013887160457670689,
-0.0034080257173627615,
0.004997737240046263,
-0.046579424291849136,
-0.0202136542648077,
0.03173140436410904,
0.0413067452609539,
0.010814604349434376,
0.013090093620121479,
-0.022531406953930855,
-0.020022215321660042,
-0.08082472532987595,
0.015624431893229485,
-0.02417362853884697,
-0.010756496340036392,
-0.04757522791624069,
0.038069188594818115,
0.035437241196632385,
0.04089036211371422,
0.03710313141345978,
0.013428041711449623,
0.016711285337805748,
0.006726521532982588,
0.012302489019930363,
0.0034673656336963177,
-0.018774019554257393,
-0.02101844549179077,
0.014069530181586742,
-0.07262267917394638,
0.0351436473429203,
0.038008976727724075,
-0.005778742954134941,
0.00631065433844924,
0.0304113682359457,
-0.033667393028736115,
0.011421993374824524,
-0.02856520749628544,
-0.019670069217681885,
-0.002432128880172968,
-0.0022473682183772326,
-0.016548743471503258,
0.10536981374025345,
0.007708223070949316,
-0.006463297642767429,
-0.008548385463654995,
-0.030906373634934425,
-0.03658709302544594,
0.04215102642774582,
0.0018579828320071101,
0.015862468630075455,
-0.012617954052984715,
-0.006767886225134134,
0.032730452716350555,
-0.03453293442726135,
0.004512651823461056,
0.02231680415570736,
-0.04021615535020828,
-0.009525954723358154,
0.05182933062314987,
0.03938055410981178,
0.012186931446194649,
-0.02246364764869213,
0.021867217496037483,
0.025042233988642693,
-0.005011254921555519,
0.01842465065419674,
0.07101605087518692,
0.04914301261305809,
0.00038310731179080904,
-0.012322920374572277,
0.018692268058657646,
0.01565803773701191,
0.020340602844953537,
0.004981681238859892,
0.01862877979874611,
-0.007033044472336769,
-0.021862437948584557,
0.0033649473916739225,
0.013156899251043797,
-0.0019558430649340153,
0.0014238550793379545,
0.005051111336797476,
0.05886601284146309,
-0.018906287848949432,
-0.024315020069479942,
-0.02210172452032566,
0.006055106874555349,
-0.021569833159446716,
0.03897611051797867,
0.026230212301015854,
-0.003332881024107337,
0.015352140180766582,
-0.025585919618606567,
-0.011168229393661022,
-0.03041280061006546,
0.011401046067476273,
0.024432485923171043,
-0.0055943080224096775,
-0.04328424483537674,
-0.0159686841070652,
0.014005273580551147,
-0.01490398682653904,
0.009928494691848755,
0.027166318148374557,
0.05990304425358772,
0.00819105003029108,
-0.0008309438708238304,
0.008545961230993271,
-0.009350251406431198,
0.011570326052606106,
0.11925506591796875,
-0.016362693160772324,
-0.03664468973875046,
-0.027666715905070305,
0.0201900452375412,
0.01868019998073578,
-0.026977961882948875
] |
<p>I'm trying to imagine in my head what happens to the universe in ten billion years, twenty billion years, etc. </p>
<p>I imagine that all mass in the universe turns to black holes, as when mass reaches the temperature of absolute zero, it automatically collapses the atoms, or is that true?</p>
<p>If all of the mass in the universe is black holes, it would still be in galaxies of black holes that used to have stars in them, around a central black hole, but some of those galaxies would have merged with each other, like how our nearest galaxy is moving towards us. </p>
<p>Over time, with all the mass in the universe existing as black holes, and all energy having gravity including dark energy, then the dark energy that fell into the black holes would be captured, and the black holes would get larger and larger. </p>
<p>If dark energy is not a constant, which seems unlikely to me, and if it changes over time, and it's density decreases, and it has no pushing effect on black holes, because they suck it in, then eventually all the energy and mass would be contained within the black holes. </p>
<p>I'm trying to understand why anyone thinks that black holes can evaporate when energy has gravity, based on the stress energy tensor of general relativity, and the escape velocity of a black hole is higher than the speed of light. </p>
<p>If a photon could pop out, wouldn't it be sucked straight back in again? There are two theories really, one says the universe will collapse, causing another big bang, and explaining why the big bang happened in the first place. </p>
<p>The other says that the universe keeps expanding until the black holes evaporate into photons which fly around forever, never causing a universe again, but this fails to explain why it ever happened in the first place. </p> | 2,886 | [
-0.03361906856298447,
-0.044255759567022324,
0.027429630979895592,
-0.057313498109579086,
0.024670463055372238,
-0.0064284419640898705,
-0.02187379263341427,
-0.031675152480602264,
-0.019377751275897026,
-0.05898943915963173,
0.009293217211961746,
0.02382693625986576,
0.031943704932928085,
-0.016848372295498848,
-0.003730005817487836,
0.013988958671689034,
-0.009550143964588642,
-0.03604408726096153,
-0.02183043397963047,
-0.02911161258816719,
0.021755410358309746,
0.030447784811258316,
-0.02464616298675537,
0.011706486344337463,
-0.04217226430773735,
0.010197162628173828,
0.007078257855027914,
0.016562029719352722,
0.038088295608758926,
0.06039957329630852,
-0.005291492212563753,
-0.023823555558919907,
-0.018570799380540848,
0.04384307935833931,
-0.003925159107893705,
0.00006939430022612214,
-0.02874923124909401,
-0.05631745234131813,
-0.029305435717105865,
-0.018262561410665512,
-0.05934673547744751,
-0.025875600054860115,
-0.024125143885612488,
0.038489293307065964,
-0.04509850963950157,
-0.00981998536735773,
0.006746068596839905,
0.007682503201067448,
0.04758104681968689,
-0.023484639823436737,
0.05755874887108803,
-0.008525563403964043,
0.047923099249601364,
0.04122704267501831,
-0.014736991375684738,
-0.02066756971180439,
0.07796469330787659,
0.0635664314031601,
-0.046335287392139435,
-0.02791876159608364,
-0.004641169682145119,
0.04180528223514557,
-0.021684395149350166,
0.013104843907058239,
-0.0018276280025020242,
0.04538420960307121,
-0.01464145164936781,
0.003485840279608965,
0.017040593549609184,
-0.010666804388165474,
0.02869267947971821,
0.007390912156552076,
0.013166720047593117,
0.025520870462059975,
0.0016933795996010303,
-0.04952634871006012,
0.02302134409546852,
0.007473708130419254,
0.056076932698488235,
0.07584194093942642,
-0.029631027951836586,
0.005419004242867231,
0.04686823859810829,
0.028522193431854248,
0.015486094169318676,
0.03155510500073433,
0.0783463642001152,
-0.013676084578037262,
0.009808138944208622,
0.04484078288078308,
0.014467752538621426,
0.009350624866783619,
0.022736914455890656,
-0.011460482142865658,
-0.030462510883808136,
0.02784748561680317,
0.0002037753292825073,
0.06299518793821335,
0.006815476808696985,
-0.008859636262059212,
0.019218193367123604,
0.028937410563230515,
0.004258186090737581,
0.05503150820732117,
0.017312852665781975,
-0.04099857807159424,
-0.09719181805849075,
0.02467437833547592,
-0.05345866456627846,
-0.020654762163758278,
-0.05726425722241402,
-0.008577673695981503,
-0.027163049206137657,
-0.03730585053563118,
0.026111392304301262,
-0.03614532947540283,
0.025498516857624054,
-0.0465044341981411,
0.08277370035648346,
0.07441073656082153,
0.0011156831169500947,
-0.014842581003904343,
0.027757367119193077,
-0.025512827560305595,
-0.04675554111599922,
-0.01845717430114746,
0.06687813252210617,
-0.026515349745750427,
-0.05329497158527374,
0.04267343878746033,
-0.006922897882759571,
-0.011605835519731045,
0.017222823575139046,
-0.018695548176765442,
0.05965747684240341,
-0.03462424501776695,
-0.09813611209392548,
-0.07472756505012512,
0.04103332757949829,
-0.00524409394711256,
0.007976874709129333,
-0.042551781982183456,
0.010547706857323647,
0.028137972578406334,
0.09060654789209366,
0.0007104967371560633,
-0.0335252620279789,
-0.01020115613937378,
0.02478048950433731,
-0.008386812172830105,
-0.011861401610076427,
-0.014375785365700722,
-0.009919564239680767,
-0.01210470125079155,
-0.008571384474635124,
-0.09448541700839996,
0.0048388405703008175,
0.04563123732805252,
0.016121281310915947,
-0.044609434902668,
0.05608709529042244,
-0.006778611335903406,
0.027582408860325813,
-0.00837582629173994,
-0.023996999487280846,
-0.03430192917585373,
0.08379612863063812,
0.046661071479320526,
-0.012970475479960442,
0.04069465398788452,
0.017740780487656593,
0.011028279550373554,
0.006017281208187342,
0.009325746446847916,
-0.023807495832443237,
-0.0518476739525795,
0.009904487058520317,
-0.026458492502570152,
0.005994222592562437,
0.027745097875595093,
-0.03773536905646324,
-0.01850602962076664,
-0.01610751636326313,
-0.049823734909296036,
0.03318968415260315,
0.0029212902300059795,
-0.004632578231394291,
-0.02376052737236023,
-0.028733214363455772,
-0.024613890796899796,
0.008104496635496616,
-0.08565837889909744,
0.013087982311844826,
0.026574427261948586,
0.02561800181865692,
-0.009573052637279034,
0.022206511348485947,
0.03945568576455116,
-0.03200571611523628,
0.0009948256192728877,
-0.010316325351595879,
0.03716618940234184,
-0.012722378596663475,
0.005377497058361769,
-0.009311259724199772,
0.04092947021126747,
0.05499829724431038,
-0.013698820024728775,
0.011691197752952576,
0.011680110357701778,
-0.010582104325294495,
0.003985836170613766,
0.012223062105476856,
0.02561347372829914,
-0.043551281094551086,
0.0036416330840438604,
0.04032480716705322,
-0.0063691106624901295,
0.03644537180662155,
0.012496371753513813,
-0.02701876312494278,
0.08391182124614716,
0.036002036184072495,
0.01725509576499462,
-0.019712800160050392,
0.052452076226472855,
-0.01978267915546894,
0.005932600703090429,
-0.038569193333387375,
-0.015505904331803322,
-0.06217329949140549,
0.008515710942447186,
0.01078782044351101,
0.02922034077346325,
-0.01117162499576807,
0.05409316346049309,
0.04071185365319252,
0.04522287845611572,
0.004332562908530235,
0.013034665957093239,
-0.022768322378396988,
-0.02510634809732437,
0.006856170948594809,
-0.014025825075805187,
0.027111617848277092,
0.030859433114528656,
0.055989429354667664,
-0.0003699568042065948,
-0.0049245222471654415,
-0.02047451213002205,
0.027022160589694977,
0.02837376855313778,
0.04723742604255676,
0.023611033335328102,
-0.003585879923775792,
-0.048635631799697876,
0.02319159172475338,
-0.01687750779092312,
0.01758621819317341,
0.002221653936430812,
0.010674390941858292,
-0.005361534189432859,
-0.07275969535112381,
-0.0001299540454056114,
-0.01561546977609396,
0.0222527626901865,
0.014703731052577496,
-0.02349056489765644,
0.025468891486525536,
-0.018530087545514107,
0.036388497799634933,
-0.016422953456640244,
-0.005051716230809689,
-0.05955255776643753,
-0.01695202849805355,
0.0036114768590778112,
0.006516997702419758,
0.0352185033261776,
-0.025722436606884003,
-0.04922502860426903,
0.014587105251848698,
-0.018776215612888336,
0.020380252972245216,
0.019393572583794594,
-0.04061776399612427,
0.03353063762187958,
0.0013007597299292684,
-0.0353628545999527,
0.0626348927617073,
0.0019146724371239543,
0.051170021295547485,
0.024193838238716125,
-0.007016964256763458,
-0.042261186987161636,
-0.005907406099140644,
-0.003984472248703241,
-0.007800809107720852,
-0.013010159134864807,
0.0037967762909829617,
0.0876498594880104,
-0.019858377054333687,
-0.05616852268576622,
0.022424772381782532,
-0.024004748091101646,
-0.040256891399621964,
-0.015586848370730877,
0.01675548031926155,
0.0027360355015844107,
-0.0317993089556694,
0.02258804813027382,
0.0024815008509904146,
-0.05390307307243347,
0.00037028672522865236,
-0.058097995817661285,
-0.0366939939558506,
0.008914795704185963,
-0.005301544442772865,
0.02546834573149681,
-0.00006879193097120151,
-0.011971483938395977,
0.06514084339141846,
0.04413222521543503,
-0.0006542342598550022,
-0.005587977822870016,
0.00432736799120903,
0.008049573749303818,
-0.0118436673656106,
0.005017001647502184,
-0.010835872031748295,
-0.011865854263305664,
-0.018028803169727325,
0.028603561222553253,
0.04645301401615143,
0.0027246891986578703,
-0.012253888882696629,
-0.022871550172567368,
0.009329495951533318,
0.0002586258633527905,
0.017811983823776245,
0.027784761041402817,
-0.0089512774720788,
-0.01644855923950672,
0.016518309712409973,
-0.005711543373763561,
0.046346310526132584,
-0.004958659410476685,
-0.06925054639577866,
0.05522659420967102,
0.006192456465214491,
-0.019888948649168015,
-0.061792127788066864,
0.013576934114098549,
-0.005626283120363951,
-0.051498547196388245,
0.009342868812382221,
-0.014910814352333546,
0.08844863623380661,
0.012995880097150803,
-0.005309144034981728,
-0.04243246465921402,
0.05433043837547302,
-0.038053859025239944,
-0.009006527252495289,
-0.004298846237361431,
-0.018921412527561188,
0.009427445940673351,
-0.023224035277962685,
0.018555572256445885,
0.060311563313007355,
0.014392102137207985,
0.048247288912534714,
-0.00599878653883934,
-0.00787933636456728,
0.005853280425071716,
-0.060735803097486496,
0.009316371753811836,
0.007447286043316126,
0.05068720877170563,
0.024618040770292282,
0.02239314652979374,
0.043435391038656235,
0.007401726674288511,
0.021184556186199188,
-0.00872049666941166,
-0.08633498847484589,
0.013033229857683182,
-0.04101301357150078,
0.001974772894755006,
-0.010465249419212341,
0.004409198649227619,
-0.01867077127099037,
0.004608610179275274,
-0.001992051489651203,
-0.00022866965446155518,
-0.01396939903497696,
-0.07745780050754547,
-0.013941656798124313,
-0.0573873296380043,
-0.034061554819345474,
0.020754564553499222,
0.02487262152135372,
0.04607018455862999,
0.004780096933245659,
0.018228892236948013,
0.021420918405056,
-0.007197539787739515,
-0.014289687387645245,
0.0037054235581308603,
-0.0024172684643417597,
0.028828836977481842,
0.010555071756243706,
0.033666953444480896,
-0.0028080062475055456,
-0.013333914801478386,
-0.000890146940946579,
0.07188241928815842,
0.0034044086933135986,
-0.010038956999778748,
0.006740833632647991,
-0.02014828845858574,
-0.034743648022413254,
-0.017820503562688828,
0.01029527373611927,
0.03711111098527908,
0.0178210511803627,
0.005870419554412365,
-0.00014487301814369857,
0.008961278945207596,
-0.007768962066620588,
0.03834572806954384,
0.04791794717311859,
-0.035132892429828644,
-0.00876752007752657,
-0.027806729078292847,
-0.012399178929626942,
0.008167632855474949,
0.006337473634630442,
0.011874892748892307,
0.0038352152332663536,
-0.06439224630594254,
0.0027788723818957806,
0.011438633315265179,
0.03191453590989113,
-0.03895175829529762,
-0.006058033090084791,
0.0123986741527915,
0.0255920197814703,
-0.014787084423005581,
0.012549894861876965,
0.02860974706709385,
0.03235306218266487,
0.06793878227472305,
-0.0008503415156155825,
0.00015729248116258532,
-0.05087050050497055,
-0.012790725566446781,
0.022592179477214813,
0.04065852239727974,
0.02621864341199398,
-0.00848799291998148,
-0.08908987045288086,
-0.05069948360323906,
0.004318114835768938,
-0.05423324555158615,
0.03369561955332756,
0.004018267150968313,
0.002246883697807789,
0.018587248399853706,
-0.030696438625454903,
0.018584372475743294,
0.008736364543437958,
-0.06012865528464317,
0.01966526359319687,
-0.0010285188909620047,
0.03269852325320244,
-0.007579074706882238,
0.022383790463209152,
0.00779081042855978,
0.05065745487809181,
-0.019538747146725655,
-0.0076143755577504635,
0.015883855521678925,
-0.01841253601014614,
-0.02209795080125332,
-0.08731015771627426,
-0.005755937192589045,
-0.005895344540476799,
-0.054568156599998474,
0.039970725774765015,
-0.027828296646475792,
-0.03503454476594925,
-0.002455846406519413,
0.014989694580435753,
-0.01838204264640808,
-0.001937180757522583,
-0.05600036308169365,
-0.011488573625683784,
0.015598244965076447,
-0.007423753850162029,
0.030999353155493736,
0.00969591736793518,
-0.010016519576311111,
0.046556469053030014,
-0.04748484119772911,
0.035103585571050644,
-0.05198167636990547,
0.02565871551632881,
-0.03623136878013611,
-0.011746321804821491,
-0.025914564728736877,
0.07035405188798904,
-0.015574745833873749,
-0.010962890461087227,
0.015923799946904182,
-0.034924183040857315,
0.026899350807070732,
0.008311263285577297,
0.020522259175777435,
0.0190923772752285,
-0.006974801886826754,
0.0023167147301137447,
-0.02150007151067257,
-0.02282324992120266,
0.03184228017926216,
0.038590069860219955,
-0.028566012158989906,
0.027868472039699554,
-0.00981350801885128,
0.03263162821531296,
0.007851004600524902,
-0.013053886592388153,
0.04332611337304115,
-0.016627423465251923,
0.04256179928779602,
0.005575313698500395,
0.014764273539185524,
0.046505045145750046,
-0.0391426682472229,
-0.028736338019371033,
-0.019391914829611778,
0.001346598844975233,
0.02135978266596794,
-0.05478351190686226,
0.017695089802145958,
0.02495257370173931,
0.030410101637244225,
-0.09233167767524719,
-0.03387826308608055,
0.05805625393986702,
0.020136002451181412,
-0.0007422813214361668,
-0.021926313638687134,
0.03944454342126846,
-0.054725393652915955,
-0.022803183645009995,
-0.024362510070204735,
0.008094741962850094,
-0.016782447695732117,
0.014657367952167988,
0.011203749105334282,
0.004520880524069071,
0.014442658051848412,
0.0033147698268294334,
-0.004509384743869305,
-0.005571021232753992,
0.019499903544783592,
-0.017965255305171013,
0.00034421030431985855,
0.07014692574739456,
-0.02898784726858139,
-0.02241748571395874,
-0.024586040526628494,
-0.025410467758774757,
0.01799842342734337,
-0.03256164863705635,
-0.0011403495445847511,
0.03340655565261841,
0.03231959789991379,
0.00752578629180789,
0.001181754400022328,
0.03803371265530586,
-0.02684045024216175,
0.02817225269973278,
-0.010393353179097176,
-0.011544148437678814,
0.022186486050486565,
-0.04925559088587761,
0.04463936388492584,
0.006336224265396595,
0.013320481404662132,
0.015611481852829456,
0.04010363295674324,
0.025334425270557404,
-0.03785278648138046,
-0.0013276367681100965,
-0.06218854710459709,
0.045184411108493805,
0.009781640954315662,
-0.0065446579828858376,
0.02887623943388462,
-0.022179823368787766,
-0.02142833173274994,
-0.025088490918278694,
-0.024820340797305107,
0.026752695441246033,
0.05978831648826599,
-0.0015572800766676664,
0.021157214418053627,
8.356902867490135e-7,
-0.01329497154802084,
-0.012262212112545967,
-0.06293656677007675,
0.012745769694447517,
0.03470249101519585,
0.008180039934813976,
-0.006859046407043934,
-0.0016587519785389304,
-0.022802235558629036,
0.030809663236141205,
0.045443180948495865,
-0.015937304124236107,
0.045228276401758194,
0.025407323613762856,
0.01738591305911541,
0.01871168240904808,
-0.008998746983706951,
-0.0376744382083416,
0.01281523797661066,
-0.04112628474831581,
0.035993412137031555,
0.010191108100116253,
0.000879844359587878,
0.0072464048862457275,
0.015402762219309807,
0.025115355849266052,
-0.016854943707585335,
-0.056275367736816406,
-0.05974720045924187,
0.01508383173495531,
-0.002763845957815647,
0.03293485566973686,
0.007342514116317034,
0.03668069839477539,
-0.0030396245419979095,
0.005094150546938181,
-0.01310085877776146,
-0.0028121343348175287,
-0.04801899567246437,
-0.040526386350393295,
-0.043807268142700195,
-0.05091625079512596,
0.04114661365747452,
0.0077434410341084,
-0.011069371365010738,
-0.011006442829966545,
-0.02960098534822464,
-0.017817789688706398,
-0.012167501263320446,
0.03928359970450401,
-0.004744500853121281,
0.05490903928875923,
0.019387559965252876,
0.001897492096759379,
-0.040480904281139374,
0.025248946622014046,
0.11182673275470734,
0.04890871420502663,
0.016525011509656906,
-0.05175688862800598,
-0.007750676479190588,
-0.02000364474952221,
0.018298545852303505,
-0.025230810046195984,
0.024260371923446655,
-0.042809173464775085,
0.015596107579767704,
0.021762780845165253,
0.036591850221157074,
-0.021424898877739906,
-0.03986199200153351,
0.04319816082715988,
-0.01659582369029522,
-0.009599780663847923,
0.007342013064771891,
0.026357518509030342,
-0.011044391430914402,
0.006538174115121365,
-0.0295504629611969,
0.01119959820061922,
-0.025148170068860054,
-0.005521783605217934,
-0.045496415346860886,
-0.018920978531241417,
-0.00874004140496254,
-0.027366291731595993,
-0.0450773611664772,
-0.002704058075323701,
-0.006592976860702038,
-0.06213581562042236,
-0.004459863994270563,
0.025944430381059647,
0.053941622376441956,
-0.02074262499809265,
0.0008846326963976026,
0.02732803300023079,
0.013099483214318752,
0.020728446543216705,
0.022460490465164185,
-0.010884454473853111,
-0.02656201831996441,
-0.016464505344629288,
-0.0056302170269191265,
0.05091134086251259,
-0.03198402747511864,
0.011194322258234024,
0.010216920636594296,
0.011796897277235985,
0.012808771803975105,
-0.035713080316782,
0.008647876791656017,
0.0009828641777858138,
-0.0005540016572922468,
0.0237483661621809,
-0.03375685587525368,
-0.018632570281624794,
0.009675517678260803,
0.02413066290318966,
0.05673130601644516,
-0.020555751398205757,
0.01377788744866848,
0.017588283866643906,
-0.045358531177043915,
0.039815954864025116,
-0.04595132917165756,
0.01477617397904396,
-0.02739529311656952,
-0.0020951025653630495,
-0.05080564320087433,
-0.01671021059155464,
0.026333361864089966,
0.04059179127216339,
-0.0053024920634925365,
0.017578428611159325,
0.028220709413290024,
-0.022406497970223427,
-0.027016660198569298,
0.03433925658464432,
-0.03872532397508621,
-0.04848195239901543,
-0.013119203969836235,
0.025958852842450142,
-0.011196578852832317,
0.04777628555893898,
-0.01798386499285698,
-0.01632179133594036,
-0.009776725433766842,
-0.0018689194694161415,
0.03473960608243942,
-0.022461693733930588,
-0.004819978028535843,
-0.014705373905599117,
-0.01969246193766594,
-0.02104308269917965,
-0.024498797953128815,
0.015075571835041046,
0.024430233985185623,
-0.008367151021957397,
0.03212941065430641,
0.01729317009449005,
0.0008707339875400066,
0.00405864417552948,
0.014176714234054089,
-0.02285071462392807,
0.006378868594765663,
0.01224495843052864,
0.030208315700292587,
-0.015914179384708405,
-0.03297604247927666,
-0.01901523768901825,
-0.023510487750172615,
-0.034136779606342316,
0.04086308926343918,
-0.03273855149745941,
0.03623928129673004,
-0.004566797520965338,
0.03249252587556839,
-0.05615072697401047,
0.003590913722291589,
-0.04513850808143616,
-0.008708607405424118,
0.015066984109580517,
-0.037131622433662415,
0.0013160081580281258,
0.016108237206935883,
-0.03644265606999397,
-0.04003320261836052,
0.01706656627357006,
0.016538508236408234,
-0.052444905042648315,
-0.01671634428203106,
0.02471873164176941,
-0.025798752903938293,
0.060888588428497314,
0.0030365935526788235,
-0.006301955319941044,
0.025019848719239235,
-0.039901670068502426,
-0.02816123329102993,
0.03412872180342674,
-0.0034946671221405268,
0.03654707223176956,
0.02164372056722641,
-0.008742417208850384,
-0.028968652710318565,
0.05606982856988907,
-0.013585702516138554,
-0.03966142237186432,
0.005022742785513401,
-0.037408702075481415,
-0.018308104947209358,
0.023580746725201607,
0.039994243532419205,
-0.007745192386209965,
-0.01770470105111599,
0.027074912562966347,
0.013190655037760735,
-0.004702274221926928,
-0.014817290008068085,
0.0007509897695854306,
-0.02855333685874939,
-0.005860479082912207,
-0.02672319859266281,
0.012569168582558632,
0.007437687832862139,
0.06498121470212936,
-0.03535007685422897,
0.06270413100719452,
0.04685655236244202,
-0.017369166016578674,
-0.11652202904224396,
-0.006094447337090969,
0.018615690991282463,
0.028467973694205284,
0.021782897412776947,
-0.01522514596581459,
0.008270823396742344,
0.0063820406794548035,
-0.053347039967775345,
0.05092403292655945,
-0.02516726776957512,
0.0077019548043608665,
-0.008243558928370476,
0.027655771002173424,
-0.011192971840500832,
0.0488707460463047,
0.06746786087751389,
0.07547341287136078,
-0.018333155661821365,
-0.005391562357544899,
-0.01491666492074728,
-0.031655535101890564,
-0.012486371211707592,
0.010092107579112053,
-0.022192249074578285,
0.017838556319475174,
0.07633121311664581,
-0.017215581610798836,
0.005059781949967146,
0.0468386672437191,
0.00940240453928709,
0.0205095075070858,
0.002474172506481409,
-0.01907631754875183,
0.013105496764183044,
0.016453085467219353,
0.015173629857599735,
-0.00024827755987644196,
0.005141956266015768,
0.03812643885612488,
0.017358576878905296,
0.0047013661824166775,
0.0011608744971454144,
0.02083793468773365,
0.007553176488727331,
-0.04775211960077286,
-0.006748414132744074,
0.028885945677757263,
0.012605803087353706,
0.013202188536524773,
-0.0018394511425867677,
0.03099449910223484,
-0.01313865277916193,
0.0023976045195013285,
-0.02719157002866268,
-0.04580123722553253,
-0.033432576805353165,
0.04322265088558197,
0.028017735108733177,
0.011878867633640766,
0.03580137714743614,
0.025378204882144928,
-0.0006239468930289149,
0.014958145096898079,
-0.006685076281428337,
0.00550821702927351,
-0.018739333376288414,
-0.02962752990424633,
-0.002945911604911089,
-0.013055036775767803,
0.0358344241976738,
-0.04323664307594299,
-0.0365806445479393,
0.05467605218291283,
0.0017938731471076608,
0.0299104992300272,
0.02923068031668663,
-0.050427522510290146,
-0.03422528877854347,
-0.05757109448313713,
-0.004197350237518549,
-0.01886121556162834,
0.029577551409602165,
-0.055602796375751495,
-0.06335737556219101,
0.005049648694694042,
-0.02666795626282692,
0.03746394068002701,
-0.03282966464757919,
-0.013844745233654976,
0.008799631148576736,
-0.017126135528087616,
0.030353542417287827,
-0.04340120777487755,
0.0028710155747830868,
0.01188978273421526,
-0.020564468577504158,
-0.015428845770657063,
0.0010393100092187524,
-0.007275271229445934,
0.006219861097633839,
0.04719660431146622,
-0.028449416160583496,
0.0518212616443634,
0.008847715333104134,
-0.01924116723239422,
0.02877884730696678,
0.026309434324502945,
0.01140371523797512,
0.03197457641363144,
-0.008866973221302032,
0.026520639657974243,
0.04862242192029953,
-0.02104826644062996,
-0.02683284319937229,
0.011341812089085579,
-0.01462292205542326,
0.00013945803220849484,
-0.011298486962914467,
-0.024598952382802963,
0.04457320272922516,
-0.03001111000776291,
-0.012268591672182083,
0.04158007353544235,
-0.02147771418094635,
-0.009160116314888,
0.05586856231093407,
-0.015230975113809109,
0.03361882269382477,
-0.02074863575398922,
0.014732680283486843,
0.0019950983114540577,
0.011846744455397129,
-0.020438237115740776,
0.017407359555363655,
0.010682014748454094,
-0.014178352430462837,
0.032455917447805405,
0.006261873058974743,
0.016106637194752693,
0.009347976185381413,
-0.026772258803248405,
0.07402756065130234,
-0.0805278941988945,
-0.023581065237522125,
0.023324856534600258,
0.003805534215644002,
0.013088499195873737,
0.012768576852977276,
-0.005826681386679411,
0.06146988645195961,
0.0038370254915207624,
0.0348600335419178,
0.024346718564629555,
-0.014154575765132904,
-0.025200366973876953,
0.03890378773212433,
-0.03172238543629646,
0.060618914663791656,
0.02704954892396927,
-0.0034491654951125383,
-0.02817806601524353,
0.03316045179963112,
0.04111049324274063,
-0.015320520848035812,
-0.01564742811024189,
-0.013877949677407742,
-0.059484366327524185,
-0.0035002974327653646,
0.0021330632735043764,
-0.026542410254478455,
-0.049595173448324203,
0.03119005262851715,
0.0038602135609835386,
0.007868768647313118,
0.013950209133327007,
0.015096595510840416,
-0.013675257563591003,
0.028092242777347565,
-0.02528950572013855,
0.002595778787508607,
-0.031505241990089417,
0.025928854942321777,
-0.01377878151834011,
-0.038836002349853516
] |
<p>If a detector is kept at the two slits the fringes disappear. But, when the detectors are removes do the fringes come up immediately without any significant time lag? </p>
<p>Can there be a way to switch on and off the detector so fast that it all happens within the time required for the light to reach the screen form the source? What would be the result if it is possible? </p> | 2,887 | [
-0.007397766225039959,
-0.03219226747751236,
0.01423152070492506,
-0.029763584956526756,
0.033602356910705566,
-0.002126529347151518,
-0.061655208468437195,
-0.037038348615169525,
-0.018346434459090233,
0.02030991017818451,
0.019621778279542923,
0.02788408473134041,
0.046475764364004135,
0.03859412670135498,
-0.0047309077344834805,
0.012377962470054626,
0.02422982268035412,
-0.02239147014915943,
-0.04746493324637413,
-0.05920368432998657,
-0.045797426253557205,
0.03482060506939888,
0.004944144748151302,
-0.013379943557083607,
-0.0551520511507988,
0.010970564559102058,
-0.0020772013813257217,
0.015124148689210415,
0.013475514948368073,
0.05914187431335449,
-0.0335957370698452,
-0.014286225661635399,
-0.0055129132233560085,
0.010868261568248272,
0.003196210600435734,
-0.02712111920118332,
-0.02053525671362877,
-0.06095011904835701,
-0.0017491267062723637,
0.007413266226649284,
-0.010975179262459278,
0.05950314551591873,
-0.009697985835373402,
0.04835237190127373,
0.004174485802650452,
-0.015143800526857376,
0.016191018745303154,
-0.003688960336148739,
0.022471588104963303,
-0.06820899993181229,
0.010216422379016876,
-0.02233472838997841,
0.028072739019989967,
0.0118856905028224,
-0.01854514703154564,
-0.0059653338976204395,
0.09799567610025406,
0.07767662405967712,
0.001400754670612514,
-0.0379459485411644,
0.013332531787455082,
0.005142589565366507,
-0.0063071902841329575,
-0.02595573477447033,
-0.03979519382119179,
-0.02187836915254593,
0.001616144785657525,
-0.016295185312628746,
0.006000125780701637,
-0.015957919880747795,
-0.0070409150794148445,
0.0000036795020150748314,
0.026773616671562195,
0.02247534692287445,
0.002084732986986637,
-0.018479758873581886,
0.007743257097899914,
0.023045368492603302,
0.018387364223599434,
0.06858936697244644,
0.012229346670210361,
0.024512235075235367,
0.0613049641251564,
0.023646602407097816,
0.011838831938803196,
-0.03744087740778923,
0.09039739519357681,
-0.016110755503177643,
0.001188703696243465,
0.008346429094672203,
-0.041553959250450134,
0.029106494039297104,
0.023056456819176674,
0.02080291323363781,
-0.0188898928463459,
0.007216158322989941,
-0.018813617527484894,
0.07889574766159058,
0.026860175654292107,
-0.04408334568142891,
-0.002683813450857997,
0.031005805358290672,
0.012002574279904366,
0.05247275531291962,
-0.0031197487842291594,
0.009554609656333923,
-0.03622495010495186,
0.029432471841573715,
-0.019020916894078255,
0.004974947776645422,
-0.03363234922289848,
-0.014277690090239048,
-0.009662512689828873,
0.046930596232414246,
0.012594419531524181,
-0.021828634664416313,
-0.025879578664898872,
-0.025386149063706398,
0.0647580549120903,
0.04339267686009407,
0.023572813719511032,
-0.024576500058174133,
-0.01738046109676361,
-0.0020000638905912638,
-0.07258778810501099,
0.025421639904379845,
0.03239889815449715,
-0.013054450042545795,
-0.004697623662650585,
0.039489515125751495,
-0.0028858238365501165,
-0.011582320556044579,
0.04650168493390083,
-0.03202489763498306,
0.029332807287573814,
0.05578929930925369,
-0.08152744919061661,
-0.07803575694561005,
0.04494829475879669,
-0.020490434020757675,
-0.014216922223567963,
-0.07032270729541779,
0.004102857783436775,
0.04092485457658768,
0.08488117903470993,
-0.028952620923519135,
-0.011900892481207848,
-0.026114773005247116,
0.005328887142241001,
-0.055167268961668015,
-0.027348030358552933,
-0.0063591934740543365,
0.021111972630023956,
-0.014468522742390633,
-0.02740301750600338,
-0.04935280606150627,
0.02698797546327114,
0.05836758017539978,
-0.027488676831126213,
-0.04466491565108299,
0.02895708568394184,
0.025049960240721703,
-0.030463332310318947,
0.02974068373441696,
-0.0031521832570433617,
-0.049545157700777054,
0.07400975376367569,
0.018111111596226692,
-0.022597137838602066,
0.020790960639715195,
-0.004409576766192913,
0.06504231691360474,
-0.025136135518550873,
-0.0018452767981216311,
0.0005183002795092762,
-0.0047921305522322655,
-0.028901107609272003,
0.03779659792780876,
-0.0009295550407841802,
0.020221618935465813,
-0.004887692630290985,
-0.01078492496162653,
-0.01860647089779377,
0.03475566953420639,
0.013742857612669468,
0.03920493647456169,
-0.016349224373698235,
-0.004654361866414547,
-0.03873762860894203,
-0.059853799641132355,
-0.0019434911664575338,
-0.06021419167518616,
0.003999505657702684,
0.03386381268501282,
0.0001650365156820044,
0.000710849417373538,
0.0015446621691808105,
-0.00855395756661892,
0.01427649985998869,
-0.045298121869564056,
-0.05030002444982529,
0.005661103408783674,
0.0014385358663275838,
-0.017844967544078827,
0.010996145196259022,
0.06831571459770203,
0.045885708183050156,
-0.0137990927323699,
0.012474884279072285,
-0.014870623126626015,
-0.006901897024363279,
0.017949284985661507,
-0.027578631415963173,
0.04595325142145157,
-0.027611834928393364,
0.0073621501214802265,
-0.007869504392147064,
0.03400196135044098,
-0.007073972839862108,
-0.012670702300965786,
-0.01768447645008564,
0.054781775921583176,
0.052587833255529404,
-0.01201185304671526,
-0.0042292228899896145,
0.020725231617689133,
0.005030212923884392,
0.026341671124100685,
0.03511121869087219,
-0.04608801379799843,
-0.06437841057777405,
-0.01585332117974758,
-0.0015933921094983816,
0.006969134323298931,
-0.00982348620891571,
0.052503857761621475,
0.01248305942863226,
0.002699389820918441,
0.02243884839117527,
0.00044370812247507274,
0.005884006153792143,
-0.01609068363904953,
-0.021062461659312248,
0.0019215613137930632,
-0.019108781591057777,
-0.005688800010830164,
0.009882702492177486,
0.004355199635028839,
0.022955534979701042,
0.0016042570350691676,
0.020635973662137985,
0.0037999190390110016,
0.008077938109636307,
0.013390859588980675,
-0.011359904892742634,
-0.02309790626168251,
0.013912567868828773,
0.023845255374908447,
0.02252987213432789,
0.021985923871397972,
0.030379557982087135,
0.0067264363169670105,
-0.03382138907909393,
-0.03691849485039711,
0.025990460067987442,
0.008846702054142952,
-0.004129687789827585,
-0.014449349604547024,
0.04929971322417259,
-0.01748993806540966,
0.02839926816523075,
-0.02967762015759945,
0.030133768916130066,
-0.030984388664364815,
0.011405122466385365,
0.02739248424768448,
0.027345115318894386,
0.05857881158590317,
-0.0577399842441082,
-0.064756378531456,
-0.0065652369521558285,
-0.047264281660318375,
0.03787264600396156,
0.020268594846129417,
-0.03035428188741207,
-0.019537346437573433,
-0.013758032582700253,
-0.04152370244264603,
0.04380146786570549,
-0.049717653542757034,
-0.0067322938703000546,
-0.005691293627023697,
0.003141924738883972,
-0.06557764858007431,
0.013044659979641438,
-0.0020628597121685743,
0.008089789189398289,
-0.0182693712413311,
0.0003280957171227783,
0.005689567886292934,
-0.0142476512119174,
-0.02176257222890854,
0.03594961762428284,
-0.029218807816505432,
0.003275438444688916,
-0.0025521067436784506,
0.0016130720032379031,
0.022310663014650345,
-0.0149518558755517,
-0.030280116945505142,
0.015921829268336296,
-0.04031869024038315,
0.046403657644987106,
-0.03642726689577103,
-0.04141795262694359,
0.028427815064787865,
0.004772906191647053,
0.05600278079509735,
-0.05159907042980194,
-0.0004684770538005978,
0.061777226626873016,
0.019498392939567566,
0.002643108833581209,
-0.003607046091929078,
-0.023355497047305107,
-0.014884491451084614,
-0.02966214530169964,
0.001252951449714601,
0.01773437112569809,
0.0009851763024926186,
0.044096142053604126,
-0.007167232688516378,
0.02264590933918953,
0.08040609955787659,
0.04714597389101982,
0.00875236839056015,
-0.005773243959993124,
-0.006344035733491182,
-0.00776721490547061,
0.036699891090393066,
0.03257795795798302,
-0.03665072098374367,
-0.013600229285657406,
-0.024195579811930656,
0.009780400432646275,
0.023268481716513634,
-0.03583887964487076,
0.04370708391070366,
0.003690662793815136,
0.01137053407728672,
0.0023043493274599314,
0.0399753712117672,
0.003631870960816741,
-0.011267619207501411,
-0.028436360880732536,
0.029224229976534843,
0.05624447017908096,
0.030674051493406296,
-0.004371866583824158,
0.01984858326613903,
0.007003989536315203,
0.02520652301609516,
-0.04434491693973541,
-0.0036265060771256685,
-0.04899357259273529,
0.04674990847706795,
-0.05345200002193451,
-0.024412179365754128,
0.051778394728899,
0.024429339915513992,
0.023641517385840416,
0.0014476249925792217,
-0.009186655282974243,
-0.02748247981071472,
-0.06341369450092316,
-0.012928804382681847,
-0.004421554040163755,
0.04140230640769005,
0.030674925073981285,
0.039634525775909424,
0.050665829330682755,
0.04928036406636238,
0.014606381766498089,
-0.006471093278378248,
-0.06217844411730766,
0.009886962361633778,
-0.016164463013410568,
-0.030962109565734863,
-0.03977353870868683,
0.013652786612510681,
-0.012714558281004429,
-0.03308240696787834,
-0.0027411554474383593,
-0.045098695904016495,
0.0223566722124815,
-0.0629764199256897,
0.02223239094018936,
-0.008236839435994625,
-0.01502913422882557,
-0.06438756734132767,
0.0496157631278038,
0.022415632382035255,
-0.010343646630644798,
0.03709273785352707,
0.006569735240191221,
-0.042165499180555344,
0.006729647517204285,
0.019761063158512115,
-0.028802843764424324,
-0.013192372396588326,
0.04370422288775444,
0.051993828266859055,
0.04152965173125267,
-0.035935916006565094,
0.020612813532352448,
0.0327521488070488,
0.08155722171068192,
0.00574989290907979,
-0.024149490520358086,
-0.020548976957798004,
0.0017931964248418808,
-0.03220613673329353,
0.004048788920044899,
0.10172157734632492,
-0.006345718167722225,
-0.05213477462530136,
-0.03174620121717453,
0.00557606341317296,
-0.030223431065678596,
0.02230474352836609,
0.04839544743299484,
0.02020109072327614,
-0.00935450755059719,
-0.04626377299427986,
-0.011296866461634636,
-0.024570494890213013,
-0.016364408656954765,
-0.018390245735645294,
0.0242658331990242,
-0.007425006944686174,
0.03378460928797722,
0.016514256596565247,
0.016626344993710518,
-0.008369680494070053,
-0.00239023519679904,
-0.02534623257815838,
-0.001002813340164721,
0.02581103704869747,
0.03766447678208351,
0.03765709325671196,
0.053453944623470306,
0.007664916105568409,
0.022015102207660675,
-0.0023054920602589846,
-0.07816660404205322,
-0.0035294268745929003,
0.027569912374019623,
0.03523500636219978,
-0.01468127965927124,
-0.013428306207060814,
-0.05930725857615471,
-0.0345582440495491,
0.056322578340768814,
-0.01614334248006344,
0.05406935513019562,
-0.02130892500281334,
-0.03892570361495018,
-0.03746543452143669,
-0.017512578517198563,
-0.02924273908138275,
0.00915397796779871,
-0.011983360163867474,
0.02399420738220215,
-0.01932366192340851,
-0.013873537071049213,
0.0077476357109844685,
0.008108100853860378,
0.018964825198054314,
0.05475518852472305,
0.023551136255264282,
0.030553266406059265,
-0.020009329542517662,
-0.01712191291153431,
-0.0440334752202034,
-0.05124221369624138,
0.03629331663250923,
0.00827416218817234,
0.002252911916002631,
0.06171400099992752,
-0.015885045751929283,
-0.043921131640672684,
0.009980854578316212,
0.008637205697596073,
0.014835934154689312,
0.01973794959485531,
-0.03907553106546402,
0.016550585627555847,
0.05198052152991295,
-0.010791621170938015,
0.04446301981806755,
0.03745291009545326,
-0.009185017086565495,
0.024025024846196175,
0.008146866224706173,
0.0339931957423687,
-0.036393702030181885,
0.04542740806937218,
0.0016832845285534859,
-0.004265305120497942,
-0.05518582463264465,
0.048537589609622955,
-0.01642811857163906,
0.028658781200647354,
0.01069729682058096,
-0.026549560949206352,
0.004289088770747185,
0.032512348145246506,
0.0032168193720281124,
0.011128352954983711,
-0.029400089755654335,
0.014522287994623184,
-0.002272620564326644,
-0.018504032865166664,
0.007506792899221182,
0.0062705776654183865,
0.05055951327085495,
0.029099658131599426,
0.028481431305408478,
0.022251155227422714,
-0.07591221481561661,
0.010643288493156433,
-0.02400062046945095,
-0.03839898109436035,
0.03862260282039642,
0.019839249551296234,
0.015561898238956928,
0.015916211530566216,
-0.023634744808077812,
-0.031037000939249992,
0.014372995123267174,
-0.031016718596220016,
0.03323780745267868,
-0.06624229997396469,
0.0525130070745945,
0.0002691859262995422,
0.001926958211697638,
-0.07141465693712234,
-0.025221457704901695,
0.017254354432225227,
0.03323068469762802,
-0.005295365583151579,
-0.014630344696342945,
0.01603170856833458,
-0.028247522190213203,
-0.019245939329266548,
-0.016624171286821365,
-0.003120800945907831,
0.007692508399486542,
0.0068513513542711735,
0.027329597622156143,
0.012704913504421711,
0.07720590382814407,
-0.0015621798811480403,
0.013630978763103485,
0.004907503258436918,
-0.019977323710918427,
-0.06716585904359818,
-0.004663196392357349,
0.02794523537158966,
-0.007497984450310469,
-0.04550285264849663,
-0.027278151363134384,
-0.006208349484950304,
0.03722350299358368,
-0.007205135188996792,
-0.012877377681434155,
0.019738657400012016,
0.022617721930146217,
-0.014788387343287468,
-0.006864398717880249,
0.009429622441530228,
0.001593196764588356,
-0.004564127419143915,
0.03986738994717598,
0.009452678263187408,
-0.030132299289107323,
-0.056585170328617096,
0.011005599051713943,
0.008293560706079006,
0.00010945525718852878,
-0.003454678226262331,
0.029781524091959,
-0.024718765169382095,
0.014830775558948517,
0.041724156588315964,
-0.020195534452795982,
0.012035306543111801,
-0.0388411208987236,
0.0017030925955623388,
0.00798034481704235,
-0.015394874848425388,
-0.014067684300243855,
-0.01782221719622612,
0.00365206110291183,
-0.03635500743985176,
0.03930050507187843,
-0.0023000508081167936,
0.04418705031275749,
-0.01960010454058647,
-0.0318363755941391,
-0.04537500813603401,
-0.01903504878282547,
0.009035525843501091,
-0.00935712642967701,
0.015214862301945686,
0.015388334169983864,
-0.016823504120111465,
0.020036527886986732,
0.005694035906344652,
0.04071579873561859,
0.015383877791464329,
-0.004847984295338392,
0.0025735122617334127,
0.01497047208249569,
0.03518865257501602,
-0.02334202453494072,
-0.01773791015148163,
0.006910907570272684,
-0.05070752650499344,
0.022855021059513092,
-0.016812985762953758,
-0.0025515123270452023,
0.02164720930159092,
-0.004432205110788345,
0.01649513840675354,
-0.04366548731923103,
0.0035762861371040344,
-0.06332335621118546,
0.009244627319276333,
-0.011499488726258278,
0.014036145992577076,
0.00022033450659364462,
-0.011539176106452942,
0.048677414655685425,
-0.004395897500216961,
0.03438976779580116,
-0.038539402186870575,
-0.061897121369838715,
-0.056971170008182526,
-0.05058765038847923,
-0.015323787927627563,
0.06288079917430878,
-0.05328984186053276,
-0.024908283725380898,
0.02372695878148079,
-0.015540216118097305,
0.02246803790330887,
0.01348467543721199,
0.07011456787586212,
-0.05550311505794525,
0.05649653077125549,
-0.0016345051117241383,
0.03212512657046318,
-0.014922804199159145,
0.017206843942403793,
0.12260045856237411,
0.032175783067941666,
0.00921966414898634,
-0.05485742166638374,
-0.007749930489808321,
-0.012495853938162327,
0.02222231775522232,
-0.01516617089509964,
0.02177472598850727,
-0.006081621628254652,
0.011999240145087242,
0.018705954775214195,
0.032499730587005615,
-0.0014523270074278116,
0.017085209488868713,
0.024361958727240562,
-0.02570565603673458,
-0.01562805473804474,
-0.003251839429140091,
0.025385349988937378,
0.012590577825903893,
0.02128126285970211,
-0.03963937610387802,
0.031038129702210426,
-0.04349658638238907,
-0.02950400486588478,
-0.006165842059999704,
-0.04185687005519867,
0.009811804629862309,
-0.029959935694932938,
-0.06060833856463432,
-0.00018660709611140192,
0.03901088982820511,
-0.019998369738459587,
-0.03921142965555191,
-0.002700028708204627,
-0.018010839819908142,
-0.025490455329418182,
0.04156520962715149,
0.07777153700590134,
0.02696843259036541,
-0.026226839050650597,
-0.007344708777964115,
0.017856314778327942,
-0.04667820408940315,
-0.033212658017873764,
0.015352881513535976,
0.03244921565055847,
-0.026820257306098938,
-0.02794613502919674,
-0.006064626853913069,
-0.01807708665728569,
0.03136799857020378,
-0.04915045574307442,
-0.030291270464658737,
-0.0024082039017230272,
-0.034429315477609634,
-0.0021209055557847023,
0.008093276992440224,
-0.016130123287439346,
0.023463372141122818,
0.0034298959653824568,
-0.025468599051237106,
-0.016099588945508003,
0.022527987137436867,
-0.016007738187909126,
0.009691034443676472,
0.05251253396272659,
0.0025310416240245104,
-0.028094667941331863,
-0.04569809138774872,
0.0010890080593526363,
0.006456680595874786,
0.061654284596443176,
-0.004489768762141466,
0.02189754508435726,
0.0046233185566961765,
-0.020830174908041954,
-0.018195684999227524,
-0.03491230309009552,
-0.07904507964849472,
0.02156737819314003,
-0.06280603259801865,
0.007092249114066362,
-0.03727403283119202,
0.003940675873309374,
0.06064038723707199,
0.03882594406604767,
-0.024365350604057312,
-0.013013656251132488,
-0.020213527604937553,
0.06568404287099838,
0.04563888907432556,
-0.026433687657117844,
-0.014216454699635506,
-0.009713908657431602,
0.003621106967329979,
0.015585814602673054,
-0.03495260700583458,
0.053011853247880936,
0.004962804727256298,
0.014170465990900993,
0.030672403052449226,
-0.005558249074965715,
-0.02156776189804077,
0.006781336851418018,
-0.005544913001358509,
-0.02491016313433647,
0.0017274690326303244,
-0.013375558890402317,
0.04211082309484482,
-0.023927031084895134,
-0.024641232565045357,
-0.020752741023898125,
-0.012696899473667145,
0.010238350369036198,
0.02763812430202961,
0.0156719870865345,
0.02523798681795597,
-0.0044057974591851234,
0.022041955962777138,
-0.03250580281019211,
0.01893300749361515,
-0.006282379850745201,
-0.00024553859839215875,
-0.000880550651345402,
-0.004745500162243843,
0.0026747884694486856,
0.06003237143158913,
0.009066267870366573,
-0.060155414044857025,
-0.004731269553303719,
0.010299080982804298,
-0.008327930234372616,
0.023011596873402596,
0.01980978436768055,
0.025420237332582474,
0.012891036458313465,
0.022344496101140976,
-0.0006210147403180599,
0.010574093088507652,
-0.04480041190981865,
-0.04127293825149536,
0.050559151917696,
0.006757904775440693,
0.014729122631251812,
0.03866200149059296,
-0.00440793763846159,
0.025946766138076782,
0.03939640149474144,
0.024040956050157547,
-0.04391436651349068,
0.024928683415055275,
-0.021263232454657555,
0.007769761141389608,
-0.009754402562975883,
-0.00488657271489501,
-0.026776570826768875,
-0.030706681311130524,
0.05343850702047348,
-0.013305412605404854,
0.01972966268658638,
0.036788709461688995,
-0.018925704061985016,
-0.009125934913754463,
-0.008809366263449192,
-0.013161100447177887,
-0.01022371742874384,
0.005545687861740589,
0.040710464119911194,
-0.004414568189531565,
0.007355334237217903,
-0.020670171827077866,
-0.03598282113671303,
-0.11059477180242538,
-0.005276505369693041,
0.007778266444802284,
0.022536693140864372,
0.04314788803458214,
-0.01986854523420334,
0.026934191584587097,
0.06619910150766373,
-0.08986867964267731,
0.037745118141174316,
-0.00844487827271223,
-0.020689548924565315,
-0.07362410426139832,
-0.001968666212633252,
-0.0033524492755532265,
0.013454700820147991,
0.03061138279736042,
0.038697656244039536,
0.022046543657779694,
0.041944440454244614,
-0.032703157514333725,
-0.02399946190416813,
0.0008075617370195687,
-0.008603248745203018,
-0.0016675455262884498,
-0.024808304384350777,
0.06705056130886078,
-0.03630789741873741,
0.02968815341591835,
0.03089989349246025,
-0.03143605589866638,
0.008576779626309872,
-0.019976934418082237,
-0.010599935427308083,
0.01506032794713974,
-0.011467298492789268,
0.00024389391182921827,
0.02406463213264942,
0.01160877663642168,
0.051996782422065735,
0.00197925278916955,
-0.010018144734203815,
-0.012940431945025921,
-0.0158853679895401,
0.016636066138744354,
-0.049293484538793564,
-0.012781181372702122,
0.004434546921402216,
0.03313670679926872,
-0.03258133679628372,
0.055332135409116745,
0.03136604279279709,
0.002221115864813328,
-0.0026921131648123264,
-0.02112785167992115,
-0.05707281082868576,
-0.023723090067505836,
-0.006070663221180439,
0.01401411835104227,
-0.0394887812435627,
-0.008733068592846394,
-0.06431138515472412,
-0.043874770402908325,
0.025371523573994637,
-0.0015453433152288198,
-0.010293329134583473,
-0.02966955490410328,
0.002784500829875469,
-0.0008224078919738531,
-0.012093406170606613,
0.03912545368075371,
-0.001324754091911018,
-0.009909207932651043,
0.02202051505446434,
-0.0385298915207386,
0.03339920938014984,
0.008925380185246468,
-0.022057918831706047,
-0.03411669656634331,
-0.05942673981189728,
0.030899643898010254,
0.024267947301268578,
-0.00042905815644189715,
-0.04348142072558403,
-0.007934868335723877,
-0.04189692437648773,
0.03293681889772415,
0.05576047673821449,
0.0019886402878910303,
-0.0036004085559397936,
0.03035149537026882,
-0.030578887090086937,
0.04463888704776764,
-0.032794807106256485,
0.0137476222589612,
0.012676602229475975,
-0.015313718467950821,
-0.018516089767217636,
-0.018281398341059685,
-0.0106924744322896,
0.022981297224760056,
0.00937211886048317,
0.03328903019428253,
0.00847095437347889,
-0.002569757169112563,
-0.02980796806514263,
0.04688509181141853,
-0.04944070801138878,
0.04133052006363869,
0.05169156566262245,
-0.028138643130660057,
0.030617134645581245,
0.00403152359649539,
-0.01694614067673683,
-0.04453674331307411,
-0.0016715772217139602,
-0.052774351090192795,
-0.027751829475164413,
-0.039168380200862885,
-0.034991029649972916,
-0.023982755839824677,
-0.06141402944922447,
-0.011419887654483318,
-0.00710624735802412,
-0.03393367677927017,
0.008107172325253487,
0.06130001321434975,
-0.01803094521164894,
0.04313208907842636,
-0.01940464973449707,
0.028326930478215218,
0.011752735823392868,
0.033433884382247925,
0.012993423268198967,
0.07191038131713867,
0.018490677699446678,
-0.007759520784020424,
0.051067035645246506,
0.014721374958753586,
0.03030211851000786,
0.0035262377932667732,
-0.02328536845743656,
0.05044788867235184,
-0.00391053780913353,
-0.030101079493761063,
0.007213381119072437,
-0.012282928451895714,
-0.016674090176820755,
0.052682697772979736,
-0.018458236008882523,
0.0702149048447609,
-0.019057463854551315,
0.03992336988449097,
-0.0008958023390732706,
-0.007218590937554836,
-0.02748437412083149,
0.03690226003527641,
0.052902691066265106,
-0.00011578728299355134,
-0.008037948049604893,
-0.000776738568674773,
-0.00826901476830244,
0.03489496186375618,
0.02628064900636673,
-0.05511624366044998,
0.03394025191664696,
-0.016192512586712837,
-0.020649129524827003,
0.036584820598363876,
-0.01121142040938139,
-0.022615911439061165,
-0.04091617465019226,
0.0012563051423057914,
0.007788552436977625,
-0.026797279715538025,
-0.013829226605594158,
0.017946548759937286,
0.0024957789573818445,
0.07152027636766434,
-0.038584984838962555,
0.02185315452516079,
-0.0070210727863013744,
0.017914874479174614,
-0.023226505145430565,
-0.003611993743106723
] |
<p>This question seems to have been asked a few times in different configurations, but none of them answer my variation. I've struggled to understand this for nearly 15 years and had conflicting answers from my school physics teachers and more recently friends who are physicists.</p>
<p>So a round leaves my gun barrel at $40$ m/s. Its initial Airspeed is $40$ m/s.</p>
<p>In another question they asked about firing down the length of a train traveling the same speed. I understand that firing toward the front of the train would result in a ground speed of $80$ m/s and an airspeed of $40$ m/s. Also, firing toward the back of the train results in a ground speed of $0$ m/s and an airspeed of $40$ m/s.</p>
<p>My question... if you were to walk to the back of the train, open the door and fire directly out the back, would you end up with a ground <strong>and</strong> airspeed of $0$ m/s? Meaning the projectile would literally just tumble in a straight trajectory down to the ground?</p>
<p>Plenty of people have thrown spanners into this one over the years - like talking about the way an explosive force will 'hang' in a certain space if not pushed, pushing the projectile away from itself as well as the firing pin of the gun, giving it extra forward momentum in that instance. (unlike firing from the front of the train would always equal $80$ m/s for air and ground. The explosion cannot be 'left behind'). I personally don't buy this one... But i don't know enough to judge.</p> | 2,888 | [
-0.029273435473442078,
-0.03562265262007713,
-0.001400961889885366,
0.018377605825662613,
0.011892625130712986,
-0.010413043200969696,
-0.007528065703809261,
-0.016899464651942253,
0.020697804167866707,
0.011697554960846901,
0.0038297732826322317,
0.07718866318464279,
0.06684237718582153,
0.017944127321243286,
0.0014797437470406294,
0.004718402866274118,
0.0011204404290765524,
-0.01040629856288433,
0.015282504260540009,
-0.026514878496527672,
-0.014684093184769154,
-0.03235837444663048,
-0.006328865885734558,
-0.03557143732905388,
-0.03211619332432747,
0.013580322265625,
0.02583039551973343,
-0.00043595032184384763,
0.022674590349197388,
0.0003033420362044126,
-0.0014357486506924033,
-0.01629844680428505,
0.01849067397415638,
0.021031437441706657,
0.028084957972168922,
-0.0029466268606483936,
-0.040330320596694946,
-0.03284424915909767,
-0.03110109269618988,
0.011385723017156124,
-0.02278655208647251,
-0.010434859432280064,
0.018057191744446754,
0.04054268077015877,
-0.02313236892223358,
0.06017656251788139,
-0.04770868644118309,
0.009205019101500511,
0.07946145534515381,
-0.062499869614839554,
0.05184140428900719,
0.004297215025871992,
-0.002118720207363367,
0.06063448265194893,
0.012709910050034523,
-0.010067221708595753,
0.07328922301530838,
0.057466063648462296,
0.008685676380991936,
-0.03387901186943054,
-0.00606931047514081,
0.006877752020955086,
-0.04036908596754074,
0.007925363257527351,
0.015207188203930855,
0.025741642341017723,
0.01461180578917265,
-0.03638985753059387,
0.028197873383760452,
-0.035326603800058365,
-0.014690719544887543,
-0.00471434136852622,
0.050634678453207016,
0.006387266796082258,
0.03391553834080696,
-0.02242271602153778,
0.07034575194120407,
0.058391865342855453,
0.036647941917181015,
0.02899067848920822,
-0.02382897399365902,
-0.01041730772703886,
0.039399050176143646,
0.055764421820640564,
0.017803490161895752,
-0.03728197142481804,
0.09141597151756287,
-0.0010000282200053334,
0.01266571320593357,
0.02979685366153717,
0.01618736982345581,
-0.009678049013018608,
0.034400574862957,
0.0022503200452774763,
-0.007191898766905069,
0.02079007402062416,
0.03497260808944702,
0.06811158359050751,
0.03991366922855377,
0.003819856094196439,
-0.012875515967607498,
-0.01927916333079338,
0.017602313309907913,
0.07297762483358383,
-0.0030425204895436764,
-0.008453970775008202,
0.011089751496911049,
0.022988546639680862,
-0.002773676300421357,
-0.011367049999535084,
-0.08918604254722595,
0.03069242276251316,
-0.016846120357513428,
-0.011297437362372875,
0.013599944300949574,
-0.025891108438372612,
0.013329628854990005,
-0.0021374893840402365,
0.021619703620672226,
0.01662726141512394,
0.05357848107814789,
-0.0012187953107059002,
0.01546372752636671,
-0.0141698457300663,
-0.05135626345872879,
-0.029285572469234467,
0.04035351797938347,
-0.026935363188385963,
0.0006082926993258297,
0.0002643807965796441,
0.014206038787961006,
-0.015697544440627098,
0.007105580996721983,
0.011229868978261948,
0.0032725101336836815,
-0.00930149294435978,
-0.11478986591100693,
-0.07831573486328125,
0.028517378494143486,
0.01343456655740738,
0.0004993195761926472,
-0.11558358371257782,
-0.02921062335371971,
0.006240427028387785,
0.04982606694102287,
-0.0287410169839859,
0.02695493772625923,
0.010815027169883251,
0.02952015958726406,
-0.004974760580807924,
-0.005326966289430857,
-0.0034702990669757128,
-0.03979302942752838,
-0.020518289878964424,
0.00669539300724864,
-0.05596868693828583,
0.03785813972353935,
0.03771505877375603,
0.0034170616418123245,
-0.039687953889369965,
0.032381538301706314,
-0.030817676335573196,
-0.00725090317428112,
-0.02162611484527588,
0.02665518783032894,
-0.017225190997123718,
0.0658421590924263,
0.04346229135990143,
-0.06296521425247192,
0.009212976321578026,
0.0403396338224411,
0.015120510011911392,
-0.005875256843864918,
-0.0419904924929142,
0.02344822883605957,
-0.06601431965827942,
-0.03299402445554733,
-0.0415511317551136,
-0.009617472998797894,
-0.0009545796201564372,
-0.029956122860312462,
-0.027393681928515434,
-0.031334299594163895,
-0.00677862111479044,
0.011270350776612759,
-0.0017273295670747757,
0.05070752650499344,
0.023487983271479607,
0.00306513044051826,
-0.023981118574738503,
-0.040419891476631165,
-0.09385106712579727,
0.08711834996938705,
-0.0069330716505646706,
-0.012737979181110859,
-0.0005115862586535513,
-0.0232014749199152,
0.018408339470624924,
-0.05231375992298126,
-0.0020293653942644596,
0.01577693037688732,
0.043601129204034805,
-0.008234224282205105,
-0.025395585224032402,
-0.020760266110301018,
0.060071397572755814,
0.031674910336732864,
0.021137336269021034,
0.007797590456902981,
0.002211173065006733,
-0.023299148306250572,
-0.01792682707309723,
-0.011363016441464424,
0.001894996385090053,
0.02554694563150406,
-0.021930068731307983,
0.016509991139173508,
-0.012193530797958374,
0.020477954298257828,
0.027113046497106552,
-0.0314355231821537,
0.08997473865747452,
0.07323849201202393,
-0.02295299805700779,
0.0014762569917365909,
0.09003083407878876,
0.024423707276582718,
0.012813136912882328,
0.022098060697317123,
-0.0370158776640892,
-0.04457373544573784,
-0.04796348139643669,
-0.009787960909307003,
-0.034103695303201675,
-0.013995921239256859,
0.04206836596131325,
0.02901606261730194,
-0.015698600560426712,
0.006804503500461578,
0.034376539289951324,
-0.023595992475748062,
-0.03738165274262428,
0.016601037234067917,
0.010331813246011734,
-0.003717332147061825,
-0.0072071366012096405,
0.003818446071818471,
-0.005185635760426521,
-0.03311048075556755,
0.006372681353241205,
-0.002639824990183115,
0.007577489595860243,
0.029215628281235695,
0.006669900380074978,
-0.01793621852993965,
-0.03319383040070534,
0.06261972337961197,
-0.01522347703576088,
0.025980932638049126,
0.01369040459394455,
0.026027163490653038,
-0.0016657195519655943,
-0.044722773134708405,
0.02246209792792797,
-0.025919834151864052,
-0.009860116057097912,
0.00011000952508766204,
-0.004953854717314243,
0.024497143924236298,
-0.05161593109369278,
0.006209910847246647,
-0.016504403203725815,
-0.00889719370752573,
0.008508188650012016,
-0.004721277859061956,
0.05214415490627289,
0.04807523638010025,
0.004721363540738821,
-0.012642632238566875,
-0.03107479214668274,
0.000742030912078917,
-0.01209994126111269,
-0.011944740079343319,
0.005633681081235409,
-0.05385855957865715,
0.05736464262008667,
-0.06298591196537018,
-0.00717118987813592,
0.028178667649626732,
0.013943850994110107,
0.02838364988565445,
0.05634387582540512,
-0.006773196626454592,
-0.057734616100788116,
-0.019578251987695694,
-0.03559134528040886,
-0.011236351914703846,
-0.033669326454401016,
-0.010097525082528591,
0.06372877210378647,
0.006551467813551426,
-0.013554966077208519,
0.04846285283565521,
-0.019355637952685356,
-0.02160686068236828,
-0.022173184901475906,
0.011969616636633873,
0.014386792667210102,
0.014769531786441803,
-0.020073862746357918,
0.01878691464662552,
-0.01199990976601839,
-0.006476449314504862,
-0.05511655658483505,
-0.029269544407725334,
-0.0007850375259295106,
0.02137008309364319,
0.04296613484621048,
0.004594923462718725,
0.010348683223128319,
0.07886774092912674,
0.03381841629743576,
-0.006427006796002388,
-0.016205595806241035,
-0.012065747752785683,
0.030359499156475067,
-0.016196276992559433,
-0.02479056641459465,
0.04491334408521652,
0.0158538818359375,
0.022455519065260887,
-0.004156885202974081,
0.047728314995765686,
0.024198628962039948,
-0.0007984578260220587,
0.003526062471792102,
-0.03899557888507843,
0.009831503033638,
0.013935893774032593,
0.001113189267925918,
0.037460971623659134,
0.014733932912349701,
0.0253858994692564,
-0.04033719003200531,
0.041297152638435364,
0.018390880897641182,
-0.03215868026018143,
0.06309983879327774,
0.01160155888646841,
-0.0386354997754097,
-0.04111956059932709,
0.06255000084638596,
-0.02434368245303631,
-0.023391522467136383,
-0.012359916232526302,
0.022162288427352905,
0.035395361483097076,
-0.01932091824710369,
0.03475372865796089,
0.014807958155870438,
0.06401131302118301,
-0.03709106519818306,
-0.06622084230184555,
-0.019900308921933174,
0.0037778469268232584,
0.018046623095870018,
0.025636501610279083,
0.0177416130900383,
0.011875920929014683,
0.03393034264445305,
0.0249681044369936,
-0.005857888143509626,
-0.0312095545232296,
0.014404384419322014,
-0.06619451195001602,
0.028757639229297638,
-0.03489840775728226,
0.021189335733652115,
-0.020017370581626892,
0.05895287171006203,
0.0007854119758121669,
0.024791523814201355,
0.016688259318470955,
0.021081622689962387,
-0.061784252524375916,
0.03124777413904667,
-0.02159440889954567,
-0.042204197496175766,
-0.031540416181087494,
0.0041830530390143394,
-0.0073653412982821465,
0.008205439895391464,
-0.028653619810938835,
-0.008430852554738522,
-0.03543904051184654,
-0.046350546181201935,
0.024240389466285706,
-0.05360693857073784,
-0.036416396498680115,
0.005024794954806566,
0.05436599627137184,
0.031781286001205444,
-0.007921773940324783,
0.02067318931221962,
0.03147031366825104,
-0.011792739853262901,
-0.01646704599261284,
-0.023458583280444145,
0.019502362236380577,
0.0026557559613138437,
0.046562470495700836,
0.008270671591162682,
-0.0027548540383577347,
-0.016670333221554756,
0.006982358638197184,
0.030557353049516678,
0.03955748677253723,
-0.006857434753328562,
0.019565420225262642,
-0.04364784061908722,
-0.02775507979094982,
0.013895359821617603,
-0.009554300457239151,
0.029292099177837372,
-0.013911326415836811,
0.017862891778349876,
0.013943999074399471,
0.025328895077109337,
0.044197697192430496,
0.04700445383787155,
0.026852691546082497,
0.02489154227077961,
0.014767219312489033,
-0.028904328122735023,
0.027562016621232033,
-0.017317647114396095,
-0.03241701424121857,
-0.026097388938069344,
0.004201880656182766,
0.008101889863610268,
0.04018742963671684,
0.05073815956711769,
0.020428821444511414,
0.01817966066300869,
0.08058366924524307,
-0.025797773152589798,
0.008521201089024544,
0.00953696295619011,
0.0014894328778609633,
-0.028465909883379936,
0.006651194766163826,
0.05622466281056404,
0.005335802212357521,
-0.012873013503849506,
-0.06298667937517166,
-0.01630045846104622,
0.04596675559878349,
0.00702268909662962,
-0.03676385432481766,
0.018119312822818756,
-0.011821956373751163,
-0.014146633446216583,
-0.0007685154560022056,
0.019494472071528435,
0.036378633230924606,
-0.029973430559039116,
-0.0016899786423891783,
0.004811718128621578,
-0.028653584420681,
-0.07247684895992279,
-0.005904873833060265,
-0.03830133378505707,
-0.014973580837249756,
-0.033565595746040344,
-0.027119336649775505,
-0.028085527941584587,
0.016745196655392647,
0.047320496290922165,
0.049692846834659576,
0.005195845849812031,
-0.01531171053647995,
-0.02642269991338253,
0.007229159120470285,
-0.031159011647105217,
-0.06303327530622482,
-0.0204798374325037,
-0.027673467993736267,
-0.012847593985497952,
0.010061994194984436,
-0.0293356254696846,
-0.042129822075366974,
0.01940515823662281,
-0.007393762469291687,
-0.029885223135352135,
0.020730027928948402,
-0.03418421745300293,
0.012020335532724857,
0.05096806213259697,
0.02694532833993435,
-0.012102074921131134,
0.008728069253265858,
-0.012391028925776482,
0.0037948417011648417,
0.012852607294917107,
0.005367849953472614,
-0.03454762324690819,
0.004901972133666277,
-0.04686122387647629,
0.02094823494553566,
-0.03264300525188446,
0.04129849374294281,
-0.019213711842894554,
-0.0065841167233884335,
0.00444671930745244,
-0.03432837128639221,
0.007258209399878979,
0.02600012719631195,
-0.01680547557771206,
0.025477075949311256,
-0.03188001364469528,
0.010106573812663555,
-0.02386455610394478,
0.0027962708845734596,
0.0021763958502560854,
0.0011938693933188915,
0.028467785567045212,
0.06919754296541214,
-0.029703672975301743,
0.003149355761706829,
-0.02635900489985943,
0.0009283199906349182,
0.021129515022039413,
-0.02925388142466545,
0.07174061238765717,
-0.008645412512123585,
-0.018720688298344612,
0.02028435841202736,
-0.019578207284212112,
-0.07092264294624329,
-0.005255776923149824,
0.001883229473605752,
0.04577527195215225,
-0.08902403712272644,
0.032659173011779785,
-0.009858169592916965,
0.010823226533830166,
-0.03824792057275772,
-0.028409196063876152,
0.0336688794195652,
-0.00743148336187005,
-0.05534268543124199,
-0.04902989789843559,
-0.02037699520587921,
-0.04699792340397835,
-0.025886503979563713,
0.023643851280212402,
0.027345534414052963,
-0.023687351495027542,
0.00856238603591919,
0.006081870291382074,
-0.022820772603154182,
0.06723032146692276,
0.02094409614801407,
-0.012666904367506504,
0.018507618457078934,
0.007540875114500523,
0.013418746180832386,
-0.017058484256267548,
0.06515130400657654,
-0.01322039496153593,
-0.00034313747892156243,
0.00636653508991003,
-0.0002996416878886521,
0.04021520912647247,
-0.009869140572845936,
0.011086485348641872,
0.029107093811035156,
-0.0013715378008782864,
0.018766211345791817,
0.019292617216706276,
0.027794137597084045,
0.0017340169288218021,
0.03086273930966854,
-0.024037355557084084,
0.01562134362757206,
-0.026427922770380974,
-0.01855703815817833,
-0.008552812971174717,
-0.010599953122437,
0.02982008270919323,
-0.023553192615509033,
0.06498023122549057,
-0.013091500848531723,
-0.011947248131036758,
0.024367930367588997,
0.010328536853194237,
0.07109270989894867,
0.0012943824985995889,
-0.01709761656820774,
-0.002913588657975197,
-0.005763601046055555,
-0.009159675799310207,
-0.030066249892115593,
-0.02417290210723877,
0.026955408975481987,
0.06709428876638412,
-0.0520457997918129,
0.036668986082077026,
-0.013462670147418976,
0.003923037089407444,
0.007542263716459274,
-0.013767104595899582,
0.03313570097088814,
-0.02915576472878456,
-0.013187737204134464,
0.026563838124275208,
-0.012851825915277004,
-0.0007424501818604767,
0.014620538800954819,
0.046117737889289856,
-0.016119932755827904,
-0.04425812512636185,
0.013361471705138683,
-0.0011122339637950063,
0.0032227644696831703,
-0.025673286989331245,
-0.043209899216890335,
0.0013475099112838507,
-0.037114523351192474,
0.00835933443158865,
0.016936227679252625,
-0.004459915217012167,
0.03308424726128578,
0.04012545198202133,
-0.014655365608632565,
-0.040026869624853134,
0.03292345628142357,
-0.026876211166381836,
-0.028717422857880592,
-0.014246230944991112,
0.00866649765521288,
-0.02240658551454544,
0.014775029383599758,
0.04716796055436134,
-0.015707384794950485,
-0.002584225730970502,
-0.0030196039006114006,
-0.02961156517267227,
-0.020678598433732986,
-0.02961777336895466,
-0.037080638110637665,
0.00819229893386364,
-0.03620690852403641,
-0.025766249746084213,
0.03852114826440811,
-0.05672162398695946,
0.03403182327747345,
-0.005369945894926786,
0.04330233484506607,
0.0018952676327899098,
0.08693374693393707,
0.006803875323385,
-0.008234384469687939,
-0.030560823157429695,
0.038224466145038605,
0.10658005625009537,
0.008585076779127121,
0.031085101887583733,
-0.04234125465154648,
-0.02591664344072342,
-0.03239048644900322,
0.018452510237693787,
0.0014981783460825682,
-0.015741679817438126,
0.029685182496905327,
-0.0009690978331491351,
0.042125310748815536,
0.03316245228052139,
-0.011015789583325386,
-0.022793790325522423,
0.014548402279615402,
-0.07528021186590195,
-0.028756150975823402,
0.01686830259859562,
-0.0011232142569497228,
0.009464460425078869,
0.010543366894125938,
-0.026673929765820503,
-0.0033427609596401453,
-0.011508005671203136,
0.019009245559573174,
-0.004831125494092703,
-0.05587335303425789,
0.0032472130842506886,
-0.0036022383719682693,
-0.0325581319630146,
-0.014995814301073551,
0.020628001540899277,
-0.026586512103676796,
-0.0608513206243515,
0.0036004872526973486,
0.03192765638232231,
-0.008698701858520508,
-0.007910333573818207,
0.029643068090081215,
0.028180528432130814,
0.004581355955451727,
0.021244173869490623,
0.014637535437941551,
-0.05626148357987404,
-0.005219985265284777,
-0.007915064692497253,
0.020469607785344124,
0.01412257831543684,
-0.0004494343011174351,
-0.010068768635392189,
-0.01904144696891308,
0.03360014408826828,
-0.04005428031086922,
-0.0184799637645483,
0.02218344435095787,
0.056289102882146835,
0.00760602205991745,
-0.0328473225235939,
-0.029359256848692894,
0.0018370718462392688,
0.01577555015683174,
-0.003478647442534566,
0.0018086389172822237,
0.04047071561217308,
-0.005109484773129225,
0.001071934588253498,
0.04622752591967583,
-0.023641547188162804,
-0.04114599898457527,
0.004170599859207869,
-0.018043717369437218,
-0.06500273197889328,
0.009369545616209507,
0.06025766208767891,
0.046162042766809464,
0.009619958698749542,
0.02637229673564434,
0.005141654517501593,
-0.02371801994740963,
-0.06249779090285301,
0.03981488198041916,
-0.040542665868997574,
0.011085364036262035,
-0.03413301706314087,
-0.0063491747714579105,
-0.0004599914245773107,
0.04331083595752716,
-0.02184487320482731,
0.011082407087087631,
-0.021525492891669273,
0.08068665862083435,
-0.00377686507999897,
-0.022227762266993523,
-0.010147915221750736,
0.04418579861521721,
-0.048537060618400574,
0.034089453518390656,
-0.03297537565231323,
0.013738488778471947,
0.035812120884656906,
0.0018214965239167213,
0.004955764394253492,
0.010393687523901463,
-0.0000869085852173157,
0.011041542515158653,
0.03531739488244057,
-0.024999435991048813,
-0.00756983645260334,
0.03803461790084839,
-0.0011933096684515476,
-0.034010741859674454,
-0.039792466908693314,
-0.017983943223953247,
-0.008391667157411575,
-0.008528478443622589,
0.026050202548503876,
0.008282606489956379,
0.023134255781769753,
-0.051635727286338806,
-0.0022492569405585527,
-0.044666633009910583,
0.01736638881266117,
-0.042069848626852036,
0.02248966507613659,
0.003196295350790024,
-0.040133047848939896,
-0.06792164593935013,
0.043351080268621445,
-0.06867595762014389,
-0.034570932388305664,
0.006399165373295546,
0.01819550432264805,
-0.0068080308847129345,
-0.006870150566101074,
-0.02732611447572708,
0.043644197285175323,
0.02918190509080887,
0.02348555624485016,
0.016736917197704315,
0.04959740489721298,
-0.01415594108402729,
-0.07637116312980652,
0.044590990990400314,
-0.008581104688346386,
0.04519841447472572,
-0.01249703299254179,
-0.014270325191318989,
-0.006900317035615444,
0.0930367112159729,
-0.00107089732773602,
-0.0011339712655171752,
-0.008349844254553318,
-0.028332069516181946,
0.021052544936537743,
-0.00114966812543571,
-0.010480143129825592,
-0.022123998031020164,
-0.01861715503036976,
0.013192790560424328,
0.011199058964848518,
-0.030963491648435593,
0.01815222203731537,
0.03227059170603752,
-0.010321631096303463,
-0.0021556480787694454,
-0.0022253331262618303,
0.012909325771033764,
0.014748994261026382,
0.060284022241830826,
-0.0017565303714945912,
0.0018267880659550428,
-0.00956402812153101,
0.02138553373515606,
-0.11902695894241333,
0.010108415968716145,
0.01650623418390751,
0.00341810192912817,
0.033854562789201736,
-0.0378037691116333,
-0.01735643856227398,
0.0353042408823967,
-0.07249034941196442,
-0.03577018156647682,
-0.026517309248447418,
0.007175167091190815,
-0.03952731564640999,
-0.02083815634250641,
-0.014888785779476166,
0.04167691245675087,
-0.004598481114953756,
0.037349067628383636,
0.004956585820764303,
-0.010611488483846188,
-0.0038310338277369738,
-0.012018091045320034,
0.019957754760980606,
0.0444914884865284,
0.022436918690800667,
0.04340149089694023,
0.05673959106206894,
-0.02524002641439438,
-0.00025861573521979153,
0.006752971094101667,
-0.02377023734152317,
-0.0025486599188297987,
-0.016371361911296844,
0.0068525513634085655,
0.011215530335903168,
0.04099179431796074,
0.0004358853038866073,
0.0027290054131299257,
0.018726127222180367,
0.04414770379662514,
-0.0127675486728549,
-0.005072306841611862,
-0.017814071848988533,
-0.005534638185054064,
0.02599913999438286,
-0.011355889961123466,
-0.020890450105071068,
0.03266870602965355,
-0.028954429551959038,
-0.023407697677612305,
0.012085664086043835,
-0.0011926518054679036,
0.036331091076135635,
-0.021756650879979134,
-0.018727922812104225,
-0.02718820422887802,
-0.007087813224643469,
0.008188623934984207,
0.016804981976747513,
-0.002634033327922225,
0.037695594131946564,
-0.052855513989925385,
-0.04088867828249931,
-0.028469175100326538,
-0.004914815071970224,
-0.04071388766169548,
-0.0358281135559082,
-0.0014607104239985347,
0.01657412387430668,
0.028663579374551773,
0.01850825361907482,
-0.033597204834222794,
0.006132667884230614,
0.039036285132169724,
0.05607043579220772,
0.047234877943992615,
0.01939520239830017,
-0.022450655698776245,
-0.01777711883187294,
-0.043414242565631866,
0.023882269859313965,
0.0015140111790969968,
-0.010778543539345264,
-0.01891646534204483,
-0.012740302830934525,
0.04718059301376343,
-0.006039937026798725,
0.03814924880862236,
-0.04865342751145363,
-0.05379442125558853,
0.044596798717975616,
-0.05310042202472687,
-0.001520512392744422,
-0.03294927254319191,
0.0031475627329200506,
0.0057244314812123775,
-0.01271563209593296,
-0.02680322155356407,
0.012603472918272018,
-0.054805878549814224,
0.02547556534409523,
0.014949869364500046,
-0.0020295109134167433,
-0.016952797770500183,
-0.00861783791333437,
-0.028768528252840042,
0.03561936691403389,
0.04657444730401039,
-0.014252893626689911,
0.04498571157455444,
0.04326366260647774,
-0.05519271269440651,
0.02485206164419651,
-0.03690829873085022,
-0.029397988691926003,
0.012829313054680824,
-0.031962886452674866,
-0.03580440953373909,
-0.008069426752626896,
-0.005339632276445627,
0.026010075584053993,
-0.04301231727004051,
-0.005204017274081707,
0.041285328567028046,
-0.025868868455290794,
0.014474489726126194,
0.014472471550107002,
0.04171286150813103,
0.03661607950925827,
-0.008771762251853943,
0.006188163533806801,
0.046986620873212814,
-0.03269879147410393,
-0.0191498976200819,
0.003756365505978465,
0.02746361494064331,
0.016051778569817543,
0.009145532734692097,
0.026126280426979065,
-0.015629785135388374,
-0.0025127262342721224,
0.014736714772880077,
0.017515016719698906,
-0.02218593843281269,
-0.013054863549768925,
0.036720287054777145,
-0.003073186846449971,
-0.013836235739290714,
-0.014609263278543949,
-0.03520423546433449,
0.04967990145087242,
0.0069615705870091915,
-0.0007839134195819497,
-0.0028392267413437366,
0.015286726877093315,
-0.00023019463696982712,
0.0013785744085907936,
-0.015796393156051636,
-0.013516083359718323,
0.004918175283819437,
-0.007112077437341213,
0.010404065251350403,
0.01019254233688116,
0.030689265578985214,
0.006719736382365227,
-0.0035964716225862503,
-0.05258303880691528,
-0.0018590932013466954,
-0.08091667294502258,
-0.04883388802409172,
-0.008438416756689548,
-0.00003226343324058689,
0.056076012551784515,
0.05104890465736389,
0.0034277501981705427,
-0.009618710726499557,
-0.0015022888546809554,
-0.023322371765971184,
0.07861514389514923,
-0.04338238388299942,
0.01375388354063034,
-0.05660012736916542,
0.050661779940128326,
0.0089176120236516,
-0.005867149215191603
] |
<p>So far I'm only tasting the quantum mechanics. Haven't gone very deep into the mathematics of it yet.</p>
<p>I read about the double slit experiment, and the weird consequences of it: if you put a detector at the slits you won't have an interference pattern. Since you basically absorbed and recorded the photon then you reemitted another one at that slit: now you have single probability wave emitted at that slit which won't interfere with the another one since it's not there: no interference pattern. At least this is my understanding so far.</p>
<p>Ok, now let's cheat: at the source you detect (absorb) and reemit the photon. You won't measure the reemitted photon again till it hits the detector. So it pass the slits in a fuzzy state and you should have an interference pattern at the detector then. Anyway the photon hits detector at a point somewhere, you record it. If you have atomic clocks you can have interval between the reemission and detection at the screen. Based on the location of the hit and the travel time measured, and knowing the light travels with $c$ the path length travelled can be estimated. From the path length you can deduce which slit it passed through.</p>
<p>Of course nature doesn't like cheaters: you cannot have "which slit" information and "interference pattern" (went through both slits) at the same time. So my thoughts:</p>
<ul>
<li><p>I think nature cannot prohibit to have a low rate photon source: you can put some lead screen in front of your radioactive gamma source, to reduce the rate. So you should be able to measure travel times occasionally when the next photon comes late enough.</p></li>
<li><p>Nature cannot mess with travel times too since from that would mean light would't go woth $c$ but slower or faster - the latter would have nasty consequences. </p></li>
<li><p>Another thing I can think of is that there will be enough uncertainty in detector response times or the reemitting apparatus so I cannot reliably measure the travel times. But this would mean that this uncertainty depends on the distance between the slits: the bigger the distance the bigger possible difference in travel times to a point on the detector through the slits. It's very hard to believe the the sole fact of changing the slit spacing can affect uncertainty of the detector response times...</p></li>
</ul>
<p><strong>So what do you think will happen?</strong> Do you know of experiment that tested this?</p> | 2,889 | [
-0.01136729121208191,
-0.05027986317873001,
0.010996321216225624,
-0.03637236729264259,
0.021788133308291435,
0.00709450151771307,
-0.017216920852661133,
-0.009446404874324799,
0.026859691366553307,
0.02459331415593624,
0.07072409987449646,
0.05338272079825401,
0.022377315908670425,
0.05090850219130516,
0.012454356998205185,
0.01737990416586399,
0.006150952074676752,
-0.0016439580358564854,
-0.055506158620119095,
-0.08412940055131912,
0.002068948931992054,
0.020432548597455025,
0.021179938688874245,
0.0025891000404953957,
-0.03157158941030502,
0.04364767670631409,
0.011812248267233372,
0.0008853108156472445,
0.00973763782531023,
0.03965436667203903,
-0.01733996346592903,
-0.02539508230984211,
0.009339571930468082,
0.013269882649183273,
-0.009267772547900677,
-0.009578048251569271,
-0.01872178725898266,
-0.03378327190876007,
0.03408971056342125,
0.0022793172392994165,
-0.018270542845129967,
0.028832977637648582,
-0.02287326380610466,
0.027980243787169456,
-0.007386476267129183,
0.008602838031947613,
0.009923631325364113,
-0.008405190892517567,
0.053139690309762955,
-0.02832912653684616,
0.032677873969078064,
-0.029204871505498886,
0.01569974794983864,
0.013925422914326191,
-0.026490584015846252,
-0.027430720627307892,
0.1011645495891571,
0.06367142498493195,
-0.005654633976519108,
-0.027614638209342957,
0.021631138399243355,
-0.0008765911916270852,
0.023889213800430298,
-0.031314633786678314,
-0.001400622189976275,
-0.012815275229513645,
0.007487065624445677,
-0.022169584408402443,
-0.004155366215854883,
-0.026734966784715652,
0.021201124414801598,
0.012146731838583946,
0.031198779121041298,
0.0477205328643322,
0.005658223759382963,
-0.006408792454749346,
0.010770938359200954,
0.04126233235001564,
0.02837735414505005,
0.040794000029563904,
0.0017410335130989552,
-0.0032543353736400604,
0.023276006802916527,
0.036541908979415894,
-0.002447013510391116,
-0.019416585564613342,
0.060817599296569824,
-0.03860248997807503,
-0.015465366654098034,
0.005218076054006815,
-0.025249233469367027,
0.02270113304257393,
0.03143395856022835,
0.026148885488510132,
-0.013389725238084793,
0.037809014320373535,
-0.005355390720069408,
0.02664346620440483,
0.009584304876625538,
-0.004895444493740797,
-0.016615482047200203,
-0.01128228846937418,
-0.01495385728776455,
0.08426269143819809,
0.0027254477608948946,
-0.01700626127421856,
-0.01006577629595995,
0.044260915368795395,
-0.011165271513164043,
-0.01563217304646969,
-0.0321858711540699,
0.0006160628981888294,
0.014890877529978752,
0.04168345779180527,
0.009075832553207874,
-0.011301275342702866,
-0.004900210537016392,
-0.045482441782951355,
0.09812940657138824,
0.06283625960350037,
0.014510727487504482,
-0.05029947683215141,
-0.004119056276977062,
-0.020305445417761803,
-0.06166719272732735,
-0.014372150413691998,
0.06064682826399803,
-0.02997235767543316,
-0.02214643731713295,
0.022092625498771667,
-0.0004072380834259093,
-0.021155117079615593,
0.03436068072915077,
-0.009120745584368706,
0.01904679462313652,
0.006962365936487913,
-0.15801730751991272,
-0.08094249665737152,
0.05386433005332947,
0.017228811979293823,
-0.055549465119838715,
-0.09022334963083267,
0.027968058362603188,
0.022952517494559288,
0.07997147738933563,
0.007369501516222954,
-0.009049968793988228,
-0.012395045720040798,
0.005654682870954275,
0.0007725445320829749,
0.0018343963893130422,
0.010676776058971882,
0.021420033648610115,
-0.01904800720512867,
-0.02944835275411606,
-0.002285482594743371,
0.03488130494952202,
0.03434227779507637,
-0.015158690512180328,
-0.011835293844342232,
0.03539341688156128,
-0.0019770644139498472,
-0.020097265020012856,
0.0020664073526859283,
-0.022191498428583145,
-0.06066840887069702,
0.08976445347070694,
0.007390713319182396,
-0.003485821420326829,
-0.0035966464783996344,
-0.019005268812179565,
0.015271375887095928,
-0.021241163834929466,
-0.026928037405014038,
0.020209742709994316,
-0.040083952248096466,
-0.022198544815182686,
0.045802973210811615,
-0.043005459010601044,
-0.001087093143723905,
-0.018560592085123062,
-0.02387663908302784,
-0.019620202481746674,
0.009519058279693127,
0.03240257874131203,
0.013235975056886673,
-0.011065032333135605,
0.006070193834602833,
-0.00036706874379888177,
-0.030758563429117203,
-0.013239894062280655,
-0.017078589648008347,
-0.022506358101963997,
0.008474308997392654,
-0.010863570496439934,
0.017530914396047592,
-0.010857752524316311,
-0.043422069400548935,
-0.008712030947208405,
-0.04444650188088417,
-0.015031723305583,
0.03228949382901192,
0.01593121699988842,
-0.00920564029365778,
0.012829759158194065,
0.057925995439291,
0.025634683668613434,
-0.019667120650410652,
0.051153514534235,
-0.011645407415926456,
-0.0037874497938901186,
-0.0207985732704401,
-0.04410683736205101,
0.018498791381716728,
0.007529828231781721,
0.025050435215234756,
0.029187729582190514,
-0.0007709101773798466,
-0.01623649150133133,
-0.025070056319236755,
-0.03319867327809334,
0.05941328778862953,
0.019356831908226013,
-0.002942026127129793,
-0.04032224416732788,
0.024980632588267326,
0.0022349078208208084,
0.027555247768759727,
0.0012177042663097382,
-0.06040644273161888,
-0.020487243309617043,
-0.025299465283751488,
0.0033069222699850798,
-0.0003085063653998077,
-0.016924431547522545,
0.06369071453809738,
-0.01266846526414156,
0.03499374911189079,
0.01884978823363781,
-0.008029138669371605,
0.011541774496436119,
-0.02583896927535534,
-0.010222640819847584,
-0.015475988388061523,
-0.023874081671237946,
0.0052352347411215305,
0.015342849306762218,
-0.020832084119319916,
-0.015137806534767151,
-0.03458608314394951,
-0.010920720174908638,
-0.02792331762611866,
-0.016883309930562973,
0.012694436125457287,
0.024817639961838722,
-0.010863613337278366,
0.011285130865871906,
-0.0006154923466965556,
0.036874860525131226,
0.008854511193931103,
-0.021590394899249077,
0.0008193220128305256,
-0.0458352193236351,
-0.017126277089118958,
0.010065291076898575,
0.018425047397613525,
-0.008561148308217525,
0.01550040952861309,
0.03808462247252464,
-0.01905880868434906,
0.03713279217481613,
-0.03415781259536743,
0.0289983581751585,
-0.0320998877286911,
-0.03500586375594139,
-0.000987691804766655,
0.021270113065838814,
0.004829843994230032,
-0.0512373186647892,
-0.03141982480883598,
-0.006271530874073505,
0.004708477295935154,
0.02040162682533264,
0.05085045099258423,
-0.017237726598978043,
0.009092330932617188,
-0.01311380136758089,
-0.012375283986330032,
0.020824475213885307,
-0.01953175850212574,
0.009906035847961903,
0.03328891098499298,
-0.009988018311560154,
-0.08328691124916077,
-0.032524023205041885,
0.0031077421735972166,
-0.013943349942564964,
-0.032840851694345474,
-0.010817733593285084,
0.060746487230062485,
0.023440511897206306,
-0.07481331378221512,
0.012020774185657501,
-0.04859653487801552,
-0.014594673179090023,
-0.019523784518241882,
-0.01955106481909752,
-0.015112697146832943,
-0.026871895417571068,
0.015513775870203972,
0.029533201828598976,
-0.03823398798704147,
-0.015214141458272934,
-0.06658550351858139,
-0.04999535158276558,
0.04066482558846474,
-0.000125780250527896,
0.03644236922264099,
-0.020158544182777405,
0.014950859360396862,
0.0771661102771759,
0.05875721946358681,
0.001607753918506205,
-0.019326016306877136,
0.019750390201807022,
0.011589148081839085,
-0.022293467074632645,
0.0204999428242445,
0.01834266632795334,
0.0027487436309456825,
0.01565597392618656,
-0.007830382324755192,
0.03167306259274483,
0.05523402616381645,
0.03512285649776459,
0.03441724553704262,
0.03005012683570385,
-0.006313422694802284,
-0.017588185146450996,
0.04377724975347519,
0.028810929507017136,
-0.044744785875082016,
-0.007516718935221434,
-0.0042670187540352345,
0.018418658524751663,
0.03961717337369919,
-0.04514310136437416,
0.04301387444138527,
0.023398220539093018,
0.012533735483884811,
-0.010469421744346619,
0.019177667796611786,
-0.011107035912573338,
-0.013759244233369827,
-0.024183016270399094,
0.03313164785504341,
0.05359885096549988,
-0.010515548288822174,
0.013073422946035862,
0.03295225277543068,
0.05385386571288109,
0.004151338245719671,
-0.03157233074307442,
0.005055469926446676,
-0.03260345011949539,
0.029829641804099083,
-0.029346123337745667,
-0.00861331820487976,
0.06217735633254051,
0.023170512169599533,
0.035877205431461334,
-0.0038876552134752274,
-0.03233926743268967,
-0.06754251569509506,
-0.031858041882514954,
-0.00921009574085474,
-0.006963217165321112,
0.06471829861402512,
0.06335968524217606,
0.021087003871798515,
0.03237801790237427,
0.0040910448879003525,
-0.02315017767250538,
-0.024669259786605835,
-0.05916864797472954,
0.021992571651935577,
-0.02011938765645027,
-0.047919079661369324,
-0.012369341216981411,
-0.02064572088420391,
-0.02304430678486824,
-0.011784635484218597,
-0.028255552053451538,
-0.0003924404736608267,
-0.0005842465907335281,
-0.04096922278404236,
0.010318904183804989,
-0.03377486392855644,
-0.03942902758717537,
-0.04211236536502838,
0.08428474515676498,
0.03498927503824234,
0.01029994897544384,
0.00032153763459064066,
-0.0031990206334739923,
-0.04144659265875816,
0.0024055487010627985,
-0.01428288035094738,
-0.031296562403440475,
0.023925337940454483,
0.02556416392326355,
0.02436862327158451,
0.0016974264290183783,
-0.006012468133121729,
-0.0107164541259408,
0.04300181567668915,
0.035412903875112534,
0.00910390354692936,
-0.023418467491865158,
-0.010195915587246418,
0.014895675703883171,
-0.016361316666007042,
-0.006762442644685507,
0.06176946684718132,
-0.024405475705862045,
0.017644980922341347,
0.032120343297719955,
-0.00993622187525034,
-0.0093871233984828,
0.028600500896573067,
0.036724649369716644,
-0.009554964490234852,
-0.008925712667405605,
-0.01396482065320015,
-0.03299974277615547,
-0.007549752481281757,
0.011129908263683319,
-0.04332543537020683,
0.021637625992298126,
-0.0043955459259450436,
-0.00027975853299722075,
0.0045111654326319695,
0.03990364447236061,
0.0073132892139256,
-0.011106296442449093,
-0.014257255010306835,
-0.023620767518877983,
0.022178133949637413,
0.0035147599410265684,
0.015498187392950058,
-0.0023419426288455725,
0.017626436427235603,
-0.003210195107385516,
0.025955036282539368,
-0.0534055121243,
-0.08739250898361206,
0.047777216881513596,
0.06301973760128021,
-0.018967635929584503,
0.031210126355290413,
-0.06083878502249718,
-0.025962820276618004,
0.04768114164471626,
-0.003579019568860531,
0.07172448933124542,
-0.004996186122298241,
-0.030032867565751076,
-0.02776058204472065,
-0.034073710441589355,
-0.02864888682961464,
0.05261997878551483,
0.023058636114001274,
-0.014441571198403835,
0.0040062665939331055,
-0.019909199327230453,
-0.017539603635668755,
-0.009205442853271961,
0.029511498287320137,
0.060028478503227234,
-0.017636612057685852,
-0.008669022470712662,
0.0029840045608580112,
-0.00009733373008202761,
-0.011158274486660957,
-0.08869121968746185,
0.04023728519678116,
0.0023881271481513977,
0.014190036803483963,
0.06767638772726059,
0.008875532075762749,
-0.03149513900279999,
0.04211749508976936,
0.0061903465539216995,
-0.014658663421869278,
0.01939256303012371,
-0.06971409171819687,
0.05514797940850258,
0.02688826434314251,
0.022964267060160637,
0.024847643449902534,
0.05722793564200401,
-0.03673768788576126,
0.04524694383144379,
-0.013487477786839008,
0.03735080361366272,
-0.013062420301139355,
0.015670040622353554,
-0.00954261515289545,
0.005475023295730352,
-0.04953884333372116,
0.04363713413476944,
0.012057977728545666,
0.004827259574085474,
0.007659259717911482,
-0.03195684775710106,
-0.025345664471387863,
0.00024213868891820312,
-0.01740945130586624,
0.03567691892385483,
-0.056075651198625565,
0.018992695957422256,
-0.005052205640822649,
-0.010064724832773209,
-0.01886427029967308,
-0.014163010753691196,
0.02483840100467205,
0.05463676154613495,
-0.031727418303489685,
0.01087776105850935,
-0.04087008908390999,
-0.009660894051194191,
0.015166639350354671,
-0.028013473376631737,
0.04611065611243248,
0.001643699361011386,
0.0035964574199169874,
-0.001105600269511342,
-0.03604510426521301,
-0.027830490842461586,
0.03543704003095627,
-0.0436893031001091,
0.012224390171468258,
-0.04980459809303284,
0.04104850813746452,
-0.022277291864156723,
0.01508774608373642,
-0.07648997753858566,
-0.027216337621212006,
0.005491739138960838,
0.0027403957210481167,
-0.03486492484807968,
-0.029454510658979416,
0.008086499758064747,
0.008033177815377712,
-0.02560426853597164,
-0.027926886454224586,
0.0354328416287899,
-0.009785467758774757,
-0.0014662048779428005,
0.03206508234143257,
0.04024598374962807,
0.05038797855377197,
0.011893241666257381,
-0.0026128285098820925,
0.010536877438426018,
-0.050148990005254745,
-0.013522619381546974,
0.006872659549117088,
-0.012301096692681313,
-0.02612476423382759,
-0.045480985194444656,
-0.010352768935263157,
0.0005462820990942419,
0.019126087427139282,
-0.05901097133755684,
-0.022036710754036903,
0.03062237799167633,
0.012763753533363342,
-0.02734173648059368,
0.006269959732890129,
-0.0004421814810484648,
0.022795915603637695,
0.022455928847193718,
0.009697427041828632,
-0.00644182413816452,
-0.026689033955335617,
-0.0369008332490921,
0.009143446572124958,
-0.004632242023944855,
-0.017738543450832367,
0.003021510783582926,
0.018979070708155632,
-0.010485024191439152,
-0.0185494776815176,
0.00503136869519949,
-0.005555571522563696,
-0.007586969994008541,
-0.03769604489207268,
0.008116340264678001,
0.034972794353961945,
-0.0024091212544590235,
-0.04457893967628479,
-0.05392023175954819,
-0.04630272835493088,
-0.018593937158584595,
0.05866453796625137,
0.022264666855335236,
0.05351465940475464,
-0.03626052290201187,
-0.004143286496400833,
-0.008769148029386997,
-0.0021033533848822117,
-0.025470314547419548,
-0.006175760179758072,
0.021757816895842552,
0.007363051641732454,
-0.0015270665753632784,
-0.010028456337749958,
0.04186348244547844,
0.05695474520325661,
-0.010956943035125732,
0.034237686544656754,
-0.00025127182016149163,
0.017879685387015343,
0.03108040802180767,
-0.01680995151400566,
-0.03956140577793121,
0.04475223273038864,
-0.07389014214277267,
0.022668732330203056,
0.02157057262957096,
0.012139733880758286,
0.06576217710971832,
0.014840028248727322,
-0.007684363052248955,
-0.04129914566874504,
0.005252078641206026,
-0.07749710232019424,
-0.00015078976866789162,
0.005230678245425224,
0.020203551277518272,
0.009715856052935123,
-0.0135323042050004,
0.02888692542910576,
-0.025979870930314064,
0.011517449282109737,
-0.013576725497841835,
-0.07278971374034882,
-0.028980541974306107,
-0.029734741896390915,
-0.03262225538492203,
0.06472700089216232,
0.009571578353643417,
-0.025777123868465424,
0.018590396270155907,
-0.01834440417587757,
0.04258880764245987,
0.03440815955400467,
0.031197553500533104,
-0.035326097160577774,
0.017558719962835312,
0.0032554208301007748,
-0.001019237213768065,
-0.022817714139819145,
-0.007914531975984573,
0.14341135323047638,
0.0384465791285038,
-0.008555040694773197,
-0.01877574622631073,
0.001494271564297378,
0.016748841851949692,
0.040970101952552795,
0.007572766859084368,
0.032515477389097214,
0.003774070180952549,
0.003950901795178652,
0.03362217918038368,
0.017237260937690735,
0.017733998596668243,
0.010826347395777702,
0.05334627255797386,
-0.03528295457363129,
-0.025611598044633865,
0.01827075146138668,
0.009260141290724277,
0.010447853244841099,
-0.010159703902900219,
0.015025366097688675,
0.037711963057518005,
-0.03083098866045475,
-0.0027012103237211704,
-0.009538466110825539,
-0.02275407500565052,
0.016542019322514534,
0.006321138236671686,
-0.04431632533669472,
-0.00592687027528882,
-0.006245110649615526,
-0.01779823563992977,
-0.011131107807159424,
0.02300669439136982,
0.04852398857474327,
-0.012504982762038708,
0.015185754746198654,
0.029022306203842163,
0.006081128027290106,
-0.022954557090997696,
-0.002801588037982583,
0.029018400236964226,
-0.04751966521143913,
-0.01343215350061655,
0.007096701301634312,
0.032241687178611755,
-0.04123682901263237,
-0.029833024367690086,
-0.01359493751078844,
-0.02692965790629387,
0.05304987356066704,
-0.04195588827133179,
0.006152295507490635,
-0.001755586126819253,
0.008548391982913017,
-0.01711973547935486,
0.006507059559226036,
0.0012236799811944366,
0.03740350157022476,
0.004209057427942753,
-0.0032958684023469687,
0.01497284509241581,
-0.005427849013358355,
-0.013944048434495926,
-0.00807563029229641,
0.011738033965229988,
0.02823496051132679,
-0.033722423017024994,
-0.029502054676413536,
0.012539948336780071,
-0.012381399050354958,
-0.005026041530072689,
0.008500726893544197,
0.008780064061284065,
0.0028642548713833094,
-0.0057399519719183445,
-0.012558193877339363,
-0.015729490667581558,
-0.05630813539028168,
0.03251132741570473,
-0.03602142259478569,
-0.016880609095096588,
-0.010035553015768528,
-0.007860764861106873,
0.02811998501420021,
0.06401151418685913,
0.0031922366470098495,
-0.002001220127567649,
0.019003789871931076,
0.062290653586387634,
0.05906154587864876,
-0.023812873288989067,
-0.006242639850825071,
0.00932300928980112,
0.00011521087435539812,
0.026477258652448654,
-0.04407064616680145,
0.02974134124815464,
0.008188951760530472,
0.01038762554526329,
0.044814255088567734,
0.01677653379738331,
-0.025569990277290344,
-0.014287899248301983,
-0.03397800773382187,
-0.03558854013681412,
-0.006806646939367056,
-0.01809767819941044,
0.061123523861169815,
-0.04013179987668991,
-0.015582788735628128,
-0.021760258823633194,
0.0055185724049806595,
-0.0200186874717474,
-0.02742387354373932,
-0.026077738031744957,
0.0180076714605093,
-0.021487591788172722,
-0.007802395150065422,
0.00183696614112705,
0.008792047388851643,
-0.007527680601924658,
0.014193054288625717,
-0.02373066172003746,
-0.005784686654806137,
-0.027576535940170288,
0.04304145649075508,
0.014990624971687794,
-0.035794928669929504,
0.011408778838813305,
0.034201543778181076,
-0.013828922994434834,
0.007183449808508158,
0.023378951475024223,
0.03669139742851257,
0.020065058022737503,
0.0012898009736090899,
0.008900130167603493,
0.006824190728366375,
-0.03078746609389782,
-0.05466294288635254,
0.07035717368125916,
-0.00674047414213419,
0.03380420058965683,
-0.010235522873699665,
-0.030093207955360413,
0.01953687146306038,
0.04908595234155655,
-0.01686355285346508,
-0.03474825248122215,
-0.01107926294207573,
0.008260110393166542,
0.018029646947979927,
-0.026471545919775963,
0.005588673520833254,
-0.008853294886648655,
0.027183037251234055,
0.022644154727458954,
-0.035127028822898865,
0.004485978279262781,
0.03072330169379711,
-0.0308969859033823,
-0.06529425829648972,
0.006835522595793009,
-0.03297107294201851,
-0.03850342705845833,
0.015613410621881485,
0.043349072337150574,
-0.03409649804234505,
0.05717416852712631,
0.02982279099524021,
-0.005676443688571453,
-0.12032146751880646,
-0.005015804432332516,
0.014726159162819386,
0.029332222416996956,
0.05387020856142044,
-0.014192432165145874,
0.025066619738936424,
0.026962885633111,
-0.06307154893875122,
-0.0009404040756635368,
0.010529167018830776,
-0.003899830160662532,
-0.016522273421287537,
-0.013623022474348545,
-0.05539857968688011,
0.018574068322777748,
0.0035999715328216553,
0.03611670434474945,
0.03521781414747238,
0.012141483835875988,
-0.036285992711782455,
-0.04382854700088501,
-0.047511711716651917,
-0.01246713474392891,
0.007075595203787088,
0.00877976045012474,
0.08463487774133682,
-0.040818747133016586,
0.037249282002449036,
0.005572667345404625,
-0.007074963301420212,
0.04954969882965088,
-0.028794603422284126,
0.016547435894608498,
0.02927332930266857,
0.014155316166579723,
0.026768481358885765,
-0.012227954342961311,
0.0365123376250267,
-0.009284712374210358,
0.005722778383642435,
-0.010684672743082047,
-0.007535016629844904,
-0.018924979493021965,
0.016986418515443802,
-0.02857038751244545,
-0.021859992295503616,
-0.0010365098714828491,
0.04006662219762802,
-0.01598302461206913,
0.02302151918411255,
0.02759833075106144,
0.014380063861608505,
-0.01835298351943493,
-0.03659278526902199,
-0.03730229660868645,
-0.011953875422477722,
0.050964463502168655,
0.05225027725100517,
-0.04918402060866356,
-0.009938535280525684,
-0.056875079870224,
-0.044939931482076645,
0.033127374947071075,
0.026212694123387337,
-0.00018256968178320676,
-0.008830079808831215,
-0.025162139907479286,
-0.018482984974980354,
0.018659358844161034,
0.019138187170028687,
0.0014684085035696626,
-0.04142313823103905,
0.01625829003751278,
-0.0010684238513931632,
0.03820086643099785,
-0.017048213630914688,
-0.0005162115558050573,
-0.015170520171523094,
-0.06489334255456924,
0.013610652647912502,
0.008971381932497025,
0.018033621832728386,
-0.05429328605532646,
-0.008734435774385929,
-0.006761197466403246,
0.004711533430963755,
0.07825089991092682,
0.0007249107584357262,
-0.005567299202084541,
0.009452331811189651,
-0.0022685921285301447,
0.04516005516052246,
-0.026764392852783203,
0.008017417974770069,
-0.016609417274594307,
0.013749485835433006,
-0.014621416106820107,
-0.018968360498547554,
-0.02742631919682026,
0.005825705826282501,
0.008232061751186848,
0.013302328996360302,
-0.02843630313873291,
-0.0168000441044569,
-0.03400348126888275,
0.04034345597028732,
-0.012944760732352734,
0.023740164935588837,
0.038200635462999344,
-0.009192995727062225,
0.058987267315387726,
0.023177659139037132,
-0.026488125324249268,
-0.07361339777708054,
0.00003125446164631285,
-0.03273843601346016,
-0.03524131327867508,
0.01116431038826704,
0.0014820999931544065,
0.008100675418972969,
-0.01983221061527729,
-0.03437997028231621,
0.04049978032708168,
-0.03419039398431778,
-0.01917736418545246,
0.07128739356994629,
-0.00760266650468111,
0.021983856335282326,
0.01336143258959055,
0.07369193434715271,
-0.0010018781758844852,
-0.009884725324809551,
-0.02908680960536003,
0.034439120441675186,
0.04123862832784653,
-0.04891132563352585,
0.024228191003203392,
0.08307353407144547,
0.06032925471663475,
-0.01039923820644617,
-0.003678125562146306,
0.039524249732494354,
-0.00210401089861989,
0.0107394028455019,
0.05549230799078941,
-0.0014643736649304628,
-0.0093463696539402,
0.041368335485458374,
-0.0053180824033916,
0.0641724020242691,
-0.009854563511908054,
0.029057210311293602,
-0.018701819702982903,
-0.014687441289424896,
-0.027399634942412376,
0.04007497802376747,
0.02825861983001232,
0.046402089297771454,
-0.011452889069914818,
0.019275769591331482,
-0.02669811248779297,
0.03877507150173187,
0.005232546478509903,
-0.10432180762290955,
-0.00935438834130764,
-0.008305361494421959,
-0.0003865248872898519,
-0.020901059731841087,
-0.0013879173202440143,
-0.0024768610019236803,
-0.03709793835878372,
0.01784120686352253,
0.0005193144315853715,
-0.02486979216337204,
0.027153898030519485,
-0.002584107220172882,
-0.02377154491841793,
0.06937021762132645,
-0.0680275410413742,
-0.01589208096265793,
-0.016059022396802902,
0.03447538614273071,
-0.01555145625025034,
-0.01610700413584709
] |
<p>Question on Section 9.1.3 in "Conformal Field Theory" by Philippe Di Francesco et. al.</p>
<blockquote>
<p><em>The basic idea of the Coulomb-gas formalism is to place a background charge in the system, making the $U(1)$ symmetry anomalous. This has the effect of modifying the conformal dimensions of the vertex operators and the central charge[...]</em></p>
</blockquote>
<p>Could anyone tell me what does he mean by $U(1)$ symmetry? I didn't see any $U(1)$ symmetry here in the context...</p> | 2,890 | [
0.019972961395978928,
0.0006550912512466311,
0.026179257780313492,
-0.01158487144857645,
0.025685740634799004,
0.019713565707206726,
-0.032567400485277176,
0.0055282991379499435,
-0.01607278175652027,
-0.05587468668818474,
0.029625698924064636,
0.020150447264313698,
0.07553207129240036,
0.01301528699696064,
0.04901905357837677,
0.02545306645333767,
-0.026394987478852272,
-0.034267544746398926,
-0.023763073608279228,
-0.01797918975353241,
0.001579312956891954,
0.02796703763306141,
0.01721516065299511,
0.0022585424594581127,
0.01710604876279831,
0.05937137454748154,
0.004521220922470093,
0.009129800833761692,
0.03139271214604378,
0.029991261661052704,
-0.026091940701007843,
-0.034664336591959,
0.007017500698566437,
-0.04385856166481972,
0.0046426295302808285,
-0.002774766180664301,
-0.00233481009490788,
-0.04206801578402519,
0.019674716517329216,
-0.003976881969720125,
-0.05620702728629112,
-0.05222006514668465,
-0.009034442715346813,
0.030297132208943367,
-0.019952645525336266,
0.010984459891915321,
-0.01602732203900814,
-0.00902090035378933,
0.025431198999285698,
-0.056263767182826996,
0.05503831058740616,
0.047238655388355255,
0.02971249260008335,
-0.008532403968274593,
0.03373970091342926,
0.012004933319985867,
0.047241613268852234,
0.08387017995119095,
0.030337098985910416,
-0.04630386456847191,
-0.016999563202261925,
-0.04304349794983864,
-0.00921581406146288,
-0.024715421721339226,
0.009946336969733238,
0.055334798991680145,
-0.02072526142001152,
-0.012171737849712372,
0.01094845775514841,
0.003061432857066393,
0.010959104634821415,
-0.030292930081486702,
-0.021183449774980545,
-0.04600748047232628,
0.018962839618325233,
-0.0022625415585935116,
0.0041483319364488125,
0.0016701725544407964,
0.040169648826122284,
0.014174247160553932,
-0.022572124376893044,
0.023287737742066383,
0.014091726392507553,
0.052424050867557526,
-0.04268191009759903,
-0.016351614147424698,
0.08245038241147995,
-0.01674959994852543,
0.019912146031856537,
0.05525596812367439,
-0.045030541718006134,
-0.006103969644755125,
0.03185863792896271,
-0.015036712400615215,
-0.029928764328360558,
0.02173120342195034,
0.010938172228634357,
0.041607003659009933,
-0.03772015497088432,
-0.0021598811727017164,
-0.030789757147431374,
-0.03515345975756645,
0.03182408958673477,
0.06000900641083717,
0.014006445184350014,
-0.009343188256025314,
-0.04417553171515465,
0.019918369129300117,
-0.020213408395648003,
0.006556221749633551,
-0.07844287157058716,
-0.0050288839265704155,
-0.017959700897336006,
-0.0038028531707823277,
-0.0006038156570866704,
-0.011583737097680569,
0.018002545461058617,
-0.0005219515296630561,
0.040858250111341476,
0.025682851672172546,
0.07523456960916519,
-0.009326014667749405,
0.03900619223713875,
0.006389191374182701,
-0.10724189132452011,
-0.007613827474415302,
0.024359887465834618,
0.012409406714141369,
-0.02410796284675598,
0.01509823091328144,
0.00719446362927556,
-0.002370154717937112,
0.024490296840667725,
0.014405803754925728,
0.05296480283141136,
-0.009646499529480934,
-0.08914867043495178,
-0.05868566781282425,
0.02205212600529194,
0.004551826510578394,
0.024396246299147606,
-0.08468782901763916,
-0.0077524129301309586,
0.022457124665379524,
0.0732942596077919,
-0.03532879799604416,
-0.0026122306007891893,
0.011977797374129295,
0.026418281719088554,
0.024114279076457024,
0.008883570320904255,
-0.0389687716960907,
-0.016528168693184853,
-0.038938652724027634,
-0.010298394598066807,
-0.07026220113039017,
0.04971502348780632,
0.02682696282863617,
0.014397107996046543,
-0.013410537503659725,
0.07313443720340729,
-0.01608179695904255,
0.01662953943014145,
-0.014191257767379284,
-0.029209326952695847,
0.02284310944378376,
0.05485234782099724,
0.005316838156431913,
-0.013230799697339535,
0.05542619526386261,
-0.009456779807806015,
0.0006416389951482415,
0.018089914694428444,
0.036016542464494705,
0.045261576771736145,
-0.03091665357351303,
-0.032719410955905914,
-0.024973945692181587,
0.013979367911815643,
0.004063484724611044,
0.003735858714208007,
-0.012891924940049648,
0.0055678533390164375,
0.025792477652430534,
-0.03203718364238739,
-0.010693187825381756,
-0.022657649591565132,
0.024681661278009415,
-0.000677077507134527,
-0.050952594727277756,
-0.04043705016374588,
-0.07965417951345444,
-0.0138752032071352,
0.007167845033109188,
0.013825357891619205,
0.06724261492490768,
-0.01796576753258705,
-0.00781891867518425,
0.0023790867999196053,
-0.041638173162937164,
-0.008593558333814144,
0.039643362164497375,
0.00594604667276144,
-0.02143271081149578,
0.02433151938021183,
0.000847287243232131,
0.04180804267525673,
0.008571299724280834,
0.025528162717819214,
-0.0040786536410450935,
0.018708208575844765,
0.00949600525200367,
-0.03999821096658707,
0.013147630728781223,
-0.03337274119257927,
0.004952194634824991,
0.003351739374920726,
-0.015101526863873005,
-0.0038755417335778475,
0.02425551973283291,
0.0016294647939503193,
0.03529416397213936,
0.05522327870130539,
-0.02060595341026783,
0.0041320133022964,
0.055305540561676025,
-0.0030652068089693785,
-0.007120315916836262,
0.018328992649912834,
-0.046032264828681946,
-0.06164596229791641,
-0.011865072883665562,
0.06709993630647659,
0.03640846535563469,
-0.016174865886569023,
-0.015018191188573837,
0.0332522876560688,
-0.002746843034401536,
0.01907283067703247,
-0.01149427704513073,
-0.01852915994822979,
-0.044824905693531036,
0.0701310858130455,
0.023797275498509407,
0.034613724797964096,
-0.03258485347032547,
0.036942411214113235,
-0.004573154728859663,
0.035120639950037,
-0.009991269558668137,
-0.054391443729400635,
-0.0028525341767817736,
-0.06222587078809738,
0.01427533570677042,
-0.026586653664708138,
0.011779934167861938,
0.042688317596912384,
-0.014680163003504276,
0.04518909752368927,
0.025679226964712143,
-0.008546398021280766,
-0.018503963947296143,
-0.02582196146249771,
-0.024145783856511116,
0.023660285398364067,
0.001287693390622735,
-0.015668272972106934,
-0.013601920567452908,
-0.004160264041274786,
-0.07401058822870255,
0.019765323027968407,
-0.012079047970473766,
-0.01868363469839096,
-0.0330263115465641,
0.016431069001555443,
0.03459317609667778,
-0.009825634770095348,
0.02213716134428978,
-0.053718775510787964,
-0.051303502172231674,
0.0021937673445791006,
-0.02298523671925068,
0.025641601532697678,
0.045347221195697784,
-0.038449905812740326,
0.037711046636104584,
-0.05563971400260925,
-0.013146648183465004,
0.013452179729938507,
-0.006827936507761478,
0.037791747599840164,
0.019637592136859894,
0.006743026431649923,
0.031003454700112343,
-0.031094331294298172,
-0.012560025788843632,
0.07176364958286285,
-0.029053807258605957,
-0.02729870192706585,
0.04052770137786865,
0.015755610540509224,
-0.00037910102400928736,
0.012783309444785118,
-0.025059137493371964,
-0.030762234702706337,
-0.016122613102197647,
0.0018553728004917502,
0.03815368935465813,
-0.026615751907229424,
0.07835856080055237,
-0.034201301634311676,
-0.0309675894677639,
0.005829602479934692,
-0.02727917581796646,
-0.045585837215185165,
0.03368997201323509,
0.007536446209996939,
0.05473978444933891,
-0.009270663373172283,
-0.062416911125183105,
0.055780451744794846,
-0.0014196379343047738,
-0.013955902308225632,
-0.01177162490785122,
0.005395874846726656,
0.0005993400700390339,
-0.020772259682416916,
-0.0014393109595403075,
0.02590661309659481,
0.0045465813018381596,
0.00790002103894949,
0.033088568598032,
0.059934020042419434,
0.03585532680153847,
0.0035980618558824062,
-0.034644994884729385,
0.0037722091656178236,
-0.0071976445615291595,
0.02864251844584942,
0.03738238289952278,
-0.043608393520116806,
0.028589241206645966,
-0.004640483297407627,
0.007667196448892355,
0.027362899854779243,
0.05053095147013664,
-0.06790845841169357,
0.06781251728534698,
0.014664535410702229,
0.03509470447897911,
-0.011374601162970066,
0.055390436202287674,
-0.0034399526193737984,
-0.06100129708647728,
-0.009428576566278934,
0.020659223198890686,
0.014074046164751053,
-0.04596300423145294,
-0.013371879234910011,
0.032082054764032364,
0.04618833214044571,
-0.03625987842679024,
-0.036185186356306076,
0.016948778182268143,
-0.01070275716483593,
0.029050664976239204,
-0.029066279530525208,
-0.014462066814303398,
0.0497632659971714,
0.058849137276411057,
0.02042221836745739,
0.01482478342950344,
-0.0716339573264122,
0.004822137299925089,
-0.04643164947628975,
0.010277090594172478,
-0.001208198838867247,
0.04470013454556465,
-0.023353254422545433,
0.011274122633039951,
0.04518060013651848,
-0.0025424519553780556,
-0.018869565799832344,
0.012589819729328156,
-0.06720222532749176,
-0.030677566304802895,
-0.024901308119297028,
0.030868971720337868,
-0.03137241676449776,
-0.036137182265520096,
-0.023296749219298363,
0.015278970822691917,
-0.01267736591398716,
0.01885933056473732,
-0.03961502015590668,
-0.02054504305124283,
0.020818419754505157,
-0.028346579521894455,
-0.044316407293081284,
-0.02109386958181858,
0.0022254411596804857,
0.05138257145881653,
-0.053670722991228104,
-0.007284738589078188,
0.020160045474767685,
0.006714264862239361,
0.01833377592265606,
-0.037777505815029144,
0.04987851157784462,
0.06868252158164978,
0.048598289489746094,
0.01953408494591713,
0.004638987127691507,
-0.01482980977743864,
-0.0010443507926538587,
0.044484980404376984,
0.0718134343624115,
-0.017549792304635048,
0.003492200281471014,
-0.006956323981285095,
-0.06037046015262604,
-0.030015522614121437,
-0.00278488639742136,
0.05442167818546295,
-0.0088481605052948,
0.03264500945806503,
0.04225312918424606,
0.022217389196157455,
-0.02195482887327671,
0.0443037711083889,
0.07566191256046295,
0.02928818017244339,
-0.10069645196199417,
-0.022767992690205574,
0.00633361516520381,
-0.003987399861216545,
-0.0120664918795228,
0.01998814195394516,
0.016941633075475693,
-0.022134460508823395,
0.023667840287089348,
0.022976329550147057,
-0.007992884144186974,
-0.040829308331012726,
-0.06138775497674942,
0.04135362431406975,
0.02581741474568844,
-0.002992155496031046,
0.00004340365558164194,
0.010062577202916145,
0.006528015248477459,
0.017266184091567993,
0.047266796231269836,
0.0062523093074560165,
-0.028690723702311516,
0.007213997654616833,
0.03762113302946091,
0.01913193240761757,
0.0007997912471182644,
-0.019456293433904648,
-0.040926311165094376,
0.039740800857543945,
0.0032410321291536093,
0.006850993260741234,
0.033508334308862686,
0.0014024010160937905,
0.0056650335900485516,
0.01861003041267395,
-0.02206600457429886,
-0.052311528474092484,
0.007727988995611668,
-0.009934522211551666,
-0.003539314726367593,
-0.015138113871216774,
-0.011687058955430984,
-0.012556158937513828,
0.02002246491611004,
-0.024065284058451653,
0.028302228078246117,
-0.01808934658765793,
0.028788670897483826,
0.023202266544103622,
0.016691749915480614,
0.0003648216661531478,
-0.07948079705238342,
-0.025952579453587532,
-0.005824510473757982,
0.0016943769296631217,
0.030207650735974312,
-0.032925378531217575,
-0.018476702272892,
-0.018388671800494194,
0.01920381747186184,
0.024267541244626045,
-0.013325454667210579,
-0.038942597806453705,
0.07382723689079285,
0.040526457130908966,
-0.05328776687383652,
0.017992453649640083,
0.010062109678983688,
-0.00758241256698966,
-0.025638865306973457,
-0.03657776489853859,
0.0443432442843914,
-0.02603248879313469,
-0.008676178753376007,
-0.018679579719901085,
-0.010569744743406773,
-0.04573867842555046,
0.018905609846115112,
-0.01123865507543087,
0.002372205490246415,
-0.001204626983962953,
-0.04460516571998596,
-0.004961955361068249,
0.010025829076766968,
-0.015529855154454708,
-0.0007476024911738932,
-0.034546513110399246,
0.005083849187940359,
0.01215788722038269,
0.007688191253691912,
0.011846572160720825,
-0.028506610542535782,
-0.008989956229925156,
0.002184507204219699,
0.012761190533638,
-0.0034335937816649675,
-0.03900034353137016,
-0.030833851546049118,
0.04051661491394043,
-0.05363998934626579,
0.05647607892751694,
-0.013641216792166233,
-0.000936269701924175,
-0.04714329168200493,
-0.04165242612361908,
-0.026395639404654503,
0.025242600589990616,
-0.03335602208971977,
0.036430902779102325,
-0.03584195300936699,
0.032230131328105927,
0.0033007615711539984,
0.022844664752483368,
-0.10112554579973221,
-0.013184722512960434,
0.006201412063091993,
0.01717934012413025,
-0.019414406269788742,
-0.02041787840425968,
-0.02762467786669731,
-0.02238304354250431,
-0.04245079308748245,
0.021415388211607933,
0.04934091493487358,
-0.008329426869750023,
0.004651809111237526,
0.030846644192934036,
0.032371826469898224,
0.025030724704265594,
-0.007095562294125557,
-0.0011629100190475583,
0.011549128219485283,
-0.034654971212148666,
-0.00001533486101834569,
0.021917888894677162,
0.02808069996535778,
-0.018325870856642723,
0.0038527532014995813,
0.004903286695480347,
0.006360806990414858,
0.012079249136149883,
-0.060388922691345215,
-0.01247287169098854,
0.023582370951771736,
0.020593540742993355,
0.03771872818470001,
0.0037777526304125786,
-0.032100845128297806,
-0.043310172855854034,
0.03554720804095268,
-0.011534611694514751,
0.013252555392682552,
-0.01287223119288683,
-0.02033071406185627,
0.057028405368328094,
0.005201338324695826,
0.0264386348426342,
0.016764190047979355,
0.04678189009428024,
0.03670568764209747,
-0.025732647627592087,
0.01069777924567461,
-0.030624868348240852,
-0.0034512504935264587,
0.019731348380446434,
0.00512038916349411,
0.040404342114925385,
-0.0025844499468803406,
-0.007063396740704775,
-0.017847029492259026,
-0.02052268572151661,
0.018898122012615204,
0.04888655245304108,
-0.0005456003127619624,
0.014834512956440449,
0.01860249787569046,
-0.03178638964891434,
0.004668844398111105,
-0.003900231095030904,
-0.02042365074157715,
0.026720911264419556,
-0.010766016319394112,
0.02955780364573002,
-0.03599875792860985,
-0.01962747797369957,
0.025085709989070892,
0.025624753907322884,
0.010975194163620472,
0.027216574177145958,
0.05018918588757515,
0.02610384114086628,
0.004215127322822809,
0.0008741333149373531,
-0.052916519343853,
0.09972863644361496,
-0.018567705526947975,
0.013224424794316292,
0.004808090161532164,
-0.018802685663104057,
0.029699955135583878,
0.009945107623934746,
0.030535316094756126,
-0.02767631784081459,
-0.04260507971048355,
-0.06307625025510788,
0.03640040010213852,
0.025445425882935524,
0.014696416445076466,
-0.027075687423348427,
0.0060906619764864445,
0.015678565949201584,
0.0028564988169819117,
0.005744498688727617,
0.030824778601527214,
-0.04319091886281967,
0.004128029104322195,
-0.02539731003344059,
-0.025399284437298775,
0.01892327144742012,
-0.0005994192324578762,
-0.02436436153948307,
0.051108039915561676,
-0.005162664223462343,
-0.00280734128318727,
0.017465872690081596,
0.027490774169564247,
-0.016603535041213036,
0.07560045272111893,
-0.00625238474458456,
0.04584158584475517,
-0.020388446748256683,
0.02007961831986904,
0.10979597270488739,
0.04151999577879906,
0.01584685780107975,
-0.05778510123491287,
0.019044054672122,
-0.0070956116542220116,
0.0037723793648183346,
-0.01925957016646862,
0.02024557627737522,
0.0267690010368824,
-0.0039080423302948475,
0.0027592831756919622,
0.04791617766022682,
-0.006708875764161348,
0.021065259352326393,
0.0615525022149086,
-0.04420265182852745,
-0.04939090833067894,
0.02281021513044834,
-0.00669365469366312,
-0.004337914753705263,
0.013975093141198158,
-0.08833812922239304,
0.015071520581841469,
0.005259497091174126,
-0.0064288838766515255,
-0.03385965898633003,
-0.039430100470781326,
0.032097846269607544,
0.03138022869825363,
0.007868636399507523,
-0.013641102239489555,
-0.04045971855521202,
-0.02565423958003521,
-0.07038520276546478,
-0.011084063909947872,
0.00367329316213727,
-0.035647232085466385,
0.02721237950026989,
0.0018986072391271591,
-0.018831375986337662,
0.033047061413526535,
-0.010306106880307198,
0.03188232332468033,
-0.04139257222414017,
0.008886709809303284,
0.01421291008591652,
0.04525686800479889,
-0.009928763844072819,
0.023198986425995827,
0.005156302358955145,
0.016563164070248604,
0.015883132815361023,
-0.036945413798093796,
-0.02144468203186989,
0.007232029922306538,
0.0401107519865036,
0.00598335824906826,
-0.0274485033005476,
-0.05367622151970863,
0.013476266525685787,
-0.026051310822367668,
0.024151822552084923,
-0.027432532981038094,
-0.017766136676073074,
0.03456637263298035,
-0.015816258266568184,
0.040217481553554535,
-0.003359817201271653,
-0.03454705700278282,
-0.01740109920501709,
-0.02184942550957203,
-0.03457823395729065,
-0.04016392305493355,
-0.013267387636005878,
-0.015105899423360825,
0.05264563485980034,
0.00958805438131094,
0.014193828217685223,
-0.011638486757874489,
-0.04153813049197197,
0.0160093754529953,
-0.013501293025910854,
0.009254097938537598,
-0.024087700992822647,
-0.02823990024626255,
0.027222180739045143,
0.033912256360054016,
0.003206187393516302,
-0.05518866330385208,
0.001348454738035798,
0.02291627787053585,
0.01628083363175392,
-0.01591331698000431,
-0.0209669042378664,
0.0023233387619256973,
-0.062278859317302704,
0.007449939846992493,
-0.010473912581801414,
-0.037918735295534134,
0.03032107651233673,
-0.035953301936388016,
-0.021054057404398918,
0.011279013007879257,
-0.04583403095602989,
-0.00891229696571827,
0.023184485733509064,
-0.025539886206388474,
-0.006232773885130882,
0.0014344966039061546,
0.007823177613317966,
0.0016235134098678827,
-0.0768226832151413,
0.0076650893315672874,
-0.006169021595269442,
0.03064660355448723,
0.011355224065482616,
-0.020704515278339386,
-0.024900294840335846,
0.009813173674046993,
-0.01320860255509615,
-0.006683766841888428,
-0.023631419986486435,
-0.057093244045972824,
0.020296039059758186,
0.00988691858947277,
0.00709201954305172,
0.0030291674192994833,
0.005258283112198114,
-0.0024788537994027138,
-0.0007089196587912738,
0.02497192844748497,
0.022538060322403908,
0.017231909558176994,
0.011282788589596748,
-0.004870369099080563,
0.024908743798732758,
0.05461655929684639,
-0.009175930172204971,
-0.00662078196182847,
0.06157800927758217,
-0.03983170911669731,
-0.049244094640016556,
0.04342649132013321,
-0.007330270949751139,
-0.009689743630588055,
0.013686014339327812,
-0.013312319293618202,
-0.043804753571748734,
0.029742229729890823,
-0.04068700224161148,
-0.019962051883339882,
-0.011499128304421902,
-0.0437757782638073,
0.014338972978293896,
-0.06032492592930794,
-0.023632852360606194,
-0.0027139114681631327,
0.004028635565191507,
0.03634706139564514,
0.041141118854284286,
-0.013860355131328106,
-0.0250545684248209,
-0.0184747576713562,
0.015245793387293816,
0.041718073189258575,
0.03688682243227959,
0.033781711012125015,
-0.007580927573144436,
0.04564902186393738,
-0.023855065926909447,
0.011404832825064659,
-0.011193971149623394,
-0.017587143927812576,
-0.08593006432056427,
-0.033311910927295685,
0.025995858013629913,
0.012929617427289486,
0.047614000737667084,
-0.0314609669148922,
0.013694560155272484,
-0.0007633612840436399,
-0.03230661898851395,
0.020040404051542282,
-0.02918371744453907,
-0.038900334388017654,
-0.03773127496242523,
-0.030580904334783554,
-0.04220229387283325,
0.052961066365242004,
0.01637236587703228,
0.004396832548081875,
-0.006584322080016136,
-0.01760191284120083,
0.003350362181663513,
-0.037103116512298584,
-0.012213495559990406,
0.02558749169111252,
-0.0008464488200843334,
-0.03301238268613815,
0.02782605029642582,
-0.0196682121604681,
-0.0157819502055645,
0.012081523425877094,
-0.004156597889959812,
-0.0435691699385643,
-0.01101895235478878,
0.027999388054013252,
0.020256150513887405,
0.02291775308549404,
0.02726520411670208,
-0.0066599491983652115,
0.006491746287792921,
-0.014595309272408485,
0.03379390388727188,
0.001959351124241948,
0.03620445728302002,
-0.011693025007843971,
-0.023872993886470795,
-0.031093332916498184,
-0.008472952991724014,
0.03585665300488472,
-0.012163658626377583,
-0.03809107467532158,
-0.018165547400712967,
-0.017047788947820663,
0.00557074137032032,
-0.036738742142915726,
0.020321931689977646,
-0.04451495036482811,
-0.00835284125059843,
0.02868226356804371,
0.014219867996871471,
0.022159019485116005,
0.03576071932911873,
-0.003883371129631996,
0.010772851295769215,
0.04981662705540657,
0.04397033900022507,
-0.030369875952601433,
-0.0578492097556591,
0.00078278046566993,
0.016782835125923157,
0.005738404579460621,
0.00523929251357913,
-0.015556888654828072,
0.0026151754427701235,
0.03675365820527077,
0.0439705029129982,
0.007957802154123783,
-0.04019111767411232,
-0.04247084632515907,
0.01245466060936451,
-0.03671586513519287,
0.052686844021081924,
-0.008706318214535713,
0.011408194899559021,
-0.011084283702075481,
-0.02445756457746029,
0.013307028450071812,
0.040378835052251816,
0.04239395633339882,
0.027333993464708328,
-0.05363750085234642,
0.012370476499199867,
-0.009924031794071198,
0.0011468383017927408,
-0.02022222802042961,
-0.004144979175180197,
0.004438499920070171,
0.006491201929748058,
0.008571443147957325,
-0.03027176670730114,
-0.01682423986494541,
0.05844976007938385,
0.0033654363360255957,
-0.039136532694101334,
-0.023439237847924232,
-0.024873284623026848,
-0.04886438697576523,
0.02838340774178505,
0.013641063123941422,
-0.005848668981343508,
0.07352569699287415,
-0.015176274813711643,
0.036114130169153214,
0.03450216352939606,
0.01484502200037241,
-0.021369101479649544,
0.0411425419151783,
-0.03904448822140694,
-0.025860413908958435,
-0.02029028721153736,
-0.007274745497852564,
0.06788908690214157,
-0.029298149049282074,
-0.02836264669895172,
0.01840590499341488,
-0.04096755385398865,
0.008648031391203403,
0.04863006994128227,
0.010390297509729862,
0.05764533206820488,
-0.005119640380144119,
-0.020134808495640755,
0.016491562128067017,
0.00486546428874135,
0.007082400377839804,
0.09034737199544907,
0.02094998210668564,
0.03423886001110077,
-0.010161284357309341,
0.02074098400771618,
-0.028678227216005325,
0.007535288576036692,
-0.00732543645426631,
0.01479550264775753,
-0.019902251660823822,
0.021252065896987915,
0.014249819330871105,
-0.018635723739862442,
0.06301850825548172,
-0.018585266545414925,
-0.015189227648079395,
0.0786663144826889,
-0.043126847594976425,
0.01989373192191124,
-0.02870607003569603,
0.0014460523379966617,
-0.006737786345183849,
0.0037969399709254503,
0.033783942461013794,
0.08105703443288803,
-0.006478570401668549,
-0.03813667595386505,
-0.03981202840805054,
0.004150028340518475,
0.02845742553472519,
-0.05207901448011398,
-0.00631778733804822,
0.01774238795042038,
-0.01367989182472229,
0.021145641803741455,
-0.015543106943368912,
0.0017033397452905774,
0.006248152814805508,
-0.016296610236167908,
0.005503020249307156,
0.03749581798911095,
0.02035875804722309,
-0.0071433428674936295,
-0.0019822828471660614,
0.06978000700473785,
-0.025002924725413322,
-0.02600393444299698,
-0.008275732398033142,
0.001377339824102819,
-0.030866580083966255,
0.019202854484319687
] |
<p>$E = h\nu$ and $P = h\nu/c$ in vacuum.
If a photon enters water, it's frequency $\nu$ doesn't change.
What are its energy and momentum : $h\nu$ ? and $h\nu/c$ ?
Since part of it's energy and momentum have been transferred to water, it should be less.</p>
<p>If water's refractive index is $n$, Are the energy and momentum equal to $h\nu/n$ and $h\nu/c/n$ ? </p> | 1,006 | [
-0.01628621481359005,
-0.03713234141469002,
-0.013009844347834587,
-0.017557520419359207,
0.02879982627928257,
0.013054721988737583,
-0.06989912688732147,
-0.03499183431267738,
-0.013446105644106865,
-0.046661291271448135,
0.055567171424627304,
0.05939000844955444,
0.059128712862730026,
0.024343734607100487,
0.025073712691664696,
0.02563830092549324,
0.0010942387161776423,
-0.014203195460140705,
-0.02335863560438156,
-0.009503325447440147,
-0.00925565604120493,
0.012836210429668427,
-0.005160490516573191,
0.01508500799536705,
-0.044478703290224075,
0.01971222274005413,
0.009403531439602375,
-0.015338613651692867,
0.046425167471170425,
0.04317817464470863,
0.017522381618618965,
-0.02846449241042137,
0.012016630731523037,
0.006586873438209295,
-0.024023201316595078,
0.016742877662181854,
-0.0392635278403759,
-0.0334429070353508,
-0.02358209155499935,
0.02535521425306797,
-0.016411883756518364,
0.01032360177487135,
-0.004849668592214584,
0.0186983123421669,
-0.012110894545912743,
0.01196425873786211,
0.03684503957629204,
-0.02355956844985485,
0.03438981622457504,
-0.06069312244653702,
0.055235642939805984,
-0.004442234989255667,
0.03576088696718216,
-0.01098545640707016,
-0.019819673150777817,
-0.01972418650984764,
0.07756944000720978,
0.06987550109624863,
0.02147306688129902,
-0.05339862033724785,
0.00830572284758091,
-0.004636374302208424,
-0.03263179957866669,
0.014361412264406681,
-0.01105231698602438,
0.007235642522573471,
-0.013749487698078156,
-0.007218597456812859,
0.02419608272612095,
0.02280295081436634,
0.011097223497927189,
-0.017491398379206657,
0.04274580627679825,
0.009768393822014332,
0.003958219196647406,
-0.01864098757505417,
0.008071132935583591,
0.052289318293333054,
0.014081091620028019,
0.05710405856370926,
-0.011882600374519825,
0.005178200546652079,
0.0313563346862793,
0.02346123196184635,
0.008039637468755245,
-0.01172583270817995,
0.046517159789800644,
-0.00929567962884903,
0.029337992891669273,
0.011634595692157745,
0.013209773227572441,
0.025501415133476257,
-0.009881170466542244,
-0.005231693387031555,
0.02102910354733467,
-0.0023233932442963123,
0.0018675463506951928,
0.043572232127189636,
0.01201130636036396,
-0.04333203285932541,
0.0021974598057568073,
0.008888088166713715,
0.02903689444065094,
0.09536609053611755,
-0.0005835004849359393,
-0.05191701650619507,
-0.0350973978638649,
0.01502174697816372,
-0.049430135637521744,
0.0015912636881694198,
-0.00939708761870861,
0.014497242867946625,
-0.03201790153980255,
-0.01499374583363533,
0.012509649619460106,
-0.03457845374941826,
0.04044269025325775,
-0.026846036314964294,
0.1107991486787796,
0.08333741128444672,
0.03461867570877075,
-0.033889420330524445,
0.00272849528118968,
-0.0029421402141451836,
-0.0808221846818924,
0.0073817092925310135,
0.027043890208005905,
0.034004487097263336,
-0.05060116946697235,
-0.013166608288884163,
-0.020446497946977615,
0.007861418649554253,
0.03319776430726051,
-0.0054297237657010555,
0.012493587099015713,
-0.016394134610891342,
-0.10630620270967484,
-0.055608369410037994,
0.03216547518968582,
-0.02986004762351513,
-0.039064932614564896,
-0.10231287777423859,
0.03325130045413971,
0.0339697003364563,
0.06565725803375244,
-0.015825051814317703,
-0.003326845122501254,
-0.004610467702150345,
0.02524413727223873,
-0.013813628815114498,
-0.009783925488591194,
0.020073657855391502,
-0.008490227162837982,
-0.025697115808725357,
0.0063943699933588505,
-0.056980956345796585,
-0.015899665653705597,
0.051030341535806656,
-0.006056393962353468,
-0.008256463333964348,
0.07135132700204849,
-0.057222072035074234,
0.0055345213040709496,
0.028966695070266724,
0.015905726701021194,
-0.04901515319943428,
0.03161304444074631,
0.04099705070257187,
0.04295574501156807,
0.0036554632242769003,
0.008458232507109642,
0.014666175469756126,
-0.02465183660387993,
0.012641137465834618,
0.04863075539469719,
-0.030129095539450645,
-0.00919399131089449,
-0.021002693101763725,
0.02902190387248993,
-0.015915624797344208,
-0.020356887951493263,
-0.041121069341897964,
-0.02744208090007305,
0.018352996557950974,
0.0020721356850117445,
0.009012117050588131,
0.007003442849963903,
-0.0328717939555645,
-0.0441630519926548,
-0.03707931563258171,
0.009959837421774864,
-0.03124101273715496,
0.011297115124762058,
0.016055865213274956,
0.019167542457580566,
0.03200994431972504,
0.002573465695604682,
-0.005202995613217354,
-0.027345459908246994,
-0.01569194719195366,
0.004066310822963715,
0.046412426978349686,
-0.0006909834919497371,
-0.008645781315863132,
0.04131621867418289,
0.037986088544130325,
0.04499756544828415,
0.013381398282945156,
-0.010972518473863602,
-0.021640703082084656,
-0.02651781029999256,
-0.005732783116400242,
0.007621940691024065,
0.016089359298348427,
-0.016828157007694244,
-0.017730308696627617,
0.02063388004899025,
-0.003823675448074937,
0.029490448534488678,
0.003213185351341963,
-0.004281005822122097,
0.0655096024274826,
0.036485057324171066,
0.0009231805452145636,
0.040536876767873764,
0.035745155066251755,
-0.017118223011493683,
0.02695555053651333,
0.005443581845611334,
-0.025574808940291405,
-0.02378653548657894,
-0.009113642387092113,
0.009951349347829819,
0.013573902659118176,
-0.02845468558371067,
0.0063902814872562885,
0.004058659076690674,
0.03399326652288437,
0.0699232742190361,
0.016487210988998413,
-0.030050046741962433,
-0.06929957866668701,
0.010539902374148369,
0.034063614904880524,
0.006452609784901142,
0.020513195544481277,
0.011509264819324017,
0.028188548982143402,
0.038988351821899414,
-0.049669794738292694,
0.022982006892561913,
0.01868426240980625,
-0.001519027748145163,
0.03000408597290516,
-0.015726344659924507,
-0.04773725941777229,
0.019271427765488625,
-0.05378109589219093,
-0.008845774456858635,
0.017368512228131294,
0.004135723225772381,
0.011618098244071007,
-0.06617701053619385,
-0.01926342584192753,
-0.026460057124495506,
-0.0034564705565571785,
0.003268191358074546,
0.007486448623239994,
0.024876421317458153,
-0.05355612933635712,
0.03647444397211075,
-0.007608933374285698,
0.011400725692510605,
-0.018325304612517357,
-0.015123811550438404,
0.044716816395521164,
-0.0003304816491436213,
0.01892741769552231,
-0.0586867593228817,
-0.039801642298698425,
0.021930571645498276,
-0.031071757897734642,
-0.06860239058732986,
-0.0078196469694376,
-0.014054295606911182,
0.013716314919292927,
-0.026631170883774757,
-0.026352014392614365,
0.024265386164188385,
-0.022905973717570305,
-0.009807722643017769,
0.06177432835102081,
0.00044493124005384743,
-0.06251528859138489,
-0.013460696674883366,
-0.032000865787267685,
-0.0043679396621882915,
-0.034000277519226074,
0.0062120044603943825,
0.06316415965557098,
-0.024570951238274574,
-0.006773435045033693,
0.01655556447803974,
-0.0026898575015366077,
-0.06549366563558578,
-0.01466224156320095,
-0.0029084256384521723,
0.002809530356898904,
-0.021992197260260582,
0.010570288635790348,
0.0216197669506073,
-0.03929658979177475,
0.029355201870203018,
-0.047974005341529846,
-0.056923553347587585,
0.05794209986925125,
-0.010459045879542828,
0.056304771453142166,
0.00398451229557395,
-0.028698373585939407,
0.053836677223443985,
0.048989683389663696,
-0.04664618894457817,
0.004703881219029427,
0.010996048338711262,
0.0012818039394915104,
-0.02313089743256569,
0.0017790067940950394,
0.045367881655693054,
-0.010823276825249195,
-0.018455343320965767,
0.0057077789679169655,
0.01625804603099823,
0.0027393102645874023,
0.030755696818232536,
0.01081722229719162,
0.013104666955769062,
0.035343315452337265,
0.009907680563628674,
0.0361679270863533,
-0.010715548880398273,
-0.00967145524919033,
0.005666179582476616,
-0.01323202159255743,
0.030034329742193222,
0.033670373260974884,
0.010914916172623634,
0.0892648994922638,
0.03217233344912529,
-0.021259592846035957,
-0.026490680873394012,
0.04780855402350426,
-0.007250593975186348,
-0.016152273863554,
0.02360999584197998,
0.004198265727609396,
0.03888353332877159,
-0.002798641799017787,
-0.0029334654100239277,
0.029180588200688362,
0.059576209634542465,
-0.023431017994880676,
-0.022350523620843887,
-0.011106803081929684,
-0.00012381054693832994,
0.024531574919819832,
-0.04866907745599747,
0.0026362251956015825,
0.06731343269348145,
0.03952733427286148,
0.03589032217860222,
-0.030075598508119583,
-0.03338941931724548,
-0.03451954945921898,
-0.0050154137425124645,
-0.014772814698517323,
0.012131527997553349,
0.04304291680455208,
0.011273442767560482,
0.0841115340590477,
0.02707475982606411,
0.03252187743782997,
0.016286587342619896,
0.004693292547017336,
-0.06875577569007874,
0.010524208657443523,
-0.029987545683979988,
-0.019708339124917984,
-0.02440699189901352,
-0.01147886086255312,
-0.027931420132517815,
-0.040496982634067535,
-0.04723856598138809,
0.004268392454832792,
-0.009025034494698048,
-0.02308196760714054,
0.03317888826131821,
-0.03738498315215111,
-0.05168737471103668,
-0.01624985598027706,
0.06166790798306465,
0.01861845888197422,
-0.006743802223354578,
-0.00027920177672058344,
0.0476592518389225,
-0.03627887740731239,
-0.0007582003017887473,
0.004277778789401054,
-0.012171564623713493,
0.004416787065565586,
0.04813414812088013,
0.04324096813797951,
-0.011196224950253963,
0.005025184713304043,
0.005502648185938597,
0.029256634414196014,
0.01743117719888687,
-0.00016788586799521,
-0.014697950333356857,
-0.023300448432564735,
-0.01614394783973694,
-0.008358332328498363,
0.0001740737061481923,
0.06041925027966499,
-0.013257256709039211,
-0.017762821167707443,
-0.0072631631046533585,
-0.032385554164648056,
-0.008815505541861057,
0.07382959872484207,
0.0331549271941185,
0.0087202750146389,
0.014421331696212292,
-0.04287385940551758,
0.026453204452991486,
-0.03527286276221275,
-0.0076440684497356415,
-0.009466107003390789,
0.013667231425642967,
-0.03783581033349037,
-0.028457747772336006,
0.007875864394009113,
-0.00031649789889343083,
-0.006467421073466539,
-0.012400317005813122,
-0.008905947208404541,
-0.03012903593480587,
-0.015945153310894966,
-0.019017472863197327,
-0.01663343794643879,
0.04717268794775009,
0.02826106734573841,
-0.019232533872127533,
0.003772302996367216,
-0.06359077990055084,
-0.021719887852668762,
0.02445726841688156,
0.05172062665224075,
-0.0030623949132859707,
-0.01800142601132393,
-0.06128431111574173,
-0.004521474242210388,
0.005711887031793594,
-0.038304708898067474,
0.002294940175488591,
0.01074344664812088,
0.02082909643650055,
0.006142243277281523,
-0.04024955630302429,
0.0015954591799527407,
0.021332425996661186,
-0.0283725094050169,
0.01815182901918888,
-0.06095300242304802,
-0.021968521177768707,
-0.00780641520395875,
0.0399644710123539,
0.030387606471776962,
0.05211954936385155,
-0.02372836135327816,
-0.007522284053266048,
0.0018654329469427466,
-0.0208907313644886,
-0.02361346408724785,
-0.09543665498495102,
0.030442597344517708,
0.00035985151771456003,
0.030186155810952187,
0.028703629970550537,
-0.020644137635827065,
-0.058818329125642776,
0.042173851281404495,
0.041149843484163284,
-0.048582859337329865,
-0.007555020973086357,
-0.04906368628144264,
0.01819349266588688,
-0.008715028874576092,
-0.00764644518494606,
0.051792848855257034,
0.0397745817899704,
-0.0494290255010128,
-0.007996858097612858,
-0.0543769933283329,
0.05296722427010536,
-0.046450212597846985,
0.006924694404006004,
-0.020502835512161255,
0.0057906522415578365,
-0.012780648656189442,
0.06709416955709457,
-0.011760907247662544,
0.0011525742011144757,
0.03324904292821884,
-0.012863815762102604,
-0.028827285394072533,
-0.0019165424164384604,
0.014222027733922005,
-0.011254626326262951,
0.01044350303709507,
0.002140440046787262,
-0.00367798563092947,
0.011729567311704159,
0.05632814019918442,
0.004047062713652849,
0.002290075644850731,
0.01761314831674099,
0.00888256635516882,
0.014679040759801865,
-0.016006426885724068,
-0.003783469321206212,
0.021126285195350647,
-0.05080694332718849,
0.027183588594198227,
-0.021908868104219437,
0.008333704434335232,
0.024600880220532417,
-0.016537144780158997,
-0.0456991046667099,
0.00996363814920187,
-0.020322391763329506,
0.03630946949124336,
-0.04719432070851326,
0.01152443140745163,
0.034803904592990875,
0.04386138916015625,
-0.01904599741101265,
-0.030345212668180466,
0.009069135412573814,
0.026193169876933098,
-0.0014839546056464314,
-0.037618979811668396,
0.03007846511900425,
-0.04044719412922859,
-0.035980015993118286,
-0.018966300413012505,
0.011547916568815708,
-0.026839181780815125,
-0.0026684929616749287,
-0.007944096811115742,
0.013196457177400589,
0.0479404516518116,
-0.006632242351770401,
-0.01800551638007164,
0.00431092968210578,
-0.0030245676171034575,
-0.01308587845414877,
-0.005893774330615997,
0.051416609436273575,
0.00032197090331465006,
-0.04495496302843094,
0.012956907972693443,
-0.007887864485383034,
0.03366360068321228,
0.012525384314358234,
-0.0017740246839821339,
0.03293294832110405,
0.020731445401906967,
-0.03031601943075657,
-0.008910313248634338,
0.03257634863257408,
0.010778963565826416,
0.07310275733470917,
-0.0076438928954303265,
-0.004550549201667309,
-0.04152604565024376,
-0.039562951773405075,
0.018146289512515068,
-0.016472306102514267,
0.020843278616666794,
-0.02589527703821659,
0.056142546236515045,
-0.035457514226436615,
0.0084356889128685,
-0.005376407410949469,
-0.0061748577281832695,
0.010501081123948097,
0.013987977057695389,
-0.034436821937561035,
-0.015921825543045998,
-0.0014695740537717938,
0.003982486668974161,
-0.04169241338968277,
-0.07315734773874283,
-0.018469538539648056,
0.08161206543445587,
0.0013704623561352491,
0.0466882698237896,
0.004354947712272406,
0.010990772396326065,
0.017532119527459145,
-0.01801576279103756,
-0.020407725125551224,
0.045740481466054916,
-0.01843889057636261,
0.02216232568025589,
0.00016043295909184963,
-0.008271756581962109,
0.04913085326552391,
0.0475088469684124,
-0.007099571172147989,
0.052934903651475906,
0.01837782748043537,
0.02281525917351246,
0.01718277484178543,
-0.06452299654483795,
-0.05622686818242073,
0.02930777333676815,
-0.039272475987672806,
0.03824681043624878,
-0.0099950535222888,
0.002994533395394683,
0.051452044397592545,
0.01719183661043644,
-0.02236303687095642,
-0.04434710741043091,
-0.0016868991078808904,
-0.040533874183893204,
-0.02665765956044197,
-0.00543340016156435,
0.00878737960010767,
-0.015155588276684284,
0.04231512174010277,
0.025407057255506516,
-0.015854671597480774,
0.034541886299848557,
0.021442923694849014,
-0.0539468377828598,
-0.0017321774503216147,
-0.04539581388235092,
-0.04856622964143753,
0.020317442715168,
-0.024998841807246208,
-0.048167746514081955,
0.020497281104326248,
-0.041050247848033905,
0.008423141203820705,
0.024408642202615738,
0.01844125986099243,
-0.013504755683243275,
0.021364636719226837,
-0.004710516892373562,
0.015430915169417858,
0.005967437289655209,
0.014959986321628094,
0.12319202721118927,
0.05530189350247383,
0.005944688338786364,
-0.013649108819663525,
-0.0057425955310463905,
-0.028082195669412613,
0.047937020659446716,
-0.05282675474882126,
0.0015367335872724652,
-0.015383250080049038,
0.04470366612076759,
0.00133921776432544,
0.03237626701593399,
0.021530408412218094,
-0.009999671019613743,
0.00897910911589861,
-0.045531801879405975,
-0.021006233990192413,
0.008463170379400253,
-0.0008224347839131951,
-0.02378041483461857,
0.051223840564489365,
-0.010920009575784206,
0.02007061429321766,
-0.03963908553123474,
-0.006902971304953098,
-0.036810118705034256,
-0.0205782949924469,
0.03753587231040001,
-0.018521519377827644,
-0.05676053464412689,
-0.004885704256594181,
-0.029380561783909798,
-0.01828865520656109,
-0.010767942294478416,
0.04821988567709923,
0.04655833542346954,
-0.01627975143492222,
-0.043193988502025604,
-0.008558991365134716,
0.014970304444432259,
0.007738926447927952,
0.019344599917531013,
0.042050834745168686,
-0.06739228963851929,
-0.002011653268709779,
-0.03933750465512276,
0.04769209027290344,
0.003040161682292819,
-0.01842888630926609,
-0.007763825822621584,
0.010466228239238262,
-0.0158360805362463,
-0.06140703707933426,
-0.008078917860984802,
0.02860134281218052,
0.042602911591529846,
0.006256479304283857,
-0.019600920379161835,
-0.007502626162022352,
0.0017403308302164078,
-0.0008178511634469032,
0.03990685194730759,
0.004679497331380844,
-0.012451370246708393,
-0.031248873099684715,
0.0257439985871315,
-0.0008663879707455635,
-0.03648122772574425,
-0.014994547702372074,
0.0004319010768085718,
-0.003215125063434243,
-0.036933623254299164,
-0.04217200726270676,
-0.0006528845988214016,
0.04108644649386406,
0.0391194112598896,
0.006120496429502964,
0.011924062855541706,
-0.04284755885601044,
-0.1062551736831665,
0.03948645293712616,
-0.007538811769336462,
-0.028341548517346382,
-0.0509026013314724,
-0.025325709953904152,
0.021242963150143623,
0.03875552862882614,
-0.008658703416585922,
0.0025000139139592648,
0.007225544657558203,
0.009657936170697212,
0.053749844431877136,
-0.010170385241508484,
-0.03347527235746384,
0.006296790670603514,
-0.0021314488258212805,
-0.017597028985619545,
-0.004778783768415451,
0.04057430103421211,
0.03560665249824524,
0.003931581974029541,
0.02329329028725624,
0.0018769513117149472,
-0.039474498480558395,
-0.010525376535952091,
0.00845222920179367,
-0.001882007927633822,
0.02374340407550335,
0.028798094019293785,
0.034212514758110046,
-0.007616604212671518,
-0.010776938870549202,
-0.012401653453707695,
0.005880150943994522,
0.0046209171414375305,
0.016639577224850655,
0.010760873556137085,
0.021004891023039818,
-0.030844461172819138,
0.05490563064813614,
-0.035100001841783524,
-0.030252065509557724,
-0.02995735965669155,
0.02569766715168953,
0.01588677428662777,
-0.04080604016780853,
-0.03835798799991608,
0.029012322425842285,
-0.028094498440623283,
-0.04632258787751198,
0.03368118777871132,
0.005935435649007559,
0.010880627669394016,
-0.011027724482119083,
0.032931748777627945,
-0.00021357109653763473,
0.0396527461707592,
0.020485326647758484,
-0.037677470594644547,
0.036580197513103485,
-0.020214727148413658,
-0.025246424600481987,
0.02249895967543125,
0.004172437824308872,
0.03943784162402153,
0.05538914352655411,
-0.03907466679811478,
0.0186112429946661,
0.06309150159358978,
-0.01145645510405302,
0.02175121009349823,
-0.014822899363934994,
-0.06714997440576553,
0.01178666576743126,
-0.012042290531098843,
0.025616910308599472,
0.015138335525989532,
-0.013923484832048416,
0.08194009214639664,
0.005537685938179493,
0.015769902616739273,
0.024049147963523865,
-0.001231457106769085,
-0.004493381828069687,
0.004765239544212818,
0.03665861859917641,
0.00854433886706829,
0.0022948223631829023,
0.03572767227888107,
-0.025090688839554787,
0.06483985483646393,
0.022503802552819252,
0.0014384511159732938,
-0.10019014775753021,
-0.017749929800629616,
-0.009229675866663456,
0.046993255615234375,
0.06312763690948486,
-0.055273570120334625,
0.03135622665286064,
0.03395400196313858,
-0.07105504721403122,
0.025032343342900276,
-0.0018909915816038847,
0.0018662931397557259,
-0.01710517331957817,
0.027907799929380417,
-0.019864259287714958,
0.028747789561748505,
-0.008812522515654564,
0.017359061166644096,
-0.015240496024489403,
0.022370614111423492,
-0.027376139536499977,
-0.01675110124051571,
-0.016755836084485054,
0.03185327723622322,
-0.009655823931097984,
0.028341813012957573,
0.05624350532889366,
-0.01128425169736147,
-0.03291129693388939,
-0.0005563122103922069,
0.0008361479267477989,
0.0412764810025692,
-0.00030763240647502244,
-0.012650692835450172,
0.02507936954498291,
0.024242443963885307,
-0.0014997405232861638,
-0.031795933842659,
-0.03858223930001259,
0.03663681447505951,
0.014491300098598003,
0.016312377527356148,
0.01934196427464485,
-0.011462943628430367,
0.030696071684360504,
-0.059932876378297806,
-0.03217506781220436,
0.004884063266217709,
-0.03366566821932793,
0.004552111960947514,
0.031507790088653564,
-0.03207375854253769,
0.007027472369372845,
-0.014395618811249733,
-0.008888608776032925,
-0.07359763979911804,
-0.006919774226844311,
0.04485532268881798,
-0.012529533356428146,
-0.0024823371786624193,
-0.01595732569694519,
0.021882439032197,
-0.02298859693109989,
0.016824087128043175,
0.015223395079374313,
-0.016169695183634758,
-0.04328934848308563,
-0.0026414920575916767,
0.012048732489347458,
-0.001882618642412126,
0.012439809739589691,
-0.03257819265127182,
-0.05429021641612053,
0.023461127653717995,
0.016503972932696342,
0.0060715447179973125,
-0.005059993825852871,
-0.01900171861052513,
-0.040487539023160934,
-0.041022591292858124,
-0.0025143357925117016,
0.010455382987856865,
0.012432023882865906,
-0.0533352755010128,
0.010569554753601551,
-0.0226282998919487,
0.038649965077638626,
0.045103125274181366,
0.02299155853688717,
-0.03040465898811817,
-0.007717120926827192,
-0.03175351023674011,
0.0042801727540791035,
-0.06391815096139908,
-0.012707548215985298,
-0.01877894066274166,
-0.022008104249835014,
-0.0031764425802975893,
0.014775378629565239,
-0.000641414662823081,
0.008952375501394272,
0.0003378350811544806,
-0.04434935376048088,
0.007615559734404087,
0.0008847369463182986,
-0.0023461373057216406,
0.03615043684840202,
-0.021414147689938545,
0.005274237133562565,
0.07148817926645279,
0.015417922288179398,
0.01966281235218048,
0.02630929835140705,
-0.037488408386707306,
-0.026304639875888824,
0.0009665442630648613,
-0.002697243122383952,
-0.003810805967077613,
0.027667813003063202,
-0.010052825324237347,
0.05351720005273819,
-0.03570377454161644,
0.023624803870916367,
0.044965483248233795,
-0.05088216811418533,
-0.01475441362708807,
0.07322640717029572,
0.007467042654752731,
0.0006488047074526548,
0.010480065830051899,
0.03381695598363876,
0.005406783893704414,
-0.03459462895989418,
-0.019813211634755135,
0.04239531233906746,
0.03434362635016441,
-0.023192143067717552,
0.05069404095411301,
0.02068718709051609,
-0.008479869924485683,
-0.01896199956536293,
0.02226434275507927,
0.01505916565656662,
-0.027755290269851685,
-0.015328693203628063,
0.05900440737605095,
0.014970047399401665,
-0.04870571568608284,
0.0036091438960283995,
-0.01982724666595459,
0.07162747532129288,
-0.0038170460611581802,
0.016017038375139236,
-0.03556215763092041,
0.0012134622083976865,
-0.012023048475384712,
0.06508933007717133,
0.0020750416442751884,
0.036465585231781006,
0.016394713893532753,
-0.0004964013351127505,
-0.035643722862005234,
-0.025448517873883247,
-0.022954218089580536,
-0.054139744490385056,
0.007273904047906399,
0.012372536584734917,
-0.009030739776790142,
-0.03335871174931526,
-0.015360025689005852,
0.011025636456906796,
-0.057668931782245636,
0.009111016988754272,
-0.008738174103200436,
0.003077048109844327,
0.028666308149695396,
0.0015102083561941981,
0.001557404757477343,
0.08450460433959961,
-0.03427968546748161,
-0.009882266633212566,
-0.022666340693831444,
0.0003640861250460148,
0.0006653174059465528,
-0.05510936304926872
] |
<p>consider the following:
<img src="http://i.stack.imgur.com/tpCcw.jpg" alt="enter image description here"></p>
<p>I need to find the minimal coeeficient of friction $\mu _{min}$ so that both recatngle boxes would remain static. The lower angle in the triangle is $2\alpha$ as indicated.
I ended up with this expression: $$\mu _{min}=\frac{m_2}{2\cdot m_1 \cdot \tan \alpha}$$
but the answer in the book is rather this one:
$$\frac{m_2}{(2m_1+m_2)\tan\alpha}$$
Who is correct?I know that the normal force that that the triangle is exerting on both is like this:
<img src="http://i.stack.imgur.com/qYGQr.jpg" alt="enter image description here">
(on both sides of course) so with geometry and soome FBD that's what I came out with.</p>
<p>Would like to hear your thoughts!</p> | 2,891 | [
-0.012064172886312008,
-0.02879459038376808,
0.0142718106508255,
0.029350636526942253,
-0.0029811707790941,
0.04855821281671524,
0.019697409123182297,
-0.018566610291600227,
-0.022659458220005035,
0.023089034482836723,
0.013004127889871597,
0.04867566004395485,
0.03683442622423172,
0.030012797564268112,
0.012991329655051231,
-0.015668462961912155,
-0.002486974699422717,
-0.03777506574988365,
0.016854729503393173,
-0.02625778317451477,
-0.018041828647255898,
0.0036369645968079567,
0.02690577507019043,
-0.01562623679637909,
-0.0073265391401946545,
0.025720592588186264,
0.021630777046084404,
-0.02257724665105343,
-0.01087562832981348,
0.013785120099782944,
-0.0071434639394283295,
-0.03808596730232239,
0.011778893880546093,
0.0010982952080667019,
-0.0066053601913154125,
0.02930673398077488,
-0.01913299970328808,
0.03159388527274132,
-0.009951517917215824,
0.026053844019770622,
-0.025430312380194664,
-0.028441201895475388,
-0.025635261088609695,
0.028602398931980133,
-0.009656621143221855,
0.006636686157435179,
0.05015973001718521,
-0.02524293027818203,
0.05390365794301033,
-0.06312884390354156,
0.05952844396233559,
-0.00018489097419660538,
0.03651520609855652,
0.03744275122880936,
-0.016289377585053444,
-0.03315316140651703,
0.06523092836141586,
0.04143517464399338,
0.01947476901113987,
-0.04616830497980118,
-0.018747126683592796,
-0.01346637774258852,
-0.028606055304408073,
-0.008333186618983746,
-0.034028828144073486,
0.014214051887392998,
-0.03523274138569832,
-0.026127316057682037,
0.045562438666820526,
0.00804179161787033,
0.006000453140586615,
0.008804828859865665,
0.03051403909921646,
-0.035965342074632645,
-0.003827114589512348,
-0.005041978321969509,
0.03174241632223129,
0.02919410727918148,
0.026641735807061195,
0.041396819055080414,
-0.008673254400491714,
0.021931298077106476,
0.06295479089021683,
0.08054604381322861,
0.0025318581610918045,
-0.04689183086156845,
0.0772458165884018,
-0.0014335568994283676,
0.0020276398863643408,
0.02277572639286518,
0.01313904207199812,
-0.003277463372796774,
0.02445967122912407,
0.029129404574632645,
-0.025314247235655785,
0.010782420635223389,
0.014158829115331173,
0.040160998702049255,
0.022649642080068588,
-0.03798568993806839,
0.001794410403817892,
-0.03689849004149437,
0.010881957598030567,
0.07392891496419907,
0.010316922329366207,
0.03298346698284149,
-0.05799777805805206,
0.02133204974234104,
0.010826978832483292,
0.017520422115921974,
-0.023906340822577477,
-0.012947818264365196,
-0.05847710743546486,
-0.011236507445573807,
0.03743957728147507,
-0.01601262390613556,
0.0058263856917619705,
0.028987431898713112,
0.05444914102554321,
0.03998022899031639,
0.045223359018564224,
-0.05485120043158531,
0.019247855991125107,
-0.035280484706163406,
-0.06317878514528275,
0.024423688650131226,
0.02684571035206318,
-0.019571814686059952,
-0.049374163150787354,
0.02977728098630905,
0.0341295450925827,
0.006829951424151659,
-0.028742533177137375,
0.012815502472221851,
0.00016002643678802997,
-0.019028792157769203,
-0.05139893665909767,
-0.07945700734853745,
0.053851548582315445,
-0.038984399288892746,
-0.000870560179464519,
-0.07529249787330627,
-0.030382433906197548,
0.038889627903699875,
0.05625046417117119,
-0.007027476094663143,
-0.006508879363536835,
0.024438146501779556,
0.04610366001725197,
-0.002077460754662752,
-0.0005441566463559866,
-0.00993327982723713,
-0.010926383547484875,
-0.03679371252655983,
-0.012884587049484253,
-0.06686271727085114,
0.015148835256695747,
0.017036257311701775,
0.010485810227692127,
-0.018749717622995377,
0.04906819015741348,
-0.028578780591487885,
-0.017828818410634995,
0.013529657386243343,
-0.004769118968397379,
-0.03963109105825424,
0.06366299837827682,
-0.0018859835108742118,
-0.00623973086476326,
0.011172092519700527,
-0.01779050938785076,
0.0413450188934803,
-0.0057907914742827415,
0.0019156774505972862,
0.030223162844777107,
-0.030558669939637184,
-0.011354795657098293,
-0.005030433181673288,
-0.026463568210601807,
0.051491886377334595,
-0.006378053221851587,
-0.0243486650288105,
-0.011508706957101822,
-0.00020982808200642467,
0.006269319914281368,
0.05199136957526207,
-0.020649243146181107,
-0.0007938433554954827,
0.0016296301037073135,
-0.03455532714724541,
-0.0272001214325428,
-0.06871446967124939,
0.0034646382555365562,
-0.0037148732226341963,
-0.02638024091720581,
-0.009160470217466354,
-0.02970314212143421,
-0.011547744274139404,
-0.027012504637241364,
-0.050723250955343246,
0.03879654034972191,
0.017938170582056046,
0.03025120683014393,
-0.011242462322115898,
0.029384389519691467,
0.040051016956567764,
0.03680599480867386,
0.007243887521326542,
0.029719054698944092,
-0.03634103387594223,
-0.0165270883589983,
0.011936760507524014,
-0.032782938331365585,
0.024618569761514664,
0.017663508653640747,
0.023986566811800003,
0.014943008311092854,
-0.013947349973022938,
-0.015017049387097359,
0.008251450955867767,
-0.03608744964003563,
0.04884491115808487,
0.027593985199928284,
0.019186461344361305,
0.019427739083766937,
0.009588485583662987,
-0.01710638590157032,
0.014792418107390404,
0.006685033906251192,
-0.02816610597074032,
-0.057949475944042206,
0.01917709968984127,
0.008897251449525356,
0.021707188338041306,
-0.08162899315357208,
0.030432425439357758,
0.00933355838060379,
-0.0031972064170986414,
0.03479781001806259,
0.024939246475696564,
0.03903123736381531,
-0.015414868481457233,
0.032162729650735855,
0.04537586122751236,
0.0077788615599274635,
0.05017402768135071,
0.021211301907896996,
0.03188614547252655,
-0.02362595871090889,
-0.003908931743353605,
-0.05147653445601463,
0.06477949023246765,
0.03193797916173935,
0.020280640572309494,
-0.021606557071208954,
0.024171948432922363,
0.035873182117938995,
-0.012283404357731342,
0.01524896640330553,
0.03582886606454849,
0.04138080030679703,
-0.011428152211010456,
-0.015934526920318604,
0.01460790354758501,
0.03250724449753761,
0.0023626945912837982,
-0.00041015702299773693,
-0.01616726815700531,
0.031468410044908524,
-0.011670132167637348,
-0.018025264143943787,
-0.0010971256997436285,
-0.006727271247655153,
0.02189873531460762,
-0.030365340411663055,
0.03282197192311287,
0.012171748094260693,
0.03826463967561722,
0.013754508458077908,
0.01845773495733738,
0.007206232752650976,
-0.02316570095717907,
0.019177313894033432,
-0.029064355418086052,
-0.05577316880226135,
-0.013956908136606216,
-0.04182146117091179,
-0.0037613986060023308,
0.05469391867518425,
0.017195964232087135,
0.018009748309850693,
0.0571635365486145,
-0.001090865582227707,
-0.07089299708604813,
-0.048479799181222916,
-0.0134474141523242,
-0.0013399255694821477,
-0.03086893819272518,
-0.034536875784397125,
0.04209394007921219,
0.02296317182481289,
-0.0205733273178339,
0.019923673942685127,
-0.040853630751371384,
-0.045098915696144104,
-0.027146872133016586,
-0.0315990149974823,
0.02838805317878723,
-0.010851101949810982,
-0.014184328727424145,
0.021022852510213852,
0.005745541770011187,
0.010995492339134216,
-0.06635267287492752,
-0.009668586775660515,
0.005399612709879875,
-0.012975207529962063,
0.05261550098657608,
-0.03285328671336174,
-0.05485542118549347,
0.09148773550987244,
0.02111678384244442,
-0.02153308503329754,
0.023749666288495064,
0.00007745454786345363,
-0.006740665063261986,
-0.06069907173514366,
-0.03375709801912308,
0.04390047490596771,
-0.0031989682465791702,
0.014492327347397804,
-0.02781650610268116,
-0.01780727505683899,
0.05182826891541481,
-0.0066805072128772736,
0.01437733881175518,
-0.006855451501905918,
0.013384628109633923,
-0.00973439496010542,
0.06384648382663727,
0.04361513629555702,
-0.0034363586455583572,
-0.009816426783800125,
0.0036234590224921703,
0.03548821061849594,
-0.014393812045454979,
-0.06891100853681564,
0.033181656152009964,
-0.007151469122618437,
0.03396528959274292,
0.030062608420848846,
0.015811609104275703,
0.024611033499240875,
-0.025286803022027016,
-0.03353162482380867,
0.006823843810707331,
0.03245091065764427,
-0.02630210854113102,
-0.025787316262722015,
0.05590157210826874,
0.038674164563417435,
0.029003048315644264,
-0.01677200011909008,
-0.030959896743297577,
0.012479698285460472,
0.034544166177511215,
-0.03428369015455246,
-0.04845617339015007,
0.016660962253808975,
0.00166303850710392,
0.03130272030830383,
0.03951515257358551,
-0.07203122973442078,
-0.0015243489760905504,
-0.07730864733457565,
-0.04605286195874214,
-0.0022921422496438026,
0.0779302567243576,
0.008501123636960983,
-0.01769883744418621,
0.021692221984267235,
0.017077984288334846,
0.01736224628984928,
0.014276187866926193,
-0.1022733524441719,
0.031208014115691185,
-0.002091832458972931,
-0.03194486349821091,
0.02337394841015339,
-0.02179950848221779,
0.016065362840890884,
-0.016184702515602112,
-0.008729137480258942,
0.008842097595334053,
0.02272108383476734,
-0.04149731621146202,
0.006999313365668058,
-0.06667710095643997,
-0.019042402505874634,
0.008348257280886173,
0.030927693471312523,
0.022001758217811584,
-0.03196168318390846,
0.020022887736558914,
0.004244939889758825,
-0.05247225612401962,
-0.007863842882215977,
-0.03835773095488548,
-0.004252567887306213,
0.021486692130565643,
0.005819259211421013,
-0.013756233267486095,
0.01634991727769375,
0.035552579909563065,
-0.022053346037864685,
0.02817046456038952,
0.04360727220773697,
0.009233912453055382,
0.0047254422679543495,
-0.01327813696116209,
-0.02736717462539673,
-0.022953752428293228,
-0.004192874766886234,
0.06297516822814941,
-0.02337365597486496,
0.004274868872016668,
0.005900389049202204,
0.052814312279224396,
-0.030511921271681786,
0.04469764232635498,
0.041514672338962555,
0.054498497396707535,
-0.04832266643643379,
-0.05494512617588043,
-0.03330693766474724,
-0.03178096562623978,
-0.002265942981466651,
0.022329561412334442,
-0.02095130831003189,
-0.017440492287278175,
-0.039024125784635544,
0.03661125898361206,
0.048743922263383865,
-0.028634196147322655,
0.05863732099533081,
-0.03643539920449257,
0.030531028285622597,
-0.023287322372198105,
0.005130839999765158,
-0.0019232395570725203,
0.01823939010500908,
0.027554700151085854,
-0.016490699723362923,
-0.034274183213710785,
-0.03858369588851929,
-0.021027911454439163,
0.013353727757930756,
0.03530857712030411,
-0.0014397675404325128,
0.028396589681506157,
-0.030338186770677567,
-0.026148192584514618,
0.03328225389122963,
-0.009989740327000618,
0.04927169159054756,
0.007579266093671322,
0.02530893124639988,
-0.015405150130391121,
-0.009667118079960346,
-0.043511513620615005,
-0.004199166316539049,
0.01565411314368248,
0.023297742009162903,
0.026415837928652763,
-0.023213056847453117,
0.007214415818452835,
0.01294693723320961,
0.04426642507314682,
0.05486341938376427,
0.007884162478148937,
-0.024491025134921074,
0.023727312684059143,
0.00800084788352251,
-0.026250025257468224,
-0.036641139537096024,
0.009089933708310127,
-0.035102006047964096,
-0.010773006826639175,
-0.002515340456739068,
0.003401425899937749,
-0.02540624514222145,
0.016094351187348366,
-0.022536631673574448,
-0.01903068833053112,
0.004041796550154686,
-0.01657875068485737,
0.03549480810761452,
0.034578897058963776,
-0.030766166746616364,
0.03167596831917763,
0.03751685097813606,
-0.03453068435192108,
0.00740393903106451,
0.003570648143067956,
0.021988600492477417,
0.015939710661768913,
-0.01024990901350975,
-0.07042208313941956,
-0.0017595416866242886,
-0.004762119147926569,
0.023805558681488037,
-0.022041017189621925,
0.03230782225728035,
-0.0472850576043129,
-0.05465658754110336,
0.006904287729412317,
0.048393018543720245,
0.015432905405759811,
0.02491767704486847,
0.03521594777703285,
-0.0014721794286742806,
-0.01412991527467966,
-0.026832839474081993,
-0.01284029521048069,
-0.03669733181595802,
0.025157658383250237,
0.05181201919913292,
-0.0462462455034256,
0.03385383263230324,
-0.04459517076611519,
-0.04163668304681778,
-0.04532672092318535,
-0.060474544763565063,
0.05189314857125282,
0.00391325494274497,
0.007614757400006056,
0.028132248669862747,
-0.02777910605072975,
-0.017810136079788208,
0.04343327879905701,
-0.014294774271547794,
0.0013151493621990085,
-0.04431954398751259,
0.03186442330479622,
0.03840840607881546,
-0.04473560303449631,
-0.018851516768336296,
-0.037819329649209976,
0.016378674656152725,
0.007937478832900524,
0.007978493347764015,
-0.008784863166511059,
-0.008352256380021572,
-0.01829432137310505,
-0.0347050279378891,
0.0024596555158495903,
0.062147244811058044,
-0.03065488301217556,
-0.024228382855653763,
0.015848373994231224,
0.02754654549062252,
0.031189478933811188,
0.034882280975580215,
-0.007278370205312967,
-0.002030016155913472,
-0.013140550814568996,
-0.02764088474214077,
-0.029448509216308594,
0.06828974932432175,
-0.03666709363460541,
-0.026701433584094048,
-0.024588489904999733,
0.022856080904603004,
0.0618547648191452,
-0.0015123395714908838,
0.015568769536912441,
0.0000755449800635688,
0.04545751214027405,
0.00681259436532855,
0.008981977589428425,
0.012800442054867744,
0.018332891166210175,
0.03278670087456703,
-0.013287066482007504,
0.03501148894429207,
0.009191098622977734,
-0.047399431467056274,
-0.008168536238372326,
0.00834820605814457,
0.045626699924468994,
-0.010443716309964657,
0.10893306136131287,
-0.034388381987810135,
-0.0008526949095539749,
-0.016237150877714157,
-0.011124774813652039,
0.055452972650527954,
0.020059604197740555,
-0.00941865798085928,
0.0033528930507600307,
-0.0023816123139113188,
-0.020121216773986816,
0.00016090030840132385,
-0.03391607478260994,
0.03565265238285065,
0.06754061579704285,
-0.04958966746926308,
0.06496254354715347,
0.039654526859521866,
-0.009470527060329914,
0.001863232464529574,
0.03201873227953911,
-0.04079098626971245,
-0.02268868312239647,
0.0018974740523844957,
0.029255066066980362,
-0.040773116052150726,
-0.002952934941276908,
0.005991925019770861,
-0.014857199974358082,
0.0242502149194479,
-0.014222623780369759,
0.039887435734272,
0.05562051013112068,
-0.02480142191052437,
-0.03149137273430824,
-0.026183784008026123,
0.04155518114566803,
0.013282394967973232,
0.03565547987818718,
-0.008995654061436653,
-0.03662952408194542,
0.03571328893303871,
0.019574439153075218,
0.019116174429655075,
-0.032509222626686096,
-0.01767629384994507,
-0.021813787519931793,
0.03340614214539528,
0.011807543225586414,
-0.004226731136441231,
-0.024198155850172043,
0.014249855652451515,
0.019955534487962723,
-0.00707051157951355,
0.04357726871967316,
-0.026982946321368217,
-0.03540000319480896,
0.02393919974565506,
-0.0017739086179062724,
-0.01788431406021118,
0.02141101099550724,
-0.0017101456178352237,
-0.023220716044306755,
0.029330341145396233,
-0.02759607695043087,
0.01420386228710413,
0.011329753324389458,
0.019227012991905212,
-0.02113126963376999,
0.10753066837787628,
-0.0031345130410045385,
0.014561992138624191,
-0.03542661294341087,
-0.035183388739824295,
0.15722587704658508,
0.011664768680930138,
0.006474029738456011,
-0.055724792182445526,
0.07059481739997864,
-0.030080171301960945,
-0.02646084688603878,
-0.04399982839822769,
-0.0006535127176903188,
-0.03526566922664642,
0.013921717181801796,
0.03739089146256447,
0.031229663640260696,
0.009901381097733974,
-0.03218141570687294,
-0.0060054222121834755,
-0.029302218928933144,
-0.07416561990976334,
-0.021510697901248932,
0.023184437304735184,
-0.027744652703404427,
-0.023489665240049362,
-0.005836882162839174,
0.050109025090932846,
-0.02539777010679245,
-0.017542462795972824,
-0.01869211345911026,
-0.025707120075821877,
-0.009179684333503246,
-0.0004759186995215714,
-0.049617912620306015,
0.021551718935370445,
0.027514351531863213,
-0.018613897264003754,
-0.03491673991084099,
0.051885418593883514,
0.040056705474853516,
-0.02847212180495262,
0.03030225820839405,
0.02958138845860958,
0.013225515373051167,
-0.003047618782147765,
0.03417213633656502,
-0.02008170448243618,
-0.026556257158517838,
0.016883406788110733,
-0.04838864505290985,
0.06561823189258575,
-0.03496275842189789,
-0.015501200221478939,
-0.0031351945362985134,
-0.01855321042239666,
-0.0022164445836097,
-0.0344587080180645,
0.006092816591262817,
0.008808364160358906,
0.012359856627881527,
-0.026382243260741234,
0.011782687157392502,
-0.012713807635009289,
0.06567966938018799,
0.02280069701373577,
-0.03648564964532852,
0.022850338369607925,
-0.0077172233723104,
-0.018549228087067604,
0.0042798626236617565,
0.08422581106424332,
-0.01943959668278694,
-0.015205667354166508,
-0.05459103733301163,
-0.017948802560567856,
-0.02591208554804325,
0.016515405848622322,
-0.0034930361434817314,
0.04057007282972336,
0.02155870385468006,
-0.008462917990982533,
-0.04977158457040787,
-0.025549065321683884,
-0.05028104782104492,
0.04023003578186035,
-0.01924395188689232,
0.008053522557020187,
-0.03853294998407364,
-0.049628112465143204,
0.02447430044412613,
0.02748061902821064,
-0.0195895005017519,
-0.0007302232552319765,
0.03820277750492096,
0.05038508400321007,
0.03289850801229477,
0.000004890340733254561,
-0.017599793151021004,
0.0019937155302613974,
-0.0041802506893873215,
-0.0280679352581501,
-0.011278653517365456,
0.02441844344139099,
0.0006786073790863156,
0.01638481579720974,
-0.013207693584263325,
-0.008769637905061245,
0.016273317858576775,
0.04092109203338623,
0.012537490576505661,
-0.06884149461984634,
0.014672953635454178,
0.0397331602871418,
0.03471606597304344,
-0.03872121125459671,
-0.011797124519944191,
-0.005101290997117758,
0.009198438376188278,
-0.002697693882510066,
0.021271824836730957,
-0.030169837176799774,
0.01246480830013752,
-0.023567212745547295,
0.016411257907748222,
-0.05552850291132927,
-0.046476222574710846,
-0.0121846878901124,
-0.006915105041116476,
0.06255229562520981,
0.011043500155210495,
-0.02636837586760521,
0.02245170809328556,
0.007381143514066935,
-0.009047378785908222,
0.0051252529956400394,
0.015078216791152954,
0.023125765845179558,
-0.017024189233779907,
-0.010927414521574974,
-0.013270102441310883,
0.056021347641944885,
-0.04733121022582054,
-0.01257242076098919,
0.02680148370563984,
0.013371693901717663,
-0.01184181310236454,
-0.019598348066210747,
-0.002878469182178378,
0.0016173392068594694,
-0.030950993299484253,
-0.02863503061234951,
-0.031060736626386642,
0.07795333862304688,
-0.06139404699206352,
-0.034912239760160446,
0.00556614063680172,
-0.006392406765371561,
0.004462008830159903,
-0.06817398965358734,
-0.03230221942067146,
-0.017697632312774658,
0.029516004025936127,
0.027780476957559586,
0.016960838809609413,
-0.004682798404246569,
-0.054597754031419754,
-0.027279339730739594,
-0.02264745533466339,
-0.02967550978064537,
0.008969738148152828,
0.02554330788552761,
0.003384330775588751,
0.027529079467058182,
-0.010206135921180248,
-0.011152490973472595,
-0.006368625443428755,
-0.0033773339819163084,
-0.08962895721197128,
-0.03893466293811798,
0.01651858352124691,
0.006628787145018578,
0.061611998826265335,
-0.045269861817359924,
0.00508735328912735,
0.003604916390031576,
-0.04190576449036598,
-0.020052503794431686,
-0.013480464927852154,
-0.03439374640583992,
-0.0024747964926064014,
-0.02732643485069275,
0.010578035376966,
0.01755692809820175,
-0.018082499504089355,
0.04334758222103119,
-0.0034623004030436277,
0.019855523481965065,
-0.026188107207417488,
-0.025275563821196556,
0.017612747848033905,
0.0002187278587371111,
0.012974652461707592,
-0.023255519568920135,
0.05926986038684845,
0.02806379459798336,
-0.03597666323184967,
0.0429733470082283,
-0.01606842875480652,
-0.020662551745772362,
-0.01139872521162033,
0.01351459976285696,
-0.0336800180375576,
0.04894072934985161,
0.005897526629269123,
0.0012382299173623323,
0.006169433239847422,
-0.012667044065892696,
0.03413223475217819,
0.019702604040503502,
0.002857898361980915,
-0.017896069213747978,
0.04118197038769722,
-0.00890442356467247,
-0.04196241497993469,
0.0308518186211586,
-0.02179861068725586,
-0.024276649579405785,
0.005842238198965788,
-0.005851132329553366,
0.0533134825527668,
-0.010635019280016422,
-0.01489025168120861,
0.0004211327468510717,
0.050040241330862045,
0.03364443778991699,
0.025580517947673798,
-0.005463302601128817,
-0.005902634002268314,
-0.00682491110637784,
-0.012524525634944439,
-0.039829108864068985,
0.008422614075243473,
-0.02061743475496769,
-0.06437428295612335,
-0.020457781851291656,
-0.0161631740629673,
-0.015024646185338497,
-0.015264153480529785,
-0.03558396175503731,
-0.06316934525966644,
0.020805425941944122,
0.0013621399411931634,
0.017014747485518456,
0.020128265023231506,
-0.013914044015109539,
-0.015937959775328636,
-0.07465995103120804,
0.006321810185909271,
-0.001983932452276349,
-0.01951058954000473,
0.0020512135233730078,
-0.034439895302057266,
-0.031987112015485764,
-0.01532187033444643,
0.09098734706640244,
-0.018676748499274254,
-0.009999650530517101,
-0.001411527511663735,
-0.04282061755657196,
0.028100397437810898,
-0.010280556045472622,
0.027273042127490044,
0.005629525054246187,
0.00596451573073864,
0.008274674415588379,
0.0005589778884314001,
0.03831204026937485,
-0.03346050903201103,
-0.006727305240929127,
-0.011697331443428993,
0.005418611690402031,
0.01254027709364891,
-0.005242777056992054,
0.0125346714630723,
-0.029680728912353516,
-0.005416637286543846,
0.07766427844762802,
-0.005099513102322817,
0.023679358884692192,
0.017879266291856766,
-0.0033676226157695055,
-0.020672189071774483,
0.05169052258133888,
-0.028118744492530823,
-0.005909533239901066,
-0.02977661043405533,
-0.008362114429473877,
0.024169405922293663,
-0.03262823075056076,
-0.011865049600601196,
0.006776442751288414,
-0.042540550231933594,
-0.03340144827961922,
0.02908969856798649,
0.013310673646628857,
0.023438220843672752,
-0.028548458591103554,
0.0483437106013298,
0.04324013367295265,
-0.012836260721087456,
0.0076026394963264465,
-0.023901093751192093,
-0.003104256931692362,
0.003953234292566776,
-0.021899716928601265,
0.056380730122327805,
-0.011079682037234306,
0.02073783613741398,
-0.022208431735634804,
-0.00949610024690628,
0.010564369149506092,
-0.04231635853648186,
0.018750982359051704,
0.010706822387874126,
-0.017491407692432404,
0.02029111422598362,
0.02525920607149601,
0.040640491992235184,
-0.055566996335983276,
0.017977416515350342,
-0.022504834458231926,
0.010102045722305775,
-0.031125083565711975,
0.02598724700510502,
0.04349128156900406,
0.01160513237118721,
0.007442664820700884,
-0.0020413356833159924,
-0.0034999207127839327,
0.011054489761590958,
0.028084613382816315,
0.010813518427312374,
0.01964501477777958,
-0.009505168534815311,
0.01910250447690487,
0.0209017563611269,
-0.012621469795703888,
-0.04148769751191139,
-0.024900641292333603,
0.03227658197283745,
0.05468667298555374,
-0.008418792858719826,
0.007909960113465786,
0.01711600087583065,
-0.02954086661338806,
0.059398017823696136,
-0.0521836020052433,
-0.055753547698259354,
-0.019640499725937843,
-0.005089022684842348,
0.02837982587516308,
0.030044836923480034
] |
<p>I have seen a lot of places talking about the Reynolds number and how it is calculated, but I have never seen an equation that actually made use of this number to calculate lift, drag, or other aerodynamic properties.</p>
<p>So, what is this number actually used for?</p> | 2,892 | [
-0.018505847081542015,
0.004392982926219702,
-0.02129591628909111,
-0.009046274237334728,
0.031524136662483215,
0.006432631518691778,
-0.02330753766000271,
0.004523731302469969,
0.0046900054439902306,
-0.042339783161878586,
0.017372485250234604,
0.06307758390903473,
0.03398134186863899,
-0.018407491967082024,
0.01411192212253809,
0.016369404271245003,
-0.024759391322731972,
0.011676509864628315,
0.033398695290088654,
-0.0012516614515334368,
-0.012475105933845043,
0.0032464023679494858,
0.03041406162083149,
0.003941754810512066,
-0.00904152076691389,
0.0054320720955729485,
0.03311620652675629,
-0.018181631341576576,
0.04549813270568848,
-0.00022522237850353122,
0.015134097076952457,
-0.011311531066894531,
0.01838403381407261,
0.03329625725746155,
0.008385170251131058,
0.015611705370247364,
-0.015073606744408607,
-0.01395965926349163,
-0.028907939791679382,
0.02954627014696598,
-0.031893227249383926,
-0.041771210730075836,
-0.0006927123758941889,
0.026298753917217255,
0.012641939334571362,
0.024817632511258125,
0.006426580250263214,
-0.0473136305809021,
0.06238885968923569,
-0.09524597227573395,
0.05176584795117378,
0.012435542419552803,
0.07391098141670227,
0.033658113330602646,
0.013492221012711525,
0.01550496555864811,
0.0719643384218216,
0.024996953085064888,
-0.032061971724033356,
-0.046729616820812225,
-0.0073943170718848705,
-0.01166535634547472,
-0.015691330656409264,
-0.015112113207578659,
-0.01911751739680767,
0.025363383814692497,
-0.00026539922691881657,
-0.04602987319231033,
0.02756515145301819,
0.004322200082242489,
-0.010585721582174301,
0.007915301248431206,
0.033582933247089386,
-0.026039401069283485,
0.00767001835629344,
-0.02095615118741989,
0.004292744677513838,
-0.030450228601694107,
0.05852266401052475,
0.051018208265304565,
-0.05362546071410179,
0.031652823090553284,
0.01630445569753647,
0.010283522307872772,
-0.00026635744143277407,
-0.007140018045902252,
0.07641258835792542,
0.01390328910201788,
0.0027788677252829075,
0.004164659418165684,
0.007455319631844759,
0.0009728071745485067,
0.04292707517743111,
-0.00444848882034421,
-0.0077824667096138,
0.02548772469162941,
-0.0017222340684384108,
0.026068732142448425,
0.039135679602622986,
-0.042382821440696716,
0.02438935823738575,
-0.043348878622055054,
0.010769852437078953,
0.07810045033693314,
-0.03551698476076126,
-0.014024892821907997,
-0.03207247704267502,
-0.0011893947375938296,
-0.00567700294777751,
-0.011297637596726418,
-0.01774773932993412,
-0.014834876172244549,
-0.01814558170735836,
-0.017917435616254807,
-0.01510410476475954,
-0.012617550790309906,
0.026830513030290604,
0.018511507660150528,
0.03208061680197716,
0.07531546801328659,
0.028396712616086006,
-0.00943375937640667,
0.027600709348917007,
0.0233168788254261,
-0.02558174729347229,
0.04018530249595642,
0.0319511815905571,
-0.03663505241274834,
-0.0191817469894886,
0.026553399860858917,
-0.035546090453863144,
-0.01131501141935587,
-0.002008354989811778,
0.003358290297910571,
0.004541127011179924,
-0.0016123822424560785,
-0.09276016801595688,
-0.06809112429618835,
0.05587349832057953,
-0.011304818093776703,
-0.025294631719589233,
-0.07359226047992706,
0.032693903893232346,
0.030528876930475235,
0.0828782171010971,
-0.00033005987643264234,
0.011257955804467201,
-0.03109288588166237,
-0.010616925545036793,
-0.027717987075448036,
-0.02651730366051197,
-0.028124051168560982,
0.012980793602764606,
-0.04793247580528259,
0.008329066447913647,
-0.049996305257081985,
0.021777844056487083,
0.026480793952941895,
-0.005285204388201237,
-0.05044914409518242,
0.03630949556827545,
-0.037232764065265656,
0.0008411536691710353,
0.016930315643548965,
-0.0017392317531630397,
-0.05147819221019745,
0.05567050725221634,
0.03560279309749603,
0.025025149807333946,
0.03996747359633446,
0.012189028784632683,
-0.001780866994522512,
0.038784608244895935,
0.02017192728817463,
0.06548938900232315,
0.025322528555989265,
-0.0008269145619124174,
-0.037370774894952774,
0.003461608197540045,
0.004393143579363823,
-0.06599831581115723,
-0.03759127855300903,
0.026297546923160553,
-0.0016168910078704357,
0.0025812573730945587,
0.041160810738801956,
-0.010575216263532639,
0.012289593927562237,
0.028386849910020828,
-0.03205876424908638,
-0.031548600643873215,
-0.07596872001886368,
-0.019525691866874695,
-0.015862517058849335,
0.007132431957870722,
0.00582846999168396,
0.02314673364162445,
0.03607437014579773,
-0.04811931401491165,
-0.015266217291355133,
-0.020570091903209686,
0.027099203318357468,
0.023475680500268936,
-0.007950256578624249,
0.028873924165964127,
0.02598697319626808,
0.036963991820812225,
-0.0009315736824646592,
0.04254140332341194,
-0.021018633618950844,
-0.034174177795648575,
-0.020979896187782288,
-0.037842802703380585,
0.030207552015781403,
-0.00589416129514575,
-0.03590817376971245,
0.03624279424548149,
-0.02158411033451557,
-0.0013288415502756834,
0.006986113265156746,
-0.02053559012711048,
0.07364189624786377,
0.04208286106586456,
0.04031649976968765,
-0.0014090754557400942,
0.01826721616089344,
0.002180473878979683,
-0.027461804449558258,
0.017646057531237602,
-0.007840102538466454,
-0.027640266343951225,
-0.02517729625105858,
0.058014970272779465,
0.04841054603457451,
-0.031045839190483093,
-0.022342680022120476,
0.04954902082681656,
0.031203899532556534,
0.0534050315618515,
0.033886633813381195,
-0.03994652256369591,
-0.001214733230881393,
-0.00132963084615767,
0.0290919728577137,
0.019275818020105362,
0.020247898995876312,
0.02767231874167919,
0.05515120550990105,
0.03154947608709335,
-0.004406485706567764,
-0.040905632078647614,
0.05728993937373161,
0.021138804033398628,
-0.03103448823094368,
0.0010395143181085587,
-0.026819687336683273,
0.050862472504377365,
-0.04243778809905052,
0.0263321902602911,
0.018337080255150795,
-0.004729151725769043,
0.01333870179951191,
0.01906287483870983,
-0.0017906451830640435,
0.04851865395903587,
0.004579909611493349,
-0.04057270288467407,
-0.015414810739457607,
0.043568652123212814,
-0.014306931756436825,
0.035065073519945145,
-0.04584699869155884,
0.004581277258694172,
-0.0433351993560791,
0.0009414448868483305,
-0.010482427664101124,
-0.011544659733772278,
0.04427126795053482,
0.023609666153788567,
-0.020474852994084358,
-0.002450097817927599,
-0.04768287390470505,
-0.028632396832108498,
0.002072669332846999,
-0.04697438329458237,
0.020639736205339432,
-0.009699897840619087,
-0.030352698639035225,
0.04293440654873848,
-0.019920798018574715,
-0.021776089444756508,
0.022804660722613335,
-0.0036469539627432823,
-0.06957992911338806,
-0.021486669778823853,
-0.03179806470870972,
0.006941226311028004,
-0.002507925033569336,
-0.020258653908967972,
0.025029068812727928,
-0.050083644688129425,
-0.0247700996696949,
0.03711351007223129,
-0.03323105722665787,
-0.040208857506513596,
-0.02453572303056717,
0.008883632719516754,
0.0071258544921875,
-0.06178201735019684,
0.0025844532065093517,
0.024898365139961243,
-0.04021509364247322,
-0.010899686254560947,
-0.01844162493944168,
-0.04422455281019211,
0.0019131600856781006,
-0.00944240391254425,
0.02441803179681301,
-0.003675149753689766,
-0.05697989463806152,
0.08552585542201996,
-0.008012982085347176,
-0.03518066927790642,
-0.012377220205962658,
-0.02278922311961651,
-0.013766121119260788,
-0.04384841024875641,
0.01880623959004879,
0.048082269728183746,
0.016849055886268616,
0.009821356274187565,
0.0010756393894553185,
0.008465858176350594,
0.030491847544908524,
-0.003877293085679412,
0.01504011545330286,
-0.013800709508359432,
0.010336157865822315,
-0.003544451203197241,
0.0393669493496418,
0.018012026324868202,
-0.04893502965569496,
0.03936099261045456,
0.007806778885424137,
0.05421315133571625,
0.009815513156354427,
-0.035493768751621246,
0.060676973313093185,
-0.01407831721007824,
0.04258764162659645,
-0.02332265116274357,
0.021627867594361305,
-0.025417203083634377,
0.020579664036631584,
0.005449971649795771,
0.04322296753525734,
0.029765892773866653,
-0.012590662576258183,
-0.007328712847083807,
0.020171629264950752,
0.03485717624425888,
-0.029375137761235237,
-0.006393085233867168,
-0.0417863205075264,
-0.035317715257406235,
0.011500025168061256,
0.002808414166793227,
0.0020257513970136642,
0.05402573198080063,
0.0451849102973938,
0.014416945166885853,
0.006654870696365833,
-0.035680294036865234,
0.03947724774479866,
-0.06202548369765282,
-0.008859778754413128,
-0.03352845087647438,
0.047074466943740845,
-0.018867559731006622,
0.08471675217151642,
-0.04414408281445503,
0.029108021408319473,
0.036525189876556396,
-0.029129523783922195,
-0.07528159767389297,
0.03437502309679985,
-0.050854358822107315,
-0.0446956604719162,
-0.04357868432998657,
-0.001881226198747754,
0.009307187981903553,
-0.03202156722545624,
-0.03441904857754707,
-0.02573993057012558,
0.0017321174964308739,
-0.030509771779179573,
0.005303547717630863,
-0.0037736499216407537,
-0.024015039205551147,
-0.006038144696503878,
0.03888924419879913,
0.041113823652267456,
-0.04001466929912567,
0.019362015649676323,
0.05818808078765869,
-0.02125382423400879,
-0.05742578208446503,
-0.02044411189854145,
-0.0006462871097028255,
-0.008381673134863377,
0.00889306329190731,
0.008839188143610954,
0.01685190200805664,
-0.041136886924505234,
0.02344507910311222,
0.017890816554427147,
0.045395608991384506,
-0.005756868980824947,
0.025522777810692787,
-0.016944460570812225,
-0.04739769175648689,
-0.006953308824449778,
0.025760699063539505,
0.010884729214012623,
-0.0007194590871222317,
0.005207451060414314,
0.028524266555905342,
0.017138540744781494,
-0.04661853238940239,
0.047130100429058075,
0.03965534642338753,
0.030945152044296265,
-0.001767619396559894,
-0.052203357219696045,
0.02377469465136528,
-0.021626198664307594,
-0.019619012251496315,
0.008496103808283806,
0.016873925924301147,
-0.022143928334116936,
-0.005043613724410534,
0.028519731014966965,
-0.03740856423974037,
-0.02876284345984459,
-0.0032391990534961224,
0.028503991663455963,
0.014781106263399124,
-0.014258161187171936,
-0.008877853862941265,
-0.022396350279450417,
0.06562825292348862,
0.03241965174674988,
0.020256029441952705,
0.0037439358420670033,
-0.07957510650157928,
-0.017495622858405113,
0.045212481170892715,
0.02006278932094574,
-0.06472089141607285,
-0.007235608994960785,
-0.0431138351559639,
-0.022925980389118195,
0.04984738305211067,
-0.01909300684928894,
0.004424435086548328,
-0.025682467967271805,
-0.010379639454185963,
-0.009632558561861515,
-0.011848891153931618,
0.008192329667508602,
0.05318209528923035,
0.016602350398898125,
0.011347674764692783,
-0.029017319902777672,
0.022381901741027832,
-0.021756289526820183,
0.054664481431245804,
0.011601517908275127,
0.06247486174106598,
-0.0007941016810946167,
0.011645296588540077,
-0.025677992030978203,
0.01630653627216816,
-0.035042788833379745,
-0.06299322098493576,
-0.0014823289820924401,
0.016962818801403046,
0.0505279116332531,
0.04286753386259079,
-0.015365826897323132,
-0.04799758270382881,
0.012524532154202461,
0.014129796996712685,
-0.008083564229309559,
-0.006160308141261339,
-0.041929494589567184,
0.01597532629966736,
0.03229924291372299,
0.0034747347235679626,
0.05802858993411064,
0.0733729675412178,
-0.013912887312471867,
-0.04081982746720314,
0.012705967761576176,
0.053850207477808,
-0.00020290956308599561,
-0.05768461525440216,
-0.014349955134093761,
-0.01990683376789093,
-0.04349055141210556,
0.04450436308979988,
-0.016065159812569618,
0.03705700486898422,
-0.0171311404556036,
-0.034955330193042755,
-0.009181017056107521,
0.038937266916036606,
0.03854683041572571,
-0.041917409747838974,
0.05555141717195511,
0.014490442350506783,
0.015069181099534035,
-0.028947459533810616,
-0.0036102572921663523,
0.026928136125206947,
-0.009548183530569077,
0.020009413361549377,
-0.00989650096744299,
-0.017649251967668533,
0.000687289284542203,
-0.03477277606725693,
0.028258508071303368,
-0.01424410194158554,
0.08421303331851959,
-0.018364913761615753,
-0.018423287197947502,
-0.0009860204299911857,
-0.09132245182991028,
-0.03744210675358772,
0.02354619838297367,
0.020754806697368622,
0.02208271622657776,
-0.03376021981239319,
0.02129194885492325,
-0.009520131163299084,
0.00957240629941225,
-0.038397178053855896,
-0.02040870673954487,
0.024018878117203712,
0.001749045797623694,
-0.0021659189369529486,
-0.012507549487054348,
-0.03373013436794281,
-0.019042089581489563,
-0.054155122488737106,
0.03506564348936081,
0.03854570537805557,
-0.03319638594985008,
-0.03548727184534073,
0.00831729918718338,
-0.03833527863025665,
0.0536254420876503,
0.00457304110750556,
-0.004240448120981455,
0.007986543700098991,
-0.027793388813734055,
-0.0003430803189985454,
-0.018255705013871193,
0.06653714925050735,
-0.034840501844882965,
0.022112609818577766,
0.0001823323400458321,
-0.024911854416131973,
0.04407805949449539,
-0.020821435377001762,
0.02629050239920616,
0.020191267132759094,
-0.010830855928361416,
0.01477346196770668,
-0.013575509190559387,
0.016482701525092125,
0.01973353698849678,
0.0172733124345541,
0.011447001248598099,
-0.0017179938731715083,
-0.04143107682466507,
-0.021413668990135193,
0.028041740879416466,
0.030584057793021202,
0.015164344571530819,
-0.007237321697175503,
0.05720401182770729,
-0.012522575445473194,
-0.017376119270920753,
-0.011518453247845173,
-0.0037412643432617188,
0.02790861763060093,
0.04092738777399063,
0.032268866896629333,
0.004442488308995962,
0.041923511773347855,
-0.01949913054704666,
-0.03860790282487869,
-0.029628515243530273,
-0.01942959986627102,
0.07059506326913834,
-0.05769883468747139,
0.024164894595742226,
0.014431791380047798,
-0.008979684673249722,
0.015253936871886253,
-0.015008050948381424,
-0.05267854779958725,
-0.00477047311142087,
-0.015044288709759712,
0.042779214680194855,
0.0007575720082968473,
-0.005750258453190327,
-0.017293788492679596,
0.003804447827860713,
0.034001365303993225,
-0.008171391673386097,
0.01312779076397419,
-0.006813615560531616,
0.002610738156363368,
0.0114597762003541,
-0.017697688192129135,
0.08023731410503387,
-0.012205530889332294,
0.022812047973275185,
-0.01941358484327793,
-0.013397683389484882,
0.04713713377714157,
-0.005663326941430569,
-0.016059478744864464,
-0.048155542463064194,
0.009491817094385624,
-0.0044786361977458,
0.03945261985063553,
0.013095545582473278,
-0.039655473083257675,
0.005095987115055323,
-0.012537584640085697,
0.010739403776824474,
-0.0077394223771989346,
0.03429965302348137,
0.0041947434656322,
-0.021100977435708046,
-0.020498720929026604,
-0.01383186224848032,
-0.02725137397646904,
0.03416815400123596,
0.02863071858882904,
-0.029554197564721107,
0.001825476996600628,
-0.0038756998255848885,
0.02155986614525318,
-0.015117033384740353,
0.022683262825012207,
-0.02658681944012642,
0.06079455837607384,
-0.006589845288544893,
-0.006756881717592478,
-0.019341595470905304,
0.01361991185694933,
0.10857924818992615,
0.041516825556755066,
0.016728920862078667,
-0.07872167974710464,
-0.005027370061725378,
-0.02899176999926567,
0.004089558497071266,
-0.03499145060777664,
0.024671001359820366,
0.001204696367494762,
0.044932711869478226,
0.04743160679936409,
0.02049580030143261,
0.013917981646955013,
-0.0002645544009283185,
0.05277400091290474,
-0.04827176779508591,
-0.023853417485952377,
0.005065544042736292,
0.013968219049274921,
-0.04046385735273361,
-0.005306045990437269,
-0.023956703022122383,
-0.0036909300833940506,
-0.005545905791223049,
-0.023354055359959602,
-0.017944935709238052,
-0.02284114994108677,
0.028343824669718742,
0.0011833272874355316,
-0.053382571786642075,
0.002922424115240574,
-0.004184769932180643,
0.011903438717126846,
-0.018054412677884102,
0.014905180782079697,
-0.008687634952366352,
-0.017747364938259125,
0.010250444523990154,
0.048279162496328354,
0.0233641155064106,
-0.012589923106133938,
-0.03234358876943588,
-0.0001422766363248229,
-0.04244052991271019,
-0.04708431661128998,
-0.024140769615769386,
-0.0008468476589769125,
-0.011395687237381935,
0.004069135058671236,
-0.014887658879160881,
0.014819556847214699,
-0.004285275470465422,
-0.056623853743076324,
-0.02219737507402897,
-0.014313248917460442,
0.03322835639119148,
-0.05229427292943001,
-0.019443906843662262,
-0.02419564127922058,
0.00717786094173789,
-0.036358270794153214,
0.007988309487700462,
0.013028916902840137,
-0.009881708770990372,
0.00103347550611943,
-0.03720039874315262,
0.0460347980260849,
-0.017102867364883423,
-0.018183080479502678,
-0.0486699715256691,
0.003053917083889246,
-0.03343570977449417,
-0.014081883244216442,
0.029161330312490463,
0.037803422659635544,
-0.008227664977312088,
0.011473213322460651,
-0.011831079609692097,
-0.01941801607608795,
-0.06326033174991608,
0.053123682737350464,
0.008704569190740585,
-0.007756334729492664,
-0.030286971479654312,
-0.047605209052562714,
0.03819550201296806,
0.04702789708971977,
0.02226334623992443,
-0.006216287612915039,
-0.05044202879071236,
0.02692730911076069,
0.0051523540169000626,
-0.014763063751161098,
-0.024074582383036613,
0.033222947269678116,
-0.017440050840377808,
-0.0020866412669420242,
0.018266217783093452,
0.04339665547013283,
0.04425358027219772,
-0.01287856325507164,
-0.028614666312932968,
0.03903980180621147,
-0.019185535609722137,
0.023330505937337875,
0.040937911719083786,
-0.054250847548246384,
0.013249790295958519,
0.005632319487631321,
0.004689931403845549,
-0.025990892201662064,
-0.0371876060962677,
-0.05551524460315704,
-0.01391590666025877,
-0.003937299828976393,
0.01636861264705658,
-0.024710582569241524,
0.0015081038000062108,
-0.013006769120693207,
0.021430768072605133,
-0.03876928985118866,
-0.018731029704213142,
-0.05703689530491829,
0.022308209910988808,
-0.002474503591656685,
0.010015265084803104,
-0.016209624707698822,
-0.007160509470850229,
-0.008559373207390308,
0.04153638705611229,
0.019635476171970367,
0.005698997061699629,
0.03134047985076904,
-0.02391388639807701,
0.017535630613565445,
-0.01852632500231266,
0.05221525579690933,
-0.030051248148083687,
-0.0267645251005888,
0.05743355676531792,
-0.04020785167813301,
-0.05851748213171959,
0.020052459090948105,
0.0011531775817275047,
0.036257851868867874,
0.037618186324834824,
-0.019230730831623077,
-0.03582492843270302,
0.04765082150697708,
-0.021722346544265747,
-0.019094761461019516,
-0.02527689002454281,
0.0027224437799304724,
0.015343341045081615,
-0.028252452611923218,
0.016851894557476044,
-0.03870171308517456,
0.017884695902466774,
0.018067261204123497,
0.0369047075510025,
-0.02705632522702217,
-0.014424305409193039,
0.035371262580156326,
-0.0010319423163309693,
-0.006980534642934799,
0.015716344118118286,
0.02116471901535988,
-0.015099463053047657,
0.031317856162786484,
-0.016593607142567635,
0.03255866840481758,
0.01993931457400322,
-0.0207015722990036,
-0.13335555791854858,
0.03606128320097923,
-0.037494026124477386,
0.006885839160531759,
0.0028554273303598166,
-0.04768030345439911,
0.030233243480324745,
0.022888749837875366,
-0.03190280869603157,
0.00010306170588592067,
-0.044140949845314026,
0.008161255158483982,
-0.05193507671356201,
0.0054087103344500065,
0.037953272461891174,
0.06162572279572487,
0.034276556223630905,
-0.021422401070594788,
0.029187092557549477,
-0.00856146588921547,
-0.020643403753638268,
-0.009617643430829048,
0.01761705055832863,
0.010892745107412338,
-0.022733120247721672,
-0.018308723345398903,
0.012387311086058617,
-0.008051350712776184,
-0.025938864797353745,
0.0408664308488369,
-0.010201758705079556,
0.04198078811168671,
-0.008607694879174232,
0.013575191609561443,
-0.0011362540535628796,
0.028521867468953133,
0.05572405084967613,
-0.0018046277109533548,
-0.05459773540496826,
0.037954628467559814,
0.005702132359147072,
0.018483974039554596,
0.007152646314352751,
-0.009041900746524334,
0.0165391992777586,
-0.032761335372924805,
-0.0440327413380146,
0.041084837168455124,
-0.013452177867293358,
-0.028810804709792137,
0.016734778881072998,
-0.007214891724288464,
0.029226375743746758,
-0.024978958070278168,
0.03251190856099129,
-0.04444897174835205,
-0.01421079970896244,
0.0014987023314461112,
-0.024297283962368965,
-0.011940645053982735,
0.049524832516908646,
0.02213999442756176,
-0.02594827301800251,
0.00822169054299593,
0.0030395633075386286,
-0.011707887053489685,
-0.07189632952213287,
-0.011885800398886204,
0.0008318696054629982,
-0.04410400614142418,
-0.0034582028165459633,
-0.023100636899471283,
0.0063920291140675545,
0.008625881746411324,
0.036741241812705994,
0.03549645468592644,
0.012789083644747734,
-0.053490541875362396,
-0.022138381376862526,
-0.03205321729183197,
0.07126270234584808,
0.032738812267780304,
-0.01151382178068161,
-0.0569499135017395,
-0.016728343442082405,
0.013533752411603928,
0.0037793749943375587,
0.05552717298269272,
-0.019151175394654274,
-0.0005783084779977798,
-0.01623213291168213,
0.038351960480213165,
-0.00735229067504406,
-0.02486204169690609,
0.002017345279455185,
0.0006090422393754125,
-0.04049425944685936,
-0.03913918882608414,
-0.025842726230621338,
-0.009369583800435066,
0.02712862752377987,
0.024089956656098366,
0.009146752767264843,
0.029798706993460655,
-0.007044826168566942,
-0.017282478511333466,
0.05550789460539818,
0.04666557535529137,
-0.022020000964403152,
0.05525588244199753,
-0.020349139347672462,
0.015944063663482666,
0.0012946876231580973,
-0.001983504043892026,
-0.027426935732364655,
0.04442902281880379,
-0.03734524920582771,
0.001142266090027988,
-0.03282666206359863,
0.022055981680750847,
0.0016249215696007013,
-0.058470580726861954,
0.030733149498701096,
0.02900623343884945,
-0.029833409935235977,
-0.004425768740475178,
0.04959365725517273,
0.05528431758284569,
0.010474521666765213,
-0.020667657256126404,
-0.011770886369049549,
0.026421822607517242,
-0.02990032359957695,
-0.016710208728909492,
0.044104356318712234,
0.04852693900465965,
0.00898611731827259,
0.012585444375872612,
0.030659645795822144,
0.01322916615754366,
0.005960431415587664,
0.04848974570631981,
0.02544211782515049,
-0.02086799591779709,
-0.026878084987401962,
-0.007649439387023449,
-0.05746440216898918,
0.025451980531215668,
0.027081865817308426,
-0.01755979098379612,
0.10875184088945389,
-0.04144394025206566,
0.014917158521711826,
-0.0051546101458370686,
0.009699060581624508,
0.002441969932988286,
-0.01674707978963852,
0.002807165728881955,
0.06701110303401947,
0.0014792383881285787,
-0.020429352298378944,
0.006516322959214449,
-0.009123141877353191,
0.03346576541662216,
-0.020392274484038353,
0.04601607844233513,
0.013708828017115593,
0.024351488798856735,
-0.05272673815488815,
-0.006753875408321619,
-0.024154681712388992,
-0.03519704192876816,
0.023899691179394722,
0.03290453180670738,
0.024701634421944618,
0.046950068324804306,
-0.028666529804468155,
-0.013604608364403248,
0.04107362776994705,
-0.05193266272544861,
-0.013069563545286655,
-0.008443338796496391,
0.04970581457018852,
-0.015095160342752934,
-0.0012912142556160688
] |
<p>I just read that in the Gaussian Units of charge The Final equation in Coulomb's law is as simple as $$\boldsymbol{F}=\frac{q_1q_2}{r^2}$$</p>
<p>No $\epsilon_0$ no $4\pi$ like you have in the $\mbox{SI}$ units of measurement . </p>
<p>The permittivity constant was the factor in the $\mbox{SI}$ system of Coulombic Force that determined the intensity of force in a medium. </p>
<p>In the Gaussian system i see no such constant . So that would mean that some other factor would govern the Quantity of charge on a body.</p>
<p>What is that factor ?</p>
<p>(I vaguely remember it as being related to the speed of light $c_0$)</p> | 2,893 | [
-0.01929866336286068,
-0.009441347792744637,
0.010524997487664223,
-0.016045011579990387,
0.0399475172162056,
0.04392668232321739,
-0.031130053102970123,
-0.032925110310316086,
-0.011450981721282005,
-0.040661752223968506,
0.024318326264619827,
0.05890423431992531,
0.09270104765892029,
0.024043960496783257,
-0.0016172154573723674,
-0.019310953095555305,
-0.01566684991121292,
-0.029862185940146446,
-0.005724451504647732,
-0.038540348410606384,
0.002817317610606551,
0.04322978854179382,
0.0030956307891756296,
0.014219461940228939,
-0.020235130563378334,
0.0660993680357933,
0.0017371318535879254,
-0.005975048989057541,
0.028794746845960617,
0.02206740900874138,
0.019289961084723473,
-0.036039743572473526,
0.019779343158006668,
-0.006023922469466925,
0.048754122108221054,
-0.015372144058346748,
-0.011073040775954723,
-0.04021953046321869,
-0.022113356739282608,
0.023647895082831383,
-0.039453618228435516,
-0.018215559422969818,
-0.0003327361773699522,
0.012921808287501335,
-0.023946773260831833,
0.007989688776433468,
0.014913243241608143,
-0.028324319049715996,
0.05645699426531792,
-0.055537786334753036,
0.04171225056052208,
0.045463867485523224,
0.06471852958202362,
0.018863646313548088,
0.004723715595901012,
-0.0047129979357123375,
0.1052447110414505,
0.04929402098059654,
-0.010247600264847279,
-0.04780630022287369,
-0.025708265602588654,
-0.029223494231700897,
-0.0001673176302574575,
-0.028011810034513474,
-0.030344607308506966,
0.026716098189353943,
-0.026869911700487137,
-0.04802460968494415,
0.024825001135468483,
0.01218124944716692,
0.021395346149802208,
0.028233665972948074,
0.01754344254732132,
-0.024712055921554565,
-0.0021739634685218334,
-0.0369485579431057,
0.010608620941638947,
-0.015394951216876507,
0.017775671556591988,
0.04397759214043617,
-0.023734526708722115,
-0.020151186734437943,
-0.04312566667795181,
0.040004000067710876,
-0.005985712166875601,
0.0023364925291389227,
0.027841748669743538,
-0.03078639879822731,
0.004894904792308807,
0.04936738312244415,
-0.04268433526158333,
0.03374670073390007,
0.024653470143675804,
-0.000724176992662251,
-0.012183169834315777,
0.02459755539894104,
-0.016244804486632347,
0.04006647691130638,
0.01641612872481346,
-0.006227417849004269,
0.020022060722112656,
-0.003977086395025253,
0.021974239498376846,
0.08666681498289108,
-0.003131488338112831,
-0.046715158969163895,
0.005865377839654684,
-0.00962686724960804,
-0.03215363249182701,
-0.018840817734599113,
-0.03827633336186409,
-0.009682770818471909,
0.017190681770443916,
0.0109532056376338,
0.023513654246926308,
-0.03846864029765129,
0.03276659548282623,
-0.03457771614193916,
0.07152271270751953,
0.06780079007148743,
0.029626337811350822,
-0.03185247629880905,
-0.004987448453903198,
-0.0213010311126709,
-0.03398553282022476,
0.040134549140930176,
0.015095366165041924,
-0.00517900800332427,
-0.0031071880366653204,
0.013437614776194096,
-0.02496652491390705,
0.008741469122469425,
-0.015377435833215714,
0.002616326091811061,
0.01440269686281681,
-0.012813273817300797,
-0.08623635023832321,
-0.04085372015833855,
0.00707945367321372,
-0.030289428308606148,
-0.01842932403087616,
-0.11045555025339127,
0.009758209809660912,
-0.014458891935646534,
0.049342650920152664,
0.0015499737346544862,
0.005491739604622126,
-0.007717892527580261,
0.03519904613494873,
0.01981951668858528,
0.01463671401143074,
-0.03074255958199501,
0.0059426892548799515,
-0.04592503607273102,
-0.013262568973004818,
-0.06395801156759262,
0.033683110028505325,
0.02558368444442749,
0.012142919935286045,
0.006516852881759405,
0.05263633280992508,
-0.033139221370220184,
-0.0007200961699709296,
0.02135337144136429,
-0.009239442646503448,
-0.05397170037031174,
0.07765531539916992,
0.020036276429891586,
0.03744916245341301,
0.033371150493621826,
0.03043998032808304,
0.00820025335997343,
0.02863646112382412,
0.028232472017407417,
0.059602152556180954,
-0.04108676314353943,
-0.04592391103506088,
-0.06953521072864532,
-0.009912344627082348,
0.015055603347718716,
-0.021300116553902626,
-0.05457074195146561,
0.03549899160861969,
-0.008221745491027832,
0.008584018796682358,
0.04535133019089699,
0.0058687408454716206,
-0.004784711170941591,
-0.0013989813160151243,
-0.031953152269124985,
0.010036579333245754,
-0.048083338886499405,
0.050792962312698364,
0.04982051998376846,
-0.041324861347675323,
0.024769527837634087,
-0.018675221130251884,
-0.006323298905044794,
-0.01787525974214077,
-0.060552291572093964,
-0.0006349815521389246,
0.031132787466049194,
-0.008850069716572762,
-0.030936988070607185,
0.025887804105877876,
-0.00269027310423553,
0.0033256770111620426,
-0.004334672354161739,
0.020261041820049286,
0.007864310406148434,
-0.03470737487077713,
0.01821890100836754,
-0.03968087583780289,
0.05961020663380623,
-0.030042869970202446,
0.004269262310117483,
0.01717223785817623,
-0.012019806541502476,
-0.019267629832029343,
0.07296436280012131,
-0.021921655163168907,
0.057624638080596924,
0.049550700932741165,
-0.00900130346417427,
-0.02214868739247322,
0.05487723648548126,
-0.021223122254014015,
0.003189072711393237,
-0.044828150421381,
-0.03416643664240837,
-0.05587054044008255,
0.009175395593047142,
0.04560576751828194,
0.005725735332816839,
-0.010759789496660233,
0.012496848590672016,
0.007190232165157795,
0.04412958025932312,
0.05359808728098869,
0.007781876251101494,
-0.03292950987815857,
-0.04198233410716057,
0.022675417363643646,
0.005844658240675926,
-0.009014100767672062,
0.029174979776144028,
-0.0061057135462760925,
0.050035540014505386,
0.03376315161585808,
-0.0075591434724628925,
0.0075818756595253944,
0.02911970019340515,
-0.013283204287290573,
0.0248011015355587,
0.002320451894775033,
-0.02877669781446457,
0.024969546124339104,
-0.03515179455280304,
0.07162976264953613,
0.04123684763908386,
-0.00586183974519372,
-0.015263566747307777,
-0.0335969552397728,
-0.019158976152539253,
0.02706298604607582,
-0.012474577873945236,
-0.04293804615736008,
-0.00891446229070425,
0.01570875570178032,
-0.07262915372848511,
0.0009118116577155888,
0.020706970244646072,
0.012736407108604908,
-0.03704014793038368,
-0.011271052993834019,
0.015840496867895126,
0.01305670291185379,
0.05261549353599548,
-0.0269336961209774,
-0.02044983208179474,
0.02156739868223667,
-0.054682374000549316,
0.00181007815990597,
0.028847089037299156,
0.0020877206698060036,
-0.021107684820890427,
-0.04356956481933594,
-0.0005735903396271169,
0.03662891313433647,
-0.01475241594016552,
0.030344510450959206,
0.036391425877809525,
-0.015411063097417355,
-0.0507158488035202,
0.015980621799826622,
-0.019726959988474846,
0.01358256209641695,
-0.03945358470082283,
-0.004200865048915148,
0.027472998946905136,
-0.0024279055651277304,
-0.04479661583900452,
0.0035931135062128305,
-0.06318308413028717,
-0.03735741600394249,
-0.02821221575140953,
-0.016374416649341583,
0.026130057871341705,
-0.02932099625468254,
0.02147967554628849,
0.03196435794234276,
-0.03237480670213699,
0.003339597722515464,
-0.03566725552082062,
-0.059498827904462814,
0.03698054701089859,
-0.006615744438022375,
0.08056231588125229,
-0.014271763153374195,
-0.041953615844249725,
0.0431172214448452,
0.025952350348234177,
0.0008701284532435238,
-0.027598990127444267,
-0.020563224330544472,
-0.008879335597157478,
-0.03719369322061539,
-0.017986152321100235,
0.049596406519412994,
0.0005256846779957414,
-0.002291629323735833,
0.03433849290013313,
0.034198641777038574,
0.030412893742322922,
0.022074438631534576,
0.02441001683473587,
0.014251923188567162,
-0.0017105161678045988,
-0.0013340882724151015,
0.09482518583536148,
0.030028989538550377,
0.012838328257203102,
0.004369140136986971,
-0.01677248254418373,
0.038480136543512344,
0.022576721385121346,
-0.029264772310853004,
0.02170882746577263,
-0.004495462402701378,
0.01546319667249918,
-0.00017627235502004623,
0.023458322510123253,
0.008116436190903187,
-0.03159390762448311,
0.04023955389857292,
0.05586766451597214,
0.012102515436708927,
-0.05146515741944313,
0.011928966268897057,
0.03407229855656624,
0.023642508313059807,
-0.010832017287611961,
-0.0014787658583372831,
0.019706733524799347,
-0.0010024323128163815,
-0.004108299966901541,
-0.02295038104057312,
-0.014707758091390133,
0.017246270552277565,
0.01101120375096798,
0.03837048262357712,
0.012337073683738708,
-0.03944609314203262,
-0.0007998484652489424,
-0.029941292479634285,
-0.06128985434770584,
0.016728175804018974,
0.06146395206451416,
0.009060884825885296,
0.0623474158346653,
0.02759694494307041,
0.012210793793201447,
-0.0017941085388883948,
0.013433948159217834,
-0.08660118281841278,
-0.004024316556751728,
-0.06382985413074493,
-0.029425090178847313,
-0.01290079578757286,
-0.003756539663299918,
-0.03363664820790291,
0.02322140522301197,
0.008370096795260906,
-0.02398623153567314,
0.0005168186035007238,
-0.04381309822201729,
0.0468631274998188,
-0.04424481838941574,
-0.04060625284910202,
-0.01145012117922306,
0.017541667446494102,
0.029311973601579666,
-0.04835248738527298,
-0.030670015141367912,
0.019420484080910683,
-0.0017496312502771616,
-0.006698503624647856,
-0.005669950041919947,
-0.015441124327480793,
0.03549649938941002,
0.02008998952805996,
0.03699714317917824,
-0.017361223697662354,
0.0015234769089147449,
-0.011180889792740345,
0.03698334842920303,
0.05687809735536575,
0.01757776364684105,
-0.01763780601322651,
-0.04194789379835129,
-0.05149662867188454,
-0.004303527530282736,
-0.029556702822446823,
0.048978954553604126,
-0.008718851022422314,
-0.005103152710944414,
0.013402692973613739,
0.006472701672464609,
0.004038272425532341,
0.03724590316414833,
0.03372616693377495,
0.04005137085914612,
-0.021016621962189674,
-0.04658006504178047,
0.023067209869623184,
-0.009976652450859547,
0.01209466066211462,
0.005222178529947996,
0.01264262292534113,
-0.012699607759714127,
-0.01816687174141407,
0.03884708136320114,
0.0034244158305227757,
0.007163945119827986,
0.009186122566461563,
0.010446829721331596,
0.017722612246870995,
-0.006487524136900902,
-0.0002982609439641237,
-0.018850143998861313,
0.026155345141887665,
0.007057584822177887,
-0.0036871840711683035,
-0.02211466059088707,
-0.07102496922016144,
0.0074967979453504086,
0.0040673743933439255,
0.040086083114147186,
-0.011236275546252728,
-0.017724573612213135,
-0.042845718562603,
-0.00793432630598545,
0.040497638285160065,
-0.028887972235679626,
0.02227010764181614,
-0.007160816807299852,
-0.00745532987639308,
-0.012665150687098503,
-0.02791677601635456,
-0.03351855278015137,
0.02046852558851242,
0.013961954973638058,
0.010732772760093212,
-0.013884373009204865,
0.02925679460167885,
0.005254110787063837,
0.05067341402173042,
0.016265587881207466,
0.058740805834531784,
0.01317194476723671,
-0.03540358692407608,
0.00529923802241683,
0.0041181775741279125,
-0.0174629595130682,
-0.061210133135318756,
-0.014122267253696918,
-0.01447176281362772,
0.03836045786738396,
0.04355893284082413,
-0.0410202331840992,
-0.03574635460972786,
0.008099762722849846,
0.009585368447005749,
0.0017922266852110624,
0.004225351847708225,
-0.03550316393375397,
0.04709872230887413,
0.00673639727756381,
0.011772846803069115,
0.04620016738772392,
0.013420670293271542,
0.009785434231162071,
-0.01489389967173338,
-0.0385567769408226,
0.04970568045973778,
-0.011633572168648243,
-0.01657417230308056,
-0.00353401736356318,
0.008025689981877804,
-0.04058804735541344,
0.02400277368724346,
-0.010575573891401291,
0.038307856768369675,
-0.022879507392644882,
-0.024815689772367477,
0.013684128411114216,
-0.015233791433274746,
-0.03542882576584816,
0.01058815699070692,
-0.0008590120705775917,
0.042713381350040436,
0.0008249543025158346,
-0.019070835784077644,
-0.00764627568423748,
0.010463424026966095,
0.005498898681253195,
0.029868947342038155,
-0.007545568980276585,
-0.002245082752779126,
-0.010262853465974331,
-0.031427960842847824,
0.004132113419473171,
-0.03627655655145645,
0.037829093635082245,
-0.021595608443021774,
0.004720828030258417,
-0.008170370012521744,
-0.07425783574581146,
-0.056217260658741,
0.01833965629339218,
0.007847126573324203,
0.030543211847543716,
-0.044506389647722244,
-0.007211755495518446,
-0.0005327917169779539,
0.03288782015442848,
-0.05459808558225632,
-0.05408777296543121,
0.02160731889307499,
0.012876494787633419,
0.008953475393354893,
0.014025384560227394,
0.0023696953430771828,
-0.015612512826919556,
-0.03873457387089729,
0.047846924513578415,
0.0314677432179451,
-0.023837074637413025,
0.016529908403754234,
0.010194838047027588,
0.031174438074231148,
0.02919968217611313,
-0.018423231318593025,
-0.029019927605986595,
0.02545294165611267,
-0.0057410201989114285,
0.015199643559753895,
0.01693488284945488,
0.029903875663876534,
-0.004430731292814016,
-0.04019073024392128,
-0.026476431638002396,
-0.011922665871679783,
0.013476657681167126,
-0.006611019838601351,
-0.0005576203693635762,
0.02898857370018959,
-0.006242537871003151,
-0.02187451161444187,
-0.002805747091770172,
0.020469868555665016,
0.01296249683946371,
0.02356651984155178,
-0.008385059423744678,
-0.0052682096138596535,
-0.0724940299987793,
-0.02846703678369522,
0.027563633397221565,
0.010443873703479767,
0.06845596432685852,
-0.017264090478420258,
0.03062216378748417,
-0.010651865974068642,
-0.024632982909679413,
0.054639339447021484,
0.006737896706908941,
0.01405318919569254,
0.01736808754503727,
-0.019768862053751945,
0.0005546595784835517,
0.011179753579199314,
-0.03009093925356865,
-0.01823611743748188,
-0.04284144937992096,
-0.005756552331149578,
0.07111562788486481,
-0.02488345094025135,
0.05481885373592377,
0.03243589773774147,
-0.041322484612464905,
0.001142527675256133,
0.011677464470267296,
-0.03561137989163399,
0.008173680864274502,
-0.014046018011868,
0.015544253401458263,
-0.011124001815915108,
-0.008920465596020222,
-0.01730608381330967,
0.055858299136161804,
-0.023918218910694122,
0.007105774711817503,
0.048157673329114914,
0.049251921474933624,
0.010676766745746136,
-0.049049291759729385,
-0.02632313221693039,
0.08994559943675995,
-0.03224842995405197,
0.0351688414812088,
0.002505987649783492,
-0.049513187259435654,
0.04438919201493263,
-0.007565113715827465,
0.011952389031648636,
-0.04333731159567833,
-0.031046155840158463,
-0.019846899434924126,
0.014375901781022549,
0.02473086677491665,
-0.019919348880648613,
-0.054042696952819824,
0.004438360221683979,
0.013443934731185436,
0.0187727939337492,
0.019524363800883293,
0.02160654403269291,
-0.057792674750089645,
-0.005790109746158123,
-0.02478751167654991,
-0.01487521082162857,
0.03950569033622742,
-0.0013630137545987964,
-0.05214208364486694,
0.02381868287920952,
-0.05605757609009743,
0.06393181532621384,
0.037080589681863785,
-0.01367233507335186,
-0.02258959412574768,
0.06624387204647064,
-0.018572591245174408,
-0.02900303341448307,
-0.012590322643518448,
0.01019221544265747,
0.12507745623588562,
0.05130406841635704,
0.01296746265143156,
-0.030880555510520935,
-0.007205749396234751,
-0.02517443709075451,
0.01599716581404209,
-0.032765455543994904,
0.006327255629003048,
-0.028803620487451553,
0.003288161475211382,
0.02916240692138672,
0.025039121508598328,
-0.009858498349785805,
0.005507896654307842,
0.05681696906685829,
-0.009076481685042381,
-0.008136170916259289,
0.028354909271001816,
0.0327872708439827,
0.017267901450395584,
0.029290905222296715,
-0.024330025538802147,
0.053813204169273376,
-0.03356843441724777,
-0.01335128117352724,
-0.0345713309943676,
0.008525186218321323,
-0.010406821966171265,
0.010164890438318253,
-0.06649239361286163,
-0.026286117732524872,
0.012385728769004345,
-0.007259644102305174,
-0.03399210050702095,
0.04493441432714462,
0.04393037036061287,
0.010884493589401245,
-0.031115248799324036,
-0.011050710454583168,
-0.0029831943102180958,
0.021832160651683807,
0.01957976259291172,
-0.0025762030854821205,
-0.027730494737625122,
-0.019365603104233742,
-0.008857103064656258,
0.04718746617436409,
-0.0023676722776144743,
0.03367769345641136,
0.012654692865908146,
0.03019709885120392,
0.0407971553504467,
-0.05165703222155571,
-0.03123011253774166,
-0.02175569348037243,
0.03132469952106476,
-0.026199596002697945,
-0.005114875268191099,
0.00262273196130991,
0.027040865272283554,
-0.046945687383413315,
0.03238607943058014,
0.00407427316531539,
-0.020271865651011467,
0.002126504899933934,
-0.012355430983006954,
0.043461430817842484,
-0.01524872612208128,
-0.026025276631116867,
0.016461525112390518,
-0.04617953673005104,
-0.049678903073072433,
-0.043964944779872894,
-0.0033681620843708515,
0.06693059951066971,
0.02587258070707321,
-0.022773507982492447,
0.011799272149801254,
-0.017511757090687752,
-0.04881545528769493,
0.038878876715898514,
-0.0036987727507948875,
0.01029136311262846,
-0.011349381878972054,
-0.030812140554189682,
0.009425210766494274,
0.03886926546692848,
-0.03075159527361393,
0.011259755119681358,
0.018109522759914398,
-0.008412550203502178,
0.015320810489356518,
-0.02626843750476837,
-0.011742142029106617,
0.016973812133073807,
-0.013595733791589737,
0.01468019001185894,
-0.0017439794028177857,
0.011336179450154305,
0.008797257207334042,
0.017581680789589882,
0.022711506113409996,
0.04931783303618431,
-0.03179853782057762,
-0.004254997707903385,
0.035024818032979965,
-0.019633715972304344,
0.014365697279572487,
-0.0046285041607916355,
0.030457574874162674,
-0.019992394372820854,
-0.03240961953997612,
-0.040773529559373856,
0.02355947345495224,
-0.01232653483748436,
0.013279987499117851,
-0.02836156077682972,
-0.036677490919828415,
-0.040432408452034,
-0.029311154037714005,
-0.013632775284349918,
-0.010792024433612823,
-0.034231141209602356,
-0.0033011811319738626,
0.008028837852180004,
0.011978681199252605,
0.011258890852332115,
0.024158254265785217,
-0.03540438786149025,
-0.021527783945202827,
0.02466881461441517,
-0.0012523517943918705,
0.00739776948466897,
-0.024429859593510628,
-0.0025425225030630827,
0.0018511858070269227,
0.04915826767683029,
-0.048820286989212036,
-0.007073713466525078,
0.02923455648124218,
-0.051819272339344025,
-0.05702298879623413,
0.03434843197464943,
-0.020656442269682884,
-0.00801985152065754,
0.02411600761115551,
0.029906099662184715,
-0.020392000675201416,
0.07272552698850632,
-0.023538725450634956,
0.036597397178411484,
-0.047232989221811295,
-0.028969965875148773,
-0.0008214718545787036,
-0.0233113132417202,
-0.00356609420850873,
0.023966750130057335,
0.024274898692965508,
0.05098084360361099,
-0.018322356045246124,
-0.012897688895463943,
0.009535827673971653,
0.03244441747665405,
-0.005094221793115139,
-0.042053937911987305,
0.05654202401638031,
0.03683124855160713,
0.007540949620306492,
0.03351340442895889,
-0.012492053210735321,
0.031865060329437256,
0.03261198848485947,
0.028599537909030914,
-0.10960550606250763,
-0.03575265407562256,
-0.014170180074870586,
0.06842342764139175,
0.01848360151052475,
-0.03499111533164978,
0.001013058004900813,
0.017191806808114052,
-0.11080256849527359,
0.0006505850469693542,
-0.027174966409802437,
-0.005071975756436586,
-0.03362010791897774,
-0.018440833315253258,
-0.0027451347559690475,
0.011482647620141506,
0.02047336846590042,
0.004004005808383226,
0.060360491275787354,
0.05005268380045891,
-0.006204121746122837,
-0.05367637798190117,
-0.011634516529738903,
0.03959575295448303,
0.010107627138495445,
-0.013712450861930847,
0.049039050936698914,
-0.0037847845815122128,
0.00889204628765583,
0.009163645096123219,
0.019770294427871704,
0.026667144149541855,
-0.01206390094012022,
0.02201743982732296,
0.023279570043087006,
0.06285729259252548,
0.009207767434418201,
-0.022940494120121002,
-0.03777588531374931,
-0.0031758735422044992,
0.030599521473050117,
0.021482039242982864,
-0.008907170966267586,
-0.01044230442494154,
0.02951527014374733,
-0.02469296008348465,
-0.020862633362412453,
0.006771779619157314,
-0.013373414054512978,
0.01191471517086029,
0.013729523867368698,
0.034226495772600174,
0.014026639051735401,
-0.028362851589918137,
-0.0015066867927089334,
-0.0686597153544426,
-0.0241687074303627,
0.03953081741929054,
0.008126189932227135,
0.004403725732117891,
0.01663055643439293,
0.009002062492072582,
-0.006700425874441862,
0.010275769978761673,
0.019784972071647644,
0.009055103175342083,
-0.05884403735399246,
0.005348300561308861,
-0.016652343794703484,
0.0006370602059178054,
0.0343300923705101,
-0.024123121052980423,
-0.07806386053562164,
0.03919435665011406,
0.020617585629224777,
-0.019510501995682716,
-0.015395138412714005,
-0.0468803234398365,
-0.0008490514010190964,
-0.04693577066063881,
0.019281351938843727,
-0.0004433011345099658,
-0.026212554425001144,
-0.006345723755657673,
-0.03641651198267937,
-0.03844306617975235,
0.012691205367445946,
0.06472722440958023,
0.009129916317760944,
-0.02796625904738903,
0.004160039126873016,
0.007865608669817448,
-0.012690417468547821,
-0.05341744050383568,
-0.012326289899647236,
0.030319461598992348,
-0.002364874817430973,
-0.009944858029484749,
0.03133651241660118,
-0.022580619901418686,
0.004316037055104971,
-0.0010845157084986567,
0.014584041200578213,
-0.003675563260912895,
-0.0769352912902832,
-0.04954216256737709,
0.05197087675333023,
0.028520386666059494,
-0.03198578953742981,
0.07638546079397202,
-0.023246638476848602,
0.025042792782187462,
0.011860695667564869,
-0.012790465727448463,
-0.025221440941095352,
0.013707287609577179,
-0.012117015197873116,
-0.01140065211802721,
-0.024818796664476395,
0.004773082211613655,
0.04113335162401199,
-0.035006310790777206,
0.003889927640557289,
0.0755431205034256,
-0.04390282183885574,
-0.005378573667258024,
0.027999918907880783,
-0.0035360006149858236,
0.03438447043299675,
0.02865608222782612,
0.0004140001838095486,
0.00007253851072164252,
-0.005067932885140181,
-0.011303774081170559,
0.043203771114349365,
0.046652503311634064,
0.00679761590436101,
0.02319241687655449,
0.09392743557691574,
-0.016410814598202705,
-0.003511363873258233,
-0.011847549118101597,
-0.015731336548924446,
-0.02297918312251568,
-0.02396344766020775,
-0.021695349365472794,
-0.018161483108997345,
0.051995571702718735,
0.0012602269416674972,
-0.038334835320711136,
0.08530888706445694,
-0.0458126999437809,
0.009288899600505829,
-0.010048394091427326,
0.04265497997403145,
-0.015574722550809383,
0.035259611904621124,
-0.00844533834606409,
0.04694964736700058,
-0.030864017084240913,
-0.027268799021840096,
-0.03811993822455406,
-0.02644437924027443,
0.01433535385876894,
-0.047023408114910126,
-0.006467697210609913,
0.02833535708487034,
0.025961628183722496,
-0.014761552214622498,
0.0038019707426428795,
-0.017063580453395844,
-0.005222979001700878,
0.020150044932961464,
-0.005275702569633722,
0.026812925934791565,
-0.0063642170280218124,
-0.017096536234021187,
-0.00462632579728961,
0.05238174647092819,
-0.03866080567240715,
-0.00395377678796649,
0.021985894069075584,
0.00950881838798523,
-0.025606874376535416,
-0.03017468750476837
] |
<p>What was the proportion of dark matter/energy to other matters/energy at the moments after the beginning of the universe (standard Big Bang model)?</p> | 2,894 | [
-0.0033168529625982046,
-0.041206493973731995,
0.018378211185336113,
-0.041112419217824936,
0.059794697910547256,
0.03566408529877663,
-0.04131055995821953,
-0.07220951467752457,
-0.02352723479270935,
-0.06449641287326813,
0.01914503611624241,
0.012716398574411869,
0.032456543296575546,
0.006605677772313356,
0.0063287788070738316,
-0.007063611876219511,
0.0036182557232677937,
-0.0016926019452512264,
-0.0069971270859241486,
-0.02823665551841259,
0.01693124882876873,
0.01309240609407425,
0.007777577266097069,
0.021889302879571915,
-0.04131193831562996,
0.027452459558844566,
0.02378763072192669,
0.01330189872533083,
0.016549041494727135,
0.053628548979759216,
-0.013681678101420403,
-0.045752692967653275,
0.021492697298526764,
0.049517132341861725,
-0.0014776276657357812,
-0.003197016194462776,
0.008646603673696518,
-0.06749697774648666,
-0.037466373294591904,
0.020121349021792412,
-0.06329861283302307,
-0.031677212566137314,
-0.024071598425507545,
0.028014589101076126,
-0.033162347972393036,
0.025525221601128578,
0.015303962863981724,
-0.04432244226336479,
0.07106687128543854,
-0.03597095236182213,
0.0737384632229805,
-0.018971653655171394,
0.06789767742156982,
0.022787533700466156,
-0.01562514528632164,
-0.0007213866920210421,
0.07710760086774826,
0.06575959920883179,
0.031705375760793686,
-0.043541811406612396,
-0.04101021960377693,
0.018089326098561287,
0.012798210605978966,
-0.0242102462798357,
-0.013461269438266754,
0.04501860588788986,
-0.031170522794127464,
-0.021431580185890198,
0.02426132932305336,
-0.0030608687084168196,
0.025828629732131958,
0.017397573217749596,
0.05443301424384117,
0.02443460375070572,
0.03065844625234604,
-0.006007628049701452,
0.012581572867929935,
0.0013727383920922875,
0.03051772527396679,
0.04607917740941048,
0.011252358555793762,
-0.014887507073581219,
0.06180055812001228,
0.03992670401930809,
0.0077849687077105045,
0.026346569880843163,
0.034293532371520996,
-0.03642282262444496,
-0.005121685564517975,
0.05865411460399628,
-0.030522260814905167,
0.014494935050606728,
0.03908587247133255,
-0.006262165028601885,
-0.03387996926903725,
0.038648493587970734,
0.0024339838419109583,
0.03711573779582977,
0.0030045886524021626,
-0.008601361885666847,
0.03837266564369202,
-0.009899293072521687,
0.011861995793879032,
0.06702565401792526,
0.02925945073366165,
-0.0026443388778716326,
-0.08580581098794937,
0.03864293918013573,
-0.059891022741794586,
-0.00028112210566177964,
-0.026987582445144653,
-0.00044224370503798127,
-0.0174849983304739,
-0.014253887347877026,
-0.01169900968670845,
-0.01487031765282154,
0.018177609890699387,
-0.049609046429395676,
0.10835031419992447,
0.052855733782052994,
0.039484549313783646,
0.025289596989750862,
0.012600965797901154,
-0.020348258316516876,
-0.02986857295036316,
-0.026995809748768806,
0.0457511804997921,
-0.03305727615952492,
-0.05264252796769142,
0.047090668231248856,
-0.041646502912044525,
-0.0216167401522398,
0.022927019745111465,
0.0149309067055583,
0.04891309514641762,
0.00009241195220965892,
-0.039138056337833405,
-0.07206979393959045,
0.04239454120397568,
-0.036481134593486786,
-0.012060667388141155,
-0.04781816527247429,
-0.0020138868130743504,
0.03471165895462036,
0.05197941139340401,
-0.0012081241002306342,
-0.009901346638798714,
-0.03965987637639046,
0.052124302834272385,
-0.012126456946134567,
-0.02728562243282795,
-0.03212175518274307,
0.007754178252071142,
-0.010762292891740799,
-0.015999797731637955,
-0.07795961946249008,
0.014078001491725445,
0.07088826596736908,
-0.024063976481556892,
-0.01096478570252657,
0.020511042326688766,
-0.03471078723669052,
0.0020761217456310987,
-0.005077562294900417,
-0.030378643423318863,
-0.054287273436784744,
0.05065988004207611,
0.035970289260149,
-0.0026961842086166143,
0.01923428662121296,
-0.006619207561016083,
0.011516997590661049,
0.03253640979528427,
0.015200313180685043,
0.03469494357705116,
-0.03537210449576378,
-0.016283519566059113,
0.016649603843688965,
0.01544980239123106,
0.011301483027637005,
-0.03337870165705681,
0.00686549162492156,
0.0016285442980006337,
0.011841602623462677,
0.025143105536699295,
0.02337820827960968,
-0.0012404146837070584,
-0.04026162996888161,
0.0009884099708870053,
-0.020172681659460068,
-0.013758908957242966,
-0.051351793110370636,
-0.04195219278335571,
-0.005828586407005787,
-0.014925525523722172,
-0.01298100408166647,
0.021783998236060143,
0.02938496135175228,
-0.032005466520786285,
-0.01792500540614128,
0.030762413516640663,
0.009463376365602016,
0.015288207679986954,
0.015831589698791504,
0.01647735945880413,
0.056844886392354965,
0.04880543053150177,
-0.018866561353206635,
-0.02550673484802246,
0.026393724605441093,
-0.04798739403486252,
0.007088349666446447,
-0.011545324698090553,
0.020661307498812675,
-0.023249197751283646,
-0.0031955488957464695,
0.009519697166979313,
0.012896453961730003,
0.004886033944785595,
0.03855077922344208,
-0.013910086825489998,
0.06648733466863632,
0.022223839536309242,
0.015113404020667076,
-0.022666707634925842,
0.020360326394438744,
0.00990260299295187,
0.022715892642736435,
-0.014219832606613636,
-0.01542358286678791,
-0.05971940606832504,
-0.020058849826455116,
0.04228843376040459,
0.045556459575891495,
-0.03768451511859894,
-0.0020161541178822517,
0.038478996604681015,
0.004668110050261021,
0.021204425022006035,
0.002659098943695426,
-0.025114422664046288,
-0.078282929956913,
-0.01872541941702366,
0.026332324370741844,
0.005906679201871157,
0.014743461273610592,
0.01359171699732542,
-0.0030155295971781015,
-0.02159682661294937,
0.015603385865688324,
-0.005082324147224426,
0.01982790045440197,
0.010691339150071144,
-0.0013312394730746746,
-0.019760051742196083,
-0.05851657688617706,
0.034364841878414154,
-0.0012063024332746863,
0.004856590647250414,
0.03358416259288788,
0.02905949391424656,
-0.016973841935396194,
-0.009389268234372139,
-0.012533733621239662,
0.010468852706253529,
0.026190251111984253,
-0.004346462432295084,
0.0005112586659379303,
0.037125807255506516,
-0.028811700642108917,
0.0329664908349514,
-0.008751741610467434,
-0.012497171759605408,
-0.06817356497049332,
-0.011375297792255878,
0.027180265635252,
-0.0028230908792465925,
0.026766527444124222,
-0.0719006359577179,
-0.02484387345612049,
-0.0008932139608077705,
0.0324089489877224,
-0.010046777315437794,
0.03388145565986633,
-0.05466853082180023,
0.041411612182855606,
-0.04534453898668289,
-0.02108030579984188,
0.005026580765843391,
-0.018596846610307693,
0.02939322032034397,
0.03443730250000954,
-0.016287105157971382,
-0.010292544960975647,
-0.021684007719159126,
-0.00001490953036409337,
-0.020618317648768425,
-0.03395682945847511,
0.002961026970297098,
0.05913212522864342,
0.013261884450912476,
-0.04428591951727867,
0.01694916933774948,
-0.0327892079949379,
-0.024896545335650444,
-0.03838691487908363,
0.021497592329978943,
0.014491809532046318,
-0.031074048951268196,
0.054823242127895355,
-0.0022602519020438194,
-0.0569247342646122,
0.020415904000401497,
-0.06332752108573914,
-0.04784431681036949,
0.02285906858742237,
-0.021211368963122368,
0.029915396124124527,
-0.023329315707087517,
-0.020222848281264305,
0.05817713961005211,
0.029574330896139145,
-0.0030543000902980566,
-0.03685056418180466,
0.002606176771223545,
0.013577746227383614,
0.006590309087187052,
0.013623755425214767,
0.01829376444220543,
0.023023556917905807,
0.016048967838287354,
0.002190271858125925,
0.06502696871757507,
0.007229181472212076,
0.020098231732845306,
-0.01424742303788662,
0.047248002141714096,
-0.03877612203359604,
0.023609058931469917,
0.03155026584863663,
0.00349063309840858,
-0.004764662589877844,
0.013981451280415058,
-0.017663590610027313,
0.048944517970085144,
0.0047138105146586895,
-0.04841922968626022,
0.05914963781833649,
0.014685260131955147,
-0.014220615848898888,
-0.03054838255047798,
0.03142281994223595,
0.026125872507691383,
0.004348968155682087,
0.033823560923337936,
-0.016839081421494484,
0.03336591273546219,
0.03223542124032974,
0.00819458719342947,
0.011655386537313461,
0.019334852695465088,
-0.0008747279644012451,
-0.03756953775882721,
-0.015416177920997143,
0.003818211378529668,
0.02270546555519104,
-0.009005310013890266,
-0.02810741774737835,
0.025097692385315895,
0.061551615595817566,
0.021820474416017532,
-0.024137023836374283,
-0.022797398269176483,
-0.020554831251502037,
-0.06593760848045349,
-0.0029093543998897076,
-0.0169768538326025,
0.02139587141573429,
-0.012751917354762554,
0.05813891068100929,
0.008595652878284454,
-0.03323310986161232,
-0.0027041519060730934,
-0.01483619213104248,
-0.07236189395189285,
-0.00409894622862339,
-0.06169284135103226,
0.024338800460100174,
-0.007728420663625002,
0.0009016169351525605,
-0.02135373279452324,
-0.047368377447128296,
-0.01008337177336216,
-0.03606318682432175,
-0.03196648135781288,
-0.044900666922330856,
0.01888478361070156,
-0.053481511771678925,
-0.04657180234789848,
0.020804155617952347,
0.007805050350725651,
0.02498331293463707,
0.009613469243049622,
0.0046858759596943855,
0.03491205349564552,
-0.0065475753508508205,
-0.008675090037286282,
0.0036144969053566456,
0.006478417199105024,
-0.0411108136177063,
0.03756168857216835,
0.05529888719320297,
0.018664736300706863,
-0.06741814315319061,
-0.008674951270222664,
0.03803809732198715,
0.05415789783000946,
0.03160574287176132,
-0.01396010722965002,
-0.022363103926181793,
-0.05099502205848694,
-0.028861194849014282,
0.015186164528131485,
0.02184845320880413,
-0.009284934028983116,
0.011892789043486118,
0.015797561034560204,
0.037451911717653275,
-0.034993406385183334,
0.04964723810553551,
0.07495466619729996,
-0.006839158479124308,
-0.044035058468580246,
-0.055089183151721954,
0.007474107667803764,
-0.01379319280385971,
0.0138281574472785,
0.02334674261510372,
-0.0005885989521630108,
-0.01852547563612461,
0.029732342809438705,
-0.020006699487566948,
0.01842103712260723,
-0.017977338284254074,
-0.022791355848312378,
0.011860765516757965,
0.033230267465114594,
-0.021739713847637177,
-0.005089706275612116,
0.011769243516027927,
0.04144762083888054,
0.05434732139110565,
0.008434638381004333,
-0.014805734157562256,
-0.05371677130460739,
-0.006055673584342003,
0.043163739144802094,
0.033025726675987244,
-0.012845391407608986,
-0.001267062034457922,
-0.05691317468881607,
-0.007599543314427137,
0.028286641463637352,
-0.01631755195558071,
0.014423207379877567,
-0.016623493283987045,
0.02513645775616169,
0.011117623187601566,
-0.0416535958647728,
-0.020361511036753654,
0.05159582197666168,
-0.003937729634344578,
0.008034791797399521,
-0.011125276796519756,
-0.0062909903936088085,
-0.035831891000270844,
0.01652379147708416,
0.03600133955478668,
0.05150096118450165,
0.00781902577728033,
0.020264338701963425,
-0.009105644188821316,
0.016720984131097794,
-0.027405930683016777,
-0.08586903661489487,
0.026966845616698265,
-0.021290283650159836,
-0.05001526325941086,
0.02965845726430416,
-0.03805899620056152,
-0.032885778695344925,
0.021238910034298897,
0.03620842844247818,
-0.019650248810648918,
-0.014088895171880722,
-0.06672410666942596,
0.038208700716495514,
0.029389750212430954,
-0.019649799913167953,
0.07128269970417023,
0.008196386508643627,
-0.0043478189036250114,
0.014549647457897663,
-0.03823256120085716,
0.052878137677907944,
-0.028746221214532852,
0.000018180449842475355,
-0.029217401519417763,
-0.033119212836027145,
-0.027517570182681084,
0.033790674060583115,
-0.009725353680551052,
0.02463844045996666,
0.0328499972820282,
-0.050743505358695984,
0.014637482352554798,
0.034347742795944214,
0.034802284091711044,
0.015907607972621918,
-0.007216621655970812,
0.012343459762632847,
0.007820989936590195,
0.0014277661684900522,
0.040441375225782394,
0.0034228633157908916,
0.002749138278886676,
-0.0045784092508256435,
-0.020741065964102745,
0.03206877410411835,
0.0035499336663633585,
-0.002840532222762704,
0.03136785328388214,
0.005124955903738737,
0.0075358496978878975,
0.009066099300980568,
0.017534403130412102,
0.006179798394441605,
-0.09114314615726471,
-0.03981387987732887,
0.019380465149879456,
-0.017732392996549606,
0.01632620021700859,
-0.038620322942733765,
0.013230960816144943,
0.005853574723005295,
0.02517389878630638,
-0.08088286966085434,
-0.031980112195014954,
0.014140729792416096,
0.01103721559047699,
-0.0008107544854283333,
-0.020022675395011902,
0.008539814502000809,
-0.05324961245059967,
-0.010242737829685211,
-0.012756227515637875,
0.050461769104003906,
-0.018703147768974304,
-0.00809877086430788,
-0.022988010197877884,
0.012324131093919277,
0.015184207819402218,
-0.03629748150706291,
-0.046471208333969116,
0.009247587993741035,
0.031827278435230255,
-0.009943458251655102,
-0.0016106029506772757,
0.036305300891399384,
-0.0379016175866127,
-0.013205600902438164,
0.010548480786383152,
-0.006486799567937851,
0.015100251883268356,
-0.05767546966671944,
-0.018434563651680946,
0.04866848140954971,
0.006955793127417564,
0.0027110727969557047,
0.013941705226898193,
0.05379325896501541,
-0.02685053087770939,
0.017702383920550346,
0.0008255686843767762,
-0.00799876730889082,
-0.01556587964296341,
-0.03622141107916832,
0.07780838757753372,
-0.010114793665707111,
0.01705794595181942,
-0.008187545463442802,
0.05032934248447418,
0.05011574178934097,
-0.06881803274154663,
0.009858155623078346,
-0.035786449909210205,
0.02100798860192299,
-0.009610382840037346,
0.03327013924717903,
0.031192386522889137,
-0.003764622611925006,
-0.026987893506884575,
-0.0158818531781435,
-0.01882857270538807,
-0.030403587967157364,
0.043682463467121124,
0.017954569309949875,
0.013464429415762424,
-0.012912639416754246,
-0.033909909427165985,
-0.00004255784733686596,
-0.026512138545513153,
0.0004322836175560951,
0.022764505818486214,
-0.001155332662165165,
0.018977012485265732,
-0.049755826592445374,
-0.016080211848020554,
0.02094142697751522,
0.026975248008966446,
-0.027502939105033875,
0.05231975391507149,
0.014675472863018513,
0.0017727934755384922,
0.04135744646191597,
-0.009116814471781254,
-0.04692784324288368,
0.013703184202313423,
-0.028958508744835854,
0.0231634471565485,
-0.013359220698475838,
-0.035801153630018234,
0.04065065458416939,
-0.004153000190854073,
-0.03505654260516167,
-0.02012561447918415,
-0.010352903045713902,
-0.042032524943351746,
0.0072622112929821014,
0.0200516190379858,
0.032176777720451355,
-0.006329192314296961,
0.043787602335214615,
0.01309698075056076,
-0.044747281819581985,
-0.0097508504986763,
0.035083550959825516,
-0.07882855087518692,
-0.04127882421016693,
-0.023636547848582268,
-0.04864197224378586,
0.03935008496046066,
-0.0274883471429348,
-0.028603915125131607,
0.004874430596828461,
-0.006048437207937241,
-0.034555546939373016,
-0.00383958057500422,
-0.011540975421667099,
0.008362587541341782,
0.0770418792963028,
-0.012965871952474117,
0.0194733664393425,
-0.047072913497686386,
0.03116939403116703,
0.12692603468894958,
0.07532726973295212,
-0.0035504898987710476,
-0.06886160373687744,
0.022097600623965263,
-0.01490784902125597,
0.007500470150262117,
-0.01855316013097763,
0.03779178485274315,
-0.007639668416231871,
0.008731134235858917,
0.003067741636186838,
0.01550295203924179,
0.00834006629884243,
-0.018290968611836433,
0.02392437309026718,
-0.023251280188560486,
-0.028787225484848022,
0.00339075131341815,
0.021413486450910568,
-0.013185421004891396,
0.025171859189867973,
-0.03784393146634102,
0.009750978089869022,
0.0149273332208395,
0.009611086919903755,
-0.02895907126367092,
-0.03943568095564842,
-0.02956954948604107,
-0.02096443623304367,
-0.043165549635887146,
-0.0038290894590318203,
0.03125632181763649,
0.0013254656223580241,
-0.018658293411135674,
-0.02750413864850998,
0.02568574622273445,
0.009603413753211498,
-0.0031191681046038866,
0.0010129810543730855,
0.02735535055398941,
0.016818180680274963,
-0.026433400809764862,
-0.019324958324432373,
-0.0477621927857399,
-0.02039257436990738,
0.0011284161591902375,
0.05373569577932358,
-0.014568011276423931,
-0.008074828423559666,
0.029749514535069466,
0.017993981018662453,
-0.014445138163864613,
-0.0070297191850841045,
-0.041116680949926376,
0.023889046162366867,
0.02671968564391136,
-0.01917341724038124,
-0.024159714579582214,
-0.01490161381661892,
0.014225499704480171,
-0.022086966782808304,
0.05917774513363838,
-0.030962707474827766,
0.04567430540919304,
0.006559806875884533,
-0.0125229237601161,
0.047137726098299026,
-0.02395438961684704,
0.0019864607602357864,
-0.013015970587730408,
-0.016835613176226616,
-0.05939781665802002,
0.02225128561258316,
0.015045869164168835,
0.02710166573524475,
0.05024781450629234,
0.008654181845486164,
-0.00925290398299694,
-0.018909430131316185,
-0.023789340630173683,
0.029812980443239212,
-0.024160826578736305,
-0.01785510964691639,
-0.01183008961379528,
0.022190894931554794,
0.0034639867953956127,
0.06651972234249115,
-0.02846038155257702,
0.021993134170770645,
-0.014734435826539993,
0.028826957568526268,
0.029380740597844124,
-0.03842121735215187,
0.007140209432691336,
-0.004674575757235289,
-0.022878650575876236,
0.0001303997269133106,
-0.04722756892442703,
0.005587500520050526,
0.019283609464764595,
-0.013476706109941006,
0.006000750232487917,
0.021107107400894165,
0.008472057059407234,
0.024075135588645935,
0.011044789105653763,
-0.05352112278342247,
-0.015270425006747246,
0.007838123477995396,
0.02937011606991291,
-0.02636137418448925,
-0.023072347044944763,
-0.032993383705616,
0.005590631626546383,
0.026417959481477737,
0.031737200915813446,
-0.035224560648202896,
0.007289315108209848,
-0.004204731900244951,
0.005609956104308367,
-0.023981692269444466,
-0.02163964882493019,
-0.03216556832194328,
0.014735457487404346,
0.003085983917117119,
-0.01272333599627018,
0.002135945251211524,
0.05224611982703209,
0.014068474993109703,
0.005372934974730015,
0.01425863616168499,
-0.03007175587117672,
-0.00941324234008789,
-0.03513837978243828,
0.024605227634310722,
-0.008415485732257366,
0.04569735378026962,
-0.0032671024091541767,
-0.009505449794232845,
0.02451612614095211,
-0.036836035549640656,
-0.07839986681938171,
0.019322311505675316,
0.0037955648731440306,
0.00434488570317626,
0.022938022390007973,
0.00406947685405612,
-0.01937001757323742,
0.0789482593536377,
-0.02622171863913536,
-0.040568362921476364,
0.043846774846315384,
0.011444524861872196,
-0.012331893667578697,
0.019423695281147957,
0.029566330835223198,
0.015682756900787354,
-0.0037657367065548897,
0.040421050041913986,
0.01639585755765438,
0.0005550741334445775,
-0.021363552659749985,
0.009062422439455986,
-0.05820484831929207,
0.02034449204802513,
-0.000601584673859179,
0.03386784344911575,
0.014627902768552303,
0.04775611683726311,
-0.03732534870505333,
0.05550013482570648,
0.060439594089984894,
-0.0026012714952230453,
-0.07813716679811478,
-0.000936210504733026,
-0.012891639955341816,
0.007173430174589157,
0.033313535153865814,
-0.02450592629611492,
0.03261220082640648,
0.022760940715670586,
-0.05984405428171158,
0.03306424245238304,
0.0020380786154419184,
-0.01320299506187439,
-0.023137765005230904,
-0.023783473297953606,
-0.03782811760902405,
0.05584972724318504,
0.03810076788067818,
0.06220554932951927,
0.024915054440498352,
0.015774257481098175,
-0.009702696464955807,
-0.010998108424246311,
-0.04084715619683266,
0.009964575059711933,
-0.00677748117595911,
0.017162781208753586,
0.049749307334423065,
-0.0030730338767170906,
-0.022011077031493187,
0.040164098143577576,
0.04876444861292839,
-0.009973835200071335,
-0.01015639677643776,
0.013980371877551079,
0.017780683934688568,
0.037921689450740814,
0.0119898971170187,
0.004289948381483555,
0.04159246385097504,
0.015148484148085117,
-0.0055389404296875,
-0.003079742658883333,
0.0010252631036564708,
-0.017446303740143776,
0.010604155249893665,
-0.025712210685014725,
-0.011116289533674717,
0.0188517514616251,
0.01859295181930065,
-0.0163071658462286,
0.02206292934715748,
0.018299071118235588,
-0.004945344757288694,
-0.03155909851193428,
-0.012849037535488605,
-0.034341685473918915,
-0.03171927109360695,
0.062176432460546494,
0.0002497129316907376,
-0.03772464394569397,
0.01929004117846489,
0.006391514558345079,
0.001733094803057611,
-0.011309823952615261,
0.010596409440040588,
-0.010996195487678051,
-0.027333268895745277,
0.021911315619945526,
-0.003168897470459342,
0.030499638989567757,
-0.002250521909445524,
-0.059123337268829346,
-0.06691072881221771,
0.04560445249080658,
-0.009723886847496033,
0.03651701286435127,
0.009012894704937935,
-0.06051411107182503,
-0.015252167358994484,
-0.06965314596891403,
0.030270323157310486,
-0.0024465646129101515,
0.028854502364993095,
-0.028183026239275932,
0.008883449248969555,
0.0003823659790214151,
-0.037143073976039886,
0.0339643694460392,
0.015224392525851727,
-0.04776640608906746,
-0.012447197921574116,
0.022023174911737442,
0.04705058038234711,
-0.0534893162548542,
0.021949702873826027,
0.010865438729524612,
-0.029530193656682968,
0.0029681213200092316,
-0.0191469918936491,
0.011416408233344555,
0.006348535418510437,
-0.010048801079392433,
-0.03225582093000412,
-0.004809913691133261,
-0.012008883990347385,
-0.01844811625778675,
0.07384713739156723,
0.007384912576526403,
-0.02705482952296734,
0.06655991822481155,
-0.0294408667832613,
0.019312243908643723,
0.06229226291179657,
0.01357906125485897,
-0.061835646629333496,
-0.019962197169661522,
-0.029977958649396896,
-0.0359228253364563,
-0.0066490680910646915,
0.01647537760436535,
0.020237524062395096,
-0.025762885808944702,
-0.00938995461910963,
0.03983073681592941,
0.0009964228374883533,
0.01019405759871006,
0.03462744876742363,
-0.032496411353349686,
0.0739673599600792,
0.0029883594252169132,
-0.0017368743428960443,
0.017125975340604782,
0.039413295686244965,
-0.019401131197810173,
0.007717933505773544,
0.03663183003664017,
0.011159569025039673,
-0.004149298649281263,
-0.004843101371079683,
-0.0000562351597181987,
0.014252817258238792,
-0.005454620812088251,
0.011158802546560764,
-0.06819644570350647,
-0.05733286961913109,
0.006335496436804533,
-0.01836409978568554,
0.03426983579993248,
0.020221058279275894,
0.00590529153123498,
0.06993745267391205,
-0.035474877804517746,
0.029203616082668304,
-0.000043844480387633666,
-0.0487443208694458,
-0.02369464375078678,
0.032588206231594086,
-0.01585344783961773,
0.03473321720957756,
0.009778453968465328,
0.0015603839419782162,
-0.030022339895367622,
0.0047737048007547855,
0.029917582869529724,
-0.06977289170026779,
0.0209212489426136,
0.025469008833169937,
0.00485110841691494,
0.008580710738897324,
-0.0006293286569416523,
-0.0026191221550107002,
-0.03430298715829849,
0.058689385652542114,
0.053068067878484726,
0.009107435122132301,
-0.022743308916687965,
-0.012130459770560265,
-0.006770401727408171,
0.032864369451999664,
-0.025854624807834625,
-0.010140231810510159,
-0.05860720947384834,
0.03500967472791672,
-0.031888946890830994,
-0.0317767933011055
] |
<p>When correlation function has branch cut in momentum space,
how to find correlation in coordinate space?
For example
$$ \tilde {G}(\omega) = \frac{2i}{\omega+(\omega^2-\nu^2)^{1/2}}$$
How to get the $G(t)$ usng Fourier transformation ?<br>
t>0 HERE.
This problem is from matrix model of Iizuka and Polchinski. They discuss the propagator in the model and find that the propagator $G(t)$ has power law decay behavior if there is branch cut in $\tilde{G}(\omega)$. If there is a pole in the lower half plane for $\tilde{G}(\omega)$, there is an exponential decay in $G(t)$.</p> | 2,895 | [
0.011020238511264324,
-0.024338718503713608,
0.0014383404050022364,
-0.029946472495794296,
0.030696069821715355,
0.019769838079810143,
-0.06747660040855408,
-0.03782416507601738,
0.07232756167650223,
-0.0682920441031456,
0.05354475975036621,
0.020296592265367508,
0.07163510471582413,
0.02658834308385849,
0.01223362609744072,
-0.0011959137627854943,
-0.01968151144683361,
-0.005381124559789896,
-0.022043652832508087,
-0.00825946033000946,
0.0009258014615625143,
0.0010464448714628816,
-0.02814083732664585,
-0.04204118996858597,
0.01513076014816761,
0.04315827414393425,
0.007066566031426191,
0.015048835426568985,
-0.0035065629053860903,
0.06618932634592056,
-0.03327637165784836,
-0.035228997468948364,
0.026043780148029327,
0.055768005549907684,
-0.03716689348220825,
0.004895852878689766,
-0.007245026994496584,
-0.02716827765107155,
0.0005049056489951909,
0.028312528505921364,
-0.05519455298781395,
-0.03011162020266056,
-0.010292037390172482,
0.024241464212536812,
0.01156921312212944,
0.06154292821884155,
0.008337199687957764,
-0.002740239491686225,
0.05944738909602165,
-0.005681774113327265,
0.04765206575393677,
-0.005991336423903704,
0.01015543658286333,
-0.028631461784243584,
0.01091047003865242,
-0.0015055786352604628,
0.0582696832716465,
0.03252952918410301,
-0.013303663581609726,
-0.04346420615911484,
-0.027375193312764168,
-0.03286103904247284,
0.05051932483911514,
0.02533610723912716,
-0.0036256934981793165,
-0.031154491007328033,
-0.00038499326910823584,
-0.050070591270923615,
0.007904318161308765,
-0.019560547545552254,
-0.032574042677879333,
0.024983199313282967,
0.026973456144332886,
-0.019689172506332397,
0.025490865111351013,
0.022760450839996338,
0.01408817432820797,
0.04567606747150421,
0.026698287576436996,
0.011035746894776821,
0.004720261320471764,
0.01795073039829731,
-0.03295677527785301,
0.010193505324423313,
-0.031115179881453514,
0.014144920744001865,
0.061079900711774826,
-0.02331259660422802,
-0.024539481848478317,
0.05627282336354256,
-0.027336740866303444,
-0.019478604197502136,
0.026374612003564835,
0.005228420719504356,
-0.017991241067647934,
0.03518258035182953,
0.000520282075740397,
0.021685946732759476,
0.012490459717810154,
-0.003150805365294218,
-0.030360136181116104,
-0.07279524952173233,
-0.042563192546367645,
0.07639245688915253,
-0.019815130159258842,
0.04261774942278862,
-0.039286769926548004,
-0.0279636662453413,
-0.05241047218441963,
-0.05247965455055237,
-0.04044928401708603,
0.014621644280850887,
-0.013251771219074726,
-0.0021342856343835592,
0.008064045570790768,
-0.002250840188935399,
-0.01730264537036419,
-0.04767507687211037,
0.07009245455265045,
0.09105131030082703,
0.027036519721150398,
0.0152988126501441,
-0.019831255078315735,
-0.01225756574422121,
-0.07328854501247406,
0.0015819132095202804,
0.06548847258090973,
-0.009118139743804932,
-0.05174567550420761,
0.031777139753103256,
0.025200508534908295,
-0.03476996719837189,
0.016795465722680092,
-0.029561689123511314,
0.046952079981565475,
0.01771155372262001,
-0.07930142432451248,
-0.018956750631332397,
0.06543656438589096,
-0.012438934296369553,
-0.0000670825393171981,
-0.05908522009849548,
0.01113069523125887,
0.03513471409678459,
0.07250912487506866,
0.01231253519654274,
-0.009600107558071613,
-0.02508450299501419,
0.037741053849458694,
0.016983637586236,
0.007298912387341261,
-0.026682816445827484,
-0.01924893632531166,
-0.03574874997138977,
-0.014194462448358536,
0.021895689889788628,
0.03127892687916756,
0.03289398178458214,
-0.0015384836588054895,
-0.0376582033932209,
0.07100129872560501,
0.025738965719938278,
0.023857509717345238,
-0.003004590282216668,
-0.02214805595576763,
-0.03431165590882301,
0.059256311506032944,
-0.003926908131688833,
-0.011720528826117516,
0.003271139459684491,
-0.015157013200223446,
0.01354470755904913,
-0.007418813183903694,
0.016783274710178375,
0.04099683836102486,
-0.021212726831436157,
-0.022342853248119354,
-0.02745632641017437,
-0.003901639487594366,
-0.0010264787124469876,
-0.030171643942594528,
0.007774919271469116,
-0.04170842468738556,
0.007011807523667812,
0.009305150248110294,
0.014720779843628407,
-0.01272000465542078,
-0.011296248063445091,
0.012805010192096233,
-0.04835767298936844,
-0.002013053745031357,
-0.014484149403870106,
0.01604474149644375,
0.015688590705394745,
-0.028560500591993332,
0.01632278598845005,
0.014737877063453197,
0.016538765281438828,
0.02447986602783203,
-0.05017634108662605,
-0.021702824160456657,
0.028721585869789124,
0.012149320915341377,
-0.03359847515821457,
0.0445382185280323,
0.03202274814248085,
0.05897993594408035,
-0.0007769297808408737,
0.059771474450826645,
-0.022092677652835846,
-0.02065199986100197,
0.020400717854499817,
-0.015754373744130135,
-0.002583777531981468,
0.001027872203849256,
-0.00023695325944572687,
0.015912793576717377,
-0.005295589100569487,
-0.01301609631627798,
0.0070935399271547794,
-0.02997535653412342,
0.05275442823767662,
0.08769797533750534,
0.0026534749194979668,
0.03255818784236908,
0.02002742514014244,
0.010833359323441982,
0.05018576979637146,
-0.03330016881227493,
-0.08517853170633316,
-0.010164160281419754,
-0.03804929554462433,
0.01528882421553135,
0.03170805051922798,
-0.03458345681428909,
-0.007753119803965092,
0.08994921296834946,
0.03305124491453171,
-0.0005205954075790942,
0.019359320402145386,
0.014018692076206207,
-0.01587829738855362,
-0.009868623688817024,
0.026714805513620377,
-0.0031629507429897785,
-0.009122245945036411,
0.0047788796946406364,
0.024024654179811478,
-0.008418744429945946,
0.0068244789727032185,
-0.059155385941267014,
0.025577668100595474,
0.008699950762093067,
-0.015139457769691944,
-0.0031276196241378784,
-0.011313017457723618,
0.05823388323187828,
0.02143033593893051,
0.019138669595122337,
0.028573811054229736,
-0.02340647019445896,
-0.0004743275640066713,
-0.01582268252968788,
-0.019165057688951492,
0.06560324877500534,
0.03450937941670418,
-0.03902909904718399,
-0.06208956614136696,
0.02057054452598095,
-0.011522641405463219,
-0.0085942093282938,
-0.004519033245742321,
-0.0046668583527207375,
-0.007392893545329571,
0.012828229926526546,
0.05708957836031914,
0.016735687851905823,
0.004371809773147106,
-0.03674562647938728,
-0.06719967722892761,
-0.009374690242111683,
0.024268319830298424,
0.000635689590126276,
0.02412409521639347,
-0.05610985681414604,
-0.01901320368051529,
-0.09726391732692719,
-0.0008420887170359492,
-0.02485373616218567,
0.015704505145549774,
0.01888289302587509,
-0.024529727175831795,
0.04328914359211922,
-0.055819638073444366,
-0.04557662457227707,
0.012462153099477291,
0.019535858184099197,
-0.021202685311436653,
0.0015179397305473685,
0.04914651811122894,
-0.026455219835042953,
-0.04787299036979675,
-0.0025135520845651627,
-0.0043704332783818245,
-0.03462822362780571,
-0.02386241778731346,
0.009904374368488789,
0.060581695288419724,
-0.022011982277035713,
0.05781598761677742,
-0.004661422222852707,
-0.026682578027248383,
-0.021598318591713905,
-0.06969928741455078,
-0.01691378280520439,
0.031237615272402763,
0.028555702418088913,
0.042123712599277496,
-0.005860581062734127,
-0.03439288213849068,
0.07739920169115067,
0.038341015577316284,
-0.04479546099901199,
-0.018788672983646393,
0.027288837358355522,
0.008104723878204823,
-0.025317933410406113,
-0.02238774485886097,
0.00926666334271431,
0.02176947332918644,
0.09882806241512299,
0.017928436398506165,
0.030619753524661064,
0.03599914535880089,
0.03951993212103844,
-0.006472749635577202,
0.030039586126804352,
0.0057624527253210545,
0.022519344463944435,
0.02333744242787361,
-0.0065489280968904495,
-0.040119051933288574,
0.01752161979675293,
0.004050404764711857,
0.012736208736896515,
0.013111126609146595,
-0.06098318472504616,
0.016818556934595108,
-0.0009315870702266693,
0.021043768152594566,
-0.012190883047878742,
0.026496876031160355,
0.015693647786974907,
-0.008992142975330353,
-0.000015391105989692733,
0.0835222601890564,
0.05352402478456497,
0.024456460028886795,
0.03367059305310249,
0.014914629980921745,
-0.00839980412274599,
-0.007271329406648874,
-0.02744693122804165,
-0.026797017082571983,
-0.011105242185294628,
0.03594975173473358,
-0.0169763695448637,
-0.040477655827999115,
0.03828136622905731,
0.032791875302791595,
-0.015319056808948517,
-0.008413385599851608,
-0.009528250433504581,
-0.040818896144628525,
-0.011956432834267616,
0.024689745157957077,
0.0033138359431177378,
0.04894530028104782,
0.022306101396679878,
0.018892329186201096,
0.02269187942147255,
0.038421910256147385,
0.028478192165493965,
0.002202882431447506,
-0.05818360298871994,
0.01054257433861494,
-0.018655357882380486,
-0.0032305375207215548,
-0.002502680290490389,
0.019978201016783714,
0.012589944526553154,
0.0035582336131483316,
-0.030557645484805107,
0.0010548614664003253,
-0.0024400122929364443,
-0.06703659892082214,
0.0437748022377491,
-0.053357429802417755,
-0.022314809262752533,
-0.02957594022154808,
0.02949429675936699,
0.06212764233350754,
-0.02462526224553585,
0.004141662735491991,
0.04382031038403511,
-0.014580112881958485,
0.021980827674269676,
-0.016455236822366714,
0.01482502743601799,
0.01405331864953041,
0.021728772670030594,
0.04617304354906082,
0.016805576160550117,
-0.01715465821325779,
0.000561828725039959,
0.012738378718495369,
0.07345155626535416,
0.020827390253543854,
-0.01749853417277336,
0.06198528781533241,
-0.04321083053946495,
0.019076215103268623,
0.0013677170500159264,
0.04133016616106033,
-0.0017969204345718026,
-0.027941126376390457,
0.0349881611764431,
-0.006473221350461245,
-0.012739377096295357,
0.027741694822907448,
0.060198575258255005,
0.007766388822346926,
-0.0029371094424277544,
-0.03176264837384224,
0.001030852785333991,
0.0015991099644452333,
-0.0024204475339502096,
0.020834781229496002,
0.00449146656319499,
-0.0016373207326978445,
-0.0010279202833771706,
0.04987050220370293,
0.05329824984073639,
-0.026543421670794487,
-0.029220450669527054,
0.011056704446673393,
0.012224017642438412,
0.004685152322053909,
-0.033019330352544785,
0.01760321855545044,
0.012582474388182163,
0.03447888419032097,
0.025105269625782967,
0.009281995706260204,
-0.032952748239040375,
-0.003824663581326604,
0.011846484616398811,
0.04027417674660683,
0.022911425679922104,
0.0037559119518846273,
-0.04580093175172806,
-0.05853993073105812,
0.04925268888473511,
-0.006263015326112509,
0.03149222955107689,
0.00013111809676047415,
-0.05710070952773094,
0.012506110593676567,
-0.033458560705184937,
-0.035497505217790604,
0.016600346192717552,
-0.014260414987802505,
-0.027610676363110542,
-0.06577040255069733,
-0.016255654394626617,
-0.011619668453931808,
-0.003468972397968173,
-0.025388294830918312,
0.021222736686468124,
0.03526570275425911,
0.015360312536358833,
-0.007991822436451912,
0.050763584673404694,
-0.02017088420689106,
-0.03970446437597275,
-0.01676127128303051,
0.008824634365737438,
-0.018767409026622772,
0.04646870493888855,
-0.035691458731889725,
-0.06027378886938095,
-0.0023662832099944353,
0.0034664191771298647,
-0.008544962853193283,
-0.009269526228308678,
-0.03245799243450165,
0.08085411041975021,
-0.003333096858114004,
-0.03922436758875847,
0.06917891651391983,
0.06182727590203285,
0.011515480466187,
-0.03605559468269348,
-0.04738900437951088,
0.03837210685014725,
-0.02319217100739479,
0.02041737549006939,
-0.04962210729718208,
0.0033811903558671474,
-0.02518695406615734,
0.024513378739356995,
-0.0324329137802124,
0.00042336893966421485,
-0.04033966735005379,
0.0070040347054600716,
0.008171754889190197,
0.030796801671385765,
-0.02390204183757305,
-0.0016381106106564403,
0.015155710279941559,
0.028917357325553894,
0.037553172558546066,
-0.022224998101592064,
-0.013527256436645985,
-0.043271154165267944,
-0.010476498864591122,
0.011775488965213299,
0.002274941187351942,
0.003741355612874031,
-0.045531559735536575,
0.0038603825960308313,
-0.007332730107009411,
-0.04240364953875542,
0.00775118125602603,
-0.005770134273916483,
-0.01993461884558201,
0.0504617802798748,
0.0018392958445474505,
-0.002804925199598074,
0.004060719627887011,
-0.016376575455069542,
0.022508060559630394,
-0.02071155235171318,
-0.0008832861203700304,
-0.01045380998402834,
0.029287759214639664,
-0.07404999434947968,
-0.040445879101753235,
-0.021146465092897415,
0.011259935796260834,
0.00556717487052083,
-0.0041107311844825745,
0.0037033807020634413,
-0.04257746413350105,
0.007989365607500076,
-0.02146308310329914,
0.014131798408925533,
0.008505984209477901,
0.01587970368564129,
0.025395523756742477,
0.0508154071867466,
0.05165278539061546,
-0.008922972716391087,
-0.028839701786637306,
0.017534973099827766,
-0.03949860855937004,
-0.03878016024827957,
0.0008743969374336302,
0.031025543808937073,
-0.048596154898405075,
-0.039026446640491486,
-0.017020683735609055,
-0.017272762954235077,
0.015262680128216743,
-0.01989889331161976,
-0.029427850618958473,
0.022019390016794205,
-0.027006225660443306,
0.049688681960105896,
0.006658783182501793,
-0.033418625593185425,
0.006795892026275396,
0.0003031415108125657,
0.0014962349086999893,
-0.01427173987030983,
-0.013752282597124577,
-0.0395069494843483,
-0.005037312861531973,
0.004158696159720421,
-0.001512272167019546,
0.023312073200941086,
0.05281275883316994,
-0.0270131416618824,
0.011645988561213017,
0.016907431185245514,
-0.0269053652882576,
-0.004887764807790518,
0.014279690571129322,
0.0046867807395756245,
0.018951762467622757,
0.006593968253582716,
-0.05133618414402008,
-0.041355252265930176,
-0.03947322070598602,
-0.0009590530535206199,
0.05147568881511688,
0.004963333252817392,
0.03300204128026962,
0.03112201951444149,
0.004899711348116398,
-0.03587576374411583,
-0.003848851192742586,
-0.006709856912493706,
0.01251427736133337,
-0.015446995384991169,
0.022868523374199867,
-0.03997638821601868,
-0.014582952484488487,
0.038334429264068604,
0.042174749076366425,
-0.04168130084872246,
0.03308948874473572,
-0.02051389217376709,
0.026993166655302048,
0.02174043096601963,
0.0024408958852291107,
0.004275698680430651,
0.031273599714040756,
-0.031987812370061874,
0.06640676409006119,
-0.05232037231326103,
0.002210075967013836,
0.008984536863863468,
0.07341772317886353,
-0.035079438239336014,
-0.025032635778188705,
-0.000981086166575551,
-0.03942697495222092,
0.005011152010411024,
0.014854389242827892,
-0.015399590134620667,
0.02578923851251602,
0.05738319084048271,
0.023194175213575363,
-0.048692528158426285,
0.02479773759841919,
-0.007948524318635464,
-0.03287038579583168,
0.009027023799717426,
-0.013682711869478226,
-0.0412159226834774,
0.06800606101751328,
0.002883777255192399,
0.0005128412158228457,
0.01597934029996395,
-0.0029790590051561594,
-0.021072663366794586,
-0.029403120279312134,
0.01262020692229271,
-0.03124384768307209,
0.09726952016353607,
-0.008065157569944859,
0.018537187948822975,
0.05450058728456497,
-0.00021989556262269616,
0.11117416620254517,
0.04731336981058121,
-0.019654717296361923,
-0.06522838026285172,
0.009897100739181042,
0.008355657570064068,
-0.00325592840090394,
-0.042414430528879166,
-0.00905615370720625,
0.023441337049007416,
0.0010561425006017089,
0.011944783851504326,
0.07795640081167221,
0.004426679573953152,
-0.03214481100440025,
0.03813247010111809,
-0.041264116764068604,
-0.0613776333630085,
-0.006011174060404301,
0.016010938212275505,
-0.03944926708936691,
0.012482156977057457,
-0.03942704573273659,
0.055352628231048584,
-0.029303602874279022,
0.0012040145229548216,
-0.0475497767329216,
-0.0011107252212241292,
0.020222000777721405,
-0.03151848539710045,
-0.014831911772489548,
0.0014244591584429145,
0.03384333476424217,
0.021980496123433113,
0.00659219129011035,
0.007487872149795294,
0.007719099521636963,
0.0423232801258564,
0.02105106972157955,
0.03950677067041397,
-0.006202453747391701,
-0.0151370819658041,
0.014200441539287567,
0.005007748957723379,
0.0002795244217850268,
-0.05649378150701523,
-0.008188086561858654,
0.05090375617146492,
-0.01567170023918152,
-0.026260139420628548,
0.0011213592952117324,
-0.0009615163435228169,
0.013533049263060093,
-0.01970483735203743,
0.005849451292306185,
0.013888605870306492,
0.04239470139145851,
-0.036025915294885635,
-0.018215220421552658,
-0.020023558288812637,
0.027123579755425453,
-0.015258404426276684,
0.004530560690909624,
0.00633263261988759,
-0.04361475631594658,
-0.03340519964694977,
0.0016216123476624489,
0.04618879407644272,
0.04437205567955971,
-0.04035920277237892,
-0.029437171295285225,
-0.0066164047457277775,
-0.015277238562703133,
-0.018067527562379837,
0.020895717665553093,
0.0001776881836121902,
0.03990417346358299,
0.009023724123835564,
-0.008357645943760872,
-0.03819436952471733,
-0.06294025480747223,
0.01680384948849678,
-0.02163068950176239,
-0.04945463314652443,
0.014286112040281296,
-0.005620777606964111,
-0.0052484492771327496,
0.03539985790848732,
0.00279691768810153,
0.002075865166261792,
-0.03963485360145569,
0.052845243364572525,
0.07329205423593521,
-0.059574153274297714,
-0.02182045392692089,
-0.02660057134926319,
-0.012942487373948097,
0.023497235029935837,
-0.014997674152255058,
0.014472578652203083,
0.02985544688999653,
-0.0011100673582404852,
0.02798650972545147,
0.010526450350880623,
-0.023569094017148018,
-0.019526580348610878,
0.04051667079329491,
-0.04505983367562294,
0.0035029894206672907,
-0.014696121215820312,
-0.006628257222473621,
-0.04214810952544212,
-0.006624918896704912,
-0.005867527332156897,
-0.013379685580730438,
0.013209620490670204,
0.005391554906964302,
-0.03230169788002968,
-0.014284511096775532,
-0.024129651486873627,
0.012565580196678638,
-0.04259355366230011,
-0.008758938871324062,
-0.04029928520321846,
-0.0019013865385204554,
-0.012721671722829342,
-0.012339416891336441,
-0.010864585638046265,
0.03589944168925285,
-0.014062921516597271,
-0.01760551892220974,
0.016587503254413605,
0.07058195024728775,
-0.02681034617125988,
-0.0074046822264790535,
0.021195152774453163,
-0.01856195740401745,
0.051006730645895004,
-0.018486443907022476,
0.029479211196303368,
0.051564596593379974,
-0.02140512876212597,
-0.0043708207085728645,
0.06039658561348915,
-0.040700096637010574,
0.03549400344491005,
-0.010067095048725605,
-0.006277423817664385,
-0.015116739086806774,
0.01201335247606039,
-0.030434589833021164,
0.006676423829048872,
0.001160179148428142,
-0.026304952800273895,
-0.027326812967658043,
-0.014816815964877605,
0.00498810363933444,
-0.003533851820975542,
-0.007876264862716198,
0.03261043131351471,
0.00888279639184475,
-0.010169078595936298,
0.011442024260759354,
0.0011759259505197406,
-0.030297165736556053,
0.01765649951994419,
0.023729505017399788,
-0.007883239537477493,
0.013979806564748287,
0.05323701724410057,
-0.000015050068213895429,
-0.009052389301359653,
-0.021910499781370163,
0.03094339556992054,
-0.06695904582738876,
-0.01951504498720169,
-0.007631808053702116,
0.005640148185193539,
0.0668395385146141,
-0.005531094036996365,
-0.01911453902721405,
0.033694181591272354,
-0.06191487982869148,
0.04163217917084694,
-0.018515171483159065,
0.010900890454649925,
-0.05954749882221222,
-0.03406279906630516,
-0.0008112475625239313,
0.04720117896795273,
0.06316036731004715,
0.08387405425310135,
0.047847580164670944,
0.013703186996281147,
0.00963333435356617,
-0.002226174110546708,
-0.020563682541251183,
0.012457575649023056,
-0.01058601401746273,
-0.02915423922240734,
0.057308729737997055,
-0.00616424810141325,
0.006222461815923452,
-0.0035517029464244843,
-0.046190742403268814,
0.026437975466251373,
-0.02116212248802185,
0.01885576732456684,
-0.0032762454356998205,
0.03826574608683586,
0.03911419212818146,
-0.011058629490435123,
0.029846224933862686,
-0.02223362773656845,
0.0010648986790329218,
0.014849182218313217,
-0.03514175862073898,
-0.003466746537014842,
-0.01623346656560898,
-0.034950174391269684,
-0.057302024215459824,
0.006534179672598839,
-0.014632079750299454,
-0.00000516803720529424,
-0.007279047742486,
-0.04568148031830788,
-0.01864524558186531,
-0.044560208916664124,
0.03089490346610546,
-0.03241276368498802,
-0.0036630656104534864,
0.01837022975087166,
0.02956567332148552,
-0.012922251597046852,
-0.006257185712456703,
-0.024002106860280037,
-0.0660586953163147,
0.02255018800497055,
-0.006707889959216118,
-0.029928091913461685,
-0.017756499350070953,
-0.03733799606561661,
-0.013786316849291325,
0.015716133639216423,
0.04479043930768967,
-0.033637017011642456,
-0.026155885308980942,
0.024014577269554138,
0.006922310683876276,
0.047092001885175705,
-0.034227315336465836,
0.00185239443089813,
-0.001674641272984445,
-0.06893440335988998,
0.026691928505897522,
0.01653214916586876,
-0.011762337759137154,
-0.006373903714120388,
0.029399780556559563,
0.008067847229540348,
0.00717275682836771,
0.036421265453100204,
-0.0037642272654920816,
0.02036326751112938,
0.000499495305120945,
-0.027944814413785934,
0.008224619552493095,
-0.04132285714149475,
-0.006197074428200722,
-0.04177634045481682,
0.015611236914992332,
-0.018159618601202965,
-0.0056579443626105785,
0.007135612424463034,
0.04370487108826637,
-0.008880648761987686,
0.015319610014557838,
0.026147276163101196,
0.021155299618840218,
-0.024613065645098686,
0.04421737790107727,
0.005435959901660681,
-0.004761826246976852,
0.04851888120174408,
0.005415929015725851,
0.002572119003161788,
0.02684127725660801,
-0.05644546449184418,
-0.05510231480002403,
0.017791656777262688,
-0.041996076703071594,
-0.034369684755802155,
-0.031970586627721786,
0.01638804003596306,
0.027084773406386375,
-0.009031254798173904,
0.0011382459197193384,
0.03299454227089882,
-0.03261003643274307,
-0.02361954376101494,
0.006335895042866468,
-0.008065068162977695,
0.007799141574651003,
0.019189761951565742,
0.03149750828742981,
0.03401806205511093,
0.024900026619434357,
0.024111812934279442,
0.04705037176609039,
0.006771900691092014,
-0.016820307821035385,
0.0027357758954167366,
-0.014435438439249992,
-0.005592184141278267,
0.016948143020272255,
-0.021828612312674522,
0.03689615800976753,
-0.05589354410767555,
-0.0028153052553534508,
0.07473568618297577,
-0.04373948276042938,
0.026410546153783798,
0.01791113056242466,
-0.018279077485203743,
0.024218598380684853,
-0.03289942443370819,
0.009010251611471176,
-0.04242816939949989,
0.01329988893121481,
-0.035149477422237396,
-0.0021794219501316547,
0.018900975584983826,
0.03186635673046112,
0.015386064536869526,
0.03241328150033951,
-0.0287978146225214,
-0.02755330689251423,
0.0038748797960579395,
-0.012805666774511337,
-0.001730030169710517,
0.012257540598511696,
-0.019445566460490227,
0.007946538738906384,
-0.04302148520946503,
-0.041763465851545334,
-0.0708179622888565,
0.021851761266589165,
0.023031990975141525,
0.013749831356108189,
-0.015530948527157307,
-0.012491187080740929,
0.0016566498670727015,
0.05406498908996582,
-0.05845002830028534,
0.025041140615940094,
-0.02431480772793293,
0.023421376943588257,
0.00817420706152916,
0.0328846238553524
] |
<p>The masses of the Z and W particle sum almost exactly to the mass of the Top quark,within the errors:</p>
<p>Z + W = 80.385±0.015 + 91.1876±0.0021 = 171.57 ±0.0171 GeV</p>
<p>Top quark 172.9± 1.5 GeV</p>
<p>A: Is this one of those simple coincidences?</p>
<p>B: The Z,W particles are decays of the T?</p>
<p>C: Someone has a not too cranky idea connecting them?</p>
<p>EDIT:
After consideration of dmckee and Lubos posts.</p>
<p>How about instead of a decay from a t quark, collide a $W^\pm$ and a $Z$ to produce a red top and anti-red bottom. </p>
<p>$$W^+ + Z^0 \to t(r) + \bar{b}(\bar{r})$$</p>
<p>this conserves charge, spin, color, confinement and energy - provided the excess energy of the bottom quark comes from the kinetic term of the collision. It immediately decays as <a href="http://physics.stackexchange.com/questions/29132/is-there-a-tb-meson">lubos and dmckee pointed out in an early question</a> </p>
<p>EDIT 2:
Also note decay time of t-quark is $4.2\ 10^{-25} s$, nearly matching the W,Z decays times of $3.0\ 10^{-25} s$ , although I'm yet to find an uncertainty for these.</p>
<p>And with incredible hubris I'm calling this the Metzgeer Momentary Meson $t\bar{b} $<br>
:) joke</p> | 2,896 | [
-0.006624763831496239,
-0.05197371542453766,
0.029070379212498665,
-0.017226330935955048,
0.030956843867897987,
0.030754949897527695,
0.0011163748567923903,
-0.015200603753328323,
0.023033970966935158,
-0.0093239052221179,
0.00933636724948883,
0.06408476829528809,
0.028043648228049278,
0.025309914723038673,
0.014419333077967167,
0.021114308387041092,
-0.0076264129020273685,
-0.05597417429089546,
0.0005663741612806916,
-0.03106270730495453,
0.012178589589893818,
0.022510677576065063,
-0.0011392702581360936,
0.04746464267373085,
0.015495941042900085,
-0.03044426627457142,
0.02690373733639717,
0.02148832567036152,
0.0025814385153353214,
0.07879950851202011,
-0.008738135918974876,
-0.057741083204746246,
0.03249741718173027,
-0.011445712298154831,
-0.0011455724015831947,
0.0007808790542185307,
-0.011905660852789879,
-0.025017263367772102,
0.00949346087872982,
0.022533433511853218,
-0.008079341612756252,
-0.005733263213187456,
-0.01609019935131073,
0.03261326253414154,
-0.04565044492483139,
0.004012151621282101,
-0.04530175030231476,
-0.015081147663295269,
0.07035262882709503,
-0.05931289866566658,
0.006066033151000738,
0.058367446064949036,
0.04053114354610443,
-0.018120303750038147,
-0.011475819163024426,
-0.01310868002474308,
0.06858740001916885,
0.06526634097099304,
0.015027008019387722,
-0.04976605996489525,
-0.01401714887470007,
-0.03507912904024124,
0.030138008296489716,
0.02312655933201313,
-0.02422935515642166,
0.03137897700071335,
-0.009170818142592907,
0.038138650357723236,
-0.015850406140089035,
-0.04129059612751007,
0.04205688089132309,
0.01442541554570198,
0.014207955449819565,
-0.014479877427220345,
0.017192447558045387,
-0.01783483847975731,
0.0025922534987330437,
0.027715470641851425,
0.061331383883953094,
0.05151526257395744,
-0.03501209244132042,
-0.004475967492908239,
0.03734047710895538,
0.04022150859236717,
0.0344056561589241,
-0.019371891394257545,
0.0682692602276802,
-0.02827354334294796,
-0.04001010209321976,
0.023103125393390656,
0.001861468655988574,
0.004834616556763649,
0.043629951775074005,
0.0053989943116903305,
-0.007091679610311985,
0.025872519239783287,
0.005989204626530409,
0.05582210794091225,
-0.022873006761074066,
0.0033698990009725094,
0.017211107537150383,
0.008720973506569862,
0.017704706639051437,
0.052273865789175034,
-0.0393388457596302,
-0.034624725580215454,
-0.011021643877029419,
-0.03075575642287731,
-0.01728256605565548,
-0.01509809773415327,
-0.0734269991517067,
-0.0020603956654667854,
-0.018166271969676018,
-0.02009592391550541,
-0.044940900057554245,
-0.04908819869160652,
0.007200607098639011,
-0.011730257421731949,
0.0824226588010788,
0.020086662843823433,
0.038956500589847565,
-0.04308995604515076,
0.010561687871813774,
-0.0687786117196083,
-0.0484066978096962,
-0.0360480360686779,
0.050213366746902466,
-0.015527247451245785,
-0.04562302306294441,
0.034045230597257614,
-0.01162686850875616,
-0.031394604593515396,
0.01419580914080143,
-0.019753053784370422,
0.058346837759017944,
-0.025189071893692017,
-0.08032779395580292,
-0.04806981980800629,
0.02005433849990368,
-0.010604476556181908,
-0.07892877608537674,
-0.07773230224847794,
-0.033333659172058105,
0.017068320885300636,
0.060603100806474686,
0.018877897411584854,
0.013478279113769531,
-0.01225198246538639,
0.05783533304929733,
0.028801536187529564,
-0.03403651341795921,
0.007139578461647034,
0.0024905845057219267,
-0.02446201629936695,
-0.01120751816779375,
-0.028409861028194427,
0.000897056539542973,
0.0013271640054881573,
-0.022984031587839127,
-0.02043679542839527,
0.04802820831537247,
-0.021353336051106453,
-0.009300678968429565,
0.019477657973766327,
0.019898127764463425,
-0.019375944510102272,
0.03760556876659393,
-0.0050249830819666386,
-0.014779484830796719,
0.03008524514734745,
0.006288181524723768,
0.018048640340566635,
0.022292213514447212,
0.0037461246829479933,
0.04590841755270958,
-0.06387703865766525,
-0.0497673898935318,
-0.013690653257071972,
0.009303729049861431,
-0.01200941577553749,
-0.026409726589918137,
-0.04745353385806084,
-0.019492527469992638,
0.002572396770119667,
0.022599434480071068,
0.023503132164478302,
-0.037301141768693924,
-0.01226110477000475,
0.04317276552319527,
-0.050728555768728256,
-0.026351679116487503,
-0.0442507378757,
-0.02357105351984501,
-0.023556174710392952,
-0.006166593171656132,
0.0007601492688991129,
-0.010397073812782764,
0.017582112923264503,
-0.035966333001852036,
-0.03317173197865486,
0.03342244774103165,
0.08728738874197006,
0.013708013109862804,
0.030986234545707703,
-0.00008922328561311588,
0.0268841739743948,
0.03830990940332413,
-0.03328350931406021,
-0.0014341871719807386,
-0.013800797052681446,
-0.026524817571043968,
-0.0052278609946370125,
0.014717869460582733,
0.013573622331023216,
-0.0009242622181773186,
-0.02863318845629692,
0.046274565160274506,
-0.027945784851908684,
0.004573544021695852,
-0.0023300042375922203,
-0.01327164750546217,
0.04648371785879135,
0.017398322001099586,
0.010778464376926422,
-0.007815013639628887,
0.062039125710725784,
0.04078258201479912,
0.04854055866599083,
-0.03135181963443756,
-0.003450996009632945,
-0.041414182633161545,
-0.026260171085596085,
0.03483467921614647,
0.022467855364084244,
-0.051026709377765656,
0.051725756376981735,
-0.010014195926487446,
0.014266129583120346,
-0.015763970091938972,
0.041079383343458176,
-0.018574554473161697,
-0.02737375535070896,
-0.00628205481916666,
0.015494706109166145,
-0.0041394419968128204,
-0.0030556381680071354,
0.015238399617373943,
-0.026866162195801735,
0.01588287204504013,
0.01473777461796999,
-0.01642562635242939,
0.011785106733441353,
0.0000331457813445013,
0.03237750008702278,
-0.008010689169168472,
-0.06628859043121338,
0.07452414184808731,
-0.03285149484872818,
0.03555672615766525,
0.026310201734304428,
0.001356571214273572,
0.02020351216197014,
0.012039918452501297,
-0.017822058871388435,
-0.045424506068229675,
0.036314938217401505,
-0.016560280695557594,
0.023500340059399605,
0.02009330317378044,
-0.02133173681795597,
-0.01456359215080738,
-0.01271636039018631,
-0.02065647393465042,
0.009354112669825554,
0.007007278967648745,
0.00972781516611576,
0.014301745221018791,
0.029582712799310684,
-0.04504692554473877,
-0.0356450155377388,
0.012271357700228691,
-0.01767541654407978,
-0.017558841034770012,
0.025488251820206642,
-0.07709912955760956,
0.01207767054438591,
-0.05719998851418495,
-0.02618892304599285,
0.006799017544835806,
0.012354731559753418,
0.017934046685695648,
0.00596414553001523,
0.007145120296627283,
-0.04182998090982437,
-0.022920824587345123,
-0.035135380923748016,
0.012894556857645512,
-0.02928619086742401,
0.034743357449769974,
0.05038100481033325,
0.0015205061063170433,
-0.05902905389666557,
0.03799154609441757,
-0.03395645692944527,
-0.02563115768134594,
-0.0009485922055318952,
0.014257920905947685,
0.02031904272735119,
-0.014433477073907852,
0.020214343443512917,
0.012725470587611198,
-0.005708707496523857,
0.03925074264407158,
-0.05508921295404434,
-0.03808973357081413,
0.027224909514188766,
0.023632656782865524,
0.05975575000047684,
0.012612104415893555,
-0.029867304489016533,
0.06903134286403656,
0.004149476066231728,
-0.029249347746372223,
-0.0012096308637410402,
0.006924286484718323,
-0.016016053035855293,
-0.03789062052965164,
0.016056986525654793,
-0.013979176059365273,
0.020010877400636673,
0.010021642781794071,
0.023525087162852287,
0.03756323829293251,
0.03438468277454376,
0.03247007727622986,
0.011096334084868431,
-0.013865534216165543,
0.026260841637849808,
-0.016333110630512238,
0.028847673907876015,
-0.03628697991371155,
-0.006171645596623421,
0.0054690046235919,
-0.0024421217385679483,
0.031037259846925735,
0.007019171956926584,
-0.04313679784536362,
0.0696122795343399,
0.03551643714308739,
-0.0007568373112007976,
0.019457634538412094,
0.029133228585124016,
-0.007390943355858326,
-0.029464608058333397,
0.017247317358851433,
0.01793176308274269,
0.056671757251024246,
0.025141071528196335,
0.022670850157737732,
0.029622117057442665,
0.06900286674499512,
-0.010447409935295582,
-0.024988386780023575,
-0.009052385576069355,
-0.02314254455268383,
0.01353719923645258,
0.0017701310571283102,
0.003702012589201331,
0.05649556964635849,
0.046598393470048904,
0.011940305121243,
-0.015270983800292015,
-0.04661701247096062,
-0.029001576825976372,
-0.07550688832998276,
0.00031827104976400733,
-0.016380079090595245,
0.04992188885807991,
-0.006430815439671278,
0.05150991305708885,
-0.011475051753222942,
-0.0009597573080100119,
0.0209724772721529,
-0.0021526755299419165,
-0.06948147714138031,
0.019713090732693672,
-0.05337625369429588,
-0.017729196697473526,
-0.007559815421700478,
-0.05157218128442764,
-0.0254215095192194,
0.005694119725376368,
-0.010093480348587036,
-0.04127741605043411,
-0.029608601704239845,
-0.029243607074022293,
-0.0038942350074648857,
-0.023867301642894745,
-0.023414960131049156,
0.013860962353646755,
0.007291324436664581,
0.04289314150810242,
-0.009545912966132164,
0.011315863579511642,
0.020358053967356682,
-0.01803559809923172,
-0.02169981598854065,
-0.019347092136740685,
0.04003290459513664,
0.013862201012670994,
0.04031955823302269,
0.03690990060567856,
0.034064121544361115,
-0.061719343066215515,
-0.009424684569239616,
0.00901641882956028,
0.06226510927081108,
0.003148399293422699,
-0.008992751128971577,
-0.019221864640712738,
-0.06574071943759918,
-0.03979116305708885,
0.04159514605998993,
0.03683265298604965,
-0.023641353473067284,
0.00823892466723919,
0.04127563536167145,
0.0141048114746809,
-0.0002045845176326111,
0.06912039965391159,
0.059490300714969635,
-0.0018006014870479703,
-0.0293661467730999,
-0.0325804203748703,
0.021838806569576263,
-0.015595950186252594,
-0.003214274300262332,
0.005677106790244579,
0.005650738254189491,
0.02008814737200737,
-0.013890337198972702,
0.015005280263721943,
0.00357381091453135,
-0.023042306303977966,
-0.02534511312842369,
-0.011326422914862633,
0.01881490647792816,
-0.032040905207395554,
-0.010023812763392925,
-0.009688200429081917,
0.009263402782380581,
0.021813400089740753,
0.010189499706029892,
-0.026086395606398582,
-0.06256092339754105,
0.008504990488290787,
0.031411461532115936,
0.08781031519174576,
-0.017953671514987946,
-0.04152319207787514,
-0.06650685518980026,
0.0195960383862257,
0.05061887949705124,
-0.019682321697473526,
0.03430778905749321,
-0.0384000726044178,
0.0051720584742724895,
-0.01500428281724453,
-0.01515072863548994,
0.026057574898004532,
0.01981702819466591,
-0.01714378595352173,
0.011056767776608467,
-0.032854221761226654,
-0.013810472562909126,
-0.02603466995060444,
0.03766939043998718,
0.07333873957395554,
0.03143265098333359,
0.02967112883925438,
0.000799413537606597,
-0.005814845208078623,
-0.029436077922582626,
-0.02014877460896969,
-0.08497533947229385,
-0.017793288454413414,
-0.04050692543387413,
-0.03308847174048424,
0.05997699871659279,
-0.019558589905500412,
-0.061680927872657776,
0.03766098991036415,
0.026748761534690857,
0.012865482829511166,
-0.003942151088267565,
-0.06558005511760712,
0.029528731480240822,
0.05889001861214638,
0.0023636145051568747,
0.015655148774385452,
0.03178492188453674,
-0.0040537952445447445,
0.0033865319564938545,
-0.013366436585783958,
0.014706693589687347,
-0.01159634068608284,
0.02459067665040493,
-0.010715180076658726,
-0.012791220098733902,
-0.006380870472639799,
0.05109450966119766,
0.01419080514460802,
-0.023901348933577538,
-0.026710575446486473,
-0.04791384935379028,
-0.018290014937520027,
-0.004559035412967205,
-0.010201841592788696,
-0.00205661216750741,
0.025006398558616638,
-0.005363227799534798,
0.02329116314649582,
-0.03455740585923195,
0.009450424462556839,
-0.013231592252850533,
-0.0024770142044872046,
0.012584864161908627,
-0.007736158557236195,
0.03737500309944153,
-0.019287709146738052,
0.026215599849820137,
0.03281235694885254,
-0.018659425899386406,
0.006352777127176523,
-0.024672074243426323,
-0.0011944096768274903,
0.029728008434176445,
-0.035429127514362335,
-0.057475555688142776,
-0.016348477452993393,
0.04267458617687225,
-0.001955693121999502,
-0.05495702847838402,
0.05244273692369461,
0.03512685000896454,
-0.013652372173964977,
-0.06429056823253632,
-0.03457555174827576,
0.0043151164427399635,
0.036754537373781204,
-0.03875153139233589,
-0.018831664696335793,
-0.001055736793205142,
-0.06137455627322197,
-0.00828497763723135,
-0.029327457770705223,
0.062142081558704376,
-0.03386344015598297,
-0.007535925600677729,
0.015467911958694458,
0.03472850099205971,
0.06683534383773804,
0.032908808439970016,
0.002728048013523221,
0.03043469227850437,
-0.0065496875904500484,
-0.004165771882981062,
0.020989958196878433,
0.034525640308856964,
-0.003306155325844884,
-0.03409542888402939,
0.007316193077713251,
-0.018080363050103188,
0.0061727226711809635,
-0.032116055488586426,
0.04067156836390495,
0.04501315578818321,
-0.016389528289437294,
0.023751070722937584,
-0.01442103274166584,
0.08002017438411713,
-0.017711378633975983,
0.010253110900521278,
0.0033484550658613443,
0.011082077398896217,
-0.0013892785646021366,
0.002733104396611452,
0.013976645655930042,
0.00019037383026443422,
-0.017062675207853317,
-0.013865831308066845,
0.028134167194366455,
0.012861434370279312,
-0.028711672872304916,
-0.0008640563464723527,
-0.03389521315693855,
-0.0039815641939640045,
-0.011273120529949665,
-0.0013339275028556585,
0.024677645415067673,
-0.017631961032748222,
-0.009342510253190994,
0.01341959834098816,
-0.021571988239884377,
0.015721527859568596,
0.05269501730799675,
0.0034437919966876507,
0.039368707686662674,
-0.017009573057293892,
-0.02602149359881878,
0.0078077157959342,
-0.009316399693489075,
0.018165988847613335,
0.0051520271226763725,
-0.006975960452109575,
-0.006403450388461351,
-0.038653962314128876,
0.0063886018469929695,
0.01484732050448656,
0.0638740211725235,
-0.001819421537220478,
0.019192392006516457,
0.042256295680999756,
-0.007965709082782269,
0.005377055145800114,
-0.0006950095994397998,
-0.042439378798007965,
0.03227085992693901,
-0.037914857268333435,
-0.004972362890839577,
0.01396521832793951,
-0.00896408874541521,
0.020515520125627518,
0.01756354607641697,
-0.013416813686490059,
-0.0008218468283303082,
-0.01797756925225258,
-0.0571950264275074,
0.014958365820348263,
0.02339360862970352,
0.023315370082855225,
0.011084887199103832,
-0.0003121672198176384,
0.012166306376457214,
-0.013142434880137444,
0.042953331023454666,
-0.04386909306049347,
-0.05893838778138161,
-0.03849003463983536,
-0.015358343720436096,
-0.06510330736637115,
0.05753002315759659,
-0.03414050489664078,
-0.029719367623329163,
0.0034555515740066767,
-0.06183784082531929,
0.027913115918636322,
-0.016581488773226738,
0.03995092585682869,
-0.028826409950852394,
0.03814869001507759,
-0.0026652091182768345,
0.005233038682490587,
-0.03323401138186455,
0.016144944354891777,
0.14508464932441711,
0.05855729058384895,
0.024329636245965958,
-0.043220508843660355,
0.036622826009988785,
-0.0006158626056276262,
0.018491366878151894,
-0.006259256042540073,
0.013155543245375156,
0.01736578345298767,
0.012285672128200531,
0.009504812769591808,
0.05958224833011627,
0.0239380095154047,
-0.01211000420153141,
0.03138013929128647,
-0.03869684785604477,
-0.05314334109425545,
-0.012469029054045677,
0.04330170154571533,
0.027067573741078377,
-0.04175819084048271,
-0.03892817720770836,
0.0006381772109307349,
-0.05843304842710495,
0.028745556250214577,
-0.02228713594377041,
-0.029710719361901283,
-0.027734730392694473,
-0.006610529962927103,
-0.06153428927063942,
0.021547658368945122,
0.012059169821441174,
0.009710211306810379,
-0.03465396165847778,
0.012150902301073074,
0.00046790088526904583,
0.024025067687034607,
0.05455849692225456,
0.02221616543829441,
0.03753958269953728,
0.0177108496427536,
0.00971085112541914,
0.03254593536257744,
-0.060717325657606125,
-0.01635822467505932,
0.013294020667672157,
0.043437566608190536,
-0.0035125042777508497,
0.006200460251420736,
0.004607268143445253,
-0.011607457883656025,
0.011557926423847675,
-0.015104995109140873,
-0.0054755196906626225,
0.013186796568334103,
0.01239237654954195,
-0.008271285332739353,
-0.0032898427452892065,
-0.030301280319690704,
0.03634938970208168,
-0.01452541071921587,
0.008004277013242245,
-0.003958438988775015,
0.0022783817257732153,
-0.010374365374445915,
0.014222202822566032,
0.047426965087652206,
0.015822259709239006,
-0.02131342701613903,
-0.0335172638297081,
0.010815607383847237,
-0.04243916645646095,
-0.01834375597536564,
-0.008382611908018589,
0.0420738160610199,
0.03745671361684799,
0.022388869896531105,
-0.003439296968281269,
-0.012655645608901978,
-0.05269176512956619,
0.04256897419691086,
0.004405095707625151,
-0.02049010992050171,
-0.019117213785648346,
-0.005277999676764011,
0.018088864162564278,
0.032112911343574524,
-0.020630069077014923,
0.0379759855568409,
-0.04682799428701401,
0.10173515975475311,
-0.045962460339069366,
-0.02906365506350994,
0.015385589562356472,
0.03713364526629448,
0.01098391693085432,
-0.004596193321049213,
-0.00617671012878418,
0.007622857112437487,
0.010747222229838371,
0.02839519828557968,
0.0025640239473432302,
0.0064657311886549,
0.013138472102582455,
0.0033572863321751356,
0.037895318120718,
-0.05011121928691864,
-0.009924065321683884,
0.011894425377249718,
0.0055274758487939835,
-0.023156357929110527,
-0.014112478122115135,
0.008656340651214123,
0.010764973238110542,
-0.016018405556678772,
-0.006808220408856869,
-0.04237080365419388,
-0.010168440639972687,
-0.05164388567209244,
0.0056022885255515575,
-0.0231771282851696,
-0.010352885350584984,
-0.06477481126785278,
-0.008231942541897297,
-0.02268097549676895,
0.00589942978695035,
0.011818730272352695,
0.024258896708488464,
-0.032772939652204514,
-0.011722668074071407,
0.018203116953372955,
0.011622123420238495,
-0.04390318691730499,
-0.0031566775869578123,
-0.006157670170068741,
0.041045673191547394,
-0.001483107334934175,
0.022824997082352638,
-0.030514387413859367,
0.04121370613574982,
-0.02094554901123047,
-0.044992994517087936,
0.05049870163202286,
0.0012438901467248797,
-0.015081891790032387,
0.002788417972624302,
-0.03763434663414955,
-0.01679828204214573,
0.05005284771323204,
-0.030231934040784836,
-0.005349430721253157,
0.03261956945061684,
-0.03436928614974022,
-0.0049239168874919415,
0.00892528984695673,
0.022974906489253044,
0.029200999066233635,
-0.009495065547525883,
-0.009207350201904774,
0.04123389348387718,
-0.024896962568163872,
0.012233889661729336,
-0.04260612279176712,
-0.006756163202226162,
0.039653073996305466,
-0.04298422113060951,
0.04782698303461075,
-0.007299898657947779,
0.054629795253276825,
-0.013456917367875576,
0.0021464009769260883,
-0.019666533917188644,
-0.015368185937404633,
-0.08943809568881989,
0.005000967998057604,
0.04129049554467201,
-0.019414657726883888,
0.04332109913229942,
-0.03456497937440872,
0.012146021239459515,
0.016835587099194527,
-0.0653376504778862,
0.021298076957464218,
-0.012520702555775642,
-0.023995518684387207,
-0.04668103903532028,
-0.023235252127051353,
0.00015042514132801443,
0.033685483038425446,
0.007262824103236198,
0.04457710310816765,
0.05817442014813423,
0.04207310825586319,
-0.042579419910907745,
-0.04052169620990753,
-0.029898202046751976,
0.04951060935854912,
0.020808309316635132,
-0.02765686623752117,
0.10073807090520859,
-0.011760585010051727,
-0.02055014669895172,
0.00326333474367857,
0.023490089923143387,
0.01674807257950306,
-0.03395865857601166,
0.020794950425624847,
0.0038942957762628794,
0.036058247089385986,
0.03654012829065323,
-0.013394472189247608,
-0.01709619350731373,
0.011922752484679222,
0.03516178950667381,
0.04044940695166588,
-0.023395376279950142,
0.015347468666732311,
-0.02459818311035633,
-0.022556694224476814,
-0.039842043071985245,
0.021057890728116035,
-0.03464173153042793,
0.012459816411137581,
0.016078725457191467,
0.02605595625936985,
-0.007013710681349039,
-0.06443558633327484,
-0.0076615228317677975,
-0.018127281218767166,
0.013317929580807686,
0.01409063022583723,
0.030765021219849586,
-0.011260210536420345,
0.018518345430493355,
0.0108990129083395,
-0.004987713880836964,
-0.003537493059411645,
-0.006927028764039278,
-0.03885011002421379,
-0.009754386730492115,
-0.014353339560329914,
-0.005152556113898754,
0.03617464751005173,
-0.009880345314741135,
-0.04528271406888962,
-0.056967269629240036,
0.05253110080957413,
-0.02622990496456623,
0.026102600619196892,
-0.01941027119755745,
0.0038155445363372564,
0.010562052950263023,
-0.05364784970879555,
0.013619806617498398,
-0.013797015883028507,
0.029983164742588997,
-0.04805319756269455,
-0.028595147654414177,
-0.007664686534553766,
-0.0064218477346003056,
0.04760134220123291,
0.013405789621174335,
-0.022972984239459038,
0.0518636479973793,
0.022364923730492592,
0.004823125433176756,
-0.04784547537565231,
0.008723931387066841,
0.007811300456523895,
-0.002142135752364993,
0.005306173115968704,
-0.016922269016504288,
-0.003339444985613227,
0.023834098130464554,
0.07707750797271729,
-0.023529041558504105,
-0.007763313595205545,
-0.006106892600655556,
-0.03834953531622887,
0.07575243711471558,
-0.04909715801477432,
-0.009878742508590221,
0.07412523031234741,
0.048949405550956726,
0.027238696813583374,
0.02641843631863594,
-0.02713661640882492,
-0.012363556772470474,
0.02551335096359253,
-0.011447180062532425,
-0.01813252829015255,
-0.01591244339942932,
-0.024608157575130463,
0.01328483410179615,
-0.036828044801950455,
0.0010821240721270442,
0.014788196422159672,
-0.004994573537260294,
-0.023553431034088135,
0.04537566006183624,
0.01362202875316143,
0.03704803064465523,
0.004753878340125084,
0.033179253339767456,
0.03677014634013176,
-0.025971371680498123,
-0.004783059936016798,
0.035436514765024185,
0.0140813197940588,
0.012242897413671017,
0.011872838251292706,
-0.0015172150451689959,
0.007234127726405859,
0.03765132650732994,
0.02693655714392662,
0.027177076786756516,
-0.014538160525262356,
-0.05629357323050499,
0.022256741300225258,
-0.009351157583296299,
0.020669108256697655,
0.02944999374449253,
-0.02533254586160183,
0.0807531550526619,
-0.024806708097457886,
-0.0411396361887455,
-0.022774282842874527,
0.015621373429894447,
-0.030349398031830788,
0.0373515784740448,
0.004953067284077406,
0.013302750885486603,
-0.005007412284612656,
0.0056079900823533535,
-0.034632716327905655,
0.021186968311667442,
-0.022822942584753036,
-0.030717037618160248,
-0.021047178655862808,
-0.0034424993209540844,
0.0168130062520504,
-0.03304510936141014,
-0.00879325345158577,
-0.009575334377586842,
-0.021174948662519455,
0.026339910924434662,
0.05847406014800072,
-0.006596362683922052,
-0.050076402723789215,
-0.03360609710216522,
-0.0437791608273983,
0.05068402737379074,
-0.023642541840672493,
-0.0058494554832577705,
-0.015473317354917526,
0.011060422286391258,
0.002110825153067708,
-0.011647211387753487
] |
<p>So a slackline is basically a bouncy tight rope. </p>
<p>I found a site that has a calculator for the tension of a static slackline </p>
<p><a href="http://www.slacklineexpress.com/force.php?linelength=40&sag=1&w=170" rel="nofollow">http://www.slacklineexpress.com/force.php?linelength=40&sag=1&w=170</a> </p>
<p>What I want to figure out is how much this tension increases when bouncing on the slackline. Is there an equation I can use to calculate this? </p>
<p>What are the variables? weight? height of jump? original tension? What else? </p>
<p>Thanks! </p> | 2,897 | [
-0.03428799659013748,
0.012031197547912598,
-0.0028677971567958593,
-0.002440094482153654,
0.031978268176317215,
0.01833195984363556,
0.019720474258065224,
-0.044287603348493576,
0.03887287527322769,
-0.023773111402988434,
0.028997614979743958,
0.026550130918622017,
-0.003744706744328141,
0.03377245366573334,
0.007066715508699417,
0.003369435900822282,
0.0037698489613831043,
-0.017752625048160553,
0.0044164215214550495,
-0.01501225121319294,
-0.04420565813779831,
-0.018643369898200035,
-0.010872517712414265,
-0.006107691675424576,
-0.024748895317316055,
0.0267802644520998,
0.0744081363081932,
-0.03996214270591736,
0.01218418125063181,
0.0410785973072052,
-0.01663309894502163,
-0.02771070972084999,
0.04255417734384537,
0.016263850033283234,
0.038961779326200485,
0.018460217863321304,
-0.04387371987104416,
-0.004375613760203123,
0.0007634201901964843,
0.019129812717437744,
0.017113246023654938,
0.008558343164622784,
-0.04248170554637909,
0.030899731442332268,
-0.032846562564373016,
0.00972131360322237,
-0.048641595989465714,
-0.03010198473930359,
0.06282952427864075,
-0.045431554317474365,
0.10125444084405899,
-0.00013369607040658593,
0.024568477645516396,
0.06481778621673584,
0.007594702765345573,
-0.01541074551641941,
0.069245345890522,
0.06449759006500244,
-0.00563188549131155,
-0.05890530347824097,
-0.007309899665415287,
-0.05030954256653786,
-0.04342636093497276,
-0.060025375336408615,
0.003443438094109297,
0.04288849979639053,
-0.012144883163273335,
-0.018114907667040825,
0.04726818948984146,
-0.036606982350349426,
-0.015787912532687187,
0.0074653420597314835,
0.08675339818000793,
-0.03971295431256294,
0.004268493503332138,
-0.026300564408302307,
0.009916773997247219,
0.040226418524980545,
0.041802890598773956,
0.07703536748886108,
-0.03051702305674553,
0.01873510517179966,
0.041483838111162186,
0.061762500554323196,
0.032106149941682816,
-0.05734603479504585,
0.07921592146158218,
-0.005651490762829781,
0.032555002719163895,
-0.013262445107102394,
0.0004820866452064365,
-0.007444420829415321,
0.0189990047365427,
0.0011347683612257242,
-0.022226061671972275,
0.007144337985664606,
0.0012008290505036712,
0.048342518508434296,
0.012419544160366058,
-0.012485885061323643,
0.025830918923020363,
-0.027625147253274918,
0.014466634020209312,
0.07848579436540604,
-0.025695063173770905,
-0.014400806277990341,
0.01034292671829462,
-0.0004887118120677769,
0.015611043199896812,
-0.013047085143625736,
-0.04033106565475464,
-0.01283629797399044,
-0.01301555149257183,
-0.009832696057856083,
-0.0037946917582303286,
-0.054515719413757324,
0.0022934849839657545,
0.031897153705358505,
0.03854351490736008,
0.038674335926771164,
0.011488670483231544,
-0.0398690290749073,
0.0598951131105423,
-0.04762249439954758,
-0.01628962904214859,
0.012860668823122978,
-0.013965494930744171,
-0.026566609740257263,
-0.014011602848768234,
0.05862952023744583,
-0.02289666421711445,
-0.017794232815504074,
0.005822673439979553,
0.016967393457889557,
0.011728215031325817,
0.016344932839274406,
-0.08723833411931992,
-0.05866970121860504,
0.05701526626944542,
-0.001641361741349101,
-0.007092727348208427,
-0.06264211237430573,
0.0017949400935322046,
0.030854402109980583,
0.029347345232963562,
0.01384822279214859,
0.040256477892398834,
0.0007761743618175387,
-0.013361467979848385,
-0.0003258641518186778,
-0.01703752391040325,
-0.024353250861167908,
-0.003909717313945293,
-0.03842060640454292,
0.015147092752158642,
-0.0480823889374733,
-0.00550999166443944,
0.029410503804683685,
-0.0016806002240628004,
-0.024697037413716316,
0.02775992825627327,
-0.010789359919726849,
-0.022148462012410164,
-0.0017220512963831425,
0.012149953283369541,
-0.029777346178889275,
0.06852895766496658,
-0.01914011687040329,
-0.03836089372634888,
0.03388219326734543,
-0.013548292219638824,
-0.032724734395742416,
-0.006820266135036945,
0.0007528449641540647,
0.03125841170549393,
-0.049669645726680756,
-0.005903014913201332,
-0.026512227952480316,
-0.01814710907638073,
-0.0016088261036202312,
-0.01483730599284172,
-0.042975280433893204,
-0.007144066970795393,
0.0097938422113657,
0.05077451467514038,
0.0433371439576149,
0.020148659124970436,
0.011166173033416271,
0.009532912634313107,
-0.02425432577729225,
-0.012257324531674385,
-0.0599060133099556,
0.07142605632543564,
0.007809773553162813,
-0.01798827387392521,
-0.0252914410084486,
0.02395005151629448,
0.044760432094335556,
-0.028559943661093712,
-0.0035928888246417046,
0.011111044324934483,
0.042233847081661224,
0.033111147582530975,
0.010422942228615284,
0.010844741016626358,
0.05548932030797005,
0.041896089911460876,
0.0006088752415962517,
0.048151928931474686,
-0.03854355588555336,
-0.039307549595832825,
0.0035673179663717747,
-0.0572027713060379,
0.027085792273283005,
0.005812749732285738,
-0.007984011434018612,
0.04123355820775032,
-0.037845954298973083,
0.0017706697108224034,
0.036525290459394455,
0.012358945794403553,
0.07158657163381577,
0.054203372448682785,
0.04998810961842537,
0.011427842080593109,
0.008941194042563438,
0.012089594267308712,
0.029170935973525047,
0.030667070299386978,
-0.023512102663517,
-0.008171571418642998,
0.02585865557193756,
0.00805871095508337,
0.00988767109811306,
-0.01901378482580185,
-0.03698291629552841,
0.016588781028985977,
0.013424060307443142,
-0.0029116065707057714,
0.04802308976650238,
-0.06501688063144684,
-0.04585083946585655,
-0.0014522229321300983,
0.022618699818849564,
0.007632826454937458,
-0.0019645681604743004,
-0.030289677903056145,
0.08515990525484085,
0.04273867607116699,
-0.037572797387838364,
0.03249846398830414,
0.01596597582101822,
-0.0021435499656945467,
-0.016723306849598885,
-0.0021738645154982805,
-0.015403838828206062,
0.06453808397054672,
-0.056414052844047546,
0.024157701060175896,
0.05577094852924347,
-0.009482139721512794,
0.0033377776853740215,
-0.011627279222011566,
-0.02929515391588211,
0.03422306478023529,
-0.03096962347626686,
-0.007267515640705824,
-0.030697111040353775,
0.02376420795917511,
-0.01148429699242115,
0.015388264320790768,
0.018392309546470642,
-0.02297295071184635,
-0.01559657696634531,
-0.017917489632964134,
-0.000046333163481904194,
-0.01675810106098652,
0.03749691694974899,
-0.014864488504827023,
-0.03493223339319229,
0.0381619855761528,
-0.012280343100428581,
0.0046144770458340645,
-0.04571055620908737,
-0.036886390298604965,
-0.000991351087577641,
-0.011293925344944,
-0.013814082369208336,
0.026632674038410187,
0.01287531666457653,
-0.017236368730664253,
0.04333991929888725,
-0.003530888818204403,
0.011993653140962124,
0.0019436043221503496,
-0.021946491673588753,
0.035673607140779495,
0.018981127068400383,
-0.02781287580728531,
0.03615624085068703,
0.033853087574243546,
0.0060819643549621105,
0.03660781681537628,
-0.05946757271885872,
-0.029022471979260445,
-0.034280337393283844,
0.03005273826420307,
0.010276640765368938,
-0.006869906093925238,
0.004130229819566011,
-0.007982838898897171,
-0.009675757959485054,
0.021098682656884193,
-0.07642921805381775,
-0.03555088862776756,
-0.03175896778702736,
-0.008749543689191341,
0.04351971298456192,
0.021242525428533554,
-0.06865064799785614,
0.09954167902469635,
-0.0003792592615354806,
-0.021105989813804626,
-0.05171390622854233,
-0.029227720573544502,
-0.004144482314586639,
-0.03628438338637352,
0.0019139571813866496,
0.0006582956993952394,
-0.022037548944354057,
-0.00000706691116647562,
0.01467466726899147,
-0.009043524973094463,
0.07079111039638519,
0.007581515237689018,
0.010298721492290497,
-0.02181961014866829,
-0.032558999955654144,
-0.01501449104398489,
0.06040119379758835,
0.021303320303559303,
-0.032240115106105804,
-0.021308695897459984,
0.016802193596959114,
0.059745222330093384,
-0.0038133077323436737,
-0.05388747900724411,
-0.00046928669326007366,
0.024808909744024277,
0.01928824931383133,
-0.030679192394018173,
0.02576986327767372,
0.043058816343545914,
-0.04542306065559387,
0.014850570820271969,
0.015285035595297813,
0.040260154753923416,
-0.02705977112054825,
0.014539632946252823,
0.06781338155269623,
0.04536812752485275,
-0.021699849516153336,
-0.06888733804225922,
-0.007406594231724739,
-0.0033949639182537794,
0.04202694818377495,
-0.03233133256435394,
-0.04581565782427788,
0.003815595293417573,
-0.009229850955307484,
0.02558162435889244,
-0.02011111192405224,
-0.05795630067586899,
0.03979010507464409,
-0.0541389174759388,
-0.006573590915650129,
0.005983508192002773,
0.04745437204837799,
0.0024534340482205153,
0.05281135067343712,
-0.02102554962038994,
0.00932799931615591,
0.07948499917984009,
0.011283840984106064,
-0.07879640907049179,
0.023030346259474754,
-0.07392359524965286,
-0.03410898894071579,
0.045898523181676865,
0.019583960995078087,
0.004998648073524237,
-0.011065112426877022,
-0.029797153547406197,
-0.0054037123918533325,
-0.012007476761937141,
-0.040761686861515045,
0.011332626454532146,
-0.05181412771344185,
0.010078560560941696,
0.03518369793891907,
0.004384204745292664,
0.018511606380343437,
-0.02349887602031231,
0.04384373128414154,
0.017609452828764915,
0.014159390702843666,
0.014645914547145367,
-0.04400897026062012,
-0.010498828254640102,
0.009443314746022224,
0.03325609490275383,
0.002256706589832902,
0.02074119634926319,
0.016387786716222763,
0.016056358814239502,
-0.027961285784840584,
-0.005357089918106794,
0.030274810269474983,
-0.01723739318549633,
-0.0016008384991437197,
-0.0793735533952713,
-0.026990946382284164,
-0.03054722398519516,
0.015680288895964622,
0.009976067580282688,
0.01680009812116623,
0.05096691474318504,
-0.028465768322348595,
-0.04026613011956215,
0.06493939459323883,
0.06780876219272614,
0.02561803348362446,
-0.012287700548768044,
-0.005266520660370588,
-0.011842219159007072,
-0.024910638108849525,
-0.03615814819931984,
-0.0065404921770095825,
0.010531089268624783,
0.011710476130247116,
0.0077226972207427025,
0.07211565971374512,
0.011086748912930489,
0.0037137840408831835,
0.009621690027415752,
0.012265819124877453,
0.013118205592036247,
-0.034199874848127365,
-0.03215121477842331,
-0.00756720220670104,
0.02128707617521286,
0.0362669937312603,
-0.04283946007490158,
0.014273326843976974,
-0.09779287129640579,
-0.05053868889808655,
0.03334272652864456,
0.04888217896223068,
-0.026608310639858246,
-0.01673479564487934,
-0.02197699062526226,
0.007897677831351757,
0.04537910595536232,
-0.057209160178899765,
0.0415346585214138,
0.0055962675251066685,
0.049434322863817215,
-0.009974265471100807,
-0.004795899149030447,
-0.005727472249418497,
0.017780514433979988,
-0.024645404890179634,
0.05039064586162567,
-0.025095688179135323,
0.001399536500684917,
0.025225359946489334,
0.02430596388876438,
0.0420568473637104,
0.06594938039779663,
0.006711248774081469,
-0.015594832599163055,
0.005577357951551676,
0.004594197031110525,
-0.029853295534849167,
-0.07990066707134247,
0.031282588839530945,
-0.007162382360547781,
-0.012505940161645412,
0.023684415966272354,
-0.005821514874696732,
-0.01868371106684208,
0.013582979328930378,
-0.007867543958127499,
-0.006376753095537424,
0.011624250560998917,
-0.003558710915967822,
0.0218765027821064,
0.06322290748357773,
0.007836979813873768,
0.026252901181578636,
0.078685462474823,
-0.03724149614572525,
0.01244370173662901,
0.02186252735555172,
0.06711794435977936,
0.00023419040371663868,
-0.038899753242731094,
-0.04804195463657379,
0.023144271224737167,
-0.051965292543172836,
0.017205210402607918,
-0.044771917164325714,
0.019988808780908585,
-0.011538737453520298,
-0.016145531088113785,
0.012888789176940918,
0.0376872718334198,
0.03405603766441345,
-0.010261745192110538,
0.04009838029742241,
0.007400793023407459,
0.01824953220784664,
0.006836887914687395,
-0.022961286827921867,
0.008541353046894073,
0.012754877097904682,
-0.03119935840368271,
-0.02825387939810753,
-0.006482892204076052,
-0.011017809621989727,
-0.05334262177348137,
0.008286982774734497,
-0.06008745729923248,
0.03733155131340027,
-0.006959560327231884,
0.0013305789325386286,
0.020791877061128616,
-0.040875501930713654,
-0.010275418870151043,
-0.019159745424985886,
0.00377023802138865,
0.020308956503868103,
-0.035207297652959824,
0.003089978825300932,
-0.024198047816753387,
0.0000329278627759777,
-0.023657849058508873,
-0.03633294254541397,
0.040283650159835815,
-0.019949525594711304,
-0.03246679902076721,
-0.03472668677568436,
0.030285269021987915,
0.0010660601546987891,
-0.010369542054831982,
0.023201672360301018,
-0.004610118921846151,
-0.013637437485158443,
0.008720919489860535,
0.03195227310061455,
-0.009551131166517735,
0.02843773551285267,
0.04606015607714653,
0.0008090768242254853,
-0.021269438788294792,
-0.020714405924081802,
-0.02809489704668522,
-0.012519685551524162,
0.032681118696928024,
-0.03287850692868233,
-0.02558831498026848,
0.019092118367552757,
-0.028130706399679184,
0.019497323781251907,
-0.04001295194029808,
0.012124009430408478,
-0.016510438174009323,
0.06024026498198509,
0.007468461524695158,
-0.023249587044119835,
-0.0027037470135837793,
0.016749639064073563,
0.03371702879667282,
-0.005042125470936298,
-0.000608846778050065,
-0.025056198239326477,
-0.007203932851552963,
-0.003396735992282629,
0.0023154295049607754,
-0.0004742502060253173,
0.0022455621510744095,
0.08384028822183609,
0.00006274379120441154,
-0.04358880966901779,
-0.014603028073906898,
0.004744881764054298,
0.06347670406103134,
0.018521329388022423,
-0.011625767685472965,
0.05504705011844635,
0.03189004957675934,
-0.022870073094964027,
-0.03030969761312008,
-0.031875528395175934,
-0.014346844516694546,
0.058579523116350174,
-0.06416115909814835,
0.0477578341960907,
0.009625260718166828,
-0.018681544810533524,
-0.0010541679803282022,
0.0069746277295053005,
0.00809446070343256,
-0.03089183010160923,
0.017218176275491714,
-0.005729182157665491,
-0.015782156959176064,
-0.00536328973248601,
0.03246582671999931,
0.006331543438136578,
0.002841957611963153,
0.01618967019021511,
0.02371053956449032,
0.020155450329184532,
0.03302598372101784,
-0.0259547121822834,
-0.02654278092086315,
0.04037661477923393,
0.005576481577008963,
0.03031599335372448,
-0.0009960174793377519,
-0.007037819363176823,
0.0597437247633934,
0.0134141119197011,
0.01623922400176525,
0.0018560040043666959,
0.024060292169451714,
-0.03364412859082222,
0.007267276290804148,
0.025475630536675453,
-0.028000568971037865,
-0.0022064708173274994,
0.040504489094018936,
-0.006123444065451622,
-0.0052486080676317215,
0.07061658054590225,
-0.07291249185800552,
-0.03971074894070625,
-0.006879531778395176,
-0.03233980014920235,
-0.025140907615423203,
0.04466751217842102,
0.028240930289030075,
-0.05265624076128006,
0.020041748881340027,
-0.011675696820020676,
0.022094091400504112,
0.005350586958229542,
0.0400334931910038,
-0.0019440705655142665,
0.08734553307294846,
-0.058628592640161514,
-0.019695548340678215,
-0.0217769555747509,
0.00030281548970378935,
0.1074083223938942,
0.036275822669267654,
0.024677056819200516,
-0.03841719776391983,
-0.007434291299432516,
0.010914303362369537,
-0.008236033841967583,
-0.011379683390259743,
-0.015795128419995308,
0.012715525925159454,
-0.041087809950113297,
0.027542969211935997,
0.03574952855706215,
-0.01823367364704609,
-0.04167264327406883,
0.045117974281311035,
-0.023653768002986908,
-0.031453974545001984,
0.027132194489240646,
-0.014414670877158642,
-0.008007355034351349,
0.016868961974978447,
-0.01567019708454609,
0.05825787037611008,
0.015998760238289833,
-0.014420907013118267,
-0.06505827605724335,
-0.030098050832748413,
0.02377980202436447,
0.003668292658403516,
-0.027424044907093048,
-0.002220147754997015,
-0.024507997557520866,
-0.029879827052354813,
-0.034530509263277054,
0.022622952237725258,
0.011669637635350227,
-0.01744876429438591,
-0.01204985287040472,
0.03469998762011528,
0.03915473073720932,
-0.004259269218891859,
-0.005775634199380875,
0.030457258224487305,
-0.0665760189294815,
-0.030897963792085648,
-0.007938814349472523,
0.01293423492461443,
0.031058168038725853,
0.012273370288312435,
-0.02214587852358818,
0.0007747446070425212,
0.003992235288023949,
-0.023566296324133873,
-0.03571326285600662,
-0.012529294937849045,
0.04620860889554024,
-0.023461828008294106,
0.015018956735730171,
-0.047365833073854446,
-0.002473716624081135,
0.007739961612969637,
0.002856811974197626,
0.015679601579904556,
-0.035687945783138275,
-0.007872053422033787,
-0.025202631950378418,
0.0515257753431797,
0.001904742675833404,
-0.03008418343961239,
-0.02089104801416397,
-0.02130347490310669,
-0.02784072235226631,
-0.017064133659005165,
0.0067359874956309795,
0.04853218048810959,
-0.03488565608859062,
-0.03499810770153999,
-0.02536437287926674,
-0.007612318266183138,
-0.03288507089018822,
0.03809966519474983,
-0.011670205742120743,
0.004648457281291485,
-0.04684910923242569,
-0.02312292903661728,
0.008504990488290787,
0.02980155684053898,
0.00943506695330143,
0.04010756313800812,
-0.02327275462448597,
0.0365557000041008,
0.00969006959348917,
-0.06409512460231781,
-0.014888858422636986,
-0.0030256733298301697,
-0.008865534327924252,
0.004805382341146469,
0.009008802473545074,
0.03712936490774155,
0.030439024791121483,
0.026843901723623276,
-0.019299708306789398,
0.03399251773953438,
-0.010844411328434944,
-0.003931810613721609,
-0.01258838176727295,
-0.03928085416555405,
0.024324942380189896,
0.009982122108340263,
0.03428882360458374,
-0.04216272383928299,
-0.0032528431620448828,
-0.0075270733796060085,
-0.02729766070842743,
-0.004924892447888851,
0.005931087303906679,
-0.04317015781998634,
0.009257265366613865,
-0.01760191284120083,
0.007372214924544096,
-0.030340926721692085,
-0.02118883654475212,
-0.0450606606900692,
-0.01933775469660759,
0.016988374292850494,
0.030751118436455727,
-0.025707848370075226,
0.011133587919175625,
-0.024599453434348106,
0.00655661104246974,
0.013808832503855228,
0.001696769380941987,
0.026530953124165535,
-0.027022218331694603,
0.05277549475431442,
-0.017768636345863342,
0.042922697961330414,
-0.008016414009034634,
-0.03381013497710228,
0.025307251140475273,
-0.031074369326233864,
-0.013196310959756374,
0.04746922850608826,
-0.04142545536160469,
0.021441519260406494,
0.030829977244138718,
-0.0405113585293293,
0.002179581206291914,
0.0295616053044796,
0.02418654039502144,
-0.009114539250731468,
-0.004858947359025478,
-0.00965835340321064,
0.02482304722070694,
-0.002850180258974433,
-0.011289823800325394,
-0.0008770165150053799,
0.01615867204964161,
-0.0014148787595331669,
0.022188030183315277,
-0.008004936389625072,
-0.005205421708524227,
0.01444191299378872,
-0.002465535420924425,
-0.027687400579452515,
0.02627689391374588,
-0.01205739751458168,
0.022298572584986687,
0.05659841373562813,
0.009733413346111774,
0.015679821372032166,
-0.020402099937200546,
0.04464832693338394,
-0.08778437227010727,
-0.0018951644888147712,
-0.0014748340472579002,
0.025200167670845985,
0.039137426763772964,
-0.04006504639983177,
0.042157843708992004,
0.024992505088448524,
-0.05175962299108505,
-0.013239062391221523,
-0.04118681326508522,
-0.004801659844815731,
-0.002278439234942198,
-0.029946206137537956,
-0.01710905320942402,
0.025553792715072632,
-0.003439083695411682,
0.05796345695853233,
0.025808457285165787,
-0.015390879474580288,
-0.02271980047225952,
-0.009065041318535805,
0.000004529842044576071,
0.022760137915611267,
0.026812827214598656,
-0.040422990918159485,
0.027943532913923264,
-0.013650252483785152,
-0.032970231026411057,
0.001711271470412612,
-0.013989068567752838,
0.001168277463875711,
0.00979789812117815,
0.03596459701657295,
0.006279576104134321,
0.022153712809085846,
-0.005908551160246134,
0.015080091543495655,
0.0008176520350389183,
0.030205244198441505,
-0.013360441662371159,
0.011491327546536922,
-0.0363718718290329,
-0.004959101788699627,
0.014339802786707878,
-0.04110986739397049,
-0.024850666522979736,
0.018433712422847748,
-0.0484614335000515,
0.013694057241082191,
-0.005817630793899298,
-0.029520973563194275,
0.011345218867063522,
-0.0316338911652565,
-0.02665729820728302,
-0.002710949629545212,
0.022001395002007484,
0.009760807268321514,
-0.030697420239448547,
0.004829796496778727,
0.04366029426455498,
-0.003162172855809331,
-0.0354718342423439,
-0.022744305431842804,
-0.009739489294588566,
-0.055120907723903656,
-0.05139469355344772,
-0.008585193194448948,
0.014803370460867882,
-0.009358745999634266,
0.029284661635756493,
-0.015116443857550621,
-0.018233785405755043,
0.05780189111828804,
0.0028069629333913326,
0.0020412111189216375,
0.012171175330877304,
-0.031474966555833817,
-0.012548375874757767,
-0.09306395053863525,
0.058091890066862106,
0.018131375312805176,
-0.0568755604326725,
-0.03407493978738785,
0.0015656802570447326,
-0.0034874877892434597,
0.023278871551156044,
0.04219662770628929,
-0.023333225399255753,
-0.0402182973921299,
-0.013406303711235523,
0.04330722615122795,
0.001198075246065855,
-0.019256409257650375,
-0.008813107386231422,
0.01656109094619751,
-0.002468657912686467,
-0.018670111894607544,
-0.013513620011508465,
-0.004095752723515034,
0.01017794944345951,
0.011457880958914757,
-0.0021565265487879515,
0.002973811235278845,
-0.03651030734181404,
-0.0015867614420130849,
0.023630166426301003,
0.014590681530535221,
-0.026784131303429604,
0.0760645940899849,
-0.044966962188482285,
-0.01820705644786358,
0.01802939921617508,
0.01523045264184475,
-0.04987751320004463,
0.05628521740436554,
-0.02568518929183483,
0.07216779887676239,
-0.007658558432012796,
-0.01713767647743225,
-0.016190633177757263,
-0.06295528262853622,
-0.003219878999516368,
0.029181864112615585,
-0.018569396808743477,
-0.02598588913679123,
0.028013696894049644,
0.03341052308678627,
0.010534594766795635,
-0.03445318341255188,
0.012456140480935574,
0.05058179423213005,
-0.036290571093559265,
-0.00023582673748023808,
0.023939451202750206,
0.05385350063443184,
-0.00004718649142887443,
-0.005962293595075607,
0.04089449718594551,
0.030163301154971123,
0.07034073770046234,
0.04571625962853432,
-0.008601921610534191,
-0.035509806126356125,
-0.058703597635030746,
-0.029104817658662796,
0.009219009429216385,
-0.012198656797409058,
0.013281350024044514,
-0.04578244313597679,
0.028568768873810768,
-0.02797197364270687,
0.012892106547951698,
0.023815689608454704,
0.029453881084918976,
0.017961371690034866,
-0.01831040158867836,
0.026771415024995804,
-0.002938302466645837,
-0.015496032312512398,
-0.014668606221675873,
-0.008676741272211075,
0.004296847619116306,
0.03551072999835014,
-0.0057347360998392105,
0.01128461118787527,
-0.0017179663991555572,
0.02662833034992218,
-0.003621090669184923,
-0.017588233575224876,
-0.020352168008685112,
-0.011759164743125439,
0.046038918197155,
0.01748848706483841,
-0.016667751595377922,
0.019971592351794243,
-0.012517400085926056,
-0.0036539374850690365,
0.05899636819958687,
-0.0250416062772274,
-0.015420131385326385,
-0.03641146048903465,
-0.007953527383506298,
-0.02512757107615471,
-0.006680393125861883
] |
<p>Consider 2 uncorrelated photon pairs (a1,a2), (b1,b2) such that (a1,a2) are entangled, and separately (b1,b2) are entangled. We wish to entangle-swap so as to end up with a new entanglement (a1,b1) by using the ancillary photon pair (a3,b3), such that (a1,a3) are entangled and (b1,b3) are entangled. This suggests that we do a multipartite (3-way in this case) entanglement preparation prior to the swap, such that (a1,a2,a3) are entangled, and separately (b1,b2,b3) are entangled.</p>
<p>The swap proceeds in the usual way by Bell state measurement on a3 and b3, and we end up having entangled (a1,b1).</p>
<p>The question is whether, after this operation, the entanglements (a1,a2) and (b1,b2) remain intact? If not, can we modify the procedure to guarantee this? If yes, will (a2,b2) now be entangled as a result of the swap? (they were uncorrelated before it). If not, how can we arrange that they are entangled, by only manipulating the other 4 photons?</p> | 2,898 | [
0.001580864773131907,
0.004415549337863922,
-0.023427149280905724,
-0.0029623250011354685,
0.052028629928827286,
0.031136423349380493,
-0.027900785207748413,
-0.05403662845492363,
-0.003645798424258828,
-0.002017189282923937,
-0.0032529723830521107,
0.023557379841804504,
-0.008446005173027515,
0.030792556703090668,
0.005300758872181177,
-0.02389412187039852,
0.0011766009265556931,
-0.020307401195168495,
0.0003637775662355125,
-0.03212811052799225,
0.005831288639456034,
0.0018685281975194812,
-0.019932417199015617,
-0.011598272249102592,
-0.012320980429649353,
-0.0038493345491588116,
0.02411150373518467,
-0.02031748928129673,
0.025076989084482193,
0.07821017503738403,
-0.014887011609971523,
-0.047254353761672974,
-0.0006289044977165759,
0.021270090714097023,
-0.004139154218137264,
-0.015256076119840145,
-0.046502068638801575,
-0.0749780684709549,
0.016903920099139214,
0.01468921173363924,
-0.02882026508450508,
0.0012091229436919093,
-0.031076179817318916,
0.04555220156908035,
-0.008450265042483807,
-0.0009593989816494286,
-0.018816525116562843,
-0.00507352827116847,
0.03556719422340393,
-0.05943640321493149,
0.06294635683298111,
0.006769122555851936,
0.003166006412357092,
-0.01330648921430111,
-0.020244469866156578,
-0.00138470355886966,
0.04730251803994179,
0.06835241615772247,
0.00883731059730053,
-0.01773853600025177,
-0.010471365414559841,
-0.006744449958205223,
0.044498711824417114,
-0.0026603240985423326,
-0.04025518521666527,
0.0036124687176197767,
-0.019269457086920738,
0.012170667760074139,
0.021228259429335594,
-0.03861524909734726,
0.011568288318812847,
-0.0022396447602659464,
0.06196189299225807,
-0.002201317809522152,
0.015376422554254532,
0.010725499130785465,
0.018955694511532784,
0.012096377089619637,
0.03749760612845421,
0.04130280017852783,
0.007455064449459314,
0.012696698307991028,
0.01810549385845661,
0.009042645804584026,
0.014252396300435066,
-0.0252677071839571,
0.03919805586338043,
-0.013895189389586449,
0.008038709871470928,
0.0057954262010753155,
0.019455427303910255,
0.015889842063188553,
0.03443834185600281,
-0.01740715466439724,
-0.027554212138056755,
0.0016532248118892312,
0.004860876593738794,
0.05707786977291107,
-0.02645307034254074,
-0.03433194011449814,
0.017049798741936684,
-0.0017262233886867762,
0.01355461310595274,
0.07152047008275986,
0.0021357876248657703,
-0.008683630265295506,
-0.022798985242843628,
0.056445542722940445,
0.01330508477985859,
-0.0288509763777256,
-0.023306572809815407,
0.014738318510353565,
-0.0016265681479126215,
-0.01849416270852089,
0.005493544973433018,
-0.03726784512400627,
0.009149203076958656,
0.007040287833660841,
0.07635486125946045,
0.05707646161317825,
0.010622210800647736,
-0.01931769959628582,
-0.0034744341392070055,
-0.039299376308918,
-0.06195179000496864,
-0.015887582674622536,
0.05205322057008743,
0.011410857550799847,
-0.060853760689496994,
0.06056554988026619,
0.012350623495876789,
-0.03943145275115967,
-0.0036328225396573544,
0.006830981466919184,
-0.006862337701022625,
-0.028931012377142906,
-0.16118347644805908,
-0.058324288576841354,
0.04821636900305748,
-0.043597348034381866,
0.0037955460138618946,
-0.06150295212864876,
0.035040147602558136,
0.03153817728161812,
0.09869461506605148,
-0.019258249551057816,
0.0008505696896463633,
0.003928312566131353,
0.022736256942152977,
0.04499528929591179,
-0.011151238344609737,
0.0009237908525392413,
0.011830967850983143,
-0.0215504951775074,
-0.03881887346506119,
-0.07579081505537033,
0.038015201687812805,
0.061988405883312225,
0.009211961179971695,
-0.02919548749923706,
0.056760769337415695,
-0.010634709149599075,
0.011552168987691402,
0.03586626425385475,
-0.02151532657444477,
-0.02059210278093815,
0.08851724863052368,
0.027362003922462463,
0.020791511982679367,
0.02285105548799038,
-0.0034533070866018534,
0.028273699805140495,
-0.03285582363605499,
0.023690098896622658,
0.012141946703195572,
-0.04097879305481911,
-0.03183532878756523,
-0.010209904983639717,
0.02753184549510479,
-0.030487949028611183,
0.009184606373310089,
-0.01617342233657837,
-0.02551969885826111,
0.028272226452827454,
0.014486316591501236,
0.00027439117548055947,
0.0026194979436695576,
0.001188709051348269,
0.005058456677943468,
-0.06342606246471405,
-0.026151753962039948,
-0.06643034517765045,
0.015345913358032703,
0.017084278166294098,
-0.057350728660821915,
0.013954046182334423,
-0.009681668132543564,
0.0195054542273283,
-0.002533877268433571,
-0.039021555334329605,
-0.020439136773347855,
0.04326939955353737,
0.029922224581241608,
-0.007434029597789049,
0.02377631515264511,
0.06886424124240875,
0.03533148393034935,
-0.011839374899864197,
0.03425859659910202,
-0.014425285160541534,
-0.032882388681173325,
0.030334895476698875,
0.004838066175580025,
0.011622893624007702,
-0.012559591792523861,
-0.02559264749288559,
-0.0032223095186054707,
0.02900281548500061,
-0.008644463494420052,
0.014810600318014622,
-0.06056694686412811,
0.050421081483364105,
0.04477463662624359,
0.0044602034613490105,
-0.004737033508718014,
0.07018768787384033,
0.0024306655395776033,
0.02121952921152115,
-0.01560682151466608,
-0.03808670863509178,
-0.035258639603853226,
-0.015506312251091003,
-0.02188817597925663,
0.042971521615982056,
-0.020215805619955063,
0.02931569516658783,
0.011409534141421318,
0.05947725847363472,
0.005435166414827108,
0.028013458475470543,
-0.015547046437859535,
-0.014001348055899143,
0.007319288328289986,
0.039080359041690826,
-0.0006279515800997615,
0.010698533616960049,
-0.012873554602265358,
-0.017450733110308647,
0.014983249828219414,
0.007677395362406969,
-0.02684706635773182,
-0.004455657675862312,
-0.025264564901590347,
0.02233101800084114,
-0.023263869807124138,
-0.05163092166185379,
-0.004003142472356558,
-0.053203340619802475,
0.0524936206638813,
-0.005020484793931246,
0.021650027483701706,
-0.01595677062869072,
0.007702721748501062,
-0.02752426080405712,
0.0007719777640886605,
0.000014781514437345322,
-0.007558959070593119,
-0.017905304208397865,
0.008016376756131649,
0.01231001503765583,
0.012597231194376945,
-0.020341243594884872,
0.02346687950193882,
-0.021210474893450737,
-0.0189531110227108,
0.02819356508553028,
-0.03962068259716034,
0.027915164828300476,
-0.03883875533938408,
-0.03826674073934555,
-0.008760577999055386,
-0.0038665151223540306,
0.01747705228626728,
-0.009304758161306381,
-0.06262814253568649,
0.0199764221906662,
0.01118586678057909,
-0.019825832918286324,
0.008626380935311317,
-0.012331748381257057,
0.04860326275229454,
0.01920182630419731,
0.008361747488379478,
-0.01723245158791542,
-0.029503287747502327,
0.0044236392714083195,
-0.029323378577828407,
-0.0044794450514018536,
-0.0019408586667850614,
0.0592343769967556,
0.013074123300611973,
-0.0493352934718132,
0.0020553492940962315,
-0.04492839798331261,
-0.00934077613055706,
0.01976049691438675,
-0.02637547254562378,
0.008811300620436668,
-0.0711388885974884,
0.03901219740509987,
0.004505754914134741,
-0.030916236340999603,
-0.0014372043078765273,
-0.057201363146305084,
-0.057628780603408813,
0.01137580070644617,
0.0013321117730811238,
0.011491645127534866,
-0.006716403178870678,
-0.018891137093305588,
0.08519849926233292,
0.027415532618761063,
-0.03246965631842613,
-0.008778572082519531,
0.030830848962068558,
-0.00813126191496849,
-0.014096954837441444,
0.022864151746034622,
0.01230771653354168,
0.004897748120129108,
0.03800231218338013,
0.023346154019236565,
0.018332237377762794,
0.03942533954977989,
0.03484809026122093,
-0.0345807783305645,
0.012437403202056885,
0.04106258600950241,
-0.0069527472369372845,
0.021342748776078224,
-0.023051287978887558,
-0.00787022989243269,
-0.0073571521788835526,
0.01351792924106121,
-0.013164530508220196,
-0.008403973653912544,
-0.013856773264706135,
0.07272330671548843,
0.0219570305198431,
0.026814905926585197,
-0.015139936469495296,
0.043898142874240875,
0.019423894584178925,
-0.027767930179834366,
-0.007481037639081478,
-0.009882606565952301,
0.021190902218222618,
-0.023520471528172493,
-0.0007926334510557353,
0.0433795340359211,
0.035416506230831146,
-0.01323326863348484,
-0.02615906111896038,
-0.006369233131408691,
-0.01372851524502039,
0.05148744583129883,
-0.018803995102643967,
-0.034713998436927795,
0.05788011476397514,
0.031927693635225296,
0.026743778958916664,
-0.007363394368439913,
-0.02571476809680462,
-0.03570985794067383,
-0.04099462181329727,
0.009372883476316929,
0.022905027493834496,
0.04686015844345093,
0.024014122784137726,
0.03594532608985901,
0.0471324659883976,
0.002294082660228014,
-0.026202771812677383,
0.005733097437769175,
-0.07893935590982437,
0.03820479288697243,
0.020461982116103172,
0.010408744215965271,
0.03450935706496239,
-0.026106078177690506,
0.000675571383908391,
-0.01165424007922411,
-0.05471618101000786,
-0.03363853693008423,
-0.008101672865450382,
-0.06010168790817261,
0.01453616376966238,
-0.02663525752723217,
-0.02727038599550724,
0.012214284390211105,
0.07101377099752426,
0.029952753335237503,
-0.015291386283934116,
0.027612779289484024,
0.006907527334988117,
-0.06123030185699463,
0.019387833774089813,
0.0052909268997609615,
0.027675099670886993,
0.013456796295940876,
0.04423314332962036,
0.0067793261259794235,
0.05379682779312134,
-0.01686425879597664,
-0.006859069690108299,
0.009483998641371727,
0.03799885883927345,
0.010527325794100761,
-0.005181886721402407,
0.006793812848627567,
-0.03566563501954079,
-0.017715182155370712,
-0.0031680078245699406,
0.053797993808984756,
0.012127986177802086,
-0.017095763236284256,
0.0496731698513031,
0.03265489637851715,
-0.027831871062517166,
0.029419925063848495,
0.08337211608886719,
-0.00175640475936234,
-0.01466695498675108,
-0.06523604691028595,
-0.00028834264958277345,
0.017255600541830063,
-0.01796872355043888,
0.010504132136702538,
0.008979404345154762,
-0.025202922523021698,
-0.01994624361395836,
0.015726421028375626,
0.0506368950009346,
-0.0008964588632807136,
0.01698419824242592,
-0.012831391766667366,
-0.0011454627383500338,
0.04899194836616516,
0.032591450959444046,
-0.009643133729696274,
0.013407304883003235,
0.012656178325414658,
0.029060952365398407,
0.008385298773646355,
-0.061436790972948074,
0.010670125484466553,
0.04507400840520859,
0.08153131604194641,
-0.018956879153847694,
0.012095986865460873,
-0.018913161009550095,
-0.022557979449629784,
0.0015099354786798358,
-0.008012542501091957,
0.044378966093063354,
-0.03766218200325966,
-0.036290813237428665,
-0.008828956633806229,
-0.017707468941807747,
0.009099794551730156,
0.027466418221592903,
-0.01021868921816349,
0.006752631161361933,
-0.003490109695121646,
-0.01460537314414978,
-0.014993172138929367,
-0.01809135265648365,
0.04438072443008423,
0.06950484216213226,
-0.0033278819173574448,
0.012568090111017227,
0.0011979397386312485,
-0.00297188269905746,
-0.012060824781656265,
-0.08837098628282547,
0.02393074706196785,
-0.015898555517196655,
-0.052437923848629,
0.0610811822116375,
-0.02234194427728653,
-0.05115089938044548,
-0.007126565091311932,
-0.005501816049218178,
0.0003314120403956622,
0.03036559373140335,
-0.03016645275056362,
0.04038945958018303,
0.0021277149207890034,
-0.006341253872960806,
0.08580683171749115,
0.05218102037906647,
-0.020534377545118332,
0.005931406281888485,
-0.015194868668913841,
0.030925439670681953,
-0.033452533185482025,
0.03309979289770126,
-0.013363850302994251,
0.03869180008769035,
-0.011920351535081863,
0.0752338171005249,
-0.013776193372905254,
0.014965814538300037,
0.04919879510998726,
-0.03603605180978775,
-0.020891807973384857,
0.021455369889736176,
0.002277838997542858,
0.008226447738707066,
-0.021286582574248314,
0.027934154495596886,
-0.025936201214790344,
-0.01464847382158041,
0.005814102943986654,
-0.013093656860291958,
0.042104002088308334,
0.053993385285139084,
-0.0065773529931902885,
0.0240931436419487,
-0.039867788553237915,
-0.01090526394546032,
0.0023924224078655243,
-0.048280347138643265,
0.03962338715791702,
0.0018067683558911085,
0.017792394384741783,
0.004729570355266333,
-0.09040304273366928,
-0.05185751989483833,
-0.026513628661632538,
-0.034437473863363266,
0.007821375504136086,
-0.07618257403373718,
0.033181071281433105,
0.0014468146255239844,
-0.008982268162071705,
-0.09095356613397598,
-0.05483332648873329,
0.009832547046244144,
0.008515452034771442,
0.003723863512277603,
-0.016268925741314888,
0.008095291443169117,
-0.02514253929257393,
-0.00260797212831676,
-0.05133768171072006,
0.06332536786794662,
-0.03350771591067314,
0.0010940131032839417,
0.0007764077745378017,
0.017674099653959274,
0.03714107349514961,
0.0039479415863752365,
0.019451579079031944,
-0.04064394533634186,
-0.0048826574347913265,
-0.0003093509003520012,
0.02662317454814911,
0.023729676380753517,
-0.019429627805948257,
-0.05877843499183655,
0.009044821374118328,
-0.0022434713318943977,
0.04415537789463997,
-0.018480485305190086,
-0.029932668432593346,
0.005295107141137123,
0.022612696513533592,
-0.00747934402897954,
-0.007670335937291384,
0.00529546057805419,
-0.005977220367640257,
0.009265445172786713,
0.013410764746367931,
0.02732481248676777,
0.002894015982747078,
-0.04578859359025955,
0.02654494345188141,
-0.004873305559158325,
-0.0015293569304049015,
-0.0004204853030387312,
0.04423230141401291,
-0.0025939354673027992,
-0.01257995143532753,
0.0004245325399097055,
-0.01410843525081873,
0.006520645692944527,
-0.002414959715679288,
0.03682740032672882,
0.0205462034791708,
-0.02517150342464447,
-0.02505878545343876,
-0.02756725810468197,
-0.032178837805986404,
-0.012849037535488605,
0.053546689450740814,
-0.03192878141999245,
0.03754429891705513,
0.07186713069677353,
-0.005509806331247091,
-0.014558440074324608,
-0.04534043371677399,
0.009944702498614788,
0.03377430886030197,
0.008565923199057579,
0.036877959966659546,
-0.035676419734954834,
0.0023399859201163054,
0.02269459329545498,
0.058679960668087006,
0.02224540151655674,
0.014739135280251503,
0.022190872579813004,
0.011871444061398506,
0.03693295642733574,
0.004518688656389713,
-0.02874556928873062,
0.018389588221907616,
-0.05539922043681145,
-0.004121747799217701,
0.0015791200567036867,
-0.01371183805167675,
0.02746584266424179,
0.004915574565529823,
0.039462052285671234,
-0.014911147765815258,
-0.03872089833021164,
-0.07545182853937149,
0.00031804165337234735,
-0.0014046912547200918,
0.019729668274521828,
0.0372195802628994,
-0.006278869695961475,
0.04838590696454048,
-0.004530974663794041,
0.032654475420713425,
-0.008160538040101528,
-0.05170115455985069,
-0.08236122876405716,
0.008186778984963894,
-0.012414208613336086,
0.03921080380678177,
-0.03994303569197655,
-0.01046446431428194,
-0.009475222788751125,
-0.020749742165207863,
0.03245406225323677,
0.004417545162141323,
0.06350098550319672,
-0.01838226430118084,
0.039789725095033646,
-0.01566959172487259,
0.03101866878569126,
0.0031246698927134275,
0.006153358146548271,
0.09337443858385086,
0.03669328987598419,
0.006497758440673351,
-0.08183294534683228,
0.03500360995531082,
-0.00503932312130928,
0.021002979949116707,
-0.051131147891283035,
0.021232830360531807,
-0.009838213212788105,
0.017296891659498215,
0.001179710030555725,
0.04362828657031059,
0.005892548244446516,
-0.027834367007017136,
0.031131921336054802,
-0.04843056946992874,
-0.07770969718694687,
-0.005650988779962063,
0.03963122516870499,
-0.0017729374812915921,
-0.03326107934117317,
-0.04651058465242386,
-0.026534639298915863,
-0.011819783598184586,
-0.020978404209017754,
-0.0009287345455959439,
0.008532198145985603,
0.0013727096375077963,
0.019443828612565994,
0.00786109920591116,
0.01139523833990097,
-0.0056365723721683025,
-0.006967366673052311,
-0.037932753562927246,
0.015532289631664753,
0.029210932552814484,
-0.03487785905599594,
0.033858247101306915,
0.022839652374386787,
0.017629029229283333,
-0.019129302352666855,
0.02418612875044346,
-0.01933467946946621,
-0.0726771429181099,
-0.015921762213110924,
0.015465429052710533,
0.032728005200624466,
-0.0245046466588974,
-0.030493156984448433,
-0.014575139619410038,
-0.052661143243312836,
0.007010296918451786,
-0.04990578442811966,
-0.03363123908638954,
-0.004153095651417971,
-0.010627144016325474,
-0.021164527162909508,
-0.02124033309519291,
0.005833975505083799,
-0.0122598335146904,
0.0028228634037077427,
0.042733460664749146,
-0.04435890540480614,
0.038596730679273605,
-0.015730109065771103,
-0.0016473173163831234,
0.006804369855672121,
-0.0027605562936514616,
-0.009823591448366642,
-0.01910366676747799,
0.003917653113603592,
-0.03402532637119293,
-0.03254585713148117,
0.0371653251349926,
0.01908744126558304,
0.03711660951375961,
0.0024474747478961945,
-0.02859468013048172,
0.007712336257100105,
-0.053617678582668304,
-0.007323696743696928,
-0.0378047339618206,
-0.0385562963783741,
-0.022862957790493965,
-0.008115507662296295,
0.05580972507596016,
0.04244111850857735,
-0.004563578870147467,
-0.024935496971011162,
0.024762708693742752,
0.01223138626664877,
0.025995463132858276,
-0.030980296432971954,
-0.0009153160499408841,
0.012478664517402649,
-0.03506651520729065,
-0.03916894644498825,
-0.04457342252135277,
0.02328602597117424,
0.030252883210778236,
0.005091504659503698,
-0.028692064806818962,
0.007439525332301855,
-0.0037588567938655615,
-0.010645261034369469,
0.015540370717644691,
-0.013152546249330044,
-0.01827107183635235,
0.02915045991539955,
0.03857716917991638,
-0.008252877742052078,
-0.0313677117228508,
-0.014329489320516586,
-0.01847883127629757,
0.003172746393829584,
-0.037766117602586746,
-0.009679010137915611,
-0.0305625032633543,
0.005460701882839203,
0.07293238490819931,
-0.034650277346372604,
-0.014113513752818108,
-0.00874511618167162,
-0.018280936405062675,
-0.0014469826128333807,
-0.01176414079964161,
0.003424334805458784,
0.021878868341445923,
0.008702045306563377,
-0.04694832116365433,
0.017001280561089516,
0.024746587499976158,
-0.006940085906535387,
-0.02779306285083294,
0.0019459686009213328,
0.020721107721328735,
0.05004166066646576,
-0.008804155513644218,
-0.046950813382864,
0.04782348498702049,
-0.0829969197511673,
-0.013383928686380386,
0.04790851101279259,
0.014216974377632141,
0.03906458243727684,
0.02997647039592266,
-0.013536608777940273,
-0.004825936630368233,
0.04977789521217346,
-0.028287125751376152,
-0.00919866282492876,
0.01201273687183857,
-0.021360401064157486,
-0.031327005475759506,
0.030356276780366898,
-0.02553495019674301,
-0.01880853995680809,
-0.021606149151921272,
0.05857802927494049,
0.03474508598446846,
0.04656121879816055,
0.009706120938062668,
-0.005366044584661722,
0.02039697952568531,
0.0660695806145668,
0.001980297267436981,
-0.017901841551065445,
-0.019656984135508537,
0.07699763774871826,
0.0027931013610213995,
0.04449668154120445,
0.028927119448781013,
-0.014972712844610214,
-0.09852328896522522,
-0.03495508432388306,
-0.00629753852263093,
0.007336069364100695,
0.044025495648384094,
-0.05047404021024704,
0.04585190489888191,
0.034402161836624146,
-0.03025783784687519,
0.026735015213489532,
-0.0012120858300477266,
-0.024543751031160355,
-0.0074454559944570065,
0.03914454206824303,
-0.027759799733757973,
0.04842372238636017,
0.02458333596587181,
0.007918104529380798,
-0.025270849466323853,
-0.025068284943699837,
-0.0362822525203228,
-0.0255108829587698,
-0.02546699531376362,
0.01592208445072174,
-0.002865429501980543,
-0.022606438025832176,
0.06105902045965195,
-0.01608567126095295,
-0.033991098403930664,
0.024460436776280403,
-0.00451341737061739,
-0.01179201528429985,
-0.016404839232563972,
0.019885899499058723,
0.004383827093988657,
-0.00034734842483885586,
0.015283367596566677,
0.01755249686539173,
0.02019873820245266,
0.02788001298904419,
0.015502328053116798,
0.014896877110004425,
0.010730299167335033,
0.0013053878210484982,
0.04453107714653015,
-0.016683919355273247,
-0.027626456692814827,
0.02266768366098404,
-0.028473099693655968,
0.02256806753575802,
-0.025957560166716576,
-0.0007719654822722077,
0.005964653566479683,
-0.042919326573610306,
0.005320962518453598,
-0.031104739755392075,
-0.017429526895284653,
0.03759516030550003,
0.009994751773774624,
0.0006563984788954258,
-0.00943536777049303,
-0.014640620909631252,
-0.039000388234853745,
0.056684430688619614,
-0.03077145852148533,
0.008814329281449318,
-0.051569610834121704,
-0.007387950550764799,
0.018708640709519386,
0.001102677546441555,
0.020473428070545197,
-0.04325498268008232,
-0.007000151090323925,
0.022210486233234406,
-0.00933036394417286,
0.01280889380723238,
-0.015881091356277466,
-0.030934926122426987,
-0.05132561922073364,
-0.05186218395829201,
0.04833757504820824,
0.027431178838014603,
0.012756094336509705,
-0.06326326727867126,
-0.024007689207792282,
-0.022533660754561424,
0.01690097525715828,
0.028105422854423523,
-0.006061858031898737,
-0.007302402053028345,
0.0022634360939264297,
0.0347234308719635,
0.04012611508369446,
-0.025871727615594864,
0.010652518831193447,
-0.007266129367053509,
-0.00422751484438777,
-0.029530907049775124,
0.012156075797975063,
-0.024925539270043373,
0.023028569296002388,
-0.03139772638678551,
-0.022804655134677887,
0.006580028682947159,
0.009838370606303215,
-0.030371814966201782,
0.039437685161828995,
-0.02881798706948757,
0.018711445853114128,
0.022328011691570282,
0.017115028575062752,
0.024640941992402077,
0.03640128672122955,
-0.00992774311453104,
-0.06745011359453201,
-0.018059028312563896,
-0.02253866195678711,
-0.009885252453386784,
-0.0016796023119241,
0.018933359533548355,
0.025936128571629524,
-0.02984301559627056,
0.02058355323970318,
0.0078013124875724316,
-0.04157689958810806,
0.020535843446850777,
0.07228817790746689,
-0.006374277174472809,
0.022574635222554207,
0.020177669823169708,
0.028150266036391258,
0.005678139626979828,
-0.04326833412051201,
0.03303223103284836,
0.040895383805036545,
0.015890667214989662,
0.007766527123749256,
0.044402461498975754,
0.006898370571434498,
-0.02668834663927555,
0.019641278311610222,
0.010012542828917503,
0.03697991371154785,
0.0005161706358194351,
0.012267115525901318,
0.06144075468182564,
0.03183890879154205,
-0.027158252894878387,
-0.011922330595552921,
-0.017876150086522102,
0.0715591162443161,
-0.06000448390841484,
0.011656008660793304,
-0.03504006564617157,
0.03141928091645241,
-0.013450147584080696,
0.018393080681562424,
0.011331834830343723,
0.0629165917634964,
-0.0022192695178091526,
-0.007026252802461386,
-0.0484255850315094,
0.019690273329615593,
0.01825839653611183,
-0.05785789340734482,
0.024753864854574203,
-0.018683824688196182,
0.0033407814335078,
0.022248081862926483,
-0.057978540658950806,
-0.021472591906785965,
-0.054564982652664185,
0.0037924854550510645,
0.001741629559546709,
0.03951619192957878,
0.015510422177612782,
-0.00532378489151597,
-0.0075337886810302734,
0.050208915024995804,
-0.015054567717015743,
-0.017442431300878525,
-0.04015834629535675,
0.04008704051375389,
-0.030490467324852943,
0.011530262418091297
] |
<p>Why does dust stick to rotating fan propeller?</p>
<p>Intuitively, most people (including I) think of the dust will not stick to rotating fan propellers.</p>
<p><strong>EDIT 1:</strong></p>
<p>Thank you for the great explanations. I am still waiting for the "better" one if any.</p> | 945 | [
-0.035116128623485565,
-0.02993009425699711,
0.009517102502286434,
0.005822014529258013,
0.004714807495474815,
-0.01766112633049488,
0.011794941499829292,
0.0038552761543542147,
-0.013502159155905247,
-0.03957299515604973,
0.021080313250422478,
0.10096406936645508,
0.05317844823002815,
0.040195923298597336,
0.0055076004937291145,
-0.03554048761725426,
-0.01913304626941681,
-0.05119003355503082,
0.020603245124220848,
0.0432429276406765,
-0.04047807678580284,
-0.004973620176315308,
0.01289861649274826,
0.007195860613137484,
0.00598178943619132,
-0.009807595983147621,
0.017268693074584007,
-0.03458778187632561,
0.047316599637269974,
0.034511372447013855,
0.0005152805824764073,
0.02153487130999565,
-0.007543433457612991,
0.05346791446208954,
-0.00027100511942990124,
-0.008687392808496952,
-0.013478363864123821,
0.02154497802257538,
-0.04945424199104309,
0.030630195513367653,
-0.06102397292852402,
-0.015510371886193752,
-0.007329736370593309,
0.027859453111886978,
-0.010911952704191208,
0.004257064778357744,
0.0006604300579056144,
0.05024385079741478,
0.04147883132100105,
-0.08792370557785034,
0.03057875484228134,
0.0003481663588900119,
0.04091254994273186,
0.04085308313369751,
0.01529956515878439,
-0.0073313661850988865,
0.076355941593647,
0.08719586580991745,
-0.04103781655430794,
-0.021519098430871964,
-0.01176436711102724,
-0.014214573428034782,
-0.024536993354558945,
-0.03154487535357475,
-0.0051291026175022125,
0.027941646054387093,
0.02001863159239292,
-0.024973900988698006,
0.03652570769190788,
0.0021039636339992285,
0.0028565204702317715,
0.025709066540002823,
0.0174301415681839,
-0.008729496039450169,
-0.01722237840294838,
-0.027950530871748924,
0.03637188300490379,
0.0004548783181235194,
0.028459111228585243,
0.059240855276584625,
-0.02693009190261364,
0.03467893227934837,
0.04464266449213028,
-0.007338054943829775,
0.010619301348924637,
-0.016876090317964554,
0.09585562348365784,
-0.011501964181661606,
0.026087168604135513,
0.02152439020574093,
0.025170184671878815,
0.024531275033950806,
0.04049697890877724,
-0.004526110831648111,
-0.00992137473076582,
0.0063309865072369576,
-0.0009129358804784715,
0.02690262719988823,
0.002431639237329364,
-0.002366723958402872,
-0.005995923187583685,
0.02031935751438141,
0.034397952258586884,
0.042386505752801895,
-0.005152491852641106,
-0.016811128705739975,
-0.06780890375375748,
0.02022150158882141,
-0.003415452316403389,
-0.03660033643245697,
-0.04728354141116142,
0.02354408986866474,
-0.025419408455491066,
-0.034560639411211014,
0.015963226556777954,
-0.018125664442777634,
0.01642517000436783,
-0.018884366378188133,
0.02312394790351391,
0.08153104037046432,
0.037453893572092056,
-0.03129581734538078,
0.014880712144076824,
-0.007920034229755402,
-0.025711191818118095,
0.018120871856808662,
0.022395482286810875,
-0.06855130195617676,
-0.002223634859547019,
0.022673102095723152,
0.001507648266851902,
-0.02658785879611969,
0.03722226992249489,
0.021983439102768898,
-0.008309071883559227,
-0.023482685908675194,
-0.10439223796129227,
-0.049472592771053314,
0.06157722696661949,
-0.02262171544134617,
-0.015754325315356255,
-0.07148025184869766,
-0.008645862340927124,
0.004244842100888491,
0.08898895978927612,
0.0003612481814343482,
0.014893095009028912,
-0.02115095593035221,
0.045471176505088806,
0.002733676228672266,
-0.04396536201238632,
0.008726958185434341,
0.026195118203759193,
-0.03252498060464859,
-0.019498106092214584,
-0.04027843475341797,
-0.015269887633621693,
0.026915008202195168,
0.04006576910614967,
-0.057425305247306824,
0.014892812818288803,
-0.01674020104110241,
-0.008850807324051857,
-0.008596964180469513,
0.032039668411016464,
-0.04624958336353302,
0.05868104100227356,
0.03093576431274414,
-0.0017263595946133137,
0.03191366791725159,
0.01373814046382904,
0.027299698442220688,
-0.026900891214609146,
0.02964293584227562,
0.039585597813129425,
-0.001103291055187583,
0.006176285445690155,
-0.011681819334626198,
0.03011576272547245,
-0.004078179597854614,
-0.06987187266349792,
-0.020608747377991676,
-0.0019414718262851238,
0.008966756984591484,
-0.012331685051321983,
0.06256629526615143,
-0.007339450065046549,
-0.039754677563905716,
-0.003598961280658841,
-0.05079979449510574,
-0.02819807641208172,
-0.09275245666503906,
0.02997712977230549,
-0.03903510421514511,
-0.024449653923511505,
0.021836327388882637,
-0.0037717949599027634,
0.04378817602992058,
-0.04201425239443779,
0.015824835747480392,
0.00627129664644599,
0.02184073068201542,
0.000196974360733293,
-0.03786540776491165,
0.0019151665037497878,
0.04584614932537079,
0.04568476974964142,
-0.008774196729063988,
0.02682773396372795,
-0.02659040130674839,
-0.004102934617549181,
0.011601031757891178,
0.013422911986708641,
-0.02037566341459751,
0.007857409305870533,
-0.008498021401464939,
0.04448342323303223,
0.0173666812479496,
0.03011235035955906,
0.025864025577902794,
-0.009690841659903526,
0.05307500436902046,
0.044599149376153946,
-0.016309980303049088,
0.031169403344392776,
0.035497669130563736,
-0.006745619233697653,
-0.0164047759026289,
-0.004179310519248247,
-0.005684467498213053,
-0.034391649067401886,
-0.01542807649821043,
0.06772562116384506,
0.0502094104886055,
-0.037503596395254135,
0.03233163431286812,
0.009504535235464573,
0.030981944873929024,
0.013457713648676872,
0.04670681059360504,
-0.009193341247737408,
-0.009340576827526093,
0.01790282130241394,
0.01604585349559784,
0.012746508233249187,
0.012971977703273296,
0.029356621205806732,
0.025149354711174965,
0.022771893069148064,
-0.002251028548926115,
-0.06911402195692062,
0.04172230884432793,
0.010578594170510769,
0.013947672210633755,
-0.0011821561492979527,
-0.0034562728833407164,
0.05089660361409187,
-0.01673470251262188,
-0.013364862650632858,
0.012015558779239655,
0.04556497186422348,
0.014802368357777596,
-0.008715307340025902,
-0.00872743222862482,
0.01862841099500656,
-0.009358517825603485,
-0.009409098885953426,
0.0031088553369045258,
0.019898591563105583,
-0.03756623715162277,
0.016422918066382408,
-0.01204284094274044,
0.011436193250119686,
0.010704942047595978,
0.0175811517983675,
0.037865228950977325,
0.006371821742504835,
0.03485514223575592,
0.008630692958831787,
-0.05238669738173485,
0.004060850013047457,
-0.04678817093372345,
-0.010978302918374538,
0.01345283817499876,
-0.011499607935547829,
0.019828524440526962,
-0.007028351537883282,
0.003283472266048193,
0.06627847254276276,
-0.020534252747893333,
-0.01585608534514904,
-0.009370764717459679,
-0.014887326397001743,
-0.05537787452340126,
0.01336693949997425,
-0.01996680721640587,
-0.01201680302619934,
-0.026645896956324577,
0.014017941430211067,
0.043103016912937164,
-0.030428335070610046,
-0.011950218118727207,
0.03647652640938759,
-0.05494268983602524,
-0.06105143949389458,
0.006708687171339989,
-0.04291540011763573,
0.03368004783987999,
-0.05972075089812279,
-0.00012783342390321195,
-0.011531919240951538,
-0.05961647629737854,
0.005216235760599375,
-0.006195736117660999,
-0.006815125700086355,
0.022352751344442368,
-0.03068104386329651,
0.0310071874409914,
-0.004593982361257076,
-0.007666722871363163,
0.06253521889448166,
0.01095446478575468,
-0.03767148777842522,
-0.004790017381310463,
-0.046760398894548416,
-0.0476887971162796,
-0.040645625442266464,
0.00138285499997437,
0.05408420041203499,
-0.005453350488096476,
0.026782426983118057,
0.032779399305582047,
-0.022027332335710526,
0.023989209905266762,
0.02065706066787243,
-0.01224540825933218,
-0.014025562442839146,
0.016614113003015518,
-0.008161834441125393,
0.035224173218011856,
0.004260864108800888,
-0.015947461128234863,
0.01744959130883217,
-0.0005974182276986539,
0.03743543475866318,
0.008466558530926704,
-0.054225850850343704,
0.021371478214859962,
-0.02694324217736721,
0.0352451391518116,
-0.05092234164476395,
0.048387616872787476,
-0.0029299675952643156,
-0.010384933091700077,
-0.011386188678443432,
-0.019361482933163643,
0.03053451143205166,
-0.0073343440890312195,
-0.010306956246495247,
0.038361579179763794,
0.04269307851791382,
-0.011945786885917187,
-0.025794025510549545,
-0.032147638499736786,
-0.03956874832510948,
0.006967185065150261,
-0.0001278723793802783,
-0.0020161739084869623,
0.04148392379283905,
0.031104907393455505,
0.025347456336021423,
-0.008541771210730076,
-0.0715341567993164,
0.03418342396616936,
-0.08134973794221878,
0.016483351588249207,
-0.03617588058114052,
0.04806491732597351,
-0.008839286863803864,
0.05500519275665283,
0.015342785976827145,
-0.011430373415350914,
-0.010161537677049637,
-0.0041315509006381035,
-0.09304999560117722,
0.029759148135781288,
0.012598861008882523,
-0.004114202689379454,
-0.014692653901875019,
-0.01748226396739483,
0.0023369460832327604,
-0.03709815815091133,
-0.0003944301279261708,
0.009939337149262428,
0.01284053549170494,
-0.034126728773117065,
0.006899788975715637,
0.00611794413998723,
-0.009116233326494694,
-0.014556233771145344,
0.024281486868858337,
0.005847196560353041,
-0.021303867921233177,
0.044152405112981796,
0.0567505769431591,
-0.05073205381631851,
0.007614341098815203,
-0.030689390376210213,
-0.023441074416041374,
-0.018855849280953407,
0.01656288467347622,
0.006776881404221058,
-0.01427810825407505,
0.019493574276566505,
-0.017492681741714478,
-0.015665076673030853,
-0.018788831308484077,
-0.000049060465244110674,
-0.0038109004963189363,
-0.02315855585038662,
-0.056626878678798676,
0.0003487037029117346,
-0.0010495043825358152,
0.037093717604875565,
-0.006316441111266613,
0.03521246463060379,
0.0019170797895640135,
-0.03778768330812454,
-0.02746417559683323,
0.01168885175138712,
0.015065410174429417,
0.04184073209762573,
-0.02077847719192505,
-0.05125853791832924,
-0.010719279758632183,
-0.03159753978252411,
0.022186903282999992,
0.025651585310697556,
-0.017192022874951363,
-0.025481002405285835,
-0.02727852389216423,
0.00021811826445627958,
-0.01846935600042343,
-0.00330646731890738,
0.03267580270767212,
0.021479861810803413,
0.03080214187502861,
-0.026498686522245407,
0.0235794298350811,
0.0028825358022004366,
0.06351880729198456,
0.04406263306736946,
0.04563908651471138,
-0.021199284121394157,
-0.04008160158991814,
-0.008060402236878872,
0.04621915891766548,
-0.01355574931949377,
-0.028992312029004097,
-0.002859392436221242,
-0.02688778191804886,
-0.03734812140464783,
0.06021065264940262,
-0.055881813168525696,
0.018091730773448944,
-0.06494302302598953,
-0.014222531579434872,
-0.020888831466436386,
-0.025811059400439262,
-0.014433476142585278,
0.0009319304954260588,
-0.010313005186617374,
0.03506575897336006,
0.004299463704228401,
-0.03437969833612442,
-0.02873140387237072,
0.01056430023163557,
0.01859707199037075,
0.05580694228410721,
0.011953859589993954,
-0.00942192506045103,
-0.02839239500463009,
-0.0020428805146366358,
-0.039096418768167496,
-0.06387683004140854,
0.009268705733120441,
0.00807247869670391,
0.00019624548440333456,
0.02182593382894993,
-0.061575908213853836,
-0.031235719099640846,
-0.022428888827562332,
0.009485317394137383,
-0.03566302731633186,
-0.014989602379500866,
-0.03791377320885658,
-0.0109959552064538,
0.016791116446256638,
0.0029358293395489454,
0.06460357457399368,
0.03450292721390724,
-0.011803027242422104,
0.00004883730071014725,
-0.010006284341216087,
0.04875623807311058,
-0.028580106794834137,
-0.03709223493933678,
-0.0317954383790493,
-0.009752378799021244,
-0.025906270369887352,
0.06424470245838165,
0.009028322994709015,
0.005392345599830151,
-0.01591278240084648,
-0.015543504618108273,
0.0007214677752926946,
0.006986605003476143,
0.011677208356559277,
-0.022309746593236923,
0.0006583330687135458,
0.03589947149157524,
0.014112209901213646,
-0.017506888136267662,
-0.014922650530934334,
0.0025708347093313932,
-0.024478977546095848,
0.04206803813576698,
0.003926098346710205,
0.026696253567934036,
-0.049949754029512405,
0.010323209688067436,
-0.010171541012823582,
-0.02213243395090103,
0.049689169973134995,
0.014188294298946857,
0.007731959223747253,
0.024724919348955154,
-0.07293635606765747,
-0.019944865256547928,
0.022049183025956154,
-0.0017823432572185993,
0.0639636293053627,
-0.04423994570970535,
0.024565428495407104,
0.0401085764169693,
-0.000977695337496698,
-0.04115575551986694,
-0.06058982387185097,
0.025288159027695656,
0.04510953277349472,
-0.01129805389791727,
-0.052880287170410156,
0.0020689202938228846,
-0.024147767573595047,
-0.063774973154068,
0.006234820932149887,
0.04288734123110771,
-0.04748399555683136,
-0.02062893845140934,
0.06066565960645676,
0.004646418150514364,
0.07141640037298203,
-0.02211044356226921,
-0.010735791176557541,
0.014166047796607018,
-0.0377935916185379,
-0.028416046872735023,
-0.04089346528053284,
0.035437434911727905,
-0.028716566041111946,
-0.04658111184835434,
0.03253756836056709,
-0.019146597012877464,
0.04950128123164177,
-0.010958598926663399,
0.03653252124786377,
0.003130948171019554,
0.007470170967280865,
-0.002500692615285516,
-0.02918851003050804,
0.017901886254549026,
0.013264288194477558,
0.046188123524188995,
-0.0029612425714731216,
-0.017641261219978333,
-0.022929009050130844,
-0.01725594326853752,
0.04550546780228615,
0.023146329447627068,
-0.005429096985608339,
0.023034002631902695,
0.07797154784202576,
-0.005626351572573185,
-0.01761772856116295,
-0.000050512346206232905,
-0.025049839168787003,
0.014710405841469765,
0.010257717221975327,
0.011780590750277042,
0.010348633863031864,
-0.0014598839916288853,
-0.010217170231044292,
-0.028341611847281456,
-0.0023494453635066748,
-0.011244090273976326,
0.05271315947175026,
-0.013078911229968071,
0.052261777222156525,
-0.010821723379194736,
0.0013165130512788892,
-0.025173187255859375,
-0.03003699518740177,
-0.000011745282790798228,
0.01890316791832447,
0.01716122031211853,
0.01072285883128643,
-0.026310404762625694,
0.017365319654345512,
0.01781364530324936,
0.034337952733039856,
0.05080761760473251,
-0.027818694710731506,
0.04430604726076126,
0.033057697117328644,
0.006420352961868048,
0.020121097564697266,
-0.03827530890703201,
0.029304850846529007,
-0.04509185999631882,
0.050911400467157364,
0.007215887773782015,
-0.020429592579603195,
0.050756823271512985,
0.0033039702102541924,
-0.0017579953419044614,
-0.06973662972450256,
-0.0018227188847959042,
0.008139064535498619,
0.004876396618783474,
0.010322782211005688,
-0.013909801840782166,
0.01387407910078764,
0.013089582324028015,
0.036851588636636734,
0.010025654919445515,
-0.009707912802696228,
-0.0085813719779253,
-0.05903644859790802,
-0.00645354762673378,
-0.016935426741838455,
-0.029188180342316628,
0.03656160831451416,
0.0333540104329586,
-0.03512302413582802,
0.015566167421638966,
-0.0133766308426857,
0.03728727251291275,
0.020043373107910156,
0.02724083513021469,
-0.007792899385094643,
0.04889870062470436,
0.00913031306117773,
0.003285325365141034,
-0.027554597705602646,
0.0319017618894577,
0.12030652910470963,
0.02645106241106987,
0.049003444612026215,
-0.07044287770986557,
-0.02712603472173214,
-0.0063719493336975574,
-0.019529933109879494,
-0.03893854841589928,
0.012156159617006779,
-0.015552513301372528,
0.06598265469074249,
0.04781068116426468,
0.0457606166601181,
0.014785018749535084,
0.042916905134916306,
0.047852858901023865,
-0.044147055596113205,
-0.01805439405143261,
-0.015500788576900959,
-0.008112083189189434,
-0.023523638024926186,
0.023203542456030846,
-0.03538498282432556,
-0.0023466567508876324,
-0.029976999387145042,
0.0015890512149780989,
0.007546924985945225,
-0.04474472627043724,
0.01994500868022442,
0.010231935419142246,
-0.032603878527879715,
0.015286492183804512,
0.027098042890429497,
-0.020510440692305565,
-0.040878262370824814,
0.003349822713062167,
-0.013221098110079765,
-0.029074324294924736,
0.017638403922319412,
-0.037463024258613586,
0.022949088364839554,
-0.005552390590310097,
0.027912195771932602,
0.037634942680597305,
-0.03520732372999191,
0.0036733471788465977,
-0.026719816029071808,
0.04231181740760803,
-0.028797807171940804,
-0.000460140872746706,
-0.023923207074403763,
-0.00011731211998267099,
0.004161621443927288,
-0.05692652612924576,
-0.0048255156725645065,
-0.0063894400373101234,
0.040074422955513,
0.0037050412502139807,
-0.03455428406596184,
-0.031641241163015366,
0.01074497401714325,
-0.006189899519085884,
-0.02874850481748581,
-0.006414189003407955,
-0.006980870384722948,
0.02152899280190468,
0.0074401493184268475,
0.021959993988275528,
-0.020983589813113213,
-0.013136861845850945,
-0.006548541598021984,
-0.012662245891988277,
-0.05363687127828598,
0.0038149449974298477,
0.02048245631158352,
0.01742047443985939,
0.02903791330754757,
-0.03310973569750786,
-0.007736680563539267,
-0.01057928241789341,
-0.08609401434659958,
0.025025179609656334,
0.0014825289836153388,
-0.03234969079494476,
-0.008965161629021168,
-0.04336731880903244,
0.008481756784021854,
0.060888055711984634,
-0.0015169490361586213,
0.03435616195201874,
-0.03721531108021736,
0.044962357729673386,
-0.004071339499205351,
0.0070444801822304726,
-0.031530775129795074,
0.054573580622673035,
-0.024891993030905724,
0.003973938524723053,
-0.004125029314309359,
0.05082057788968086,
0.03614802286028862,
0.017080141231417656,
0.005363878794014454,
0.03659506514668465,
-0.034578707069158554,
0.01602972112596035,
0.020111849531531334,
0.008500616066157818,
-0.01672774739563465,
0.03865617513656616,
0.003721322864294052,
-0.06064947694540024,
-0.05318541079759598,
-0.05064115673303604,
-0.015790827572345734,
0.00387779762968421,
0.04073071479797363,
-0.02582884579896927,
-0.018689794465899467,
-0.017260197550058365,
0.03747076168656349,
-0.03825883939862251,
-0.010995696298778057,
-0.10320650786161423,
0.028378847986459732,
-0.013584699481725693,
0.0023612009827047586,
-0.0028157203923910856,
0.015818016603589058,
-0.03109930455684662,
0.0042940168641507626,
0.005038196220993996,
-0.009805391542613506,
0.027223309502005577,
0.04121382534503937,
-0.009593058377504349,
-0.017260262742638588,
0.05264115706086159,
-0.02510395087301731,
-0.041823841631412506,
0.06618593633174896,
-0.03552285581827164,
-0.06296372413635254,
-0.020828185603022575,
-0.010994693264365196,
0.030119722709059715,
0.021150769665837288,
0.005216585472226143,
0.009315883740782738,
0.041714537888765335,
-0.008845895528793335,
-0.029518458992242813,
-0.021455861628055573,
-0.010602343827486038,
0.008908139541745186,
-0.019498832523822784,
0.00932818092405796,
-0.043601348996162415,
-0.020805316045880318,
0.02970130369067192,
0.03805684670805931,
0.014377264305949211,
-0.013413146138191223,
0.025096233934164047,
-0.0017848873976618052,
-0.012094555422663689,
0.027744997292757034,
0.033313021063804626,
0.0037058370653539896,
0.03898531571030617,
-0.058688946068286896,
0.016285289078950882,
-0.011973738670349121,
-0.027247101068496704,
-0.10797975212335587,
0.02597181685268879,
0.00028312241192907095,
-0.006168955471366644,
0.01812971755862236,
-0.01362611074000597,
0.007032320369035006,
0.05031026527285576,
-0.0807836577296257,
0.009780632331967354,
-0.05636027082800865,
-0.011192543432116508,
-0.044546645134687424,
0.0018478352576494217,
0.022518420591950417,
0.03038770891726017,
0.017576027661561966,
0.013654151931405067,
0.030603118240833282,
0.00824612844735384,
-0.01464054360985756,
-0.019376959651708603,
0.023002542555332184,
0.04718900844454765,
-0.02007732354104519,
0.020639881491661072,
0.05762204900383949,
0.02502078004181385,
-0.0038374511059373617,
0.015261593274772167,
-0.005527779459953308,
0.005352752283215523,
-0.005028183571994305,
0.005863240920007229,
-0.020041795447468758,
0.005330326966941357,
0.02659347839653492,
-0.014481473714113235,
-0.03306294605135918,
0.039743974804878235,
0.019799215719103813,
0.0069181486032903194,
0.020423833280801773,
0.0019117128103971481,
0.02176283299922943,
-0.03816530108451843,
0.000004495157099881908,
0.035230591893196106,
-0.03222738206386566,
-0.0014446572167798877,
-0.011455299332737923,
0.013582082465291023,
0.030199628323316574,
-0.02952166460454464,
-0.013798090629279613,
-0.042917534708976746,
0.004535415209829807,
0.034422699362039566,
0.0035252710804343224,
-0.010921361856162548,
0.022112010046839714,
0.005945310927927494,
-0.029153574258089066,
-0.00610441854223609,
0.01164634246379137,
-0.012762900441884995,
-0.022392218932509422,
-0.046068158000707626,
-0.0021084884647279978,
-0.03141038119792938,
-0.010920706205070019,
-0.008347702212631702,
-0.030339976772665977,
0.04324200004339218,
0.003257322357967496,
0.0006840992718935013,
0.011057429946959019,
-0.07057729363441467,
-0.01366210263222456,
-0.045383572578430176,
0.008737888187170029,
-0.010256904177367687,
-0.03330949321389198,
-0.060427214950323105,
-0.05776066705584526,
0.01969674974679947,
0.011137389577925205,
0.04922807589173317,
-0.009738226421177387,
-0.022770602256059647,
-0.02346806973218918,
-0.009543932974338531,
0.0350310243666172,
-0.04252462461590767,
0.033240947872400284,
0.010374206118285656,
-0.03617626056075096,
-0.012230731546878815,
-0.0042223553173244,
-0.028795070946216583,
-0.002783955540508032,
0.06818057596683502,
-0.017300216481089592,
0.062441375106573105,
0.020585190504789352,
-0.024568011984229088,
0.02161603420972824,
0.046383894979953766,
0.024447815492749214,
0.05423273891210556,
-0.021062038838863373,
0.028482550755143166,
0.03219054639339447,
-0.019323118031024933,
-0.024690257385373116,
0.057922348380088806,
-0.031049363315105438,
0.0016690983902662992,
0.003516986034810543,
0.011214402504265308,
0.034726742655038834,
-0.0380629263818264,
0.00868495088070631,
0.003275773487985134,
-0.0061754402704536915,
-0.022768359631299973,
0.010627984069287777,
0.03748941048979759,
0.0486447848379612,
-0.0018551500979810953,
0.00026033606263808906,
0.009702733717858791,
-0.019346432760357857,
0.0156689565628767,
0.062382303178310394,
0.016978908330202103,
0.038463007658720016,
0.022798174992203712,
-0.011166827753186226,
-0.003195900935679674,
0.022243306040763855,
-0.000452523585408926,
0.06676631420850754,
-0.024953559041023254,
-0.04291073605418205,
0.010622537694871426,
-0.020399823784828186,
0.01206703670322895,
0.02106460928916931,
-0.029722237959504128,
0.09319216012954712,
-0.051750510931015015,
0.04218069091439247,
0.00006059627776267007,
0.001343878568150103,
-0.0167190320789814,
0.014871369116008282,
0.0030609704554080963,
0.057359859347343445,
0.023944851011037827,
-0.027777697890996933,
0.017553435638546944,
0.03007439151406288,
0.00896508526057005,
0.014107096940279007,
0.00250348262488842,
-0.00874721072614193,
0.005045022815465927,
-0.04444698989391327,
-0.01940365508198738,
-0.0010167784057557583,
-0.021162860095500946,
-0.00324145401827991,
0.06631958484649658,
-0.003907982259988785,
0.013387469574809074,
-0.02517971210181713,
-0.04853101074695587,
0.04963397979736328,
-0.06924058496952057,
-0.02095218189060688,
0.0016510364366695285,
0.03435128182172775,
-0.023807696998119354,
0.013912257738411427
] |
<p>If the light velocity is a vector quantity, why vector addition cannot be applied to it?</p>
<p>Or the light velocity is not a vector quantity?</p> | 2,899 | [
-0.015432456508278847,
-0.0187462717294693,
-0.02470962516963482,
-0.03447370603680611,
0.07663179934024811,
0.025001708418130875,
-0.04520286247134209,
0.006458786316215992,
-0.001810007612220943,
-0.004546720068901777,
0.027494564652442932,
0.05142468959093094,
0.07786739617586136,
0.011253001168370247,
0.023015853017568588,
0.028786133974790573,
0.00288305152207613,
0.03352487459778786,
-0.00756426015868783,
-0.00204443815164268,
-0.01933630369603634,
0.02235020510852337,
0.035618383437395096,
0.02104843780398369,
0.027836572378873825,
0.041471466422080994,
0.05163304880261421,
-0.008196372538805008,
0.020449141040444374,
0.04653047025203705,
0.02006496675312519,
-0.018070511519908905,
0.041667718440294266,
0.06149924173951149,
0.019398421049118042,
0.0018048108322545886,
-0.03760598599910736,
-0.007798011880367994,
0.0028093939181417227,
0.0011859893565997481,
-0.015379898250102997,
0.0017865138361230493,
-0.024346616119146347,
0.06277871131896973,
-0.016985639929771423,
0.03897538781166077,
0.011538760736584663,
0.013592954725027084,
0.055955950170755386,
-0.04632299393415451,
0.058291956782341,
-0.019355187192559242,
0.04233209788799286,
0.006514310371130705,
-0.033304326236248016,
-0.0038688837084919214,
0.08841761201620102,
0.05983518436551094,
0.002609424525871873,
-0.024259140715003014,
0.010881735943257809,
0.01847275160253048,
0.013110908679664135,
-0.042087048292160034,
-0.00959464069455862,
0.03465726599097252,
-0.022053034976124763,
-0.00471690995618701,
0.0014526044251397252,
0.02359834872186184,
0.006525897886604071,
-0.0012128547532483935,
0.005164940841495991,
-0.01290728710591793,
-0.009670896455645561,
-0.04302046447992325,
0.01517659891396761,
0.019321799278259277,
0.036959458142519,
0.027094636112451553,
-0.00409923680126667,
0.00911225937306881,
0.06229506433010101,
0.029650988057255745,
0.014528368599712849,
-0.02546563930809498,
0.024238569661974907,
0.015301749110221863,
0.007228436879813671,
0.03525959700345993,
-0.0295841246843338,
0.007563674356788397,
0.008414984680712223,
0.013662281446158886,
-0.03875638544559479,
0.017855539917945862,
-0.023385215550661087,
0.01506697665899992,
0.023469924926757812,
-0.01793067529797554,
0.010306878946721554,
0.0025897426530718803,
0.016994381323456764,
0.07310178875923157,
0.0042480588890612125,
-0.02742975391447544,
-0.02289244532585144,
0.03279143571853638,
-0.03147096559405327,
-0.030142124742269516,
-0.02708323486149311,
0.004825414624065161,
0.006492758635431528,
0.016520380973815918,
0.004207232501357794,
-0.05351024493575096,
0.005146785639226437,
-0.024079956114292145,
0.09201501309871674,
0.07328999787569046,
0.03286309167742729,
-0.03703717887401581,
-0.017468353733420372,
-0.018807435408234596,
-0.050715941935777664,
0.0037280770484358072,
0.012733793817460537,
-0.013082904741168022,
-0.01103874109685421,
0.003588128602132201,
0.016072766855359077,
-0.051569320261478424,
-0.007734003476798534,
-0.0072753895074129105,
0.0075197480618953705,
-0.04460970312356949,
-0.1119818314909935,
-0.07285342365503311,
0.042796652764081955,
-0.003868366125971079,
-0.03570268675684929,
-0.07368860393762589,
0.0307352002710104,
0.014267416670918465,
0.09258066862821579,
0.020238863304257393,
0.022881759330630302,
0.01707763969898224,
0.05294269323348999,
-0.009048148058354855,
-0.007745231501758099,
-0.0330619141459465,
-0.012973939999938011,
-0.06009584292769432,
0.00017009784642141312,
-0.0709960088133812,
0.0037914011627435684,
0.013927680440247059,
-0.021828830242156982,
0.0027770777232944965,
0.02483450248837471,
-0.03972848504781723,
0.020850980654358864,
0.018235020339488983,
0.00997887458652258,
-0.028532974421977997,
0.05850141495466232,
0.04593714699149132,
0.02227625623345375,
0.04699927568435669,
-0.023252155631780624,
0.04115020111203194,
0.008802979253232479,
0.039418306201696396,
0.05550696700811386,
-0.01951075904071331,
-0.021461177617311478,
0.009178456850349903,
0.01528917532414198,
-0.004620689898729324,
-0.03726932033896446,
-0.06319203227758408,
-0.016082292422652245,
0.02615938149392605,
0.027223119512200356,
0.06297779828310013,
0.002845771610736847,
0.02945142425596714,
-0.033307500183582306,
-0.03446502611041069,
0.01462149154394865,
-0.05577242001891136,
0.01242458913475275,
0.05248168483376503,
-0.03901994600892067,
-0.014300115406513214,
0.016386372968554497,
0.01142127625644207,
-0.006691788788884878,
-0.004468756727874279,
-0.025798272341489792,
0.0489431731402874,
0.014877775683999062,
-0.02485443465411663,
0.012963036075234413,
0.05161835998296738,
0.07930745929479599,
0.0015814438229426742,
-0.0020247928332537413,
0.010486917570233345,
-0.04091943800449371,
0.016947342082858086,
0.017862102016806602,
0.020543498918414116,
0.007566456217318773,
0.0009112715488299727,
0.0016405879287049174,
0.031797733157873154,
-0.020498042926192284,
0.05252749100327492,
-0.032641761004924774,
0.08497816324234009,
0.046478476375341415,
0.00744372745975852,
-0.0100180609151721,
0.061940573155879974,
-0.010864488780498505,
-0.014801548793911934,
0.00786579493433237,
-0.01101849414408207,
-0.022526511922478676,
0.03540724515914917,
0.03702165558934212,
0.0022984622046351433,
-0.06236135959625244,
0.013709116727113724,
0.05373213812708855,
0.053561732172966,
0.028765635564923286,
0.02686537429690361,
-0.022646142169833183,
-0.05522426217794418,
0.017315926030278206,
0.01769087091088295,
0.016407757997512817,
0.006370864808559418,
0.03299034386873245,
-0.002462695585563779,
0.00022303157311398536,
-0.002699248492717743,
-0.04211493581533432,
0.024638168513774872,
0.016580507159233093,
-0.011224482208490372,
0.012537435628473759,
-0.01321464218199253,
0.03149121254682541,
-0.010524319484829903,
0.030118970200419426,
0.03239342197775841,
-0.010837842710316181,
-0.007054933346807957,
-0.012150966562330723,
-0.021073946729302406,
0.013172381557524204,
-0.025784913450479507,
-0.030423056334257126,
-0.04809565469622612,
0.030264057219028473,
-0.02895711548626423,
0.010746547020971775,
-0.03298528492450714,
0.0006752877379767597,
-0.051841747015714645,
-0.029327360913157463,
0.022055597975850105,
0.0016438373131677508,
0.029928196221590042,
-0.0330890491604805,
-0.0300998967140913,
0.013910384848713875,
-0.04957522079348564,
-0.014096487313508987,
0.00114351452793926,
-0.04433867335319519,
0.0266219861805439,
-0.01395943108946085,
-0.061353325843811035,
0.04344483092427254,
-0.01385680865496397,
0.013680771924555302,
0.021028226241469383,
-0.019076675176620483,
-0.07441077381372452,
-0.011084833182394505,
-0.022002145648002625,
-0.008712904527783394,
-0.0204071756452322,
-0.014251464046537876,
0.018858732655644417,
-0.015046769753098488,
-0.06293053925037384,
-0.010984309017658234,
-0.02443118765950203,
-0.041815146803855896,
-0.009961624629795551,
-0.04458722099661827,
0.014936457388103008,
-0.061324343085289,
0.018190691247582436,
0.02422782965004444,
-0.05549947917461395,
0.02523724175989628,
-0.056955330073833466,
-0.033200155943632126,
0.007944171316921711,
0.0006078482838347554,
0.054276637732982635,
0.01244419440627098,
-0.0424715019762516,
0.06797131150960922,
0.05161665752530098,
-0.015480287373065948,
-0.02695511095225811,
0.0020419785287231207,
-0.0008539941045455635,
-0.03195967525243759,
0.021345730870962143,
0.0063929082825779915,
0.002099164528772235,
0.02216554433107376,
0.009449324570596218,
0.004890681244432926,
0.029193563386797905,
0.024660460650920868,
-0.0345304049551487,
-0.004814543295651674,
-0.003907205071300268,
0.02781798131763935,
0.039635591208934784,
0.04369726777076721,
-0.049761053174734116,
0.022324679419398308,
0.03133319318294525,
0.06181086599826813,
-0.012569372542202473,
-0.02037244476377964,
0.04545735940337181,
0.021184470504522324,
0.030036773532629013,
-0.03191928192973137,
0.04851268604397774,
0.03718382492661476,
0.03860606998205185,
0.003162059932947159,
0.0007481036591343582,
0.013398840092122555,
-0.03406424820423126,
0.013811249285936356,
0.002219065325334668,
0.03997064754366875,
-0.025149187073111534,
-0.012775002047419548,
-0.010843350552022457,
0.002815745072439313,
0.018479585647583008,
-0.02204563096165657,
0.004554694052785635,
0.05803085118532181,
0.04757732152938843,
-0.0006928591756150126,
0.004633833654224873,
-0.027202988043427467,
-0.0003968645178247243,
-0.043591953814029694,
0.005791380535811186,
-0.012610252946615219,
0.01635323092341423,
0.019036050885915756,
0.04148833081126213,
0.040101032704114914,
0.021896464750170708,
0.037406351417303085,
-0.025345418602228165,
-0.08695361018180847,
-0.010560035705566406,
-0.023130828514695168,
-0.03679216280579567,
-0.04702390357851982,
-0.019649647176265717,
-0.06338756531476974,
-0.042295441031455994,
-0.029049186035990715,
-0.04742112010717392,
-0.03554677963256836,
-0.035835087299346924,
0.02333868108689785,
-0.0018990497337654233,
-0.01941823586821556,
-0.00467818696051836,
0.006275069899857044,
0.04901072755455971,
-0.0397406741976738,
0.006597430910915136,
0.04409664496779442,
-0.012276138179004192,
-0.020785653963685036,
-0.0011051518376916647,
0.0025235682260245085,
0.015469887293875217,
0.010491325519979,
0.03359948471188545,
0.03929821029305458,
-0.017371948808431625,
0.026424702256917953,
0.02102348394691944,
0.03266766667366028,
0.02669643610715866,
-0.012865858152508736,
-0.06115660443902016,
-0.03675699979066849,
0.01726173236966133,
-0.019148075953125954,
0.06398741155862808,
0.022780418395996094,
-0.003907579928636551,
0.0394565686583519,
0.02132510207593441,
-0.005366064142435789,
0.03032965399324894,
0.040320634841918945,
0.004853782244026661,
-0.011057867668569088,
-0.06699919700622559,
-0.0007986486307345331,
-0.021669577807188034,
-0.03601738438010216,
0.03999195992946625,
0.012062441557645798,
-0.02711586095392704,
-0.013880245387554169,
-0.008381596766412258,
-0.014553158544003963,
-0.009460295550525188,
0.016570504754781723,
-0.01588580571115017,
-0.02773791365325451,
0.033042822033166885,
0.004511613864451647,
-0.029490744695067406,
0.04518565535545349,
0.03601415455341339,
-0.012695906683802605,
-0.004025943111628294,
-0.08971888571977615,
-0.00134141999296844,
0.022619204595685005,
0.03910796716809273,
-0.02548781968653202,
-0.016205618157982826,
-0.05868158116936684,
-0.020406639203429222,
0.04150799661874771,
-0.04881999269127846,
0.014627265743911266,
-0.014744888991117477,
-0.015250596217811108,
-0.010293788276612759,
-0.04610755667090416,
-0.03385850787162781,
0.03209478035569191,
-0.010117201134562492,
-0.00018978879961650819,
-0.008914729580283165,
0.010382437147200108,
-0.0007971423910930753,
-0.0022036985028535128,
0.036288563162088394,
0.028087511658668518,
0.012320182286202908,
0.000025596933483029716,
-0.0047630383633077145,
0.02071981690824032,
-0.018294667825102806,
-0.07852884382009506,
0.001049450715072453,
0.031009767204523087,
-0.0036978682037442923,
0.029144028201699257,
-0.02732081338763237,
-0.03391748294234276,
0.056572798639535904,
0.011006265878677368,
-0.0013056518509984016,
0.013278829865157604,
-0.042341262102127075,
0.0013889651745557785,
0.01410604640841484,
0.002324288012459874,
0.053169287741184235,
0.00041014226735569537,
-0.005767658818513155,
-0.011700727045536041,
-0.026030760258436203,
0.01777675747871399,
-0.032945480197668076,
-0.014768901281058788,
-0.011987072415649891,
0.0002719794283621013,
0.0032322374172508717,
0.06524616479873657,
-0.010738859884440899,
-0.024458151310682297,
-0.010661751963198185,
-0.015280411578714848,
-0.021541893482208252,
0.016891878098249435,
0.018657049164175987,
-0.010025948286056519,
-0.028709623962640762,
0.021090632304549217,
-0.008783455938100815,
0.002340518170967698,
0.03938911855220795,
-0.002048914087936282,
-0.025549624115228653,
0.014662261120975018,
0.02232157252728939,
0.016026683151721954,
0.025574849918484688,
0.020256366580724716,
0.016076792031526566,
-0.019622402265667915,
0.03591522201895714,
-0.028356164693832397,
0.01519704144448042,
0.01676696538925171,
-0.0545312874019146,
-0.04897165670990944,
-0.018237661570310593,
-0.02679428830742836,
0.03334057703614235,
-0.06382725387811661,
0.01770227961242199,
0.01952696032822132,
0.014577946625649929,
-0.06468257308006287,
-0.05307968705892563,
0.008694939315319061,
0.010606754571199417,
0.0045497664250433445,
-0.0033187458757311106,
0.015230766497552395,
-0.048620037734508514,
-0.01829642988741398,
-0.02452862821519375,
0.06104012951254845,
-0.02021612413227558,
-0.0359465628862381,
-0.020026393234729767,
0.012645111419260502,
0.00023502239491790533,
-0.033713001757860184,
0.000958217482548207,
0.034554895013570786,
-0.020622408017516136,
-0.0025298804976046085,
-0.004854707513004541,
0.06608866155147552,
-0.033044811338186264,
-0.05232645198702812,
-0.010277021676301956,
-0.022790372371673584,
0.006279330234974623,
0.007444843649864197,
0.02210192196071148,
0.0332646481692791,
-0.019464360550045967,
-0.010819931514561176,
-0.02844344452023506,
0.04771605134010315,
0.02054213546216488,
0.023030871525406837,
0.0040131257846951485,
0.005383975338190794,
-0.036790378391742706,
-0.012089557014405727,
0.03909948840737343,
0.02187899313867092,
0.020532000809907913,
-0.03610539436340332,
0.06171092763543129,
-0.027280448004603386,
0.002732738619670272,
0.015599420294165611,
0.01906147040426731,
-0.009663430042564869,
-0.009232188574969769,
-0.034541741013526917,
0.020125864073634148,
-0.013454591855406761,
-0.05009472370147705,
-0.006887322757393122,
-0.008027716539800167,
-0.0005563691374845803,
0.09826330840587616,
-0.044042084366083145,
0.03077714517712593,
-0.0067249177955091,
-0.014200877398252487,
-0.007281251717358828,
-0.020646845921874046,
-0.03299401327967644,
0.017138855531811714,
-0.0016653694910928607,
0.019095763564109802,
-0.02785462513566017,
-0.021814625710248947,
0.0119638592004776,
0.059887081384658813,
-0.007502775173634291,
-0.029152654111385345,
0.02809283323585987,
0.021536188200116158,
0.0070047699846327305,
0.0009870899375528097,
-0.028904788196086884,
0.02508590929210186,
-0.021225329488515854,
0.00841962918639183,
-0.006289258133620024,
-0.024883046746253967,
0.053620874881744385,
-0.035318225622177124,
-0.0018782848492264748,
-0.01837986335158348,
-0.014228451997041702,
-0.02693394385278225,
-0.005493032746016979,
0.00883062556385994,
0.017855599522590637,
0.001930659986101091,
-0.013192736543715,
0.03294980525970459,
0.01462447177618742,
0.018224311992526054,
-0.01987360417842865,
-0.08717063814401627,
-0.05620734766125679,
-0.02613893523812294,
-0.03113868460059166,
0.06544725596904755,
0.01755140721797943,
-0.02570347487926483,
-0.022177746519446373,
-0.024605847895145416,
0.023491233587265015,
0.00733931316062808,
0.04852500185370445,
-0.030547620728611946,
0.03275896608829498,
-0.001984881702810526,
0.02770170196890831,
-0.01828417181968689,
0.009606649167835712,
0.09937198460102081,
0.031107833608984947,
-0.0010204288410022855,
-0.055650319904088974,
0.034024428576231,
-0.023930085822939873,
0.019991867244243622,
-0.06645779311656952,
0.0655180960893631,
-0.03203124925494194,
0.038654934614896774,
0.021683406084775925,
0.02802448719739914,
0.007231682538986206,
-0.02366340160369873,
0.010303393006324768,
-0.06267938017845154,
-0.043513305485248566,
-0.00398143008351326,
0.03325388580560684,
0.021415341645479202,
0.0508233867585659,
-0.021828342229127884,
-0.01577967405319214,
-0.01177883055061102,
-0.010047207586467266,
-0.038745246827602386,
-0.012122215703129768,
0.0015518113505095243,
0.031125321984291077,
-0.0661102682352066,
0.00975959561765194,
0.04793282225728035,
-0.010226307436823845,
-0.06955656409263611,
0.007360981777310371,
0.028209131211042404,
-0.01174534484744072,
0.03592747822403908,
0.011416294611990452,
0.031955596059560776,
0.02061353623867035,
0.00279194675385952,
0.014432240277528763,
-0.07086799293756485,
0.025857675820589066,
-0.0016419474268332124,
0.0750710666179657,
-0.022238997742533684,
0.023919036611914635,
0.006651442963629961,
0.014397623017430305,
-0.02224000170826912,
-0.07693714648485184,
-0.011335926130414009,
-0.015886319801211357,
0.017097344622015953,
0.043924130499362946,
0.002238744404166937,
-0.0011175216641277075,
0.028228165581822395,
-0.0004872643912676722,
0.04444300755858421,
-0.002186656231060624,
-0.01405321341007948,
0.012964108027517796,
-0.004091339185833931,
0.032483141869306564,
-0.020479395985603333,
-0.02030332013964653,
-0.0022078955080360174,
0.00001547299871162977,
-0.01615513116121292,
0.006158196832984686,
0.02005908451974392,
0.02589261718094349,
0.019717713817954063,
-0.036806169897317886,
0.022114872932434082,
-0.015699701383709908,
-0.07470470666885376,
0.004244157113134861,
-0.019361980259418488,
-0.04970879480242729,
-0.017797501757740974,
0.011146587319672108,
0.034097664058208466,
0.044559601694345474,
-0.05285008251667023,
-0.019646668806672096,
-0.0030267632100731134,
0.037565458565950394,
0.029017917811870575,
0.006601887755095959,
-0.021118314936757088,
0.012962334789335728,
0.017326965928077698,
-0.021213330328464508,
-0.02297818474471569,
0.0018856129609048367,
0.04656590521335602,
0.025045856833457947,
-0.017055237665772438,
0.014684358611702919,
-0.012213293462991714,
-0.029506582766771317,
0.035738054662942886,
-0.009665410965681076,
0.01980581134557724,
0.01081877201795578,
0.030126383528113365,
-0.028493165969848633,
-0.015149618498980999,
-0.03249698504805565,
-0.020486053079366684,
0.0185183547437191,
0.01597137562930584,
-0.030539708212018013,
-0.005502237007021904,
-0.03469343110918999,
0.030218303203582764,
-0.03696857765316963,
-0.021044015884399414,
-0.028940333053469658,
0.021049201488494873,
-0.03369165584445,
-0.02990136854350567,
-0.013293495401740074,
0.03235684335231781,
-0.034599561244249344,
0.004086922388523817,
0.023964788764715195,
0.030604081228375435,
0.0023006275296211243,
0.0021401296835392714,
0.013225521892309189,
-0.010921470820903778,
0.05183382332324982,
-0.00012056665582349524,
-0.06676243990659714,
0.045153334736824036,
-0.03993726149201393,
-0.028715338557958603,
0.04178484156727791,
-0.00907982513308525,
0.031947676092386246,
0.029529301449656487,
-0.0011236016871407628,
-0.01659960113465786,
0.05523725226521492,
-0.012737561017274857,
-0.027315082028508186,
0.012628860771656036,
-0.047395627945661545,
-0.023528724908828735,
-0.005581690929830074,
0.01748744212090969,
-0.013795583508908749,
-0.010661984793841839,
0.031999196857213974,
0.00910651870071888,
-0.027823006734251976,
0.008461027406156063,
0.008259914815425873,
-0.005918027833104134,
0.017670951783657074,
0.039968669414520264,
-0.024194421246647835,
-0.01084295753389597,
0.03381185978651047,
-0.022230636328458786,
0.04038327559828758,
0.03679930791258812,
-0.0006737385992892087,
-0.12568053603172302,
0.018943553790450096,
-0.006017003208398819,
0.02388925850391388,
0.03203294426202774,
-0.04461948573589325,
0.04590780660510063,
0.02386738732457161,
-0.10912468284368515,
0.010271328501403332,
-0.048429328948259354,
-0.020655827596783638,
-0.026531198993325233,
0.0048196385614573956,
0.01132091972976923,
0.05811378359794617,
0.05709029734134674,
0.02928566187620163,
0.03454113379120827,
0.006052702199667692,
-0.013938028365373611,
-0.05088553577661514,
-0.04114160314202309,
0.03363316133618355,
-0.037687499076128006,
0.001345705590210855,
0.041982751339673996,
0.014890024438500404,
-0.016186563298106194,
-0.008437692187726498,
0.024782443419098854,
0.04526067525148392,
0.01313160452991724,
0.03322966396808624,
0.02254079096019268,
0.018117209896445274,
0.007794457022100687,
-0.01979263313114643,
-0.054200462996959686,
0.03217166289687157,
0.00505667831748724,
0.030460238456726074,
-0.014231300912797451,
-0.017501162365078926,
0.025319131091237068,
-0.03949641063809395,
-0.030584780499339104,
0.009201142936944962,
-0.0336991511285305,
-0.02421717718243599,
0.011282019317150116,
0.0208661500364542,
0.027173781767487526,
-0.03626173362135887,
0.00034686928847804666,
-0.04897693544626236,
-0.01818728819489479,
0.03163941204547882,
-0.03310942277312279,
-0.027865905314683914,
-0.014692330732941628,
0.019244065508246422,
-0.01097661443054676,
0.00020530595793388784,
0.0068237972445786,
0.05387096479535103,
-0.06636971235275269,
0.0030877855606377125,
0.04266227409243584,
-0.03153255209326744,
0.01946069300174713,
-0.03445983678102493,
-0.028821732848882675,
0.03253566101193428,
0.024003930389881134,
0.023807242512702942,
-0.02366640232503414,
-0.006576645188033581,
-0.02713920548558235,
-0.0521833598613739,
0.02628246508538723,
0.015944942831993103,
0.0010864445939660072,
-0.030351491644978523,
-0.018414273858070374,
-0.01973409205675125,
0.03482187166810036,
0.06781208515167236,
-0.010560442693531513,
-0.04836828634142876,
0.024220408871769905,
0.012127981521189213,
0.02347072958946228,
-0.036287371069192886,
-0.0022872474510222673,
-0.025264287367463112,
-0.03098558634519577,
-0.014020249247550964,
-0.015223649330437183,
-0.012641244567930698,
-0.009806440211832523,
0.00012922352470923215,
-0.009668122977018356,
0.03428378701210022,
-0.012236942537128925,
-0.045784056186676025,
0.02508632279932499,
0.01769069954752922,
-0.010706954635679722,
0.051878854632377625,
0.012231730856001377,
0.03000251017510891,
0.039352670311927795,
-0.015281063504517078,
-0.037506233900785446,
0.009892044588923454,
-0.02692507393658161,
-0.010309256613254547,
-0.006733401212841272,
0.01034982968121767,
0.020688775926828384,
-0.034800343215465546,
0.00040611810982227325,
0.06712177395820618,
-0.04305179789662361,
-0.003191041760146618,
0.056598059833049774,
-0.0156780444085598,
0.033216338604688644,
0.009256412275135517,
0.0367591455578804,
0.01651032827794552,
-0.006742458324879408,
0.012385547161102295,
0.0323287695646286,
0.010842536576092243,
0.005061993841081858,
0.021976759657263756,
0.054620008915662766,
-0.0003095428692176938,
-0.0011462444672361016,
-0.0010355679551139474,
0.02496962621808052,
-0.03436019644141197,
0.0061789825558662415,
-0.017340226098895073,
-0.010432467795908451,
0.02103220671415329,
0.040649574249982834,
0.006226781290024519,
0.07631485164165497,
-0.06101839989423752,
0.009023354388773441,
-0.01357235386967659,
-0.01765843667089939,
-0.018755583092570305,
0.004223213065415621,
-0.020385324954986572,
0.03258582204580307,
0.011266494169831276,
-0.034748706966638565,
-0.021867424249649048,
-0.02698253095149994,
0.019153784960508347,
-0.04004558548331261,
-0.005004990845918655,
0.005884916987270117,
-0.022599373012781143,
0.002464093966409564,
0.0020626189652830362,
-0.018384112045168877,
0.007680156268179417,
-0.002814952516928315,
0.027686046436429024,
0.01307937316596508,
-0.0007605297141708434,
-0.011574908159673214,
-0.019270986318588257,
0.028100555762648582,
-0.05874454602599144,
-0.015078692696988583,
-0.03113577328622341,
0.04366595298051834,
-0.015802305191755295,
-0.0173102505505085
] |
<p>In quantum information and quantum computation, we generally use Bell type states which are maximally entangled. I find that the set of entangled states as interesting objects from a mathematical point of view and one can ask many questions regarding their structure and so on. But my question is, what are the practical uses of such states and why are they physically interesting.</p>
<p>The only case I can find out is, when due to some environmental interaction such states are created. However I can only see the use of maximally entangled states in literature. Caveat: In multipartite cases, maximal entanglement can be tricky.</p>
<p>I am not sure, whether I have have phrased the question correctly. Feel free to ask and edit. Advanced thanks for any help, suggestion etc.</p> | 2,900 | [
0.012891514226794243,
0.009383898228406906,
-0.024291284382343292,
-0.031234579160809517,
0.026658572256565094,
0.04262058809399605,
-0.01565932296216488,
-0.044112224131822586,
0.009280097670853138,
-0.03432932123541832,
0.023028703406453133,
0.036849044263362885,
-0.01848013699054718,
0.006823963485658169,
0.014187079854309559,
-0.011776557192206383,
-0.020012836903333664,
-0.009724176488816738,
-0.016700951382517815,
-0.016386251896619797,
0.0019509840058162808,
0.02725043147802353,
0.0017163408920168877,
-0.007790847215801477,
0.01581631228327751,
0.025953777134418488,
-0.012348542921245098,
-0.011982542462646961,
0.04623434692621231,
0.06559046357870102,
-0.0008138578850775957,
-0.033048927783966064,
-0.018166059628129005,
0.029285522177815437,
-0.01623307541012764,
-0.03500247746706009,
-0.029146600514650345,
-0.015582073479890823,
0.014757911674678326,
0.01951713114976883,
-0.045132044702768326,
-0.04775552451610565,
0.013520949520170689,
0.02454385533928871,
-0.013383193872869015,
0.01433564256876707,
-0.001924058306030929,
-0.05446086451411247,
0.022931858897209167,
-0.08411667495965958,
0.039157263934612274,
0.029442818835377693,
0.024588285014033318,
-0.0101942028850317,
0.017063338309526443,
0.025867126882076263,
0.060784514993429184,
0.06915216892957687,
-0.008091350086033344,
-0.051877621561288834,
-0.006449779029935598,
0.0008968042675405741,
0.005235683638602495,
-0.03382975235581398,
-0.013694779016077518,
0.018425660207867622,
0.0026167877949774265,
0.015751846134662628,
0.029753511771559715,
0.021466821432113647,
-0.008511541411280632,
0.040813200175762177,
0.04094750061631203,
-0.008852992206811905,
0.0005557535332627594,
-0.027446700260043144,
0.018155332654714584,
-0.008479321375489235,
0.024378184229135513,
0.033839885145425797,
-0.0013435703003779054,
-0.005030492320656776,
0.023090718314051628,
-0.005191233940422535,
-0.011049952358007431,
-0.015017539262771606,
0.08024410903453827,
-0.023004397749900818,
0.0009711487800814211,
0.017352288588881493,
-0.03495296835899353,
-0.009933963418006897,
0.0398835688829422,
0.03173735365271568,
-0.04824186861515045,
-0.008742617443203926,
-0.00005336648609954864,
0.05054847151041031,
0.006936977617442608,
-0.05775005742907524,
-0.023025253787636757,
-0.024851642549037933,
0.007534682750701904,
0.08627158403396606,
-0.011353261768817902,
-0.030916377902030945,
-0.012156335636973381,
0.030032645910978317,
0.028078455477952957,
0.0008733204449526966,
-0.008475286886096,
-0.005185609683394432,
0.019019130617380142,
0.013287042267620564,
0.036119017750024796,
-0.026755046099424362,
0.01573808118700981,
-0.023045912384986877,
0.02962939813733101,
0.06932895630598068,
0.025798287242650986,
-0.03219898045063019,
0.024880146607756615,
-0.041094597429037094,
-0.06306049227714539,
0.031136000528931618,
0.017239635810256004,
0.02531932108104229,
-0.044788699597120285,
0.051169730722904205,
-0.008718613535165787,
-0.022006286308169365,
0.021611148491501808,
-0.014936380088329315,
0.021551696583628654,
-0.061746031045913696,
-0.14613816142082214,
-0.05519410967826843,
0.06908071786165237,
0.007906085811555386,
-0.03245898708701134,
-0.06639714539051056,
0.03751341998577118,
0.057310428470373154,
0.07291708141565323,
-0.022020509466528893,
-0.02113397605717182,
0.021315019577741623,
0.029981525614857674,
0.03621184080839157,
-0.028186548501253128,
-0.02752244658768177,
0.024002863094210625,
-0.04366570711135864,
0.02298903837800026,
-0.07007790356874466,
0.008998517878353596,
0.030665092170238495,
0.002487502759322524,
-0.03304295614361763,
0.08034060895442963,
-0.026430200785398483,
-0.003334771143272519,
0.02760012075304985,
-0.028701242059469223,
-0.01536406297236681,
0.1045164242386818,
0.003579799085855484,
0.02746051736176014,
0.05571475997567177,
0.008567334152758121,
0.03738321736454964,
0.040371719747781754,
0.027890710160136223,
0.01131262257695198,
-0.007004637271165848,
0.025958342477679253,
0.018615366891026497,
0.008577379398047924,
-0.02373519167304039,
-0.017279770225286484,
-0.015017286874353886,
-0.027405349537730217,
-0.00051592115778476,
-0.013222823850810528,
0.02151522971689701,
-0.029907064512372017,
-0.038561947643756866,
0.02152871899306774,
-0.07712647318840027,
-0.008623764850199223,
-0.05488262698054314,
0.04041333124041557,
0.0016176797216758132,
-0.014611252583563328,
0.041207313537597656,
-0.005293358117341995,
0.012026291340589523,
-0.027180248871445656,
-0.03130374848842621,
-0.03367585316300392,
0.03033355064690113,
0.04888680949807167,
-0.008238700218498707,
-0.0030025956220924854,
0.024671494960784912,
0.007379260379821062,
-0.016332106664776802,
0.01627807319164276,
-0.010613038204610348,
-0.02834085375070572,
-0.03552312031388283,
-0.009866946376860142,
0.030533842742443085,
-0.023883221670985222,
-0.014227168634533882,
0.004388287663459778,
0.0076934341341257095,
-0.01827865093946457,
0.01865866221487522,
-0.04084277153015137,
0.04719426482915878,
0.006756172515451908,
0.010250959545373917,
-0.019785428419709206,
0.034620508551597595,
0.02210410311818123,
-0.01420297659933567,
0.004193721804767847,
-0.018089450895786285,
-0.09714681655168533,
0.03598986566066742,
0.0039174738340079784,
0.05232438072562218,
-0.03959759697318077,
0.02863982692360878,
-0.022862816229462624,
0.05343243479728699,
0.020393403246998787,
-0.003189855720847845,
-0.04664337635040283,
0.017140235751867294,
0.024811048060655594,
0.01770612597465515,
0.020140739157795906,
0.0232203658670187,
0.004520569462329149,
0.035890888422727585,
0.010912677273154259,
0.00048105395399034023,
-0.023917192593216896,
0.04421103000640869,
-0.055446427315473557,
0.022359536960721016,
-0.002793399151414633,
-0.045656006783246994,
-0.011458526365458965,
-0.06201127544045448,
0.021423693746328354,
0.015496584586799145,
-0.0032411019783467054,
0.001119885710068047,
-0.013605255633592606,
-0.05359091982245445,
0.004638911224901676,
0.012259460054337978,
-0.020221104845404625,
-0.013248300179839134,
0.027727805078029633,
-0.014403506182134151,
0.039354171603918076,
-0.0014360290952026844,
-0.003278534160926938,
-0.008203051052987576,
0.018775656819343567,
0.04095400497317314,
-0.029934681951999664,
0.019073354080319405,
-0.01809648424386978,
-0.033821556717157364,
-0.004810686688870192,
-0.04659760743379593,
0.0076327198185026646,
-0.005199956241995096,
-0.09550536423921585,
0.022420203313231468,
-0.028675740584731102,
-0.025688806548714638,
0.008602743968367577,
-0.028322311118245125,
0.019339393824338913,
-0.023822948336601257,
-0.011465692892670631,
-0.02440170757472515,
-0.014976494014263153,
-0.04388302192091942,
0.02029556781053543,
-0.0122749675065279,
0.00015905270993243903,
0.034499555826187134,
-0.03152335807681084,
-0.05625477433204651,
-0.033452749252319336,
-0.05233807861804962,
-0.04960281774401665,
-0.02994709461927414,
-0.040258780121803284,
0.01404697448015213,
-0.02347981557250023,
0.001140233944170177,
0.0328696146607399,
-0.05851211026310921,
-0.016342639923095703,
-0.05425703898072243,
-0.06033254787325859,
0.006831035017967224,
-0.018011024221777916,
0.021368306130170822,
-0.025255724787712097,
-0.010544558987021446,
0.05163521692156792,
0.017559362575411797,
-0.05299164354801178,
0.0026055537164211273,
-0.0028813101816922426,
-0.01763329654932022,
0.002202784875407815,
-0.0022194988559931517,
0.046902649104595184,
-0.0037497393786907196,
0.0679490938782692,
0.037660788744688034,
0.0007519287755712867,
0.018536794930696487,
0.010726114735007286,
-0.04358614236116409,
-0.011576691642403603,
-0.014963354915380478,
0.0011606029001995921,
0.036732859909534454,
0.012645890936255455,
-0.047171592712402344,
0.024240577593445778,
0.035688214004039764,
-0.01017235592007637,
-0.004151059314608574,
-0.012147795408964157,
0.05710599198937416,
0.006028668489307165,
0.008763088844716549,
-0.0010801160242408514,
0.02337859570980072,
-0.04866327345371246,
0.019430598244071007,
-0.015742098912596703,
0.03896303474903107,
-0.0018857354298233986,
-0.0333499014377594,
0.019126377999782562,
0.04063921421766281,
0.004818255547434092,
-0.032150328159332275,
-0.002627098932862282,
-0.021369734779000282,
-0.010482428595423698,
0.008776169270277023,
0.010466581210494041,
-0.03390684351325035,
0.05462080240249634,
0.011682341806590557,
0.023507526144385338,
0.008532938547432423,
-0.024859534576535225,
-0.020223336294293404,
-0.05247649922966957,
-0.01757425256073475,
0.007801431696861982,
0.016672898083925247,
0.015583744272589684,
0.05720552057027817,
0.02591772936284542,
-0.0011265728389844298,
-0.011019298806786537,
-0.02661929465830326,
-0.0934184193611145,
0.025236664339900017,
-0.0327024944126606,
0.03969811275601387,
0.0054529584012925625,
-0.03342326730489731,
0.015445583499968052,
-0.05633139982819557,
-0.04984123632311821,
-0.006497793830931187,
0.005163409747183323,
-0.08428167551755905,
-0.027306748554110527,
-0.0005473638884723186,
-0.016369186341762543,
-0.026576535776257515,
0.03254295513033867,
-0.0012083310866728425,
-0.011336772702634335,
0.009197879582643509,
0.03272351995110512,
-0.045976657420396805,
0.004351630341261625,
0.015655942261219025,
0.006649489514529705,
0.03719224035739899,
0.014603222720324993,
0.02221004292368889,
0.049543946981430054,
-0.019162524491548538,
0.023799104616045952,
-0.02154514193534851,
0.06953329592943192,
-0.02088300511240959,
-0.015477197244763374,
-0.004741038661450148,
-0.02016948163509369,
-0.024462297558784485,
-0.0009384746663272381,
0.033982302993535995,
0.002554604783654213,
-0.01174946315586567,
0.031407058238983154,
0.026987671852111816,
-0.006284397095441818,
0.017339305952191353,
0.046899933367967606,
0.00011621112207649276,
-0.027461757883429527,
-0.01730751432478428,
-0.04760294035077095,
-0.028824778273701668,
0.012531106360256672,
0.029674984514713287,
-0.014517859555780888,
-0.010457613505423069,
0.03881335258483887,
0.00952201709151268,
0.013793932273983955,
-0.0321849025785923,
-0.020627612248063087,
0.0019727954640984535,
0.012449495494365692,
0.01157313585281372,
0.01836341619491577,
-0.031804054975509644,
0.0177462100982666,
0.00995298195630312,
0.01285585854202509,
0.0005790548748336732,
-0.07809538394212723,
0.002077175537124276,
0.043769050389528275,
0.030826888978481293,
0.0063223871402442455,
-0.011432270519435406,
-0.022431567311286926,
-0.03085203468799591,
0.038142357021570206,
-0.033057644963264465,
0.04196443036198616,
-0.034306786954402924,
-0.034753166139125824,
-0.04361370950937271,
0.014752110466361046,
0.03150634467601776,
0.023163123056292534,
0.024426784366369247,
0.022877614945173264,
-0.012154994532465935,
-0.010199210606515408,
-0.014293206855654716,
0.003081722417846322,
0.01394239068031311,
0.04256206378340721,
0.0030532258097082376,
-0.02013777755200863,
0.01433758158236742,
0.01741756685078144,
-0.01274266466498375,
-0.0857967808842659,
-0.00948299653828144,
0.007020221557468176,
-0.024584338068962097,
0.04522332921624184,
-0.026822909712791443,
-0.06825491040945053,
-0.0325939767062664,
-0.03162931278347969,
-0.005602061748504639,
0.024586303159594536,
0.00961229670792818,
0.04579099640250206,
0.018691645935177803,
-0.023158397525548935,
0.013398705050349236,
0.0464697889983654,
-0.020898282527923584,
-0.011139363050460815,
0.0007988506113179028,
0.058898232877254486,
-0.04243160039186478,
0.027023298665881157,
-0.014641877263784409,
0.031110545620322227,
-0.02270200476050377,
0.06417396664619446,
-0.03718021884560585,
0.030087025836110115,
0.0041266572661697865,
-0.042861249297857285,
-0.039066292345523834,
0.05630865693092346,
0.0029315075371414423,
-0.018410401418805122,
-0.010931589640676975,
0.0071154870092868805,
0.00880054198205471,
-0.03182997182011604,
-0.005131712649017572,
0.013516162522137165,
0.03047206439077854,
0.044954679906368256,
-0.029476890340447426,
0.029370322823524475,
-0.030932286754250526,
-0.019367525354027748,
0.03365709260106087,
-0.036930929869413376,
0.01948276162147522,
-0.012481281533837318,
-0.021329624578356743,
0.042076535522937775,
-0.09255995601415634,
-0.04521442577242851,
0.03339123725891113,
-0.002326398389413953,
0.03101767599582672,
-0.028853319585323334,
0.0364234484732151,
-0.035980094224214554,
-0.0028024823404848576,
-0.05067327991127968,
-0.054362233728170395,
0.03771344572305679,
0.014070640318095684,
0.008146741427481174,
-0.013260108418762684,
0.039471425116062164,
-0.00422787806019187,
0.011343481950461864,
-0.03243767470121384,
0.07858852297067642,
-0.028950629755854607,
-0.005038139410316944,
0.0016241749981418252,
0.016544295474886894,
0.06350579857826233,
0.007789835799485445,
0.007993590086698532,
0.022012053057551384,
0.02584989368915558,
0.02878934144973755,
0.015289020724594593,
0.0036270003765821457,
-0.016524892300367355,
-0.03823087736964226,
0.010692502371966839,
0.025505006313323975,
0.028863711282610893,
-0.0110858753323555,
0.013373874127864838,
0.02111029252409935,
0.021111616864800453,
0.012360711582005024,
-0.013231697492301464,
-0.0132905850186944,
-0.026397140696644783,
0.020212426781654358,
0.018310103565454483,
-0.0023922170512378216,
0.006261453498154879,
-0.0652855783700943,
0.036231908947229385,
0.007538022939115763,
-0.004083776380866766,
0.008400908671319485,
0.039737969636917114,
0.021167142316699028,
-0.004853361751884222,
0.00825355015695095,
-0.006453940644860268,
0.017129234969615936,
-0.016955778002738953,
0.006364172790199518,
0.015607391484081745,
0.045968394726514816,
-0.009200839325785637,
-0.04461940750479698,
-0.025330105796456337,
-0.006132566835731268,
0.07740301638841629,
-0.017345933243632317,
0.04306044802069664,
0.057496655732393265,
-0.012081882916390896,
-0.002685613464564085,
-0.030791431665420532,
-0.02309376932680607,
0.020535971969366074,
-0.027642766013741493,
0.02530583366751671,
-0.009488966315984726,
0.012937331572175026,
0.01755998283624649,
0.028598640114068985,
-0.03188643604516983,
0.009198368526995182,
0.03163530305027962,
0.04615549370646477,
0.006920179817825556,
-0.028483660891652107,
-0.030313491821289062,
0.053669825196266174,
-0.055485907942056656,
-0.013216200284659863,
0.0015642830403521657,
-0.007620107848197222,
-0.007622065022587776,
-0.0325038768351078,
0.009126059710979462,
-0.04784752056002617,
0.0014923503622412682,
-0.038023691624403,
0.016962090507149696,
0.022148502990603447,
-0.031234029680490494,
-0.002324405824765563,
0.011097492650151253,
0.014138339087367058,
-0.020428292453289032,
0.027362173423171043,
-0.016025513410568237,
-0.08196230977773666,
-0.04420109838247299,
0.014522201381623745,
-0.04729221388697624,
0.03668680042028427,
-0.00034938324824906886,
-0.01781582646071911,
0.02855135314166546,
-0.04866192862391472,
0.02532733604311943,
-0.013169344514608383,
0.0324980802834034,
-0.01697639375925064,
0.061591438949108124,
-0.01596597023308277,
0.0036623282358050346,
0.011007610708475113,
0.004366531036794186,
0.0970463752746582,
0.0459560789167881,
-0.0015368962194770575,
-0.07802306115627289,
0.018960025161504745,
0.008142449893057346,
0.028774848207831383,
-0.05246707797050476,
0.038222189992666245,
0.04761405661702156,
0.03521386533975601,
0.018450642004609108,
0.036659110337495804,
0.02280966006219387,
0.02856791950762272,
0.03769788146018982,
-0.04750152304768562,
-0.06070387735962868,
-0.01170351356267929,
0.031624648720026016,
-0.0029428740963339806,
-0.012124789878726006,
-0.04789397865533829,
-0.01999920979142189,
-0.03612174466252327,
-0.0141151063144207,
0.0014021380338817835,
0.01603170856833458,
0.03524290397763252,
0.025244958698749542,
0.012614418752491474,
0.015761272981762886,
-0.00232992647215724,
0.006672975141555071,
-0.06782753020524979,
0.022772973403334618,
0.03439567610621452,
0.0017469582380726933,
0.008978213183581829,
0.010876365937292576,
0.012366157956421375,
-0.026819342747330666,
-0.0011514890938997269,
0.014806495979428291,
-0.04504000395536423,
0.0029544015415012836,
-0.013567270711064339,
0.05348693206906319,
-0.03721696510910988,
0.014834013767540455,
-0.027738599106669426,
0.001793489558622241,
-0.02100706845521927,
0.005445006303489208,
-0.04431483522057533,
-0.015963919460773468,
0.037910256534814835,
-0.025641977787017822,
-0.016690533608198166,
-0.008470551110804081,
-0.0032406290993094444,
-0.00576598197221756,
0.051421236246824265,
-0.04404788836836815,
0.003656089771538973,
0.0037061867769807577,
-0.021802082657814026,
-0.0031529490370303392,
0.018934287130832672,
-0.018438175320625305,
-0.03613990917801857,
0.009218733757734299,
-0.03485843166708946,
-0.025908811017870903,
0.048947520554065704,
-0.01468744594603777,
0.027316726744174957,
0.02928190678358078,
-0.026165444403886795,
0.031220033764839172,
-0.03534082695841789,
0.020433392375707626,
-0.020751003175973892,
-0.03805597126483917,
-0.016147013753652573,
-0.005015940871089697,
0.0345032699406147,
0.02347835898399353,
0.010016599670052528,
-0.017335159704089165,
-0.0053416658192873,
0.002399210352450609,
-0.012653783895075321,
-0.002113959053531289,
-0.014364274218678474,
0.012685080990195274,
-0.03214295580983162,
-0.0017664629267528653,
-0.028307391330599785,
0.01808910444378853,
-0.0009469517390243709,
-0.03912734240293503,
0.0005582625162787735,
0.023968063294887543,
-0.011849296279251575,
-0.009365705773234367,
0.05545363202691078,
-0.05039700120687485,
0.012571736238896847,
0.0006055216654203832,
0.034722648561000824,
-0.0253689456731081,
-0.0372718870639801,
-0.010528963059186935,
-0.012118249200284481,
0.020118148997426033,
0.016057824715971947,
-0.020815663039684296,
0.004303673282265663,
-0.00031807602499611676,
0.06493277847766876,
-0.0067961690947413445,
-0.04697764292359352,
-0.052869632840156555,
0.02205698937177658,
0.00539811747148633,
-0.020130716264247894,
-0.006524180062115192,
0.004543767776340246,
0.027110505849123,
-0.005094278138130903,
0.038051456212997437,
0.04734037443995476,
-0.012862562201917171,
-0.008472239598631859,
0.016480151563882828,
0.006747126113623381,
0.05417649820446968,
-0.019827082753181458,
-0.03328748419880867,
0.05606667324900627,
-0.039113081991672516,
-0.01994204893708229,
0.0361909419298172,
-0.003188912756741047,
0.049429748207330704,
0.03920666128396988,
-0.008097155019640923,
-0.045951224863529205,
0.028660081326961517,
0.006356589961796999,
0.03159571811556816,
0.0389409177005291,
0.0003976323059760034,
-0.035339437425136566,
0.016777699813246727,
-0.012007179670035839,
0.013053042814135551,
-0.01878863200545311,
0.008297926746308804,
0.03693925589323044,
0.05492740124464035,
0.012824596837162971,
0.012284483760595322,
0.015480759553611279,
0.05147562548518181,
0.028444694355130196,
-0.0058316499926149845,
0.06358051300048828,
0.056253962218761444,
-0.03571177273988724,
0.04650101065635681,
0.023009376600384712,
0.004828011151403189,
-0.06870865076780319,
-0.0081091383472085,
0.026616962626576424,
-0.02678055129945278,
0.03383401408791542,
-0.040280867367982864,
0.02394673228263855,
0.037437696009874344,
-0.030013104900717735,
0.03550577908754349,
-0.013373059220612049,
-0.013990670442581177,
-0.019010204821825027,
0.008223862387239933,
-0.05277739837765694,
0.0858251228928566,
0.013469778001308441,
0.008534609340131283,
0.018353544175624847,
0.011327202431857586,
-0.0033063467126339674,
-0.019989533349871635,
-0.02629481442272663,
0.02664867416024208,
-0.004029400181025267,
-0.00048617663560435176,
0.10274232178926468,
-0.01622920110821724,
-0.039097193628549576,
0.03639920800924301,
-0.01925402693450451,
-0.015543223358690739,
-0.02568472921848297,
0.003745027119293809,
-0.0023700715973973274,
0.05897632613778114,
0.036525461822748184,
-0.018272027373313904,
-0.018817372620105743,
0.027222272008657455,
0.025479206815361977,
0.02327684871852398,
0.03809871897101402,
-0.011179409921169281,
0.01203929539769888,
-0.03171763941645622,
-0.031125640496611595,
0.014833499677479267,
0.022816088050603867,
-0.031594160944223404,
-0.01138489879667759,
0.006639613304287195,
0.03318070247769356,
-0.022448062896728516,
0.02287895604968071,
-0.049578942358493805,
-0.007910726591944695,
0.006446584593504667,
0.019482338801026344,
0.002095275791361928,
0.02970532700419426,
-0.025345714762806892,
-0.03328455239534378,
0.022820264101028442,
0.006666283588856459,
0.013471919111907482,
-0.042774152010679245,
-0.017047712579369545,
0.020367683842778206,
-0.006903218105435371,
-0.009367218241095543,
-0.018955379724502563,
-0.049671005457639694,
0.03402023762464523,
-0.028042368590831757,
0.04214491695165634,
-0.03330836445093155,
-0.034772176295518875,
-0.03412533551454544,
-0.04209847375750542,
0.04883024841547012,
-0.011626157909631729,
0.04388045892119408,
-0.03179958462715149,
-0.01169715728610754,
0.012024233117699623,
0.003642172319814563,
0.037493448704481125,
0.003173524048179388,
-0.00011807412374764681,
0.022677814587950706,
0.037015434354543686,
0.039989739656448364,
0.02365848794579506,
-0.002400787780061364,
-0.02799551747739315,
-0.003966341260820627,
-0.034342046827077866,
0.00859676580876112,
-0.010348721407353878,
0.0004174507048446685,
0.04716556891798973,
0.00308495806530118,
-0.013136360794305801,
-0.012465025298297405,
0.01573275588452816,
0.09226864576339722,
-0.022010017186403275,
0.0012616799212992191,
0.05385100468993187,
-0.02119647152721882,
0.020067306235432625,
-0.008078139275312424,
-0.025189140811562538,
-0.0391777865588665,
0.023452484980225563,
0.01200723648071289,
-0.02873200736939907,
0.014772855676710606,
0.03008393757045269,
0.006922353990375996,
-0.04444703087210655,
-0.0020818125922232866,
0.027336573228240013,
-0.06348924338817596,
-0.0007705552852712572,
0.07023000717163086,
0.016109982505440712,
0.015040348283946514,
0.0033231417182832956,
0.03682234510779381,
0.0010823238408192992,
-0.011269115842878819,
-0.004018452949821949,
0.053844477981328964,
0.05323726311326027,
0.0014853492612019181,
0.021497635170817375,
0.013131439685821533,
-0.04743964970111847,
0.06109834089875221,
-0.0005748150288127363,
0.013983291573822498,
-0.0366051159799099,
-0.011611642315983772,
0.030065730214118958,
-0.01927349902689457,
0.01517353393137455,
-0.01896301470696926,
0.0014589880593121052,
0.07878292351961136,
-0.032845016568899155,
-0.015146508812904358,
-0.008975079283118248,
-0.00042273133294656873,
-0.02154247649013996,
-0.03623998165130615,
0.02459833025932312,
0.06789804250001907,
-0.02494472824037075,
0.020704224705696106,
-0.011496581137180328,
-0.00815771147608757,
0.002528185723349452,
-0.03237517178058624,
0.03158542886376381,
-0.0004709501226898283,
0.008328556083142757,
0.0035410255659371614,
-0.04984823241829872,
-0.03005080297589302,
-0.03477620333433151,
0.027009980753064156,
0.057466842234134674,
0.01092338003218174,
-0.007842160761356354,
-0.03705880418419838,
-0.021408643573522568,
0.05095865577459335,
-0.03835451975464821,
-0.004197477363049984,
-0.025478681549429893,
0.030051149427890778,
-0.02058701030910015,
0.0184639785438776
] |
<p>A circuit, has current $A$ flowing at a certain $V$.</p>
<p>When there is a change in magnetic-flux, based on Faraday's law of induction & Lenz's law, we know that there is change in <strong>Potential Difference</strong> now, aside from the source $V$ now we have a induced $-V$ due to the change in magnetic-flux, and it opposes the current, why would it? I understood from lenz's law that it will, but not great detail as to why.</p>
<p>Another thing, if the power-source can be increased, $V$ can potentially increase to oppose the $-V$? And maintain $A$ at the same value it was?</p> | 2,901 | [
-0.042063746601343155,
0.01588861271739006,
-0.009966294281184673,
-0.004577061627060175,
0.04910307377576828,
0.002015110570937395,
-0.027139650657773018,
0.005403699818998575,
0.028322668746113777,
-0.04440722241997719,
0.03874482214450836,
0.019950928166508675,
0.06826210767030716,
-0.0012111812829971313,
0.02336066961288452,
-0.0012750213500112295,
0.009774832986295223,
-0.004152198322117329,
-0.006101155187934637,
-0.014471008442342281,
-0.02555087022483349,
0.04660319909453392,
0.02928519807755947,
0.009410243481397629,
-0.0542195700109005,
0.02704181894659996,
0.02664904110133648,
0.012062839232385159,
-0.010778297670185566,
0.056538961827754974,
0.012423567473888397,
-0.030020330101251602,
-0.015373536385595798,
0.03727074712514877,
0.012157582677900791,
-0.0013193341437727213,
-0.022697092965245247,
-0.05880456045269966,
-0.005036379676312208,
0.05523640289902687,
0.006459323689341545,
0.004040508531033993,
0.011188894510269165,
0.04876232519745827,
-0.02207142300903797,
-0.009941483847796917,
-0.006529789883643389,
0.00047276783152483404,
0.028266670182347298,
-0.04630538448691368,
0.004181802272796631,
-0.044698283076286316,
0.04021542891860008,
0.034086599946022034,
-0.022279612720012665,
-0.018638286739587784,
0.08121328055858612,
0.05861324444413185,
-0.0026495836209505796,
-0.006378730293363333,
-0.009074507281184196,
-0.02841833047568798,
-0.008119901642203331,
-0.01214148011058569,
-0.026560353115200996,
0.04857390746474266,
0.001505265710875392,
0.0027580340392887592,
0.031798288226127625,
-0.017181837931275368,
0.008446786552667618,
0.006020703352987766,
-0.035863157361745834,
-0.0234259944409132,
-0.004594293888658285,
-0.0365317240357399,
0.02577940933406353,
0.014245348982512951,
0.009135148487985134,
0.02472584880888462,
-0.026379162445664406,
0.02018425054848194,
0.017189867794513702,
0.05712437257170677,
0.00896231085062027,
0.0012984140776097775,
0.037937916815280914,
-0.0460784025490284,
0.015812277793884277,
0.01975059323012829,
-0.014815599657595158,
0.005879022181034088,
0.0386936292052269,
-0.0546763613820076,
0.0029818371403962374,
-0.00010996877972502261,
-0.013786331750452518,
0.043763455003499985,
0.0350610688328743,
-0.0115598663687706,
0.030240153893828392,
0.009486869908869267,
0.016767263412475586,
0.03579210862517357,
0.016665516421198845,
-0.03858500346541405,
-0.020480694249272346,
0.03829414024949074,
-0.013335146941244602,
-0.022921249270439148,
-0.019048960879445076,
0.03455282747745514,
0.028757352381944656,
-0.009040921926498413,
0.016979657113552094,
-0.03267718851566315,
0.02455276995897293,
-0.045675426721572876,
0.023755859583616257,
0.013242218643426895,
0.04529151692986488,
-0.03744909539818764,
0.03334358334541321,
-0.033850185573101044,
-0.04075891524553299,
-0.01599125936627388,
0.01445846725255251,
0.013842458836734295,
-0.013904063031077385,
0.03175764158368111,
-0.0000570172633160837,
-0.03399617597460747,
-0.008986459113657475,
0.0252519678324461,
0.04046371951699257,
0.007738342974334955,
-0.08757872134447098,
-0.06841185688972473,
0.021259518340229988,
-0.04592564329504967,
0.006873736623674631,
-0.06623529642820358,
-0.026790348812937737,
0.04620055854320526,
0.08312690258026123,
-0.012542957440018654,
-0.02962641604244709,
0.02354322373867035,
0.03125258907675743,
0.008989911526441574,
-0.01697024330496788,
-0.0031272643245756626,
-0.009976677596569061,
-0.03703601285815239,
-0.005525066517293453,
-0.06272946298122406,
0.051440417766571045,
0.01788957417011261,
-0.007881599478423595,
-0.029302578419446945,
0.04785224795341492,
-0.04099129140377045,
-0.0033413798082619905,
0.001572442939504981,
-0.024399399757385254,
-0.0195679422467947,
0.10042498260736465,
0.013514550402760506,
-0.005033052060753107,
0.05570443347096443,
0.010837828740477562,
0.04519613832235336,
0.007434862200170755,
0.012382359243929386,
0.05273202434182167,
-0.042970530688762665,
-0.025790341198444366,
-0.02425306849181652,
0.04290231317281723,
-0.026765326038002968,
-0.008617542684078217,
-0.037809956818819046,
-0.006276017986238003,
0.028968334197998047,
-0.015154091641306877,
0.05748225003480911,
-0.034272294491529465,
0.008157165721058846,
-0.0011638065334409475,
-0.04085226356983185,
-0.0009096133871935308,
-0.03733208030462265,
0.06221448630094528,
0.0008533665095455945,
-0.044550392776727676,
0.0488089993596077,
0.009799287654459476,
0.010164931416511536,
-0.019539855420589447,
0.00779773248359561,
0.024599170312285423,
0.020703963935375214,
-0.0212046280503273,
-0.012174994684755802,
0.005793021060526371,
0.001143545494414866,
0.027544058859348297,
0.029244665056467056,
0.06090329959988594,
-0.021173063665628433,
-0.04249772056937218,
0.027642980217933655,
-0.04624838009476662,
0.014838740229606628,
0.03553873673081398,
-0.011067939922213554,
-0.02284182421863079,
-0.0009618676849640906,
-0.006231897044926882,
0.026213090866804123,
-0.012147863395512104,
0.08395044505596161,
0.0805920735001564,
0.0006129692774266005,
-0.0034954065922647715,
0.05674578621983528,
-0.00749821774661541,
-0.028442028909921646,
-0.04756902530789375,
-0.028914237394928932,
-0.04657609388232231,
0.019531408324837685,
0.03860311582684517,
0.02080485038459301,
-0.05640876665711403,
0.04089011624455452,
-0.0026527782902121544,
0.00011867517605423927,
0.014140059240162373,
0.0021391010377556086,
-0.03822854906320572,
-0.031125864014029503,
0.03317972645163536,
0.04057362675666809,
-0.009694132022559643,
-0.012548599392175674,
0.017411474138498306,
0.03460637852549553,
-0.013762137852609158,
0.0042445724830031395,
-0.014396622776985168,
0.04294642060995102,
0.003526364453136921,
0.013885924592614174,
0.030424263328313828,
-0.01569691300392151,
-0.007074291352182627,
-0.042554210871458054,
0.052506379783153534,
-0.0012749029556289315,
-0.016065986827015877,
0.0057061901316046715,
-0.03555583581328392,
-0.03605774790048599,
0.014712712727487087,
-0.03737546503543854,
-0.016988100484013557,
0.005362842231988907,
0.016467949375510216,
-0.05655629560351372,
0.016444459557533264,
-0.012400198727846146,
0.03849649429321289,
-0.04549563676118851,
-0.017556041479110718,
-0.023355768993496895,
0.02407905086874962,
0.043038684874773026,
-0.020950617268681526,
-0.012925183400511742,
-0.038949575275182724,
-0.02383701130747795,
-0.008558491244912148,
0.025922026485204697,
-0.02192041464149952,
0.025141358375549316,
0.0029521689284592867,
-0.013308067806065083,
0.06182453781366348,
0.025742728263139725,
-0.009730818681418896,
0.02951359562575817,
0.025022076442837715,
-0.07492434233427048,
0.019744226709008217,
-0.009076503105461597,
0.028019467368721962,
0.007710477337241173,
-0.02559894323348999,
0.046587347984313965,
0.036943063139915466,
-0.04084298014640808,
0.01047115121036768,
-0.06389325857162476,
-0.019247079268097878,
0.026730963960289955,
-0.0496092215180397,
0.033212799578905106,
-0.0272877998650074,
0.042173661291599274,
0.011858722195029259,
-0.06735746562480927,
-0.00975744891911745,
-0.05786437913775444,
-0.010467900894582272,
-0.016186898574233055,
-0.006659497041255236,
0.051764968782663345,
-0.0036693732254207134,
-0.030665844678878784,
0.07765639573335648,
0.0594179630279541,
-0.03921908885240555,
-0.02774643711745739,
-0.034095972776412964,
-0.01667654700577259,
-0.04370184615254402,
-0.01523337047547102,
0.07875266671180725,
-0.006896335165947676,
0.05592138320207596,
0.044376518577337265,
0.041085969656705856,
0.007122080307453871,
0.009007615968585014,
-0.008631131611764431,
0.0091922702267766,
-0.011991116218268871,
0.011647973209619522,
0.05983826890587807,
-0.004100376740098,
-0.0003567072853911668,
0.009000403806567192,
0.008767571300268173,
0.05002480745315552,
-0.0008854852057993412,
0.02948874607682228,
0.04597219452261925,
-0.04948103055357933,
0.02834540605545044,
-0.062405046075582504,
0.06927546113729477,
0.0013062636135146022,
0.020776182413101196,
-0.02289995364844799,
0.028020311146974564,
0.030331378802657127,
-0.10628717392683029,
-0.013143591582775116,
0.03234093636274338,
0.009186780080199242,
-0.03231189399957657,
-0.04508035257458687,
-0.016356216743588448,
-0.013376432470977306,
0.018558284267783165,
-0.0011400239309296012,
-0.016499314457178116,
0.04373277723789215,
0.017634278163313866,
-0.005312258843332529,
0.021002762019634247,
-0.007856915704905987,
-0.010376296937465668,
-0.024296632036566734,
-0.011692711152136326,
0.009814262390136719,
0.027548111975193024,
0.0076556759886443615,
0.03352334350347519,
0.010354459285736084,
0.020109886303544044,
-0.01823257841169834,
-0.01197995524853468,
-0.08955179899930954,
0.018300969153642654,
-0.04337413236498833,
0.002504332922399044,
-0.027128342539072037,
0.01726619526743889,
-0.03616727516055107,
-0.0426439493894577,
0.01601194031536579,
-0.03672349452972412,
-0.0034540854394435883,
-0.04265374317765236,
-0.016067029908299446,
-0.029080698266625404,
-0.0129435695707798,
-0.06596049666404724,
0.01639079488813877,
0.03676316514611244,
-0.07044099271297455,
0.019136719405651093,
-0.0036662607453763485,
-0.025054439902305603,
0.01153665129095316,
-0.05540664866566658,
-0.008455980569124222,
0.03889622166752815,
0.022438036277890205,
0.06435555219650269,
-0.005090055055916309,
0.01673228293657303,
0.0003926244389731437,
-0.005868096835911274,
0.04040618613362312,
0.03706923872232437,
0.0007437223684974015,
-0.028305789455771446,
-0.04933412745594978,
-0.03494616597890854,
-0.016637640073895454,
0.034311555325984955,
-0.011092977598309517,
0.05526875704526901,
0.024511903524398804,
0.012392270378768444,
-0.028120238333940506,
0.03731989115476608,
0.043935626745224,
0.007744047325104475,
0.006620276719331741,
-0.029538685455918312,
0.000430099869845435,
-0.030594024807214737,
-0.033726856112480164,
0.006731615401804447,
-0.023791249841451645,
-0.01883436180651188,
0.0016356197884306312,
0.02592567913234234,
0.036995671689510345,
-0.0034346426837146282,
0.023305030539631844,
0.020771123468875885,
0.02096717618405819,
0.03557631000876427,
0.025358542799949646,
0.0073395357467234135,
-0.00143085524905473,
0.046739306300878525,
-0.038914553821086884,
-0.008776452392339706,
-0.12156858295202255,
-0.04064089432358742,
0.05548166111111641,
0.05753060057759285,
0.0008847956196404994,
-0.002435676520690322,
-0.037588559091091156,
-0.02028357982635498,
0.013040177524089813,
-0.037196047604084015,
0.026917174458503723,
-0.03188606724143028,
-0.023752134293317795,
-0.04772445186972618,
-0.0702926367521286,
-0.01845964416861534,
0.010137662291526794,
0.009564828127622604,
0.040324144065380096,
-0.024426642805337906,
0.006831172853708267,
0.014407949522137642,
-0.0026599254924803972,
0.028613809496164322,
0.04249172285199165,
-0.022854475304484367,
-0.029907742515206337,
-0.01224125549197197,
0.063631072640419,
-0.010231812484562397,
-0.06585066765546799,
0.0037866472266614437,
0.023688217625021935,
-0.02654036320745945,
0.03584742546081543,
-0.012042849324643612,
-0.017457399517297745,
0.014875363558530807,
-0.005659671500325203,
-0.0001740705774864182,
-0.022378982976078987,
-0.009587734006345272,
0.05933623015880585,
0.016220511868596077,
-0.01417614333331585,
0.05131785571575165,
0.003434903919696808,
-0.03228510916233063,
-0.027666931971907616,
0.005426931194961071,
0.030665051192045212,
-0.01845500059425831,
-0.026586279273033142,
-0.007026262581348419,
0.0030859417747706175,
-0.03609767183661461,
0.07904443889856339,
0.0026139705441892147,
-0.00875023566186428,
-0.011432504281401634,
0.006487106438726187,
-0.007593255490064621,
0.00961363036185503,
-0.004695760551840067,
-0.0016724640736356378,
-0.011336712166666985,
0.03832739219069481,
0.023275915533304214,
-0.025216152891516685,
0.03232463076710701,
-0.038377176970243454,
0.024442657828330994,
0.04001239687204361,
-0.020235249772667885,
-0.004600849002599716,
-0.017641538754105568,
-0.04423275962471962,
0.015800023451447487,
-0.035209137946367264,
0.04041349142789841,
-0.007234911900013685,
0.0017323954962193966,
-0.010072178207337856,
-0.04074930399656296,
-0.047498732805252075,
0.05163699761033058,
-0.042700279504060745,
0.0031891765538603067,
-0.0525638572871685,
0.05497109144926071,
0.010531973093748093,
-0.009097822941839695,
-0.06542397290468216,
-0.049747418612241745,
0.01545879989862442,
0.012255571782588959,
0.012336964718997478,
0.014078997075557709,
-0.05906146019697189,
0.013999000191688538,
-0.03105233609676361,
0.0020993344951421022,
0.005143153481185436,
-0.02970750257372856,
-0.010160171426832676,
0.01441115327179432,
0.02191544882953167,
0.037546996027231216,
-0.030174773186445236,
-0.00954508502036333,
0.003259719582274556,
-0.05177788436412811,
0.00014034932246431708,
-0.017373230308294296,
0.024376068264245987,
-0.026819784194231033,
-0.009895683266222477,
0.046150486916303635,
-0.01817837357521057,
0.04855289310216904,
-0.01915990374982357,
-0.04597471281886101,
0.021834533661603928,
-0.020414428785443306,
-0.009305599145591259,
-0.01845303550362587,
0.001336186658591032,
0.00929377693682909,
0.041033387184143066,
0.029064323753118515,
-0.024555351585149765,
-0.051269304007291794,
-0.008684090338647366,
0.0215789582580328,
0.014071742072701454,
-0.009207936935126781,
-0.007677750196307898,
0.06101193279027939,
-0.016786260530352592,
-0.002029936760663986,
0.023466015234589577,
0.035565171390771866,
0.036429181694984436,
-0.027348659932613373,
0.012765510007739067,
0.001084961462765932,
-0.017418617382645607,
-0.053288619965314865,
-0.028070123866200447,
-0.02226843126118183,
0.015982411801815033,
0.03025803342461586,
-0.007926060818135738,
0.05156287923455238,
-0.0034148909617215395,
-0.014058577828109264,
-0.008576933294534683,
-0.027296343818306923,
-0.00235144910402596,
0.017679039388895035,
-0.03846285864710808,
0.020315956324338913,
-0.011559359729290009,
0.029965275898575783,
0.0025547349359840155,
0.023984011262655258,
-0.006736024748533964,
-0.025823542848229408,
0.03347800672054291,
0.043546706438064575,
0.043681420385837555,
0.029231088235974312,
-0.0574481338262558,
0.010402582585811615,
-0.03843295946717262,
0.03392660990357399,
-0.0007403410854749382,
0.0037589084822684526,
0.0522618368268013,
-0.012267849408090115,
0.002793756779283285,
-0.09434052556753159,
-0.01459888182580471,
-0.04511716216802597,
-0.02544996328651905,
-0.015788698568940163,
0.037288907915353775,
0.03199910372495651,
0.0005417597712948918,
0.008883262984454632,
-0.02136431634426117,
0.016497500240802765,
-0.03913683444261551,
-0.05571708828210831,
-0.04299935698509216,
-0.005852357484400272,
0.008975998498499393,
0.03909103944897652,
-0.0018168211681768298,
-0.010241496376693249,
0.012833341024816036,
-0.05177780240774155,
0.04223381355404854,
0.020222419872879982,
0.015977881848812103,
-0.015709560364484787,
0.08184268325567245,
-0.024044286459684372,
0.05544453486800194,
-0.02182415872812271,
-0.01308812852948904,
0.1034158319234848,
0.055526770651340485,
0.030232716351747513,
-0.05352112278342247,
0.0139974569901824,
-0.015464916825294495,
0.01825990341603756,
-0.02840566635131836,
0.03977099806070328,
-0.0033494795206934214,
0.02348947525024414,
-0.017905788496136665,
0.02507055178284645,
-0.0019446229562163353,
0.035447023808956146,
0.047702353447675705,
-0.04308652505278587,
-0.017654839903116226,
0.02263302356004715,
0.03332928568124771,
-0.0038631705101579428,
0.021852439269423485,
-0.023347917944192886,
0.011459453031420708,
-0.036244165152311325,
-0.022038664668798447,
-0.012334831058979034,
-0.00255072140134871,
0.030930669978260994,
0.018998606130480766,
-0.021426917985081673,
0.0572659969329834,
0.008658531121909618,
-0.013372344896197319,
-0.0766177549958229,
0.009257973171770573,
-0.0026797668542712927,
0.028145426884293556,
0.017369423061609268,
0.018247565254569054,
0.019170129671692848,
0.0015265134861692786,
0.008107917383313179,
0.02423999272286892,
-0.023667041212320328,
0.009071217849850655,
-0.053700368851423264,
0.0046236817725002766,
0.04165720194578171,
0.04150770232081413,
0.023078130558133125,
0.04726378992199898,
0.018756108358502388,
-0.002703029429540038,
-0.06948482245206833,
-0.010746086947619915,
-0.005959066562354565,
-0.008834226056933403,
-0.04478522017598152,
-0.01743066869676113,
0.030787469819188118,
0.005929245613515377,
-0.006147137377411127,
-0.008531896397471428,
0.005812524817883968,
0.01174958236515522,
0.027163749560713768,
0.041790299117565155,
-0.0007282589795067906,
-0.016780121251940727,
0.0010351692326366901,
0.029940033331513405,
-0.008393747732043266,
-0.011528147384524345,
0.007319626398384571,
0.0009449500357732177,
-0.0033466899767518044,
-0.005491381045430899,
0.005959227215498686,
0.0024882731959223747,
-0.07135653495788574,
0.04623943939805031,
-0.008990908041596413,
0.007533245254307985,
-0.023905940353870392,
0.02907380275428295,
0.01398052740842104,
0.010515561327338219,
-0.024046845734119415,
-0.020205028355121613,
0.014659691601991653,
0.06252218037843704,
0.025056371465325356,
-0.029513195157051086,
-0.03769158944487572,
0.0014226149069145322,
-0.0722697377204895,
-0.0019560069777071476,
0.03422975912690163,
0.06022791564464569,
-0.0010986289707943797,
-0.0010539456270635128,
0.0006570785189978778,
0.015868928283452988,
-0.01553570106625557,
-0.003961976617574692,
0.010348479263484478,
-0.02493247576057911,
0.0029695192351937294,
-0.017187947407364845,
-0.006131031550467014,
0.008988378569483757,
-0.003466209163889289,
0.034066420048475266,
-0.011152035556733608,
0.06424202769994736,
0.013893763534724712,
0.007346176542341709,
-0.01769915223121643,
-0.003747473703697324,
0.012283490970730782,
-0.018908606842160225,
-0.0075132413767278194,
-0.03132801502943039,
-0.003740479703992605,
0.0031670164316892624,
0.010207588784396648,
0.014874718151986599,
0.02773258648812771,
-0.01884995587170124,
-0.022213062271475792,
0.00139602180570364,
0.043004829436540604,
0.006871290970593691,
-0.031070582568645477,
0.013029132969677448,
-0.02737942337989807,
0.03497707098722458,
-0.025282753631472588,
-0.06786593049764633,
0.0600765235722065,
-0.03275619074702263,
-0.021577494218945503,
0.039567865431308746,
-0.017352716997265816,
0.03297485411167145,
-0.007287216372787952,
0.015236493200063705,
-0.00203733891248703,
0.017347177490592003,
0.017971761524677277,
0.02845093607902527,
0.0022712245117872953,
-0.021699698641896248,
-0.008048063144087791,
-0.013034782372415066,
-0.006707075517624617,
0.020729856565594673,
0.019909385591745377,
-0.009561770595610142,
0.07510055601596832,
-0.018653053790330887,
-0.03628319874405861,
-0.004007269628345966,
0.03202022984623909,
-0.007250410038977861,
0.034030403941869736,
0.013333834707736969,
0.020328981801867485,
0.009549996815621853,
-0.006419321987777948,
-0.0022400026209652424,
-0.006536415778100491,
-0.007945066317915916,
-0.08483090996742249,
0.0027967148926109076,
-0.0018073591636493802,
-0.011802693828940392,
0.007562316954135895,
-0.07978099584579468,
0.011764961294829845,
0.01231295894831419,
-0.07198261469602585,
-0.026846930384635925,
-0.03255423530936241,
0.0039072465151548386,
-0.0034059579484164715,
-0.049954287707805634,
0.0007149339071474969,
0.024138381704688072,
0.011282960884273052,
0.011590026319026947,
0.015824126079678535,
-0.029398294165730476,
-0.0011817185441032052,
-0.033333878964185715,
-0.007607439532876015,
0.0018203593790531158,
0.002021219814196229,
-0.0237065888941288,
0.05763707682490349,
-0.002551817335188389,
-0.024382198229432106,
0.03436315059661865,
-0.036331940442323685,
-0.04708017408847809,
0.005577291827648878,
0.03522574156522751,
0.011501367203891277,
0.03814349323511124,
-0.008622459135949612,
0.020065955817699432,
0.00029693415854126215,
0.004411076661199331,
0.004847581032663584,
0.039019253104925156,
0.017863694578409195,
-0.0008065678994171321,
0.024591805413365364,
-0.02496226876974106,
0.02274916134774685,
0.012569883838295937,
-0.03351564705371857,
-0.027272887527942657,
-0.027230514213442802,
0.024988602846860886,
0.028614269569516182,
-0.03989143669605255,
-0.0009558257879689336,
-0.03695892170071602,
-0.07030222564935684,
0.055625323206186295,
0.009391618892550468,
0.03292519599199295,
0.00025149344583041966,
-0.0006106336950324476,
-0.056084901094436646,
0.03207920119166374,
0.004020205233246088,
-0.013928903266787529,
-0.05629119277000427,
0.0062079764902591705,
0.010402006097137928,
-0.02211676351726055,
-0.011875397525727749,
-0.022944169119000435,
-0.05387413129210472,
0.0349259078502655,
0.017520492896437645,
0.0036972975358366966,
-0.03175369277596474,
-0.07551170885562897,
-0.016707882285118103,
-0.017710577696561813,
0.04723183810710907,
0.006043989676982164,
-0.0077593144960701466,
-0.004758444149047136,
-0.027183573693037033,
0.02070118859410286,
0.017835458740592003,
0.03389908745884895,
-0.0059105949476361275,
-0.029595553874969482,
0.06735198199748993,
-0.020882494747638702,
0.020606432110071182,
-0.025674346834421158,
0.029992002993822098,
0.021824313327670097,
0.03511098772287369,
0.05303347483277321,
-0.00048618356231600046,
-0.0019368879729881883,
0.02876110188663006,
-0.006510844454169273,
0.020373117178678513,
-0.00505586713552475,
-0.03338996693491936,
-0.016457485035061836,
0.008855779655277729,
0.007125802803784609,
-0.002151783090084791,
0.06790129840373993,
0.007209218107163906,
0.03622918576002121,
-0.03685629367828369,
0.02831650897860527,
-0.041534751653671265,
0.02120482549071312,
-0.015295181423425674,
0.015106016770005226,
-0.007109628524631262,
-0.0248034056276083,
0.057842232286930084,
-0.01575551927089691,
-0.05600091069936752,
0.049795184284448624,
-0.030115224421024323,
0.0020120306871831417,
0.06146271899342537,
-0.006844735238701105,
-0.008109831251204014,
0.0009837695397436619,
0.017347831279039383,
-0.015123365446925163,
0.02225596457719803,
-0.0002856435894500464,
0.04963413253426552,
-0.0022786431945860386,
-0.025494346395134926,
-0.017294174060225487,
0.05402819812297821,
0.019660569727420807,
0.008868333883583546,
0.0266075748950243,
0.028799889609217644,
-0.022137077525258064,
-0.014748264104127884,
0.015838555991649628,
0.015356508083641529,
0.01675811968743801,
0.0036854781210422516,
-0.004623494576662779,
0.07061226665973663,
-0.030283069238066673,
0.030822066590189934,
-0.014570232480764389,
0.012554288841784,
-0.027064228430390358,
-0.01183781586587429,
-0.0012610049452632666,
0.05281533673405647,
-0.021959345787763596,
-0.05597192421555519,
0.0027478046249598265,
-0.0067663779482245445,
0.012000336311757565,
-0.04624257609248161,
0.012786125764250755,
-0.004086834844201803,
-0.03204208239912987,
-0.03875257447361946,
-0.013509654439985752,
-0.02156771533191204,
-0.034562140703201294,
0.04216625913977623,
0.05674465373158455,
0.05380663648247719,
0.01521286740899086,
-0.04571647569537163,
-0.0320994108915329,
0.04494578018784523,
-0.031097527593374252,
-0.018397124484181404,
-0.0021664851810783148,
0.005023612175136805,
-0.007193622644990683,
-0.004336497746407986
] |
<p>I've known for a long time that if you heat a magnet, there is a point it loses its magnetism (the <a href="https://en.wikipedia.org/wiki/Curie_temperature" rel="nofollow">Curie temperature</a>). It isn't clear to me if this applies to induced magnetism like iron sticking to a magnet.</p>
<p>Will molten iron behave like a ferrofluid and be attracted to a magnet or will it just have a very weak paramagnetic attraction?</p> | 2,902 | [
-0.031567465513944626,
-0.017148764804005623,
-0.0036947547923773527,
-0.03525755554437637,
0.03623030707240105,
0.013365302234888077,
-0.04408903047442436,
-0.01829145848751068,
0.012392111122608185,
-0.05419505015015602,
0.027744775637984276,
0.042547889053821564,
0.04796407371759415,
-0.013268839567899704,
0.036510907113552094,
-0.0019292321521788836,
0.0015547245275229216,
-0.02713111974298954,
0.018754301592707634,
-0.007176739163696766,
-0.005986468400806189,
0.022547898814082146,
0.023826558142900467,
-0.007969976402819157,
-0.028844425454735756,
-0.00043882927275262773,
-0.021907474845647812,
0.005002155900001526,
0.04116811603307724,
0.023843301460146904,
0.0041524870321154594,
-0.030266575515270233,
-0.0013639468234032393,
0.009305424988269806,
0.042365387082099915,
0.008027700707316399,
-0.03696049749851227,
-0.03924453631043434,
-0.02808394841849804,
0.023864414542913437,
-0.049715425819158554,
-0.03179969638586044,
-0.02188826911151409,
0.039129700511693954,
0.025424787774682045,
-0.05234025791287422,
-0.006114703603088856,
-0.030466660857200623,
0.034601472318172455,
-0.047969184815883636,
0.01338438130915165,
-0.0036290897987782955,
0.03254659101366997,
0.023395732045173645,
0.00895020179450512,
-0.04542960971593857,
0.07917216420173645,
0.04521331563591957,
0.005302829667925835,
-0.03440461680293083,
0.00948869064450264,
-0.021698791533708572,
-0.029456576332449913,
-0.03127317875623703,
-0.042557112872600555,
0.032515134662389755,
0.0017764837248250842,
-0.01571049354970455,
0.0321464017033577,
-0.010757758282124996,
-0.0025995103642344475,
0.0020031570456922054,
0.03047277219593525,
0.0023339472245424986,
0.02163960412144661,
-0.011675613932311535,
0.008744371123611927,
0.022319158539175987,
0.02454686537384987,
0.04773218557238579,
-0.012559514492750168,
0.039621081203222275,
0.05348633602261543,
0.04214082285761833,
0.006359065417200327,
0.0006644207169301808,
0.044229768216609955,
-0.014419525861740112,
0.06336692720651627,
0.042390819638967514,
-0.0012564375065267086,
0.025255240499973297,
0.03318607807159424,
-0.0334508903324604,
-0.036928560584783554,
-0.014582046307623386,
-0.019265638664364815,
0.05785109102725983,
-0.0008369701099582016,
-0.03551383689045906,
-0.005231424234807491,
-0.00103386165574193,
0.010139398276805878,
0.0735553577542305,
0.04275991767644882,
-0.0689035952091217,
-0.033460866659879684,
-0.012989330105483532,
-0.029031140729784966,
-0.04728249832987785,
-0.0018585483776405454,
0.0016935518942773342,
-0.00012418333790265024,
-0.051639068871736526,
0.037572626024484634,
0.006618955172598362,
0.0037855706177651882,
-0.03941209614276886,
0.01522109005600214,
0.054307784885168076,
0.03761803358793259,
-0.019102560356259346,
0.016142377629876137,
-0.02808261103928089,
-0.05527377873659134,
0.010609456337988377,
0.03406110033392906,
-0.027520647272467613,
-0.009929945692420006,
0.017274513840675354,
-0.014537316747009754,
-0.03342244774103165,
-0.01723303087055683,
0.004579904954880476,
0.017941556870937347,
0.013516549952328205,
-0.08841496706008911,
-0.023771418258547783,
0.06506507843732834,
-0.04177996143698692,
0.014353270642459393,
-0.07708580046892166,
-0.011581230908632278,
0.05184473469853401,
0.06698235869407654,
-0.004179405979812145,
0.008291265927255154,
-0.05259573832154274,
0.040381450206041336,
-0.018895689398050308,
-0.03246403858065605,
-0.03285546973347664,
0.0042337337508797646,
-0.0578334778547287,
-0.0017622221494093537,
-0.04062776267528534,
0.04516606032848358,
0.03860447183251381,
0.010303287766873837,
-0.038397166877985,
0.028090309351682663,
-0.05988302454352379,
0.019151516258716583,
0.03749676048755646,
0.004891317803412676,
-0.038840778172016144,
0.08611486852169037,
-0.0031701275147497654,
0.04949672520160675,
0.015742382034659386,
-0.011210513301193714,
0.020507652312517166,
0.003341472940519452,
0.05458424612879753,
0.034968290477991104,
-0.032293181866407394,
-0.027208548039197922,
-0.016385303810238838,
0.03963180631399155,
0.04084796831011772,
-0.06332146376371384,
-0.009349907748401165,
-0.018926529213786125,
0.02079802192747593,
-0.009613384492695332,
0.08929212391376495,
0.004920686595141888,
-0.032812442630529404,
-0.010569901205599308,
-0.06140857934951782,
-0.019609514623880386,
-0.0715344101190567,
0.013055313378572464,
-0.008962098509073257,
-0.014946921728551388,
0.044723134487867355,
0.01548587717115879,
0.020893147215247154,
-0.025932475924491882,
-0.051246821880340576,
0.035079799592494965,
0.005557555239647627,
0.023493068292737007,
-0.046692945063114166,
0.01004986185580492,
0.05450898036360741,
0.02397160977125168,
0.019060492515563965,
0.03332158550620079,
-0.06414586305618286,
-0.04543128237128258,
-0.04721780866384506,
0.01698632724583149,
0.009073085151612759,
0.020709948614239693,
-0.04634014889597893,
0.013101532123982906,
-0.010477595962584019,
-0.029517842456698418,
0.009786373004317284,
-0.008891770616173744,
0.07940198481082916,
-0.013753588311374187,
-0.015561171807348728,
0.008814568631350994,
0.028310423716902733,
0.01953633688390255,
0.0068601928651332855,
-0.017206531018018723,
-0.013848714530467987,
-0.04162045940756798,
-0.005552750080823898,
0.05132751539349556,
0.051972366869449615,
-0.051574815064668655,
0.02792578935623169,
-0.003440883941948414,
0.04062187671661377,
-0.015391513705253601,
0.02208041213452816,
0.0020976460073143244,
-0.030931701883673668,
0.03561369702219963,
0.013549578376114368,
0.024551887065172195,
0.02472633309662342,
0.007631190121173859,
0.030771875753998756,
0.052106183022260666,
0.011888479813933372,
-0.01472612377256155,
0.019611695781350136,
-0.012929044663906097,
-0.03248506039381027,
0.005497995298355818,
-0.02086917869746685,
0.025378402322530746,
-0.01266317069530487,
-0.019527342170476913,
-0.015223607420921326,
0.026928560808300972,
0.008784892968833447,
-0.015941280871629715,
-0.024812055751681328,
0.0029202389996498823,
-0.026084627956151962,
0.005266097839921713,
-0.028149396181106567,
0.02469010464847088,
-0.01426859013736248,
-0.019882656633853912,
-0.009038719348609447,
0.03867119550704956,
0.0022217780351638794,
0.03308394178748131,
-0.027983587235212326,
0.009423956274986267,
-0.01789834536612034,
-0.0326995924115181,
-0.051022257655858994,
-0.0036218122113496065,
-0.04922988638281822,
0.02258303016424179,
0.029478570446372032,
-0.0411878302693367,
-0.0010129553265869617,
-0.029354587197303772,
0.03041655197739601,
0.04902062937617302,
0.00180327077396214,
-0.0016972693847492337,
-0.02360186167061329,
-0.008869119919836521,
-0.05992667004466057,
-0.030200691893696785,
0.02697412483394146,
0.013995463959872723,
-0.021447939798235893,
0.027932483702898026,
0.046627458184957504,
-0.01034510787576437,
-0.013469861820340157,
0.014363301917910576,
-0.02077520079910755,
-0.030133096501231194,
0.0005114062805660069,
-0.03705728426575661,
0.042680345475673676,
-0.019675876945257187,
0.043904609978199005,
0.065178781747818,
-0.0741453766822815,
0.002064742613583803,
-0.0544106587767601,
-0.014814795926213264,
0.03400929272174835,
-0.04000925272703171,
0.002389049855992198,
0.0050016832537949085,
-0.033108074218034744,
0.052157338708639145,
0.016573388129472733,
-0.032068442553281784,
-0.00730540556833148,
-0.014931552112102509,
-0.01472464483231306,
-0.042960792779922485,
-0.002819334389641881,
0.030609633773565292,
-0.035807304084300995,
-0.009042092598974705,
-0.001757426536642015,
0.02617226168513298,
0.014164760708808899,
0.046221934258937836,
0.014041822403669357,
0.026485303416848183,
0.0289462897926569,
-0.00047326303320005536,
0.022841986268758774,
0.014177070930600166,
-0.017090266570448875,
0.06402165442705154,
0.025953246280550957,
0.07959640771150589,
0.0623825304210186,
-0.031822554767131805,
0.04411187767982483,
-0.0230905432254076,
0.0055649494752287865,
-0.04643978923559189,
0.0557587631046772,
-0.0036437627859413624,
-0.016732346266508102,
-0.002393328817561269,
0.05166648328304291,
0.05016889423131943,
-0.029252823442220688,
-0.009553847834467888,
0.0467270165681839,
0.006263775285333395,
-0.004290509968996048,
-0.013314209878444672,
0.0055281855165958405,
-0.03824622556567192,
0.02693987637758255,
-0.021210961043834686,
0.03328797221183777,
0.03186680004000664,
-0.0008542599389329553,
0.008694877848029137,
-0.003938635345548391,
-0.001524797989986837,
-0.019306493923068047,
-0.06863240152597427,
0.008073481731116772,
0.02181306481361389,
0.05421053618192673,
0.015089821070432663,
0.018358081579208374,
0.03168337419629097,
0.03646033629775047,
-0.008108635433018208,
0.008886722847819328,
-0.11101240664720535,
0.018351761624217033,
-0.023192673921585083,
-0.0011322417994961143,
0.004015698563307524,
-0.018102917820215225,
0.0006637520855292678,
-0.034783340990543365,
0.036383479833602905,
-0.025087201967835426,
-0.022366724908351898,
-0.03240008279681206,
0.012721065431833267,
-0.029826384037733078,
-0.025286974385380745,
-0.01064803171902895,
0.00896226055920124,
0.02493642084300518,
-0.038894593715667725,
0.021187949925661087,
-0.02181130275130272,
-0.03799469769001007,
0.012825742363929749,
-0.03296086937189102,
-0.0009259959915652871,
0.009171981364488602,
0.035334695130586624,
0.042954444885253906,
0.016918059438467026,
-0.026774123311042786,
-0.0014634066028520465,
0.04552550986409187,
0.014636710286140442,
0.005752310156822205,
-0.008754760026931763,
-0.045314375311136246,
-0.09347973763942719,
-0.03634859248995781,
0.014257569797337055,
0.07108856737613678,
-0.036790523678064346,
0.003853917820379138,
-0.0007806834182702005,
-0.038684748113155365,
-0.024347931146621704,
0.0298055037856102,
0.030512431636452675,
0.050531428307294846,
-0.017291372641921043,
-0.02108946070075035,
-0.019398339092731476,
-0.01971488445997238,
0.01311974786221981,
0.016593672335147858,
0.021211737766861916,
-0.03418907895684242,
-0.021501990035176277,
0.01641980931162834,
-0.012041674926877022,
-0.010904998518526554,
-0.015917275100946426,
0.014485793188214302,
0.03041159361600876,
-0.006044609937816858,
0.011010738089680672,
0.011118995025753975,
0.036166105419397354,
0.03826306760311127,
0.0029498357325792313,
-0.015578771010041237,
-0.07403737306594849,
0.01799093559384346,
0.05902668833732605,
0.040690794587135315,
0.007272821385413408,
-0.012094116769731045,
-0.05426809564232826,
-0.014350245706737041,
0.0380382165312767,
-0.03063964657485485,
0.02698492258787155,
-0.017897561192512512,
-0.0449054017663002,
-0.001446358161047101,
-0.038300372660160065,
-0.02411140687763691,
-0.004398059565573931,
-0.008155918680131435,
0.053872495889663696,
-0.0613446906208992,
-0.03572683036327362,
0.0013511312426999211,
-0.005663831252604723,
0.02113521471619606,
0.011266404762864113,
0.01260494627058506,
0.01812376081943512,
-0.006168005056679249,
0.01669333316385746,
-0.008845317177474499,
-0.1217140257358551,
-0.013209857977926731,
0.0014803839148953557,
-0.027348751202225685,
0.028122102841734886,
-0.011278385296463966,
-0.07405298948287964,
0.032021667808294296,
0.03623158112168312,
-0.01487741805613041,
-0.002921927021816373,
-0.0499093160033226,
0.05725604668259621,
-0.010493891313672066,
-0.019001150503754616,
0.04919474199414253,
0.02135540172457695,
0.006879183929413557,
-0.008404035121202469,
-0.012216806411743164,
0.04646812006831169,
-0.016421379521489143,
0.035570114850997925,
-0.03622150421142578,
0.01678997464478016,
-0.011156094260513783,
0.050646815448999405,
-0.0075704846531152725,
-0.034630611538887024,
-0.00902239978313446,
-0.021492116153240204,
0.003033401444554329,
0.002749234903603792,
0.028589727357029915,
-0.04520879685878754,
-0.007460412569344044,
0.018008243292570114,
-0.027558473870158195,
0.008569353260099888,
0.017148299142718315,
-0.03704799339175224,
0.009772169403731823,
0.001718614948913455,
-0.04857123643159866,
0.009402671828866005,
0.002495790598914027,
-0.022965744137763977,
-0.016171300783753395,
-0.02140113152563572,
0.058557428419589996,
-0.004523038398474455,
0.024400804191827774,
-0.004242352209985256,
-0.041184861212968826,
0.03716558590531349,
-0.0021632264833897352,
0.024601725861430168,
0.04770244285464287,
-0.029810158535838127,
0.04069134593009949,
0.027908219024538994,
0.005049077793955803,
-0.04438875988125801,
-0.07963164895772934,
-0.0012946168426424265,
-0.0112809082493186,
-0.025638656690716743,
0.005055416375398636,
-0.007023542653769255,
-0.028501179069280624,
-0.055853795260190964,
0.02123265340924263,
0.05133465304970741,
-0.033245403319597244,
-0.008556557819247246,
0.045325618237257004,
-0.004345725290477276,
0.07252278178930283,
-0.0009866816690191627,
-0.05101398006081581,
0.005480984691530466,
-0.02435750514268875,
0.004829995334148407,
-0.008459449745714664,
0.062436312437057495,
-0.011127768084406853,
-0.00916242878884077,
0.0034493370912969112,
-0.02506396174430847,
0.01682729832828045,
0.020182829350233078,
-0.015635034069418907,
0.016227619722485542,
0.027493348345160484,
-0.0344163216650486,
-0.034062739461660385,
0.014266304671764374,
0.05198133364319801,
0.01682290807366371,
0.013644436374306679,
0.003545707557350397,
0.011872476898133755,
-0.01804390363395214,
0.047468144446611404,
-0.003095444058999419,
0.03403428569436073,
0.015659738332033157,
0.10066978633403778,
0.00028288864996284246,
-0.001708313007839024,
0.011252328753471375,
-0.013426549732685089,
0.031936679035425186,
-0.01740446500480175,
-0.012297661043703556,
-0.011570047587156296,
-0.014875629916787148,
-0.036069270223379135,
-0.022753924131393433,
-0.014165567234158516,
-0.00792965292930603,
0.04237290471792221,
-0.03129655495285988,
0.02769952267408371,
0.016224455088377,
-0.02200775220990181,
-0.0076421089470386505,
-0.006240503862500191,
0.0073950341902673244,
0.01992335170507431,
-0.03352821245789528,
0.03861766681075096,
0.008865263313055038,
0.0005909653846174479,
0.046684496104717255,
0.030985016375780106,
-0.002042488195002079,
0.008595556952059269,
0.004939473699778318,
0.039217013865709305,
0.052124686539173126,
-0.008632301352918148,
-0.056361593306064606,
0.023448748514056206,
-0.03428599610924721,
0.03617739677429199,
-0.019091034308075905,
-0.024141283705830574,
0.043755609542131424,
0.027440357953310013,
0.04764468967914581,
-0.04792863875627518,
-0.04586745426058769,
-0.005726612638682127,
0.016009099781513214,
0.043192725628614426,
0.013089139945805073,
0.005748882424086332,
-0.007381992880254984,
0.02184322476387024,
0.013827846385538578,
-0.017224451526999474,
0.027999255806207657,
-0.03859642148017883,
0.010598614811897278,
-0.024226540699601173,
-0.01750769466161728,
0.039481502026319504,
0.006935419514775276,
-0.03997627645730972,
-0.0006609178963117301,
-0.010760880075395107,
0.018272481858730316,
0.02140396647155285,
0.005522776860743761,
-0.04427328705787659,
0.06261211633682251,
-0.034678734838962555,
0.027417946606874466,
-0.01736164651811123,
0.03916658088564873,
0.11121493577957153,
0.04736891761422157,
0.03198561072349548,
-0.07370539009571075,
0.028400300070643425,
-0.05137230455875397,
-0.023623807355761528,
-0.0353807657957077,
-0.019008232280611992,
-0.02497374452650547,
0.012327746488153934,
0.03707073628902435,
0.06040140613913536,
-0.017794668674468994,
0.003520518308505416,
0.039927590638399124,
-0.030147599056363106,
0.009954158216714859,
-0.022352328523993492,
0.009072491899132729,
-0.013092154636979103,
-0.0044360412284731865,
-0.028864480555057526,
-0.006410038564354181,
-0.005315382964909077,
0.008954114280641079,
-0.011269806884229183,
-0.022263802587985992,
0.035799797624349594,
0.009407649748027325,
-0.027027349919080734,
0.0173710398375988,
-0.004648348316550255,
-0.023023467510938644,
-0.030415253713726997,
0.01746923290193081,
0.025149939581751823,
-0.025966353714466095,
0.021004317328333855,
0.005687460768967867,
0.04255640134215355,
0.005443723872303963,
0.021962564438581467,
0.06729605048894882,
-0.009894566610455513,
-0.006188299972563982,
-0.011023709550499916,
0.0512177012860775,
-0.01792762614786625,
0.014864612370729446,
-0.011222800239920616,
0.01897139474749565,
0.0525531992316246,
-0.0044189030304551125,
-0.021529601886868477,
0.0080393822863698,
0.023517122492194176,
-0.002929101698100567,
0.0014604578027501702,
-0.03776693716645241,
0.03846688196063042,
0.024563131853938103,
-0.015798214823007584,
0.0357956737279892,
-0.024635074660182,
0.010112413205206394,
0.027586419135332108,
0.059000492095947266,
0.0185395535081625,
-0.01641901209950447,
-0.06112322583794594,
-0.003957721870392561,
-0.0160483680665493,
0.003632789943367243,
0.013633373193442822,
0.01848551072180271,
0.02673252299427986,
-0.029599208384752274,
-0.022366132587194443,
-0.015751346945762634,
-0.053375184535980225,
0.05907636880874634,
0.00008211025851778686,
0.004824270959943533,
-0.015308314934372902,
-0.016665901988744736,
0.017982246354222298,
0.044724173843860626,
-0.028599509969353676,
-0.016929682344198227,
0.021362368017435074,
-0.017811832949519157,
0.0076505765318870544,
-0.01259453035891056,
-0.006947679445147514,
0.028245216235518456,
-0.04399178922176361,
0.0034815403632819653,
0.028062596917152405,
0.06793142855167389,
0.0475756861269474,
-0.016996631398797035,
0.030174115672707558,
0.009219199419021606,
-0.005667793098837137,
0.00827608909457922,
0.006822730880230665,
-0.01471151877194643,
-0.0355772040784359,
-0.01318423356860876,
-0.026078026741743088,
-0.02867876924574375,
-0.042448706924915314,
-0.04036131501197815,
-0.0041515277698636055,
0.019777491688728333,
0.043756309896707535,
-0.03436190262436867,
-0.01349667552858591,
0.012282189913094044,
0.06634584069252014,
-0.026288999244570732,
-0.05253667011857033,
-0.06313932687044144,
-0.061040036380290985,
0.03622563183307648,
-0.008292936719954014,
0.0010696550598368049,
0.006651987321674824,
-0.0007456025341525674,
0.017277348786592484,
0.012055403552949429,
0.0051371855661273,
0.009252007119357586,
-0.016756972298026085,
0.010745597071945667,
-0.005408367607742548,
0.030310381203889847,
-0.03536694496870041,
-0.06448493152856827,
0.06203429028391838,
-0.007958208210766315,
-0.046761393547058105,
0.039224110543727875,
-0.017148979008197784,
0.019478661939501762,
0.03518422320485115,
0.02463594079017639,
-0.003351496532559395,
0.056694190949201584,
0.03131118416786194,
0.004018766805529594,
0.0005161208100616932,
0.011383580975234509,
0.016123998910188675,
-0.009328433312475681,
0.044301606714725494,
-0.015825778245925903,
0.011279186233878136,
0.027583518996834755,
0.06122559681534767,
0.017193984240293503,
-0.020566515624523163,
-0.009805699810385704,
0.02752659283578396,
-0.04758875444531441,
0.04821338877081871,
0.030309537425637245,
0.006672073621302843,
0.031133458018302917,
-0.011380445212125778,
0.011225263588130474,
-0.006174215581268072,
-0.019010376185178757,
-0.11426477879285812,
-0.006624279543757439,
0.027205239981412888,
-0.014959392137825489,
0.0076130167581140995,
-0.05157556012272835,
0.01457356195896864,
0.032297685742378235,
-0.05466475710272789,
0.007199291605502367,
-0.027050327509641647,
-0.025262190029025078,
-0.03446487709879875,
-0.017208829522132874,
-0.009570731781423092,
0.03525308519601822,
0.024940764531493187,
0.0534183606505394,
0.030433865264058113,
0.03099069744348526,
-0.02725781686604023,
0.010419935919344425,
-0.023630835115909576,
0.011212289333343506,
-0.02344237081706524,
-0.0019442227203398943,
0.04806818440556526,
-0.003017635550349951,
-0.0372743159532547,
0.01669616438448429,
-0.005306043662130833,
-0.005268264561891556,
0.010629014112055302,
0.0015067568747326732,
-0.016767175868153572,
-0.011639101430773735,
0.00871805939823389,
-0.018160300329327583,
0.027903879061341286,
0.06366484612226486,
0.023719269782304764,
0.05140608176589012,
-0.00873369351029396,
-0.006658857222646475,
-0.004995178896933794,
-0.038034047931432724,
0.0329577773809433,
0.058098845183849335,
-0.060614246875047684,
0.009424945339560509,
-0.010613318532705307,
0.024953287094831467,
-0.00876286905258894,
0.0037593215238302946,
0.004453468602150679,
-0.04818487539887428,
-0.013205314055085182,
0.019151676446199417,
-0.010666253976523876,
0.02768307365477085,
0.023890387266874313,
-0.021703124046325684,
0.0022374617401510477,
-0.005383764393627644,
-0.023368971422314644,
-0.04812859743833542,
-0.013031525537371635,
-0.019180061295628548,
0.010958084836602211,
0.004920418374240398,
-0.0336785614490509,
0.007620361167937517,
-0.02025512047111988,
0.04484374076128006,
0.04217115417122841,
0.022784439846873283,
0.0006138220196589828,
-0.03908732160925865,
-0.029788071289658546,
-0.013936043716967106,
0.018768390640616417,
-0.06610427796840668,
-0.030829237774014473,
-0.03304825350642204,
-0.016694841906428337,
0.017025480046868324,
-0.006377478130161762,
0.03849560394883156,
-0.009258240461349487,
0.018854321911931038,
0.006072547752410173,
-0.029060203582048416,
-0.008105207234621048,
-0.06251642853021622,
0.01047590747475624,
-0.023032963275909424,
0.009367330931127071,
-0.007387362886220217,
-0.007175578735768795,
-0.01288346666842699,
-0.007086846046149731,
0.03499064967036247,
-0.004591869655996561,
0.0047508785501122475,
-0.01570967771112919,
-0.01524342317134142,
0.020923176780343056,
0.003760534105822444,
-0.012213272042572498,
0.042324770241975784,
-0.027931619435548782,
0.0031505913939327,
-0.00927647203207016,
-0.011596443131566048,
-0.03951064124703407,
0.02623431384563446,
-0.013006256893277168,
0.014938045293092728,
0.001687380950897932,
-0.03499547764658928,
0.016912158578634262,
-0.02064027450978756,
0.03592938184738159,
0.009488865733146667,
-0.04591408744454384,
-0.011369617655873299,
-0.011948037892580032,
0.012233308516442776,
0.017520172521471977,
-0.0118849603459239,
0.02579922415316105,
0.010017608292400837,
0.005146840121597052,
0.0010921419598162174,
0.053282998502254486,
0.005164270754903555,
0.020657049492001534,
0.0036772575695067644,
-0.0031411501113325357,
0.006132262293249369,
-0.016950612887740135,
0.03421003744006157,
0.03471178561449051,
-0.043399449437856674,
-0.05065802484750748,
0.03716601803898811,
-0.01836932636797428,
0.027204537764191628,
-0.0065726605243980885,
-0.015774710103869438,
0.0693824514746666,
-0.04483276605606079,
0.001591437146998942,
-0.03135770559310913,
0.015355806797742844,
0.0183693990111351,
0.04304630681872368,
0.019613567739725113,
0.05837421491742134,
-0.009130419231951237,
-0.02130504511296749,
0.02021653577685356,
0.022296689450740814,
0.04518735036253929,
-0.021390147507190704,
0.030556948855519295,
-0.03860881179571152,
0.0216206107288599,
-0.03937608003616333,
-0.0191954355686903,
-0.02766089141368866,
-0.016991207376122475,
0.008275623433291912,
0.01532194297760725,
0.00955921784043312,
-0.0010908403201028705,
-0.01895814761519432,
-0.00842135027050972,
0.033391524106264114,
-0.09296726435422897,
-0.002236232627183199,
-0.04575168341398239,
0.043314266949892044,
-0.03131365403532982,
0.02784240059554577
] |
<p>In an alternating current, the flow of electric charge periodically reverses direction, and the number of times it does that is called the frequency of the current. However, if the frequency of an AC is made infinite, would any current flow? I asked this question to my school teacher and he was unable to provide me with an answer unfortunately.</p>
<p>If I consider a horizontal wire, through which an AC is flowing, then I can say that an electron in the wire is moving 50 times left and 50 times right, if the frequency is assumed to be 50Hz. It seems to me that if I increase the frequency, the displacement of the electrons in both the directions, that is left and right, will gradually decrease, and finally become 0, when frequency is infinite, thus making I = 0.</p>
<p>What have I got wrong?</p> | 2,903 | [
-0.026021791622042656,
-0.014991938136518002,
0.01919078454375267,
-0.01406665239483118,
0.02437606453895569,
-0.02815171889960766,
-0.04826647788286209,
0.007622618228197098,
-0.01450742781162262,
-0.011648591607809067,
0.054265230894088745,
0.01765376701951027,
0.04625273495912552,
0.02638021856546402,
0.013792004436254501,
0.014045746996998787,
-0.014059854671359062,
-0.017421899363398552,
-0.020512642338871956,
0.008982991799712181,
-0.0008643559995107353,
0.03772479295730591,
0.0017897888319566846,
0.025572096928954124,
-0.025322433561086655,
0.022921472787857056,
0.05185212194919586,
0.02434534579515457,
0.02103516459465027,
0.031251341104507446,
0.007183408364653587,
-0.012320674024522305,
0.0013546568807214499,
-0.002579008461907506,
0.062467847019433975,
0.01101695653051138,
-0.01792651228606701,
-0.051600344479084015,
-0.0015486852498725057,
0.024283723905682564,
-0.0026011127047240734,
0.01551614049822092,
0.016234204173088074,
0.038667142391204834,
-0.009182685986161232,
0.0011415970511734486,
0.04631439596414566,
-0.0012380445841699839,
0.055311162024736404,
-0.06719709187746048,
0.07119443267583847,
-0.03486764430999756,
0.04022687301039696,
-0.028414977714419365,
0.026342254132032394,
-0.013477219268679619,
0.040501922369003296,
0.04425068199634552,
-0.010003265924751759,
-0.04850539565086365,
-0.0014629976358264685,
-0.002016437239944935,
-0.0465935543179512,
-0.03758620843291283,
-0.03564242273569107,
0.020041022449731827,
-0.01887977495789528,
-0.02809583581984043,
0.018101505935192108,
0.00665675476193428,
0.019619274884462357,
0.022250305861234665,
0.034249257296323776,
-0.005998212844133377,
0.008746710605919361,
-0.039617251604795456,
0.016404395923018456,
0.015667200088500977,
0.00038689497159793973,
0.061565037816762924,
-0.041326411068439484,
-0.00600757310166955,
0.02164897881448269,
0.03432076424360275,
0.03618162125349045,
-0.06669990718364716,
0.027972308918833733,
-0.010174152441322803,
0.013396019116044044,
0.044701386243104935,
-0.0013644588179886341,
0.006051462609320879,
0.008553504943847656,
-0.009184777736663818,
-0.017065687105059624,
0.036152422428131104,
0.0018661357462406158,
0.05864599719643593,
-0.013375155627727509,
-0.03125305473804474,
0.032209914177656174,
-0.020299535244703293,
0.030014965683221817,
0.06516999006271362,
-0.000141836644615978,
0.003361087990924716,
0.009835069999098778,
0.003044223878532648,
-0.026836413890123367,
-0.02841273508965969,
-0.041583117097616196,
0.01125112734735012,
0.02504335157573223,
0.05554208531975746,
-0.008407690562307835,
-0.00185851298738271,
0.049490656703710556,
-0.017498131841421127,
0.01917644776403904,
0.06882856041193008,
0.00741747859865427,
-0.0557003952562809,
0.03199685737490654,
-0.014557023532688618,
-0.06159905344247818,
0.009446860291063786,
-0.014342965558171272,
0.015724830329418182,
-0.026018595322966576,
0.03650110587477684,
-0.03113928996026516,
-0.0008403435349464417,
0.009682733565568924,
-0.003160052001476288,
0.05909739062190056,
-0.025760140269994736,
-0.08536060154438019,
-0.054857563227415085,
0.030606407672166824,
-0.02720649167895317,
-0.024772753939032555,
-0.077775739133358,
0.012180950492620468,
0.017162617295980453,
0.07541158050298691,
-0.02786966599524021,
0.002313944511115551,
-0.024031247943639755,
0.04433842748403549,
0.02430250309407711,
-0.02363373525440693,
0.0033567945938557386,
0.00010869377001654357,
-0.02447834052145481,
-0.007440758403390646,
-0.01688414253294468,
0.04808961972594261,
0.013699748553335667,
0.033787086606025696,
-0.029836198315024376,
0.04644136130809784,
0.008923135697841644,
-0.03406016156077385,
0.018994441255927086,
-0.02966468036174774,
-0.038018204271793365,
0.06785473227500916,
0.011378725990653038,
-0.013508372008800507,
0.0012097429716959596,
0.02052496373653412,
0.023609817028045654,
0.007422198541462421,
0.021897796541452408,
0.05392605811357498,
-0.057230912148952484,
-0.00833564717322588,
-0.05874329432845116,
0.01627417467534542,
-0.004909947980195284,
-0.009919418953359127,
-0.0036884844303131104,
-0.009982832707464695,
0.02901070937514305,
0.010677220299839973,
0.02165313996374607,
-0.012620927765965462,
0.022422246634960175,
-0.0010477780597284436,
-0.04186981916427612,
-0.002055671764537692,
-0.04413532838225365,
0.04484378919005394,
-0.008131254464387894,
-0.024845002219080925,
0.014972174540162086,
-0.010999559424817562,
0.021717427298426628,
-0.03793680667877197,
-0.02484949305653572,
-0.012174948118627071,
0.01354747824370861,
-0.020502733066678047,
-0.015294686891138554,
-0.00018816778901964426,
0.04615449532866478,
0.0029837193433195353,
0.033073894679546356,
0.03783310204744339,
0.006346551701426506,
-0.01614013873040676,
-0.006932076998054981,
0.0035239942371845245,
0.054345689713954926,
0.06330452859401703,
0.007764296140521765,
-0.019011033698916435,
-0.026141811162233353,
0.01277330331504345,
0.04991034045815468,
-0.010287974029779434,
0.05757888779044151,
0.04755232110619545,
-0.010307720862329006,
0.017384132370352745,
0.05731619894504547,
0.021160783246159554,
-0.03212853521108627,
-0.016035107895731926,
-0.006757664494216442,
-0.07644578814506531,
0.022986846044659615,
0.014624443836510181,
0.021222908049821854,
-0.025411995127797127,
0.0086094681173563,
0.006237756926566362,
0.05225132033228874,
0.04600442573428154,
0.05948837846517563,
-0.004432956222444773,
-0.03062749095261097,
0.0012795217335224152,
-0.03484853729605675,
0.010629837401211262,
0.008156871423125267,
0.045926690101623535,
-0.008638860657811165,
0.019477615132927895,
0.00024139544984791428,
-0.019477589055895805,
0.04361242428421974,
0.015427523292601109,
0.017569884657859802,
0.02669716626405716,
-0.017327824607491493,
-0.0013963676756247878,
-0.032386694103479385,
0.0029242869932204485,
0.017338650301098824,
-0.01853357069194317,
0.00673792464658618,
0.02183046005666256,
0.046153582632541656,
0.0052084727212786674,
-0.034753017127513885,
-0.019114341586828232,
-0.03560244292020798,
0.02515924908220768,
-0.03752533346414566,
0.008492927998304367,
-0.0013362305471673608,
0.019705330953001976,
-0.03197302296757698,
-0.02570953406393528,
0.03227963298559189,
0.034829095005989075,
0.07071834802627563,
-0.04339814558625221,
-0.00042876933002844453,
0.03900422528386116,
-0.055276643484830856,
0.01266128197312355,
0.018891947343945503,
0.015360786579549313,
0.015609943307936192,
-0.0017505971482023597,
-0.06462962180376053,
0.03313605114817619,
0.0133329713717103,
0.026961447671055794,
0.027374446392059326,
-0.03208297863602638,
-0.049926210194826126,
-0.004938004072755575,
-0.04734963923692703,
0.024944234639406204,
-0.052300289273262024,
0.0002601484302431345,
0.06944366544485092,
-0.00877391453832388,
-0.00504410732537508,
0.023021524772047997,
-0.04940888285636902,
-0.05767783150076866,
-0.033492561429739,
-0.011541634798049927,
0.04184233769774437,
-0.037692148238420486,
0.00796468835324049,
-0.007593957707285881,
-0.058901671320199966,
-0.007659977301955223,
-0.020686687901616096,
-0.06710991263389587,
0.008747749030590057,
0.005890872795134783,
0.030211836099624634,
0.01421807985752821,
-0.04071005806326866,
0.04444478824734688,
0.04604130610823631,
-0.018279705196619034,
-0.02481488138437271,
-0.05823994800448418,
-0.017092715948820114,
-0.04945133626461029,
0.01095753163099289,
0.06453561037778854,
-0.04893233999609947,
-0.01610514149069786,
0.0109788179397583,
0.042064886540174484,
0.027898021042346954,
0.030611345544457436,
-0.02104969322681427,
0.017270652577280998,
0.00789655838161707,
0.041394446045160294,
0.05464541167020798,
-0.010394048877060413,
-0.014603450894355774,
-0.0023295427672564983,
-0.004227101802825928,
0.05277097225189209,
0.03380270674824715,
0.00363764725625515,
0.0086974473670125,
0.00622783787548542,
0.02103559300303459,
-0.02428164891898632,
0.03355714678764343,
0.024813132360577583,
0.01770177111029625,
-0.016122475266456604,
0.00006061331077944487,
0.040907666087150574,
0.0023240509908646345,
-0.00472598010674119,
0.027059486135840416,
0.000658999546431005,
-0.01719655655324459,
-0.04869770258665085,
-0.014628725126385689,
0.012994068674743176,
0.022716591134667397,
-0.055104102939367294,
-0.045520614832639694,
0.02765500545501709,
0.024653641507029533,
0.02977815642952919,
0.02117651328444481,
-0.038211528211832047,
0.006703637540340424,
-0.03675701469182968,
-0.015983378514647484,
-0.02056248113512993,
0.06438829004764557,
0.003516608849167824,
0.06292403489351273,
-0.008727219887077808,
0.04942956566810608,
0.013496728613972664,
-0.00006432868394767866,
-0.10723666101694107,
0.014818582683801651,
-0.010229176841676235,
-0.00988285057246685,
-0.012217762880027294,
-0.010926032438874245,
-0.00523138465359807,
-0.011676833033561707,
-0.017161935567855835,
-0.014413716271519661,
-0.052360668778419495,
-0.024904068559408188,
0.026024986058473587,
-0.015864329412579536,
-0.003787619760259986,
-0.019911259412765503,
0.011427592486143112,
0.05876019969582558,
-0.060395970940589905,
0.05432920902967453,
0.034530218690633774,
-0.01742149144411087,
-0.001653518178500235,
-0.02024882100522518,
0.006369966082274914,
0.03696290776133537,
0.020796749740839005,
0.04975789785385132,
0.0014521899865940213,
-0.021583667024970055,
0.005103638861328363,
0.018445894122123718,
0.04496525228023529,
-0.006248386111110449,
-0.020014198496937752,
-0.010084305889904499,
-0.024367913603782654,
-0.029352400451898575,
-0.0028324415907263756,
0.06255270540714264,
0.038611747324466705,
0.018253766000270844,
0.05795900896191597,
0.001370913116261363,
-0.0018121033208444715,
0.04157736524939537,
-0.0037543606013059616,
0.04388664662837982,
-0.011482861824333668,
-0.03825924172997475,
0.016148969531059265,
-0.03201891854405403,
0.021827900782227516,
0.01592954620718956,
-0.03073403239250183,
0.0071574123576283455,
-0.027844395488500595,
0.03114284574985504,
0.025852343067526817,
0.0003670030855573714,
0.016949711367487907,
-0.018148498609662056,
-0.0075830090790987015,
0.0023887164425104856,
-0.00561404787003994,
0.035269420593976974,
0.017307640984654427,
0.01838541403412819,
-0.0004520838556345552,
-0.021342892199754715,
-0.11211387813091278,
-0.023651061579585075,
0.005624501965939999,
0.051943179219961166,
0.001905254670418799,
-0.017717579379677773,
-0.04049326106905937,
-0.03269483521580696,
0.019680121913552284,
-0.009309457615017891,
0.021458711475133896,
-0.03644772246479988,
-0.0012559972237795591,
-0.018698040395975113,
-0.0682152658700943,
-0.037961483001708984,
0.0033593089319765568,
-0.02255392260849476,
-0.0016454487340524793,
-0.016478421166539192,
-0.014637679792940617,
-0.02138146385550499,
0.01446045096963644,
0.044752977788448334,
0.015074070543050766,
-0.03754431754350662,
0.027600122615695,
0.004305580165237188,
0.01164045836776495,
-0.0066851661540567875,
-0.09703066945075989,
0.033440474420785904,
-0.003762017237022519,
0.05099434778094292,
0.030707458034157753,
-0.028259679675102234,
-0.031488824635744095,
0.01643703319132328,
0.015042324550449848,
-0.020680444315075874,
0.010056080296635628,
-0.05535496771335602,
0.06379923224449158,
-0.0045333486050367355,
0.028755763545632362,
0.03401385620236397,
0.03177482634782791,
-0.0064821867272257805,
-0.017342770472168922,
0.01594180427491665,
0.05801129341125488,
-0.014761595986783504,
0.02772654965519905,
-0.014426016248762608,
0.03278295323252678,
-0.04333312809467316,
0.057214196771383286,
0.01055826060473919,
0.014307096600532532,
-0.03076872229576111,
0.005290241912007332,
0.01879284717142582,
0.012977320700883865,
-0.014428739435970783,
-0.020964477211236954,
-0.04565790295600891,
0.013139484450221062,
-0.005005813669413328,
-0.03507276996970177,
0.000001913637333927909,
-0.02276488207280636,
-0.0026572956703603268,
0.04990679770708084,
-0.0131834726780653,
0.018305258825421333,
-0.029862476512789726,
-0.007189618889242411,
-0.005704743321985006,
-0.03648770973086357,
0.04231981560587883,
-0.05799119919538498,
-0.005493856966495514,
-0.01174640841782093,
-0.037081919610500336,
-0.03777489811182022,
0.050877537578344345,
-0.021780209615826607,
0.012201502919197083,
-0.027525778859853745,
0.026845447719097137,
0.019776485860347748,
0.005443349480628967,
-0.0641823261976242,
-0.09286696463823318,
0.010100155137479305,
0.044708702713251114,
-0.036505408585071564,
-0.0010017640888690948,
-0.008056272752583027,
-0.02614959515631199,
-0.013689433224499226,
0.01124995481222868,
0.00647014519199729,
-0.03314996883273125,
0.007445163559168577,
0.05778763070702553,
-0.0071324841119349,
0.03522113710641861,
0.0038229518104344606,
-0.021520966663956642,
0.009036536328494549,
-0.023263873532414436,
-0.013048790395259857,
-0.03237917274236679,
0.06716527789831161,
-0.030293982475996017,
-0.03048321232199669,
0.030673207715153694,
-0.014205735176801682,
0.04211411625146866,
0.011062728241086006,
-0.03562237694859505,
0.04376872256398201,
-0.009091694839298725,
0.02091902308166027,
-0.022230181843042374,
0.005717058200389147,
0.017778456211090088,
0.018403641879558563,
0.009885587729513645,
-0.0219938512891531,
-0.0616651251912117,
-0.04885396733880043,
0.00820855237543583,
0.02030836045742035,
-0.01031812746077776,
0.010872287675738335,
0.04356304928660393,
-0.0552472360432148,
-0.01066145021468401,
0.024002477526664734,
0.0018550152890384197,
0.014025540091097355,
-0.0054300338961184025,
0.014365713112056255,
-0.031015969812870026,
0.00877030286937952,
-0.01983870007097721,
-0.010703065432608128,
-0.02269606664776802,
0.0050116414204239845,
0.042176853865385056,
-0.006947264540940523,
0.010010048747062683,
-0.029483256861567497,
0.014454023912549019,
-0.003775315824896097,
0.014002678915858269,
-0.0052391961216926575,
0.019644539803266525,
0.0022637159563601017,
-0.02944718487560749,
-0.04654162749648094,
-0.012139650993049145,
0.03095344826579094,
0.011389882303774357,
-0.010191943496465683,
-0.012128373607993126,
0.03418367728590965,
-0.010579422116279602,
0.037046365439891815,
-0.002780546899884939,
-0.02607746422290802,
0.024566538631916046,
-0.022844433784484863,
0.05736099183559418,
-0.00001213848554471042,
-0.0432044081389904,
0.06245877593755722,
0.0035751627292484045,
-0.005280541721731424,
-0.010862063616514206,
0.002229767618700862,
-0.015682630240917206,
0.0075912075117230415,
-0.003976540174335241,
0.02215067483484745,
0.006853548344224691,
0.004715568386018276,
0.026131846010684967,
-0.0061535947024822235,
0.04040059074759483,
-0.006512992549687624,
-0.03659403324127197,
0.0004900034400634468,
-0.07056785374879837,
-0.03504837304353714,
0.07376853376626968,
0.015216995030641556,
-0.024194983765482903,
-0.011873974464833736,
-0.008913153782486916,
0.028021054342389107,
0.03215610980987549,
0.03906673565506935,
-0.021486962214112282,
0.07409778982400894,
0.001638846006244421,
0.061774514615535736,
-0.017460916191339493,
0.029182320460677147,
0.11537738889455795,
0.01151580736041069,
0.002117638476192951,
-0.05160228908061981,
0.037224479019641876,
-0.03292384371161461,
0.019541475921869278,
-0.015074001625180244,
0.01994692161679268,
-0.018299676477909088,
0.014499368146061897,
0.010491293855011463,
0.046019092202186584,
-0.019501186907291412,
-0.0029505754355341196,
0.04778600111603737,
-0.04689193144440651,
-0.01574796624481678,
-0.006886104587465525,
-0.011489002965390682,
0.023957254365086555,
0.047811586409807205,
-0.05467476695775986,
0.024910200387239456,
-0.05513020604848862,
-0.01958269625902176,
-0.015854904428124428,
-0.03015179932117462,
0.03623181954026222,
0.00040754195651970804,
-0.07309319078922272,
0.0021371846087276936,
0.04635697975754738,
0.0023216872941702604,
-0.040964704006910324,
0.008619163185358047,
0.023324161767959595,
0.03206747770309448,
0.024436205625534058,
0.037024617195129395,
0.02810545265674591,
0.03604193031787872,
0.018358439207077026,
0.03158597648143768,
-0.01779465563595295,
-0.010311446152627468,
-0.04305579513311386,
0.030083272606134415,
-0.012673385441303253,
-0.019316431134939194,
-0.021229920908808708,
0.03614985942840576,
-0.01986723579466343,
-0.03508680313825607,
-0.0509556382894516,
-0.042528629302978516,
0.021822640672326088,
-0.0018895388348028064,
-0.01506445650011301,
-0.04368671402335167,
0.005669457837939262,
-0.0009512162068858743,
0.005962496157735586,
0.021239258348941803,
-0.03153901547193527,
-0.007598905358463526,
0.011505845934152603,
0.08097555488348007,
-0.0037730964832007885,
-0.031620703637599945,
-0.0011450407328084111,
-0.0017337100580334663,
-0.038269009441137314,
0.013375732116401196,
0.01783338561654091,
0.036370936781167984,
0.030554525554180145,
-0.03333730250597,
-0.05325254797935486,
-0.010211838409304619,
-0.07891886681318283,
0.04103313386440277,
0.06740041077136993,
-0.003968141507357359,
0.003322501201182604,
-0.010986431501805782,
-0.004330568015575409,
0.02543449215590954,
-0.06097404286265373,
0.005756700877100229,
0.027552280575037003,
0.008723544888198376,
0.031245414167642593,
-0.02535989321768284,
-0.041119836270809174,
-0.01927962526679039,
-0.03192196041345596,
0.011559844017028809,
0.01198076456785202,
0.03225373849272728,
0.030136369168758392,
0.01898883655667305,
0.006555334664881229,
0.04918651282787323,
-0.03361334279179573,
0.008969038724899292,
0.009302712045609951,
-0.010670469142496586,
0.005806442815810442,
0.056610845029354095,
0.02989017777144909,
-0.036781471222639084,
-0.020395975559949875,
-0.02461370639503002,
0.035280320793390274,
0.012594104744493961,
0.039473336189985275,
-0.024251768365502357,
0.0023841639049351215,
-0.033554427325725555,
0.027215121313929558,
-0.040989626199007034,
-0.03115645982325077,
-0.0809197723865509,
0.0034658382646739483,
0.025244807824492455,
-0.002472540130838752,
-0.0025243726558983326,
0.03721180930733681,
-0.035387322306632996,
-0.016214214265346527,
0.04218795895576477,
0.01909729093313217,
-0.039408911019563675,
-0.013842159882187843,
0.005964384414255619,
0.007810098584741354,
0.025724850594997406,
-0.03231086581945419,
-0.03648267686367035,
0.06429928541183472,
-0.021372349932789803,
0.0029859128408133984,
0.022789200767874718,
-0.034972839057445526,
0.0042874375358223915,
0.013248651288449764,
-0.014011664316058159,
0.0011670634848996997,
0.04890681430697441,
-0.005894904490560293,
0.020844148471951485,
-0.024024879559874535,
-0.021898124366998672,
0.0025700931437313557,
-0.012417617253959179,
-0.01978832110762596,
-0.013607405126094818,
0.016090357676148415,
0.02498123049736023,
0.04947473481297493,
0.006613783072680235,
-0.01488303393125534,
-0.008451906964182854,
-0.0010059773921966553,
0.008808951824903488,
0.04307498782873154,
-0.009620004333555698,
0.0007546471315436065,
0.033850979059934616,
-0.029598869383335114,
0.011806311085820198,
-0.017428690567612648,
0.013163057155907154,
-0.0936952456831932,
0.004340397659689188,
-0.005979952868074179,
-0.004700222052633762,
0.020681709051132202,
-0.013869709335267544,
-0.06409943103790283,
0.027756331488490105,
-0.10207457095384598,
0.04118317365646362,
-0.025153253227472305,
-0.021555466577410698,
-0.04824913293123245,
-0.026446761563420296,
-0.024429209530353546,
0.013765770941972733,
0.06681373715400696,
0.06878070533275604,
-0.017563696950674057,
-0.011992955580353737,
-0.009961606003344059,
-0.06033504754304886,
0.018226495012640953,
0.031192993745207787,
0.0011662943288683891,
0.010960083454847336,
0.006275258958339691,
-0.03590192645788193,
-0.01122323703020811,
0.03969523310661316,
-0.020894793793559074,
0.03784671425819397,
-0.025740116834640503,
0.007749747484922409,
0.0052347262389957905,
0.05625437945127487,
-0.017940539866685867,
0.0011294912546873093,
-0.006597217638045549,
0.028077444061636925,
0.026897769421339035,
0.016090964898467064,
-0.014678855426609516,
0.007265712134540081,
0.04609459638595581,
-0.0392463393509388,
-0.014726408757269382,
0.03298300877213478,
-0.02235097624361515,
0.026973677799105644,
0.022564413025975227,
0.005075777415186167,
0.020701482892036438,
-0.019634580239653587,
-0.01848224364221096,
-0.018451755866408348,
-0.05591902509331703,
0.013600613921880722,
0.005203405860811472,
0.0032906162086874247,
-0.017339568585157394,
-0.014399823732674122,
-0.023636238649487495,
0.03149253875017166,
0.005166271235793829,
-0.01783541589975357,
-0.07333743572235107,
0.00177728570997715,
0.003648801241070032,
-0.00649489089846611,
0.013109300285577774,
-0.04541327804327011,
0.0013052838621661067,
0.0035934930201619864,
0.015899358317255974,
-0.01411465834826231,
-0.0028297947719693184,
-0.07254201173782349,
-0.021004509180784225,
-0.04361160844564438,
0.05466095730662346,
0.004295389633625746,
0.009506670758128166,
-0.046652842313051224,
-0.06317797303199768,
-0.0145321786403656,
0.045261040329933167,
0.07029660046100616,
-0.007560196332633495,
0.0052656810730695724,
0.016891220584511757,
0.009361918084323406,
0.03910394012928009,
-0.0342712439596653,
-0.004034802317619324,
-0.011063933372497559,
-0.0034491003025323153,
0.00761130265891552,
-0.010849551297724247,
-0.05704990029335022,
0.0009999076137319207,
-0.030594896525144577,
-0.0300655085593462,
0.010738154873251915,
-0.012345150113105774,
-0.04569413512945175,
0.020072445273399353,
0.047155894339084625,
-0.014858131296932697,
0.06363797187805176,
-0.00267229788005352,
0.03920197859406471,
0.0010460293851792812,
-0.01574547030031681,
-0.053085699677467346,
0.006854830775409937,
-0.03234244883060455,
0.04110584035515785,
-0.02687867172062397,
-0.008317962288856506,
0.0352821983397007,
-0.01841706782579422,
-0.012099339626729488,
0.05460979416966438,
-0.05017763003706932,
-0.0310080386698246,
0.036521248519420624,
-0.016110505908727646,
0.01527691725641489,
-0.037937067449092865,
-0.02051936462521553,
-0.006909211166203022,
0.018656132742762566,
-0.0031099054031074047,
0.044987618923187256,
-0.026319582015275955,
-0.01958520896732807,
0.01579360105097294,
0.03768746927380562,
0.009649334475398064,
-0.002534671686589718,
0.012516270391643047,
0.020974082872271538,
-0.012935807928442955,
-0.029170827940106392,
0.006635169964283705,
-0.025853238999843597,
-0.0009276416967622936,
0.03483093902468681,
-0.019755570217967033,
0.04262314736843109,
0.009513822384178638,
0.03215084969997406,
0.0128921614959836,
-0.005772816948592663,
0.008504655212163925,
0.021011386066675186,
0.014684341847896576,
0.0200786292552948,
-0.05607592314481735,
-0.040561579167842865,
-0.012884726747870445,
0.000445218407548964,
0.04974675551056862,
-0.0806378647685051,
-0.0035378665197640657,
-0.002345767104998231,
-0.02497071772813797,
-0.030679650604724884,
0.02010999247431755,
-0.0482320711016655,
-0.004311420023441315,
0.03645472228527069,
0.03134093061089516,
0.014254830777645111,
-0.014192712493240833,
0.010137399658560753,
-0.025214320048689842,
0.05552564561367035,
-0.02715371549129486,
-0.00632703211158514,
-0.007199387531727552,
0.03215543553233147,
0.015604648739099503,
-0.022326571866869926
] |
<p><strong>Space-like</strong> separated events are events that, in a well-chosen reference frame, can take place at the <strong>same time</strong> but <em>never</em> happen at the <em>same</em> <em>location</em>.</p>
<p>On the other hand for <a href="http://en.wikipedia.org/wiki/Spacetime#Time-like_interval" rel="nofollow"><strong>time-like events</strong></a>, one can chose a reference frame such that they happen at the <strong>same</strong> <strong>place</strong> but <em>never</em> <em>simultaneously</em>.</p>
<p>I can't help thinking that the labels are therefore very ill-chosen... Is there another motivation for these names?</p> | 2,904 | [
-0.01043134555220604,
-0.04233761876821518,
-0.009812106378376484,
-0.0031789233908057213,
0.012614437378942966,
0.0043996344320476055,
-0.01561202947050333,
-0.00783206894993782,
0.024802042171359062,
-0.003534059040248394,
0.033495157957077026,
0.030319757759571075,
0.01730325259268284,
0.022950852289795876,
0.005260603502392769,
0.024491136893630028,
0.054550401866436005,
-0.004116523545235395,
-0.01980915665626526,
-0.060855377465486526,
0.01753936894237995,
0.005821194965392351,
-0.00657670758664608,
0.015773728489875793,
-0.030336961150169373,
0.001212532166391611,
-0.003377782180905342,
0.010773906484246254,
-0.03428805246949196,
0.048458803445100784,
-0.06752500683069229,
-0.028932034969329834,
-0.009208984673023224,
-0.009582885541021824,
-0.013008993119001389,
-0.03523015230894089,
-0.007359112612903118,
-0.021613869816064835,
0.007010755129158497,
-0.012334776110947132,
-0.06400618702173233,
-0.005727388896048069,
-0.03595786541700363,
0.10218718647956848,
-0.04290753975510597,
0.02194936014711857,
0.006456168834120035,
-0.029860610142350197,
0.0340408980846405,
-0.013261688873171806,
0.03690941631793976,
-0.04193664714694023,
0.04040920361876488,
-0.007297216914594173,
-0.004842380061745644,
0.02002144046127796,
0.05089974403381348,
0.041829485446214676,
-0.006910334806889296,
-0.03057893179357052,
-0.003749825991690159,
0.005649701226502657,
0.041578520089387894,
-0.0032316066790372133,
-0.008316772989928722,
0.026158709079027176,
-0.000005172555120225297,
0.0008417761418968439,
0.014026230201125145,
-0.024365441873669624,
0.0020234694238752127,
0.01157978642731905,
0.04994650557637215,
-0.033543799072504044,
0.030355827882885933,
-0.03492685779929161,
0.029363637790083885,
0.023749414831399918,
0.05194396153092384,
0.032519031316041946,
0.020228998735547066,
0.0061812191270291805,
0.01358635164797306,
-0.04237747564911842,
0.018366510048508644,
-0.03391944617033005,
0.04938233271241188,
-0.013597065582871437,
-0.04343411698937416,
0.02400076389312744,
-0.024635380133986473,
0.00992392934858799,
0.04945623129606247,
0.02555663324892521,
-0.022473590448498726,
0.057061389088630676,
0.0072008599527180195,
0.008691336028277874,
0.01794709637761116,
-0.027388881891965866,
-0.040809545665979385,
-0.025805655866861343,
0.037490349262952805,
0.0871114507317543,
-0.01367210317403078,
-0.04511508345603943,
-0.0447939895093441,
0.03016001358628273,
-0.03178279846906662,
0.04314689338207245,
-0.02295641414821148,
0.010227039456367493,
0.014321641065180302,
0.033382024616003036,
0.008825399912893772,
-0.00936575885862112,
0.004192942753434181,
0.008556094951927662,
0.005411400925368071,
0.0701771080493927,
0.06176368147134781,
-0.03346416354179382,
0.02995987795293331,
-0.009304194711148739,
-0.059479113668203354,
0.01791178621351719,
0.046480707824230194,
0.0020179003477096558,
-0.011895712465047836,
0.04003868252038956,
-0.035828862339258194,
0.015286522917449474,
0.029721282422542572,
-0.02386309951543808,
0.02874896302819252,
-0.010957516729831696,
-0.0801827684044838,
-0.06441180408000946,
0.05757426097989082,
-0.004297429695725441,
-0.0378737598657608,
-0.05207085981965065,
0.013545447960495949,
-0.009276083670556545,
0.06191638857126236,
0.010071633383631706,
-0.011366252787411213,
0.013110359199345112,
0.02139178104698658,
0.023749716579914093,
-0.06046793982386589,
0.02521786466240883,
0.019312608987092972,
-0.043746467679739,
-0.004471212159842253,
-0.04708990827202797,
-0.005551083479076624,
0.05280391499400139,
-0.03174714744091034,
0.03159049153327942,
0.05387885868549347,
-0.009735572151839733,
0.010611631907522678,
0.006437414791435003,
0.02349526435136795,
-0.029742073267698288,
0.10180602967739105,
0.010256530717015266,
0.0015498473076149821,
0.07006077468395233,
0.023206442594528198,
0.04472268745303154,
-0.0018614348955452442,
0.021906793117523193,
0.01938297413289547,
-0.017747770994901657,
-0.01905137673020363,
0.030146101489663124,
-0.028791280463337898,
-0.023662159219384193,
-0.04735605791211128,
-0.000383979466278106,
-0.04272133857011795,
0.0004943019594065845,
-0.03887223079800606,
0.06068228930234909,
0.019794482737779617,
0.003870451357215643,
0.026554053649306297,
-0.018852610141038895,
-0.014378751628100872,
-0.06626385450363159,
-0.026730496436357498,
-0.02207028865814209,
-0.00821036659181118,
0.039910249412059784,
-0.02525915391743183,
0.0058983126655220985,
-0.02496771141886711,
-0.011965016834437847,
-0.037581752985715866,
0.04378866031765938,
-0.007942250929772854,
-0.023690368980169296,
-0.0015603475039824843,
0.0648668184876442,
0.02911554090678692,
0.015790855512022972,
-0.007254180498421192,
-0.009494195692241192,
-0.05948367714881897,
-0.023936839774250984,
-0.03206392005085945,
0.039163511246442795,
-0.006874092388898134,
-0.011160503141582012,
0.0024798251688480377,
0.01450231671333313,
-0.036407943814992905,
0.016933845356106758,
-0.04863372817635536,
0.03572602942585945,
0.019508350640535355,
-0.006670965347439051,
-0.008723994717001915,
0.030388442799448967,
0.05976075679063797,
0.017683949321508408,
-0.0076895165257155895,
-0.04207824915647507,
-0.03363180533051491,
-0.024154137820005417,
0.04177621752023697,
0.03790498897433281,
-0.0004999066004529595,
0.02093597501516342,
0.010422993451356888,
0.03227826952934265,
0.01617933250963688,
0.04618214815855026,
-0.016751382499933243,
-0.014659011736512184,
0.029794946312904358,
0.02458159066736698,
0.016042126342654228,
-0.011099004186689854,
0.02194010093808174,
0.00842250045388937,
0.03865332528948784,
-0.05462321639060974,
-0.004996387753635645,
0.018951857462525368,
-0.0185288954526186,
0.006829217076301575,
0.02386140078306198,
-0.03968404233455658,
0.01815447211265564,
-0.019688427448272705,
0.016257528215646744,
0.06000927463173866,
0.024518974125385284,
-0.007080171722918749,
-0.03257838636636734,
-0.03316871076822281,
-0.034697532653808594,
0.017378363758325577,
-0.028083311393857002,
0.013409384526312351,
0.014748205430805683,
-0.021839918568730354,
-0.004207089077681303,
-0.05741801857948303,
0.0004204092256259173,
-0.008083775639533997,
-0.023223863914608955,
0.0229598730802536,
0.018247833475470543,
0.03609699383378029,
-0.02066100761294365,
0.022234942764043808,
-0.010022527538239956,
-0.011739679612219334,
0.0014018603833392262,
0.020775089040398598,
-0.03595179691910744,
0.05133191868662834,
-0.003317426424473524,
-0.03583632409572601,
0.024292411282658577,
-0.01699759252369404,
0.0007868766551837325,
0.0086955102160573,
-0.0013538217172026634,
-0.048827122896909714,
-0.0004607283917721361,
-0.01686909981071949,
0.022720886394381523,
-0.02332676388323307,
-0.03817901760339737,
0.09853772073984146,
-0.01252047996968031,
-0.06542997062206268,
0.018201926723122597,
-0.038631610572338104,
-0.007849648594856262,
-0.04008285328745842,
0.012107624672353268,
0.016355037689208984,
-0.06194484978914261,
-0.01591193489730358,
0.059046827256679535,
-0.018291382119059563,
-0.007929760031402111,
-0.028914395719766617,
-0.055335383862257004,
0.00692253140732646,
-0.013253376819193363,
0.06073353812098503,
-0.008615054190158844,
0.012207439169287682,
0.09026341885328293,
0.047692351043224335,
0.011050015687942505,
-0.05003608390688896,
0.0006284349365159869,
-0.036735422909259796,
0.004202645272016525,
-0.009723291732370853,
0.020649582147598267,
0.0003674117033369839,
0.004347057081758976,
0.045837439596652985,
0.0499260239303112,
0.03353462368249893,
0.014007600955665112,
0.00749962916597724,
-0.03535003215074539,
0.007680476643145084,
-0.04602480307221413,
0.044342584908008575,
0.0277036614716053,
-0.03409617766737938,
-0.02161484584212303,
-0.03891254961490631,
0.02407514862716198,
0.030080610886216164,
-0.08794770389795303,
0.03125301003456116,
-0.004047020338475704,
-0.0015296575147658587,
0.0074434950947761536,
0.02241312712430954,
0.009434453211724758,
-0.01206101756542921,
-0.04605180025100708,
-0.012486543506383896,
0.04429532214999199,
-0.013093199580907822,
-0.010743048042058945,
0.034844860434532166,
0.08358419686555862,
-0.036701492965221405,
-0.022661419585347176,
-0.006763100624084473,
0.0059293108060956,
0.050410281866788864,
-0.04290309548377991,
-0.022019539028406143,
0.06361265480518341,
0.019262561574578285,
0.011220135726034641,
0.028278907760977745,
-0.03289021924138069,
-0.00831688940525055,
-0.08417972922325134,
0.03603542968630791,
-0.005120798014104366,
0.012610599398612976,
0.015681428834795952,
0.04649171978235245,
0.03815767541527748,
-0.020767198875546455,
0.0006415256066247821,
0.010449223220348358,
-0.030501501634716988,
0.020580291748046875,
-0.03864125907421112,
-0.03298671916127205,
-0.0070049818605184555,
0.027113094925880432,
-0.016160065308213234,
-0.00015349395107477903,
0.003578754374757409,
-0.010681623592972755,
-0.003343521151691675,
-0.07369891554117203,
-0.00487891398370266,
-0.009533149190247059,
-0.03473465517163277,
-0.0175284706056118,
0.003558967262506485,
0.05873321369290352,
-0.0011244973866268992,
0.05016595870256424,
0.002981045050546527,
-0.011446247808635235,
0.002257324056699872,
0.014551613479852676,
-0.005238056648522615,
0.028715070337057114,
-0.011675537563860416,
-0.003398499684408307,
0.017810780555009842,
0.019054925069212914,
0.017759663984179497,
0.008695939555764198,
0.01856139674782753,
-0.014708010479807854,
-0.013900455087423325,
-0.04759464040398598,
-0.02466597594320774,
-0.011541053652763367,
0.022834166884422302,
0.032366037368774414,
0.030839703977108,
0.012810062617063522,
0.0026012181770056486,
0.05908150225877762,
0.0009591542766429484,
0.010813609696924686,
0.04642952233552933,
-0.014407364651560783,
-0.01618187315762043,
-0.027102407068014145,
-0.012240791693329811,
0.02834150940179825,
-0.013916968367993832,
0.01993933506309986,
0.014592746272683144,
0.016648856922984123,
0.02722429297864437,
0.022537557408213615,
0.014544499106705189,
-0.03623048588633537,
0.006930766627192497,
-0.026142261922359467,
-0.02324046939611435,
-0.0046876235865056515,
-0.010295841842889786,
-0.01717105321586132,
0.02287975512444973,
0.04383555054664612,
0.04209262505173683,
-0.0051128556951880455,
-0.07955406606197357,
0.006707415450364351,
0.049342647194862366,
0.0229960847645998,
0.037419550120830536,
-0.035607460886240005,
-0.058608707040548325,
-0.031817853450775146,
0.0065664988942444324,
-0.05374385043978691,
0.028749164193868637,
-0.012630757875740528,
0.021305853500962257,
-0.027996430173516273,
-0.03550188988447189,
-0.000076483549491968,
-0.01481714192777872,
0.024636777117848396,
0.02877429500222206,
-0.023890715092420578,
-0.02279495820403099,
-0.003204751992598176,
-0.007718021050095558,
-0.023771706968545914,
0.01753057911992073,
0.010224791243672371,
0.0222023818641901,
-0.025466760620474815,
0.009172718971967697,
-0.04079606756567955,
-0.09533531963825226,
-0.014089416712522507,
0.052368633449077606,
0.0035088895820081234,
0.06480683386325836,
-0.04284665733575821,
-0.015290169045329094,
0.011482248082756996,
-0.022153466939926147,
-0.013380619697272778,
0.027699684724211693,
-0.03855076804757118,
0.042383983731269836,
0.03237927332520485,
-0.01902599073946476,
0.011371737346053123,
0.05411895737051964,
-0.028741981834173203,
-0.004508236888796091,
-0.006841147784143686,
0.04561778903007507,
-0.02942095696926117,
0.03094617649912834,
-0.0448775552213192,
-0.009678146801888943,
-0.05864330008625984,
0.035176780074834824,
-0.05252072215080261,
-0.021677808836102486,
0.002542866626754403,
-0.02111721783876419,
-0.019725775346159935,
0.05320553854107857,
0.023448094725608826,
-0.0004137653158977628,
-0.027252137660980225,
0.00328730302862823,
-0.029708290472626686,
0.03527325019240379,
0.030500441789627075,
-0.011961978860199451,
0.012661485932767391,
0.05207455903291702,
0.03062533773481846,
0.02705620601773262,
-0.041867271065711975,
-0.016630742698907852,
0.049273788928985596,
-0.03729259595274925,
0.047924283891916275,
-0.02584744617342949,
-0.008506985381245613,
0.03736110031604767,
-0.03511621430516243,
-0.030287865549325943,
0.002075321739539504,
-0.015543540008366108,
0.027216466143727303,
-0.057030800729990005,
0.01662748120725155,
0.009440193884074688,
0.0034431677777320147,
-0.07890331745147705,
-0.044089362025260925,
0.06664677709341049,
-0.0034268763847649097,
-0.047703929245471954,
-0.03555910661816597,
0.014568991027772427,
-0.0368625707924366,
-0.002664622850716114,
-0.03655976802110672,
0.051092203706502914,
-0.020575042814016342,
-0.07327435165643692,
-0.019564317539334297,
0.048859331756830215,
0.019754542037844658,
0.037753067910671234,
-0.008761714212596416,
-0.024336066097021103,
0.037329308688640594,
-0.0075115663930773735,
0.0013567802961915731,
0.049267400056123734,
-0.03230323642492294,
-0.018917137756943703,
-0.019175877794623375,
-0.0034318813122808933,
0.011106899008154869,
-0.024695776402950287,
-0.01128360815346241,
0.029182711616158485,
-0.0076762959361076355,
-0.00668694730848074,
-0.008419565856456757,
0.03824048861861229,
0.012179405428469181,
-0.0069768475368618965,
0.01296237949281931,
0.018409252166748047,
0.02676510438323021,
-0.015253978781402111,
-0.009504012763500214,
-0.03422170504927635,
-0.0019756483379751444,
0.025867028161883354,
0.023900849744677544,
0.00014406924310605973,
-0.00230786413885653,
0.04785778000950813,
0.029985785484313965,
0.04651110619306564,
-0.03648088127374649,
-0.023248719051480293,
-0.002894146367907524,
-0.008211862295866013,
-0.031744133681058884,
0.018930694088339806,
-0.0164762195199728,
0.007903797551989555,
0.04511071741580963,
-0.025293996557593346,
0.05667060986161232,
0.026194419711828232,
-0.029901443049311638,
-0.0010136773344129324,
-0.04242739826440811,
0.02906453236937523,
-0.009960120543837547,
0.00955707672983408,
0.039831165224313736,
-0.010734671726822853,
0.0009286256972700357,
0.016861114650964737,
0.052211832255125046,
0.015487289987504482,
0.020158816128969193,
0.04781565070152283,
-0.0011184457689523697,
0.03107147477567196,
-0.0005827246932312846,
-0.04959738254547119,
0.024451037868857384,
-0.029250547289848328,
-0.009689743630588055,
0.005895030684769154,
-0.02207573503255844,
0.03930993750691414,
0.005866471212357283,
-0.03244054690003395,
-0.03436506912112236,
0.018238313496112823,
-0.049633774906396866,
0.022692957893013954,
0.03199239820241928,
0.015550797805190086,
0.027641570195555687,
-0.05203259736299515,
0.05245206877589226,
-0.0011775637976825237,
-0.01887190155684948,
0.014829359948635101,
-0.07282309234142303,
-0.011509762145578861,
-0.08022986352443695,
-0.05059796944260597,
0.06293443590402603,
-0.03742159157991409,
-0.03701429441571236,
0.003255319083109498,
-0.014270474202930927,
0.0019891138654202223,
0.028350533917546272,
0.028142089024186134,
-0.03265047073364258,
0.05331609770655632,
0.012632726691663265,
-0.02502092346549034,
-0.039107922464609146,
-0.03820427507162094,
0.12426009029150009,
0.03953101113438606,
0.01569751463830471,
-0.041496697813272476,
0.01444875169545412,
0.03091631457209587,
0.04151018336415291,
-0.013001197949051857,
0.004189180675894022,
0.028780099004507065,
0.017901424318552017,
0.05210462957620621,
0.04528724029660225,
0.05985796079039574,
-0.03209839016199112,
0.021230077371001244,
-0.039094407111406326,
-0.0028064206708222628,
-0.02666749246418476,
0.002993607195094228,
-0.0014444288099184632,
-0.026771854609251022,
-0.03842051699757576,
0.016729136928915977,
0.017682213336229324,
0.03194141760468483,
-0.035090092569589615,
-0.04856244847178459,
0.02636215277016163,
0.034692056477069855,
-0.007082084193825722,
-0.007885608822107315,
0.028461184352636337,
-0.010745416395366192,
-0.025432845577597618,
0.011164621450006962,
0.023397421464323997,
-0.0251588374376297,
0.01846224069595337,
0.020670907571911812,
0.019680676981806755,
-0.03220086172223091,
0.0193590447306633,
-0.02134992554783821,
-0.06866946816444397,
-0.019804786890745163,
-0.03237733244895935,
0.016523586586117744,
0.008053800091147423,
0.006390189751982689,
-0.026286451146006584,
0.005093365907669067,
0.02477814257144928,
-0.018781617283821106,
-0.005712305195629597,
-0.016013916581869125,
-0.013579818420112133,
0.021263428032398224,
0.001392811187542975,
-0.03414681926369667,
-0.00001806729233067017,
-0.005557882599532604,
0.004542114678770304,
0.004303460940718651,
0.007572729606181383,
0.010393508709967136,
-0.020544258877635002,
0.00648330245167017,
-0.018867764621973038,
0.028721041977405548,
-0.015986092388629913,
-0.012183522805571556,
-0.06004955619573593,
0.014846233651041985,
-0.00033301967778243124,
0.004189513623714447,
0.04485718905925751,
-0.005774671211838722,
-0.007900280877947807,
-0.02698545716702938,
-0.015936940908432007,
0.023569708690047264,
-0.023754196241497993,
-0.01620563678443432,
0.01429523341357708,
0.0519719123840332,
0.027298135682940483,
0.033432312309741974,
0.020399531349539757,
0.054155733436346054,
-0.029871325939893723,
0.07192135602235794,
0.0194349754601717,
-0.04271281883120537,
-0.015888817608356476,
-0.007031202781945467,
0.0008655089768581092,
-0.00511113042011857,
0.011290345340967178,
0.03524616360664368,
0.01666206121444702,
-0.012383333407342434,
0.03608156740665436,
-0.004851356148719788,
0.01399815920740366,
-0.012135163880884647,
0.04287630319595337,
-0.028384514153003693,
-0.044384073466062546,
0.019460855051875114,
0.009314697235822678,
-0.0314432829618454,
-0.026811761781573296,
0.012363825924694538,
-0.0021975922863930464,
0.007909520529210567,
0.00404942873865366,
-0.03718375414609909,
0.021653451025485992,
-0.00790876243263483,
0.03865436092019081,
-0.03188026323914528,
-0.023791514337062836,
-0.06284887343645096,
-0.00717618502676487,
-0.044182077050209045,
-0.016344740986824036,
0.0005247053341008723,
0.030525680631399155,
-0.015285074710845947,
0.010131604969501495,
0.022745579481124878,
0.0076269847340881824,
-0.037843331694602966,
-0.012676249258220196,
0.035823967307806015,
-0.020271267741918564,
0.011792121455073357,
-0.026282576844096184,
-0.02998286858201027,
-0.025601105764508247,
-0.03945283964276314,
-0.08560426533222198,
0.04593592882156372,
-0.004318975377827883,
0.007356354966759682,
0.010788148269057274,
-0.012082492001354694,
0.020111005753278732,
0.04736555367708206,
-0.05945262685418129,
-0.05257482826709747,
0.03125768154859543,
-0.01719685271382332,
-0.0036323650274425745,
0.004877733998000622,
0.022544700652360916,
0.02284931391477585,
-0.04228750243782997,
0.015010696835815907,
0.02393460087478161,
0.013734354637563229,
-0.0057351430878043175,
-0.016653964295983315,
-0.02973589487373829,
0.024396751075983047,
-0.022846652194857597,
0.014372020028531551,
0.033273693174123764,
0.02366679720580578,
-0.05076390504837036,
0.0065481397323310375,
0.03261200711131096,
0.036103881895542145,
-0.07798325270414352,
-0.010684259235858917,
0.004309832118451595,
0.027378365397453308,
0.03806377202272415,
-0.029146289452910423,
0.017081957310438156,
0.024193374440073967,
-0.06908977031707764,
0.034711576998233795,
0.010751316323876381,
-0.002046239096671343,
-0.009607559069991112,
0.008952583186328411,
-0.017790233716368675,
0.05479339510202408,
0.054962098598480225,
0.008721732534468174,
0.0018336802022531629,
0.04235903546214104,
-0.03437509015202522,
-0.05203734338283539,
-0.01729847490787506,
-0.015408964827656746,
-0.007064815144985914,
-0.0010513311717659235,
0.05949989706277847,
0.008508427999913692,
-0.04239973425865173,
0.02670537494122982,
-0.0077524855732917786,
-0.022760964930057526,
-0.0023314831778407097,
0.02811499312520027,
0.0012439921265468001,
-0.012797128409147263,
0.0009787481976673007,
-0.05160775035619736,
-0.02930000238120556,
0.013112490065395832,
-0.012293361127376556,
0.049588873982429504,
0.016559040173888206,
-0.06015260890126228,
-0.004759335424751043,
-0.08106549829244614,
-0.038912247866392136,
0.0037278139498084784,
0.010610237717628479,
-0.027397625148296356,
-0.020347757264971733,
0.023635225370526314,
0.021805591881275177,
-0.007217543665319681,
-0.007907602936029434,
-0.0022703688591718674,
0.01956227980554104,
0.03850267827510834,
-0.03552030399441719,
0.0005330450949259102,
0.01134814228862524,
-0.018887639045715332,
-0.027520712465047836,
-0.0021664935629814863,
0.008667067624628544,
-0.02276083454489708,
-0.05055409297347069,
-0.016391513869166374,
-0.02082217112183571,
-0.007464097812771797,
-0.012655528262257576,
-0.02176067605614662,
0.015987252816557884,
0.03965553268790245,
0.02037419006228447,
-0.016255538910627365,
0.00806389283388853,
0.0030133796390146017,
-0.01524986419826746,
-0.0856594443321228,
0.02387179061770439,
-0.009259486570954323,
0.0017094968352466822,
-0.05221325904130936,
-0.019470902159810066,
-0.027487460523843765,
0.045403867959976196,
0.06671980023384094,
0.050592269748449326,
-0.015332638286054134,
0.051702238619327545,
-0.009421289898455143,
0.02343510091304779,
-0.03750402107834816,
0.009629130363464355,
0.006625629495829344,
0.021277975291013718,
0.023294704034924507,
-0.044100452214479446,
-0.007238970138132572,
0.01440128032118082,
0.034526169300079346,
-0.04651986435055733,
0.022774547338485718,
-0.0017947963206097484,
0.0013965031830593944,
0.03364243730902672,
0.02688288874924183,
-0.02879536710679531,
0.0543423630297184,
-0.0016162324463948607,
-0.0007740345317870378,
0.010211191140115261,
-0.017755625769495964,
-0.04243827611207962,
0.006361310835927725,
-0.013610280118882656,
-0.0435296855866909,
0.004623676184564829,
-0.02683330327272415,
0.027868125587701797,
-0.035577595233917236,
-0.008014529943466187,
0.03205391764640808,
-0.04192814603447914,
0.037808023393154144,
0.05901264399290085,
0.042191725224256516,
0.024634359404444695,
0.012546909041702747,
0.013995649293065071,
-0.009284013882279396,
-0.026568913832306862,
0.0244604479521513,
0.034303467720746994,
0.026259560137987137,
0.03587186336517334,
0.005412680096924305,
-0.012930383905768394,
0.004439342301338911,
0.012278137728571892,
0.03759872168302536,
0.050998490303754807,
0.007747369818389416,
-0.005170354153960943,
0.01564047485589981,
0.033627402037382126,
0.0024603791534900665,
0.062305886298418045,
0.0033382195979356766,
0.03293084353208542,
0.017789138481020927,
0.02744997665286064,
-0.050077226012945175,
-0.010784492827951908,
0.00586153008043766,
0.016921386122703552,
0.017143072560429573,
0.006536372471600771,
-0.03480952978134155,
-0.02511487528681755,
-0.0031628671567887068,
-0.009632013738155365,
0.01835443079471588,
-0.04197068139910698,
0.006407119799405336,
-0.015448924154043198,
0.03273148834705353,
0.03798716142773628,
0.0025296853855252266,
-0.00030787161085754633,
-0.019099785014986992,
-0.0008034036145545542,
0.03753324970602989,
0.017900098115205765,
-0.0234636589884758,
-0.036452192813158035,
-0.04297691583633423,
0.042334455996751785,
-0.07037776708602905,
-0.0008388454443775117,
-0.017056653276085854,
0.052050672471523285,
-0.02036377228796482,
-0.00818969402462244
] |
<p><img src="http://i.stack.imgur.com/in7Xf.jpg" alt="enter image description here"></p>
<p>A sends out a series of flashes of light to B, where the interval between flashes is denoted by T according to A's clock. Then it is plausible to assume that the intervals of reception by B's clock are proportional to T, say KT. (K is the K-factor)</p>
<p>I dont understand this at all. How is it plausible to assume the proportionality of K?</p>
<p>Source : Ray D'Inverno's Relativity Book.</p> | 2,905 | [
-0.015161380171775818,
-0.025747206062078476,
0.007019429467618465,
-0.04031350091099739,
0.05821789801120758,
-0.015614842064678669,
-0.0027031428180634975,
-0.00625016912817955,
0.00775133678689599,
0.015070217661559582,
0.04222383722662926,
0.027780629694461823,
0.024344468489289284,
0.006190629210323095,
0.01953691802918911,
0.005483389366418123,
0.02434323914349079,
-0.025271249935030937,
-0.02100895345211029,
-0.05641652271151543,
0.02984173223376274,
0.022571196779608727,
0.005158105865120888,
-0.01664413884282112,
-0.05096658691763878,
0.03432546555995941,
0.034544456750154495,
0.005391890648752451,
0.031848467886447906,
0.028069905936717987,
0.014804289676249027,
-0.024319682270288467,
0.014201024547219276,
0.02754990942776203,
0.032143961638212204,
0.024819552898406982,
-0.03049449622631073,
-0.013525190763175488,
0.017137600108981133,
0.013526526279747486,
-0.022362112998962402,
0.008913117460906506,
0.0040582469664514065,
0.05709974095225334,
-0.028006622567772865,
0.015700673684477806,
0.012467484921216965,
-0.04084241762757301,
0.021723030135035515,
-0.03305446356534958,
0.051853425800800323,
0.004793681204319,
0.03383545204997063,
0.02273704670369625,
-0.05525097995996475,
0.017091931775212288,
0.11358222365379333,
0.08310248702764511,
-0.01533952634781599,
-0.04127303138375282,
-0.003515708725899458,
-0.026921382173895836,
-0.042911410331726074,
0.01099751889705658,
0.02132529765367508,
0.019068662077188492,
-0.02721400372684002,
-0.019045528024435043,
0.009593876078724861,
-0.04648576304316521,
0.025058947503566742,
-0.011675369925796986,
0.06162498518824577,
-0.03256693854928017,
-0.033134542405605316,
-0.05624211207032204,
0.01950158178806305,
0.002966337138786912,
0.03956998139619827,
0.04912629351019859,
-0.007643287070095539,
-0.008617463521659374,
0.017459411174058914,
0.021694030612707138,
0.021514536812901497,
-0.017490606755018234,
0.037323299795389175,
0.006111594848334789,
-0.0023347127716988325,
0.019194476306438446,
-0.06747353076934814,
0.05131252482533455,
0.01983187533915043,
-0.010179242119193077,
-0.020921992138028145,
0.0514729879796505,
0.03308500349521637,
0.03695216029882431,
-0.00685458816587925,
-0.031166795641183853,
-0.0018132837722077966,
-0.0006694776238873601,
0.018760349601507187,
0.061090003699064255,
0.0009752415935508907,
-0.016534671187400818,
-0.02221325784921646,
0.039053305983543396,
0.0009673683089204133,
0.00559749873355031,
-0.06269136816263199,
0.003087228164076805,
-0.001983226975426078,
0.05481009930372238,
0.0284828282892704,
-0.04855017364025116,
-0.020195672288537025,
-0.003945722710341215,
0.07818470150232315,
0.02955569326877594,
0.023668350651860237,
-0.032976169139146805,
0.02896774746477604,
0.003333015600219369,
-0.024721013382077217,
0.028199533000588417,
0.013047224842011929,
0.0006119849276728928,
0.006865188479423523,
0.053870830684900284,
-0.017396027222275734,
-0.02141995169222355,
0.01629151776432991,
0.03171052783727646,
0.007969537749886513,
-0.0478949248790741,
-0.10305753350257874,
-0.059672288596630096,
0.050950437784194946,
-0.002750011393800378,
-0.037098485976457596,
-0.09380827099084854,
0.04216107726097107,
0.02526346780359745,
0.0853973999619484,
-0.011138776317238808,
-0.00240340456366539,
-0.03360018506646156,
0.02774158865213394,
0.029397841542959213,
-0.03344494849443436,
-0.02910720929503441,
0.006673830095678568,
-0.043001044541597366,
0.005140500143170357,
-0.06892718374729156,
-0.018041521310806274,
0.027246003970503807,
0.007792325224727392,
-0.013424097560346127,
0.0608181469142437,
0.008569146506488323,
-0.017844272777438164,
0.04500362649559975,
0.01618902198970318,
-0.03380455821752548,
0.09571757167577744,
0.016260627657175064,
-0.013178026303648949,
0.03043331950902939,
0.012626354582607746,
0.02921498566865921,
-0.0036905822344124317,
0.030495796352624893,
0.011207031086087227,
-0.05136136710643768,
0.0028042190242558718,
0.029797418043017387,
-0.00895455852150917,
-0.0032898872159421444,
-0.05159027501940727,
-0.03640802204608917,
-0.017105618491768837,
0.005147947929799557,
0.018561363220214844,
0.03532879054546356,
-0.01689363270998001,
0.04922080785036087,
0.01492087822407484,
-0.013319171965122223,
0.0007424541399814188,
-0.07250159233808517,
-0.0082684475928545,
0.017133696004748344,
-0.029435930773615837,
-0.0034570349380373955,
-0.011918873526155949,
0.016179701313376427,
-0.03384208679199219,
-0.033011820167303085,
0.0017644403269514441,
-0.01277413871139288,
0.00017000165826175362,
-0.010197127237915993,
0.035584285855293274,
0.07572422176599503,
0.04242901876568794,
-0.0070063392631709576,
0.009617127478122711,
-0.008347922936081886,
-0.01425844058394432,
0.013105105608701706,
-0.009005999192595482,
0.018216008320450783,
-0.008501498028635979,
0.0005220792372711003,
0.0055944356136024,
0.022355763241648674,
0.006460326258093119,
0.02162005938589573,
-0.06473518908023834,
0.04921196773648262,
0.0469413660466671,
-0.002658914541825652,
-0.008271086029708385,
0.04447520896792412,
0.020103929564356804,
0.032001055777072906,
0.0066449339501559734,
-0.05319194495677948,
-0.026085127145051956,
0.002515871077775955,
0.023022349923849106,
0.008450900204479694,
0.0020665235351771116,
0.01415550708770752,
0.005669890437275171,
0.034958768635988235,
0.006901106331497431,
0.03424656391143799,
-0.0010476058814674616,
-0.035184282809495926,
-0.0041513568721711636,
-0.01367812231183052,
-0.014368539676070213,
-0.0046487171202898026,
0.03767476975917816,
-0.007370261009782553,
-0.02714650146663189,
-0.009585180319845676,
-0.009652960114181042,
-0.004481116775423288,
-0.011692157946527004,
0.040754303336143494,
0.01239751186221838,
-0.014866713434457779,
0.04602953791618347,
-0.010830438695847988,
0.03355321288108826,
0.03667905926704407,
-0.02224770374596119,
0.033178795129060745,
-0.004248522687703371,
-0.03042149916291237,
-0.006985370069742203,
-0.005130029749125242,
-0.024351641535758972,
-0.052899908274412155,
0.016086310148239136,
-0.01937813311815262,
-0.0015578053425997496,
-0.025291990488767624,
-0.023939387872815132,
-0.022795699536800385,
-0.057062480598688126,
0.011334056966006756,
0.02121264487504959,
0.04871208965778351,
-0.03157607838511467,
0.010127643123269081,
-0.0030799515079706907,
-0.012745575048029423,
-0.015262720175087452,
-0.005554540082812309,
-0.0246356762945652,
0.022536955773830414,
0.020574193447828293,
-0.05689024552702904,
0.027568573132157326,
-0.03759137913584709,
0.0363188236951828,
0.025502484291791916,
-0.026087574660778046,
-0.045473795384168625,
-0.018545007333159447,
-0.016482550650835037,
-0.020669136196374893,
-0.03558892384171486,
0.009703565388917923,
0.05260809510946274,
0.015070159919559956,
-0.042352113872766495,
0.001015869784168899,
-0.060830071568489075,
-0.017676258459687233,
-0.023362889885902405,
-0.018503395840525627,
0.0023383034858852625,
-0.038161396980285645,
0.025993557646870613,
-0.02010234259068966,
-0.06091129779815674,
-0.03260041028261185,
-0.040284983813762665,
-0.06365616619586945,
0.02699156291782856,
0.016420800238847733,
0.09189293533563614,
0.02586350403726101,
-0.05050929635763168,
0.07932102680206299,
0.03743636980652809,
0.006092780269682407,
-0.03492648899555206,
-0.04261840879917145,
0.0007169219315983355,
-0.0233596358448267,
0.014276472851634026,
0.05135742202401161,
-0.008349845185875893,
0.039223454892635345,
0.03473035246133804,
-0.0033969434443861246,
0.0482814647257328,
0.001100007677450776,
-0.004186359699815512,
-0.02330073155462742,
-0.015453048050403595,
0.015046849846839905,
0.04372090473771095,
0.04490227624773979,
-0.056028712540864944,
-0.009763938374817371,
-0.002561466069892049,
0.01203160360455513,
0.028260447084903717,
-0.05422527343034744,
0.0012158360332250595,
-0.0014610964572057128,
0.000672473746817559,
-0.053035635501146317,
0.03396831080317497,
0.0026277992874383926,
0.007584484294056892,
0.010782294906675816,
-0.0005117252003401518,
0.03071286343038082,
-0.021542059257626534,
0.0038875574246048927,
0.04943440482020378,
0.02999143861234188,
-0.011082314886152744,
-0.05497578904032707,
-0.008361033163964748,
-0.012241560034453869,
0.007737305946648121,
-0.04607655480504036,
-0.003484314074739814,
0.06406864523887634,
0.026785405352711678,
0.029264183714985847,
-0.0031785699538886547,
-0.030960001051425934,
-0.024666307494044304,
-0.07512969523668289,
-0.03640788048505783,
-0.008165467530488968,
0.04494105279445648,
-0.011633616872131824,
0.05753862485289574,
0.031399115920066833,
0.0036582667380571365,
-0.0012007532641291618,
-0.04445558041334152,
-0.059800297021865845,
0.01822664774954319,
-0.04438574239611626,
-0.05373721942305565,
-0.013483705930411816,
-0.03140396624803543,
-0.010226234793663025,
-0.04676945134997368,
-0.04344520717859268,
0.009969932027161121,
0.017298920080065727,
-0.06072590872645378,
-0.018242929130792618,
-0.0013836727011948824,
-0.06237519532442093,
-0.03511893004179001,
-0.023406982421875,
0.06310927122831345,
-0.015513534657657146,
0.033458810299634933,
0.060596220195293427,
-0.01907104253768921,
-0.011451692320406437,
0.005370498634874821,
-0.01632777228951454,
0.04055856913328171,
0.027809273451566696,
0.04120099917054176,
-0.010191701352596283,
-0.032789506018161774,
0.02591755799949169,
0.043360427021980286,
0.060211293399333954,
0.04446830973029137,
-0.016127990558743477,
-0.05065615847706795,
-0.023725371807813644,
-0.03142385557293892,
0.000993570196442306,
0.07294143736362457,
-0.00722709484398365,
-0.007227167021483183,
0.04116145893931389,
0.04001931473612785,
0.03092663548886776,
0.01421708706766367,
0.0058340695686638355,
-0.013852878473699093,
-0.0033317245543003082,
-0.02397778071463108,
-0.009524867869913578,
-0.01077432930469513,
0.015512526966631413,
0.024932926520705223,
-0.01860683225095272,
0.03231872245669365,
0.008871279656887054,
0.023225273936986923,
0.013248495757579803,
0.009732763282954693,
0.026785563677549362,
-0.010889104567468166,
-0.0013032251736149192,
0.006742291618138552,
0.013044415973126888,
0.0020740381442010403,
0.027491241693496704,
0.04103930667042732,
0.0068632569164037704,
-0.023617522791028023,
-0.09314537793397903,
-0.004321020096540451,
0.005982608534395695,
0.02825172059237957,
-0.015371323563158512,
-0.02426653541624546,
-0.06345435976982117,
0.01047012023627758,
0.033855658024549484,
-0.03898497670888901,
0.05345122143626213,
0.029195085167884827,
0.005546615459024906,
-0.033388227224349976,
-0.03013784810900688,
0.021228002384305,
0.04976944997906685,
0.005533882882446051,
0.010378814302384853,
0.008003833703696728,
0.005267621949315071,
0.01888936199247837,
-0.035439737141132355,
0.06995889544487,
0.02732538804411888,
0.0029020761139690876,
-0.046033572405576706,
0.023049866780638695,
0.009292633272707462,
-0.030492955818772316,
-0.06738804280757904,
0.01957595907151699,
0.013108177110552788,
-0.027033617720007896,
0.06859107315540314,
-0.037728212773799896,
-0.0059770578518509865,
0.047671232372522354,
0.017429068684577942,
-0.025008540600538254,
0.0041468460112810135,
-0.05202745273709297,
0.03298250958323479,
0.0102800028398633,
0.0031282054260373116,
0.04040062054991722,
0.02255231700837612,
-0.024456467479467392,
-0.007323171477764845,
0.007352080196142197,
0.01376837957650423,
-0.02277749963104725,
0.04320545122027397,
-0.005777432583272457,
0.010265513323247433,
-0.010579032823443413,
0.01841752417385578,
-0.00016887464153114706,
0.013654008507728577,
0.008465409278869629,
-0.03001592494547367,
-0.01641412079334259,
0.011094901710748672,
-0.005447078961879015,
0.04895705357193947,
-0.026960883289575577,
0.008082468062639236,
0.020038357004523277,
-0.05006363242864609,
0.025721590965986252,
-0.022579316049814224,
0.010495128110051155,
0.018991690129041672,
0.019713081419467926,
-0.004489305429160595,
-0.027851831167936325,
-0.017801547423005104,
0.028840776532888412,
-0.025790497660636902,
0.025107504799962044,
-0.029607506468892097,
-0.01734057627618313,
0.043064482510089874,
0.006094770506024361,
-0.030917396768927574,
-0.01800835132598877,
-0.015474516898393631,
0.08814720064401627,
-0.045460090041160583,
0.030100511386990547,
0.013460819609463215,
0.00505415815860033,
-0.09019361436367035,
-0.005282310768961906,
0.06093835085630417,
-0.0070616574957966805,
-0.03635036200284958,
-0.029479697346687317,
0.0033215670846402645,
-0.049191057682037354,
-0.03545470908284187,
0.011625031940639019,
0.055765360593795776,
-0.020861957222223282,
-0.04276588559150696,
-0.020610665902495384,
0.009124260395765305,
0.01860210672020912,
0.003395614679902792,
-0.009959232993423939,
-0.0002971929498016834,
-0.0206952802836895,
-0.025502584874629974,
-0.02652045153081417,
0.047445148229599,
-0.025955719873309135,
-0.024267811328172684,
-0.01627056673169136,
0.022357013076543808,
0.0029099739622324705,
-0.020876925438642502,
-0.015270354226231575,
0.04242038354277611,
0.004870209842920303,
0.0009793017525225878,
-0.034704048186540604,
0.0007929911371320486,
0.02845623902976513,
0.02255803719162941,
0.002916573779657483,
-0.0037984950467944145,
-0.02126932516694069,
0.0026798537001013756,
0.009956011548638344,
0.018564410507678986,
0.021255575120449066,
-0.027716917917132378,
0.06270062923431396,
-0.014094420708715916,
-0.014121823944151402,
0.029751528054475784,
-0.015031141228973866,
0.014904352836310863,
-0.010583373717963696,
-0.012794776819646358,
0.01567140221595764,
-0.020083410665392876,
-0.029835622757673264,
-0.0048924656584858894,
-0.05296081677079201,
-0.027589980512857437,
0.08009180426597595,
-0.045705124735832214,
0.04912397265434265,
0.005501405335962772,
-0.027344664558768272,
0.008624925278127193,
-0.004583686590194702,
-0.02322438918054104,
-0.022717371582984924,
0.010852273553609848,
0.018993942067027092,
-0.05385999381542206,
-0.023631002753973007,
0.04432210698723793,
0.056911516934633255,
-0.0011454093037173152,
0.02880849875509739,
0.03519359230995178,
0.04524844512343407,
0.017651300877332687,
0.04131562262773514,
-0.0665397047996521,
0.02234138362109661,
-0.023162145167589188,
0.010486782528460026,
0.0075951977632939816,
0.012203427962958813,
0.05263533443212509,
0.00592352170497179,
-0.009178871288895607,
-0.05684622749686241,
-0.024141719564795494,
-0.03362337499856949,
-0.019043942913413048,
0.00845372024923563,
0.019865931943058968,
0.024932025000452995,
-0.0040919785387814045,
0.04782181978225708,
0.03182455152273178,
0.010625742375850677,
-0.044086117297410965,
-0.05524829402565956,
-0.03979816287755966,
-0.043783433735370636,
-0.04439867287874222,
0.04423799365758896,
-0.017911799252033234,
-0.04349120333790779,
0.006116134580224752,
-0.03147614002227783,
0.01673056185245514,
0.017474070191383362,
0.03657497093081474,
-0.036043327301740646,
0.08176807314157486,
0.007023986428976059,
-0.02146030031144619,
-0.03551007807254791,
0.018436377868056297,
0.11749927699565887,
0.03769221901893616,
0.01393370795994997,
-0.050522394478321075,
0.05028296634554863,
-0.014898666180670261,
0.024358510971069336,
-0.05782484635710716,
0.031597405672073364,
-0.024093005806207657,
0.0009660060168243945,
0.03356580808758736,
0.029698126018047333,
0.02966955304145813,
-0.0191185362637043,
0.036013465374708176,
-0.011492718942463398,
-0.02424648031592369,
0.01501381490379572,
-0.004331083036959171,
-0.003540716366842389,
-0.020302949473261833,
-0.016562918201088905,
0.028076065704226494,
-0.04750481992959976,
0.016805194318294525,
-0.0188568327575922,
0.008036877028644085,
0.0032486978452652693,
0.016728272661566734,
-0.06896694004535675,
0.04585416987538338,
0.05302782729268074,
-0.032930824905633926,
-0.033245962113142014,
0.010735527612268925,
0.026581311598420143,
-0.0024711827281862497,
0.03117216005921364,
0.01394521165639162,
0.01667500101029873,
-0.003496624529361725,
0.038000114262104034,
0.017132705077528954,
-0.02020810730755329,
0.02312147244811058,
-0.034217510372400284,
0.041581302881240845,
-0.019627267494797707,
0.01618717610836029,
0.005447228439152241,
0.003815879113972187,
-0.0032002103980630636,
-0.049615126103162766,
-0.0025058782193809748,
0.0006315363571047783,
-0.024970436468720436,
-0.00842783972620964,
-0.02034432254731655,
-0.010635496117174625,
0.013997096568346024,
-0.006563683971762657,
0.021665096282958984,
0.029278798028826714,
0.030891891568899155,
-0.0012419697595760226,
-0.01043750625103712,
0.014630946330726147,
-0.018305491656064987,
-0.018585409969091415,
-0.016801541671156883,
-0.006595562677830458,
-0.054575078189373016,
-0.016483012586832047,
0.02054867520928383,
0.03234240412712097,
0.012195207178592682,
0.006292553152889013,
-0.0025375434197485447,
-0.024830356240272522,
-0.035740021616220474,
0.012267310172319412,
-0.0029340172186493874,
-0.03919389098882675,
-0.007440866436809301,
0.00855359435081482,
0.02769361063838005,
0.021463647484779358,
-0.02280460298061371,
0.010890805162489414,
-0.006945021916180849,
0.007521682418882847,
0.013906306587159634,
-0.0650545284152031,
0.01794842816889286,
-0.021767964586615562,
0.005084701348096132,
-0.03064584545791149,
-0.001147257862612605,
0.04459862411022186,
0.045224521309137344,
0.014072463847696781,
0.040466345846652985,
-0.0009716039639897645,
-0.053139738738536835,
-0.0028404057957232,
0.01422291062772274,
-0.025864047929644585,
0.01567303016781807,
0.01193629577755928,
0.024143733084201813,
-0.0119595592841506,
-0.036089371889829636,
0.02288712188601494,
0.011468106880784035,
0.002968414453789592,
-0.017690613865852356,
-0.016461307182908058,
-0.02131771855056286,
-0.014626890420913696,
-0.0015611795242875814,
-0.032820288091897964,
0.009441684931516647,
-0.0016864077188074589,
-0.0025164468679577112,
-0.05264344811439514,
0.013230303302407265,
0.0037907364312559366,
0.057716771960258484,
-0.01998298056423664,
-0.008437211625277996,
0.01415745448321104,
0.020258547738194466,
0.0035509502049535513,
-0.015723181888461113,
0.016857530921697617,
-0.038598041981458664,
0.02903437241911888,
-0.0480022057890892,
-0.03821958974003792,
0.025569729506969452,
-0.060851991176605225,
-0.02839263528585434,
0.027382487431168556,
-0.015954090282320976,
0.009047036990523338,
0.011759109795093536,
0.000047198533138725907,
0.0002743121876846999,
0.07528367638587952,
-0.02915729396045208,
0.009236852638423443,
0.02878541685640812,
-0.033044468611478806,
0.015833621844649315,
-0.03438973054289818,
0.001199956750497222,
0.009175486862659454,
0.0034326203167438507,
0.017131663858890533,
0.040370430797338486,
-0.04467090591788292,
0.037914663553237915,
-0.006962394807487726,
-0.0015130984829738736,
-0.021689312532544136,
0.01738322339951992,
-0.004777770023792982,
0.02338402532041073,
0.03803374245762825,
-0.031638551503419876,
0.014355265535414219,
-0.02629612758755684,
0.0007116287015378475,
-0.08167939633131027,
0.022691089659929276,
-0.0009721545502543449,
0.01629113033413887,
0.04156821221113205,
-0.02343430183827877,
-0.0350986048579216,
0.022662853822112083,
-0.06438475847244263,
0.029058897867798805,
0.009993009269237518,
-0.027468789368867874,
-0.04067108780145645,
0.020847326144576073,
-0.00335851963609457,
0.02279864437878132,
0.04010411351919174,
-0.012362509034574032,
0.010695640929043293,
0.00045409915037453175,
0.005952460691332817,
-0.03636439889669418,
0.002861485118046403,
0.018898438662290573,
0.00804754439741373,
0.006067783106118441,
0.08627144247293472,
0.0026653960812836885,
0.0017880733357742429,
0.044099148362874985,
0.031522419303655624,
0.03056192211806774,
-0.014287249185144901,
0.01840980537235737,
0.03208984434604645,
0.023778295144438744,
-0.0013099589850753546,
-0.032828256487846375,
0.019876305013895035,
0.00045727231190539896,
0.013517145998775959,
0.01463374588638544,
-0.015822067856788635,
-0.019070854410529137,
0.02678767219185829,
-0.06561533361673355,
-0.05258319899439812,
0.011330708861351013,
0.015877751633524895,
-0.010639701038599014,
0.054692357778549194,
0.05729752779006958,
0.005288632120937109,
-0.03941866755485535,
-0.005291813984513283,
-0.07146433740854263,
0.01859128475189209,
0.02614559605717659,
-0.006368468515574932,
-0.013735268265008926,
-0.014334998093545437,
-0.04860581457614899,
-0.012776127085089684,
0.0051483032293617725,
0.015799179673194885,
0.011745342053472996,
-0.046449244022369385,
-0.011808741837739944,
-0.014379163272678852,
0.0272955484688282,
0.00970972329378128,
-0.04349066689610481,
-0.04828786849975586,
0.014843003824353218,
-0.0005405352567322552,
-0.0008770305430516601,
-0.0036912579089403152,
-0.011038953438401222,
-0.0344591923058033,
-0.07868362963199615,
0.03818263113498688,
-0.008960493840277195,
0.015052770264446735,
-0.07598056644201279,
-0.03403489664196968,
-0.01867738552391529,
0.02260376699268818,
0.054283954203128815,
0.029870998114347458,
-0.027518853545188904,
0.031546108424663544,
-0.010480662807822227,
0.016317151486873627,
-0.06733375787734985,
0.0173601396381855,
0.01137771736830473,
-0.0433671697974205,
0.00989290326833725,
-0.009789596311748028,
-0.017754171043634415,
-0.008121450431644917,
0.003147274721413851,
-0.00403258902952075,
0.06861606985330582,
0.024483947083353996,
-0.037689290940761566,
0.026703407987952232,
0.008705628104507923,
-0.0016991480952128768,
0.04999871179461479,
0.03186417371034622,
0.02674882300198078,
0.030139829963445663,
-0.0019769964274019003,
-0.06043457239866257,
0.031047677621245384,
-0.039125990122556686,
0.03788939490914345,
-0.0477888286113739,
-0.01085547637194395,
0.02648875117301941,
-0.040268052369356155,
-0.018400028347969055,
0.06538751721382141,
-0.0347910150885582,
0.0005264575011096895,
0.046992458403110504,
-0.022225085645914078,
0.0478791818022728,
0.0004807795339729637,
0.04382892698049545,
0.003094505053013563,
-0.016551638022065163,
-0.0013517934130504727,
0.029026146978139877,
0.01104158628731966,
-0.021602481603622437,
-0.01102838572114706,
0.03436422348022461,
0.003035278059542179,
0.016800478100776672,
-0.012474171817302704,
0.005842362064868212,
-0.005769216921180487,
-0.011108760721981525,
0.012293746694922447,
-0.003256821073591709,
0.0017448008293285966,
0.034126173704862595,
0.0010932112345471978,
0.05542367696762085,
-0.040229447185993195,
0.014233504422008991,
-0.03008827567100525,
0.009357164613902569,
0.0062602306716144085,
0.05152962729334831,
0.03553815186023712,
0.006338916253298521,
-0.03375043720006943,
0.00950195174664259,
0.015962189063429832,
-0.020644206553697586,
0.028329461812973022,
-0.03503691777586937,
-0.0129513805732131,
-0.018303997814655304,
-0.028821220621466637,
-0.00008919892570702359,
0.004583335947245359,
0.0010306976037099957,
-0.023838885128498077,
0.01664116606116295,
0.024350546300411224,
-0.004635692108422518,
-0.030457284301519394,
-0.009761021472513676,
-0.013188490644097328,
0.05675211176276207,
-0.050796028226614,
0.020763948559761047,
-0.03536824509501457,
0.0110634109005332,
0.016855942085385323,
-0.019809721037745476
] |
<p>Given that in the ballistic regime a particle (electron) can move freely without scattering (there are no impurities ), is the resistance through a ballistic sample zero?</p> | 2,906 | [
0.0042141457088291645,
-0.02778465859591961,
0.02892165817320347,
-0.05674833059310913,
0.02698226273059845,
-0.0036711201537400484,
-0.00609270203858614,
0.004859908949583769,
-0.01937316730618477,
-0.03146999701857567,
0.03438104689121246,
0.0058458829298615456,
0.03780894726514816,
0.002001818036660552,
0.006469886749982834,
0.01864037662744522,
-0.03076370432972908,
0.021550454199314117,
-0.00932950247079134,
-0.038344524800777435,
0.016981106251478195,
0.022967902943491936,
0.05198146030306816,
0.007334708236157894,
-0.02510187402367592,
0.006783884949982166,
0.00014192445087246597,
-0.04854071885347366,
0.008963343687355518,
0.02285706251859665,
-0.01833932474255562,
0.02937385067343712,
0.007364298216998577,
0.013177383691072464,
0.01776203326880932,
0.0019529334967955947,
-0.04602517932653427,
-0.032314836978912354,
-0.013529859483242035,
0.0002600389998406172,
-0.03463594615459442,
-0.03058004379272461,
0.018226725980639458,
0.06405649334192276,
0.0010449494002386928,
-0.027837198227643967,
0.0448281392455101,
-0.03102588839828968,
0.015471335500478745,
-0.05998837947845459,
0.027944426983594894,
-0.04722775146365166,
0.04916298761963844,
0.005292967427521944,
0.023711200803518295,
-0.02552027255296707,
0.0968603640794754,
0.07515782862901688,
-0.03860617056488991,
0.01013178750872612,
-0.01834195666015148,
-0.05452843755483627,
0.015894543379545212,
-0.02314147725701332,
-0.034559231251478195,
0.03190598264336586,
-0.004522119648754597,
-0.07975685596466064,
0.01931273564696312,
-0.012483230791985989,
-0.009148837067186832,
0.020015649497509003,
0.0080241234973073,
-0.006213964428752661,
0.02040313184261322,
0.003924884367734194,
0.0412483736872673,
0.02215580642223358,
0.015237697400152683,
0.05673784390091896,
-0.03059515915811062,
-0.02209240384399891,
0.03413909301161766,
0.030445460230112076,
0.002934735734015703,
-0.0626644492149353,
0.052019257098436356,
-0.01429975125938654,
0.020014751702547073,
0.004469271749258041,
-0.01854691468179226,
0.000794256804510951,
0.016387468203902245,
0.001330956001766026,
-0.05457407981157303,
0.01180809736251831,
-0.013085177168250084,
0.07233330607414246,
-0.02927812933921814,
-0.05734299123287201,
0.010793803259730339,
-0.0033595345448702574,
0.0698259249329567,
0.06944993138313293,
-0.0005342169897630811,
0.003960185218602419,
-0.009991366416215897,
0.020084066316485405,
-0.025666777044534683,
-0.0054145026952028275,
-0.05581750348210335,
0.038350384682416916,
0.016517452895641327,
-0.009162039496004581,
0.02233610674738884,
-0.0075899348594248295,
0.00373490690253675,
-0.036862846463918686,
0.027047190815210342,
0.035734131932258606,
0.027848562225699425,
-0.008409624919295311,
0.013549115508794785,
0.0074712494388222694,
-0.05715681239962578,
0.04990793764591217,
0.014733638614416122,
-0.010992157272994518,
-0.007409760728478432,
0.015566712245345116,
0.0019433191046118736,
-0.007070215418934822,
0.027869874611496925,
-0.02078423649072647,
0.07068416476249695,
-0.017114873975515366,
-0.07351859658956528,
-0.08764035999774933,
0.04999574273824692,
0.007722475565969944,
-0.020930781960487366,
-0.07307573407888412,
0.004466257058084011,
0.024185119196772575,
0.06702367216348648,
0.003107429016381502,
0.022347740828990936,
-0.013143904507160187,
-0.0005644304910674691,
0.018902774900197983,
-0.01591476984322071,
-0.044472191482782364,
0.01385454647243023,
-0.01098338421434164,
0.040238942950963974,
-0.07211960107088089,
0.04116344079375267,
0.02129977196455002,
0.007028872147202492,
-0.03423984721302986,
0.024204889312386513,
-0.04084964469075203,
0.003450727090239525,
-0.0015930962981656194,
-0.021400820463895798,
-0.03614584356546402,
0.04589882120490074,
0.025821836665272713,
0.005201038904488087,
0.0067804185673594475,
0.05968604236841202,
0.05089893937110901,
0.017100531607866287,
0.012539775110781193,
0.035135071724653244,
-0.05508871003985405,
-0.020719505846500397,
-0.004877618048340082,
-0.019883187487721443,
0.008064690977334976,
-0.023241253569722176,
-0.018147161230444908,
0.019794099032878876,
0.030863791704177856,
0.01789618283510208,
0.004384782165288925,
0.017938336357474327,
-0.0025347708724439144,
0.01130269467830658,
0.001889439532533288,
-0.005942073184996843,
-0.0587124228477478,
0.02907237596809864,
0.042024578899145126,
-0.017105979844927788,
0.04779043048620224,
0.01144972164183855,
0.00023742545454297215,
-0.03353431075811386,
-0.018714722245931625,
-0.015588893555104733,
0.0054977526888251305,
-0.02645675465464592,
-0.0481809638440609,
0.015037663280963898,
0.030253170058131218,
0.03730051591992378,
-0.002746144076809287,
0.025970129296183586,
0.01389729417860508,
-0.030268162488937378,
-0.024566039443016052,
-0.012863394804298878,
0.06648512184619904,
0.015273906290531158,
-0.0021323994733393192,
0.023682767525315285,
-0.02315688692033291,
-0.010829273611307144,
0.06640926748514175,
-0.04160350561141968,
0.07891705632209778,
0.05185585469007492,
0.021068766713142395,
-0.07074170559644699,
0.03132069483399391,
0.012821467593312263,
-0.0223112590610981,
-0.003138202941045165,
-0.003235836047679186,
-0.05902184173464775,
0.008393201977014542,
0.03345184028148651,
0.01759631745517254,
-0.03319872170686722,
0.004615139216184616,
0.029860375449061394,
0.0334179624915123,
0.03358660265803337,
0.029015954583883286,
-0.017050346359610558,
-0.028557617217302322,
0.03034301847219467,
-0.009338824078440666,
0.007337456103414297,
-0.01378918718546629,
0.0003615323221310973,
-0.011420007795095444,
0.022247975692152977,
-0.009492896497249603,
0.021014630794525146,
0.0169619619846344,
0.0376446396112442,
-0.013088271021842957,
0.02940821833908558,
-0.046180471777915955,
0.007339149247854948,
0.013878646306693554,
0.028174608945846558,
0.02472870983183384,
-0.013028755784034729,
0.0041784802451729774,
-0.01767093688249588,
0.005926590412855148,
0.010051610879600048,
-0.02656026929616928,
-0.002794070867821574,
-0.014757447876036167,
0.039632029831409454,
-0.05103260278701782,
0.022217607125639915,
-0.024399209767580032,
0.019267383962869644,
-0.02201741747558117,
-0.02608848735690117,
0.042483966797590256,
0.02981451340019703,
0.03285116329789162,
-0.055384598672389984,
-0.04811481386423111,
0.011964075267314911,
-0.030433889478445053,
-0.017016997560858727,
0.03128223866224289,
-0.03563211113214493,
-0.004865203984081745,
-0.015590782277286053,
-0.042184069752693176,
0.03603546693921089,
-0.009729315526783466,
0.001948577701114118,
0.029739083722233772,
-0.04458991438150406,
-0.046749066561460495,
0.02173054963350296,
0.02679908461868763,
-0.02123733051121235,
-0.05705232173204422,
0.04455183073878288,
0.03804701566696167,
0.023399004712700844,
-0.015496236272156239,
-0.017305588349699974,
-0.007952706888318062,
-0.062444839626550674,
-0.004859245382249355,
-0.028922999277710915,
0.03508187457919121,
-0.03936034068465233,
0.03990508243441582,
0.048067059367895126,
-0.058161210268735886,
-0.0016229372704401612,
-0.041498422622680664,
-0.05607236921787262,
0.04447995871305466,
-0.036525335162878036,
0.0060021537356078625,
0.005666663404554129,
-0.04605596885085106,
0.030532097443938255,
0.031077878549695015,
-0.009033391252160072,
-0.012208152562379837,
-0.06287816166877747,
-0.017588548362255096,
-0.009674062952399254,
-0.011767134070396423,
0.025909174233675003,
0.0013517275219783187,
-0.014122405089437962,
0.014739595353603363,
0.06904789060354233,
0.011418002657592297,
-0.023347480222582817,
0.00528318714350462,
0.004667663015425205,
-0.0026883739046752453,
-0.0014745703665539622,
0.033467259258031845,
0.028266550973057747,
-0.0512213334441185,
0.05896921828389168,
0.00007537285273429006,
0.04360390082001686,
0.04089638963341713,
-0.03231262415647507,
0.05063734948635101,
0.01189645566046238,
0.043674103915691376,
-0.034065768122673035,
0.04647958278656006,
-0.014581294730305672,
0.013921965844929218,
-0.01260552927851677,
0.028625087812542915,
0.018517371267080307,
-0.00830613262951374,
0.013592131435871124,
0.015781844034790993,
0.035034600645303726,
-0.017740806564688683,
0.005033133085817099,
0.03270583599805832,
-0.014963137917220592,
-0.009150552563369274,
0.012305917218327522,
-0.009963134303689003,
-0.014180031605064869,
0.02868231013417244,
0.03237329423427582,
-0.0040578050538897514,
-0.01639738865196705,
-0.01096288114786148,
-0.025175079703330994,
0.0073798284865915775,
-0.014703207649290562,
0.032020702958106995,
0.0029372400604188442,
0.055749546736478806,
0.035699136555194855,
0.04575309529900551,
0.009080205112695694,
-0.005377178080379963,
-0.059398114681243896,
-0.008906607516109943,
-0.059748098254203796,
-0.03154916316270828,
-0.03594502434134483,
0.025139009580016136,
-0.04528477415442467,
-0.024868614971637726,
-0.03582911565899849,
-0.00047686498146504164,
0.012403171509504318,
-0.06836732476949692,
0.018602821975946426,
-0.02317153289914131,
-0.019435228779911995,
-0.01406604703515768,
0.034449175000190735,
0.013710021041333675,
-0.02270088903605938,
0.006304826587438583,
0.021738586947321892,
0.028023259714245796,
-0.00729709304869175,
-0.00005137830521562137,
0.0027599523309618235,
-0.00011268998787272722,
0.06319170445203781,
0.034299638122320175,
0.01703084073960781,
-0.05719035491347313,
0.007818033918738365,
0.013018450699746609,
0.0655365064740181,
-0.011211312375962734,
-0.04635315388441086,
-0.023619288578629494,
-0.08145924657583237,
-0.028011273592710495,
-0.02963598445057869,
0.022738639265298843,
-0.006056048441678286,
0.009545433335006237,
0.0361078679561615,
0.007650370243936777,
-0.022388145327568054,
-0.0005893218913115561,
0.019020909443497658,
0.0515563078224659,
-0.005783646833151579,
-0.03205570951104164,
-0.022996380925178528,
-0.021046994253993034,
-0.002531909616664052,
0.05433141440153122,
-0.002262096619233489,
-0.004468926694244146,
0.005678714718669653,
-0.0044280230067670345,
0.032926805317401886,
-0.017119551077485085,
-0.0014838005881756544,
-0.011783202178776264,
0.014133064076304436,
-0.0007868069806136191,
0.007990523241460323,
0.0398518331348896,
0.00376711948774755,
-0.0022625115234404802,
0.027164293453097343,
-0.058546293526887894,
-0.06617163866758347,
0.002322249347344041,
0.012637223117053509,
0.025836624205112457,
-0.03654736280441284,
0.020240694284439087,
-0.02394944801926613,
-0.03919527307152748,
0.05369394272565842,
-0.005121840629726648,
0.0038293979596346617,
-0.022943999618291855,
-0.01867949217557907,
-0.051338616758584976,
-0.011382595635950565,
-0.002192125655710697,
0.02720324881374836,
0.03121080808341503,
-0.02851239964365959,
-0.042795903980731964,
-0.003283262485638261,
0.0017693863483145833,
0.017176058143377304,
0.01176852360367775,
0.08831482380628586,
-0.013164522126317024,
0.03019607625901699,
0.005500858649611473,
-0.001807298744097352,
-0.020197749137878418,
-0.07356121391057968,
0.01509819645434618,
0.0026347064413130283,
0.03717416524887085,
0.027112927287817,
-0.010486390441656113,
-0.031306907534599304,
0.07214787602424622,
-0.018895842134952545,
0.01811608299612999,
0.03532205894589424,
-0.02399379014968872,
0.04260283336043358,
-0.002835918916389346,
-0.03096310794353485,
0.033795882016420364,
0.027169661596417427,
0.005362463183701038,
0.000023269101802725345,
-0.030615998432040215,
0.05547945201396942,
-0.04411095008254051,
-0.012008038349449635,
-0.0383145846426487,
0.021384116262197495,
-0.011687693186104298,
0.036431267857551575,
-0.003909827675670385,
0.040684930980205536,
0.023167872801423073,
-0.05351380258798599,
-0.007760356646031141,
0.001529197907075286,
0.0004683051083702594,
-0.000544535054359585,
-0.04825253784656525,
0.028546851128339767,
-0.028044307604432106,
-0.0454685352742672,
-0.02591126598417759,
0.01045829989016056,
-0.00751787843182683,
0.03484141454100609,
0.0024366809520870447,
0.01618398353457451,
-0.05669703334569931,
0.004660492762923241,
-0.013964858837425709,
-0.036046575754880905,
0.08305758237838745,
-0.010580355301499367,
-0.039477333426475525,
0.0245659239590168,
-0.056144580245018005,
-0.010343166068196297,
0.04651159793138504,
-0.006445914972573519,
0.019569450989365578,
-0.05308478698134422,
0.051800165325403214,
-0.012233876623213291,
0.036103229969739914,
-0.09550373256206512,
-0.037064164876937866,
-0.016723185777664185,
0.012231261469423771,
0.0035784796345978975,
-0.014153894037008286,
-0.015819590538740158,
0.0010324673494324088,
-0.03743017464876175,
0.03351260721683502,
0.04464443773031235,
0.013077217154204845,
-0.012839491479098797,
0.022346392273902893,
0.009178407490253448,
0.03844893351197243,
-0.00008995868847705424,
-0.04241013526916504,
0.025536907836794853,
-0.05413137376308441,
0.0016140725929290056,
-0.03732411563396454,
0.05979539453983307,
-0.028995882719755173,
-0.015958601608872414,
0.000961036013904959,
-0.05839994177222252,
0.031590528786182404,
0.009772059507668018,
-0.03186120465397835,
0.018133241683244705,
-0.025586171075701714,
-0.01481580175459385,
-0.0022500113118439913,
0.006710025016218424,
0.016362128779292107,
0.027621015906333923,
-0.00825272686779499,
0.023179596289992332,
-0.05838169902563095,
-0.04294312372803688,
0.057622671127319336,
0.013095995411276817,
0.001671084901317954,
-0.006403006613254547,
0.060029469430446625,
-0.008183147758245468,
-0.017031576484441757,
0.018884005025029182,
-0.0047401259653270245,
0.01163487695157528,
-0.01928197592496872,
-0.012317217886447906,
0.005911160726100206,
-0.010160166770219803,
-0.002011179458349943,
-0.04658413678407669,
-0.03316367045044899,
-0.013489965349435806,
0.04621991142630577,
-0.03760291263461113,
0.0037160199135541916,
-0.037740495055913925,
-0.016806980594992638,
-0.0005568531341850758,
-0.0011030955938622355,
-0.011279357597231865,
0.02610296942293644,
-0.021487120538949966,
0.029630910605192184,
-0.024672918021678925,
0.008958945982158184,
0.01991225965321064,
0.04622570425271988,
-0.02021508850157261,
-0.003035485278815031,
0.027818357571959496,
-0.004819689784198999,
0.029200468212366104,
0.01639878749847412,
-0.002608604496344924,
0.02735665626823902,
-0.046197496354579926,
0.057161685079336166,
0.008648506365716457,
-0.05757180228829384,
0.05832306295633316,
-0.013166679069399834,
0.01792188361287117,
-0.01997022144496441,
0.0020217387937009335,
-0.04319394752383232,
0.03346777707338333,
-0.004732236731797457,
0.023860514163970947,
-0.02477383054792881,
0.001187242567539215,
0.015816612169146538,
0.021311283111572266,
0.010512844659388065,
0.020273828878998756,
-0.05221015587449074,
0.0055547673255205154,
-0.007244978100061417,
-0.040204811841249466,
0.01189076155424118,
0.005988325458019972,
0.01648414507508278,
0.05280008167028427,
-0.011345072649419308,
0.04866614192724228,
0.013502025976777077,
0.03939935192465782,
-0.042351264506578445,
0.05556546896696091,
0.01046857051551342,
0.05662032589316368,
-0.022315002977848053,
0.03428000584244728,
0.10872731357812881,
0.03713072091341019,
0.02524108625948429,
-0.03806490823626518,
-0.009884839877486229,
-0.006259857676923275,
0.032257746905088425,
-0.022401852533221245,
0.011644366197288036,
0.0030086219776421785,
-0.00992466788738966,
-0.0009463411406613886,
0.04824172332882881,
-0.029172785580158234,
0.05642080307006836,
0.04424519091844559,
-0.03253632411360741,
-0.011782701127231121,
-0.018097547814249992,
0.046693477779626846,
-0.01884683221578598,
0.022107353433966637,
-0.03766566142439842,
0.02165152132511139,
-0.058434147387742996,
-0.0025044837966561317,
-0.035164136439561844,
-0.034263975918293,
0.027799664065241814,
0.011461464688181877,
-0.03758244216442108,
-0.01411498710513115,
0.04805529862642288,
0.004085680935531855,
-0.055353645235300064,
0.021783942356705666,
0.05497103929519653,
0.0030627178493887186,
0.005924583412706852,
0.03413925692439079,
0.02481074258685112,
0.01713445596396923,
0.0032578196842223406,
-0.001531889196485281,
-0.04610392078757286,
-0.0065345545299351215,
0.004903420340269804,
0.020733939483761787,
-0.04702981188893318,
0.04034341126680374,
-0.007481567095965147,
-0.0225085262209177,
0.012314382009208202,
-0.05747615918517113,
-0.04193510860204697,
-0.02303512766957283,
0.019344162195920944,
0.011483381502330303,
-0.008755743503570557,
-0.027814451605081558,
0.022399984300136566,
-0.005154432728886604,
-0.011778486892580986,
-0.00840297807008028,
0.034793443977832794,
-0.0025149097200483084,
0.01061736699193716,
0.038708921521902084,
-0.035908740013837814,
-0.03336609527468681,
-0.03600810095667839,
-0.013143559917807579,
-0.057850394397974014,
-0.023936601355671883,
0.022699901834130287,
0.0312756784260273,
0.04969699680805206,
-0.010120942257344723,
0.0016039313049986959,
-0.006492112763226032,
-0.06968553364276886,
0.03797556459903717,
-0.029772503301501274,
0.00636723916977644,
-0.031139828264713287,
-0.018271097913384438,
0.000530579942278564,
0.05320785194635391,
-0.06106971949338913,
-0.03325749933719635,
0.00506582111120224,
0.041836582124233246,
0.012185050174593925,
-0.01982818730175495,
-0.007419160567224026,
0.013399352319538593,
-0.033719588071107864,
0.05514714866876602,
0.0064210668206214905,
0.011551318690180779,
0.012534675188362598,
0.05386954918503761,
-0.027530796825885773,
0.02299865148961544,
-0.0501655749976635,
0.014809221029281616,
0.019800469279289246,
-0.03333905339241028,
-0.0075636617839336395,
0.04309920221567154,
0.035935044288635254,
0.003680021967738867,
-0.058311332017183304,
-0.049121059477329254,
0.005431474186480045,
-0.012140423990786076,
0.011221339926123619,
-0.0173188429325819,
-0.02934293821454048,
-0.025616617873311043,
0.00830411072820425,
-0.05165879800915718,
0.028550907969474792,
-0.027301758527755737,
-0.013324575498700142,
0.015413133427500725,
0.019218819215893745,
0.012961207889020443,
0.016792023554444313,
-0.014604092575609684,
0.0002473386120982468,
0.03379717096686363,
0.021991603076457977,
0.028482632711529732,
-0.0070587145164608955,
0.035508766770362854,
-0.002869520103558898,
0.03972177952528,
-0.04054828733205795,
-0.00997955072671175,
0.07643713057041168,
-0.039501070976257324,
-0.029716070741415024,
0.029060592874884605,
-0.024646569043397903,
0.048858653753995895,
-0.013588243164122105,
-0.021552134305238724,
0.004392977338284254,
0.07857245206832886,
-0.02295556664466858,
0.028119103983044624,
-0.007273732218891382,
-0.055219512432813644,
-0.02219942770898342,
-0.01170543022453785,
-0.006817875429987907,
0.0040338728576898575,
-0.00758744589984417,
0.06981272250413895,
0.003398053115233779,
-0.018364880234003067,
0.019229518249630928,
0.029132356867194176,
-0.022463100031018257,
-0.01610538549721241,
0.021459974348545074,
-0.006874182261526585,
-0.008102214895188808,
0.05954895168542862,
-0.0060755545273423195,
0.06694432348012924,
0.022188754752278328,
-0.00763286417350173,
-0.06715282797813416,
-0.006779080722481012,
-0.022054364904761314,
0.015965735539793968,
0.015193924307823181,
-0.028118690475821495,
-0.02063680812716484,
0.03393278270959854,
-0.1004335805773735,
-0.0050852857530117035,
-0.015481297858059406,
-0.01076256949454546,
-0.0526355504989624,
0.005466590169817209,
-0.03140318766236305,
0.011881034821271896,
0.03687143325805664,
0.0261639766395092,
0.005263529717922211,
0.033867157995700836,
-0.002345239045098424,
-0.001274965237826109,
-0.034290116280317307,
0.01205329317599535,
-0.01066229585558176,
0.004913551267236471,
0.00655457004904747,
-0.011644864454865456,
0.016674133017659187,
0.0011598254786804318,
0.024037687107920647,
-0.008002878166735172,
-0.010442445985972881,
0.025958815589547157,
0.05316295474767685,
0.0284471046179533,
-0.010290408506989479,
-0.0010717993136495352,
-0.010082407854497433,
-0.00009103431511903182,
0.015392310917377472,
0.025807058438658714,
-0.03749149665236473,
-0.00007578318036394194,
0.00006262936221901327,
-0.04794817045331001,
-0.0321151465177536,
-0.007943987846374512,
-0.015539229847490788,
-0.018201779574155807,
0.02558106742799282,
0.030390191823244095,
0.011969386599957943,
0.006346953567117453,
0.022237936034798622,
-0.07164929807186127,
-0.02103365957736969,
0.03997645527124405,
0.023016225546598434,
-0.020035604014992714,
0.012680906802415848,
-0.023290371522307396,
-0.04011289030313492,
0.02819574438035488,
0.022248754277825356,
-0.024942435324192047,
-0.06071263179183006,
-0.030004629865288734,
-0.017839008942246437,
0.020557168871164322,
-0.005132520571351051,
-0.04263962805271149,
-0.013055466115474701,
0.012504661455750465,
0.019075937569141388,
0.03200341388583183,
-0.019818995147943497,
-0.019552094861865044,
-0.02529270015656948,
-0.04514644294977188,
0.04233662784099579,
-0.015684423968195915,
0.01252338569611311,
-0.03374641761183739,
-0.04074424132704735,
-0.014155273325741291,
0.03042806126177311,
0.06667449325323105,
-0.01236432883888483,
0.01032918319106102,
0.012291165068745613,
-0.0021743502002209425,
0.049368716776371,
-0.03631189092993736,
0.006165479309856892,
-0.03529820963740349,
-0.04011636972427368,
-0.015281402505934238,
0.007547551300376654,
-0.03720575198531151,
0.03192239627242088,
0.013417176902294159,
0.0062487805262207985,
-0.01800314337015152,
-0.025443626567721367,
-0.033557191491127014,
0.027705417945981026,
0.0654999166727066,
0.014138388447463512,
0.06539303809404373,
-0.035158511251211166,
0.029852760955691338,
0.007169704418629408,
-0.0027329279109835625,
-0.04401204735040665,
0.046973131597042084,
-0.028771257027983665,
-0.011653551831841469,
0.007254009135067463,
0.03466664254665375,
0.005086373072117567,
-0.010239179246127605,
0.013970991596579552,
0.04168619215488434,
-0.03301404416561127,
-0.005968316458165646,
0.04018436744809151,
0.035181086510419846,
0.05407334491610527,
-0.004537058994174004,
-0.009722109884023666,
0.005874664522707462,
0.013720978051424026,
-0.02822490595281124,
0.05729440599679947,
0.01864609494805336,
-0.01887882500886917,
-0.01019058283418417,
0.03279619663953781,
-0.01907886378467083,
-0.0071718282997608185,
0.009702499024569988,
-0.0060379090718925,
-0.022592157125473022,
-0.002603039378300309,
0.03741907328367233,
-0.026143858209252357,
0.016490807756781578,
0.02326725423336029,
0.009134258143603802,
0.10010481625795364,
-0.011162240989506245,
0.018302446231245995,
0.007808065041899681,
0.007208291906863451,
-0.0015042852610349655,
0.03521678224205971,
-0.017764873802661896,
0.023675328120589256,
-0.03537236154079437,
-0.04506141319870949,
-0.03505104407668114,
-0.009151456877589226,
0.05893583595752716,
-0.0682157501578331,
0.01919352263212204,
-0.011316950432956219,
-0.046564631164073944,
-0.02031525783240795,
-0.015305859036743641,
-0.01906789280474186,
0.034048378467559814,
-0.01002935878932476,
0.013842781074345112,
0.005130402743816376,
0.011596585623919964,
0.0186593160033226,
-0.008135044015944004,
0.029252158477902412,
-0.03318019211292267,
0.02347746305167675,
-0.020281696692109108,
0.049345437437295914,
-0.009887879714369774,
0.0048326775431632996
] |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.