question
stringlengths 37
38.8k
| group_id
int64 0
74.5k
| sentence_embeddings
sequencelengths 1.02k
1.02k
|
|---|---|---|
<p>I was reading upon Faraday effect when it said </p>
<blockquote>
<p>Faraday effect causes a rotation of the plane of polarization</p>
</blockquote>
<p>That in mind, does this mean the light can be bent around or does the light loose energy when its waves rotate? Can someone explain more about this effect simply as I'm a middle school going kid, make sure the explanation is simple yet precise please. </p>
<p>Thanks!</p> | 1,400 | [
-0.03546372801065445,
-0.00753159960731864,
0.011364258825778961,
-0.013290581293404102,
0.07034360617399216,
0.014762256294488907,
-0.03395799919962883,
-0.011101918295025826,
0.003885904559865594,
-0.04189160093665123,
0.01391342468559742,
0.047230131924152374,
0.024331962689757347,
0.03825625404715538,
0.011598493903875351,
0.01961240917444229,
0.010578721761703491,
0.010626990348100662,
-0.004299430176615715,
-0.043949928134679794,
-0.02501634694635868,
0.024145744740962982,
-0.024379178881645203,
-0.0010321771260350943,
-0.0371420755982399,
0.009339278563857079,
0.037499118596315384,
0.0023622834123671055,
0.05599431321024895,
0.030476897954940796,
0.002422833349555731,
-0.02100544609129429,
0.004009764175862074,
0.010504442267119884,
0.005924530792981386,
-0.03428855165839195,
-0.026173003017902374,
-0.052269209176301956,
-0.0013879126636311412,
0.01344513799995184,
-0.009186594747006893,
0.00043428788194432855,
-0.01784295029938221,
0.03961856663227081,
-0.03193104267120361,
-0.00415298854932189,
-0.016983021050691605,
0.017406584694981575,
0.07094267010688782,
-0.07174775749444962,
0.05499669164419174,
-0.03697372227907181,
0.022761600092053413,
0.002744092606008053,
-0.0132336700335145,
0.017073869705200195,
0.07375217229127884,
0.09070508927106857,
-0.011915982700884342,
-0.037281785160303116,
-0.016928477212786674,
-0.043819207698106766,
-0.013259852305054665,
-0.0440773069858551,
-0.016921278089284897,
-0.0074396999552845955,
-0.017856517806649208,
-0.030668973922729492,
0.049260981380939484,
0.021750250831246376,
0.030793942511081696,
0.0340234749019146,
0.01114139799028635,
-0.025926968082785606,
-0.009925875812768936,
-0.04549984261393547,
0.030193805694580078,
0.016738327220082283,
0.05201515182852745,
-0.004325272049754858,
0.015650171786546707,
0.032007113099098206,
0.01405533030629158,
0.00786785688251257,
0.011626622639596462,
-0.053941760212183,
0.1062823012471199,
-0.0022953818552196026,
0.03653879091143608,
0.010175391100347042,
0.012603284791111946,
0.021868642419576645,
-0.01838512532413006,
0.033046260476112366,
-0.046326782554388046,
0.027758685871958733,
-0.005473122466355562,
0.02941187471151352,
0.008314287289977074,
-0.015417915768921375,
0.016914043575525284,
0.02945520728826523,
0.028715558350086212,
0.062405746430158615,
0.01691698469221592,
-0.030974961817264557,
-0.02819666638970375,
0.000689331442117691,
-0.006627968512475491,
-0.02187388762831688,
0.006433453410863876,
0.01649787649512291,
-0.02071182057261467,
-0.012355901300907135,
0.019682206213474274,
-0.03534252196550369,
0.008174982853233814,
-0.011190241202712059,
0.04987095296382904,
0.05883469805121422,
0.014551719650626183,
-0.03733571618795395,
0.002101983642205596,
-0.05275052785873413,
-0.06694196164608002,
0.04657047986984253,
0.03731660172343254,
-0.030501479282975197,
-0.02921944484114647,
0.020960897207260132,
0.009139910340309143,
-0.019785193726420403,
-0.013299760408699512,
-0.004661714658141136,
-0.0027685523964464664,
-0.02712894044816494,
-0.11111084371805191,
-0.008810021914541721,
0.019905131310224533,
0.018117040395736694,
-0.009776740334928036,
-0.06332740932703018,
-0.007905414327979088,
0.027527671307325363,
0.091032013297081,
0.0011735333828255534,
0.011968712322413921,
-0.02668968215584755,
0.05315496399998665,
-0.021240316331386566,
-0.020737648010253906,
0.006688989233225584,
0.012882369570434093,
-0.016783902421593666,
-0.007493218872696161,
-0.07047046720981598,
-0.0055763921700417995,
0.04705294966697693,
-0.010368880815804005,
-0.05109342932701111,
0.021550659090280533,
-0.03575708344578743,
0.006417402531951666,
0.03018319047987461,
-0.03876108676195145,
-0.03223508223891258,
0.11510651558637619,
0.02451755665242672,
0.009062451310455799,
0.026490788906812668,
-0.02534841187298298,
0.048813965171575546,
-0.010777316987514496,
0.02917507477104664,
0.0541909821331501,
-0.03137604892253876,
-0.00759038096293807,
0.0008234056876972318,
0.044381238520145416,
-0.027605237439274788,
-0.03441184014081955,
-0.03246782347559929,
0.004233031999319792,
0.015586860477924347,
-0.018146775662899017,
0.07149212807416916,
-0.014189190231263638,
-0.002189270220696926,
-0.006262936629354954,
-0.07548018544912338,
0.013070980086922646,
-0.026449041441082954,
0.045287225395441055,
-0.023898711428046227,
-0.03883726894855499,
0.00155234697740525,
0.013804362155497074,
0.05219500511884689,
-0.024056322872638702,
-0.039357662200927734,
-0.024035630747675896,
0.037623897194862366,
-0.03009137138724327,
-0.028966348618268967,
0.027658505365252495,
0.046653762459754944,
0.021520953625440598,
0.027719125151634216,
0.006386107765138149,
-0.025430111214518547,
0.014732355251908302,
0.0034277806989848614,
-0.01458085048943758,
0.008202758617699146,
0.018418699502944946,
-0.02161695808172226,
-0.018509387969970703,
0.004077001940459013,
0.008314449340105057,
0.021960971876978874,
-0.003767553251236677,
0.050481926649808884,
0.044975925236940384,
-0.01282750628888607,
0.025254832580685616,
0.06472749263048172,
-0.0124411191791296,
0.0010269023478031158,
-0.007262468338012695,
-0.022653622552752495,
-0.031155886128544807,
0.028701873496174812,
0.03657812997698784,
-0.0060301367193460464,
-0.03082123212516308,
0.016292650252580643,
0.030982812866568565,
0.02815156988799572,
0.015020070597529411,
0.014062927104532719,
-0.029229484498500824,
-0.016202423721551895,
0.000991066568531096,
-0.00992870144546032,
0.0028272513300180435,
0.02948755770921707,
0.05259332433342934,
0.006417922675609589,
0.007476185914129019,
0.031169814988970757,
-0.04796590656042099,
0.06705023348331451,
0.010342651046812534,
0.045086819678545,
0.03907785192131996,
-0.03444666042923927,
0.012273546308279037,
-0.01784149371087551,
0.008820189163088799,
0.016379157081246376,
-0.033748600631952286,
0.014134339056909084,
-0.04122830927371979,
0.004936086945235729,
-0.014198582619428635,
-0.010731679387390614,
-0.0108672259375453,
-0.03611897677183151,
0.018599631264805794,
-0.035090167075395584,
0.023257041350007057,
0.0056740702129900455,
0.004284219816327095,
-0.001710286596789956,
-0.03564974293112755,
0.03106030635535717,
0.03122311271727085,
0.020553477108478546,
0.0041085416451096535,
-0.029668837785720825,
0.006821038667112589,
-0.0511556901037693,
-0.018319102004170418,
0.0008043016423471272,
-0.03383989632129669,
0.018870137631893158,
-0.041104067116975784,
-0.021252406761050224,
0.04002494364976883,
-0.02699512615799904,
-0.01307591050863266,
0.006696423515677452,
-0.006578716449439526,
-0.06795679777860641,
-0.002588586648926139,
-0.02697649411857128,
-0.01348081137984991,
-0.0263864453881979,
0.001861785538494587,
0.006402264814823866,
-0.013605566695332527,
0.003968040458858013,
0.010433145798742771,
-0.021778838708996773,
-0.05110558122396469,
-0.020296618342399597,
0.006062702275812626,
0.04427730292081833,
-0.0256335586309433,
0.03795316815376282,
0.0005749990232288837,
-0.03301073610782623,
0.012970282696187496,
-0.024326283484697342,
-0.01580793596804142,
0.04010316729545593,
-0.013723127543926239,
0.0027081749867647886,
-0.03489760681986809,
-0.037520501762628555,
0.044087495654821396,
0.02466607838869095,
-0.040651388466358185,
-0.01695963926613331,
-0.028119992464780807,
0.0038297614082694054,
-0.017037108540534973,
-0.018302366137504578,
0.056386832147836685,
-0.008130929432809353,
0.02527594566345215,
0.010775136761367321,
0.005213676020503044,
0.01622321829199791,
0.018609900027513504,
-0.03038579411804676,
0.0033412654884159565,
-0.005798254162073135,
-0.007288723718374968,
0.015609586611390114,
0.013194241560995579,
-0.057072099298238754,
-0.016239451244473457,
0.0178192351013422,
0.049616146832704544,
0.02154279686510563,
-0.026982681825757027,
0.055432312190532684,
-0.01283598504960537,
0.01275561098009348,
0.005519247613847256,
0.06147800013422966,
-0.0012135085416957736,
0.012554831802845001,
0.04372994974255562,
0.03813300281763077,
0.058121208101511,
-0.019835367798805237,
-0.004787153098732233,
0.008105450309813023,
0.021348483860492706,
-0.012161098420619965,
-0.02070734277367592,
0.009702671319246292,
-0.028837833553552628,
0.05808769166469574,
-0.02527151070535183,
-0.020856576040387154,
0.03779373690485954,
0.012684003449976444,
0.01953679695725441,
-0.017165495082736015,
-0.02040831185877323,
0.0023961085826158524,
-0.040693603456020355,
0.03871772810816765,
0.00790888536721468,
0.033827830106019974,
0.01858646795153618,
0.026687879115343094,
0.005245053209364414,
0.008641091175377369,
0.04721630737185478,
-0.008776073344051838,
-0.061019089072942734,
0.03652578964829445,
-0.011576930060982704,
-0.010723439045250416,
-0.03257226198911667,
0.03188072144985199,
-0.029241999611258507,
-0.0066392202861607075,
-0.007635130546987057,
-0.07504349946975708,
-0.036333825439214706,
-0.040821392089128494,
0.006452382542192936,
-0.005876043811440468,
-0.010907314717769623,
-0.047837983816862106,
0.042452942579984665,
0.00575752928853035,
-0.0479351170361042,
0.023845365270972252,
0.011495131999254227,
-0.028565440326929092,
0.0042866300791502,
0.00006730866152793169,
-0.016399795189499855,
0.016381194815039635,
0.007083670701831579,
0.062038324773311615,
-0.019121257588267326,
-0.016168776899576187,
0.023419639095664024,
0.01600164733827114,
0.045004989951848984,
0.005300356540828943,
-0.018317898735404015,
-0.03282985836267471,
0.0026042924728244543,
-0.016398489475250244,
-0.02490846998989582,
0.06791448593139648,
0.0013280311832204461,
0.04563898593187332,
-0.0042261905036866665,
-0.015607606619596481,
-0.002577500883489847,
0.01790291629731655,
0.029151789844036102,
0.046612128615379333,
-0.016067814081907272,
-0.06758008152246475,
0.024774672463536263,
-0.044874634593725204,
0.011713358573615551,
0.005796437617391348,
-0.028730297461152077,
-0.029021726921200752,
-0.02075468748807907,
-0.005490147043019533,
0.016301855444908142,
0.0107386140152812,
0.023374447599053383,
-0.006466207560151815,
-0.01183412317186594,
0.009302228689193726,
0.007177665829658508,
0.015554026700556278,
0.04092737287282944,
0.06257826089859009,
-0.006371270399540663,
0.005373856518417597,
-0.07624119520187378,
0.025422368198633194,
0.019038327038288116,
0.028890255838632584,
-0.016533752903342247,
0.0031794540118426085,
-0.031401898711919785,
-0.01721160113811493,
0.014866783283650875,
-0.03801296278834343,
0.022340118885040283,
-0.03175769001245499,
-0.017975078895688057,
-0.03060227818787098,
0.007267098408192396,
-0.02241191454231739,
0.029893528670072556,
-0.014563939534127712,
0.031105412170290947,
-0.024843471124768257,
0.00005030341708334163,
-0.005152570083737373,
-0.012362412177026272,
0.017552705481648445,
0.05273625999689102,
0.017950210720300674,
0.011425906792283058,
0.0046070646494627,
0.05509227514266968,
-0.008702422492206097,
-0.0869331955909729,
-0.015080833807587624,
-0.0073062460869550705,
-0.016465790569782257,
0.07823097705841064,
-0.030563965439796448,
-0.031370609998703,
-0.0019103571539744735,
0.014620265923440456,
-0.0022693676874041557,
-0.016438860446214676,
-0.03113534301519394,
0.013902522623538971,
-0.003036471549421549,
-0.010248559527099133,
0.0628184974193573,
0.06144373491406441,
-0.038895029574632645,
-0.00707586295902729,
-0.009290655143558979,
0.05057091638445854,
-0.04099235311150551,
-0.012434565462172031,
-0.017669109627604485,
0.022064287215471268,
-0.01996888965368271,
0.03643990680575371,
-0.023064959794282913,
-0.01793794520199299,
-0.005446150898933411,
-0.017714286223053932,
-0.027528397738933563,
0.013502184301614761,
-0.000024325256163137965,
-0.02770739607512951,
-0.05844396352767944,
0.03181621804833412,
-0.0024175215512514114,
-0.012324084527790546,
-0.0038474712055176497,
0.009093674831092358,
0.018929919227957726,
0.04012097418308258,
0.0007663228316232562,
-0.0011918536620214581,
-0.04952055215835571,
-0.012786498293280602,
-0.02823602594435215,
-0.03433705493807793,
0.028302635997533798,
-0.013395038433372974,
0.005228654947131872,
0.03620395064353943,
-0.07851272821426392,
-0.025050323456525803,
0.007857571355998516,
-0.046060893684625626,
0.05457771196961403,
-0.043769631534814835,
0.017126932740211487,
0.02715742215514183,
0.03412773832678795,
-0.03551175817847252,
-0.05701950192451477,
0.022383827716112137,
0.0032728465739637613,
-0.023332031443715096,
0.0258644986897707,
0.011000041849911213,
-0.0312952883541584,
-0.04900417849421501,
-0.022957442328333855,
0.0007955768960528076,
-0.029330287128686905,
0.01451016589999199,
0.04643647372722626,
-0.038209471851587296,
0.07963571697473526,
-0.02327323704957962,
-0.033420536667108536,
0.016674937680363655,
-0.02575059048831463,
-0.03632497042417526,
-0.025490418076515198,
0.07052269577980042,
-0.0050407820381224155,
-0.03710271045565605,
0.0038473675958812237,
0.009832782670855522,
0.02674376405775547,
-0.014150415547192097,
0.003462510649114847,
-0.003749406198039651,
0.008538666181266308,
0.012951059266924858,
-0.022483527660369873,
0.014260013587772846,
0.003752180142328143,
0.023791851475834846,
0.03337917476892471,
-0.0013761777663603425,
-0.06005815044045448,
-0.04474532976746559,
0.017331814393401146,
-0.009831869974732399,
0.024262040853500366,
-0.007338713854551315,
0.08914799243211746,
-0.01864713244140148,
0.012299040332436562,
0.006992310285568237,
-0.01662399433553219,
0.009450978599488735,
0.02182990126311779,
0.007359965704381466,
0.023561222478747368,
0.015475007705390453,
0.013789796270430088,
-0.031977102160453796,
-0.003458418883383274,
0.0007866273517720401,
0.09625750780105591,
-0.016736609861254692,
0.04557148739695549,
0.01540502067655325,
0.007791601121425629,
-0.005531640257686377,
-0.011724195443093777,
0.017354434356093407,
0.03699983283877373,
-0.006911911070346832,
0.02220712974667549,
-0.03394988924264908,
-0.009599917568266392,
-0.0026208427734673023,
0.03941701352596283,
-0.03095904551446438,
0.004042091313749552,
0.030505787581205368,
0.025713101029396057,
-0.017537089064717293,
0.029078248888254166,
-0.05916948616504669,
0.01822921819984913,
-0.047148197889328,
0.032390449196100235,
0.00001106611580325989,
0.007012293208390474,
0.040524959564208984,
-0.02397952415049076,
0.02659664675593376,
-0.04359307885169983,
-0.005460192449390888,
-0.021445343270897865,
0.028223518282175064,
-0.025249771773815155,
0.045239660888910294,
-0.03311977908015251,
0.016880450770258904,
0.052964385598897934,
0.028205828741192818,
0.009816307574510574,
-0.017417961731553078,
-0.05099007114768028,
-0.0368390753865242,
-0.006397967226803303,
-0.030256150290369987,
0.06008972227573395,
-0.004589535761624575,
-0.037760525941848755,
-0.027590563520789146,
-0.017727212980389595,
0.014861401170492172,
0.040900819003582,
0.010225539095699787,
0.01068213488906622,
0.0463411808013916,
-0.025568827986717224,
0.02437574788928032,
0.012390601448714733,
-0.007808869704604149,
0.11933719366788864,
0.01284838654100895,
0.02953389659523964,
-0.0739881619811058,
-0.003164146328344941,
-0.04833719879388809,
0.015904491767287254,
-0.03163325786590576,
0.014815833419561386,
-0.0358085110783577,
0.06316962093114853,
0.010757538489997387,
0.0465097650885582,
-0.0015978551236912608,
-0.028781618922948837,
0.018923811614513397,
-0.030552219599485397,
-0.02934826910495758,
0.03859963268041611,
0.022352168336510658,
-0.024206597357988358,
0.06306178122758865,
-0.09916085004806519,
0.005762177053838968,
-0.06537773460149765,
0.01666201837360859,
-0.027768807485699654,
-0.049543123692274094,
0.007451224606484175,
-0.008673002943396568,
-0.036864105612039566,
0.021950945258140564,
0.004973375704139471,
-0.003240531776100397,
-0.07081177085638046,
0.04281644523143768,
0.016784360632300377,
-0.0032214305829256773,
0.005330974236130714,
0.014563305303454399,
-0.0015074831899255514,
-0.004870044067502022,
0.04772612079977989,
0.034661341458559036,
-0.023810453712940216,
-0.007947844453155994,
-0.014680709689855576,
0.028435513377189636,
0.006684667430818081,
0.024586716666817665,
0.016472777351737022,
0.03440343961119652,
-0.00305767310783267,
-0.06136240437626839,
-0.007171770557761192,
0.005740482825785875,
0.005742637440562248,
-0.009358919225633144,
-0.010968406684696674,
-0.0029923939146101475,
0.012638172134757042,
-0.0027506796177476645,
0.029195906594395638,
-0.044211357831954956,
0.019614070653915405,
0.02218480408191681,
0.022897759452462196,
0.03788663074374199,
-0.032647013664245605,
-0.021044226363301277,
-0.054669421166181564,
-0.006143676117062569,
-0.027074523270130157,
-0.00828013475984335,
0.03634825721383095,
0.0037875052075833082,
0.013005067594349384,
-0.0041831801645457745,
-0.04249560460448265,
0.009390034712851048,
-0.06264260411262512,
0.046343836933374405,
-0.018056219443678856,
-0.040089335292577744,
-0.008620592765510082,
0.026461996138095856,
0.06377143412828445,
0.015056384727358818,
-0.02727050893008709,
0.025273272767663002,
-0.014458981342613697,
0.005399894900619984,
0.025510044768452644,
0.005000625271350145,
-0.02388414368033409,
0.02710716240108013,
-0.02455095387995243,
-0.02018921822309494,
-0.002647527027875185,
0.005983334966003895,
0.058773674070835114,
-0.03286837786436081,
-0.018968917429447174,
0.014500943012535572,
-0.025945747271180153,
-0.004828400444239378,
0.015965018421411514,
-0.0018550545210018754,
0.014087111689150333,
0.005322854500263929,
0.0014082355191931129,
-0.04386841505765915,
-0.014434251934289932,
-0.02177743799984455,
-0.024493709206581116,
0.021665064617991447,
0.04008159041404724,
0.009973832406103611,
0.016941547393798828,
-0.04118349775671959,
0.04584858939051628,
-0.02807917818427086,
-0.02181747741997242,
-0.08115608990192413,
0.02457922324538231,
0.024350468069314957,
0.022688325494527817,
-0.008618107996881008,
0.03288332372903824,
0.010846422053873539,
-0.05039437487721443,
0.04265975579619408,
0.03445138782262802,
0.025985559448599815,
0.04241684824228287,
0.0660540759563446,
-0.025866078212857246,
0.052140239626169205,
-0.00631032744422555,
-0.04391821473836899,
0.02721964195370674,
-0.024624958634376526,
-0.04339505359530449,
0.020734887570142746,
-0.02656123973429203,
0.04371454939246178,
0.03760108724236488,
-0.008649778552353382,
0.006766053847968578,
0.03855736181139946,
0.01049113366752863,
-0.010525056160986423,
0.0017030584858730435,
-0.05332748219370842,
0.0014406334375962615,
-0.008315853774547577,
-0.005991996265947819,
-0.030118072405457497,
-0.03760407865047455,
0.059170108288526535,
0.04303177073597908,
-0.024695919826626778,
-0.02878008596599102,
0.013752114027738571,
-0.006757747381925583,
-0.0201812032610178,
0.0023213648237288,
0.017337387427687645,
0.011027233675122261,
0.02778421901166439,
-0.03559510409832001,
0.03830091282725334,
0.001702114357613027,
0.018985982984304428,
-0.122901551425457,
-0.013447795063257217,
0.01937740668654442,
0.008755321614444256,
0.034458182752132416,
-0.03773237764835358,
0.022839471697807312,
0.02248852141201496,
-0.09678314626216888,
0.01070400420576334,
-0.0394965335726738,
-0.032664474099874496,
-0.013208379969000816,
0.019215403124690056,
0.011613535694777966,
0.05856410041451454,
0.011024815030395985,
0.017311792820692062,
0.011645879596471786,
0.020475758239626884,
-0.04291766881942749,
0.0015396025264635682,
-0.0017519500106573105,
0.05908811837434769,
0.010606891475617886,
-0.0045545464381575584,
0.05726216733455658,
0.010305237956345081,
-0.03584414720535278,
0.03825484588742256,
-0.01769830659031868,
0.0034499578177928925,
0.01055122260004282,
0.005330280400812626,
-0.0068582273088395596,
-0.013288646005094051,
-0.02151390165090561,
-0.031086359173059464,
-0.019689440727233887,
0.030426442623138428,
0.03165236487984657,
0.021139729768037796,
-0.00861319899559021,
-0.01891438290476799,
0.006892719771713018,
-0.0546732023358345,
-0.010948765091598034,
0.02637062780559063,
-0.026148153468966484,
0.0015341303078457713,
-0.001842074329033494,
-0.013729632832109928,
-0.009329067543148994,
-0.028629368171095848,
0.009836331941187382,
-0.05579492822289467,
-0.024555491283535957,
-0.005235413555055857,
-0.0027232368011027575,
0.011372234672307968,
0.02443174459040165,
0.029391467571258545,
-0.058319561183452606,
0.04325803741812706,
-0.022582225501537323,
-0.050919417291879654,
-0.021346602588891983,
0.02042853645980358,
0.005511652212589979,
-0.01679874025285244,
0.037830520421266556,
-0.032654304057359695,
-0.0249625276774168,
0.02930983528494835,
0.03403032571077347,
-0.012148338370025158,
-0.015925375744700432,
-0.059155091643333435,
-0.05823242664337158,
-0.03164101019501686,
0.03266589343547821,
-0.0301287192851305,
-0.01823502592742443,
-0.02585824951529503,
-0.013059529475867748,
-0.023542996495962143,
0.01722053997218609,
0.07509519159793854,
-0.004201107192784548,
0.004128326661884785,
0.0019176623318344355,
-0.0021117094438523054,
0.002494945889338851,
-0.05452403053641319,
-0.013242585584521294,
0.005847598426043987,
-0.028545057401061058,
0.012889908626675606,
-0.01951964944601059,
-0.022670090198516846,
0.0011427876306697726,
0.020675908774137497,
0.0019462868804112077,
0.035886697471141815,
-0.0321880541741848,
-0.02516559511423111,
0.04330688714981079,
0.018922381103038788,
-0.0026573764625936747,
0.058071356266736984,
-0.01898898370563984,
-0.006471550557762384,
0.007440774701535702,
-0.033094726502895355,
-0.010811747051775455,
-0.017944755032658577,
-0.03145165368914604,
0.037644386291503906,
-0.009746274910867214,
0.0058957175351679325,
0.060963403433561325,
-0.027614479884505272,
0.002810053527355194,
0.03339596092700958,
-0.0658373311161995,
0.013266208581626415,
0.06492962688207626,
0.006998216267675161,
0.019453180953860283,
-0.022026654332876205,
0.031105604022741318,
-0.012340757064521313,
-0.019991764798760414,
0.013943906873464584,
0.05735034868121147,
0.00308237480930984,
0.05094875022768974,
0.05748293176293373,
0.019014088436961174,
0.0007248320034705102,
0.010757671669125557,
-0.003922419156879187,
0.04053539037704468,
-0.013854177668690681,
-0.029467454180121422,
0.025783952325582504,
0.008910228498280048,
-0.014497523196041584,
0.040399905294179916,
-0.014966853894293308,
0.05753519386053085,
-0.023847995325922966,
0.01845557615160942,
-0.015386362560093403,
-0.036849167197942734,
0.009462656453251839,
-0.008487366139888763,
0.03345964848995209,
0.0427277535200119,
0.013997656293213367,
-0.01764066144824028,
-0.019647732377052307,
-0.007986737415194511,
0.028573544695973396,
-0.014844277873635292,
0.026196938008069992,
-0.02354659140110016,
-0.009144418872892857,
-0.019159676507115364,
0.012813039124011993,
-0.019908206537365913,
-0.006407302338629961,
0.0005847871652804315,
0.017031356692314148,
0.04531706124544144,
0.036370281130075455,
-0.0064989919774234295,
-0.009709667414426804,
0.06555640697479248,
-0.07273921370506287,
-0.01625795289874077,
-0.021126294508576393,
0.015110079199075699,
-0.008040492422878742,
0.02815347909927368
] |
<p>The mass of a nucleus if less than the mass of the protons and nucleus. The difference is knows as binding energy of the nucleus. This nuclear binding energy is derived from the strong nuclear force. </p>
<p>Now my question is that does the strong nuclear force provide this energy? How does the mass decrease if the force provides the energy?</p> | 1,401 | [
-0.022740162909030914,
-0.033137209713459015,
-0.00633177999407053,
-0.02893827110528946,
0.012338103726506233,
0.039389774203300476,
-0.023222526535391808,
-0.06600575894117355,
0.011546432971954346,
-0.07469478994607925,
0.036486487835645676,
0.009556073695421219,
0.06874893605709076,
-0.027626823633909225,
0.006077281199395657,
0.007397622801363468,
0.003435221966356039,
-0.033052362501621246,
-0.013226364739239216,
-0.012559914030134678,
-0.014713728800415993,
0.024174237623810768,
-0.003125517163425684,
0.03474699333310127,
-0.02380337193608284,
0.034849245101213455,
0.04183574020862579,
0.011316495016217232,
0.0352327898144722,
0.06087503209710121,
0.013609426096081734,
-0.037947218865156174,
0.01232865359634161,
0.028964228928089142,
0.02014736272394657,
-0.01428942196071148,
-0.030430076643824577,
-0.01713019236922264,
-0.002138165757060051,
0.039898406714200974,
-0.03247244283556938,
-0.021292077377438545,
-0.0124580729752779,
0.03787378594279289,
-0.016480600461363792,
0.029898077249526978,
0.037340857088565826,
-0.006919200532138348,
0.044145483523607254,
-0.041452255100011826,
0.06219499930739403,
0.025227701291441917,
0.048262231051921844,
0.004694529343396425,
-0.02494753524661064,
-0.033087633550167084,
0.04758688807487488,
0.052466269582509995,
-0.02128412388265133,
-0.04850592836737633,
-0.0032334630377590656,
-0.0018006954342126846,
0.005138217005878687,
-0.010369488969445229,
-0.013182372786104679,
0.04087028652429581,
-0.048755042254924774,
-0.026730868965387344,
0.031853873282670975,
0.02327166311442852,
0.04457933455705643,
-0.0011364856036379933,
0.014041912741959095,
0.004505007993429899,
-0.013365901075303555,
-0.029574310407042503,
0.020908813923597336,
0.033464450389146805,
0.038784127682447433,
0.05894581973552704,
-0.04599074646830559,
0.006594998762011528,
0.042784612625837326,
0.030894700437784195,
0.014904328621923923,
0.002352569717913866,
0.04976286366581917,
-0.03094632551074028,
0.004148808307945728,
0.03734718635678291,
-0.007512007839977741,
-0.0068089039996266365,
0.02925381064414978,
-0.015058387070894241,
-0.012503419071435928,
0.021909398958086967,
-0.0006071319803595543,
0.05818115547299385,
0.029488788917660713,
0.016177237033843994,
0.050324082374572754,
-0.017309531569480896,
0.02064298279583454,
0.07675057649612427,
0.01740099862217903,
-0.012877027504146099,
-0.0417446605861187,
0.003911454696208239,
-0.020583316683769226,
0.020584063604474068,
-0.037494998425245285,
-0.026469774544239044,
-0.0016927075339481235,
-0.040625348687171936,
0.013937854208052158,
-0.04504775628447533,
0.013966036960482597,
-0.014922731555998325,
0.03748263418674469,
0.05020279064774513,
0.0464324876666069,
-0.026483388617634773,
0.0057226913049817085,
-0.024341436102986336,
-0.03952174633741379,
-0.01608075015246868,
0.04083418473601341,
-0.01639573648571968,
-0.02941589057445526,
0.028285548090934753,
-0.007997550070285797,
-0.01856217160820961,
-0.015438933856785297,
0.008867389522492886,
0.041048116981983185,
0.002635684795677662,
-0.11751937121152878,
-0.03857966512441635,
0.05558883398771286,
-0.03420022875070572,
-0.008408209308981895,
-0.09464091807603836,
0.013204260729253292,
0.014076507650315762,
0.06000741943717003,
0.01953935995697975,
-0.029066702350974083,
0.0010543287498876452,
0.03242979571223259,
0.00148291839286685,
0.013020630925893784,
-0.01796237751841545,
-0.0034930510446429253,
-0.038726143538951874,
-0.01747211441397667,
-0.08798892796039581,
0.0168344397097826,
0.016818000003695488,
-0.011114663444459438,
-0.005612615961581469,
0.05471818521618843,
-0.04705394059419632,
0.023754116147756577,
0.003110634395852685,
0.006603950634598732,
-0.03469329699873924,
0.03671387583017349,
0.014907659031450748,
-0.025713838636875153,
0.04977234825491905,
0.013227446936070919,
0.04693133011460304,
0.012359051033854485,
0.027581075206398964,
0.02039824239909649,
-0.054066237062215805,
-0.03269042447209358,
-0.0371815450489521,
0.002387097803875804,
0.020451674237847328,
-0.060563210397958755,
-0.01134007889777422,
-0.008319507353007793,
-0.000906667672097683,
-0.0004604351706802845,
0.03514230251312256,
-0.002548075281083584,
-0.0054852599278092384,
0.010188561864197254,
-0.021102095022797585,
-0.031158985570073128,
-0.1024186909198761,
0.02071145735681057,
0.005787372589111328,
-0.01930130645632744,
0.005808009300380945,
0.03837312012910843,
0.0031103540677577257,
-0.02511702850461006,
-0.00924675539135933,
-0.02838355116546154,
0.021983547136187553,
-0.025547850877046585,
0.020897360518574715,
0.029392052441835403,
0.03087841160595417,
0.024350356310606003,
0.0027235562447458506,
0.01794871687889099,
0.0030916195828467607,
-0.03537208214402199,
0.029212171211838722,
-0.013425622135400772,
-0.018309475854039192,
0.004802485927939415,
-0.0001119171065511182,
0.008455474860966206,
-0.026991097256541252,
0.02271452359855175,
0.040863171219825745,
-0.023105842992663383,
0.08875592797994614,
0.01741069369018078,
-0.005039639305323362,
0.018487626686692238,
0.0729333758354187,
0.012831710278987885,
0.008801010437309742,
-0.06288538128137589,
-0.03869570419192314,
-0.05105636268854141,
-0.036566365510225296,
0.012514927424490452,
0.04172947630286217,
-0.06039359048008919,
0.024211592972278595,
0.036152102053165436,
0.013229669071733952,
0.025181833654642105,
0.012969129718840122,
-0.019931772723793983,
-0.05074687674641609,
0.020722854882478714,
0.010487837716937065,
-0.004318848717957735,
0.0429781973361969,
0.015281797386705875,
0.044770173728466034,
0.0036401310935616493,
-0.011130860075354576,
-0.0005886243307031691,
0.04678398743271828,
-0.015181419439613819,
-0.0019809461664408445,
0.004503874108195305,
-0.07520163059234619,
0.037729911506175995,
-0.02510399930179119,
0.02423010766506195,
-0.006977746728807688,
-0.025180669501423836,
-0.010209913365542889,
-0.03552744910120964,
-0.027752572670578957,
-0.0016028808895498514,
0.016983512789011,
0.0008968394249677658,
0.002549063181504607,
0.006045101676136255,
-0.03754792362451553,
0.014035710133612156,
-0.01677234098315239,
-0.001104220631532371,
-0.017901942133903503,
-0.024931656196713448,
0.037391919642686844,
-0.016631076112389565,
0.023094788193702698,
-0.02928447350859642,
-0.016335047781467438,
-0.040665339678525925,
-0.08480434864759445,
-0.021176952868700027,
0.02549721673130989,
-0.044510554522275925,
0.006063124630600214,
-0.03458305448293686,
-0.0039146277122199535,
0.03483128175139427,
-0.0181384589523077,
0.00920875370502472,
0.04078998789191246,
-0.015319829806685448,
-0.0327962264418602,
-0.012548287399113178,
-0.04044444486498833,
-0.017663871869444847,
0.0011837832862511277,
0.020458607003092766,
0.07181121408939362,
-0.01234790962189436,
-0.00765388086438179,
0.007447785697877407,
-0.020485907793045044,
-0.030326174572110176,
-0.02034403383731842,
-0.0019409587839618325,
0.03130380064249039,
-0.019747931510210037,
0.021615780889987946,
0.0553828701376915,
-0.0345570370554924,
0.00059082533698529,
-0.04022280126810074,
-0.0006425596075132489,
0.06543026119470596,
-0.019258366897702217,
0.06304536759853363,
0.014496780931949615,
-0.03367914259433746,
0.10728810727596283,
0.04428033530712128,
-0.024284960702061653,
-0.008557732217013836,
-0.024585818871855736,
-0.0036222978960722685,
-0.02594231255352497,
0.016018347814679146,
0.00003338428359711543,
0.029958272352814674,
0.011125653050839901,
0.040700897574424744,
0.01638725958764553,
-0.003028129693120718,
-0.018313778564333916,
-0.03262697532773018,
-0.0026851268485188484,
0.013896909542381763,
-0.012099361047148705,
0.05158683657646179,
0.004037649370729923,
-0.025590645149350166,
-0.008408477529883385,
0.021802326664328575,
0.06942860782146454,
-0.033514074981212616,
-0.040404096245765686,
0.04867817834019661,
0.026239758357405663,
-0.002964530372992158,
-0.04596315696835518,
0.05881381779909134,
-0.008637049235403538,
0.02414563111960888,
0.04436898231506348,
0.008597344160079956,
0.048543788492679596,
-0.010410744696855545,
0.015415096655488014,
0.007577294018119574,
0.042907994240522385,
-0.020810281857848167,
-0.045515451580286026,
0.0010493590962141752,
-0.052741024643182755,
0.02343624271452427,
-0.001845542574301362,
-0.009885569103062153,
0.017577791586518288,
0.02222118340432644,
0.04313413426280022,
0.004663652740418911,
-0.027755726128816605,
0.0009172161226160824,
-0.06594083458185196,
-0.011411165818572044,
0.03841543570160866,
0.051374033093452454,
-0.0037298223469406366,
0.06709279865026474,
0.0170937217772007,
0.04421582072973251,
0.027711713686585426,
-0.042810216546058655,
-0.08787179738283157,
0.0475478433072567,
-0.06156514585018158,
-0.004639584105461836,
-0.007900668308138847,
-0.03191085904836655,
-0.026598777621984482,
-0.012908749282360077,
0.000334720010869205,
-0.038193441927433014,
0.008072692900896072,
-0.04140323027968407,
-0.002388063818216324,
-0.030009495094418526,
-0.0167654138058424,
-0.01122088823467493,
0.04013027623295784,
0.03325258940458298,
-0.022338148206472397,
0.005972967017441988,
0.017336951568722725,
-0.05830751731991768,
-0.024584395810961723,
-0.03696858137845993,
0.0024623689241707325,
-0.018792301416397095,
0.023875482380390167,
0.03900803253054619,
0.03215976804494858,
-0.021770775318145752,
0.007041746284812689,
0.017786283046007156,
0.025197088718414307,
0.017404822632670403,
-0.008551346138119698,
0.007264992687851191,
-0.05380212515592575,
-0.02343529462814331,
-0.0013373550027608871,
0.015702536329627037,
0.0038541073445230722,
0.017344878986477852,
0.01365592796355486,
-0.00040529784746468067,
-0.030251171439886093,
0.08978630602359772,
0.06360969692468643,
0.051264870911836624,
-0.00005897029404877685,
-0.07060897350311279,
0.022824915125966072,
-0.05326661467552185,
-0.021566420793533325,
0.021783698350191116,
-0.024963311851024628,
-0.038957610726356506,
0.0334068201482296,
-0.011768681928515434,
0.019292300567030907,
-0.03836400806903839,
-0.008916908875107765,
0.004164611455053091,
0.016242317855358124,
-0.01625058986246586,
-0.01676078885793686,
0.039449311792850494,
0.0200908575206995,
0.03422427177429199,
-0.013937394134700298,
0.0029404517263174057,
-0.06658057868480682,
-0.01821569912135601,
0.036127977073192596,
0.061314262449741364,
-0.03001348301768303,
0.0038770148530602455,
-0.024216309189796448,
-0.009638875722885132,
0.03849685192108154,
-0.04214262217283249,
0.03403113782405853,
-0.015577416867017746,
0.006877280306071043,
0.009631937369704247,
-0.04876786097884178,
-0.014299560338258743,
0.01853596791625023,
-0.010386936366558075,
-0.006121966056525707,
-0.031031761318445206,
-0.011403440497815609,
0.009755809791386127,
0.030507395043969154,
0.04873311519622803,
0.04169580712914467,
0.006758642848581076,
0.015793640166521072,
-0.008121234364807606,
0.017124328762292862,
-0.02241518720984459,
-0.09015210717916489,
-0.006781893782317638,
-0.014068283140659332,
-0.01748170331120491,
0.027002420276403427,
-0.04663277789950371,
-0.08035680651664734,
0.0004554857441689819,
0.011646020226180553,
-0.037496503442525864,
-0.039883218705654144,
-0.060464903712272644,
0.02270696870982647,
0.03784431889653206,
-0.0333777517080307,
0.04128646478056908,
0.019518934190273285,
-0.04057618975639343,
0.022014271467924118,
-0.03021474927663803,
0.008510890416800976,
-0.05228756368160248,
0.0038510120939463377,
-0.04514681547880173,
0.016843009740114212,
-0.021561192348599434,
0.035850364714860916,
-0.022241933271288872,
0.02202610857784748,
0.003967786207795143,
-0.01410316675901413,
0.00437810318544507,
0.023612044751644135,
0.0018325875280424953,
0.01524415798485279,
-0.03553059324622154,
0.014338885433971882,
0.009713005274534225,
-0.05075303465127945,
-0.004007265437394381,
0.03624802082777023,
-0.010298267006874084,
0.011757707223296165,
-0.013188177719712257,
0.015652881935238838,
0.003578637260943651,
-0.05164378136396408,
0.0407540500164032,
-0.041213519871234894,
0.04286474362015724,
-0.01642053760588169,
-0.014276874251663685,
0.002817046595737338,
-0.07161988317966461,
-0.017871014773845673,
0.0007539056241512299,
-0.028692984953522682,
-0.02225027047097683,
0.007208897266536951,
0.052767615765333176,
0.03587186709046364,
-0.0035066925920546055,
-0.06298084557056427,
-0.031668152660131454,
-0.005018624477088451,
0.017693331465125084,
-0.0014329474652186036,
-0.024641631171107292,
0.004863768815994263,
-0.05424206331372261,
-0.019237888976931572,
0.007304752711206675,
0.028026433661580086,
-0.04039756581187248,
-0.015511598438024521,
0.04609069600701332,
-0.008411839604377747,
0.05519527196884155,
-0.010824570432305336,
-0.040772244334220886,
-0.0005075740627944469,
0.008491591550409794,
0.0006482446915470064,
-0.002054741606116295,
0.07496517151594162,
-0.015061432495713234,
-0.034852586686611176,
0.010746946558356285,
-0.017467230558395386,
0.05265478044748306,
-0.01463804766535759,
0.008842027746140957,
0.048524871468544006,
0.01637253724038601,
0.005281815305352211,
-0.030781297013163567,
0.029806140810251236,
-0.011288324370980263,
0.07031640410423279,
0.019576188176870346,
0.0022979890927672386,
-0.038149695843458176,
-0.053515154868364334,
0.018308540806174278,
0.0063554393127560616,
0.008517645299434662,
-0.0016264357836917043,
0.04925108328461647,
0.007799927145242691,
0.01798968017101288,
-0.008116318844258785,
-0.030001213774085045,
0.02836970053613186,
0.011487067677080631,
0.017337583005428314,
0.007728503085672855,
0.011010764166712761,
-0.011818035505712032,
-0.022036878392100334,
-0.05539180338382721,
0.00550597719848156,
0.05395810678601265,
-0.019651567563414574,
0.007893630303442478,
-0.003897547721862793,
-0.012072108685970306,
0.02395758405327797,
-0.02141084522008896,
0.0007340225856751204,
-0.014317612163722515,
0.004826654680073261,
0.023012468591332436,
0.003358981106430292,
0.018898358568549156,
0.07149367779493332,
0.04255486652255058,
-0.022196641191840172,
0.02985294722020626,
0.0430443249642849,
0.03060184419155121,
0.005327360238879919,
-0.025244997814297676,
-0.037370339035987854,
0.012220500968396664,
-0.002930079586803913,
0.03439091145992279,
-0.012046832591295242,
-0.009290172718465328,
0.011331520043313503,
-0.00045729862176813185,
0.0439586415886879,
-0.029180217534303665,
-0.028433021157979965,
-0.0038509187288582325,
0.01817685179412365,
0.006547457072883844,
0.011404525488615036,
0.0011287805391475558,
0.039675191044807434,
0.01975368894636631,
0.032930951565504074,
0.02446950040757656,
0.023550327867269516,
-0.05834304913878441,
-0.008334049955010414,
-0.01329956203699112,
-0.050334632396698,
0.00012254132889211178,
-0.044642847031354904,
-0.042931001633405685,
0.03586588427424431,
0.000006995500370976515,
0.028832798823714256,
0.018179096281528473,
0.01768317073583603,
0.0000057703359743754845,
0.07112963497638702,
0.03643013909459114,
0.03145739808678627,
0.003914948087185621,
0.031528424471616745,
0.09237981587648392,
0.05028892308473587,
0.0007416930166073143,
-0.06400937587022781,
0.00542585039511323,
-0.023582948371767998,
0.010908237658441067,
0.00323021924123168,
0.0058651757426559925,
-0.017595041543245316,
0.03449228033423424,
0.0052838679403066635,
0.06611645221710205,
-0.012265815399587154,
0.011916439980268478,
0.056925900280475616,
-0.03586051985621452,
-0.05094761773943901,
0.0036165197379887104,
-0.0015035823453217745,
-0.028291005641222,
0.0011850494192913175,
-0.03631877154111862,
0.01585056632757187,
0.007030729204416275,
-0.0042233592830598354,
-0.032905708998441696,
-0.009035356342792511,
0.009760551154613495,
-0.001020694267936051,
-0.04734335467219353,
-0.00039780259248800576,
-0.013510286808013916,
-0.02216089703142643,
-0.05766558274626732,
0.016091950237751007,
0.019604045897722244,
-0.0018213804578408599,
-0.00938788615167141,
0.006543884519487619,
0.009365912526845932,
0.015117127448320389,
-0.011908327229321003,
0.008518771268427372,
-0.021012019366025925,
0.01071811094880104,
-0.010874887928366661,
0.03691979497671127,
-0.02699289843440056,
0.011589858680963516,
0.016791678965091705,
0.028338413685560226,
-0.00405542366206646,
-0.031404048204422,
-0.0035566361621022224,
0.008082911372184753,
0.019103100523352623,
-0.02876025252044201,
-0.030712438747286797,
-0.0534965842962265,
0.008544421754777431,
-0.02193133719265461,
0.02580157108604908,
0.024377750232815742,
0.026508476585149765,
0.021596040576696396,
-0.022870225831866264,
0.016247553750872612,
-0.04076176509261131,
-0.0010522397933527827,
-0.010909678414463997,
0.016486668959259987,
-0.03711942583322525,
-0.06046590954065323,
0.03226429596543312,
0.04266316816210747,
0.030163828283548355,
0.023889726027846336,
0.004310736432671547,
-0.033727142959833145,
-0.09438607096672058,
0.06904861330986023,
-0.02278265543282032,
-0.039851486682891846,
-0.011097519658505917,
-0.000036551078665070236,
0.01384518202394247,
0.03678041324019432,
-0.03014875203371048,
-0.0017101663397625089,
-0.027302460744976997,
0.008348213508725166,
0.021071232855319977,
-0.04968501999974251,
-0.01022755354642868,
0.045457273721694946,
-0.022726088762283325,
0.0046945600770413876,
-0.0016882239142432809,
-0.006014953833073378,
0.042036257684230804,
-0.010255789384245872,
0.016662204638123512,
0.026085874065756798,
-0.021001849323511124,
-0.0008309401455335319,
0.0023180246353149414,
-0.03519795462489128,
0.026185179129242897,
0.022752420976758003,
-0.015524343587458134,
-0.02370334230363369,
-0.0136661222204566,
-0.026937684044241905,
-0.016006991267204285,
0.0286822821944952,
0.04727141559123993,
-0.01748173125088215,
0.035675156861543655,
-0.014677812345325947,
0.006933094933629036,
-0.019776180386543274,
0.0007388544618152082,
-0.07957686483860016,
0.019627142697572708,
0.027905484661459923,
-0.025553995743393898,
-0.0473843477666378,
0.030186250805854797,
-0.014024299569427967,
0.007293422240763903,
0.021837586537003517,
0.001538592390716076,
-0.012988109141588211,
-0.0017166022444143891,
0.026918502524495125,
-0.021937163546681404,
0.07110273092985153,
0.013453284278512001,
-0.005452155135571957,
0.03132470324635506,
-0.06185339763760567,
-0.031062401831150055,
0.0012578063178807497,
-0.033195387572050095,
0.008484252728521824,
0.03397838771343231,
-0.013633005321025848,
-0.020315665751695633,
0.07069888710975647,
-0.007767044007778168,
0.012953785248100758,
0.028106292709708214,
-0.017320426180958748,
0.002274793339893222,
0.0005448104930110276,
-0.011496084742248058,
-0.004404562991112471,
-0.015596526674926281,
0.03910384327173233,
0.03803402557969093,
-0.015769554302096367,
-0.001587653998285532,
-0.0013513303129002452,
-0.013590032234787941,
0.013035779818892479,
0.005373021587729454,
0.031929776072502136,
0.011034970171749592,
0.032943762838840485,
-0.013585010543465614,
0.007195735815912485,
-0.023134272545576096,
0.00187470274977386,
-0.1079530343413353,
-0.0322503037750721,
-0.03160598874092102,
-0.013493864797055721,
0.036818746477365494,
-0.039238736033439636,
0.05174269154667854,
-0.013317246921360493,
-0.056194208562374115,
-0.013010325841605663,
-0.018713660538196564,
0.0024404849391430616,
-0.011394914239645004,
-0.009629842825233936,
-0.012029808014631271,
0.02644440159201622,
0.013745413161814213,
0.06821775436401367,
0.0053806123323738575,
0.019116641953587532,
0.025769678875803947,
-0.008859225548803806,
-0.033679865300655365,
0.020164042711257935,
-0.002282160334289074,
-0.007909177802503109,
0.0735124945640564,
-0.004014178644865751,
-0.015971260145306587,
0.04484591633081436,
-0.01166514866054058,
0.019734850153326988,
-0.011667448095977306,
-0.007156085222959518,
-0.02223285287618637,
0.037809837609529495,
-0.0066422270610928535,
-0.00916213821619749,
-0.00021286214177962393,
0.046676214784383774,
-0.020939696580171585,
0.017375845462083817,
0.010269209742546082,
0.013799785636365414,
0.027362285181879997,
-0.042132459580898285,
0.0013841581530869007,
0.011086092330515385,
0.0067915101535618305,
0.017790475860238075,
-0.022353660315275192,
0.01091974601149559,
0.04300221428275108,
-0.015400578267872334,
-0.02441663108766079,
-0.01956942304968834,
-0.01358881127089262,
0.029366597533226013,
0.014135885052382946,
0.0009814187651500106,
0.03473161533474922,
0.01606150157749653,
-0.0002568331838119775,
-0.012841042131185532,
0.025528376922011375,
-0.03265791013836861,
-0.031605519354343414,
0.028485428541898727,
0.03306421637535095,
0.03848657011985779,
-0.007485852111130953,
-0.05659062787890434,
-0.05987559258937836,
0.03813339024782181,
0.016823168843984604,
0.026859141886234283,
-0.0451333150267601,
-0.04490938037633896,
-0.006735946051776409,
-0.04827548563480377,
0.018331943079829216,
-0.025315968319773674,
-0.007358929608017206,
-0.03592810034751892,
-0.002323699649423361,
0.014516337774693966,
-0.008136490359902382,
0.032993946224451065,
0.00960331317037344,
-0.03997316583991051,
0.02899717353284359,
-0.014495900832116604,
0.01281169056892395,
-0.032195545732975006,
0.009204069152474403,
-0.024142729118466377,
-0.016887299716472626,
-0.014939768239855766,
-0.004808120429515839,
-0.045634813606739044,
0.048206161707639694,
0.008494053967297077,
0.00500806188210845,
0.011456227861344814,
-0.017467884346842766,
0.0035287041682749987,
0.06620963662862778,
-0.010899599641561508,
0.007723574060946703,
0.0840434581041336,
-0.011860947124660015,
0.005621790885925293,
0.03967193886637688,
-0.03251463174819946,
-0.03155335783958435,
0.019080527126789093,
-0.04631885513663292,
0.018936216831207275,
-0.004811916500329971,
-0.013230899348855019,
0.016330737620592117,
-0.021341264247894287,
-0.0036303787492215633,
0.05765099450945854,
-0.03517328202724457,
-0.029290765523910522,
0.027172446250915527,
0.03229870647192001,
0.03405707702040672,
0.03552901744842529,
0.027213994413614273,
0.0013033250579610467,
0.012822967022657394,
0.029615549370646477,
0.04703059792518616,
0.03595046326518059,
0.01925906166434288,
0.022206680849194527,
0.027910280972719193,
0.023926932364702225,
-0.006345393601804972,
0.03130882978439331,
0.017748823389410973,
-0.043965019285678864,
-0.0699567198753357,
0.0019631418399512768,
-0.014136625453829765,
0.029064808040857315,
0.00731211481615901,
-0.02082551084458828,
0.07959796488285065,
-0.027997778728604317,
0.026895320042967796,
-0.019424783065915108,
-0.008021295070648193,
-0.055858463048934937,
0.015708928927779198,
-0.01467518974095583,
0.03078494966030121,
0.01980883814394474,
0.0006466309423558414,
0.0023919453378766775,
-0.004312749952077866,
0.013327150605618954,
-0.03408745676279068,
-0.01636854000389576,
0.012282113544642925,
-0.012697366997599602,
-0.04802436754107475,
0.014195836149156094,
-0.0246603861451149,
-0.014869260601699352,
0.03697220981121063,
0.061652205884456635,
0.03408569097518921,
-0.002393868053331971,
-0.008421892300248146,
-0.01828017830848694,
0.07934053242206573,
-0.04542684555053711,
0.0018219451885670424,
-0.027466297149658203,
-0.014221258461475372,
-0.037729959934949875,
-0.022457769140601158
] |
<p>If we are to believe that holographic principle holds over a wide number of dimensions, and gravitational theories, but specially, those that are relevant to our universe, then there must be some 3D QFT that is the dual description of our current 4D General relativity, over what it seems to be asymptotically flat de-Sitter spacetime.</p>
<blockquote>
<p>What QFT theories are candidates for being the holographic dual of
gravitational theory in <em>our</em> universe?</p>
</blockquote> | 1,402 | [
0.015685394406318665,
0.009208357892930508,
0.03535658121109009,
-0.038183048367500305,
0.05277770012617111,
-0.003694697516039014,
-0.04875689372420311,
-0.03260045871138573,
0.007721447851508856,
-0.05836731195449829,
0.0019226620206609368,
0.00459360470995307,
0.02825317718088627,
0.03903955593705177,
0.00659762229770422,
-0.023073121905326843,
-0.001604856108315289,
-0.043034713715314865,
-0.04406459629535675,
-0.05243271216750145,
0.028699710965156555,
0.05438072606921196,
0.015751108527183533,
0.008443831466138363,
-0.019534341990947723,
0.002350329654291272,
0.012708849273622036,
0.0492643378674984,
0.020080892369151115,
0.06501282006502151,
-0.003956367261707783,
-0.010470593348145485,
-0.009549101814627647,
0.05694827064871788,
-0.014502350240945816,
0.00914047658443451,
-0.0075433277525007725,
0.0014719772152602673,
-0.012536861002445221,
-0.005280979443341494,
-0.06269475817680359,
-0.014289489015936852,
-0.03337255120277405,
0.0601937510073185,
-0.016714921221137047,
0.01322156935930252,
0.004939020145684481,
-0.009377001784741879,
0.027133865281939507,
-0.07564584910869598,
0.06566902995109558,
0.0022675874643027782,
0.024627942591905594,
0.0151794059202075,
-0.011099046096205711,
-0.011688819155097008,
0.08410423994064331,
0.0793284922838211,
0.003577067516744137,
-0.03998823091387749,
-0.03901161253452301,
0.006872904486954212,
0.03681163117289543,
-0.04277387261390686,
-0.036702960729599,
0.05345688387751579,
-0.008361417800188065,
0.01567409746348858,
-0.03689030185341835,
-0.013221507892012596,
-0.010916429571807384,
0.009460014291107655,
0.04852840676903725,
0.03491684049367905,
0.00629896204918623,
0.021689727902412415,
-0.036202482879161835,
0.010685932822525501,
0.02656484767794609,
-0.0007436156738549471,
0.0011558133410289884,
0.0014862560201436281,
0.03819999843835831,
0.003104420844465494,
0.00556501280516386,
0.006550658494234085,
0.05600770562887192,
0.008890396915376186,
-0.02646160125732422,
0.06070699542760849,
-0.0027155003044754267,
-0.006025169510394335,
0.04976223036646843,
-0.01491456013172865,
-0.01519620232284069,
0.026315879076719284,
0.02616698108613491,
0.029682500287890434,
-0.0172075554728508,
-0.004009386524558067,
-0.010459529235959053,
-0.01087980717420578,
0.0015420069685205817,
0.05830831080675125,
0.015262876637279987,
-0.03812643140554428,
-0.03571915253996849,
0.010326867923140526,
-0.017752498388290405,
0.003358956892043352,
-0.05169496685266495,
0.0380047969520092,
-0.03965918347239494,
-0.004636803176254034,
-0.014077218249440193,
0.00041865441016852856,
0.0365910679101944,
-0.05721519514918327,
0.03591635823249817,
0.08055173605680466,
0.030764922499656677,
-0.021644042804837227,
0.032507311552762985,
-0.037132877856492996,
-0.06427054107189178,
-0.0063788569532334805,
0.014714429154992104,
-0.010529913939535618,
-0.018780404701828957,
0.01522486936300993,
0.008937862701714039,
-0.027965635061264038,
-0.0007711397483944893,
0.008128524757921696,
0.05758579075336456,
-0.028066551312804222,
-0.09514930844306946,
-0.04344620928168297,
0.017516743391752243,
-0.012605566531419754,
-0.013335201889276505,
-0.04521026462316513,
0.031102290377020836,
0.02779954858124256,
0.05466519668698311,
0.011972976848483086,
-0.012739090248942375,
0.02868478000164032,
0.056540217250585556,
0.020520176738500595,
-0.04738372191786766,
-0.0257941372692585,
-0.006658650003373623,
-0.027561349794268608,
-0.014018439687788486,
-0.0904507040977478,
-0.004463186953216791,
0.006772776134312153,
-0.003985965624451637,
-0.02139076218008995,
0.05708710849285126,
-0.0229796189814806,
-0.03468449041247368,
0.011754950508475304,
0.010094130411744118,
-0.021837450563907623,
0.06500991433858871,
0.005093554966151714,
0.03009016625583172,
0.04454215243458748,
-0.018455328419804573,
0.009455504827201366,
0.023935727775096893,
0.03902033343911171,
0.004116763360798359,
-0.01836336776614189,
-0.0006512615364044905,
-0.022067466750741005,
0.005198844242841005,
-0.023516271263360977,
-0.006503426469862461,
-0.022239239886403084,
-0.007541371509432793,
-0.005738462321460247,
-0.000555214355699718,
0.01676889881491661,
-0.005460378248244524,
-0.013517405837774277,
0.016536450013518333,
-0.032275084406137466,
0.0061608292162418365,
-0.039147697389125824,
-0.005111444275826216,
0.03639242798089981,
0.019569749012589455,
0.011247899383306503,
0.04128725454211235,
0.026015106588602066,
-0.0526830218732357,
-0.02118213102221489,
-0.022818049415946007,
0.0504244789481163,
0.018987780436873436,
0.030334321781992912,
0.025128060951828957,
0.01305939070880413,
0.03943880647420883,
-0.04174994304776192,
0.0015092747053131461,
0.007873687893152237,
-0.041613202542066574,
0.02320009283721447,
-0.0020562547724694014,
0.044298797845840454,
-0.06943272054195404,
0.014768212102353573,
0.03601628914475441,
0.007191182114183903,
-0.044637084007263184,
0.04791731387376785,
-0.08419983088970184,
0.008180691860616207,
0.017279041931033134,
-0.026670405641198158,
0.011566131375730038,
0.024408407509326935,
-0.02424880489706993,
0.012890501879155636,
0.008545449003577232,
-0.01855364814400673,
-0.0486120842397213,
-0.006838936358690262,
0.03413252905011177,
0.05736970156431198,
-0.02217136137187481,
0.04797947779297829,
0.048768091946840286,
0.032962579280138016,
0.012604352086782455,
0.030452733859419823,
-0.04220619052648544,
-0.02343999221920967,
0.013032550923526287,
-0.020935487002134323,
0.014765431173145771,
0.01601535454392433,
0.011071204207837582,
0.0028708025347441435,
-0.0333503857254982,
-0.026543835178017616,
-0.04806332290172577,
0.03615526109933853,
-0.018103651702404022,
0.002367798937484622,
0.009665449149906635,
-0.04593399167060852,
0.013887114822864532,
-0.0362614244222641,
-0.010837716981768608,
0.03398289531469345,
-0.010289989411830902,
0.019127991050481796,
0.0004134450282435864,
-0.010550297796726227,
0.016977358609437943,
0.02208995632827282,
-0.035993002355098724,
-0.01416452694684267,
0.03164106234908104,
-0.05082280561327934,
-0.011155841872096062,
-0.03442881256341934,
0.0019355160184204578,
0.010957231745123863,
0.034030839800834656,
0.01822558231651783,
-0.024250101298093796,
0.04429347440600395,
-0.02346792444586754,
-0.04556604474782944,
0.052930720150470734,
-0.028078719973564148,
-0.0013448488898575306,
0.011317705735564232,
-0.04145488888025284,
0.022421197965741158,
-0.031868185847997665,
-0.038918450474739075,
0.03847292438149452,
-0.015446791425347328,
0.03432375192642212,
0.0021342977415770292,
-0.01036653108894825,
-0.00937905628234148,
0.011659839190542698,
-0.0023539273533970118,
0.028876498341560364,
-0.010765118524432182,
0.00088274828158319,
0.03396264463663101,
0.02476506680250168,
-0.028749894350767136,
-0.012559234164655209,
-0.014728021807968616,
-0.030989322811365128,
0.012746711261570454,
-0.00005717906969948672,
0.0072923218831419945,
-0.044766299426555634,
0.031740929931402206,
0.023358497768640518,
-0.0448121652007103,
0.0023642012383788824,
-0.07341490685939789,
-0.028035936877131462,
0.04645783081650734,
-0.0035949195735156536,
0.03850219026207924,
0.010933910496532917,
-0.015077788382768631,
0.07725062966346741,
0.03864581510424614,
-0.008670254610478878,
0.0012929689837619662,
-0.0049324301071465015,
-0.017915867269039154,
-0.008145966567099094,
0.07373832166194916,
-0.03267700970172882,
0.0007124731782823801,
0.008143424987792969,
0.021384654566645622,
-0.013073657639324665,
0.016213731840252876,
0.014076204970479012,
-0.005911972839385271,
0.011405485682189465,
0.01818814128637314,
0.02295740880072117,
0.04430340602993965,
-0.008038164116442204,
-0.037918757647275925,
-0.0023770269472151995,
0.007825195789337158,
-0.02889789640903473,
0.004779915791004896,
-0.045391373336315155,
0.0384712852537632,
0.0035227567423135042,
0.023523706942796707,
0.021579455584287643,
0.01598619855940342,
-0.005408767610788345,
-0.024317434057593346,
-0.007360242772847414,
0.02981756255030632,
-0.00009959658927982673,
0.02169044129550457,
0.015515472739934921,
-0.016680581495165825,
0.015524455346167088,
-0.03311276063323021,
-0.018985208123922348,
0.002150573767721653,
-0.01826636679470539,
0.019257554784417152,
-0.013707982376217842,
-0.04229855537414551,
0.06595705449581146,
0.03840961679816246,
0.013954163528978825,
-0.011035431176424026,
-0.03034055605530739,
0.0010799601441249251,
-0.06592992693185806,
-0.004317689221352339,
0.011913505382835865,
0.06272613257169724,
0.020538300275802612,
0.015671327710151672,
0.03745199367403984,
-0.002151800785213709,
-0.014230664819478989,
0.01265924796462059,
-0.1036071851849556,
-0.011095385067164898,
-0.03520304337143898,
0.03664863854646683,
0.0007668072357773781,
-0.029722576960921288,
-0.01790078543126583,
-0.007783512584865093,
-0.07621733099222183,
-0.037768810987472534,
-0.02374454028904438,
-0.07520279288291931,
0.004711704794317484,
-0.010828597471117973,
-0.03292708471417427,
0.007544258143752813,
0.031227249652147293,
0.035327550023794174,
-0.027717214077711105,
0.0012635408202186227,
0.032010264694690704,
-0.03924015536904335,
0.014829328283667564,
0.029973862692713737,
0.03571334481239319,
0.006128591950982809,
0.05244358256459236,
-0.00541567662730813,
0.012399151921272278,
-0.00022041653573978692,
-0.008420681580901146,
0.024819200858473778,
0.034049466252326965,
-0.01035011000931263,
-0.047734107822179794,
-0.008849404752254486,
-0.04148034751415253,
-0.0008716217707842588,
0.014863524585962296,
0.07620620727539062,
0.009386125952005386,
-0.001971453195437789,
0.023215003311634064,
0.014210328459739685,
-0.02780769392848015,
0.01525503396987915,
0.0655452162027359,
0.01612655445933342,
-0.03321368992328644,
-0.028574766591191292,
-0.012535654939711094,
-0.002742376644164324,
-0.00129093904979527,
0.055082183331251144,
-0.010148080997169018,
-0.034660808742046356,
0.028496939688920975,
-0.0019248822936788201,
-0.008082902058959007,
-0.0464102178812027,
-0.007638086564838886,
0.017168894410133362,
0.015407482162117958,
-0.04296538233757019,
-0.010619260370731354,
-0.027944987639784813,
0.08395081013441086,
0.0508766695857048,
0.03438960760831833,
-0.029762189835309982,
-0.08128508925437927,
0.018265485763549805,
0.02490187995135784,
0.03446980193257332,
0.01842145062983036,
-0.03166532516479492,
-0.06118841469287872,
-0.008104176260530949,
0.030274920165538788,
-0.03154716640710831,
0.009411647915840149,
-0.007758929394185543,
0.007063666358590126,
-0.003645054530352354,
-0.011987132020294666,
0.011440089903771877,
-0.01303511206060648,
-0.00438748998567462,
-0.005429880693554878,
-0.002141539705917239,
0.03901278227567673,
0.011463352479040623,
0.04347750544548035,
-0.007632314693182707,
0.016361450776457787,
0.05213625729084015,
0.019749268889427185,
-0.001832206966355443,
0.018306804820895195,
-0.05244509503245354,
-0.042533598840236664,
0.017116110771894455,
0.024512432515621185,
-0.03744914010167122,
0.03556961938738823,
-0.04118049889802933,
-0.03890766575932503,
-0.01298469491302967,
-0.030744018033146858,
-0.028500081971287727,
0.013827623799443245,
-0.04092172160744667,
0.009208612143993378,
0.027028165757656097,
-0.0014846029225736856,
0.023941684514284134,
0.023457935079932213,
-0.017875051125884056,
0.003985809162259102,
-0.021952515468001366,
0.03026863932609558,
-0.03701738268136978,
0.010854366235435009,
0.001635402557440102,
-0.024033471941947937,
-0.055282171815633774,
0.028532056137919426,
-0.03457580506801605,
0.001833004062063992,
0.004890513140708208,
-0.02729172818362713,
-0.036343056708574295,
-0.00133613683283329,
-0.004130914807319641,
-0.0020877018105238676,
0.0019021682674065232,
-0.0013354653492569923,
0.027785025537014008,
0.013195779174566269,
0.03353051841259003,
0.036096084862947464,
-0.021019376814365387,
0.015250232070684433,
0.01825913041830063,
0.010306541807949543,
-0.0017278239829465747,
0.005347591359168291,
0.0030377854127436876,
-0.039205607026815414,
0.05496465042233467,
-0.007326134946197271,
0.01976250857114792,
0.008022390305995941,
-0.07415545731782913,
-0.019518960267305374,
-0.018853764981031418,
-0.004999688360840082,
0.008609786629676819,
-0.01877567172050476,
0.026047874242067337,
-0.00016844893980305642,
0.025565655902028084,
-0.10676871985197067,
-0.025868475437164307,
0.029890676960349083,
0.04475591704249382,
-0.013768492266535759,
-0.03268108144402504,
0.020193446427583694,
-0.07248324155807495,
-0.006372975185513496,
-0.008926534093916416,
0.07301580905914307,
-0.006812030449509621,
0.0039927237667143345,
0.036145877093076706,
0.031718846410512924,
0.012322093360126019,
-0.008133298717439175,
-0.009594962932169437,
0.006881745997816324,
0.0006030104705132544,
0.0028236168436706066,
-0.0047337980940938,
0.03244078531861305,
-0.012057874351739883,
-0.020876821130514145,
-0.015952538698911667,
-0.04199822247028351,
-0.025878649204969406,
-0.056537363678216934,
0.0020293593406677246,
0.016862815245985985,
0.019781863316893578,
-0.035153504461050034,
-0.06776424497365952,
0.0341973714530468,
0.006738359108567238,
0.02709749899804592,
-0.045103494077920914,
0.003955009393393993,
0.015375840477645397,
-0.04354647174477577,
0.056134119629859924,
0.012913431040942669,
-0.028366629034280777,
-0.008430029265582561,
0.036884356290102005,
0.019644560292363167,
-0.05256626382470131,
0.025341244414448738,
-0.039810910820961,
0.007935933768749237,
-0.03628935664892197,
0.030457591637969017,
0.01783841662108898,
0.017538808286190033,
-0.028149625286459923,
-0.05608720704913139,
-0.02163553610444069,
0.0016765884356573224,
0.03781075403094292,
-0.02012360841035843,
0.056795984506607056,
0.03383682295680046,
-0.03287858888506889,
-0.010410081595182419,
-0.03203416243195534,
-0.01117490604519844,
0.033386290073394775,
-0.01689469814300537,
0.02952764369547367,
-0.02800331823527813,
0.008522390387952328,
0.027076909318566322,
0.048610229045152664,
-0.037116385996341705,
0.058002226054668427,
0.02041269838809967,
0.044190097600221634,
0.02701042778789997,
-0.03324568271636963,
-0.05803890526294708,
0.07609880715608597,
-0.04892020300030708,
0.01885892264544964,
-0.0008086705929599702,
-0.005164915230125189,
0.020098330453038216,
0.007460824213922024,
0.03628230839967728,
-0.005800297018140554,
-0.046858690679073334,
-0.05730530992150307,
0.03999168425798416,
0.029708392918109894,
0.0512249618768692,
-0.011843047104775906,
0.017499547451734543,
0.0243439432233572,
-0.010182896628975868,
0.00849753525108099,
0.019072026014328003,
-0.06630319356918335,
-0.02670423500239849,
-0.02834964357316494,
-0.031795356422662735,
0.04433061555027962,
0.004507342353463173,
-0.05249392241239548,
-0.01682172901928425,
-0.03943989425897598,
0.009460506960749626,
0.010374156758189201,
0.03706364706158638,
-0.02509355917572975,
0.049161024391651154,
-0.012223483994603157,
0.03346303477883339,
-0.022515112534165382,
0.03245462104678154,
0.11659108102321625,
0.06706426292657852,
0.03648364171385765,
-0.08238942921161652,
0.04379744082689285,
-0.0023915187921375036,
0.01934131421148777,
-0.05735574662685394,
0.03110353834927082,
-0.01611422933638096,
0.04231051355600357,
-0.0005494279903359711,
0.06742128729820251,
-0.008994758129119873,
-0.05192413181066513,
0.04167705401778221,
-0.043478868901729584,
-0.03188985586166382,
0.008679247461259365,
0.028637263923883438,
-0.009541676379740238,
0.028157677501440048,
-0.029461702331900597,
0.011028103530406952,
0.016708090901374817,
0.018748925998806953,
-0.03328024595975876,
-0.029016420245170593,
0.004339207895100117,
0.0010667676106095314,
-0.0621916688978672,
-0.01594836823642254,
-0.011005525477230549,
-0.04296121746301651,
-0.026157034561038017,
0.003764642169699073,
-0.033941250294446945,
-0.031711142510175705,
0.0019417389994487166,
0.019701503217220306,
-0.0021901249419897795,
-0.01698250323534012,
-0.007083276752382517,
-0.002500019036233425,
-0.05445713922381401,
0.008357029408216476,
-0.02631361596286297,
0.020593920722603798,
-0.04688467085361481,
-0.021099239587783813,
0.006433142814785242,
-0.013606110587716103,
0.039277154952287674,
-0.018610956147313118,
-0.031092962250113487,
-0.010235980153083801,
0.039399176836013794,
-0.02316092699766159,
-0.0347505547106266,
-0.010923393070697784,
0.03181051090359688,
-0.011884089559316635,
0.03352798894047737,
-0.022487716749310493,
-0.0012255634646862745,
0.004724230617284775,
0.004604946356266737,
0.054317645728588104,
-0.016757285222411156,
-0.0002786640543490648,
-0.018343405798077583,
0.01422993466258049,
-0.038202013820409775,
-0.02243371680378914,
0.006286787334829569,
0.0169264767318964,
0.04076754301786423,
0.0014889888698235154,
0.0038996057119220495,
-0.01687425933778286,
-0.029686853289604187,
0.01237490214407444,
-0.03219357132911682,
-0.0039457897655665874,
-0.0016790974186733365,
0.0028021526522934437,
0.04366214945912361,
0.05140114203095436,
0.017641009762883186,
-0.02593931369483471,
-0.018619874492287636,
-0.018991099670529366,
0.010442017577588558,
-0.01879262551665306,
-0.0022751830983906984,
-0.008903931826353073,
-0.04257805272936821,
-0.02209986187517643,
-0.03398510441184044,
-0.015706844627857208,
0.023916974663734436,
0.007023546379059553,
0.01811450906097889,
0.03652503341436386,
-0.01279203500598669,
0.011705473996698856,
-0.002724338322877884,
0.0005270759575068951,
0.0062731592915952206,
0.024083564057946205,
0.04429274797439575,
-0.026886433362960815,
-0.048132169991731644,
-0.00008761937351664528,
0.008849705569446087,
-0.049391716718673706,
0.011241110041737556,
-0.03769276663661003,
-0.006449059583246708,
0.0048254868015646935,
0.006864657625555992,
-0.07322853058576584,
0.001279423595406115,
-0.04041106253862381,
0.013857993297278881,
-0.006049229763448238,
-0.00411198427900672,
0.014156588353216648,
0.004151341505348682,
-0.02666490152478218,
-0.05018095672130585,
-0.007855791598558426,
-0.012280061841011047,
-0.07059811055660248,
0.056854914873838425,
0.029753997921943665,
0.015836242586374283,
0.03720787912607193,
0.030348338186740875,
-0.023060642182826996,
-0.00421168003231287,
-0.04606495797634125,
-0.06797470897436142,
0.0331634022295475,
-0.027854396030306816,
0.01099738571792841,
0.029008710756897926,
-0.008774115703999996,
-0.04082559049129486,
0.012373681180179119,
-0.024502333253622055,
-0.0007363819750025868,
0.01906277798116207,
-0.022161196917295456,
-0.0002766261750366539,
-0.011194761842489243,
0.031193939968943596,
-0.0030744816176593304,
-0.03593172878026962,
0.020316656678915024,
0.011279492639005184,
0.03345136716961861,
0.011666808277368546,
0.006959959864616394,
-0.015426822938024998,
0.021316194906830788,
0.024852903559803963,
0.014244688674807549,
0.03699728846549988,
0.06847276538610458,
-0.031949032098054886,
0.041443340480327606,
0.04111109673976898,
0.04548296704888344,
-0.11841300129890442,
-0.005113828927278519,
0.04635477066040039,
0.0183128472417593,
0.049195196479558945,
-0.03167388588190079,
0.012173959985375404,
0.0017739207250997424,
-0.07976144552230835,
0.06946409493684769,
0.007711405865848064,
-0.019589822739362717,
-0.03521191328763962,
0.002005490008741617,
-0.016707681119441986,
0.06227489933371544,
0.02440132386982441,
0.013985573314130306,
-0.021042248234152794,
0.02863704226911068,
0.007858970202505589,
-0.010754222050309181,
-0.012100092135369778,
0.004834143444895744,
-0.014654122292995453,
0.022045735269784927,
0.07751797884702682,
-0.03234785422682762,
-0.043758824467659,
0.041207827627658844,
0.03018972836434841,
-0.0034374925307929516,
-0.008257494308054447,
-0.041487421840429306,
0.023744728416204453,
0.037306345999240875,
0.03412628918886185,
-0.017473159357905388,
-0.009569346904754639,
-0.008581447415053844,
0.03213953226804733,
0.036628104746341705,
0.0034449019003659487,
0.020898571237921715,
-0.013363678939640522,
-0.03900972381234169,
-0.005766435991972685,
0.029568202793598175,
0.004598662722855806,
-0.02500775270164013,
-0.03265218064188957,
0.015628598630428314,
-0.010991460643708706,
-0.026887742802500725,
-0.010919452644884586,
-0.05811074748635292,
-0.014036636799573898,
0.007892738096415997,
-0.015510305762290955,
0.0036505572497844696,
0.04231688007712364,
0.024562664330005646,
-0.008601974695920944,
0.01350373774766922,
0.007170746568590403,
0.014805098995566368,
-0.020221130922436714,
-0.005367044359445572,
0.0053117419593036175,
0.002767404308542609,
0.01997881755232811,
-0.03464462235569954,
0.005614533554762602,
0.06963756680488586,
-0.020075390115380287,
0.039816685020923615,
-0.0005557472468353808,
-0.010133655741810799,
0.0006737670628353953,
-0.07843746244907379,
0.018424229696393013,
0.01000221073627472,
-0.009659902192652225,
-0.01747926138341427,
-0.019907260313630104,
0.019173569977283478,
-0.010414865799248219,
0.05073140189051628,
0.005947730038315058,
-0.001163878827355802,
-0.0009530067909508944,
-0.0019175761844962835,
0.01572931930422783,
-0.02202630788087845,
-0.03362172469496727,
0.014326078817248344,
-0.018947787582874298,
-0.0006313782650977373,
-0.01963322050869465,
-0.012959612533450127,
0.01616608537733555,
0.03666691482067108,
-0.015105180442333221,
0.03806677088141441,
0.03139814734458923,
-0.027125904336571693,
0.06261858344078064,
0.0020746327936649323,
0.017116084694862366,
0.07397566735744476,
-0.01793256215751171,
-0.003920072689652443,
0.01576404459774494,
-0.0053373887203633785,
-0.0026977320667356253,
-0.00931096076965332,
-0.013526959344744682,
-0.03710394352674484,
-0.005815278273075819,
0.01508062519133091,
0.027154000476002693,
-0.019471460953354836,
-0.03053574077785015,
0.054143816232681274,
-0.011826411820948124,
0.025003870949149132,
0.07036462426185608,
-0.0013219108805060387,
0.0526541993021965,
-0.01859382353723049,
0.004023436922580004,
0.019329383969306946,
0.013719694688916206,
0.0027762141544371843,
0.005102648865431547,
0.03856048732995987,
0.01509779877960682,
0.011689200066030025,
0.018018465489149094,
-0.01710345782339573,
-0.001128827454522252,
0.015052934177219868,
0.06163683533668518,
-0.04287285357713699,
0.006681061815470457,
0.02869798056781292,
-0.004442369565367699,
0.03383353725075722,
0.02123260498046875,
-0.0284640621393919,
0.10004033893346786,
-0.033667728304862976,
-0.03648054599761963,
-0.007336503826081753,
-0.01930886320769787,
-0.030328597873449326,
0.03629854694008827,
0.023143555968999863,
0.06567256897687912,
-0.013063431717455387,
-0.004128430504351854,
-0.0005866800784133375,
0.015166191384196281,
-0.021595416590571404,
-0.004420901648700237,
0.0029355271253734827,
-0.004591676406562328,
-0.003002237295731902,
0.019215650856494904,
-0.02062329463660717,
-0.02862934023141861,
0.000054715710575692356,
0.017819635570049286,
0.028231561183929443,
0.03502364456653595,
0.0002964006853289902,
0.005484648514539003,
-0.04255110025405884,
0.05262655019760132,
-0.05828941613435745,
-0.001678689499385655,
0.020124899223446846,
0.02571926824748516,
0.027891971170902252,
-0.02275833487510681
] |
<blockquote>
<p><strong>Possible Duplicate:</strong><br>
<a href="http://physics.stackexchange.com/questions/15/what-experiment-would-disprove-string-theory">What experiment would disprove string theory?</a> </p>
</blockquote>
<p>We carefully observe things, observe patterns and then build theories that predict. </p>
<p>String theory is frequently criticized for not providing quantitative experimental prediction. </p>
<p>What are the problems that prevent this theory from producing quantitative experimental predictions? </p>
<p>Is there no experiment suggested by string theorists to verify validity of their theory?
Is the problem mathematical? <em>(or it just requires many dimensional equipments...just kidding).</em></p>
<p>I am not criticizing the theory because to do that I should understand it first, but I haven't studied it. I just want to know. </p> | 19 | [
-0.02966945990920067,
-0.03955668956041336,
-0.0035985573194921017,
-0.07854729145765305,
0.03552986681461334,
0.004931449890136719,
-0.0027865737210959196,
-0.031642187386751175,
0.0013999668881297112,
-0.000595447956584394,
0.04499760642647743,
0.020138949155807495,
0.0103070717304945,
0.01863621547818184,
0.009291552007198334,
0.0246882326900959,
-0.02969290129840374,
0.006412815768271685,
-0.008007591590285301,
0.017853865399956703,
-0.017134614288806915,
0.023348761722445488,
-0.00511307455599308,
0.005240693222731352,
-0.027165699750185013,
-0.00260798423551023,
0.03615295886993408,
0.011844485066831112,
0.02468637004494667,
0.06856688857078552,
-0.01161973550915718,
0.005529268179088831,
0.029898766428232193,
0.025318076834082603,
-0.009861528873443604,
0.0012085638009011745,
-0.0034861804451793432,
0.012919378466904163,
0.006152687594294548,
-0.006010583136230707,
0.004567990079522133,
-0.007138559594750404,
-0.01764565147459507,
0.054601073265075684,
-0.033728089183568954,
0.011901283636689186,
-0.0011940354015678167,
-0.03781508654356003,
0.06281095743179321,
-0.06380295753479004,
0.05507751554250717,
-0.010899307206273079,
0.00822500791400671,
0.04887138679623604,
0.004677623510360718,
-0.04614102095365524,
0.07481912523508072,
0.07377789914608002,
-0.036756061017513275,
-0.07963772863149643,
-0.05531894415616989,
-0.008912269026041031,
0.0060190544463694096,
-0.02257927879691124,
-0.03898126631975174,
0.06538178026676178,
-0.015411284752190113,
0.04625248163938522,
0.023975707590579987,
-0.003463572124019265,
-0.004498641937971115,
0.012646124698221684,
0.025518422946333885,
0.034489862620830536,
-0.021400440484285355,
0.02200707606971264,
0.014150197617709637,
0.0036739851348102093,
0.02049204707145691,
0.08266020566225052,
-0.04375826567411423,
-0.012880618683993816,
0.011274240911006927,
0.051730677485466,
0.028441255912184715,
-0.04306712746620178,
0.058455437421798706,
0.012396941892802715,
-0.012649466283619404,
0.040796633809804916,
-0.029211226850748062,
-0.04033660143613815,
0.0321359746158123,
0.004657483194023371,
-0.022583113983273506,
0.010230643674731255,
-0.008321094326674938,
0.07556673139333725,
-0.009757865220308304,
-0.028096357360482216,
-0.015251150354743004,
0.00019208133744541556,
0.04341362044215202,
0.07676166296005249,
-0.001622355543076992,
-0.009889444336295128,
0.002686459105461836,
0.04178711771965027,
-0.024416610598564148,
-0.00931672751903534,
-0.017256146296858788,
0.028719749301671982,
-0.0005123774171806872,
-0.024999422952532768,
0.0327935516834259,
-0.032755911350250244,
0.00674300966784358,
-0.056188296526670456,
0.06777117401361465,
0.062279339879751205,
-0.002108104759827256,
-0.028276748955249786,
0.01680031605064869,
-0.012765024788677692,
-0.02163676731288433,
-0.0395006500184536,
0.03974410146474838,
-0.0006009435746818781,
-0.0016794437542557716,
0.023710565641522408,
-0.009894858114421368,
0.0030867736786603928,
0.027413740754127502,
-0.015959450975060463,
0.08586043119430542,
-0.0012005115859210491,
-0.09670370817184448,
-0.07919522374868393,
0.09540429711341858,
0.0004931427538394928,
-0.010797523893415928,
-0.0714581087231636,
-0.014934645034372807,
0.018595239147543907,
0.0714515820145607,
-0.005407333839684725,
0.006437357515096664,
0.03769171983003616,
0.05691792443394661,
0.02926228940486908,
-0.012809861451387405,
0.006812309846282005,
0.003542786929756403,
-0.038655173033475876,
-0.016340503469109535,
-0.03375856950879097,
0.015399031341075897,
0.04187296703457832,
-0.019305527210235596,
-0.015329977497458458,
0.036529697477817535,
-0.01898938976228237,
0.00048223085468634963,
0.019636433571577072,
-0.008913148194551468,
-0.006756715942174196,
0.09443487226963043,
0.014190101996064186,
-0.029983382672071457,
-0.0000419295065512415,
-0.04837765917181969,
0.004614893347024918,
0.023867914453148842,
0.0011578418780118227,
0.017971795052289963,
-0.042489148676395416,
-0.028944319114089012,
0.032641638070344925,
0.012503008358180523,
-0.014710786752402782,
-0.03749166801571846,
-0.019047744572162628,
-0.009223971515893936,
0.012141058221459389,
-0.005480808671563864,
0.046874724328517914,
-0.04034803807735443,
0.00904159713536501,
0.028293324634432793,
-0.045631080865859985,
-0.024016743525862694,
-0.06637163460254669,
0.008384435437619686,
0.009860279969871044,
-0.0084218829870224,
-0.016513662412762642,
-0.013477676548063755,
0.013404825702309608,
-0.03731615096330643,
-0.01910231076180935,
0.01567920111119747,
0.05337774381041527,
0.01171046495437622,
0.020634246990084648,
0.022806981578469276,
0.04253316670656204,
0.08099635690450668,
-0.030003642663359642,
0.013041331432759762,
-0.018922658637166023,
-0.03486831113696098,
-0.007358998525887728,
-0.029559966176748276,
0.012720027007162571,
-0.05545392259955406,
0.0076117548160254955,
0.03839273378252983,
0.004711695946753025,
-0.008700384758412838,
0.04580855742096901,
-0.014687704853713512,
0.08210612088441849,
0.020748451352119446,
-0.00046430190559476614,
0.013145167380571365,
0.010537353344261646,
-0.006742727942764759,
0.0025568653363734484,
-0.0017328166868537664,
-0.020658530294895172,
-0.07450780272483826,
-0.0031417440623044968,
0.058870796114206314,
0.010377872735261917,
-0.03846912086009979,
0.05470341444015503,
0.007706425152719021,
0.05366717651486397,
0.0037612963933497667,
0.029298068955540657,
-0.011155514977872372,
-0.035450030118227005,
0.009000809863209724,
0.010861349292099476,
-0.014960452914237976,
0.009233281016349792,
0.03942878544330597,
0.01797899603843689,
-0.010936751030385494,
0.020501146093010902,
-0.012308238074183464,
0.03788134083151817,
-0.022213244810700417,
0.004011106211692095,
0.006714106537401676,
-0.012245465070009232,
0.034205712378025055,
-0.01430125255137682,
0.017846640199422836,
0.026883624494075775,
-0.0009052116656675935,
0.012228494510054588,
-0.052183184772729874,
0.012612981721758842,
-0.005074138753116131,
0.03795686736702919,
-0.030181417241692543,
-0.02204405888915062,
0.004989491775631905,
-0.06894824653863907,
-0.00392732210457325,
-0.00782602559775114,
0.0291530042886734,
-0.020676426589488983,
0.010549071244895458,
0.010386756621301174,
-0.00329259573481977,
0.006027981638908386,
-0.05853092670440674,
-0.03922336921095848,
0.019546829164028168,
-0.04131457209587097,
-0.0038265855982899666,
-0.0002684050996322185,
-0.03392517566680908,
0.012188882566988468,
-0.031085144728422165,
-0.01908819191157818,
0.03838736563920975,
-0.02169092744588852,
0.04175720363855362,
0.021504471078515053,
-0.02709156461060047,
-0.011876246891915798,
-0.023074226453900337,
-0.03797655925154686,
0.034040167927742004,
-0.023694293573498726,
-0.023258162662386894,
0.05969664081931114,
0.004701450001448393,
-0.028908804059028625,
0.0018396558007225394,
-0.022860080003738403,
-0.0434797964990139,
0.017259981483221054,
0.010474705137312412,
0.014370990917086601,
-0.05318965017795563,
0.05017085373401642,
-0.018908247351646423,
-0.052115023136138916,
0.014187303371727467,
-0.03164801374077797,
-0.05518559738993645,
0.024190068244934082,
0.005124660674482584,
0.01644177921116352,
-0.011941363103687763,
-0.05193401873111725,
0.06350693851709366,
0.021235669031739235,
-0.0541737824678421,
-0.0133361229673028,
-0.017685389146208763,
-0.028438907116651535,
-0.006957642268389463,
0.0256609208881855,
0.00936005637049675,
0.00026415562024340034,
0.0054735587909817696,
0.02869958057999611,
0.02412259764969349,
0.0078261848539114,
0.012582913041114807,
-0.03752139210700989,
-0.004755428992211819,
0.015017366036772728,
0.025324232876300812,
0.05236770212650299,
0.0081460140645504,
-0.020690053701400757,
-0.015653619542717934,
-0.0004801216418854892,
0.004789012484252453,
-0.022659290581941605,
-0.06709084659814835,
0.06035781651735306,
-0.0006642946973443031,
0.020416220650076866,
-0.027943236753344536,
0.016688307747244835,
-0.009275496006011963,
-0.004347914829850197,
-0.01320218201726675,
-0.01013813354074955,
0.042196352034807205,
0.004275745712220669,
0.01650187000632286,
0.019882410764694214,
0.039933133870363235,
-0.023742012679576874,
-0.009993229061365128,
-0.012821671552956104,
-0.013176034204661846,
-0.00870969332754612,
-0.01741916872560978,
-0.02699708379805088,
0.04474381357431412,
0.051103346049785614,
0.04047027975320816,
-0.024003518745303154,
-0.032583024352788925,
-0.009089643135666847,
-0.031208358705043793,
0.005872560199350119,
-0.040965620428323746,
0.032264452427625656,
0.012037219479680061,
0.03350265696644783,
0.02105742134153843,
-0.008512238040566444,
-0.008402837440371513,
0.00218817382119596,
-0.09614034742116928,
0.03171135112643242,
-0.056728873401880264,
-0.0141367819160223,
0.012755326926708221,
-0.004783726762980223,
-0.005169708747416735,
0.007082689553499222,
-0.00027541760937310755,
-0.009785642847418785,
0.03238225355744362,
-0.07137342542409897,
-0.03977086395025253,
-0.045881327241659164,
-0.021013662219047546,
-0.011965954676270485,
0.04859665781259537,
0.0674365907907486,
-0.034932829439640045,
0.003744950285181403,
-0.014949713833630085,
-0.04274964705109596,
-0.038812827318906784,
-0.03870971128344536,
0.004144447855651379,
0.027526507154107094,
0.06441929191350937,
0.015793876722455025,
0.008848927915096283,
-0.03271503373980522,
-0.0034418348222970963,
0.049003906548023224,
0.038254834711551666,
-0.0223116185516119,
0.003542991355061531,
-0.02263678051531315,
-0.045152097940444946,
-0.010152901522815228,
-0.010576141066849232,
0.06715415418148041,
-0.009825663641095161,
0.0033680680207908154,
0.03925788402557373,
-0.009928179904818535,
-0.015373303554952145,
0.05005693435668945,
0.039093244820833206,
0.007087751757353544,
-0.002563260728493333,
-0.021641813218593597,
-0.04477313905954361,
-0.022928306832909584,
0.006119235884398222,
0.030382437631487846,
-0.013673204928636551,
0.00013458903413265944,
0.02899833954870701,
0.015296018682420254,
0.023020977154374123,
-0.04059925675392151,
0.025150520727038383,
-0.009247181937098503,
0.03350639343261719,
-0.004320372361689806,
0.027139466255903244,
-0.0017961361445486546,
0.029084615409374237,
0.03159619867801666,
0.012907621450722218,
-0.013905172236263752,
-0.06255266815423965,
-0.0027308077551424503,
0.003291751490905881,
0.037420231848955154,
-0.004957135766744614,
-0.006895489525049925,
-0.040877144783735275,
-0.006652331445366144,
0.026223689317703247,
-0.04765266925096512,
0.03728362172842026,
-0.014803081750869751,
0.020985566079616547,
-0.03548986837267876,
0.007269138004630804,
-0.008591982536017895,
-0.0017966123996302485,
0.014446873217821121,
0.03767203167080879,
-0.01754562184214592,
-0.005180777050554752,
-0.008672865107655525,
0.01510988175868988,
0.024671826511621475,
0.04747436195611954,
0.0011794815072789788,
0.052853409200906754,
0.009565095417201519,
-0.004881252069026232,
-0.028567779809236526,
-0.06246441602706909,
0.03456565737724304,
0.01242453046143055,
-0.016102997586131096,
0.027842678129673004,
-0.0310067031532526,
-0.06789355725049973,
0.01578706130385399,
-0.000898992526344955,
0.000732516054995358,
0.0046762204729020596,
-0.05592266097664833,
-0.00048015188076533377,
0.013925858773291111,
-0.009897464886307716,
0.02416703850030899,
0.041010476648807526,
-0.019348403438925743,
0.015484749339520931,
0.004093032795935869,
0.015159616246819496,
-0.03780683875083923,
-0.001563980826176703,
-0.01918681710958481,
0.018453869968652725,
-0.06596728414297104,
0.04393954575061798,
0.007271835580468178,
-0.019835669547319412,
-0.03242642804980278,
-0.022225674241781235,
-0.0064654359593987465,
0.012146093882620335,
0.009150457568466663,
0.02391611598432064,
-0.010688384994864464,
0.02025168016552925,
-0.03016759641468525,
-0.0343993715941906,
0.025987280532717705,
0.01271527074277401,
-0.010556782595813274,
0.009982638992369175,
0.001413054415024817,
0.0016843491466715932,
-0.019510410726070404,
0.009492632001638412,
0.03592309728264809,
-0.024166623130440712,
0.050316788256168365,
-0.021547038108110428,
-0.013093438930809498,
0.01351071521639824,
-0.08032321184873581,
-0.03256258741021156,
-0.004047263413667679,
-0.01391830574721098,
0.03885204344987869,
-0.027024324983358383,
0.007798837032169104,
-0.019641008228063583,
-0.007219233550131321,
-0.05708830803632736,
-0.041630882769823074,
-0.0017455967608839273,
0.02408440224826336,
-0.024375619366765022,
0.0030478222761303186,
-0.010113496333360672,
-0.05435912683606148,
-0.003204776905477047,
-0.04278896003961563,
0.022871939465403557,
-0.022178728133440018,
-0.011571389622986317,
0.012076428160071373,
-0.01202191412448883,
0.031163988634943962,
-0.0009045197512023151,
-0.02196410670876503,
-0.0369718037545681,
-0.06670265644788742,
-0.02107774093747139,
-0.003415390383452177,
0.009370093233883381,
-0.009358900599181652,
-0.04358060285449028,
-0.02482178620994091,
-0.025144347921013832,
-0.0001923982345033437,
-0.021697087213397026,
0.0023974613286554813,
0.0005123494192957878,
0.028111327439546585,
0.010890796780586243,
-0.02522609382867813,
0.04855513200163841,
-0.02315094694495201,
0.03752405196428299,
-0.02578609250485897,
0.005068659316748381,
-0.027219433337450027,
-0.019013291224837303,
0.03610564023256302,
0.023954860866069794,
-0.0443570502102375,
-0.0008755194721743464,
0.04298606142401695,
0.017737088724970818,
-0.03107640892267227,
0.003231840208172798,
-0.02776912786066532,
0.017610160633921623,
0.01030346006155014,
0.03423473984003067,
0.005145201925188303,
0.016294043511152267,
-0.02390013076364994,
-0.09179838746786118,
-0.010063826106488705,
0.012855500914156437,
0.0579707957804203,
-0.011475220322608948,
0.07665776461362839,
0.0262580718845129,
-0.027849288657307625,
0.007227212656289339,
-0.0015570302493870258,
0.02557465061545372,
0.019991453737020493,
0.02603370137512684,
0.010341640561819077,
-0.020802972838282585,
0.0196683369576931,
0.03459220007061958,
0.02526504546403885,
-0.008660546503961086,
0.04980333521962166,
0.06472806632518768,
0.03270013630390167,
0.04874781519174576,
-0.030722271651029587,
-0.035882625728845596,
0.035952527076005936,
-0.04945972561836243,
0.03859894350171089,
0.0008429838344454765,
0.017286648973822594,
0.026281926780939102,
0.014156710356473923,
0.0012324261479079723,
0.008250332437455654,
-0.027014819905161858,
-0.05131429806351662,
0.0262928269803524,
0.013981224037706852,
0.044519294053316116,
0.03712281584739685,
-0.01691771112382412,
-0.019128864631056786,
-0.0014143218286335468,
0.05124492198228836,
-0.023395603522658348,
-0.09983056038618088,
-0.03711554780602455,
-0.028421854600310326,
-0.04714883118867874,
0.09582018852233887,
0.04933518171310425,
-0.029781019315123558,
0.008011306636035442,
-0.052079442888498306,
0.02356283739209175,
0.02506239153444767,
0.035754259675741196,
-0.06522110849618912,
0.009584920480847359,
-0.03857824206352234,
0.0295889750123024,
-0.03247520700097084,
0.017624376341700554,
0.11493273079395294,
0.052018411457538605,
0.00366617226973176,
-0.09329097718000412,
0.029406288638710976,
-0.015109733678400517,
0.004385957960039377,
-0.04488372057676315,
0.030986536294221878,
0.043314818292856216,
-0.01512183342128992,
-0.0111079141497612,
0.04581057280302048,
-0.005210851784795523,
-0.008990136906504631,
0.04779614880681038,
-0.045487865805625916,
-0.05558161437511444,
0.010776584036648273,
-0.001196302124299109,
0.02518603578209877,
0.014141860418021679,
-0.016856908798217773,
0.005218925885856152,
-0.04326581582427025,
-0.02398046851158142,
-0.002855751197785139,
-0.03734314441680908,
0.009540948085486889,
0.043848976492881775,
-0.02720903418958187,
-0.01840883679687977,
0.023892996832728386,
-0.047177400439977646,
-0.06929531693458557,
0.01165019441395998,
-0.009204812347888947,
-0.00845276564359665,
0.01574683003127575,
0.04605046659708023,
0.0075848340056836605,
0.0010085690300911665,
0.006047285161912441,
0.04385494440793991,
-0.06955751031637192,
-0.018923692405223846,
0.005714419297873974,
0.034309033304452896,
0.00392789114266634,
-0.024689406156539917,
-0.004109239671379328,
-0.019508937373757362,
-0.012828728184103966,
-0.011444189585745335,
0.0010929873678833246,
-0.011063026264309883,
0.0442720465362072,
-0.044934697449207306,
-0.02946493774652481,
0.010217929258942604,
0.03227844834327698,
-0.011430969461798668,
0.02259143628180027,
0.021810531616210938,
-0.008344070985913277,
-0.03087785840034485,
0.00067582365591079,
0.01195712573826313,
0.0066764624789357185,
-0.00014981110871303827,
-0.049246616661548615,
0.0020651218947023153,
-0.03948643058538437,
0.025743607431650162,
0.031007293611764908,
0.051479537039995193,
0.05768462270498276,
0.0453948974609375,
0.031019136309623718,
0.022480668500065804,
-0.00915534794330597,
0.018568482249975204,
-0.03736155107617378,
-0.01992272213101387,
-0.05610883980989456,
-0.004723962862044573,
0.030543947592377663,
0.043840523809194565,
-0.003586497390642762,
0.0021857386454939842,
0.00736412825062871,
0.013875788077712059,
0.015572631731629372,
-0.018627209588885307,
-0.014949553646147251,
-0.02516181580722332,
-0.019253836944699287,
-0.04103555530309677,
0.0016534836031496525,
0.019327761605381966,
0.03460867702960968,
0.014625792391598225,
0.00192641734611243,
0.031182855367660522,
-0.060140788555145264,
-0.015599530190229416,
0.034246776252985,
-0.03357300907373428,
0.0028445469215512276,
0.04441189020872116,
0.031041691079735756,
-0.021280799061059952,
-0.07185281813144684,
0.017248641699552536,
-0.018155671656131744,
0.02998320385813713,
0.004753839690238237,
-0.04674664884805679,
0.026979373767971992,
-0.014953317120671272,
0.004229121841490269,
-0.04808288440108299,
-0.01793861947953701,
-0.053110070526599884,
-0.004083828069269657,
-0.02460387535393238,
-0.02423476055264473,
0.004542974755167961,
0.01148703508079052,
-0.02938678301870823,
-0.03556868061423302,
0.03805938735604286,
0.026774661615490913,
0.012423599138855934,
0.018163859844207764,
0.012325025163590908,
0.03409090265631676,
-0.000543599424418062,
0.002203522017225623,
-0.022928060963749886,
0.0626654103398323,
-0.052588894963264465,
-0.030639734119176865,
0.04168601334095001,
-0.06799329817295074,
0.012205212377011776,
0.021454108878970146,
0.0035045798867940903,
0.0000269765605480643,
0.043322596698999405,
-0.04685644060373306,
0.007296003866940737,
-0.0018884451128542423,
-0.038979023694992065,
-0.01821792684495449,
0.006747295614331961,
0.010052439756691456,
0.002014165511354804,
-0.008993451483547688,
0.02710147760808468,
0.013665166683495045,
0.04325798153877258,
-0.015154191292822361,
0.005160890985280275,
0.0005877375369891524,
0.03364848718047142,
0.02311781235039234,
-0.01804632879793644,
-0.027580291032791138,
0.047957513481378555,
-0.040289927273988724,
0.02403634786605835,
-0.02035696990787983,
-0.021962929517030716,
-0.09987964481115341,
0.012623235583305359,
0.04644372686743736,
0.0168681051582098,
0.03392759710550308,
0.006718980148434639,
0.019298631697893143,
0.045623987913131714,
-0.047634273767471313,
0.06157407537102699,
-0.033311713486909866,
0.0017268427181988955,
-0.03751834109425545,
-0.02896655723452568,
-0.041031718254089355,
0.017161088064312935,
0.02597185969352722,
0.046759724617004395,
-0.02201014570891857,
0.027777569368481636,
-0.0034738790709525347,
0.004853944759815931,
0.01056677382439375,
0.019429804757237434,
-0.005643473006784916,
-0.004733916837722063,
0.06021197885274887,
-0.0452137216925621,
-0.007415905594825745,
0.01031394861638546,
0.026736723259091377,
0.022773081436753273,
0.017678087577223778,
-0.014877007342875004,
-0.006105956621468067,
0.014931299723684788,
0.04489804431796074,
-0.017971187829971313,
0.011459806933999062,
0.026766277849674225,
-0.024723311886191368,
0.026302900165319443,
-0.007679169066250324,
-0.01754535734653473,
-0.011880729347467422,
-0.02208891324698925,
-0.024753237143158913,
0.010002752766013145,
-0.012116027064621449,
0.00406523235142231,
-0.0018729099538177252,
0.00987763050943613,
0.004709308966994286,
-0.005202018655836582,
-0.03148181363940239,
-0.02347484789788723,
0.026549791917204857,
0.008621239103376865,
0.03577374294400215,
-0.020388487726449966,
0.017638005316257477,
-0.0027177452575415373,
-0.006618622224777937,
0.018751250579953194,
-0.006565425079315901,
-0.0028426749631762505,
-0.04189831018447876,
-0.0006659196224063635,
-0.003909193444997072,
0.02291613444685936,
0.020560462027788162,
-0.03505169227719307,
0.00013231376942712814,
0.052895400673151016,
0.0044285147450864315,
0.0200309157371521,
-0.02012474462389946,
-0.054203931242227554,
-0.005661435425281525,
-0.07238710671663284,
0.049494147300720215,
-0.020420603454113007,
0.017587849870324135,
-0.05053811892867088,
0.031853970140218735,
0.02293788455426693,
0.03276606649160385,
0.018404316157102585,
-0.009651999920606613,
-0.014857318252325058,
0.051588013768196106,
-0.0035319942981004715,
0.003584805876016617,
-0.04178212583065033,
-0.009323488920927048,
-0.0033483514562249184,
-0.035590533167123795,
-0.05126482620835304,
-0.038816094398498535,
0.006963478401303291,
0.01987232267856598,
0.04840024560689926,
-0.012312287464737892,
-0.01970377378165722,
0.008819838985800743,
-0.015647506341338158,
0.0589674673974514,
-0.02136298455297947,
0.011839150451123714,
0.055449988692998886,
-0.007710197940468788,
0.030133089050650597,
0.008057615719735622,
-0.016159294173121452,
-0.008675818331539631,
0.031608328223228455,
-0.027650075033307076,
0.02416713535785675,
-0.013582266867160797,
0.028673265129327774,
0.02092975564301014,
-0.010063741356134415,
0.031778112053871155,
0.042948730289936066,
-0.020098140463232994,
-0.002373855095356703,
0.050783902406692505,
0.0030745714902877808,
0.021690694615244865,
-0.02364952489733696,
0.008213072083890438,
0.04757388308644295,
0.0034473442938178778,
0.0005270815454423428,
0.03806491568684578,
0.0448562428355217,
0.005693634506314993,
0.006970745977014303,
0.04276252165436745,
-0.006373299285769463,
0.008014874532818794,
0.010220413096249104,
0.037088338285684586,
-0.024538381025195122,
-0.000567318347748369,
-0.0011610017390921712,
-0.038051482290029526,
0.0035889402497559786,
0.024786951020359993,
-0.012546713463962078,
0.09574346989393234,
-0.0017489911988377571,
-0.004695213865488768,
0.019291596487164497,
-0.026208730414509773,
-0.01069976482540369,
0.032723892480134964,
-0.007956293411552906,
0.04761337861418724,
-0.01699727773666382,
0.02298823557794094,
0.01621544174849987,
0.003030055668205023,
-0.002385558560490608,
0.0030656440649181604,
-0.025473006069660187,
-0.004338737111538649,
-0.027977144345641136,
-0.008232777006924152,
-0.01889350637793541,
-0.03129350021481514,
-0.030115172266960144,
0.02747538685798645,
0.010243961587548256,
-0.0032201437279582024,
-0.027943415567278862,
0.007841820828616619,
-0.0003102717746514827,
0.04716968536376953,
-0.04289634898304939,
0.011039354838430882,
-0.03516314923763275,
0.033292993903160095,
-0.025149865075945854,
-0.01588601991534233
] |
<p>I have heard before that the 4th dimension is time, however, another theory makes a lot more sense to me. This is that the 4th dimension is the third dimension stacked on top of each other in a similar in which 3d objects are just many 2d planes.</p>
<p>I have seen many articles related to the 4thdimension being time, but how do we know this?</p> | 1,403 | [
-0.023478200659155846,
-0.039242640137672424,
0.01191038079559803,
-0.04675886407494545,
0.043412789702415466,
0.028404437005519867,
0.00859483890235424,
0.0021735539194196463,
0.00880376622080803,
-0.0345655232667923,
0.008876465260982513,
0.03739817067980766,
0.015175547450780869,
0.02145358920097351,
0.008464428596198559,
0.009462971240282059,
-0.003220829414203763,
-0.01773381233215332,
0.0029391443822532892,
-0.02745061367750168,
0.02069970592856407,
0.006747125647962093,
0.01050681620836258,
0.008000143803656101,
-0.017473280429840088,
0.029898205772042274,
0.05315438285470009,
0.01058402843773365,
0.038885220885276794,
0.06940238177776337,
-0.0020093240309506655,
-0.005581595469266176,
0.018008265644311905,
0.04681314527988434,
0.011324438266456127,
-0.04325888305902481,
-0.019553368911147118,
0.009750201366841793,
0.0022540774662047625,
0.054982904344797134,
0.005481064319610596,
-0.000956533185672015,
-0.01679232344031334,
0.07780883461236954,
-0.030747199431061745,
0.035057179629802704,
-0.02744663879275322,
-0.0035148318856954575,
0.01651458814740181,
-0.07924477010965347,
0.0847192034125328,
-0.02673964947462082,
0.019306065514683723,
-0.005765877664089203,
0.006366847548633814,
0.02360868640244007,
0.07902112603187561,
0.06977495551109314,
-0.008916844613850117,
-0.040149908512830734,
-0.052320268005132675,
-0.012677978724241257,
0.0352649949491024,
-0.028709085658192635,
-0.012002041563391685,
0.040105003863573074,
-0.040547505021095276,
-0.021583963185548782,
0.008371655829250813,
-0.02500251494348049,
-0.030710551887750626,
0.02189807966351509,
0.06188935413956642,
0.005974871572107077,
-0.0001169444658444263,
-0.03426691144704819,
0.028600795194506645,
0.015374227426946163,
0.04783429205417633,
0.02760894224047661,
0.00029401853680610657,
-0.005803901236504316,
0.005959248170256615,
-0.005276313982903957,
0.011639511212706566,
0.0016117291525006294,
0.06182963028550148,
0.014049987308681011,
-0.022849055007100105,
0.02798156999051571,
-0.027667861431837082,
0.015236335806548595,
0.025022277608513832,
-0.015043491497635841,
-0.005230651702731848,
0.008464065380394459,
0.027655096724629402,
0.037472132593393326,
0.01418356504291296,
-0.02198246493935585,
0.030389269813895226,
0.005084736738353968,
0.0015229714335873723,
0.05735647305846214,
0.007401950191706419,
-0.0003358958347234875,
-0.034672096371650696,
0.04027481749653816,
0.011129260063171387,
-0.001077144406735897,
-0.060863759368658066,
0.016639821231365204,
0.014084065333008766,
-0.0008128704503178596,
0.008352470584213734,
-0.028516996651887894,
0.04767528921365738,
-0.012099235318601131,
0.03703147545456886,
0.07558543235063553,
-0.00838637724518776,
-0.05593506246805191,
0.012192049995064735,
-0.014903844334185123,
-0.09257658571004868,
0.02229907177388668,
0.03038889355957508,
-0.018948767334222794,
-0.0013177647488191724,
0.05230463296175003,
0.018741760402917862,
-0.020450381562113762,
0.03326312080025673,
-0.007527901325374842,
0.07675844430923462,
0.019299475476145744,
-0.11187341809272766,
-0.052474040538072586,
0.04621154069900513,
-0.011686914600431919,
-0.04356750473380089,
-0.06742820888757706,
0.020976683124899864,
-0.010722285136580467,
0.06886695325374603,
0.002037968020886183,
0.02039465121924877,
0.03206409513950348,
0.007108376827090979,
0.020310062915086746,
-0.028626015409827232,
-0.011953881941735744,
0.017517173662781715,
-0.0336054228246212,
0.01568281464278698,
-0.05338757485151291,
0.006813107989728451,
0.0062957159243524075,
0.0006709210574626923,
-0.04276036098599434,
0.06177631393074989,
-0.010111236944794655,
-0.01815790869295597,
0.036731697618961334,
-0.015012790448963642,
-0.02378924749791622,
0.06602998822927475,
-0.003381508169695735,
0.004883051384240389,
0.030078191310167313,
0.012808702886104584,
0.04124396666884422,
0.04574066027998924,
0.07514239102602005,
0.010542759671807289,
0.009223314933478832,
-0.03418077528476715,
0.013728863559663296,
-0.03270849958062172,
-0.014875569380819798,
-0.04711629077792168,
-0.03201868385076523,
0.01637505367398262,
0.0033612584229558706,
0.003809634828940034,
0.0551895909011364,
0.004124405328184366,
-0.02543945051729679,
-0.02442546933889389,
-0.0415908619761467,
-0.007197878323495388,
-0.08040415495634079,
0.002428875770419836,
-0.00369277223944664,
-0.018211279064416885,
0.0037186723202466965,
0.022079547867178917,
0.02236412651836872,
-0.0715693011879921,
-0.04831122234463692,
-0.06204382702708244,
0.0480385385453701,
0.01333367358893156,
-0.03851502016186714,
0.03571084886789322,
0.03445207327604294,
0.025146393105387688,
-0.031493257731199265,
0.00789634883403778,
0.01618918962776661,
-0.011016862466931343,
0.01957385428249836,
0.0018507830100134015,
0.007313293870538473,
-0.009515314362943172,
-0.013958181254565716,
0.0167375635355711,
0.006993460468947887,
-0.018544891849160194,
0.041324034333229065,
-0.026307808235287666,
0.05804181843996048,
0.020095333456993103,
0.004919607192277908,
0.0021854357328265905,
0.01996498741209507,
0.008721468970179558,
-0.01436613779515028,
0.006003095302730799,
-0.017340131103992462,
-0.049196790903806686,
-0.028109077364206314,
0.0034117752220481634,
0.05575462430715561,
-0.013714676722884178,
0.02133280597627163,
0.003140255343168974,
0.05849849432706833,
0.01134238950908184,
0.03239142894744873,
-0.01748737134039402,
-0.032842379063367844,
-0.03130127862095833,
-0.013988629914820194,
0.027208613231778145,
0.024678494781255722,
0.02712358720600605,
0.023404203355312347,
-0.0019782877061516047,
-0.028454789891839027,
-0.04259127750992775,
0.04764213040471077,
-0.006616219412535429,
0.030863726511597633,
0.013485636562108994,
-0.0481131449341774,
0.022686326876282692,
-0.03161417692899704,
0.02037239819765091,
0.02845023386180401,
0.007647193036973476,
0.006854033563286066,
-0.009731288067996502,
-0.03254466503858566,
0.02848174050450325,
0.04119856283068657,
-0.03732714429497719,
0.0010601822286844254,
0.03555675968527794,
-0.01747305504977703,
0.005866853054612875,
-0.01910073310136795,
-0.038546446710824966,
-0.033566903322935104,
0.005954104941338301,
0.010346357710659504,
-0.004782902542501688,
0.048665303736925125,
0.005030198488384485,
-0.052188653498888016,
0.022385435178875923,
-0.0458185076713562,
0.0010433217976242304,
-0.03074236959218979,
-0.05752294883131981,
0.004933703225106001,
-0.017601873725652695,
-0.03147832304239273,
0.03931974619626999,
0.010650325566530228,
0.03649236261844635,
0.029282892122864723,
-0.027910036966204643,
-0.024396443739533424,
-0.015142044052481651,
0.0023972904309630394,
0.043829161673784256,
-0.04676461219787598,
0.01115318015217781,
0.0056382762268185616,
-0.050310615450143814,
-0.03135288506746292,
0.0160731989890337,
-0.03397281467914581,
-0.04601506143808365,
-0.027622506022453308,
-0.003052789019420743,
-0.00145235366653651,
-0.02694268524646759,
-0.00001286280166823417,
0.02054227516055107,
-0.02785547822713852,
0.010722091421484947,
-0.005682666786015034,
-0.054626621305942535,
0.04798369109630585,
-0.0168113075196743,
0.040186356753110886,
-0.022889768704771996,
-0.04931436851620674,
0.07041622698307037,
0.011481287889182568,
-0.013455688022077084,
-0.012138014659285545,
-0.027144746854901314,
-0.01203516311943531,
-0.01295881811529398,
0.045236736536026,
0.0074445875361561775,
-0.0008509843610227108,
0.019154991954565048,
0.01346391811966896,
0.016806108877062798,
0.0383041575551033,
0.012798392213881016,
-0.021712016314268112,
0.00397501653060317,
0.020009782165288925,
-0.017215745523571968,
0.012815221212804317,
0.0017457890789955854,
-0.027121033519506454,
0.0239812470972538,
-0.012419764883816242,
0.040385905653238297,
-0.010635390877723694,
-0.024803774431347847,
0.03396189212799072,
-0.007826919667422771,
0.026275428012013435,
0.004125986713916063,
0.02572770230472088,
-0.01811921037733555,
0.010275819338858128,
-0.000625886837951839,
0.024859894067049026,
0.0383220799267292,
0.009388858452439308,
0.027231993153691292,
0.0144496476277709,
0.005118531174957752,
-0.057250700891017914,
-0.0034916475415229797,
-0.03360065072774887,
-0.0013540947111323476,
0.03983823210000992,
-0.013977501541376114,
-0.022842220962047577,
0.053246207535266876,
0.028145743533968925,
0.022138340398669243,
0.023223131895065308,
-0.02505398727953434,
-0.019108980894088745,
-0.08204586803913116,
0.0011358611518517137,
0.014190645888447762,
0.057862360030412674,
-0.0020044457633048296,
0.0664292722940445,
0.016732249408960342,
-0.004565386101603508,
0.03225065395236015,
-0.019634073600172997,
-0.06163541227579117,
-0.0165769811719656,
-0.049580130726099014,
0.03155054897069931,
-0.02292882651090622,
-0.02344333566725254,
0.01112003717571497,
-0.018122730776667595,
-0.025172661989927292,
0.0003458063874859363,
-0.04221881181001663,
-0.07646492123603821,
-0.0005119240377098322,
-0.012351631186902523,
0.00638603325933218,
-0.012757417745888233,
0.03126361593604088,
0.0560101680457592,
0.003960999194532633,
0.002719736425206065,
0.06534434854984283,
-0.008813705295324326,
0.00903075560927391,
0.0002504520525690168,
-0.018040206283330917,
0.028403837233781815,
0.029744580388069153,
-0.0017896954668685794,
-0.028629614040255547,
-0.03408132493495941,
0.0041180746629834175,
-0.026364877820014954,
0.04171722009778023,
-0.027342703193426132,
-0.0256570503115654,
-0.021756822243332863,
-0.04645214602351189,
0.0059389458037912846,
-0.018231051042675972,
0.06348400563001633,
0.018671853467822075,
0.006602293346077204,
0.03545519337058067,
0.013308349065482616,
-0.04282094165682793,
0.03111344575881958,
0.06835566461086273,
-0.002738354494795203,
-0.04194043204188347,
-0.05831511318683624,
-0.028639445081353188,
-0.0470082089304924,
-0.021348660811781883,
0.04132269322872162,
-0.009247269481420517,
-0.02782672457396984,
0.023924028500914574,
0.0013325094478204846,
-0.028452282771468163,
-0.009435041807591915,
-0.001101834699511528,
-0.008658484555780888,
0.01758759096264839,
0.003924422897398472,
-0.0020233625546097755,
-0.014911344274878502,
0.04289856553077698,
0.03363567218184471,
0.00960187241435051,
-0.03651859983801842,
-0.09341736882925034,
-0.011642232537269592,
0.022084366530179977,
0.02772952802479267,
-0.028708770871162415,
0.003501164261251688,
-0.028587937355041504,
-0.020652713254094124,
0.032597094774246216,
-0.01825829967856407,
0.045979198068380356,
-0.025787271559238434,
-0.013307107612490654,
-0.05818360298871994,
0.004782992880791426,
0.03684333339333534,
0.005183483939617872,
0.029203269630670547,
0.03526437655091286,
0.005808197893202305,
0.01467512920498848,
-0.029726402834057808,
0.019947599619627,
0.01884300634264946,
0.017443398013710976,
0.03680490702390671,
0.00895489752292633,
-0.014238419942557812,
0.020303841680288315,
-0.05060732737183571,
-0.0553896464407444,
0.016902154311537743,
0.025377318263053894,
-0.03024386242032051,
0.0061341021209955215,
-0.022122398018836975,
-0.026306211948394775,
0.0021061564330011606,
-0.006947358604520559,
-0.007117317523807287,
0.019028788432478905,
-0.022749224677681923,
0.0017831276636570692,
0.014674960635602474,
-0.004261593334376812,
0.02459678426384926,
-0.0011091267224401236,
-0.0028549637645483017,
-0.01561067346483469,
-0.01789618842303753,
0.05986787751317024,
-0.029823534190654755,
0.025812698528170586,
-0.0053779855370521545,
-0.01851276308298111,
-0.054115407168865204,
0.042003169655799866,
-0.011176474392414093,
0.0049725486896932125,
0.007602892816066742,
-0.01060667634010315,
-0.031281184405088425,
0.02066415548324585,
0.020729292184114456,
-0.01622955873608589,
0.012940438464283943,
-0.018602436408400536,
0.003446885384619236,
-0.01802736334502697,
0.0070829507894814014,
0.0073730419389903545,
-0.008441606536507607,
0.01854616403579712,
0.029811356216669083,
0.017243962734937668,
-0.021602869033813477,
-0.03114159218966961,
0.01587950624525547,
-0.05044713616371155,
0.03603573516011238,
-0.02426667883992195,
-0.019402455538511276,
0.011739675886929035,
-0.08903656899929047,
-0.03225276991724968,
0.0016485502710565925,
-0.018412230536341667,
0.026323305442929268,
-0.059987932443618774,
0.04756234958767891,
0.005134437698870897,
0.027849106118083,
-0.0901152491569519,
-0.04493062570691109,
0.039891354739665985,
0.03286619856953621,
-0.03465534746646881,
-0.052133169025182724,
0.015719950199127197,
-0.04403563216328621,
-0.0423884242773056,
-0.015022589825093746,
0.08602281659841537,
-0.006021230947226286,
-0.02532212622463703,
0.031631797552108765,
-0.002962983213365078,
0.04433605819940567,
-0.002672672038897872,
-0.015272472985088825,
-0.02279416285455227,
0.005691870581358671,
0.013368157669901848,
-0.01841558888554573,
0.03427836298942566,
-0.02501959353685379,
0.007432530168443918,
-0.022862747311592102,
-0.004042177926748991,
0.027719220146536827,
-0.06593342870473862,
0.021171247586607933,
0.013959360308945179,
0.027791252359747887,
-0.012248637154698372,
-0.07531525939702988,
0.04745984077453613,
0.004856174346059561,
0.009604486636817455,
-0.017754005268216133,
0.0324137844145298,
-0.0032399864867329597,
-0.021285124123096466,
0.021151334047317505,
-0.01772278919816017,
0.006804853677749634,
-0.014030562713742256,
0.04786813631653786,
-0.0014503312995657325,
0.0025709618348628283,
-0.003277956508100033,
-0.023602597415447235,
-0.0016494576120749116,
0.006019246764481068,
-0.006659353617578745,
0.025534803047776222,
0.030288362875580788,
-0.04116225987672806,
-0.011671842075884342,
-0.010456874966621399,
-0.007023361511528492,
0.05034973472356796,
-0.07393316924571991,
0.07640428096055984,
0.0491185337305069,
-0.041115179657936096,
0.014238269068300724,
-0.016444439068436623,
-0.0037707146257162094,
0.043556179851293564,
0.00009058004070539027,
0.04061629995703697,
-0.018566502258181572,
0.0028366977348923683,
0.03236450254917145,
0.022481275722384453,
-0.02311774343252182,
0.026133831590414047,
0.02725731022655964,
-0.0021607857197523117,
0.027255481109023094,
-0.023652635514736176,
-0.04925670847296715,
0.07793091237545013,
-0.01875254325568676,
0.004295106511563063,
0.01620158925652504,
-0.01777210831642151,
0.044111452996730804,
0.01225100178271532,
0.008382020518183708,
-0.03781969100236893,
-0.01755690388381481,
-0.02544950135052204,
-0.014948082156479359,
0.012826741673052311,
0.06085235998034477,
-0.005022179801017046,
0.0017622360028326511,
0.027703113853931427,
0.015196788124740124,
0.023410160094499588,
0.03327131271362305,
-0.06107058748602867,
-0.03335375338792801,
0.00011592118971748278,
-0.007425785530358553,
0.03856772556900978,
0.0002651415707077831,
-0.039932090789079666,
-0.031169379130005836,
-0.021875735372304916,
0.010442369617521763,
0.018167629837989807,
0.05474039167165756,
-0.04843607544898987,
0.05585847422480583,
0.017802082002162933,
0.010218065232038498,
-0.006310441065579653,
0.024630986154079437,
0.1021876111626625,
0.08791203796863556,
-0.010031999088823795,
-0.06019231304526329,
0.039853811264038086,
-0.023758772760629654,
0.01419458631426096,
-0.06686848402023315,
0.033309049904346466,
-0.01645824685692787,
0.03367408737540245,
-0.01034767646342516,
0.060045719146728516,
0.02373671345412731,
-0.023939399048686028,
0.056867536157369614,
-0.014878058806061745,
-0.033791784197092056,
-0.023946475237607956,
0.037742745131254196,
0.014555639587342739,
-0.006126294378191233,
-0.05636300891637802,
0.02800346165895462,
-0.014396880753338337,
-0.00009511521056992933,
-0.0074203964322805405,
-0.03051956743001938,
0.022183749824762344,
0.003272128291428089,
-0.038286905735731125,
-0.008851482532918453,
0.029366157948970795,
-0.035600241273641586,
-0.05938058719038963,
0.03137560561299324,
-0.009093891829252243,
-0.014376530423760414,
0.015039234422147274,
0.019480353221297264,
0.009049792774021626,
-0.012879236601293087,
-0.024556977674365044,
0.040012747049331665,
-0.04926154017448425,
-0.03734446316957474,
-0.03005749173462391,
0.011124810203909874,
-0.011234613135457039,
0.024818306788802147,
0.005875557195395231,
0.005774382036179304,
0.009089336730539799,
-0.06224457547068596,
-0.024384118616580963,
0.0029293897096067667,
0.04894455894827843,
-0.020859844982624054,
-0.029367515817284584,
-0.007214571349322796,
0.004263737704604864,
-0.0291602686047554,
0.03327101469039917,
-0.01959044486284256,
0.009584429673850536,
0.021960781887173653,
-0.02317744866013527,
0.012640728615224361,
-0.03198925778269768,
-0.0009614370646886528,
-0.03613247349858284,
0.0054815541952848434,
-0.030393021181225777,
0.004816995933651924,
0.03082142397761345,
0.043369799852371216,
0.002123540034517646,
-0.0013568740105256438,
-0.03980851545929909,
-0.005067416001111269,
-0.026054851710796356,
-0.0030906526371836662,
-0.0062645431607961655,
-0.0007837682496756315,
-0.027028966695070267,
0.010887054726481438,
0.060076966881752014,
0.019681822508573532,
-0.02410958707332611,
0.02359403856098652,
-0.030795615166425705,
-0.01501804031431675,
0.0033410738687962294,
-0.04574470967054367,
0.007840913720428944,
0.027205662801861763,
-0.008667025715112686,
0.008399221114814281,
-0.0245179645717144,
0.01134752668440342,
0.038962554186582565,
-0.007733151316642761,
0.003085710806772113,
0.04448124021291733,
-0.036543287336826324,
0.0011355670867487788,
0.035138942301273346,
-0.019574444741010666,
-0.002388081979006529,
0.0029011170845478773,
0.014821569435298443,
-0.05078892037272453,
-0.037258680909872055,
-0.03505242243409157,
0.02397751808166504,
-0.02833881601691246,
0.004168189130723476,
-0.01419347058981657,
-0.0020735845901072025,
-0.004172033630311489,
0.016975216567516327,
-0.027041977271437645,
-0.022856974974274635,
-0.05773165076971054,
-0.001286769867874682,
-0.008737677708268166,
-0.024537120014429092,
0.007523803971707821,
0.008153801783919334,
-0.02607218362390995,
-0.043097130954265594,
0.009158875793218613,
0.0050292592495679855,
-0.047166284173727036,
-0.00378234195522964,
0.019992677494883537,
-0.004230991937220097,
0.03831605985760689,
0.004602717701345682,
-0.03460894525051117,
0.02560093253850937,
-0.040374211966991425,
-0.0505191832780838,
0.03976309299468994,
-0.01025101263076067,
0.013111473061144352,
0.030462276190519333,
0.014740913175046444,
-0.01846623793244362,
0.04342344030737877,
-0.05155659094452858,
0.008662691339850426,
0.0016629884485155344,
-0.029496651142835617,
-0.028849054127931595,
0.008480343967676163,
0.00305699510499835,
-0.0065946732647717,
-0.03302538022398949,
0.003907020203769207,
0.003515083808451891,
0.033137910068035126,
-0.018229734152555466,
0.026030289009213448,
-0.018783802166581154,
0.04001997411251068,
0.03451577201485634,
0.0034711798653006554,
0.037243060767650604,
0.06414728611707687,
-0.03028947487473488,
0.047317374497652054,
0.029215535148978233,
-0.007281256373971701,
-0.08747956901788712,
0.0033089155331254005,
0.021198967471718788,
0.012309605255723,
0.051978446543216705,
-0.05876518040895462,
0.00809382926672697,
0.037229590117931366,
-0.08819706737995148,
0.051680002361536026,
-0.0285948533564806,
-0.007590480148792267,
-0.00243885675445199,
-0.02824501134455204,
0.008038852363824844,
0.04613909497857094,
0.05201796814799309,
0.029561353847384453,
-0.006330340169370174,
0.018247326835989952,
0.0031275548972189426,
-0.029976412653923035,
0.0054894364438951015,
0.06531928479671478,
-0.022673632949590683,
-0.015592449344694614,
0.046239547431468964,
-0.016638565808534622,
-0.02347448654472828,
0.036802954971790314,
0.007136504165828228,
0.04185176268219948,
0.012505029328167439,
0.011318708769977093,
-0.006310725584626198,
-0.0059773907996714115,
-0.0018919322174042463,
-0.028461717069149017,
-0.00880521908402443,
0.04312970116734505,
0.03015650436282158,
0.03945564851164818,
0.03123101033270359,
-0.01912090741097927,
-0.0019655448850244284,
-0.02834748849272728,
-0.0011365552200004458,
0.02961404249072075,
-0.002631228184327483,
0.019087808206677437,
-0.0013069864362478256,
-0.0040014623664319515,
0.017501840367913246,
-0.03989629074931145,
-0.0022474899888038635,
-0.022804202511906624,
-0.014794658869504929,
0.0349125899374485,
-0.004772694315761328,
-0.011913223192095757,
0.01244139764457941,
-0.01603354699909687,
-0.0347205251455307,
0.027919452637434006,
0.00402420898899436,
0.0008079248364083469,
-0.04973060265183449,
-0.005291980691254139,
0.014034639112651348,
-0.0005024932324886322,
0.023297131061553955,
-0.025894436985254288,
-0.022427288815379143,
0.046802718192338943,
0.03105202130973339,
0.0224621519446373,
0.013515649363398552,
-0.0693792998790741,
-0.028002699837088585,
-0.05171947926282883,
0.05145605653524399,
0.022904137149453163,
-0.049227360635995865,
-0.05691399425268173,
-0.00044789264211431146,
-0.005699703469872475,
0.03593701869249344,
0.076563760638237,
-0.024372970685362816,
-0.003342218464240432,
-0.012620708905160427,
0.02837516739964485,
0.033786967396736145,
-0.03558487445116043,
-0.04422491788864136,
0.03767363354563713,
-0.05806645750999451,
-0.007696684915572405,
-0.024218406528234482,
-0.041091009974479675,
-0.004223421681672335,
0.02014988474547863,
-0.026571141555905342,
0.06387173384428024,
0.005843753926455975,
-0.007875915616750717,
0.035951029509305954,
-0.0012005737517029047,
-0.02383228950202465,
0.04810776934027672,
-0.017595572397112846,
-0.024253562092781067,
0.020551882684230804,
-0.01236001867800951,
-0.004880297463387251,
-0.0029045750852674246,
-0.02715938910841942,
0.02139694057404995,
-0.00493999058380723,
-0.00016283105651382357,
0.05515698716044426,
-0.034844234585762024,
-0.027275122702121735,
0.03930630534887314,
-0.023159507662057877,
0.012529941275715828,
0.0703132152557373,
0.012428907677531242,
0.01964525692164898,
-0.03765169903635979,
0.005112363025546074,
0.00841816607862711,
0.0040564630180597305,
0.04615185037255287,
0.03940386325120926,
0.028213294222950935,
-0.012429756112396717,
0.016775719821453094,
0.041620247066020966,
0.009750178083777428,
0.00034793943632394075,
-0.015238496474921703,
0.0651053935289383,
-0.03246433660387993,
-0.004032233264297247,
-0.02110777236521244,
-0.036803651601076126,
0.023166481405496597,
0.04340968653559685,
-0.025211898609995842,
0.07746147364377975,
-0.022682467475533485,
-0.012299635447561741,
-0.019684718921780586,
-0.020122356712818146,
-0.030675526708364487,
0.027084633708000183,
0.014703997410833836,
0.015692567452788353,
-0.0383283868432045,
0.0033790995366871357,
-0.011119743809103966,
0.001669278834015131,
0.014078214764595032,
0.005550454370677471,
0.025372611358761787,
0.0005278934258967638,
0.011771461926400661,
-0.018450019881129265,
-0.016935404390096664,
-0.03119632601737976,
-0.02072199247777462,
0.027217673137784004,
0.019675610587000847,
0.04628109186887741,
0.006944024469703436,
0.010614312253892422,
-0.023599527776241302,
0.05290139093995094,
-0.08952725678682327,
-0.005389656405895948,
-0.054933469742536545,
0.05648375302553177,
0.004838027060031891,
-0.0029349434189498425
] |
<p>Reading this question and its answer</p>
<p><a href="http://physics.stackexchange.com/questions/130121/seesaw-type-1-and-integrating-out-heavy-fields">Seesaw type-1 and integrating out heavy fields</a></p>
<p>The diagonalization of the see-saw is described as going from "<em>interaction basis" right (and left) handed neutrinos</em> to <em>"mass basis" right (and left) handed neutrinos</em>.</p>
<p>Now, can chirality refer to a particular basis? Is it not a general property connected with parity? I would think that our "left handed neutrino" after seesaw is not a left neutrino anymore, but that it has a small mixing with the "right handed neutrino".</p>
<p>EDIT: and if it is so... is it always so, or there is some see-saw mechanism that preserves chirality?</p> | 1,404 | [
-0.00018974344129674137,
-0.033544640988111496,
-0.03216351941227913,
-0.012595348991453648,
0.05080575495958328,
0.0755070149898529,
-0.045607808977365494,
-0.03142927214503288,
0.0465850830078125,
-0.035044580698013306,
0.031150059774518013,
0.010042836889624596,
0.03682844713330269,
0.028079628944396973,
0.016991037875413895,
0.017223747447133064,
-0.005729324650019407,
-0.0034198903013020754,
-0.005346314981579781,
-0.03480348736047745,
-0.004979899153113365,
0.008029174990952015,
0.007745819631963968,
0.03611372783780098,
-0.02449820376932621,
0.000653219351079315,
-0.009755386970937252,
0.01937105879187584,
0.048436082899570465,
0.05309096723794937,
0.000299155421089381,
-0.05469818413257599,
0.05478500574827194,
0.014733368530869484,
0.036969419568777084,
-0.02810838259756565,
0.0012317276559770107,
-0.030783750116825104,
0.012190256267786026,
0.035738762468099594,
-0.012046640738844872,
-0.0026528523303568363,
-0.045811932533979416,
0.05250558257102966,
-0.02916039153933525,
0.02065258100628853,
-0.011300398968160152,
-0.017786985263228416,
0.1033068522810936,
-0.07415897399187088,
0.0433773472905159,
-0.009137554094195366,
0.0375077985227108,
0.00997211690992117,
-0.008551402017474174,
-0.009357348084449768,
0.056638069450855255,
0.01922518201172352,
0.031173100695014,
-0.04749272018671036,
0.0006522972253151238,
0.0008686269866302609,
0.019211014732718468,
-0.010309803299605846,
-0.03279368579387665,
0.04295768588781357,
0.016346951946616173,
-0.01652613654732704,
0.008277003653347492,
0.0039030532352626324,
0.010487881489098072,
0.0025137297343462706,
0.010799298994243145,
0.006529901176691055,
0.026704689487814903,
-0.0566851869225502,
0.017887931317090988,
0.016058089211583138,
0.004677224438637495,
0.008744866587221622,
-0.032607465982437134,
0.0293588750064373,
0.0003839573182631284,
0.001113042002543807,
0.026305072009563446,
-0.01933763548731804,
0.07479646056890488,
-0.02887319214642048,
-0.02407008595764637,
0.0692293718457222,
0.0035080842208117247,
0.004138527438044548,
0.025353364646434784,
-0.01645771414041519,
-0.02986653707921505,
0.009864152409136295,
0.022557727992534637,
0.027005022391676903,
-0.01914449967443943,
-0.022754596546292305,
0.013629852794110775,
-0.0004391615802887827,
0.010000851936638355,
0.07222869992256165,
-0.006919704843312502,
-0.02225564233958721,
-0.039880406111478806,
0.04910491779446602,
-0.027561143040657043,
-0.008687473833560944,
-0.02659730426967144,
-0.04536278545856476,
-0.015897853299975395,
0.006502815987914801,
0.007925852201879025,
-0.05684075132012367,
-0.028079789131879807,
-0.0038758825976401567,
0.029767515137791634,
0.06359434127807617,
0.059948693960905075,
-0.028467653319239616,
-0.008909893222153187,
-0.01594521291553974,
-0.055670540779829025,
0.002245608251541853,
0.0047266483306884766,
-0.010968747548758984,
-0.01721133105456829,
0.02570503205060959,
0.03220270574092865,
-0.02275478094816208,
0.012757734395563602,
-0.007101527415215969,
0.04605502262711525,
-0.01686181128025055,
-0.11473044753074646,
-0.07949677109718323,
0.02739773318171501,
-0.05138782784342766,
-0.057970114052295685,
-0.07320443540811539,
-0.012226478196680546,
0.029974831268191338,
0.09979905933141708,
-0.002957660239189863,
0.002613744931295514,
0.001488847890868783,
0.02070494554936886,
0.03366909548640251,
-0.006019174586981535,
-0.031167952343821526,
-0.02067442424595356,
-0.03783747926354408,
-0.0514318086206913,
-0.03546988219022751,
0.042167264968156815,
0.013782000169157982,
-0.0008629372459836304,
-0.03496711328625679,
0.09000153094530106,
-0.002810226520523429,
0.026904521510004997,
0.0006022186717018485,
0.012483371421694756,
-0.030199989676475525,
0.08380483835935593,
-0.011735600419342518,
0.012157616205513477,
0.03392481058835983,
-0.02751154638826847,
-0.011158300563693047,
0.004497705027461052,
0.055349770933389664,
0.04803335666656494,
-0.021224666386842728,
-0.035401850938797,
-0.026877563446760178,
0.0016201509861275554,
-0.02085062488913536,
-0.05750978738069534,
-0.017336275428533554,
-0.028246982023119926,
0.025816550478339195,
0.015421618707478046,
0.044230666011571884,
-0.021302683278918266,
-0.04873385652899742,
0.020364081487059593,
-0.051025066524744034,
-0.017531735822558403,
-0.06145365536212921,
-0.018626563251018524,
0.017041917890310287,
-0.02286519668996334,
0.008103022351861,
0.027269698679447174,
0.04215383157134056,
-0.026903683319687843,
0.0065566906705498695,
-0.01205039769411087,
0.03686946630477905,
0.03453775495290756,
0.006547124125063419,
0.0001920027134474367,
0.0015841454733163118,
0.030667169019579887,
-0.046665724366903305,
0.03692556917667389,
0.025519125163555145,
-0.045156218111515045,
0.012394997291266918,
0.017039120197296143,
0.029304949566721916,
-0.0037634619511663914,
-0.006543740164488554,
-0.0018137997249141335,
0.005752136465162039,
0.0007250549970194697,
0.04886612668633461,
-0.00776281300932169,
0.06155332922935486,
-0.011796643026173115,
-0.018266895785927773,
0.010167659260332584,
0.03829594701528549,
0.05725957825779915,
-0.0004989170702174306,
-0.033849578350782394,
-0.013474557548761368,
-0.025574278086423874,
-0.014622281305491924,
0.02668730728328228,
-0.014079147018492222,
-0.038676049560308456,
0.024495575577020645,
0.01934894360601902,
0.011928955093026161,
0.045554254204034805,
0.014516834169626236,
-0.008028039708733559,
-0.02272590436041355,
0.006432145833969116,
-0.02160577103495598,
0.005884008947759867,
0.008609230630099773,
0.03504873067140579,
-0.025753483176231384,
0.009899070486426353,
0.04105309024453163,
-0.04191745072603226,
0.008980988524854183,
0.006254579406231642,
0.0017034021439030766,
-0.005324746016412973,
-0.04957960173487663,
0.033483512699604034,
-0.029210515320301056,
0.028640251606702805,
0.005446215625852346,
0.0024276229087263346,
-0.036782070994377136,
-0.0268898606300354,
0.028889767825603485,
0.012406250461935997,
-0.00511006498709321,
-0.004805780481547117,
0.009646584279835224,
0.01618865877389908,
0.009730657562613487,
0.012186887674033642,
-0.041821934282779694,
0.0013686305610463023,
0.008496008813381195,
-0.0055353520438075066,
0.05928017571568489,
0.004159664269536734,
0.05084122717380524,
-0.024294162169098854,
-0.003068877849727869,
-0.0012866860488429666,
-0.021870089694857597,
-0.016267944127321243,
0.0767669826745987,
-0.03841359540820122,
-0.021762052550911903,
-0.07214517146348953,
-0.004850355442613363,
-0.0041759805753827095,
0.000687476946040988,
0.0005196902202442288,
0.01721419207751751,
-0.03011252172291279,
-0.050081782042980194,
-0.02505449578166008,
-0.037611111998558044,
-0.00040529287070967257,
-0.0022328521590679884,
-0.004771750885993242,
0.041637666523456573,
0.02709837444126606,
-0.01839357614517212,
-0.01674063876271248,
-0.03552096337080002,
-0.04622524604201317,
-0.0069653345271945,
-0.003233501920476556,
0.02775247022509575,
-0.016856683418154716,
0.0072045521810650826,
0.022815225645899773,
-0.04790450260043144,
0.024240124970674515,
-0.011196942068636417,
-0.04038656875491142,
0.008431162685155869,
-0.03972524031996727,
0.01960010640323162,
0.028496408835053444,
-0.012809596955776215,
0.07505175471305847,
0.026645053178071976,
-0.026670711115002632,
0.013347792439162731,
-0.01582728698849678,
-0.015808729454874992,
-0.035325322300195694,
0.03872402012348175,
0.00019078129844274372,
0.0033595282584428787,
0.025931747630238533,
0.02535303309559822,
0.04141940921545029,
0.01484918873757124,
0.013840009458363056,
-0.041591595858335495,
-0.0011265520006418228,
-0.012283938936889172,
-0.011157155968248844,
0.02261507883667946,
-0.026821618899703026,
-0.038255997002124786,
-0.000735954032279551,
0.008718579076230526,
0.03706514462828636,
0.01975031942129135,
-0.029194718226790428,
0.07169296592473984,
0.010761601850390434,
0.02556285634636879,
-0.044316794723272324,
0.034242380410432816,
0.017751850187778473,
-0.013792073354125023,
-0.004839875269681215,
0.02091914974153042,
0.059732746332883835,
-0.05167946591973305,
-0.0029135807417333126,
-0.0034054045099765062,
0.0146262152120471,
-0.001579785137437284,
-0.007308164611458778,
0.011843121610581875,
-0.016479797661304474,
0.042529504746198654,
-0.038170404732227325,
0.01837615855038166,
0.033360570669174194,
0.011565614491701126,
-0.004386435728520155,
0.010519963689148426,
-0.024649307131767273,
-0.00208214670419693,
-0.04753600060939789,
0.018133018165826797,
0.006964591797441244,
0.03367524594068527,
0.004247069824486971,
0.03920384868979454,
0.029752204194664955,
-0.032341860234737396,
-0.011982366442680359,
-0.015194051899015903,
-0.08008377999067307,
0.025130249559879303,
-0.03631944581866264,
-0.02415097877383232,
-0.027662130072712898,
-0.01981084980070591,
-0.029529068619012833,
-0.028389187529683113,
-0.04050437733530998,
-0.04796146601438522,
-0.019811667501926422,
-0.010824407450854778,
0.07605863362550735,
-0.030501607805490494,
-0.03973744064569473,
-0.013832793571054935,
0.0728844627737999,
0.054664649069309235,
-0.01935403048992157,
-0.013941871002316475,
0.009764322079718113,
-0.043692696839571,
0.007189149037003517,
-0.02405446209013462,
0.0416344590485096,
0.006805917713791132,
0.03264801204204559,
0.04088875278830528,
0.03435229882597923,
-0.018758993595838547,
-0.006134276743978262,
0.027140606194734573,
0.055627189576625824,
0.008582555688917637,
0.017664382234215736,
0.01559987012296915,
-0.04320812597870827,
-0.00981660932302475,
0.006503179669380188,
0.04382568225264549,
0.013627610169351101,
0.014115232042968273,
0.039148278534412384,
0.009077566675841808,
-0.06096798554062843,
0.05176931619644165,
0.06119110435247421,
-0.0029845978133380413,
0.001451702555641532,
-0.07858002930879593,
0.0209453534334898,
0.007729113567620516,
0.002536060055717826,
-0.014851350337266922,
0.0010044942609965801,
-0.00004100716614630073,
-0.0127971600741148,
-0.010336156003177166,
-0.007964865304529667,
-0.0033760801889002323,
-0.01531941257417202,
-0.024769432842731476,
0.03470861539244652,
-0.04318385198712349,
-0.010974877513945103,
-0.005319203250110149,
0.04500091075897217,
0.05212399363517761,
-0.012997371144592762,
0.02800833433866501,
-0.026980571448802948,
-0.01512887142598629,
0.06819088011980057,
0.06361741572618484,
-0.015536152757704258,
-0.011859584599733353,
-0.06287667900323868,
-0.021691277623176575,
0.01977674849331379,
-0.019858581945300102,
0.025517307221889496,
-0.03146546706557274,
0.000012534199413494207,
-0.024856772273778915,
-0.04556046426296234,
-0.01651824824512005,
0.021642914041876793,
-0.012186173349618912,
-0.0064375139772892,
-0.05202685669064522,
-0.013131354935467243,
-0.056438446044921875,
0.00016724910528864712,
0.02716253511607647,
0.013609679415822029,
-0.0058519961312413216,
0.03713436424732208,
-0.0087040476500988,
0.043797239661216736,
0.00014559067494701594,
-0.11755229532718658,
0.03611667826771736,
0.046352457255125046,
0.007521586026996374,
0.03435857221484184,
-0.03686971962451935,
-0.04917997866868973,
0.024611735716462135,
0.03252095729112625,
-0.008549985475838184,
-0.05106397718191147,
-0.04759542644023895,
0.0655398964881897,
0.03647705912590027,
0.025924120098352432,
0.020031685009598732,
0.02983075939118862,
-0.025835473090410233,
-0.029220959171652794,
-0.021201424300670624,
0.013792160898447037,
-0.044865697622299194,
0.005094504449516535,
-0.030446533113718033,
-0.013726344332098961,
-0.02033073827624321,
0.05235709622502327,
0.02319350838661194,
0.061770398169755936,
0.026061857119202614,
-0.025744041427969933,
-0.05695526674389839,
0.03181784227490425,
0.017635403200984,
-0.012592852115631104,
0.005077574402093887,
0.0038496125489473343,
-0.0004784077755175531,
-0.014538352377712727,
0.004405078943818808,
-0.022948602214455605,
-0.0301655400544405,
-0.0036072460934519768,
-0.01716633141040802,
0.06113158538937569,
-0.027543606236577034,
-0.04229287430644035,
0.00018532772082835436,
-0.05155503377318382,
0.0022583468817174435,
-0.04743056744337082,
0.009203966706991196,
0.00563437957316637,
-0.07421087473630905,
0.0031543446239084005,
0.012695671990513802,
-0.012230967171490192,
-0.022874103859066963,
-0.041478801518678665,
0.021487150341272354,
0.027718551456928253,
0.02274760976433754,
-0.06846540421247482,
-0.0411921888589859,
0.0003387416072655469,
0.027883443981409073,
0.0032589563634246588,
-0.02558378130197525,
-0.0005945476586930454,
-0.0011715629370883107,
-0.02900932915508747,
0.0024356802459806204,
0.029765186831355095,
-0.050589825958013535,
-0.0028201609384268522,
0.02653837576508522,
0.032820262014865875,
0.08176901191473007,
-0.014029353857040405,
-0.008069092407822609,
0.04130154475569725,
-0.03323899582028389,
0.00969743262976408,
-0.0007600636454299092,
0.05231206491589546,
-0.0017221494344994426,
-0.028798529878258705,
-0.009329481050372124,
-0.009680652059614658,
0.02981763519346714,
0.007051998749375343,
-0.008494855836033821,
0.01604854315519333,
-0.022815575823187828,
0.017244206741452217,
-0.048599112778902054,
-0.005551852751523256,
0.03128115087747574,
0.05657368153333664,
-0.00564385112375021,
-0.018505586311221123,
-0.019878901541233063,
-0.03037421405315399,
-0.02019437588751316,
-0.029424510896205902,
0.01941792666912079,
-0.01140520628541708,
0.016117433086037636,
-0.003514374839141965,
-0.006490196567028761,
0.04616721719503403,
-0.04138176515698433,
-0.001739179715514183,
-0.016384519636631012,
0.03485554829239845,
0.007730448618531227,
0.022676048800349236,
0.0057088821195065975,
0.000994957867078483,
-0.03948120027780533,
0.0040647489950060844,
0.05538870021700859,
0.015678759664297104,
0.025358403101563454,
0.0006419239216484129,
-0.023769346997141838,
-0.03849157318472862,
-0.056752029806375504,
0.0027652776334434748,
-0.013519171625375748,
0.008294574916362762,
0.030495941638946533,
-0.038939252495765686,
0.003907658159732819,
0.0294937863945961,
0.04078096151351929,
-0.01848631724715233,
0.03414592891931534,
0.04528876021504402,
-0.0223594531416893,
0.02490529976785183,
0.00824782345443964,
-0.06517527252435684,
0.04337489604949951,
-0.023304756730794907,
0.02222193218767643,
0.023365022614598274,
-0.002620527520775795,
0.03552255034446716,
0.03157222270965576,
0.034497763961553574,
-0.024278348311781883,
-0.04094107821583748,
-0.02198564074933529,
-0.030659237876534462,
-0.00549842556938529,
-0.003238799748942256,
-0.02588559500873089,
-0.013431594707071781,
0.041519083082675934,
0.01629144325852394,
-0.018287574872374535,
-0.028252091258764267,
-0.049090106040239334,
-0.012050471268594265,
-0.03574885427951813,
-0.05394211411476135,
0.028993472456932068,
-0.03460387513041496,
-0.018352869898080826,
-0.01142862718552351,
-0.03998568654060364,
0.017736662179231644,
0.002991365035995841,
0.06464417278766632,
-0.0273040309548378,
0.035582154989242554,
0.0030651662964373827,
0.05130802467465401,
-0.02278204821050167,
-0.01340456772595644,
0.12290918081998825,
0.027996055781841278,
0.01787499710917473,
-0.040633294731378555,
0.02381729520857334,
-0.051792409271001816,
0.018955150619149208,
-0.030760865658521652,
0.007425509858876467,
0.006122522056102753,
0.030144361779093742,
-0.004980116151273251,
0.06732107698917389,
-0.008918195962905884,
-0.018152067437767982,
0.0497896783053875,
-0.021831898018717766,
-0.04956962540745735,
-0.0018307510763406754,
0.01804499700665474,
-0.029535215348005295,
0.012970050796866417,
-0.05189293995499611,
0.003976199310272932,
0.028405537828803062,
-0.03858889639377594,
0.006961476057767868,
-0.03187932074069977,
0.009335671551525593,
0.013865015469491482,
-0.04379745200276375,
-0.008963096886873245,
-0.010647482238709927,
0.026624437421560287,
-0.029101496562361717,
-0.006170391570776701,
-0.01345662772655487,
0.006904678884893656,
0.04239128530025482,
0.04806111007928848,
0.027833372354507446,
-0.01418356690555811,
0.03853004053235054,
0.04241764917969704,
-0.03424876183271408,
0.0004167060542386025,
0.001659609959460795,
0.047254934906959534,
-0.010048475116491318,
-0.015784630551934242,
-0.006564236246049404,
-0.018792353570461273,
0.06924670189619064,
-0.06172877550125122,
-0.004255706910043955,
0.007221842184662819,
0.014292240142822266,
-0.007232052739709616,
0.030814388766884804,
0.017124418169260025,
0.0024465799797326326,
-0.005676683504134417,
-0.003335442626848817,
-0.005467986222356558,
-0.004327983595430851,
-0.004878198262304068,
-0.014137312769889832,
0.003842091653496027,
0.023783443495631218,
-0.023591548204421997,
0.01312454603612423,
-0.011817725375294685,
-0.045783594250679016,
0.01826930046081543,
0.048121072351932526,
0.015095178969204426,
0.04717518761754036,
-0.015101078897714615,
-0.0017195023829117417,
-0.030708612874150276,
-0.066224604845047,
0.049672309309244156,
-0.022418182343244553,
-0.0403335765004158,
0.03656863421201706,
0.007848288863897324,
0.014926263131201267,
0.0578024797141552,
-0.04654536023736,
0.005980758462101221,
0.0034287776798009872,
0.024320174008607864,
0.01064540259540081,
-0.06184722110629082,
-0.034896139055490494,
-0.0025615780614316463,
-0.046204693615436554,
-0.008702728897333145,
-0.047602973878383636,
0.015123666264116764,
0.01156290341168642,
0.005841556470841169,
-0.005515404511243105,
0.03735990822315216,
0.006852681748569012,
-0.010736139491200447,
0.036620400846004486,
-0.00846672710031271,
0.006947712507098913,
-0.014107928611338139,
0.02653060480952263,
-0.015135598368942738,
-0.038236428052186966,
-0.014129392802715302,
-0.01710105501115322,
-0.01099796686321497,
0.03155349940061569,
-0.06544774025678635,
0.00039213625132106245,
-0.03764248266816139,
-0.006027659401297569,
-0.008188714273273945,
-0.031213602051138878,
-0.05557655543088913,
-0.008927718736231327,
-0.01787693239748478,
-0.014035550877451897,
0.036314625293016434,
0.01407210435718298,
-0.007151270285248756,
0.0021121117752045393,
0.023024188354611397,
-0.004208813887089491,
-0.02179093286395073,
-0.01331235934048891,
0.025913652032613754,
0.03861984238028526,
0.034391023218631744,
-0.007141557987779379,
-0.020735643804073334,
0.04004420340061188,
-0.017123088240623474,
-0.05556328967213631,
0.0664127990603447,
-0.02964704856276512,
0.037319526076316833,
0.006786333862692118,
-0.03020906075835228,
-0.006577536463737488,
0.04999314993619919,
-0.011496067978441715,
-0.006460949778556824,
0.015063107013702393,
-0.01539293210953474,
0.004391235765069723,
-0.014926791191101074,
-0.020884260535240173,
0.019759399816393852,
-0.032370686531066895,
0.04763583838939667,
0.013867661356925964,
0.008696227334439754,
-0.006613265257328749,
-0.0336180105805397,
0.004045824985951185,
0.01511430274695158,
0.016513708978891373,
0.0005877054645679891,
-0.011456367559731007,
0.04609993100166321,
-0.03368040919303894,
0.02957761660218239,
0.03244203329086304,
0.015357114374637604,
-0.08440180122852325,
-0.05578410625457764,
0.01646334119141102,
0.03525308892130852,
0.011551384814083576,
-0.06120302900671959,
0.04707321897149086,
-0.016863007098436356,
-0.05624144896864891,
0.010692532174289227,
-0.007420277688652277,
-0.0025927098467946053,
-0.03178201988339424,
-0.03138063848018646,
0.002818099921569228,
0.047715820372104645,
0.026065431535243988,
0.06118054315447807,
0.010736094787716866,
0.005914820358157158,
0.0021866660099476576,
-0.010441585443913937,
-0.018217269331216812,
0.0202067568898201,
-0.015175840817391872,
-0.05876551568508148,
0.07900503277778625,
-0.016703002154827118,
-0.03560552000999451,
0.043696656823158264,
-0.014201348647475243,
0.017128804698586464,
0.029270948842167854,
0.021924078464508057,
0.008097909390926361,
0.014388957992196083,
0.007500701118260622,
-0.03743373602628708,
-0.026580266654491425,
0.033519115298986435,
0.04774991795420647,
0.03796305134892464,
0.013822777196764946,
0.007688427343964577,
-0.036560360342264175,
-0.040564000606536865,
0.02016248181462288,
0.016918450593948364,
-0.04962581396102905,
-0.008615922182798386,
-0.03995005041360855,
-0.025203971192240715,
0.021158307790756226,
0.01677301526069641,
0.025715934112668037,
-0.014959417283535004,
-0.01018341351300478,
0.017100946977734566,
0.021748453378677368,
-0.009105576202273369,
0.03715244680643082,
0.04905761033296585,
-0.036772727966308594,
0.009312163107097149,
0.03446211293339729,
-0.0019696198869496584,
-0.028651781380176544,
-0.03499685972929001,
0.02139393612742424,
0.003266416024416685,
0.01618724875152111,
-0.02966177649796009,
-0.033726777881383896,
0.03403497114777565,
-0.02726711705327034,
0.02467792108654976,
-0.023120969533920288,
-0.02705705724656582,
-0.003183690831065178,
-0.04791590943932533,
0.009290066547691822,
0.004892001394182444,
0.04056113213300705,
-0.03617764264345169,
-0.00760213378816843,
-0.010982098057866096,
-0.004192273132503033,
0.08343072235584259,
0.025998972356319427,
-0.027343614026904106,
0.01952752098441124,
-0.006435230374336243,
0.020412247627973557,
0.009746115654706955,
0.020377440378069878,
-0.019818469882011414,
-0.01628168299794197,
-0.00017056462820619345,
-0.021203145384788513,
0.008535107597708702,
0.03556413948535919,
0.027290236204862595,
-0.014703660272061825,
-0.0012391454074531794,
0.005138922017067671,
-0.058335136622190475,
0.04928288981318474,
0.011890201829373837,
-0.012256513349711895,
0.07852865010499954,
-0.0003612508298829198,
0.01876860298216343,
0.022165166214108467,
-0.03873179852962494,
-0.011500447057187557,
0.005866577848792076,
-0.03520282357931137,
-0.03001793660223484,
-0.0018062619492411613,
0.01978510431945324,
0.06324980407953262,
-0.020125171169638634,
0.001544478116557002,
0.0324852280318737,
-0.004838313441723585,
-0.02051106095314026,
0.05499738082289696,
0.0016001862240955234,
0.027454469352960587,
0.022759728133678436,
0.006766961421817541,
0.009669705294072628,
0.013239511288702488,
0.0209200382232666,
0.04859157279133797,
-0.0033480129204690456,
0.03107002004981041,
-0.015288334339857101,
0.0303685013204813,
0.014615236781537533,
0.017571762204170227,
0.008787608705461025,
0.03384096547961235,
-0.004878389183431864,
0.008172021247446537,
0.017537977546453476,
0.010688754729926586,
0.0335201732814312,
0.007458877749741077,
-0.00889678206294775,
0.0695577934384346,
-0.005647861864417791,
0.012655709870159626,
-0.014437510631978512,
-0.014066067524254322,
0.0070084333419799805,
-0.0005296004237607121,
0.009532946161925793,
0.06523533910512924,
0.013822820968925953,
-0.039952028542757034,
-0.020984984934329987,
0.017260899767279625,
0.0339369997382164,
-0.06834617257118225,
0.008720279671251774,
-0.0015727984718978405,
0.00631431769579649,
-0.029457097873091698,
-0.0013208441669121385,
0.002410819986835122,
-0.0185825414955616,
0.005067287944257259,
0.05617298185825348,
0.03345207870006561,
-0.027708107605576515,
-0.03392890468239784,
0.0015323074767366052,
0.040449757128953934,
-0.028294159099459648,
0.0012959816958755255,
-0.020847270265221596,
0.013376230373978615,
-0.017985466867685318,
-0.0024600711185485125
] |
<p>There was a <a href="http://www.redorbit.com/news/science/1112700495/perpetual-clock-uses-4-dimensional-crystals-092512/" rel="nofollow">recent article</a> about the <a href="http://arxiv.org/abs/1206.4772" rel="nofollow">creation of 4D spacetime crystals</a> based on recent theory proposed by Frank Wilczek. This theory is based on breaking <a href="http://theory.uwinnipeg.ca/mod_tech/node9.html" rel="nofollow">time translational symmetry</a> which basically is the assumption that the laws of physics are time invariant (e.g. that we can expect our physical laws are the same as we move through time). </p>
<p>The concept of <a href="http://www.ctc.cam.ac.uk/stephen70/talks/swh70_wilczek.pdf" rel="nofollow">spactime crystals</a> is relatively new, and there are <a href="http://arxiv.org/pdf/1202.2537v2.pdf" rel="nofollow">classical</a> and <a href="http://arxiv.org/abs/1202.2539" rel="nofollow">quantum</a> versions. Since the time crystal reportedly returns to its ground state periodically, and it reportedly is not in violation of the second law of thermodynamics, the layman might be tempted to look at it as a some sort of pulsating refrigerator.</p>
<p>Is there some better description of the time crystal that makes it obvious that this is really a new concept?</p> | 1,405 | [
0.001850075088441372,
-0.05459119752049446,
-0.0035021468065679073,
-0.0472235269844532,
0.05878347530961037,
0.0003763111890293658,
-0.013608806766569614,
-0.011048928834497929,
0.002539092442020774,
-0.028807347640395164,
0.014989480376243591,
0.024735238403081894,
0.016740191727876663,
0.03631214797496796,
0.021440107375383377,
0.02735833078622818,
0.0069201174192130566,
-0.043720223009586334,
-0.016560763120651245,
-0.02685580588877201,
0.0238451287150383,
0.008042904548346996,
-0.039546433836221695,
0.012148077599704266,
-0.027393018826842308,
0.0018743531545624137,
0.010457870550453663,
0.02584092505276203,
0.0060970899648964405,
0.0730053186416626,
-0.031776465475559235,
-0.01767142489552498,
-0.0030802423134446144,
-0.013635543175041676,
0.01304810680449009,
-0.019236816093325615,
-0.02251601591706276,
-0.0517113022506237,
0.02018290013074875,
0.017798643559217453,
-0.004993134643882513,
0.015401026234030724,
-0.03820902854204178,
0.03694598376750946,
-0.04085155576467514,
0.021394032984972,
0.008715194649994373,
-0.0027981398161500692,
0.050689272582530975,
-0.05455747991800308,
0.046215400099754333,
0.011125454679131508,
0.01365578081458807,
0.003352701896801591,
-0.009073399007320404,
-0.00830062571913004,
0.04241591691970825,
0.04597863554954529,
-0.014264757744967937,
-0.03624560311436653,
-0.03516078367829323,
0.011668399907648563,
0.022071244195103645,
-0.022909563034772873,
-0.004335314035415649,
0.03478686884045601,
-0.0069757914170622826,
-0.031495824456214905,
0.028322041034698486,
-0.034303098917007446,
0.02295789122581482,
0.029256997630000114,
0.035596903413534164,
0.007769276387989521,
0.0012473491951823235,
-0.0034154816530644894,
-0.00736778462305665,
0.016420286148786545,
0.02155856043100357,
0.042908743023872375,
-0.00491782370954752,
0.00040471323882229626,
0.012762579135596752,
0.03996036946773529,
-0.0160645954310894,
0.0005892929621040821,
0.09307307004928589,
-0.022579018026590347,
0.004557445645332336,
0.032132018357515335,
0.01958971656858921,
0.030081216245889664,
0.04159042611718178,
0.0005646708304993808,
-0.03349406644701958,
0.0037591673899441957,
0.03058222122490406,
0.05129722133278847,
-0.020465074107050896,
-0.03343397006392479,
0.011401922442018986,
-0.004943800158798695,
0.01602177321910858,
0.0682387575507164,
-0.0031570186838507652,
-0.025607122108340263,
-0.015181655995547771,
0.00854686088860035,
-0.003703140188008547,
-0.012860334478318691,
-0.05505916476249695,
0.009581180289387703,
0.008157276548445225,
-0.007426786702126265,
0.0010145239066332579,
-0.01067468523979187,
0.009744402021169662,
0.0007713643135502934,
0.04101159796118736,
0.06687412410974503,
0.026012422516942024,
-0.03587420657277107,
0.013044402934610844,
-0.03375660255551338,
-0.09446613490581512,
-0.005915077403187752,
0.026012856513261795,
-0.03268389776349068,
-0.023050662130117416,
0.0397760383784771,
-0.00444558821618557,
-0.007004046346992254,
0.026231762021780014,
-0.0008161493460647762,
0.0358305387198925,
-0.013970349915325642,
-0.11725988239049911,
-0.029758227989077568,
0.07257875800132751,
0.007916657254099846,
-0.024891506880521774,
-0.08761706203222275,
0.025236623361706734,
-0.02383463643491268,
0.08665003627538681,
-0.010033613070845604,
-0.005425336770713329,
-0.011351813562214375,
0.0448739230632782,
0.01631615124642849,
-0.04570554569363594,
0.033101920038461685,
0.054111625999212265,
-0.05110393837094307,
-0.01614021509885788,
-0.061277616769075394,
0.014817259274423122,
0.019901517778635025,
0.0054845865815877914,
-0.012474630028009415,
0.06238920986652374,
0.0015307159628719091,
-0.03283712640404701,
0.012534328736364841,
-0.013015502132475376,
0.001294026500545442,
0.06229982525110245,
-0.038784246891736984,
-0.004949586931616068,
0.04259449243545532,
-0.002937094774097204,
0.024398384615778923,
-0.008368934504687786,
0.017354875802993774,
0.01562667265534401,
-0.00542812142521143,
0.00933136511594057,
0.008559942245483398,
-0.006448050029575825,
-0.00585306016728282,
-0.039472922682762146,
-0.01973242312669754,
0.014443238265812397,
-0.007184967398643494,
-0.013227364048361778,
0.05425567924976349,
-0.006789344362914562,
0.017156952992081642,
0.0071862624026834965,
-0.03741776570677757,
-0.014722603373229504,
-0.06791917234659195,
0.021589234471321106,
-0.000271880766376853,
0.004412501584738493,
0.04591383412480354,
0.007209116593003273,
0.033851202577352524,
-0.03532842546701431,
-0.05529991537332535,
-0.024869540706276894,
0.06506115198135376,
-0.01209036074578762,
-0.018578043207526207,
0.033824898302555084,
0.04692350700497627,
0.016298066824674606,
-0.01474986132234335,
0.01215349044650793,
-0.01733563281595707,
-0.03760780394077301,
0.003158077597618103,
-0.012609429657459259,
0.01567636802792549,
-0.0012067087227478623,
-0.014133403077721596,
0.019716279581189156,
0.037800297141075134,
-0.03287522867321968,
0.01201598346233368,
-0.021554389968514442,
0.030687356367707253,
-0.00016949685232248157,
0.015144193544983864,
-0.01591017097234726,
0.029730545356869698,
0.012566231191158295,
0.03899718075990677,
-0.02759646624326706,
-0.03418825939297676,
-0.028604287654161453,
-0.008005392737686634,
0.02613910473883152,
0.0454150065779686,
-0.0027386625297367573,
0.0807197317481041,
0.0038459545467048883,
0.03565237298607826,
0.019066810607910156,
0.021387847140431404,
-0.027037154883146286,
-0.020363150164484978,
0.015590278431773186,
-0.0071438332088291645,
0.006232961546629667,
0.005558471195399761,
-0.0003361368435434997,
0.005290525499731302,
-0.03946541249752045,
-0.020024947822093964,
-0.02921176888048649,
0.020038265734910965,
-0.016618505120277405,
0.031709473580121994,
0.003984736278653145,
-0.05756911262869835,
0.007927454076707363,
0.009764350950717926,
0.0034220684319734573,
0.015908678993582726,
0.010540970601141453,
0.006000002380460501,
-0.04963413253426552,
-0.04395753890275955,
-0.036398984491825104,
0.01742197386920452,
0.006707962602376938,
-0.023296384140849113,
0.014422512613236904,
-0.027459261938929558,
0.007084449753165245,
-0.003726074006408453,
0.00153590296395123,
-0.01692269556224346,
0.004179907962679863,
0.03305349498987198,
0.019189458340406418,
0.04016619175672531,
-0.032802823930978775,
-0.036754075437784195,
0.024174237623810768,
-0.014149555936455727,
-0.007211403455585241,
0.028684141114354134,
-0.008610086515545845,
0.01919318363070488,
-0.03627888485789299,
-0.048354506492614746,
0.04129015654325485,
-0.015732716768980026,
0.022511275485157967,
0.00829990953207016,
-0.010835157707333565,
-0.028923530131578445,
0.013316131196916103,
-0.018810724839568138,
0.04035105183720589,
-0.043533679097890854,
0.011380440555512905,
0.016505081206560135,
-0.039213377982378006,
-0.05832628905773163,
0.002096540527418256,
-0.02800126187503338,
-0.01977536641061306,
-0.014239375479519367,
-0.020152408629655838,
0.012278523296117783,
-0.007277113385498524,
0.0036085715983062983,
0.058447252959012985,
-0.05142803117632866,
0.0020678651053458452,
-0.051522985100746155,
-0.06393202394247055,
0.041778139770030975,
-0.055667027831077576,
0.03889937326312065,
-0.024430369958281517,
-0.014408322051167488,
0.04964907467365265,
0.03429928421974182,
-0.01743173412978649,
0.014615586027503014,
-0.022960983216762543,
-0.012429272755980492,
-0.03371682018041611,
-0.005335934925824404,
0.04228837043046951,
-0.00005105650416226126,
-0.008529746904969215,
0.031730327755212784,
0.027240321040153503,
0.03607809171080589,
0.03254742547869682,
-0.00915390346199274,
-0.01030257623642683,
0.019201647490262985,
-0.0002576765255071223,
0.060058485716581345,
0.0008599077118560672,
-0.038729071617126465,
-0.013072564266622066,
-0.025604061782360077,
0.03814386576414108,
0.04969343915581703,
-0.058161407709121704,
0.05148787051439285,
0.014849795028567314,
-0.0009793752105906606,
-0.013910857029259205,
0.03974531590938568,
-0.014097983948886395,
-0.018087709322571754,
-0.01845278963446617,
0.054232340306043625,
0.026623956859111786,
0.019980575889348984,
0.0038779296446591616,
0.022627046331763268,
0.046016719192266464,
-0.02214127406477928,
-0.00607697106897831,
-0.029372651129961014,
-0.010714332573115826,
0.02538658306002617,
0.015156141482293606,
0.0009039102587848902,
0.062222741544246674,
0.028024382889270782,
0.0536092184484005,
0.033534109592437744,
-0.010143961757421494,
-0.017904404550790787,
-0.08848465234041214,
-0.010039624758064747,
-0.022975847125053406,
0.0713065043091774,
0.037764646112918854,
0.027833357453346252,
0.008253302425146103,
-0.004968678578734398,
0.038619302213191986,
-0.026311630383133888,
-0.0858822837471962,
0.0066611808724701405,
-0.05094233155250549,
0.003972811158746481,
0.0109480619430542,
0.04925316199660301,
-0.0013296260731294751,
0.020137816667556763,
-0.03643207997083664,
-0.01540942583233118,
-0.01925867423415184,
-0.05858973041176796,
0.014915036968886852,
-0.01602744683623314,
-0.02589632011950016,
-0.01773923821747303,
-0.025543108582496643,
0.07954081892967224,
-0.02218017354607582,
-0.0022507079411298037,
-0.009780525229871273,
-0.025381579995155334,
0.0392194539308548,
0.03366748243570328,
-0.006315478589385748,
0.026458032429218292,
-0.0006282769609242678,
0.002883036620914936,
0.020195037126541138,
-0.012630335055291653,
0.0074471840634942055,
0.019736355170607567,
0.029431790113449097,
-0.05032728239893913,
0.02932198904454708,
-0.053516507148742676,
-0.04303395375609398,
0.017807360738515854,
0.01091796811670065,
0.05418532341718674,
0.03145011514425278,
0.031026529148221016,
-0.0074950712732970715,
0.02125755324959755,
0.008768288418650627,
0.055188171565532684,
0.030574902892112732,
-0.0515880361199379,
-0.0011156793916597962,
-0.01338791474699974,
-0.030405353754758835,
-0.00736926170065999,
-0.02749761939048767,
0.030495278537273407,
0.016552651301026344,
-0.003164328169077635,
0.03018907457590103,
-0.015956910327076912,
0.015511855483055115,
-0.015288766473531723,
0.012185629457235336,
-0.01977955549955368,
0.013742572627961636,
-0.02298552542924881,
0.01793104223906994,
-0.03910185769200325,
0.042572736740112305,
0.039297427982091904,
-0.005224213469773531,
-0.0317886620759964,
-0.09967479854822159,
0.0085250623524189,
0.052970729768276215,
0.039276573807001114,
-0.0018667239928618073,
-0.03613097593188286,
-0.06977826356887817,
-0.04469125345349312,
0.007950418628752232,
-0.018362388014793396,
0.05291447788476944,
0.01401396095752716,
-0.014859630726277828,
-0.055327896028757095,
0.0038272819947451353,
0.07109937071800232,
0.021616721525788307,
-0.0013091418659314513,
0.03009078837931156,
0.02924913913011551,
-0.0022072819992899895,
0.01464297529309988,
0.004087554756551981,
0.017884952947497368,
0.011479584500193596,
-0.029861871153116226,
0.017503971233963966,
-0.00538354879245162,
0.011708175763487816,
-0.06050710380077362,
-0.09253595024347305,
-0.006136717740446329,
0.000883673201315105,
-0.03990987315773964,
0.023022247478365898,
-0.053218599408864975,
-0.03791428357362747,
-0.029742715880274773,
0.0054742200300097466,
-0.01996677741408348,
-0.008127918466925621,
-0.026449766010046005,
0.028692184016108513,
0.006725682411342859,
0.015163296833634377,
0.03336380422115326,
0.07073954492807388,
-0.03124808520078659,
-0.005671631544828415,
0.002822941169142723,
0.046128712594509125,
-0.023095542564988136,
0.0535641647875309,
-0.029739322140812874,
0.008962975814938545,
-0.05796864256262779,
0.059183746576309204,
-0.048903655260801315,
-0.01280997134745121,
0.020400097593665123,
0.0037970307748764753,
-0.010322625748813152,
0.0050279912538826466,
-0.015386835671961308,
-0.017198581248521805,
-0.026456749066710472,
0.0306893028318882,
-0.029832933098077774,
-0.015393600799143314,
0.008067804388701916,
-0.011539711616933346,
0.02279880829155445,
0.05480974540114403,
0.022963592782616615,
0.028767595067620277,
-0.053709909319877625,
0.0013686090242117643,
-0.0018783760024234653,
-0.047687333077192307,
0.04636940732598305,
-0.011239193379878998,
0.022514009848237038,
0.03213886544108391,
-0.048764802515506744,
-0.023559028282761574,
-0.015681631863117218,
-0.018320497125387192,
0.009211020544171333,
-0.05531388148665428,
0.04588257521390915,
0.008190159685909748,
0.007231601048260927,
-0.09270072728395462,
-0.04843148961663246,
0.05075416341423988,
-0.008312493562698364,
-0.06670420616865158,
-0.031841374933719635,
-0.005375884473323822,
-0.055890120565891266,
-0.03144484758377075,
-0.007717293221503496,
0.03016732446849346,
-0.03656546398997307,
-0.03706889599561691,
-0.005661432631313801,
0.040733277797698975,
0.07221248745918274,
0.02664417028427124,
-0.029576459899544716,
-0.00632507586851716,
0.005635779816657305,
0.00010767567437142134,
-0.005768423434346914,
-0.00023867048730608076,
-0.03245152160525322,
-0.016024788841605186,
-0.00597491767257452,
0.028404394164681435,
0.02822418510913849,
-0.03985763341188431,
0.022352617233991623,
0.03839511796832085,
0.01168464869260788,
-0.017614660784602165,
-0.05498639494180679,
0.02087295986711979,
0.012344235554337502,
0.019195185974240303,
-0.002560701221227646,
-0.010144581086933613,
0.008127720095217228,
-0.02335604466497898,
0.02858724817633629,
-0.02847777120769024,
0.0014848839491605759,
-0.006240908056497574,
0.05568695068359375,
0.009595956653356552,
-0.009141975082457066,
0.007795453537255526,
-0.05100453272461891,
0.013626365922391415,
-0.002602200023829937,
0.023662952706217766,
-0.02081434801220894,
-0.011627740226686,
-0.024598274379968643,
-0.06098044663667679,
-0.026011275127530098,
0.03146134316921234,
0.05118592455983162,
-0.017167096957564354,
0.05907764658331871,
0.031644757837057114,
-0.02798435091972351,
-0.00008548468031222001,
-0.0006939870654605329,
0.027166062965989113,
0.03939618542790413,
0.0015207050601020455,
0.006470493506640196,
-0.039555761963129044,
-0.01465495303273201,
0.03712141886353493,
0.024770688265562057,
-0.010285048745572567,
0.017921777442097664,
0.056365691125392914,
0.006565663032233715,
0.00881467666476965,
-0.008620883338153362,
-0.03712120279669762,
0.0969846248626709,
-0.02245149202644825,
0.027096997946500778,
0.046416833996772766,
0.01659049466252327,
0.028871696442365646,
0.00285666948184371,
0.006916852667927742,
-0.05425876006484032,
-0.017066780477762222,
-0.057259924709796906,
0.0037471656687557697,
-0.02364383637905121,
0.0334373340010643,
-0.012713585048913956,
-0.03147173300385475,
-0.0018639768240973353,
0.03108365833759308,
0.0049288636073470116,
0.007055187132209539,
-0.08327603340148926,
-0.021258918568491936,
0.011125285178422928,
-0.004956587217748165,
0.07063869386911392,
0.024205172434449196,
-0.03034484013915062,
-0.017081549391150475,
-0.04506024718284607,
0.03092743642628193,
0.036674559116363525,
0.06124791502952576,
-0.05941850319504738,
0.030458470806479454,
-0.03684531897306442,
0.009235023520886898,
-0.030209239572286606,
0.010696787387132645,
0.12318378686904907,
0.031411945819854736,
0.009324563667178154,
-0.04863031581044197,
0.0368606261909008,
-0.014054317958652973,
0.05424664169549942,
-0.03387759253382683,
-0.0059778145514428616,
-0.008704762905836105,
0.041324224323034286,
0.017216186970472336,
0.06817471235990524,
0.017393670976161957,
-0.0076587144285440445,
0.03321811184287071,
-0.03070390596985817,
-0.010368140414357185,
0.002437569899484515,
0.012342091649770737,
0.010013955645263195,
0.017529988661408424,
-0.039794083684682846,
0.04206370189785957,
-0.024319963529706,
-0.003755310783162713,
-0.015459113754332066,
-0.030109047889709473,
0.022342506796121597,
0.02259835973381996,
-0.020225292071700096,
0.008666519075632095,
0.010730711743235588,
-0.004606959410011768,
-0.027677984908223152,
0.012711736373603344,
-0.017381703481078148,
0.008156423456966877,
0.03078724443912506,
0.06311377137899399,
0.02640162780880928,
-0.04478202387690544,
0.04502265527844429,
0.041892897337675095,
-0.04316459223628044,
0.006062638480216265,
-0.03282276913523674,
-0.005102021619677544,
-0.02924303337931633,
0.00992914754897356,
0.01023032795637846,
-0.0317995510995388,
-0.008952661417424679,
-0.04200373962521553,
0.0017020475352182984,
-0.011824289336800575,
0.031225699931383133,
-0.009088166058063507,
-0.013083923608064651,
-0.02505120262503624,
0.025895744562149048,
-0.015778224915266037,
0.0073144626803696156,
-0.003782806685194373,
0.008924710564315319,
0.043081387877464294,
-0.02826881967484951,
0.012954415753483772,
0.002600797452032566,
0.002527603879570961,
-0.06367714703083038,
0.003289224812760949,
-0.06583939492702484,
-0.0018284323159605265,
-0.026379400864243507,
0.016719074919819832,
0.044535670429468155,
0.0010005945805460215,
-0.006784148048609495,
0.007538434583693743,
-0.0328957699239254,
0.009990833699703217,
0.0032534743659198284,
-0.018360722810029984,
-0.01454190630465746,
0.0152007220312953,
0.035164106637239456,
0.03378130495548248,
-0.03248753771185875,
0.03436461091041565,
0.0003940821625292301,
0.007447334937751293,
0.031033240258693695,
-0.06092727184295654,
0.026681890711188316,
0.005214932840317488,
-0.011417626403272152,
0.006420892663300037,
-0.03184265270829201,
0.03017404116690159,
0.05784674361348152,
-0.012287003919482231,
0.021347487345337868,
0.040192097425460815,
-0.03920723870396614,
-0.009684025309979916,
0.03277949243783951,
-0.018006591126322746,
-0.011099970899522305,
0.014371512457728386,
0.005945006851106882,
-0.013850171118974686,
-0.050232212990522385,
0.0007224679575301707,
0.001740423496812582,
-0.008533082902431488,
0.02744241990149021,
-0.02972208522260189,
-0.0007971646264195442,
-0.018209997564554214,
0.0034086788073182106,
-0.05478445440530777,
-0.005441469140350819,
-0.027147293090820312,
-0.0029873698949813843,
-0.013088441453874111,
0.008389148861169815,
0.0033579771406948566,
0.051544297486543655,
-0.016569238156080246,
-0.023586533963680267,
0.026611242443323135,
0.0481787845492363,
-0.042929138988256454,
0.008500360883772373,
-0.01609678938984871,
0.04132555425167084,
0.014765951782464981,
-0.024661267176270485,
-0.06123063713312149,
0.010861122980713844,
-0.026371240615844727,
-0.06806347519159317,
0.027401460334658623,
-0.027888337150216103,
-0.03168772533535957,
0.0006483304896391928,
-0.023603525012731552,
0.002604725304991007,
0.03579774871468544,
-0.011091357097029686,
0.002570725977420807,
0.03619470074772835,
-0.046164412051439285,
-0.01679590716958046,
0.009074409492313862,
0.009083570912480354,
-0.0015948164509609342,
-0.021389754489064217,
0.030018433928489685,
0.047508057206869125,
-0.01052758377045393,
-0.03777414932847023,
-0.014834928326308727,
-0.020275495946407318,
-0.021751681342720985,
0.000050836253649322316,
0.00013059181219432503,
0.05211561918258667,
0.05884500592947006,
-0.013963472098112106,
0.008972038514912128,
0.0042756046168506145,
-0.009224236942827702,
-0.08951255679130554,
0.019873477518558502,
0.019421478733420372,
0.031372491270303726,
0.018428584560751915,
-0.03888382762670517,
0.03870410844683647,
0.036444004625082016,
-0.0757625550031662,
0.0509885735809803,
-0.02475530467927456,
-0.06174345314502716,
-0.02174360677599907,
-0.012705828994512558,
-0.007273712195456028,
0.04714684933423996,
0.04301771521568298,
0.03280927985906601,
-0.010868578217923641,
0.030848825350403786,
0.0021358588710427284,
-0.03443174809217453,
-0.007596512790769339,
0.02909996546804905,
0.013001535087823868,
-0.0004167841689195484,
0.03810720890760422,
-0.029782762750983238,
-0.05102858319878578,
0.03526382893323898,
-0.009465881623327732,
-0.007236307952553034,
0.0039606038480997086,
-0.0021504806354641914,
-0.008634975180029869,
0.020073838531970978,
0.04253815859556198,
-0.011266481131315231,
-0.008127220906317234,
0.014576779678463936,
0.0052527314983308315,
0.04102357104420662,
0.05066179856657982,
-0.0021845668088644743,
-0.003908097743988037,
-0.03813156113028526,
-0.0013909786939620972,
0.0152791952714324,
-0.03250603750348091,
0.022377805784344673,
-0.011633655987679958,
-0.008065137080848217,
0.020282812416553497,
-0.009941961616277695,
-0.017047816887497902,
-0.020454727113246918,
0.011006392538547516,
0.033243510872125626,
-0.006544956937432289,
0.009233326651155949,
0.027328426018357277,
-0.04005610570311546,
0.006565446965396404,
0.02870306558907032,
-0.02272517792880535,
-0.008327380754053593,
-0.044221777468919754,
0.0017681693425402045,
0.0020315356086939573,
0.012770092114806175,
-0.0004056106845382601,
-0.038988564163446426,
-0.0336080864071846,
0.03361443057656288,
0.02136310562491417,
-0.010180873796343803,
-0.033181607723236084,
0.00929409358650446,
0.002781026531010866,
-0.05126790329813957,
0.029000064358115196,
-0.014080817811191082,
0.02023223787546158,
-0.03251618146896362,
-0.016853831708431244,
-0.007425876799970865,
0.06793050467967987,
0.08607660233974457,
-0.022239120677113533,
-0.010718549601733685,
0.007829729467630386,
-0.012287402525544167,
0.010617966763675213,
-0.024489589035511017,
-0.006418218370527029,
0.034278761595487595,
0.015185979194939137,
0.008592036552727222,
-0.008931256830692291,
-0.041420742869377136,
-0.0033360221423208714,
0.05369092524051666,
-0.009285138919949532,
0.01068197563290596,
0.03426622599363327,
-0.023580290377140045,
0.07023913413286209,
0.0038290214724838734,
-0.042354829609394073,
0.05380191281437874,
-0.006703220307826996,
0.038598909974098206,
0.02815582975745201,
-0.006751036737114191,
-0.010060573928058147,
0.01678154058754444,
-0.04730720445513725,
0.00979841873049736,
-0.031462427228689194,
-0.023403067141771317,
0.04346112161874771,
-0.030377211049199104,
-0.03873709961771965,
0.021614473313093185,
-0.006268614903092384,
0.00771424500271678,
0.029508547857403755,
0.014762657694518566,
0.049895696341991425,
-0.01257857121527195,
0.01583612896502018,
-0.011266633868217468,
-0.006954205688089132,
-0.03996659070253372,
0.07273402065038681,
0.04820282384753227,
-0.0058330027386546135,
0.019489958882331848,
0.016585778445005417,
-0.0016517085023224354,
-0.018202781677246094,
0.03354479372501373,
0.03637271374464035,
-0.010011876001954079,
0.0013370986562222242,
0.04286981746554375,
-0.02035495825111866,
-0.01001607533544302,
0.03888292983174324,
-0.002560094930231571,
0.052959587424993515,
-0.03364650905132294,
0.016600381582975388,
-0.03141293302178383,
-0.010494035668671131,
-0.006503927521407604,
-0.006188439670950174,
0.010418453253805637,
0.03554495424032211,
-0.021084565669298172,
-0.016637327149510384,
-0.03918949514627457,
0.027614397928118706,
0.0033309159334748983,
-0.06427711248397827,
0.0064130206592381,
-0.05576932802796364,
0.008348194882273674,
-0.014701256528496742,
-0.005602866876870394,
-0.03371047601103783,
-0.017673710361123085,
0.020933818072080612,
0.02767311781644821,
0.022508857771754265,
-0.02878103218972683,
0.0007424164796248078,
-0.0123553816229105,
0.055535003542900085,
-0.04820612445473671,
0.017336340621113777,
-0.030955638736486435,
0.037733182311058044,
-0.027007225900888443,
-0.011157393455505371
] |
<p>I'm currently studying the operator methods in Quantum Mechanics, but I can't figure out the general procedure and its relations with the diagonalization problem.</p> | 1,406 | [
-0.007328537758439779,
-0.007846007123589516,
-0.004490791819989681,
-0.043383385986089706,
0.02714502438902855,
0.00967448204755783,
-0.025185953825712204,
-0.04902549460530281,
0.024145592004060745,
-0.027488714084029198,
0.04755661264061928,
0.028774596750736237,
0.0907425805926323,
-0.003021529410034418,
0.035259928554296494,
-0.008751661516726017,
-0.021843671798706055,
-0.024846673011779785,
0.005468771792948246,
0.01816735416650772,
0.014743032865226269,
0.03819693252444267,
0.020037941634655,
-0.009277362376451492,
-0.00689577404409647,
0.020222630351781845,
0.015666544437408447,
0.0343807078897953,
0.023881709203124046,
0.07082381099462509,
-0.02626543492078781,
-0.034842830151319504,
0.015797706320881844,
0.016159629449248314,
0.013263911008834839,
-0.0007065120153129101,
-0.02642868086695671,
-0.0251799076795578,
-0.01830669678747654,
0.015637077391147614,
-0.04196732118725777,
-0.0567317008972168,
-0.02871810644865036,
0.03989791125059128,
-0.014418399892747402,
0.029483739286661148,
-0.00036697203177027404,
-0.018730174750089645,
0.03391356021165848,
-0.04129922389984131,
0.08981146663427353,
-0.014821060933172703,
0.04425748810172081,
0.008777466602623463,
-0.042178668081760406,
0.05595327913761139,
0.0617310032248497,
0.048006512224674225,
0.009366917423903942,
-0.04582579806447029,
-0.019194815307855606,
-0.033704422414302826,
-0.00541641004383564,
0.011105711571872234,
-0.012897776439785957,
0.003315084148198366,
0.0013295861426740885,
-0.05005328729748726,
-0.010845518670976162,
-0.010847882367670536,
-0.01070406287908554,
0.030725723132491112,
0.052215367555618286,
-0.058296725153923035,
0.00002000522545131389,
-0.039624184370040894,
0.018327681347727776,
0.03153723478317261,
0.040190912783145905,
-0.010153385810554028,
-0.0009863449959084392,
0.03855924308300018,
0.009909511543810368,
0.02621501311659813,
-0.03160305693745613,
-0.008879728615283966,
0.07958093285560608,
-0.01840793527662754,
0.0032179211266338825,
0.024742187932133675,
-0.01483289897441864,
0.028709720820188522,
0.03248005360364914,
0.012882860377430916,
-0.030678514391183853,
0.024640504270792007,
0.0022128561977297068,
0.05746743083000183,
-0.00023308621894102544,
-0.02386002242565155,
0.009710896760225296,
-0.018818901851773262,
0.0035797462332993746,
0.045753080397844315,
-0.015640243887901306,
0.006129256449639797,
-0.0471641980111599,
0.04282902926206589,
-0.005179968662559986,
-0.028889156877994537,
-0.045818157494068146,
0.022104134783148766,
-0.03906715661287308,
0.020648179575800896,
0.007281867787241936,
-0.008337230421602726,
-0.011875351890921593,
-0.02583269774913788,
0.037501510232686996,
0.07719430327415466,
0.014761559665203094,
-0.023648789152503014,
0.028353719040751457,
-0.058166198432445526,
-0.04156383499503136,
0.008085029199719429,
0.026856189593672752,
-0.009095732122659683,
-0.05069039762020111,
0.015691326931118965,
0.015403804369270802,
-0.029020704329013824,
0.01957383193075657,
0.005712736397981644,
0.0004520124348346144,
-0.04003322497010231,
-0.1034860834479332,
-0.07541188597679138,
0.023112043738365173,
-0.02496386505663395,
-0.004651979543268681,
-0.07825694233179092,
-0.001835255534388125,
0.03903902694582939,
0.08644401282072067,
0.004834591876715422,
0.014189884066581726,
-0.0029822150245308876,
0.0012204861268401146,
-0.006111646071076393,
0.000808053882792592,
-0.053482089191675186,
0.003177311969920993,
-0.027859976515173912,
0.001303561613894999,
-0.05529887601733208,
0.012918930500745773,
0.016419021412730217,
-0.006283982656896114,
-0.017579320818185806,
0.06342954933643341,
-0.0078422911465168,
-0.020716272294521332,
0.008873539045453072,
0.02122570388019085,
-0.037639956921339035,
0.07847180962562561,
0.03720468655228615,
-0.006225863937288523,
0.04479735717177391,
-0.005107022821903229,
0.01598772592842579,
0.01668599806725979,
0.04153076186776161,
0.031180528923869133,
-0.05123298987746239,
-0.025755494832992554,
-0.05072211101651192,
0.02838420867919922,
0.01820078119635582,
-0.05487602576613426,
-0.017864929512143135,
0.02199001982808113,
-0.005616721697151661,
-0.005787335801869631,
0.029571782797574997,
0.00023771887936163694,
0.014111108146607876,
-0.009445972740650177,
-0.06657356768846512,
0.003751517040655017,
-0.05430685356259346,
0.025880174711346626,
0.006583499722182751,
-0.025417422875761986,
0.029183512553572655,
0.02452854812145233,
0.009653650224208832,
-0.019260583445429802,
-0.08294502645730972,
-0.03883158415555954,
0.0189522635191679,
0.013544593937695026,
-0.005967175588011742,
0.0495743453502655,
0.07270834594964981,
0.07741843909025192,
-0.0024001786950975657,
0.08004652708768845,
-0.05063705891370773,
-0.01810877025127411,
-0.006890172604471445,
0.0003236063348595053,
0.027259839698672295,
0.02253217063844204,
-0.011141804978251457,
-0.005586928687989712,
-0.02921648696064949,
-0.0026083316188305616,
0.021281355991959572,
-0.05996926128864288,
0.052550073713064194,
0.0413750559091568,
0.035989243537187576,
-0.0023667896166443825,
0.05570940300822258,
0.037073034793138504,
0.0008598832646384835,
0.03132230043411255,
-0.048946917057037354,
-0.01644909754395485,
0.02806045114994049,
0.04057438299059868,
0.020839747041463852,
-0.0674324482679367,
0.0005516484961844981,
0.03487193211913109,
0.060193151235580444,
0.036607954651117325,
0.03594671189785004,
-0.03774675354361534,
0.0048675802536308765,
-0.015628544613718987,
0.007574806455522776,
-0.00706027215346694,
0.03396317735314369,
0.011313401162624359,
-0.013544161804020405,
0.02527099847793579,
-0.0016799697186797857,
-0.038398899137973785,
0.038609035313129425,
-0.016514072194695473,
0.01985786110162735,
0.002437202027067542,
-0.04906165972352028,
0.021477555856108665,
-0.02975216694176197,
0.0026472180616110563,
0.007437705993652344,
-0.015087869018316269,
0.02362283132970333,
-0.024386700242757797,
0.00011939885735046118,
0.025730660185217857,
-0.0038558815140277147,
-0.05448044091463089,
0.024225320667028427,
0.04154282063245773,
0.0033658514730632305,
0.030723944306373596,
-0.04515345022082329,
0.0002240273024654016,
-0.03793860971927643,
-0.035242047160863876,
0.050021443516016006,
0.002746999030932784,
0.04009716212749481,
-0.03516404703259468,
-0.04126045107841492,
-0.018616588786244392,
-0.041724514216184616,
0.016752861440181732,
0.04048236832022667,
-0.048076193779706955,
0.0035766835790127516,
-0.062337055802345276,
-0.018437080085277557,
0.015382630750536919,
0.010673925280570984,
0.003382432274520397,
0.007762826047837734,
0.009719124995172024,
-0.04905949905514717,
-0.03221616894006729,
0.02051078900694847,
0.011015644297003746,
-0.04523808881640434,
0.04327107593417168,
0.041893262416124344,
-0.008573583327233791,
-0.004643342457711697,
0.016948310658335686,
-0.03494223952293396,
-0.015022714622318745,
-0.02660437487065792,
-0.02266974374651909,
0.02802620455622673,
-0.03461337089538574,
0.02642383985221386,
0.03783699497580528,
-0.039082642644643784,
0.0021735529880970716,
-0.04641949012875557,
-0.028322234749794006,
0.02759275957942009,
0.03040958009660244,
0.02080570161342621,
0.019409749656915665,
-0.007524420041590929,
0.09143257141113281,
-0.0007931377040222287,
-0.029884658753871918,
-0.033352117985486984,
0.008007638156414032,
-0.014927939511835575,
-0.002617462305352092,
0.025188660249114037,
0.030343547463417053,
-0.021357623860239983,
0.01584003120660782,
0.010134773328900337,
0.010461365804076195,
0.056794147938489914,
0.0018482382874935865,
-0.0031790032517164946,
0.019536802545189857,
0.012206470593810081,
0.006885576993227005,
0.03990022465586662,
-0.0344831645488739,
-0.04008230194449425,
0.026883509010076523,
0.012039915658533573,
0.020332133397459984,
0.02001308836042881,
-0.02475193701684475,
0.033482931554317474,
0.008751904591917992,
-0.008630056865513325,
-0.02081891894340515,
0.06887298077344894,
-0.03539947047829628,
-0.014746630564332008,
0.0282780509442091,
0.008086233399808407,
0.018716398626565933,
-0.029561275616288185,
-0.007238664664328098,
0.022573553025722504,
0.024379057809710503,
-0.042375098913908005,
-0.009151982143521309,
-0.003086293116211891,
-0.03098970092833042,
0.02358722873032093,
-0.0575154647231102,
-0.0647590309381485,
0.05090232565999031,
0.03050123155117035,
0.0037345446180552244,
-0.026202991604804993,
-0.03200254961848259,
0.01447993516921997,
-0.049544014036655426,
0.0075988927856087685,
0.008769725449383259,
0.04782794788479805,
0.0032427310943603516,
0.0813705176115036,
0.00842144712805748,
0.019251329824328423,
0.05042615160346031,
-0.002900519873946905,
-0.05250590667128563,
0.02272159233689308,
-0.009914116002619267,
-0.02174399420619011,
0.0077885910868644714,
-0.0025573461316525936,
0.01882069744169712,
-0.004077710676938295,
-0.04359208792448044,
-0.04276597127318382,
-0.026874467730522156,
-0.051174867898225784,
0.041062477976083755,
-0.029886219650506973,
-0.03280787169933319,
-0.020307814702391624,
0.013166620396077633,
0.04913322627544403,
-0.016454298049211502,
-0.004436410963535309,
0.02175331674516201,
-0.0447835735976696,
-0.0015460947761312127,
0.002508801408112049,
0.04047621414065361,
0.033829618245363235,
0.03642551228404045,
0.03824139013886452,
0.04244334250688553,
-0.04788155481219292,
0.013529486022889614,
0.011287861503660679,
0.08620980381965637,
0.005282582715153694,
-0.03774089366197586,
0.0025190752930939198,
-0.027434365823864937,
0.025254277512431145,
-0.01705634593963623,
0.049492623656988144,
-0.019920121878385544,
0.03351854160428047,
0.02576279267668724,
0.039387769997119904,
-0.03598538786172867,
-0.0008883076952770352,
0.0752566009759903,
0.04199539124965668,
-0.016415607184171677,
-0.03174043074250221,
0.03901663050055504,
-0.00794044230133295,
0.021152781322598457,
0.0011589436326175928,
-0.011257348582148552,
-0.01378665491938591,
0.010374337434768677,
0.046875808387994766,
-0.009392796084284782,
-0.01785322092473507,
-0.020003246143460274,
-0.006125937681645155,
0.013360414654016495,
-0.0410495288670063,
-0.008417662233114243,
0.030423788353800774,
0.025111915543675423,
0.04891829192638397,
0.012963555753231049,
0.009561074897646904,
-0.03126998618245125,
-0.0029349997639656067,
0.017852993682026863,
0.030369054526090622,
-0.010851917788386345,
0.028291795402765274,
-0.04487910494208336,
-0.028799181804060936,
0.05717410519719124,
-0.015036712400615215,
0.035756129771471024,
-0.03429298475384712,
-0.03544308990240097,
-0.025708632543683052,
-0.007415234576910734,
-0.000247699354076758,
0.02241278626024723,
0.006296529900282621,
0.026786668226122856,
-0.01859230361878872,
-0.006387032568454742,
-0.0793110728263855,
-0.007356440648436546,
0.01688433438539505,
0.05864213407039642,
-0.0021906939800828695,
-0.0007032830035313964,
0.00940508209168911,
0.056435611099004745,
-0.017713099718093872,
-0.05539451912045479,
0.005022433586418629,
0.029229329898953438,
-0.013755498453974724,
0.044877178966999054,
-0.032288022339344025,
-0.04126179218292236,
0.024306494742631912,
0.012435865588486195,
-0.004216356668621302,
0.008192191831767559,
-0.018781626597046852,
0.03964812308549881,
0.03303270414471626,
-0.022716574370861053,
0.05905986577272415,
0.008214264176785946,
-0.01333580445498228,
-0.005812143441289663,
-0.04588587209582329,
0.02900894358754158,
0.006456839852035046,
0.0007648870814591646,
-0.03204067796468735,
0.010162017308175564,
-0.0077145094983279705,
0.013282784260809422,
-0.0026015634648501873,
0.03194419667124748,
0.006813508924096823,
-0.045260123908519745,
-0.03190794214606285,
0.04073989763855934,
-0.040313392877578735,
-0.03085530921816826,
0.018560409545898438,
0.033453699201345444,
0.019721418619155884,
-0.03747392073273659,
0.0033028125762939453,
-0.027533313259482384,
0.010326705873012543,
0.02193034067749977,
-0.03314170241355896,
0.0361044704914093,
-0.05702226981520653,
-0.030867047607898712,
0.01779276318848133,
-0.06120211258530617,
0.02476024441421032,
-0.021368788555264473,
-0.0035765976645052433,
0.013035924173891544,
-0.05610469728708267,
-0.02939959615468979,
0.007504770997911692,
-0.01502372045069933,
0.017615394666790962,
-0.022219998762011528,
0.01304173655807972,
0.011963826604187489,
-0.005847672466188669,
-0.06427542120218277,
-0.0485745370388031,
0.017743360251188278,
0.004055501893162727,
-0.01623832993209362,
-0.06408334523439407,
0.018343763425946236,
-0.011837531812489033,
-0.011554625816643238,
-0.006490624975413084,
0.01536573376506567,
-0.06017402559518814,
-0.013393348082900047,
0.042600519955158234,
-0.0007214101497083902,
0.04883057624101639,
0.005720862653106451,
-0.0004968753200955689,
0.00397142767906189,
-0.02355531044304371,
-0.013926729559898376,
-0.008285687305033207,
0.05506456643342972,
-0.0229461882263422,
-0.031715162098407745,
-0.04227172210812569,
0.01554692629724741,
0.03187687695026398,
-0.015962615609169006,
-0.019189957529306412,
0.014414114877581596,
0.040287308394908905,
0.001795085147023201,
-0.029865412041544914,
-0.0051686870865523815,
0.004280015826225281,
0.028956947848200798,
0.01008659042418003,
-0.009374349378049374,
-0.022697191685438156,
-0.03980819135904312,
0.021840745583176613,
-0.007192997261881828,
-0.0039073023945093155,
0.0028343142475932837,
0.07008673250675201,
0.0028630858287215233,
0.017121121287345886,
0.052025143057107925,
-0.018531877547502518,
-0.009875895455479622,
-0.002050084061920643,
0.0077512506395578384,
0.021279215812683105,
-0.0019460903713479638,
0.0051074218936264515,
-0.04845718294382095,
-0.03990080952644348,
0.035274505615234375,
0.03061913698911667,
-0.004002343397587538,
0.05560419335961342,
0.0649937242269516,
0.010258927941322327,
-0.01664159446954727,
-0.014346443116664886,
-0.030382681638002396,
0.009124643169343472,
-0.0005036781076341867,
0.04590437188744545,
-0.03801250830292702,
0.014646844938397408,
0.032941605895757675,
0.06241168826818466,
-0.04459962248802185,
-0.015252845361828804,
0.017073260620236397,
0.03015889786183834,
0.05105547606945038,
0.0073600453324615955,
-0.028379809111356735,
0.008629122748970985,
-0.020850809291005135,
0.03605278953909874,
-0.019779330119490623,
-0.01855044811964035,
0.035046450793743134,
0.018726900219917297,
0.01828875206410885,
-0.0013682740973308682,
-0.006155636627227068,
-0.03725259378552437,
0.027910714969038963,
-0.0009465105249546468,
0.009368320927023888,
0.002661133883520961,
0.035167984664440155,
0.0358119010925293,
0.004183468408882618,
0.003294007619842887,
0.0022792138624936342,
-0.05218364670872688,
-0.0053940024226903915,
-0.00958635751157999,
-0.07561550289392471,
0.01374801341444254,
-0.008823796175420284,
-0.015951016917824745,
-0.007598616182804108,
-0.00572007242590189,
0.007489298935979605,
0.009565353393554688,
0.047855768352746964,
-0.015376991592347622,
0.05721116065979004,
0.011562795378267765,
-0.006758238188922405,
0.019481679424643517,
-0.00942998006939888,
0.10120456665754318,
0.06940287351608276,
0.0458432100713253,
-0.09319446235895157,
0.002223610645160079,
-0.01974715106189251,
-0.016069963574409485,
-0.010223819874227047,
0.036039311438798904,
-0.008920358493924141,
0.001340476213954389,
-0.005929543636739254,
0.026358712464571,
0.003266611834987998,
0.0021320744417607784,
0.04733079671859741,
-0.04016871377825737,
-0.05545967072248459,
0.034914370626211166,
0.029048144817352295,
-0.004319428466260433,
-0.00008642058674013242,
-0.045862145721912384,
0.0007252061041072011,
-0.06116275489330292,
-0.01903459057211876,
-0.023718344047665596,
-0.030443266034126282,
0.02443826012313366,
-0.0068998695351183414,
-0.04098205640912056,
-0.008448497392237186,
0.0010716792894527316,
0.00042822549585253,
-0.0410117581486702,
0.043806739151477814,
0.04908212646842003,
-0.009714372456073761,
0.03873760625720024,
0.00702705979347229,
0.012765067629516125,
-0.0020735186990350485,
0.004423166159540415,
-0.0019345114706084132,
-0.023086385801434517,
-0.004843936301767826,
-0.02067404054105282,
0.05760316550731659,
-0.010177112184464931,
-0.0031153596937656403,
0.0013248671311885118,
-0.011983171105384827,
0.0051763830706477165,
-0.05675995722413063,
0.02113531529903412,
0.022017644718289375,
0.04524039849638939,
-0.03362099826335907,
0.010596985928714275,
-0.03598029166460037,
-0.000112785906821955,
-0.006654133554548025,
0.014604123309254646,
0.018743837252259254,
-0.007049431558698416,
0.03276869282126427,
-0.02500970847904682,
-0.00418512336909771,
-0.023689744994044304,
-0.02277141436934471,
-0.0331217423081398,
-0.020629703998565674,
-0.021159762516617775,
-0.038367122411727905,
0.030291996896266937,
0.011931329034268856,
0.05725731700658798,
-0.03476852551102638,
0.022530414164066315,
0.00325033999979496,
-0.11447280645370483,
0.012006971053779125,
-0.032727617770433426,
-0.012829754501581192,
0.029621152207255363,
0.010526795871555805,
0.0472867377102375,
0.05226258933544159,
-0.02401912398636341,
0.02741394378244877,
0.000690670742187649,
0.012304853647947311,
0.03139989450573921,
-0.02251303195953369,
-0.03131985664367676,
-0.008851280435919762,
-0.031750455498695374,
0.01994352973997593,
-0.03141026943922043,
-0.017484290525317192,
0.027403928339481354,
-0.010980169288814068,
-0.0048856972716748714,
0.034798335283994675,
-0.02811904437839985,
-0.004400925245136023,
-0.017128022387623787,
-0.03898262977600098,
0.009542166255414486,
0.010351057164371014,
-0.004832050297409296,
-0.049549974501132965,
-0.026194307953119278,
-0.054678551852703094,
0.03440513089299202,
-0.005067482590675354,
0.032994940876960754,
-0.030312353745102882,
-0.028545614331960678,
-0.01107054017484188,
0.04606436938047409,
-0.00986129604279995,
-0.0031586450058966875,
-0.033446211367845535,
0.040468376129865646,
0.004912687931209803,
-0.002032957272604108,
-0.015221723355352879,
-0.00028334822854958475,
0.03147739917039871,
-0.01825304515659809,
0.037429049611091614,
0.012204310856759548,
-0.00931768398731947,
-0.00853017345070839,
0.014002681709825993,
-0.018632056191563606,
0.06242692098021507,
0.023309046402573586,
-0.007464604452252388,
0.030925722792744637,
-0.062309809029102325,
-0.006010538898408413,
0.013274447992444038,
-0.009071393869817257,
0.041894376277923584,
0.03512263298034668,
-0.022766953334212303,
-0.018127841874957085,
0.04591546580195427,
-0.045729268342256546,
-0.02173817902803421,
-0.0006743991398252547,
-0.00007364737393800169,
-0.005153853911906481,
0.005808018613606691,
0.004986984189599752,
-0.005793015472590923,
-0.0062638637609779835,
0.000889714399818331,
0.013541641645133495,
-0.030410312116146088,
-0.015559368766844273,
0.021196000277996063,
0.014110215939581394,
0.018344135954976082,
0.03385603055357933,
0.00568919675424695,
-0.011662712320685387,
0.07308513671159744,
-0.05073324590921402,
0.045312825590372086,
0.01095290295779705,
0.022764066234230995,
-0.09519743174314499,
-0.016045071184635162,
-0.019057229161262512,
-0.024049045518040657,
0.05232168734073639,
-0.055837057530879974,
0.008272693492472172,
0.03359641879796982,
-0.04129931703209877,
0.05762188136577606,
-0.021386273205280304,
-0.010591653175652027,
-0.025463487952947617,
-0.013400359079241753,
-0.018004799261689186,
0.025169728323817253,
0.02268502116203308,
0.025741102173924446,
0.015873676165938377,
0.02333502657711506,
-0.0297166109085083,
-0.015696318820118904,
0.02998373843729496,
0.003431672928854823,
0.015509350225329399,
-0.03258385881781578,
0.03074081614613533,
-0.02011115290224552,
-0.03944907337427139,
0.021792717278003693,
-0.030685484409332275,
-0.016385383903980255,
-0.0007904614321887493,
0.011829310096800327,
-0.021756205707788467,
0.005520455073565245,
0.02000720240175724,
-0.012248240411281586,
0.007679685950279236,
-0.010247493162751198,
0.04547811299562454,
0.025874346494674683,
-0.005480780266225338,
0.021936073899269104,
0.02342023327946663,
-0.04734451323747635,
-0.06463310122489929,
0.052738334983587265,
0.00916125439107418,
0.01503031700849533,
-0.02048712596297264,
-0.017704254016280174,
-0.0019459379836916924,
0.00013242335990071297,
0.023696696385741234,
-0.03234337270259857,
-0.03149701654911041,
0.005037671886384487,
0.025839943438768387,
0.0006514022825285792,
0.009548905305564404,
0.009304950945079327,
-0.04753345251083374,
0.022231558337807655,
0.016216637566685677,
-0.009665151126682758,
-0.07982618361711502,
-0.02194925583899021,
0.02590508572757244,
-0.013816163875162601,
-0.011385800316929817,
-0.06580953299999237,
-0.025751842185854912,
0.003989307675510645,
0.0019853159319609404,
-0.009043554775416851,
-0.03014763817191124,
-0.027428487315773964,
-0.021821917966008186,
-0.0463179275393486,
0.0507296547293663,
0.0013784312177449465,
-0.015176893211901188,
-0.027273118495941162,
-0.02605416439473629,
-0.019156720489263535,
0.0020835602190345526,
0.05312835052609444,
-0.0034931343980133533,
-0.0219891220331192,
-0.02341187745332718,
0.0011333165457472205,
0.01336462702602148,
-0.02258545719087124,
0.004759662784636021,
-0.022733841091394424,
-0.003943870309740305,
-0.017819296568632126,
-0.01979043148458004,
0.008095001801848412,
0.005806077737361193,
-0.017467167228460312,
0.007008100859820843,
-0.004781960044056177,
-0.024411814287304878,
-0.04178294911980629,
0.042319778352975845,
0.023142876103520393,
0.02175341360270977,
0.045400820672512054,
-0.024607229977846146,
0.01842665858566761,
0.055930621922016144,
-0.058038514107465744,
-0.05304818972945213,
0.015496616251766682,
-0.04418519139289856,
-0.0033082703594118357,
-0.003901527728885412,
-0.015629969537258148,
0.03505972400307655,
-0.023641886189579964,
-0.04647081717848778,
0.031820155680179596,
-0.05721711367368698,
-0.007744130212813616,
0.04969931021332741,
0.05441976338624954,
0.0187954343855381,
0.004646294750273228,
0.0158589668571949,
0.05039936304092407,
0.0277014821767807,
0.006334097124636173,
0.03470918908715248,
0.02208869904279709,
0.04422925040125847,
0.028063373640179634,
-0.0124600725248456,
-0.005298681557178497,
0.04906526952981949,
0.012484260834753513,
-0.00395498052239418,
-0.04055304080247879,
-0.004692009184509516,
0.042871952056884766,
-0.03139813244342804,
-0.00032717903377488256,
0.02074848674237728,
-0.043487004935741425,
0.06217779219150543,
-0.017973994836211205,
0.01578124612569809,
-0.014499731361865997,
0.013684157282114029,
0.01797640509903431,
-0.0002031512703979388,
0.02566870115697384,
0.042609844356775284,
-0.0551346130669117,
0.02825734205543995,
0.006925123278051615,
0.0019388528307899833,
0.010232692584395409,
-0.04840622469782829,
0.018618138507008553,
0.016459966078400612,
0.0015968175139278173,
-0.0444023497402668,
-0.03497409075498581,
-0.013984006829559803,
-0.008120161481201649,
0.017907939851284027,
0.04812629148364067,
-0.0070334807969629765,
0.00618197163566947,
0.009565930813550949,
-0.02034459076821804,
0.004531940445303917,
-0.03183875232934952,
-0.01761048100888729,
-0.017635783180594444,
0.053067684173583984,
-0.01605229265987873,
0.018501807004213333
] |
<p>When ever i look this up all I get is sites saying how its because general relativity says "-" why does it do it though? it is because there is more motion near gravity than further away? Or is it something completely different?</p> | 1,407 | [
-0.01714330166578293,
-0.049717534333467484,
0.004362272098660469,
-0.021435512229800224,
0.028304211795330048,
0.04079205170273781,
-0.013784380629658699,
-0.012569064274430275,
-0.017051419243216515,
-0.005438103806227446,
-0.012961909174919128,
0.05069655179977417,
0.03786048665642738,
-0.015500753186643124,
0.014135926961898804,
0.002519944217056036,
-0.011855141259729862,
0.010846761986613274,
-0.004060310777276754,
-0.057935621589422226,
0.002975317183881998,
0.03419006988406181,
0.029622310772538185,
0.012530773878097534,
-0.026412436738610268,
0.005253755021840334,
0.0328642912209034,
0.00670405151322484,
0.033377643674612045,
0.04055687412619591,
0.0019210170721635222,
0.016598664224147797,
-0.0005211700918152928,
0.054601822048425674,
0.04012298211455345,
-0.011708134785294533,
-0.015702730044722557,
-0.0002763456723187119,
-0.012899319641292095,
0.01622796431183815,
-0.05921260640025139,
-0.028093991801142693,
-0.031393006443977356,
0.06887980550527573,
-0.010139049962162971,
0.011593411676585674,
0.017832845449447632,
-0.008696751669049263,
0.0764651969075203,
-0.05234799161553383,
0.06290773302316666,
-0.015056872740387917,
0.037127237766981125,
0.014577807858586311,
-0.00030263554072007537,
0.03484340384602547,
0.09114079922437668,
0.06764877587556839,
-0.027490701526403427,
-0.03716807812452316,
-0.012021836824715137,
-0.01610133983194828,
-0.008469818159937859,
-0.01169243548065424,
0.01866871863603592,
0.05505024641752243,
-0.014705433510243893,
-0.02973499335348606,
0.013905821368098259,
0.008224661462008953,
0.016092248260974884,
0.014272366650402546,
0.03800790011882782,
-0.043137215077877045,
0.010371585376560688,
-0.02585766464471817,
0.029969267547130585,
-0.0031138488557189703,
0.036600638180971146,
0.029362015426158905,
-0.03032812289893627,
-0.008788513951003551,
0.029535027220845222,
0.028545701876282692,
-0.01229829341173172,
-0.007092899642884731,
0.06557422131299973,
-0.005115734878927469,
0.0012331579346209764,
0.06019958481192589,
-0.03389035910367966,
-0.00045175853301770985,
0.024521613493561745,
0.004411268979310989,
-0.022235456854104996,
0.0513329952955246,
0.013086079619824886,
0.052639514207839966,
0.03145432472229004,
-0.010039332322776318,
-0.01847584918141365,
-0.020368728786706924,
-0.0011453056940808892,
0.07250110805034637,
-0.00268232892267406,
-0.020529398694634438,
-0.06547189503908157,
0.009494202211499214,
-0.017109761014580727,
0.026803147047758102,
-0.017882762476801872,
0.01006580051034689,
0.006827277131378651,
-0.040853068232536316,
0.03212571516633034,
-0.044755350798368454,
0.028360547497868538,
-0.012110038660466671,
-0.005029003135859966,
0.0823916420340538,
0.030769577249884605,
-0.037349995225667953,
0.03451094031333923,
0.004592690151184797,
-0.044545844197273254,
0.03577873855829239,
0.05336075648665428,
-0.008588399738073349,
-0.012833905406296253,
0.0004806682700291276,
0.0028354735113680363,
-0.033711936324834824,
0.022851884365081787,
0.001505363150499761,
0.04680672287940979,
-0.0014289456885308027,
-0.09356679767370224,
-0.07942011952400208,
0.06688518077135086,
0.0037149768322706223,
0.007786113303154707,
-0.07546332478523254,
0.02931889332830906,
0.008581709116697311,
0.08772625774145126,
0.025453152135014534,
0.003957934211939573,
0.03147353231906891,
0.020096568390727043,
-0.0011290446855127811,
-0.003341785864904523,
-0.01556469313800335,
-0.011492571793496609,
-0.04396168515086174,
-0.00018499535508453846,
-0.09238335490226746,
0.006598531734198332,
0.02064792439341545,
-0.0065573942847549915,
-0.04231901839375496,
0.07479376345872879,
-0.017987443134188652,
0.02049991488456726,
0.013197865337133408,
0.011933847330510616,
-0.01853288523852825,
0.10117889195680618,
0.04685044288635254,
-0.024156933650374413,
0.07479047030210495,
-0.0004791318206116557,
0.04913990944623947,
-0.0068981098011136055,
0.05167311802506447,
0.027695106342434883,
-0.03578859567642212,
-0.029603680595755577,
-0.013158859685063362,
0.003780853236094117,
0.0010557729983702302,
-0.03688089922070503,
-0.03237314894795418,
0.015393855981528759,
-0.0009520920575596392,
-0.021159127354621887,
0.03862413391470909,
-0.004577898886054754,
-0.006367300171405077,
0.0043479627929627895,
-0.04101814702153206,
-0.0015606265515089035,
-0.06531912088394165,
0.010219023562967777,
-0.008756069466471672,
-0.008424660190939903,
-0.0013630659086629748,
0.04783492907881737,
0.03276662528514862,
-0.056908681988716125,
-0.03224222734570503,
-0.0005776610923931003,
0.0358828604221344,
-0.03185933083295822,
-0.025337494909763336,
0.0041084070689976215,
0.08116015046834946,
0.0400666706264019,
0.009461827576160431,
0.017372271046042442,
0.013461144641041756,
-0.004356379620730877,
0.03198965638875961,
0.009236043319106102,
-0.00002132025474566035,
-0.012592126615345478,
-0.03165557608008385,
-0.0009219966013915837,
0.013020344078540802,
-0.014705738984048367,
0.04689789563417435,
-0.044413913041353226,
0.08100936561822891,
0.06136593967676163,
-0.0013915112940594554,
-0.0067088608630001545,
0.04155263677239418,
-0.023109769448637962,
-0.005016638897359371,
0.007475975435227156,
-0.018967151641845703,
-0.0274423249065876,
-0.040451373904943466,
0.04094300791621208,
0.008716398850083351,
-0.016330691054463387,
0.013885492458939552,
0.04761893302202225,
0.040180254727602005,
0.020768316462635994,
0.04670010507106781,
-0.011297130957245827,
-0.03001762367784977,
-0.008555609732866287,
0.006919632200151682,
0.011750618927180767,
0.002646754262968898,
0.07789703458547592,
0.03231188654899597,
0.004844417795538902,
-0.01130953710526228,
-0.0570296011865139,
0.037459272891283035,
0.0042910040356218815,
0.029745716601610184,
0.02015923708677292,
-0.019033143296837807,
0.03204670175909996,
-0.028596609830856323,
0.022511638700962067,
0.009744662791490555,
-0.007310695014894009,
0.010781931690871716,
-0.057051870971918106,
-0.015165499411523342,
0.020414933562278748,
0.015440447255969048,
-0.013580769300460815,
-0.007742912974208593,
0.014901847578585148,
-0.05912536755204201,
0.015079864300787449,
-0.034767840057611465,
-0.019331540912389755,
-0.027724269777536392,
0.025089729577302933,
0.02374906837940216,
0.021446404978632927,
0.03464902564883232,
-0.005848018452525139,
-0.0418105386197567,
-0.01532511506229639,
-0.06186696141958237,
0.0008597050909884274,
-0.00005711409903597087,
-0.037756506353616714,
0.05013398826122284,
-0.02480793185532093,
-0.025917282328009605,
0.06460931897163391,
-0.022453857585787773,
0.013575111515820026,
0.011162033304572105,
-0.008991177193820477,
-0.015215357765555382,
-0.010469897650182247,
-0.04598068818449974,
-0.019753726199269295,
-0.003576408140361309,
0.0131544079631567,
0.06565987318754196,
-0.02919931709766388,
-0.043565791100263596,
0.003588164923712611,
-0.04733889922499657,
-0.0544360876083374,
-0.007626410573720932,
0.004337525926530361,
0.02564655989408493,
-0.05213768407702446,
0.019921397790312767,
-0.012414844706654549,
-0.06724818795919418,
0.001053394633345306,
-0.023564592003822327,
-0.018767613917589188,
0.03025241382420063,
-0.00201171706430614,
0.010401406325399876,
-0.029219258576631546,
-0.023112013936042786,
0.05218883603811264,
0.007233019452542067,
0.00913466326892376,
-0.03317440673708916,
0.01265503279864788,
-0.008396575227379799,
0.0010831095278263092,
0.03275701403617859,
0.03367551043629646,
0.01876339130103588,
0.036308933049440384,
0.049508508294820786,
0.02539253607392311,
0.006611803080886602,
0.00499641103670001,
-0.009313637390732765,
-0.031425509601831436,
-0.007570770103484392,
-0.018277985975146294,
0.026200491935014725,
0.016250336542725563,
-0.06352592259645462,
0.006893699057400227,
0.010741544887423515,
0.02328905463218689,
-0.029797647148370743,
-0.05420512333512306,
0.05804179608821869,
-0.01790737174451351,
0.032296035438776016,
-0.0037544388324022293,
0.016663573682308197,
0.004514198284596205,
0.02031559683382511,
0.0031992236617952585,
0.006404447834938765,
0.058227114379405975,
-0.021440114825963974,
-0.0022501808125525713,
-0.018774161115288734,
0.021557141095399857,
-0.04462258890271187,
-0.012111114338040352,
-0.017388202250003815,
-0.02177654765546322,
0.031085746362805367,
-0.024681217968463898,
-0.03597194328904152,
0.05156875029206276,
0.022937504574656487,
0.0013589492300525308,
0.01433363277465105,
-0.04484039172530174,
-0.004834217485040426,
-0.062489692121744156,
0.002838438842445612,
0.011510034091770649,
0.016837015748023987,
-0.010398497804999352,
0.03937701880931854,
0.022760583087801933,
0.027963778004050255,
0.015216564759612083,
-0.023870989680290222,
-0.0943663939833641,
0.02478504367172718,
-0.045277420431375504,
-0.02722533605992794,
-0.010850409045815468,
-0.03574194386601448,
-0.02888273447751999,
-0.02848409116268158,
-0.01809678226709366,
0.015454323962330818,
-0.02204696647822857,
-0.074118971824646,
-0.0009155355510301888,
-0.005838107783347368,
-0.024653634056448936,
-0.03051517903804779,
0.020328959450125694,
0.03772895410656929,
0.0019283165456727147,
0.01896655187010765,
0.044982731342315674,
0.0018236818723380566,
-0.02499464340507984,
0.005365187767893076,
0.03443719074130058,
0.03489697352051735,
0.006231748964637518,
0.006767969578504562,
-0.004150093533098698,
-0.010844213888049126,
0.013138403184711933,
-0.0057099005207419395,
0.016180751845240593,
0.030456051230430603,
-0.024274837225675583,
-0.041060879826545715,
-0.05574796721339226,
-0.004553765989840031,
0.00441382871940732,
0.0482984259724617,
0.023558488115668297,
0.014438883401453495,
0.026707760989665985,
0.02187737263739109,
0.016537485644221306,
0.024582816287875175,
0.03697500005364418,
-0.010616489686071873,
-0.018227258697152138,
-0.05869297683238983,
-0.03264852240681648,
-0.03505405783653259,
-0.007708292454481125,
0.05011596530675888,
-0.02192137949168682,
-0.06324692070484161,
0.015619737096130848,
0.016788635402917862,
-0.004847957752645016,
-0.011802557855844498,
-0.021805990487337112,
-0.015968112275004387,
0.007813867181539536,
0.0005916890222579241,
0.0009886642219498754,
-0.019518984481692314,
0.030165696516633034,
0.06680671870708466,
-0.00950773898512125,
0.004204850643873215,
-0.07831666618585587,
0.004964249208569527,
0.0365259051322937,
0.0037091553676873446,
-0.01159313227981329,
0.007196997758001089,
-0.04788495972752571,
-0.002507280558347702,
0.03707818686962128,
-0.040501922369003296,
0.0032891223672777414,
-0.030692631378769875,
0.005349741782993078,
0.007275324314832687,
-0.023932259529829025,
-0.01227730605751276,
-0.009977372363209724,
0.009959081187844276,
-0.025367580354213715,
0.0007262099534273148,
0.031742412596940994,
-0.024007894098758698,
-0.0039206272922456264,
0.0099948076531291,
0.044300418347120285,
0.041264161467552185,
0.007274898700416088,
0.002655335934832692,
0.03279094398021698,
-0.05023083835840225,
-0.04861641302704811,
-0.010648878291249275,
0.022212069481611252,
0.003303679870441556,
0.0421186201274395,
-0.04555586725473404,
-0.020315993577241898,
0.000610278220847249,
-0.004322883207350969,
0.003224964952096343,
-0.019783979281783104,
-0.027277760207653046,
-0.0020503527484834194,
0.028731273487210274,
-0.01421893946826458,
0.05398929491639137,
-0.02756551280617714,
-0.022561220452189445,
-0.02139788679778576,
-0.005758841522037983,
0.058884426951408386,
-0.05095917358994484,
-0.029279133304953575,
-0.005810180678963661,
-0.00780660891905427,
-0.04156283289194107,
0.04613533243536949,
-0.02547123283147812,
-0.004606542643159628,
-0.011828615330159664,
-0.02797652594745159,
-0.04125094786286354,
0.04382799193263054,
0.0385274663567543,
-0.0038492921739816666,
0.013845407404005527,
-0.004166520666331053,
0.018897656351327896,
-0.02355991117656231,
0.03242379054427147,
-0.008418984711170197,
-0.05383556708693504,
0.042516570538282394,
-0.005626336205750704,
-0.015236482955515385,
0.026603300124406815,
-0.0008865923155099154,
0.03993195667862892,
-0.03810114786028862,
0.0050874631851911545,
-0.0032986332662403584,
-0.03359440714120865,
0.021841986104846,
-0.05875282734632492,
-0.0608767494559288,
-0.00857065711170435,
-0.01910477690398693,
0.03874558210372925,
-0.04922917112708092,
0.012795344926416874,
0.04161596670746803,
0.028794489800930023,
-0.09988811612129211,
-0.053567610681056976,
0.03230273351073265,
-0.004887143615633249,
-0.022036725655198097,
-0.012077716179192066,
-0.01663323864340782,
-0.03691248223185539,
-0.017454689368605614,
-0.0340370275080204,
0.05355958640575409,
-0.015797611325979233,
-0.02253090590238571,
-0.00110425497405231,
0.0013030838454142213,
0.0417403019964695,
-0.00576786370947957,
-0.028627369552850723,
-0.014376080594956875,
0.007061252370476723,
-0.019634980708360672,
0.009172379970550537,
0.05556502938270569,
-0.01185136940330267,
-0.0036043061409145594,
-0.000996098853647709,
-0.015368916094303131,
-0.014459756202995777,
-0.022431042045354843,
0.006072611082345247,
0.048484668135643005,
0.011628881096839905,
0.026998033747076988,
-0.04226062074303627,
0.03655984252691269,
-0.010089927352964878,
0.006413578987121582,
0.007258136291056871,
-0.027071213349699974,
-0.010599910281598568,
-0.023073330521583557,
0.04317827522754669,
0.016207724809646606,
0.008824418298900127,
-0.022454695776104927,
0.0368245430290699,
0.002483433810994029,
-0.03762028366327286,
0.012440402060747147,
0.005700114648789167,
0.03230709955096245,
-0.008947058580815792,
0.009929982014000416,
0.020262695848941803,
0.005836905911564827,
-0.029251443222165108,
-0.003281231736764312,
0.003808870678767562,
0.009471813216805458,
0.07372128218412399,
-0.009886674582958221,
0.05653576925396919,
0.007395504508167505,
-0.007346433587372303,
0.01837889291346073,
-0.02457030490040779,
-0.013432948850095272,
0.007688518147915602,
-0.011228450573980808,
0.019204141572117805,
-0.02779381535947323,
0.0164974182844162,
-0.008469190448522568,
0.06127317622303963,
-0.022737011313438416,
0.009480736218392849,
0.020335489884018898,
0.037449225783348083,
0.007836437784135342,
0.030979381874203682,
-0.04952945187687874,
0.050873249769210815,
-0.00976738054305315,
0.046460527926683426,
0.01015488337725401,
-0.023289253935217857,
0.026183778420090675,
-0.022040996700525284,
0.003399745561182499,
-0.03517337515950203,
-0.024007515981793404,
-0.04223725572228432,
0.007385158445686102,
0.0029230995569378138,
0.0283755362033844,
0.0038660881109535694,
0.009569017216563225,
0.024707838892936707,
0.03422506898641586,
0.011227277107536793,
-0.0007511649164371192,
-0.06843877583742142,
-0.030390074476599693,
-0.06435141712427139,
-0.038305021822452545,
0.03503400832414627,
-0.006207267753779888,
-0.04348871111869812,
0.010549730621278286,
-0.033871907740831375,
-0.017937012016773224,
0.03843247517943382,
0.031060434877872467,
-0.015211985446512699,
0.08197183907032013,
0.007346623111516237,
0.015277480706572533,
-0.015063648112118244,
0.012601498514413834,
0.09369032084941864,
0.04801063984632492,
0.003806270193308592,
-0.07130008935928345,
0.001209088135510683,
-0.019850783050060272,
0.013278812170028687,
-0.05873217061161995,
0.03830304741859436,
-0.015982063487172127,
0.013054126873612404,
0.05084284022450447,
0.05882954224944115,
0.02754845656454563,
-0.03399211913347244,
0.06532344222068787,
-0.04162735864520073,
-0.036297522485256195,
-0.0007618370000272989,
0.014063742943108082,
0.010311285965144634,
0.007875019684433937,
-0.007773247547447681,
0.02946333959698677,
-0.028266480192542076,
0.01641293428838253,
-0.039758313447237015,
-0.049010615795850754,
-0.0007401324110105634,
0.055069901049137115,
-0.07334302365779877,
0.012688640505075455,
0.015696736052632332,
0.0015146869700402021,
-0.04938604310154915,
0.0009322872501797974,
0.0248070377856493,
-0.026375388726592064,
-0.0011916281655430794,
0.00021779126836918294,
-0.026941316202282906,
0.02924460358917713,
-0.006440120283514261,
-0.009541732259094715,
-0.053567733615636826,
0.02230736054480076,
-0.02141740918159485,
0.02747933939099312,
-0.008915495127439499,
0.02724405750632286,
0.022560667246580124,
0.02498636581003666,
-0.016084983944892883,
-0.05360216647386551,
-0.01187050249427557,
-0.013441212475299835,
-0.008930657058954239,
-0.003910718485713005,
-0.05938822403550148,
-0.027499858289957047,
0.011935705319046974,
0.010903655551373959,
0.023643985390663147,
0.008461355231702328,
0.019755812361836433,
0.02293984591960907,
-0.02007053792476654,
0.024018891155719757,
-0.03185874968767166,
-0.015952253714203835,
0.0005063951830379665,
0.017727071419358253,
-0.060201700776815414,
-0.0028321221470832825,
0.03265006095170975,
0.011497083120048046,
0.023384373635053635,
0.007759199943393469,
-0.008749707601964474,
0.008020920678973198,
-0.011316363699734211,
0.03149006515741348,
-0.04951927065849304,
-0.018333202227950096,
-0.0441388338804245,
0.0025560413487255573,
0.01222490519285202,
0.015647659078240395,
-0.009894389659166336,
0.02756914123892784,
-0.06025802344083786,
0.035660307854413986,
-0.02558625489473343,
0.00823474396020174,
-0.020339462906122208,
-0.005499031860381365,
-0.036559414118528366,
-0.025645442306995392,
-0.0006050021038390696,
0.03882679343223572,
0.0358177088201046,
0.009982098825275898,
0.01936950720846653,
0.02095450833439827,
-0.04263421148061752,
0.013409554958343506,
0.03798395395278931,
-0.001916582346893847,
-0.014839116483926773,
0.017942452803254128,
-0.03278753161430359,
-0.03235267847776413,
-0.015983691439032555,
-0.025189844891428947,
0.005242190323770046,
0.02219855971634388,
0.07237470149993896,
-0.002252972451969981,
0.04541822150349617,
0.01614777185022831,
0.02712920680642128,
-0.03237215429544449,
-0.006629613693803549,
-0.08374223858118057,
0.04735702648758888,
0.0012286757118999958,
-0.03641928732395172,
-0.012117934413254261,
-0.0025456713046878576,
-0.00006430119537981227,
-0.03141002729535103,
0.023131966590881348,
0.016395146027207375,
0.00393615011125803,
0.029340246692299843,
0.07833792269229889,
-0.03386610373854637,
0.05662565305829048,
0.0021421071141958237,
-0.025339210405945778,
0.003106292337179184,
-0.05812235549092293,
-0.05744588002562523,
0.03696659207344055,
-0.0168312918394804,
0.01437212061136961,
0.01818670704960823,
-0.010204244405031204,
-0.009015550836920738,
0.08483284711837769,
-0.0342087484896183,
0.008636175654828548,
-0.0026312670670449734,
-0.03064689226448536,
-0.00906717125326395,
-0.025752250105142593,
0.003545579267665744,
-0.0345645509660244,
-0.019749201834201813,
0.02282152697443962,
0.019642559811472893,
-0.016898391768336296,
0.01911865547299385,
0.0008326151291839778,
-0.02790834568440914,
-0.00285590928979218,
0.022183094173669815,
0.006771331187337637,
0.025718148797750473,
0.026687564328312874,
-0.04995321109890938,
0.021349096670746803,
0.02924024499952793,
0.0385676808655262,
-0.07937437295913696,
0.003600489115342498,
-0.014951168559491634,
-0.01153827365487814,
0.04134431853890419,
-0.05008197948336601,
0.021465200930833817,
0.011996091343462467,
-0.05103789642453194,
0.02931036241352558,
-0.03574727475643158,
-0.014017852023243904,
-0.03747077286243439,
-0.008869072422385216,
0.014301184564828873,
0.06278559565544128,
0.04904480278491974,
0.018742941319942474,
-0.00005965571472188458,
-0.010047176852822304,
-0.04383587837219238,
-0.018602624535560608,
-0.018765870481729507,
0.027230678126215935,
-0.02544180117547512,
-0.00034334653173573315,
0.04461488500237465,
0.010332050733268261,
-0.036832284182310104,
0.039926137775182724,
-0.0025444820057600737,
-0.02300272136926651,
0.0016866832738742232,
0.02875995635986328,
0.003448519157245755,
0.016717221587896347,
0.03289336711168289,
-0.01812712475657463,
-0.0262291356921196,
0.03791748359799385,
0.012495131231844425,
0.05020682513713837,
-0.014033462852239609,
-0.0030673735309392214,
-0.006572629325091839,
-0.05547298863530159,
-0.02469312772154808,
0.02030680514872074,
0.011231614276766777,
0.015909915789961815,
-0.024330755695700645,
0.03720692917704582,
0.029319943860173225,
-0.04920674487948418,
0.007186532951891422,
-0.05954701825976372,
-0.003103065537288785,
0.019324172288179398,
0.003459495259448886,
-0.02436227537691593,
0.006866266950964928,
0.012099622748792171,
-0.014962791465222836,
-0.020254433155059814,
-0.024733174592256546,
0.031851306557655334,
-0.021222040057182312,
-0.003949368372559547,
0.011725925840437412,
-0.020286282524466515,
0.01232769526541233,
-0.046700671315193176,
-0.025923578068614006,
0.033034756779670715,
0.044030096381902695,
0.017422836273908615,
0.0028849237132817507,
-0.023258566856384277,
-0.027439752593636513,
-0.09209492802619934,
0.0292685367166996,
-0.023604271933436394,
0.008314970880746841,
-0.032206255942583084,
0.005342151504009962,
-0.005476101767271757,
0.002842662623152137,
0.045592647045850754,
-0.002976616146042943,
-0.017252514138817787,
0.033302173018455505,
0.004320000298321247,
-0.005895619280636311,
-0.02355419099330902,
0.0030575254932045937,
0.007940176874399185,
-0.05939650908112526,
0.0181207824498415,
-0.030177637934684753,
-0.02645776979625225,
0.031296875327825546,
0.005628317594528198,
-0.006876975763589144,
0.06875022500753403,
-0.024808863177895546,
-0.02435283549129963,
0.0504816435277462,
0.04587627574801445,
-0.022255495190620422,
0.0761241689324379,
-0.004476428497582674,
0.002487464575096965,
0.04286729916930199,
-0.01684211567044258,
-0.028207777068018913,
0.022258669137954712,
0.011193886399269104,
-0.001318304450251162,
-0.026431476697325706,
-0.015144862234592438,
0.01792192831635475,
-0.01748274266719818,
0.025158103555440903,
0.04190865531563759,
-0.03317345678806305,
0.001685895724222064,
0.060117606073617935,
0.02495644986629486,
0.021721798926591873,
-0.005849884357303381,
-0.004820604342967272,
0.003607990685850382,
0.011655211448669434,
0.013360812328755856,
0.0456022173166275,
-0.0011990820057690144,
0.024075889959931374,
0.015490604564547539,
0.018307138234376907,
-0.012056147679686546,
0.015104508958756924,
-0.009586588479578495,
0.0656265988945961,
-0.033448394387960434,
0.01841859519481659,
-0.013266487047076225,
-0.017163584008812904,
0.04774850234389305,
0.029292557388544083,
-0.02878156676888466,
0.08139513432979584,
-0.03829389810562134,
0.011020386591553688,
0.01976119726896286,
-0.0001272622321266681,
-0.023782074451446533,
-0.017005834728479385,
-0.001951055135577917,
0.04408439248800278,
0.018871717154979706,
-0.016265055164694786,
0.0002343690284760669,
-0.027552472427487373,
0.018134169280529022,
-0.012502128258347511,
0.02359052188694477,
-0.002273834077641368,
0.004784360993653536,
0.007026078179478645,
-0.006810310296714306,
-0.03656240552663803,
-0.0269667636603117,
0.028995342552661896,
0.028225675225257874,
0.02773655392229557,
-0.04628104716539383,
-0.03494445979595184,
-0.028894029557704926,
0.027127018198370934,
-0.07125310599803925,
-0.02912433259189129,
0.005596876610070467,
0.013845257461071014,
-0.006897818762809038,
-0.00902069266885519
] |
<p>Why is <a href="http://en.wikipedia.org/wiki/Metallic_hydrogen" rel="nofollow">metallic hydrogen</a> considered a form of degenerate matter, akin to neutronium and electron-degenerate matter? I can understand that for the other two, degeneracy pressure is the only force countering inward gravity for very massive stars, but how does this concept also apply to super pressurised hydrogen? Furthermore, why would being supported by degeneracy pressure make the hydrogen metallic in nature? </p> | 1,408 | [
-0.06632097065448761,
-0.02458668127655983,
0.0007757687708362937,
-0.05103481188416481,
0.0567682646214962,
0.019061090424656868,
-0.033243726938962936,
-0.033973440527915955,
-0.009029694832861423,
-0.05310777202248573,
0.03842244669795036,
0.007911904715001583,
0.06365031749010086,
-0.004588260315358639,
0.009536763653159142,
0.011541398242115974,
0.025018885731697083,
-0.022675177082419395,
0.008872851729393005,
-0.01643996872007847,
-0.01343690138310194,
-0.007657209876924753,
0.016859831288456917,
0.027199864387512207,
-0.014070696197450161,
0.015169413760304451,
0.029323702678084373,
0.0388801172375679,
0.026256272569298744,
0.04376800358295441,
0.009540395811200142,
-0.004880860913544893,
-0.0025027371011674404,
0.03039446286857128,
-0.007880560122430325,
0.008778144605457783,
-0.025032062083482742,
-0.030306776985526085,
-0.040596261620521545,
0.019924666732549667,
-0.049192313104867935,
-0.02812996134161949,
0.0027200402691960335,
0.031537171453237534,
-0.0075896610505878925,
0.0038919327780604362,
0.023064203560352325,
-0.017667122185230255,
0.0023088380694389343,
-0.046307530254125595,
0.03490343317389488,
0.01867227628827095,
0.011975167319178581,
0.02394939586520195,
0.002449582563713193,
0.005273294635117054,
0.06903098523616791,
0.12355750799179077,
-0.011414937674999237,
-0.052707601338624954,
-0.03445862978696823,
-0.0176080334931612,
-0.01747085712850094,
-0.022158067673444748,
-0.009338894858956337,
0.05763748660683632,
0.0018149502575397491,
-0.023378433659672737,
0.0247811209410429,
0.037531156092882156,
0.014830227009952068,
-0.009341968223452568,
-0.0006642072112299502,
-0.012073592282831669,
0.029864277690649033,
-0.012273194268345833,
0.004747922997921705,
-0.004362189676612616,
0.029311027377843857,
0.058254748582839966,
-0.004564343485981226,
0.005226226523518562,
-0.0071792760863900185,
0.03822137042880058,
0.0007282450096681714,
-0.005339012015610933,
0.07413429766893387,
0.01701560616493225,
-0.002325653564184904,
0.046160053461790085,
-0.006345947738736868,
0.005715017206966877,
0.02576286904513836,
-0.016240959987044334,
-0.004027309827506542,
0.02319907955825329,
0.02018734999001026,
0.04819679260253906,
-0.0371820367872715,
-0.0010434456635266542,
-0.01321566291153431,
-0.0018016130197793245,
0.030572930350899696,
0.07998165488243103,
0.030169744044542313,
-0.0543505921959877,
-0.043208085000514984,
0.03495076671242714,
-0.01966630481183529,
0.011740084737539291,
-0.015208753757178783,
-0.008312941528856754,
-0.022145528346300125,
-0.04810082167387009,
0.0015450664795935154,
-0.03818367421627045,
0.03930466249585152,
0.006755142938345671,
0.043731074780225754,
0.087124302983284,
0.014241942204535007,
0.006753257010132074,
0.035256706178188324,
-0.024843905121088028,
-0.051769956946372986,
0.00039901089621707797,
0.032737962901592255,
-0.011933143250644207,
0.00877367053180933,
0.014199883677065372,
-0.01004403829574585,
-0.027677783742547035,
0.02373668923974037,
0.007773089688271284,
0.03784741461277008,
-0.02720780298113823,
-0.07005714625120163,
-0.05912943184375763,
0.028752103447914124,
0.013201732188463211,
-0.040685996413230896,
-0.04541836306452751,
0.03362679481506348,
0.0243229940533638,
0.06262905895709991,
0.01282415073364973,
-0.0015255635371431708,
-0.0046482267789542675,
0.04942908138036728,
0.02609959803521633,
0.011153532192111015,
-0.027794163674116135,
-0.0013584031257778406,
-0.05609467253088951,
0.0022314293310046196,
-0.08787104487419128,
-0.00887069758027792,
-0.01098738331347704,
0.019816482439637184,
-0.028781792148947716,
0.09230827540159225,
-0.032672278583049774,
0.01846974343061447,
-0.02237579971551895,
-0.0072452533058822155,
0.010754791088402271,
0.07357057929039001,
0.014063271693885326,
-0.0075593930669128895,
0.05884698033332825,
0.026751980185508728,
0.033965401351451874,
0.026463106274604797,
0.07395578920841217,
0.01033678650856018,
-0.048672765493392944,
-0.008421608246862888,
-0.059463948011398315,
0.022421978414058685,
-0.0012068344512954354,
-0.034272536635398865,
-0.01567930541932583,
-0.011216669343411922,
0.03422626107931137,
0.03374050557613373,
0.026968061923980713,
0.013767987489700317,
-0.023292245343327522,
0.011684438213706017,
-0.06734132021665573,
-0.0026693358086049557,
-0.0477144680917263,
0.02372431755065918,
-0.014724571257829666,
0.0030587282963097095,
0.01950882375240326,
0.043062131851911545,
0.019839083775877953,
-0.03829415887594223,
-0.020712675526738167,
-0.011214318685233593,
0.06288246810436249,
0.020226897671818733,
-0.003301423043012619,
0.0349721722304821,
0.04267997667193413,
0.00600337004289031,
-0.010891427285969257,
-0.00935788918286562,
-0.007035005837678909,
-0.04376891255378723,
0.017366502434015274,
-0.005790823604911566,
-0.01800263114273548,
-0.0016104017850011587,
-0.0141148641705513,
0.009734357707202435,
0.009919494390487671,
-0.0010816458379849792,
0.053228043019771576,
-0.019577253609895706,
0.10733897238969803,
0.02877933904528618,
0.02171117067337036,
0.00406500743702054,
0.02956273779273033,
-0.014648010022938251,
0.0030316272750496864,
-0.018523693084716797,
0.011945122852921486,
-0.08800549060106277,
-0.00730501813814044,
0.057660188525915146,
0.029392246156930923,
-0.03413361683487892,
0.005015845876187086,
-0.00510125607252121,
0.023400699719786644,
0.0525457039475441,
0.029711049050092697,
-0.04942287877202034,
-0.009808840230107307,
-0.006255785468965769,
0.013822437264025211,
0.002209038008004427,
0.006559605710208416,
0.014691979624330997,
0.03719457983970642,
0.010999702848494053,
-0.029639098793268204,
0.006878909654915333,
0.07585649192333221,
-0.005886065308004618,
-0.019467361271381378,
-0.01712053269147873,
-0.07146425545215607,
0.03673918545246124,
-0.023986002430319786,
0.005065325181931257,
0.050892267376184464,
0.029544584453105927,
0.039545975625514984,
-0.07063878327608109,
-0.012146851047873497,
0.015191313810646534,
-0.0069993906654417515,
-0.009240737184882164,
-0.027017027139663696,
0.0068875933066010475,
-0.037509553134441376,
0.0033805277198553085,
-0.05052589997649193,
0.027341637760400772,
-0.033046405762434006,
-0.006279021967202425,
-0.012967833317816257,
0.008388839662075043,
0.026225225999951363,
-0.008378378115594387,
-0.032286420464515686,
0.01441117748618126,
-0.053462184965610504,
-0.003533395938575268,
0.0023066196590662003,
-0.023800263181328773,
0.005939804948866367,
-0.04085705429315567,
-0.027755768969655037,
0.0331382229924202,
0.040569134056568146,
0.012871718034148216,
-0.030472781509160995,
-0.012457119300961494,
-0.05382241681218147,
0.0026834530290216208,
-0.015599432401359081,
-0.017756981775164604,
-0.03362574055790901,
0.007344772107899189,
0.06287909299135208,
-0.012755366042256355,
-0.01603962853550911,
0.009776157326996326,
-0.03003479354083538,
-0.05479114502668381,
-0.010181600227952003,
-0.01590750366449356,
-0.01874893717467785,
-0.02159249596297741,
0.04166259989142418,
0.06790772825479507,
-0.06402869522571564,
-0.007697617169469595,
-0.010249749757349491,
-0.028964435681700706,
0.006682387553155422,
-0.03826058655977249,
0.0009422065922990441,
-0.008323459886014462,
-0.03731577470898628,
0.07041126489639282,
-0.0026852984447032213,
-0.03676706179976463,
-0.012637781910598278,
-0.0018533208640292287,
0.002972235670313239,
-0.0017803115770220757,
0.03900451958179474,
0.07101014256477356,
0.029931707307696342,
-0.0040175579488277435,
0.0402338020503521,
0.03864467889070511,
-0.002991310553625226,
-0.008881459943950176,
-0.03634214773774147,
-0.012366581708192825,
0.010727307759225368,
-0.008671718649566174,
0.055204715579748154,
0.019150864332914352,
-0.017967015504837036,
0.021820586174726486,
-0.023382479324936867,
0.047926150262355804,
0.0282321497797966,
-0.020572949200868607,
0.047494642436504364,
0.023522093892097473,
0.009061886928975582,
-0.060557011514902115,
0.026845257729291916,
-0.012396377511322498,
-0.032508719712495804,
0.018517782911658287,
-0.01418459601700306,
0.03152386471629143,
-0.00938157457858324,
-0.027129264548420906,
0.04362209141254425,
0.010226857848465443,
-0.030824122950434685,
-0.006620883475989103,
0.034891895949840546,
0.007680434733629227,
-0.0063567799516022205,
-0.029062116518616676,
-0.01302030123770237,
0.03732514753937721,
0.03276066109538078,
0.016134392470121384,
-0.030752532184123993,
-0.02276724763214588,
0.0029636130202561617,
-0.08702347427606583,
-0.004067664034664631,
0.008339726366102695,
0.03227989375591278,
-0.031248513609170914,
0.046181902289390564,
0.030238721519708633,
0.01729576848447323,
-0.007278994657099247,
-0.01787986047565937,
-0.0954657644033432,
-0.01977853663265705,
-0.03593501076102257,
0.003413289785385132,
-0.012191583402454853,
-0.0018622259376570582,
-0.03184583783149719,
-0.04835599660873413,
-0.03366914018988609,
-0.04422132298350334,
-0.028854403644800186,
-0.020716320723295212,
0.0025136242620646954,
-0.05065866932272911,
-0.04196887090802193,
-0.011171764694154263,
0.01749340258538723,
0.03934476524591446,
-0.008622927591204643,
0.03127407655119896,
0.01999768614768982,
-0.010517014190554619,
0.0047364807687699795,
-0.009741416200995445,
-0.0011235064594075084,
-0.011906095780432224,
0.04285067319869995,
0.033449430018663406,
0.016973599791526794,
0.02441507764160633,
-0.045223385095596313,
0.011139820329844952,
0.03727664798498154,
0.015327145345509052,
-0.012207522056996822,
0.016859717667102814,
-0.04341857135295868,
-0.027385784313082695,
0.016276048496365547,
0.01791108399629593,
-0.002848325064405799,
0.04257051274180412,
-0.002454190282151103,
-0.014127662405371666,
-0.032787006348371506,
0.047049783170223236,
0.023975443094968796,
0.017881445586681366,
-0.027137909084558487,
-0.0495290532708168,
-0.05182649940252304,
-0.06038255989551544,
-0.003705813782289624,
0.03752986341714859,
-0.0015487450873479247,
-0.018649287521839142,
0.022319985553622246,
-0.028305156156420708,
0.004232577979564667,
0.008535543456673622,
-0.036602701991796494,
-0.014880135655403137,
0.02171296998858452,
-0.038585562258958817,
0.034669291228055954,
0.046226587146520615,
0.034789908677339554,
0.057228054851293564,
-0.020189616829156876,
-0.01397562026977539,
-0.09275911003351212,
-0.009649139828979969,
0.02714751660823822,
0.03050556778907776,
-0.02526865340769291,
-0.01883563958108425,
-0.0798024982213974,
-0.008348212577402592,
0.04509503021836281,
-0.027032529935240746,
0.0006034481921233237,
-0.030520938336849213,
-0.0143613051623106,
0.0015259834472090006,
-0.018728194758296013,
-0.011118951253592968,
0.016729548573493958,
0.02064378745853901,
0.002920629922300577,
-0.03718815743923187,
0.005979709327220917,
-0.020557692274451256,
0.01399399247020483,
0.011226090602576733,
0.007509990595281124,
0.01290134061127901,
0.023700596764683723,
0.01155867800116539,
0.0342835932970047,
-0.01370200514793396,
-0.09097295254468918,
-0.030856922268867493,
0.01673136092722416,
0.00509596336632967,
0.01638733595609665,
-0.052702996879816055,
-0.07125670462846756,
0.010181289166212082,
0.028580568730831146,
-0.0033435060176998377,
0.005898491945117712,
-0.014499804936349392,
0.027812590822577477,
0.05963219702243805,
-0.005397528409957886,
0.024053102359175682,
0.02598652057349682,
0.005361961666494608,
-0.03452382981777191,
-0.03377818688750267,
0.02783852070569992,
-0.0500202476978302,
0.011278193444013596,
-0.024334842339158058,
0.01548371184617281,
-0.03158075362443924,
0.031531188637018204,
0.0040344055742025375,
0.012858355417847633,
-0.004683481529355049,
-0.019997192546725273,
-0.0026029255241155624,
0.011918208561837673,
0.022343380376696587,
-0.03861925005912781,
-0.010988106019794941,
0.030033143237233162,
0.013207114301621914,
-0.01684647984802723,
0.02213619090616703,
-0.012296517379581928,
0.0012821530690416694,
0.02513013407588005,
-0.02175877057015896,
0.008053366094827652,
0.010614179074764252,
-0.04393264278769493,
0.04723602533340454,
-0.0373273603618145,
0.027269396930933,
-0.016641274094581604,
0.0149493757635355,
0.029225340113043785,
-0.01886179856956005,
0.003907821606844664,
-0.023542452603578568,
-0.04429620876908302,
0.016188988462090492,
-0.018119221553206444,
0.030123844742774963,
0.030920160934329033,
0.017272699624300003,
-0.0927957072854042,
-0.029923127964138985,
0.022516852244734764,
0.0033821447286754847,
-0.03316169232130051,
-0.03877687826752663,
0.01858709007501602,
-0.03025030344724655,
-0.02038484252989292,
0.0024305391125380993,
0.040001560002565384,
-0.05928092077374458,
-0.003931686282157898,
0.011001323349773884,
0.020291993394494057,
0.07430753111839294,
-0.04892171174287796,
-0.05652036890387535,
-0.005823434330523014,
0.01501221489161253,
0.00441166153177619,
-0.03375914320349693,
0.04799051582813263,
-0.005875434726476669,
-0.02060137689113617,
0.022512957453727722,
-0.026824865490198135,
0.013591173104941845,
-0.004928696434944868,
0.02487325668334961,
0.03892498090863228,
0.01090333890169859,
0.005846917629241943,
-0.010639896616339684,
0.02734224498271942,
-0.012533620931208134,
0.05567352846264839,
-0.02892259694635868,
0.011307315900921822,
0.0023847392294555902,
-0.01666751690208912,
0.06377376616001129,
-0.016256310045719147,
0.009231445379555225,
0.01926681026816368,
0.07479792833328247,
0.03232891857624054,
0.03331136703491211,
-0.011612523347139359,
-0.06284137815237045,
-0.002169158775359392,
-0.00015736478962935507,
0.006397091317921877,
0.022489557042717934,
0.02686709724366665,
0.009448761120438576,
-0.019956106320023537,
-0.023384468629956245,
0.006666718982160091,
0.04942690581083298,
-0.04186922684311867,
0.04516637325286865,
-0.023477207869291306,
-0.010067727416753769,
-0.017107082530856133,
-0.030945483595132828,
-0.027130767703056335,
0.015644032508134842,
-0.01664937473833561,
0.004805207718163729,
0.00990857370197773,
0.010202297940850258,
0.04064621403813362,
0.030306123197078705,
-0.01951710879802704,
0.006855927407741547,
0.06302335113286972,
0.02457374893128872,
0.028544805943965912,
-0.03079499490559101,
-0.048371560871601105,
0.024551207199692726,
-0.02519811876118183,
0.015091517940163612,
-0.013911639340221882,
-0.013585921376943588,
0.0011019007069990039,
-0.013660194352269173,
0.014277582988142967,
-0.07303082197904587,
-0.021150294691324234,
-0.020713940262794495,
0.03452547267079353,
0.026486894115805626,
0.0038220055866986513,
0.015499630942940712,
0.013659553602337837,
0.015076696872711182,
0.006690239068120718,
-0.005463812034577131,
0.01976744644343853,
-0.031463466584682465,
-0.0210981834679842,
-0.03945184126496315,
-0.02637915126979351,
0.037697307765483856,
0.02059977315366268,
-0.06557689607143402,
0.006230736616998911,
-0.023605264723300934,
0.011946565471589565,
-0.009733741171658039,
0.003478148253634572,
0.012325202114880085,
0.05899665877223015,
-0.028555136173963547,
0.030271725729107857,
0.024597881361842155,
0.013416092842817307,
0.101099893450737,
0.018981415778398514,
0.046896934509277344,
-0.051940422505140305,
-0.020458022132515907,
0.01046496070921421,
0.009595421142876148,
-0.023847220465540886,
0.000615489378105849,
-0.03090902976691723,
0.050260987132787704,
-0.009060736745595932,
0.027865685522556305,
-0.011807280592620373,
0.02466093935072422,
0.05434081330895424,
-0.028215549886226654,
0.033167216926813126,
-0.013587203808128834,
-0.0014521265402436256,
0.011805262416601181,
0.041878797113895416,
-0.057223182171583176,
0.011134875006973743,
-0.020493019372224808,
0.022207872942090034,
-0.042212896049022675,
-0.02932407706975937,
0.00003141563502140343,
0.021122384816408157,
-0.05422988533973694,
0.0004311680095270276,
-0.007816784083843231,
-0.012638469226658344,
-0.012392614036798477,
0.01634380780160427,
0.010731933638453484,
-0.003358515677973628,
0.026390811428427696,
-0.024336038157343864,
0.002614037599414587,
0.011523495428264141,
0.004755677655339241,
0.011991427280008793,
-0.040987417101860046,
0.03672828525304794,
-0.0266746636480093,
0.040175799280405045,
-0.03338653966784477,
0.004121015779674053,
0.04500859975814819,
0.0009468623902648687,
0.00916807446628809,
-0.007598591968417168,
-0.023527279496192932,
-0.02167474292218685,
0.01987442560493946,
0.023748619481921196,
-0.04892267659306526,
0.002955034840852022,
0.03942465782165527,
-0.017731035128235817,
0.021362129598855972,
-0.0340658538043499,
-0.006398271303623915,
0.041000302881002426,
0.0034020126331597567,
0.008416867814958096,
-0.011122122406959534,
0.01013148296624422,
-0.02147768810391426,
0.0007087857229635119,
-0.05990322679281235,
0.0012589794350787997,
0.020301882177591324,
0.021125370636582375,
0.0323764942586422,
0.02636015973985195,
0.0022623692639172077,
-0.0039154523983597755,
-0.04649145528674126,
0.07624229043722153,
-0.021737346425652504,
-0.02974782884120941,
-0.020973382517695427,
-0.02361203171312809,
0.01869877800345421,
0.04809661954641342,
-0.0258198119699955,
0.02829809859395027,
-0.007296169642359018,
0.01874733902513981,
0.009828537702560425,
-0.032188765704631805,
-0.031519945710897446,
0.02556523308157921,
-0.03693186491727829,
0.00423229718580842,
-0.005447186529636383,
0.011078630574047565,
0.03421313315629959,
-0.016471795737743378,
0.009375429712235928,
0.033040065318346024,
0.003099387511610985,
0.0006407676846720278,
0.00707270298153162,
-0.016991134732961655,
0.028366152197122574,
-0.005414995830506086,
0.013118121773004532,
-0.053639501333236694,
-0.02537291869521141,
-0.02156352996826172,
-0.024016808718442917,
0.000167206977494061,
0.014932990074157715,
-0.02695280872285366,
0.020942434668540955,
-0.03079528920352459,
-0.004817537497729063,
-0.034309182316064835,
0.005008118227124214,
-0.043105676770210266,
0.013693703338503838,
0.0031586047261953354,
-0.024702047929167747,
-0.005935981869697571,
0.023829882964491844,
-0.043201226741075516,
0.02198851853609085,
0.03033134900033474,
0.013813463971018791,
-0.01474213320761919,
0.027477875351905823,
0.06953858584165573,
-0.04910929501056671,
0.028742536902427673,
-0.009744273498654366,
0.00025055964943021536,
0.02288546971976757,
-0.03558460623025894,
-0.07582647353410721,
-0.005304576363414526,
0.007508956361562014,
0.0062240902334451675,
0.0024385147262364626,
-0.022147616371512413,
-0.02021997980773449,
0.0606209971010685,
-0.015376091934740543,
0.004780888557434082,
-0.008525840006768703,
-0.008892245590686798,
0.002970938105136156,
-0.00041718417196534574,
-0.006487214472144842,
-0.03743020072579384,
-0.01681278459727764,
0.04817993566393852,
0.031674016267061234,
-0.03036689944565296,
0.01117247436195612,
-0.025781510397791862,
-0.029920756816864014,
0.05430157482624054,
0.024675913155078888,
0.029667936265468597,
0.011489265598356724,
0.02827155962586403,
-0.040277741849422455,
0.06345480680465698,
0.035690560936927795,
0.0006292567704804242,
-0.07098551839590073,
0.01504752691835165,
-0.013417907059192657,
-0.013646494597196579,
0.04330942779779434,
-0.011603514663875103,
0.01878342032432556,
0.0007574236369691789,
-0.032122138887643814,
0.026739895343780518,
-0.045877374708652496,
-0.06140872836112976,
-0.0415160246193409,
-0.02285640873014927,
-0.02877655066549778,
0.0711582750082016,
0.019409306347370148,
0.05827207863330841,
0.053471338003873825,
-0.00043444085167720914,
-0.0029300081077963114,
0.005783519241958857,
-0.009932356886565685,
0.00983670074492693,
-0.01247318647801876,
-0.010527996346354485,
0.03441416099667549,
0.006406235974282026,
-0.02575702965259552,
0.02052953466773033,
-0.007521096616983414,
-0.010518115013837814,
0.013953923247754574,
0.02226897142827511,
-0.015110984444618225,
-0.0034266121219843626,
-0.0015403581783175468,
-0.014123504981398582,
-0.02358113043010235,
0.05056212097406387,
-0.000898504804354161,
0.030296048149466515,
-0.010194623842835426,
-0.014308319427073002,
0.014972801320254803,
-0.03119836002588272,
-0.001107444753870368,
0.03884875774383545,
-0.007920232601463795,
0.0026552139315754175,
0.015068250708281994,
0.019260527566075325,
0.032900236546993256,
-0.009080699644982815,
-0.020807253196835518,
-0.03793228790163994,
0.0016785258194431663,
0.028769968077540398,
0.021071305498480797,
-0.003652706043794751,
0.04014135152101517,
0.006140424404293299,
-0.02154727093875408,
-0.004267702344805002,
0.02770543470978737,
-0.04620230942964554,
-0.023939689621329308,
0.0010142928222194314,
0.016252582892775536,
-0.01652202196419239,
-0.026903534308075905,
-0.02820231206715107,
-0.02742576226592064,
0.07984799146652222,
0.027513716369867325,
0.0331023745238781,
-0.05240418389439583,
-0.06833753734827042,
-0.005652709864079952,
-0.07269096374511719,
0.03548579290509224,
-0.06273434311151505,
0.005125836469233036,
0.013326304033398628,
-0.02712268941104412,
-0.026852618902921677,
0.008562379516661167,
0.0465281642973423,
-0.023461949080228806,
0.005025604274123907,
0.0020546801388263702,
-0.02433682046830654,
0.00017554110672790557,
-0.0539180189371109,
0.014526734128594398,
0.014584243297576904,
-0.04721206799149513,
0.056761085987091064,
0.009771817363798618,
-0.02832779660820961,
0.010307552292943,
0.042145006358623505,
-0.013860361650586128,
0.01429994311183691,
0.01935827173292637,
-0.008476980961859226,
0.06038431450724602,
0.003735097823664546,
-0.0023396937176585197,
0.09606713056564331,
-0.009034795686602592,
0.019004279747605324,
0.028284452855587006,
0.018986430019140244,
-0.029946651309728622,
0.004974656272679567,
-0.003498299280181527,
-0.01159315649420023,
-0.005141700152307749,
-0.01982540637254715,
0.020768024027347565,
-0.061275921761989594,
0.050134945660829544,
0.033699437975883484,
-0.061134498566389084,
-0.032767459750175476,
0.04200579598546028,
0.034103937447071075,
0.0653391107916832,
-0.02843296341598034,
-0.01250410545617342,
-0.0036446554586291313,
0.01507261861115694,
-0.004237464163452387,
0.06492302566766739,
0.056319769471883774,
0.026020482182502747,
0.006715009920299053,
0.025862887501716614,
-0.016125954687595367,
0.012112806551158428,
-0.006638530641794205,
0.005769812036305666,
-0.06497326493263245,
-0.019583895802497864,
0.023400308564305305,
-0.026130715385079384,
0.030869778245687485,
0.024329375475645065,
-0.01845146343111992,
0.08960607647895813,
-0.011349324136972427,
0.0005141718429513276,
-0.035129714757204056,
0.017816556617617607,
0.037345509976148605,
0.02076593227684498,
-0.02145249955356121,
0.05372702702879906,
0.006745647173374891,
-0.014084693044424057,
-0.00951424054801464,
0.0076457965187728405,
0.053964029997587204,
0.002988923341035843,
0.019108016043901443,
0.00529936607927084,
-0.023087015375494957,
-0.010964741930365562,
-0.005337913986295462,
0.005330756772309542,
-0.002401755889877677,
-0.016161566600203514,
0.02558351680636406,
0.00006100150858401321,
0.0040700179524719715,
-0.0015572422416880727,
-0.038210075348615646,
0.01760638877749443,
-0.06843221187591553,
-0.021254170686006546,
-0.05604303628206253,
0.005768786650151014,
-0.02363508567214012,
-0.010197996161878109
] |
<p>When I searched the net about magnetic field lines, <a href="http://en.wikipedia.org/wiki/Magnetic_field#Magnetic_field_lines" rel="nofollow">Wikipedia</a> told something about contour lines and that magnetic materials placed along a magnetic field has some specific loci, which i did not understand. Can someone explain it to me in details.
Also how do we know that tangent to a magnetic field line gives the direction of magnetic field?
I am very confused.</p> | 423 | [
0.002374212723225355,
-0.012471434660255909,
-0.0248261708766222,
-0.034474123269319534,
0.0626508817076683,
0.04120812192559242,
-0.01942027360200882,
-0.014393997378647327,
0.020818935707211494,
-0.035176120698451996,
0.026209568604826927,
0.050691258162260056,
0.03555940091609955,
0.017674345523118973,
0.032692112028598785,
-0.025558462366461754,
-0.01623694598674774,
-0.0020620834548026323,
0.006521768402308226,
-0.04151817783713341,
0.013113897293806076,
-0.0008346316171810031,
0.012372996658086777,
0.03938755393028259,
-0.03525274619460106,
0.027119776234030724,
0.020135508850216866,
0.024205941706895828,
0.034739844501018524,
0.031119367107748985,
0.005312168505042791,
-0.039295658469200134,
0.006650150287896395,
-0.0011573509545996785,
0.030265819281339645,
-0.03217868506908417,
0.013497164472937584,
-0.027541516348719597,
-0.008016625419259071,
0.012527848593890667,
-0.03170904517173767,
-0.06570672243833542,
0.009423601441085339,
0.06507240980863571,
-0.040596041828393936,
-0.023337550461292267,
0.020755376666784286,
-0.03814169391989708,
0.029963577166199684,
-0.07716086506843567,
0.06979501992464066,
0.006983715109527111,
0.04526339843869209,
0.030580203980207443,
0.02232242375612259,
0.00796200055629015,
0.03387404605746269,
0.05437260866165161,
-0.027894295752048492,
-0.04719734564423561,
-0.013913586735725403,
-0.014924542047083378,
-0.0016909317346289754,
-0.023347966372966766,
-0.049446333199739456,
0.06251011043787003,
-0.03540008142590523,
0.0037513677962124348,
0.04225271940231323,
0.0022825428750365973,
-0.005776590667665005,
0.027190571650862694,
0.024846820160746574,
-0.01662449538707733,
0.006685315165668726,
-0.044576387852430344,
0.039365481585264206,
0.001339873531833291,
0.0571884848177433,
0.030702834948897362,
-0.0030514525715261698,
0.026434265077114105,
0.03057161159813404,
0.03566976264119148,
0.03180045261979103,
0.015954801812767982,
0.054501477628946304,
-0.0026645357720553875,
0.025784827768802643,
0.006513044238090515,
0.03788153454661369,
0.025421416386961937,
0.01384666282683611,
-0.035882968455553055,
-0.033357199281454086,
0.010479654185473919,
0.01192378718405962,
0.0244890283793211,
0.008632255718111992,
-0.012171050533652306,
0.013471420854330063,
0.006888826377689838,
0.016165418550372124,
0.02441631257534027,
0.014241785742342472,
-0.021744338795542717,
-0.0032407334074378014,
0.02531558647751808,
-0.047611650079488754,
0.000899171456694603,
-0.008742996491491795,
0.020627817139029503,
0.0402415506541729,
-0.009941158816218376,
0.009450862184166908,
-0.012601238675415516,
0.020661141723394394,
-0.018034059554338455,
0.053727876394987106,
0.07025492936372757,
0.016023261472582817,
-0.05893789604306221,
0.032308127731084824,
-0.01277891919016838,
-0.08251279592514038,
-0.02113230898976326,
0.029493408277630806,
0.00750986160710454,
-0.009877979755401611,
0.0075224172323942184,
0.004479741211980581,
-0.023799793794751167,
0.0022581336088478565,
0.022646429017186165,
0.04750366136431694,
-0.0018443061271682382,
-0.10385500639677048,
-0.06434747576713562,
0.05236714333295822,
-0.011046535335481167,
0.026173152029514313,
-0.04318894073367119,
-0.0019436319125816226,
0.021751470863819122,
0.06360489875078201,
-0.013463086448609829,
0.0034325863234698772,
-0.005045115947723389,
0.029732508584856987,
-0.023051109164953232,
-0.01054892223328352,
-0.019843515008687973,
-0.009460579603910446,
-0.05576154589653015,
-0.01217127125710249,
-0.06405046582221985,
0.040100522339344025,
0.0326697900891304,
0.0018063377356156707,
-0.07081825286149979,
0.0818493664264679,
-0.028299499303102493,
0.006573555991053581,
0.01914365030825138,
-0.036674827337265015,
-0.022665878757834435,
0.08289117366075516,
0.00373543007299304,
0.0183015875518322,
0.060760747641325,
-0.008523023687303066,
0.03091985546052456,
0.022145245224237442,
0.04591413959860802,
0.037252575159072876,
-0.05969458073377609,
-0.026953892782330513,
0.004785629920661449,
0.017246684059500694,
-0.009671967476606369,
-0.07715039700269699,
-0.05169331282377243,
0.027618536725640297,
0.05169099569320679,
0.0029156289529055357,
0.06175261735916138,
-0.030193336308002472,
-0.02484791725873947,
0.006248661316931248,
-0.06442069262266159,
0.00780266709625721,
-0.04132038354873657,
0.029181141406297684,
-0.06140817701816559,
-0.054076187312603,
0.008234658278524876,
0.00896057765930891,
0.007059754803776741,
-0.04677928239107132,
-0.04513034224510193,
0.007076832000166178,
0.02871994860470295,
0.0061858296394348145,
-0.014368928037583828,
0.022049633786082268,
0.04709530994296074,
0.004987005610018969,
0.005657790694385767,
0.05478086322546005,
-0.06873565912246704,
-0.029220592230558395,
0.01830296963453293,
-0.028080012649297714,
0.024374598637223244,
0.018929433077573776,
-0.02610178291797638,
-0.026369614526629448,
0.014973202720284462,
-0.03186587616801262,
0.019439654424786568,
-0.030345426872372627,
0.08109910041093826,
0.04152161255478859,
0.012427244335412979,
-0.010171308182179928,
0.013599355705082417,
-0.00983855314552784,
-0.0024840424302965403,
-0.008788171224296093,
-0.026418181136250496,
-0.05239579454064369,
0.01569870300590992,
0.052430517971515656,
-0.009743714705109596,
-0.026514897122979164,
-0.03150288015604019,
0.0066945902071893215,
0.05396924912929535,
0.02389826998114586,
0.031134121119976044,
-0.029346147552132607,
-0.027116427198052406,
-0.03924572095274925,
0.00834315549582243,
-0.026245160028338432,
0.043242234736680984,
0.03983624279499054,
0.03356306627392769,
0.028720783069729805,
0.0022602835670113564,
-0.007444129325449467,
0.08205609768629074,
-0.02735423855483532,
-0.01050085760653019,
0.03064904734492302,
-0.018164027482271194,
0.022572634741663933,
-0.039508670568466187,
0.019395736977458,
-0.008825122378766537,
0.0007692986982874572,
0.010340369306504726,
0.0029227586928755045,
0.02828522026538849,
0.005193349905312061,
-0.02409905381500721,
-0.04777314513921738,
-0.022813498973846436,
0.025436729192733765,
-0.02916542813181877,
0.011283121071755886,
-0.014678710140287876,
-0.015690729022026062,
-0.003681306028738618,
-0.004451326094567776,
0.041451595723629,
0.0010358327999711037,
0.03766435757279396,
-0.0030495321843773127,
-0.039327532052993774,
0.0039855241775512695,
-0.06394603103399277,
0.02082369662821293,
0.003620699979364872,
-0.05707571282982826,
0.011317542754113674,
-0.035067081451416016,
-0.026003384962677956,
0.04839922487735748,
-0.001757152727805078,
0.008696993812918663,
0.018404105678200722,
-0.0006203782395459712,
-0.05817653238773346,
-0.04214818403124809,
-0.014942497946321964,
0.04085114225745201,
0.0007445144583471119,
0.007643780205398798,
0.03740965947508812,
-0.027632886543869972,
-0.007713131606578827,
0.032766491174697876,
-0.04922962561249733,
-0.0005644944030791521,
-0.013698753900825977,
-0.011402239091694355,
0.02725856937468052,
0.001622497453354299,
0.01757422275841236,
0.02884860336780548,
-0.06841859221458435,
-0.021280601620674133,
-0.016848169267177582,
-0.012308364734053612,
0.0008339767227880657,
-0.03278445079922676,
0.027792004868388176,
-0.024431539699435234,
-0.03889314830303192,
0.06880564987659454,
0.05164294317364693,
-0.07267028093338013,
-0.03921026736497879,
-0.0021114309784024954,
-0.03211980313062668,
-0.04534158483147621,
0.01406401302665472,
0.06108420342206955,
-0.015911338850855827,
0.013882294297218323,
0.008749336004257202,
0.02611653320491314,
0.032922592014074326,
0.016801033169031143,
-0.0012739149387925863,
0.004380577709525824,
0.01369030773639679,
-0.02635171264410019,
0.05705362930893898,
0.012955681420862675,
-0.04255835711956024,
0.028771640732884407,
0.008473084308207035,
0.05737462639808655,
0.025413118302822113,
-0.01738390326499939,
0.03171776980161667,
-0.028217988088726997,
0.005879813339561224,
-0.022623620927333832,
0.01399990450590849,
0.011605891399085522,
0.03485395759344101,
0.006816953420639038,
0.013756837695837021,
0.03415922820568085,
-0.04771699011325836,
-0.007771466858685017,
0.021749379113316536,
-0.008771735243499279,
-0.05149390548467636,
0.0056397817097604275,
-0.02177712321281433,
-0.002693929011002183,
0.016298195347189903,
-0.040860213339328766,
-0.016790710389614105,
0.04500458762049675,
0.05356896296143532,
0.02866227552294731,
0.002278163330629468,
-0.018816852942109108,
0.00622446509078145,
-0.06505454331636429,
0.01322369184345007,
0.010958179831504822,
0.037423864006996155,
-0.000570701144170016,
0.056495681405067444,
0.022486895322799683,
-0.003321971045807004,
0.02214306965470314,
-0.010129699483513832,
-0.09942539036273956,
0.03288154676556587,
-0.024182675406336784,
-0.0014515346847474575,
-0.021770766004920006,
-0.03194145858287811,
0.015414821915328503,
-0.0017845011316239834,
-0.03549790754914284,
-0.03511955589056015,
-0.01006181351840496,
-0.0715322345495224,
0.022719131782650948,
-0.035902660340070724,
-0.0356975756585598,
-0.021286385133862495,
0.05980192497372627,
0.017925221472978592,
-0.021319609135389328,
0.005811842158436775,
0.007577124517410994,
-0.01341329887509346,
0.009726864285767078,
-0.013098929077386856,
-0.02138080820441246,
0.05827616527676582,
0.03076723776757717,
0.017353245988488197,
-0.02140538953244686,
-0.019927866756916046,
0.03446265310049057,
0.005551924929022789,
0.05808046832680702,
0.026376884430646896,
-0.001089734025299549,
-0.02000165730714798,
-0.04859417676925659,
0.004786663688719273,
-0.023266809061169624,
0.056202564388513565,
-0.003875597845762968,
-0.01350551750510931,
0.05809640884399414,
-0.0032548760063946247,
-0.015903912484645844,
0.0095689557492733,
0.021568663418293,
0.026409940794110298,
0.009154612198472023,
-0.07750321924686432,
-0.024186911061406136,
-0.03011476807296276,
-0.000008198137038561981,
-0.0052406382746994495,
-0.006456785835325718,
-0.033215101808309555,
-0.025302303954958916,
0.04733860492706299,
-0.0053123245015740395,
0.016584055498242378,
0.017763258889317513,
0.014124225825071335,
0.020951062440872192,
-0.0012816139496862888,
0.0027077714912593365,
0.025062886998057365,
0.01714927703142166,
0.06604674458503723,
0.005898154340684414,
-0.03370006009936333,
-0.09340543299913406,
0.001272247638553381,
0.02481650561094284,
0.02293379046022892,
0.0092185502871871,
-0.01915348321199417,
-0.03530524671077728,
0.0076500545255839825,
0.04441533610224724,
-0.016849715262651443,
0.018171504139900208,
-0.02252669259905815,
-0.01110703032463789,
-0.03108018822968006,
0.0035896438639611006,
-0.016641536727547646,
0.021933432668447495,
0.0037853699177503586,
0.03788164258003235,
-0.030480345711112022,
0.01689133234322071,
-0.019807377830147743,
-0.010527816601097584,
0.016985852271318436,
0.03690816089510918,
0.04563938081264496,
0.0168074369430542,
0.014942244626581669,
0.02661041170358658,
-0.0015099080046638846,
-0.08697602897882462,
0.0018850060878321528,
0.023089203983545303,
-0.006452079862356186,
0.04314500093460083,
0.0196714885532856,
-0.038596250116825104,
0.006565678399056196,
0.03280564397573471,
0.02752375416457653,
0.011360803619027138,
-0.018133820965886116,
0.03390539065003395,
0.03067425824701786,
0.014533745124936104,
0.06147311255335808,
0.004167943727225065,
-0.015085012651979923,
-0.012276997789740562,
-0.002060171915218234,
0.04248432815074921,
-0.008824650198221207,
0.00042199392919428647,
-0.0009983195923268795,
0.014473711140453815,
-0.025410223752260208,
0.0385064035654068,
-0.03152241185307503,
-0.0313800647854805,
-0.040680885314941406,
-0.025004826486110687,
-0.026647144928574562,
0.04478047415614128,
0.002691672882065177,
-0.02860955521464348,
0.010689887218177319,
0.028390513733029366,
0.022752879187464714,
-0.03456563875079155,
0.014031264930963516,
-0.02010492794215679,
0.017539743334054947,
0.035639580339193344,
0.004671922419220209,
-0.01662670448422432,
-0.015689397230744362,
-0.013406719081103802,
-0.005719236098229885,
-0.06601858884096146,
0.05097249150276184,
-0.018133508041501045,
-0.030671745538711548,
0.03672948479652405,
-0.046979378908872604,
-0.031599260866642,
-0.00568110216408968,
-0.011019381694495678,
0.036668144166469574,
-0.0536687932908535,
0.014213941060006618,
0.007447139825671911,
0.03497745469212532,
-0.04905890300869942,
-0.06831065565347672,
0.002009515417739749,
-0.004329924006015062,
-0.04722733795642853,
0.02123512700200081,
-0.003364319447427988,
-0.01468424778431654,
-0.06606782972812653,
0.008035384118556976,
0.038259152323007584,
-0.0643799677491188,
-0.018207993358373642,
0.036627430468797684,
-0.016405882313847542,
0.07075921446084976,
0.010442640632390976,
-0.03332008048892021,
0.017086749896407127,
-0.01618480123579502,
-0.006007264833897352,
-0.0407378263771534,
0.02323049120604992,
-0.008422345854341984,
-0.029917143285274506,
-0.008096431382000446,
0.012047873809933662,
0.03131191059947014,
0.0028654728084802628,
0.01171092502772808,
0.026308897882699966,
0.05181097984313965,
-0.0381682887673378,
-0.032498978078365326,
0.00501885823905468,
-0.00498907919973135,
0.008136536926031113,
-0.03543834760785103,
-0.000028086566089768894,
-0.037681322544813156,
-0.014252997003495693,
0.0054632979445159435,
0.005848881788551807,
0.05292554572224617,
0.011475561186671257,
0.05947377532720566,
-0.03277427703142166,
-0.013839726336300373,
0.002060015220195055,
-0.01481279730796814,
0.019908975809812546,
-0.00007139958324842155,
0.022162772715091705,
0.0036433066707104445,
0.024309804663062096,
-0.015383649617433548,
0.013241428881883621,
-0.01588914357125759,
-0.0029196320101618767,
0.06479714810848236,
-0.023471612483263016,
0.04497702047228813,
0.03094201348721981,
-0.021643225103616714,
0.003331836313009262,
-0.01752306893467903,
-0.042579710483551025,
-0.009486212395131588,
-0.02175900712609291,
0.04188095033168793,
-0.03101189061999321,
0.014187666587531567,
-0.0028726886957883835,
0.0021610490512102842,
-0.03243749588727951,
-0.022202415391802788,
0.01056637056171894,
0.04446449130773544,
0.05054639279842377,
0.05330076068639755,
-0.05061809718608856,
0.039791371673345566,
-0.010649491101503372,
0.02412744238972664,
0.027369877323508263,
-0.0023640329018235207,
0.0506768599152565,
-0.015296022407710552,
-0.005968771409243345,
-0.03675016388297081,
-0.021108409389853477,
-0.0007679120753891766,
0.03437486290931702,
0.02390439063310623,
-0.003649895777925849,
-0.029077282175421715,
0.01003938913345337,
0.028268519788980484,
-0.0010626846924424171,
-0.005521213635802269,
0.007380267605185509,
-0.028963379561901093,
-0.042888887226581573,
-0.034416019916534424,
-0.034881360828876495,
0.02914874255657196,
-0.006137927994132042,
-0.05946360155940056,
0.0013403460616245866,
-0.032569143921136856,
0.039991945028305054,
0.006536591798067093,
-0.003384237177670002,
-0.01752600073814392,
0.06264877319335938,
-0.02575213462114334,
0.017314473167061806,
-0.018661413341760635,
-0.01585513725876808,
0.11029502749443054,
0.05770104378461838,
0.015713274478912354,
-0.0989353358745575,
0.011115539819002151,
-0.016821790486574173,
-0.0025501237250864506,
-0.035842809826135635,
0.05188105255365372,
-0.03137355297803879,
0.03177253529429436,
0.021574193611741066,
0.04283760488033295,
-0.019542472437024117,
0.03367060795426369,
0.04544571414589882,
-0.014645193703472614,
-0.034045279026031494,
-0.028017202392220497,
0.021372105926275253,
0.0036023491993546486,
0.019118869677186012,
-0.05701726675033569,
0.005475909914821386,
-0.030649662017822266,
0.013316209428012371,
-0.02717779204249382,
-0.029931308701634407,
0.037179917097091675,
0.010855704545974731,
-0.05138121545314789,
0.01642434112727642,
0.006831522565335035,
-0.021861037239432335,
-0.04860372468829155,
0.011012096889317036,
0.03892957419157028,
0.015494229272007942,
-0.006579372566193342,
0.020150648429989815,
0.015509633347392082,
-0.01994219422340393,
0.01826431043446064,
0.05526729300618172,
-0.020248044282197952,
0.014413632452487946,
-0.036981161683797836,
0.011678812094032764,
-0.012641021981835365,
-0.0027805548161268234,
0.0068128095008432865,
0.05555453151464462,
0.025182383134961128,
-0.023530038073658943,
-0.03370245546102524,
0.005651995074003935,
0.01667023077607155,
-0.019575119018554688,
0.005484644789248705,
-0.005837269127368927,
0.0181108471006155,
-0.007533254101872444,
0.009086276404559612,
-0.02214750275015831,
0.010221699252724648,
0.02940966747701168,
-0.014537214301526546,
0.07025567442178726,
-0.024955058470368385,
-0.003786058397963643,
-0.012251926586031914,
-0.008453288115561008,
-0.038405466824769974,
0.00981459766626358,
0.0012127619702368975,
0.017332658171653748,
0.019211912527680397,
0.013059025630354881,
-0.05147761106491089,
0.043431464582681656,
-0.018154093995690346,
0.03784799203276634,
0.015379649586975574,
-0.025721825659275055,
-0.016738055273890495,
0.012210216373205185,
0.06451748311519623,
0.037467487156391144,
-0.0011379317147657275,
0.016939379274845123,
-0.00891414750367403,
-0.02367989905178547,
-0.0001262725272681564,
-0.01794796623289585,
-0.03597131744027138,
0.016309566795825958,
-0.04157259687781334,
-0.005356492940336466,
-0.015864260494709015,
0.026995373889803886,
0.05429592356085777,
0.009092847816646099,
-0.0033101073931902647,
0.04716269299387932,
-0.004914276301860809,
-0.01073284912854433,
-0.01146577950567007,
-0.03870100528001785,
0.018971681594848633,
-0.012680400162935257,
-0.02056216076016426,
-0.07404448837041855,
-0.05010518804192543,
-0.025075197219848633,
-0.0016597278881818056,
0.015216811560094357,
0.04365689307451248,
-0.02507300116121769,
0.002452986780554056,
0.019434627145528793,
0.03153034299612045,
-0.021329419687390327,
-0.017157405614852905,
-0.03855934366583824,
0.011997132562100887,
0.0005838234210386872,
0.018303804099559784,
-0.005209721624851227,
0.022220429033041,
-0.0314786359667778,
0.0045547159388661385,
0.023294761776924133,
0.024875689297914505,
-0.016728274524211884,
0.027035728096961975,
0.037108249962329865,
0.017661212012171745,
0.045879654586315155,
-0.0009461813024245203,
-0.02059747651219368,
-0.004886672832071781,
-0.032733894884586334,
-0.08474909514188766,
0.010534419678151608,
-0.005384042859077454,
0.014765570871531963,
0.012824858538806438,
0.010741492733359337,
0.0029912141617387533,
0.06656646728515625,
0.02076052688062191,
-0.0004873137513641268,
-0.026572594419121742,
0.00947618018835783,
0.007956905290484428,
-0.03308805823326111,
0.029293866828083992,
-0.025816410779953003,
0.010961505584418774,
-0.0044226255267858505,
0.029330290853977203,
-0.0027293777093291283,
-0.02460203506052494,
-0.0016029621474444866,
0.017663057893514633,
-0.024592000991106033,
0.011101649142801762,
-0.007854119874536991,
0.02008715085685253,
0.04503464326262474,
-0.031178388744592667,
0.0244662556797266,
0.013760293833911419,
0.006939813960343599,
-0.0879712775349617,
-0.016429739072918892,
0.010740697383880615,
-0.02166239731013775,
0.02881423942744732,
-0.055285997688770294,
-0.007046851329505444,
0.0686957910656929,
-0.04075537249445915,
0.011872776784002781,
-0.03853638842701912,
-0.04038399085402489,
-0.027469396591186523,
-0.026324890553951263,
0.02480604685842991,
0.060763902962207794,
0.026481080800294876,
0.03162313997745514,
0.026671340689063072,
-0.002504125703126192,
-0.05311531201004982,
-0.006173201836645603,
-0.019597714766860008,
0.028195325285196304,
-0.01079037319868803,
-0.028034009039402008,
0.05991488695144653,
0.0045020002871751785,
0.0017401514342054725,
0.028066186234354973,
-0.016472971066832542,
-0.01611616276204586,
0.028057778254151344,
0.023249415680766106,
-0.001998660620301962,
-0.01804446615278721,
0.010013998486101627,
-0.01158158015459776,
-0.021241459995508194,
0.009420068934559822,
0.01298851054161787,
0.028002340346574783,
-0.011048837564885616,
0.00863594375550747,
0.022594595327973366,
-0.024387024343013763,
0.021181104704737663,
0.03595661371946335,
-0.04109423607587814,
0.0004925561370328069,
-0.01492968201637268,
0.017434004694223404,
0.007607196923345327,
-0.041286081075668335,
0.020277155563235283,
-0.03183434158563614,
-0.012465362437069416,
0.008829197846353054,
-0.024289892986416817,
0.01901146210730076,
0.01867855153977871,
-0.003246910637244582,
-0.040461912751197815,
0.02850072830915451,
-0.0011327678803354502,
0.020729171112179756,
-0.03562492877244949,
0.029373830184340477,
0.020655376836657524,
-0.0017711621476337314,
-0.0002556759282015264,
-0.014176665805280209,
-0.026588188484311104,
0.038859423249959946,
0.040112417191267014,
0.008915791288018227,
-0.011675373651087284,
-0.037132877856492996,
-0.03701500594615936,
-0.03758919984102249,
0.03323028236627579,
-0.018462002277374268,
-0.05924548953771591,
-0.04764241352677345,
-0.04599433392286301,
-0.003084970638155937,
0.021155480295419693,
0.04176216945052147,
-0.01540448609739542,
0.05155269056558609,
-0.009549319744110107,
0.026142491027712822,
0.030320309102535248,
-0.05508580803871155,
-0.0011938551906496286,
0.034563399851322174,
-0.028965752571821213,
0.013701703399419785,
-0.010899371467530727,
-0.0009688652353361249,
0.030345914885401726,
0.00007745229231659323,
0.022310150787234306,
0.03719888627529144,
-0.027586083859205246,
-0.025128906592726707,
-0.015499313361942768,
0.0019835601560771465,
-0.034680869430303574,
0.058068860322237015,
-0.035495344549417496,
-0.01163013931363821,
0.0003418783890083432,
-0.025391437113285065,
-0.04419109970331192,
-0.024584418162703514,
-0.03948058933019638,
0.0262775681912899,
-0.005881818477064371,
-0.01175497006624937,
0.06019590049982071,
-0.034538544714450836,
0.019450556486845016,
0.022384660318493843,
-0.04501723125576973,
-0.010266803205013275,
0.06271137297153473,
0.007268853951245546,
0.0008424227125942707,
-0.008836674503982067,
0.03790770843625069,
0.01358896866440773,
-0.04044605419039726,
-0.004053977318108082,
0.037697844207286835,
0.022023120895028114,
0.02764422819018364,
0.009920953772962093,
0.053712982684373856,
-0.009294130839407444,
0.033255014568567276,
0.002567227929830551,
0.03940272331237793,
-0.02025648020207882,
-0.020084936171770096,
0.036089297384023666,
-0.02855030633509159,
-0.0035071992315351963,
0.012968385592103004,
-0.03856451064348221,
0.09128384292125702,
-0.07430127263069153,
-0.004033236298710108,
-0.021095598116517067,
0.007311529014259577,
-0.005864368285983801,
0.017589859664440155,
0.01117949839681387,
0.004461181815713644,
0.02238950878381729,
0.004047646187245846,
-0.00641985796391964,
0.0015812544152140617,
0.03798219934105873,
-0.01848548650741577,
0.05494247376918793,
-0.016709189862012863,
-0.007965418510138988,
-0.014382871799170971,
-0.02196723036468029,
-0.02309977263212204,
-0.03026396967470646,
0.015292090363800526,
0.019391538575291634,
0.0168771855533123,
0.0010636936640366912,
0.01697630248963833,
-0.05077704042196274,
0.030425846576690674,
-0.09544394165277481,
-0.027706634253263474,
-0.030860399827361107,
0.017215821892023087,
-0.013635940849781036,
0.001781814033165574
] |
<p>In string theory, consistency with Weyl invariance imposes dynamics on the background fields through the vanishing of the beta functions. Those dynamics can also be derived from the so-called <em>low energy effective action</em>:
$$S = \frac{1}{2\kappa_0^2}\int d^{26} X\; \sqrt{-G}\; \mathrm{e}^{-2\Phi}\,(R-\frac{1}{12}H_{\mu\nu\lambda}H^{\mu\nu\lambda}+4 \partial_{\mu}\Phi\partial^{\mu}\Phi)$$
(at least in bosonic string theory)</p>
<p>Maybe I shouldn't worry over lexical denomination, but I find this naming of "low-energy" a bit obscure. In what sense is it used?
Would it be because the background fields are supposed to emerge from the fundamental strings? Or because we forget the massive excited states of the string (with masses around the Planck scale and irrelevant for low energy phenomenology)?</p> | 1,409 | [
0.011125254444777966,
-0.011846068315207958,
0.004273711238056421,
-0.03873757645487785,
-0.025711478665471077,
0.04193198308348656,
-0.044542096555233,
-0.02418689988553524,
-0.009382299147546291,
-0.05636363849043846,
0.009880537167191505,
0.005582338664680719,
0.07275746017694473,
0.013788537122309208,
0.017951255664229393,
0.012465658597648144,
-0.014328044839203358,
-0.0294977817684412,
-0.040130168199539185,
-0.03343195468187332,
0.04861443489789963,
0.01789966970682144,
-0.030546410009264946,
0.04304859787225723,
-0.03406273201107979,
0.0075353351421654224,
0.0008136694668792188,
-0.004169509280472994,
-0.03658132255077362,
0.04810820892453194,
-0.010862820781767368,
-0.04797348380088806,
0.01900089904665947,
0.01296218391507864,
-0.006472568027675152,
-0.006618554703891277,
-0.03248734027147293,
-0.04714489355683327,
0.002630462171509862,
0.027524439617991447,
-0.07346733659505844,
-0.01693713292479515,
-0.027060266584157944,
0.03269366919994354,
-0.053939368575811386,
0.0009254590258933604,
0.007822560146450996,
-0.04143690690398216,
0.06694207340478897,
-0.06388881802558899,
0.059293232858181,
0.008252907544374466,
0.0069332607090473175,
0.004073259420692921,
-0.027260012924671173,
-0.03520011156797409,
0.04449233412742615,
0.07639774680137634,
0.015392471104860306,
-0.06570883095264435,
-0.056038420647382736,
-0.04520506411790848,
-0.009819901548326015,
-0.024920137599110603,
0.03141454607248306,
0.016522791236639023,
0.0004220260016154498,
0.0006761529948562384,
0.02215460315346718,
0.006462499964982271,
0.0009703044197522104,
0.03439788520336151,
0.028672974556684494,
0.024471979588270187,
0.03238148242235184,
0.0015787103911861777,
0.018059276044368744,
-0.03063693642616272,
-0.005916668102145195,
0.0376904234290123,
-0.016737528145313263,
-0.02579553984105587,
0.043274376541376114,
0.06760040670633316,
0.011931917630136013,
0.0009038053103722632,
0.0651819109916687,
-0.018272507935762405,
-0.018254535272717476,
0.03390145301818848,
-0.013658754527568817,
0.007132865488529205,
0.050519753247499466,
-0.006555622909218073,
-0.04599183052778244,
0.04487380385398865,
0.03952453285455704,
0.06525059789419174,
-0.016414212062954903,
0.028105759993195534,
-0.03901781886816025,
-0.03092995472252369,
0.009458957239985466,
0.09916888922452927,
-0.00038704395410604775,
-0.05156813934445381,
-0.04507008194923401,
-0.013770592398941517,
-0.05006486922502518,
-0.01879415288567543,
-0.05373259261250496,
-0.017092853784561157,
-0.004899589344859123,
-0.015521206893026829,
-0.003109060227870941,
-0.02315254509449005,
-0.028672998771071434,
-0.011460060253739357,
0.04478784278035164,
0.067905493080616,
0.017223037779331207,
-0.0023273162078112364,
0.027711838483810425,
-0.024065321311354637,
-0.068712018430233,
0.00808615330606699,
0.05577830225229263,
-0.026257233694195747,
-0.07087258249521255,
0.0001726368791423738,
0.0003028899373020977,
-0.016899026930332184,
0.01672966219484806,
-0.01134850736707449,
0.05293818935751915,
0.0070789167657494545,
-0.044602613896131516,
-0.05018908530473709,
0.042503222823143005,
-0.0007511841249652207,
-0.017228571698069572,
-0.06252503395080566,
-0.03460001200437546,
0.02934274822473526,
0.09604297578334808,
-0.004840186797082424,
-0.006470754276961088,
-0.0006917036371305585,
-0.002401941455900669,
-0.006267382297664881,
-0.010237894020974636,
-0.038911230862140656,
-0.0262820515781641,
-0.018371839076280594,
-0.03990350291132927,
-0.02020527608692646,
0.07449062913656235,
0.012331565842032433,
0.0009473784011788666,
0.00848183874040842,
0.08339966088533401,
-0.02624448947608471,
0.03396853432059288,
0.016851773485541344,
0.009465862065553665,
0.013349346816539764,
0.047960229218006134,
0.03537031635642052,
-0.00043823005398735404,
-0.002513119950890541,
-0.034955501556396484,
0.024187911301851273,
0.022243507206439972,
0.04154938459396362,
0.03297152742743492,
-0.04498368129134178,
-0.033807720988988876,
-0.009016885422170162,
0.008515562862157822,
-0.007552967872470617,
-0.0284749586135149,
-0.026139430701732635,
-0.017747804522514343,
0.012996116653084755,
-0.012347272597253323,
0.03306519240140915,
-0.03092285618185997,
-0.04231930524110794,
0.016134826466441154,
-0.033897437155246735,
-0.005458074621856213,
-0.063651442527771,
0.004514199681580067,
0.005522964056581259,
-0.024251805618405342,
0.020142117515206337,
0.004849160555750132,
0.0008651121752336621,
-0.029537932947278023,
-0.023137502372264862,
-0.014212182722985744,
-0.0069836280308663845,
0.0026491640601307154,
0.006084773689508438,
0.012055032886564732,
0.016764527186751366,
0.028314068913459778,
-0.008922770619392395,
0.04215101897716522,
-0.03352518007159233,
-0.04374449700117111,
0.000041396229789825156,
-0.009367045946419239,
0.04167623072862625,
0.00020747401867993176,
-0.016403814777731895,
-0.006343693006783724,
-0.033967435359954834,
-0.007679299917072058,
0.04253474622964859,
-0.09494847059249878,
0.00881468690931797,
0.03210746869444847,
0.04227999225258827,
0.012355957180261612,
0.032482534646987915,
-0.0335155613720417,
0.013850340619683266,
0.011326988227665424,
-0.0215512253344059,
-0.0279983039945364,
-0.021787423640489578,
0.06344838440418243,
0.016935214400291443,
-0.023585094138979912,
0.014960321597754955,
0.034888945519924164,
-0.003932584077119827,
0.05087332800030708,
0.01610894687473774,
0.02015332132577896,
-0.04041420295834541,
0.03482568636536598,
0.009460829198360443,
0.00898504164069891,
0.02353011816740036,
0.04460420832037926,
0.014141208492219448,
-0.0050755394622683525,
0.0221615731716156,
-0.006726057734340429,
0.01889202371239662,
-0.011035044677555561,
0.012205268256366253,
-0.006513537373393774,
-0.018675366416573524,
0.0308237262070179,
-0.0150552187114954,
0.05134964361786842,
0.035817667841911316,
0.023978369310498238,
0.026682615280151367,
0.0007415443542413414,
-0.02519281953573227,
0.021557528525590897,
0.005220684222877026,
0.019246714189648628,
-0.017665553838014603,
0.023106740787625313,
-0.028287788853049278,
0.010858179070055485,
-0.0007937580230645835,
-0.016703851521015167,
-0.011958496645092964,
0.02899041585624218,
0.03030080534517765,
0.011300191283226013,
0.022783244028687477,
-0.045798931270837784,
-0.03378598764538765,
0.0466235987842083,
0.01757410354912281,
0.008343474939465523,
0.0626014918088913,
-0.00968969613313675,
-0.007182316854596138,
-0.03683172166347504,
-0.006353194825351238,
0.03251851350069046,
0.005934406071901321,
-0.0009306834544986486,
-0.011100435629487038,
0.014016257598996162,
-0.026622718200087547,
0.00639257812872529,
-0.018254578113555908,
0.011083826422691345,
0.0007936325273476541,
-0.006603623740375042,
0.0692349523305893,
0.03570909798145294,
-0.022490203380584717,
0.014772147871553898,
-0.027675483375787735,
-0.03855440020561218,
-0.02693561278283596,
0.009459452703595161,
0.013701135292649269,
-0.02610819973051548,
0.059908002614974976,
0.020793769508600235,
-0.026155566796660423,
0.005474115256220102,
-0.06608228385448456,
-0.015115810558199883,
-0.00007563907274743542,
0.00278731738217175,
0.007706368342041969,
0.014387586154043674,
-0.04100950434803963,
0.09958043694496155,
0.016395650804042816,
-0.007095510605722666,
0.016892652958631516,
-0.05268463119864464,
-0.018962666392326355,
-0.0413113497197628,
-0.010399478487670422,
0.01331633236259222,
-0.005268798675388098,
0.01985238492488861,
0.02779325097799301,
0.04971535503864288,
0.000043035801354562864,
-0.01921786740422249,
-0.026030469685792923,
0.014995163306593895,
0.00672944588586688,
-0.0036191334947943687,
0.054371822625398636,
-0.002391747897490859,
0.00864938274025917,
-0.0016422413755208254,
0.01066397875547409,
0.014950151555240154,
0.04608006402850151,
-0.04967778921127319,
0.06724054366350174,
0.018487364053726196,
0.0010728731285780668,
0.006897393148392439,
0.03376209735870361,
0.01489260233938694,
-0.026411307975649834,
-0.03809209540486336,
-0.020832078531384468,
0.046067215502262115,
-0.011277922429144382,
0.027772821485996246,
-0.0049038780853152275,
0.019122576341032982,
-0.03302234411239624,
-0.04833734780550003,
0.027197791263461113,
0.005159483291208744,
0.02298601344227791,
-0.022875109687447548,
-0.02447841875255108,
0.04806247353553772,
0.046508707106113434,
-0.002647005021572113,
-0.012600716203451157,
-0.06759369373321533,
0.006271464750170708,
-0.06068692356348038,
-0.011698422022163868,
-0.05317804962396622,
-0.0027046019677072763,
-0.01289695780724287,
-0.003914315719157457,
0.027117973193526268,
0.025654718279838562,
-0.007520389277487993,
0.010788487270474434,
-0.08282652497291565,
-0.023732099682092667,
-0.04100169241428375,
-0.02431451342999935,
-0.008443985134363174,
0.0008513848297297955,
-0.01471933163702488,
0.005047460552304983,
-0.04755905643105507,
-0.0564621202647686,
-0.032748736441135406,
-0.013508359901607037,
0.006099388003349304,
-0.04153657332062721,
-0.042144566774368286,
-0.003814692609012127,
0.031078612431883812,
0.04134625568985939,
-0.017919661477208138,
-0.030540525913238525,
0.018704324960708618,
-0.00655648997053504,
-0.018160955980420113,
-0.004789297003298998,
0.019069835543632507,
0.004627600312232971,
0.006802810821682215,
0.040875304490327835,
0.03158089518547058,
-0.022846436128020287,
0.007347409147769213,
0.06997768580913544,
0.05478599667549133,
0.015605404041707516,
-0.013368213549256325,
0.029234685003757477,
-0.008797490037977695,
-0.01515212096273899,
0.011547691188752651,
0.08440563082695007,
0.013300566002726555,
0.021633945405483246,
0.030051080510020256,
0.012736806645989418,
0.005543896928429604,
0.02642383798956871,
0.03608417510986328,
-0.009434604085981846,
-0.028114696964621544,
-0.06861823797225952,
0.025654766708612442,
-0.014317896217107773,
0.022993013262748718,
-0.039080798625946045,
-0.02365526556968689,
-0.016757531091570854,
-0.023696167394518852,
0.030041489750146866,
-0.0009919052245095372,
-0.026220904663205147,
-0.026413636282086372,
-0.006720918230712414,
-0.0030880761332809925,
-0.008003654889762402,
-0.003288756590336561,
0.05055857077240944,
0.030376382172107697,
0.05205117538571358,
0.013400125317275524,
0.0026045716367661953,
-0.04451366886496544,
0.019454455003142357,
0.030995333567261696,
0.004492746666073799,
0.05076073110103607,
-0.029923230409622192,
-0.04783955216407776,
-0.022338401526212692,
0.02437632344663143,
0.0004423688806127757,
0.00399296497926116,
-0.011779419146478176,
0.004156268201768398,
-0.013634799979627132,
-0.03671744838356972,
-0.004622134380042553,
0.04809395968914032,
0.004172810819000006,
0.007261208258569241,
-0.012446871958673,
-0.02412671409547329,
-0.03276342898607254,
0.03971739113330841,
-0.005019708536565304,
0.00026332642300985754,
0.043100230395793915,
0.022617986425757408,
0.01353906188160181,
0.0071085612289607525,
-0.028569292277097702,
-0.07451646029949188,
-0.0037146618124097586,
0.01406704168766737,
-0.041285354644060135,
0.044567834585905075,
-0.03646841645240784,
0.007648065686225891,
0.010242993012070656,
-0.009544013999402523,
-0.014222023077309132,
0.006466323044151068,
-0.05241731181740761,
0.00944183673709631,
0.0631520226597786,
0.012730355374515057,
0.06898970156908035,
0.03764568641781807,
-0.05746644735336304,
-0.006601674947887659,
-0.027122249826788902,
0.016864756122231483,
-0.0501403845846653,
0.03849491849541664,
-0.05569591373205185,
-0.030273444950580597,
-0.027227988466620445,
0.040505778044462204,
-0.002227684948593378,
0.03381681069731712,
-0.017944203689694405,
-0.04006590694189072,
-0.04067999869585037,
0.019672032445669174,
0.01161855086684227,
-0.021643105894327164,
0.0003784848377108574,
0.031769126653671265,
-0.02725343033671379,
-0.009401736781001091,
0.024450723081827164,
0.03551586717367172,
-0.007385059725493193,
0.03643162176012993,
0.03763268142938614,
0.026297785341739655,
0.0010620200773701072,
-0.030879026278853416,
0.06004825979471207,
-0.04301941394805908,
0.016519488766789436,
-0.005126404110342264,
-0.029600663110613823,
-0.01905464567244053,
-0.0363628976047039,
-0.031758103519678116,
-0.0073278979398310184,
-0.03777305409312248,
0.017128203064203262,
0.007852796465158463,
0.028736621141433716,
0.04375406354665756,
0.025575263425707817,
-0.07962508499622345,
-0.025677399709820747,
-0.03377746045589447,
0.004982592072337866,
0.023442815989255905,
0.0004919212078675628,
0.02208675630390644,
-0.028094381093978882,
-0.02307175099849701,
-0.006023111287504435,
0.04760138690471649,
-0.018308980390429497,
0.05095865949988365,
0.005234787240624428,
0.044579677283763885,
0.03130567818880081,
0.022722993046045303,
-0.010762253776192665,
0.0390496626496315,
-0.016586866229772568,
-0.02716592513024807,
-0.014955940656363964,
0.0687783882021904,
-0.011685794219374657,
0.023086724802851677,
-0.0008612468955107033,
-0.02828010730445385,
-0.004659679252654314,
0.005189618095755577,
0.014525195583701134,
0.06762567162513733,
0.05287700891494751,
0.022236155346035957,
-0.015189516358077526,
-0.00862783845514059,
-0.03815073519945145,
0.03791007027029991,
-0.0033888989128172398,
-0.01972169242799282,
-0.02068101055920124,
0.011083036661148071,
0.050747714936733246,
0.0055792611092329025,
-0.0186258964240551,
-0.010429986752569675,
0.06328031420707703,
-0.0019157687202095985,
-0.012247450649738312,
0.04327425733208656,
-0.0011481523979455233,
-0.010093691758811474,
0.02417091093957424,
0.007683766074478626,
0.006253715138882399,
0.00945258792489767,
-0.016314733773469925,
-0.040959108620882034,
-0.042420893907547,
0.02145703323185444,
0.0468214750289917,
-0.024632517248392105,
0.03228292986750603,
-0.026737280189990997,
-0.05158017575740814,
0.02617749385535717,
-0.052206851541996,
-0.029149718582630157,
-0.029729753732681274,
-0.04200370982289314,
0.005354577209800482,
-0.06518283486366272,
0.004908343311399221,
0.03620455786585808,
0.021734995767474174,
-0.05558476969599724,
0.053795911371707916,
0.03300138935446739,
0.032388895750045776,
0.005984484683722258,
-0.04539243131875992,
-0.04542110115289688,
0.016828827559947968,
-0.025231746956706047,
0.034897804260253906,
0.00044787576189264655,
0.002941813552752137,
0.028042176738381386,
0.028584295883774757,
0.0018693270394578576,
-0.020795758813619614,
0.014050677418708801,
-0.04311224818229675,
0.03903700038790703,
-0.0055214702151715755,
-0.01781178079545498,
-0.016517406329512596,
-0.028549442067742348,
0.019453851506114006,
-0.0022903545759618282,
0.02843109890818596,
0.006324794143438339,
-0.03590709716081619,
0.003913545981049538,
-0.03915025293827057,
-0.02968929521739483,
0.07924365997314453,
-0.023958556354045868,
-0.046873342245817184,
-0.009003706276416779,
-0.007328590378165245,
0.017194101586937904,
0.024187389761209488,
0.010440670885145664,
-0.010835888795554638,
0.04077082872390747,
-0.020192204043269157,
0.042959194630384445,
-0.009194270707666874,
-0.009418806992471218,
0.16799086332321167,
0.07568216323852539,
-0.002020900836214423,
-0.06413277983665466,
-0.018129821866750717,
-0.02126624621450901,
0.015284388326108456,
-0.011558075435459614,
0.009695827960968018,
0.001661800779402256,
-0.022288616746664047,
0.00006091135219321586,
0.07101085782051086,
0.024951398372650146,
-0.027043528854846954,
0.047822386026382446,
-0.025330377742648125,
-0.03928500413894653,
0.011843965388834476,
0.04193495959043503,
-0.005816285964101553,
0.006045706570148468,
-0.025051556527614594,
0.006331045646220446,
0.002671946305781603,
0.03377040848135948,
0.01910017617046833,
-0.042363688349723816,
0.014687390066683292,
0.008325750939548016,
-0.026323352009058,
-0.0017205437179654837,
-0.014224805869162083,
0.015040089376270771,
-0.0047470941208302975,
-0.009609905071556568,
0.017378341406583786,
-0.00936836563050747,
0.016269706189632416,
0.019972696900367737,
0.0035101345274597406,
0.0003305959398858249,
0.01696052774786949,
0.03263774886727333,
-0.03607618808746338,
-0.01396365836262703,
0.004749126732349396,
0.08051720261573792,
-0.021873412653803825,
-0.0052876719273626804,
-0.03825131431221962,
-0.018248319625854492,
0.00716101611033082,
-0.0344671793282032,
-0.019195258617401123,
-0.022730739787220955,
-0.007316813804209232,
-0.023577982559800148,
0.018535234034061432,
0.003607751801609993,
0.023920942097902298,
0.04356987401843071,
0.013070216402411461,
0.0019396488787606359,
-0.013528525829315186,
0.015858709812164307,
-0.007955770939588547,
0.010277987457811832,
-0.010306254960596561,
-0.02716783434152603,
0.009589750319719315,
-0.003814473282545805,
-0.04566684737801552,
-0.008747464045882225,
-0.010165173560380936,
0.005066073499619961,
0.034383706748485565,
-0.01176363043487072,
0.017255334183573723,
-0.02816598303616047,
-0.06198909506201744,
0.06211339309811592,
0.001963389106094837,
-0.005717494059354067,
0.005874051712453365,
-0.01872813142836094,
-0.011396129615604877,
0.012150716036558151,
-0.021625053137540817,
0.0010606354335322976,
-0.02490071952342987,
0.0746421366930008,
0.00862687174230814,
-0.027114519849419594,
-0.05675426498055458,
0.00948223378509283,
-0.03674668073654175,
-0.0038621469866484404,
0.02351783774793148,
-0.013097244314849377,
-0.02486659772694111,
-0.007841345854103565,
-0.013339081779122353,
0.04244815185666084,
-0.014372949488461018,
-0.02738949842751026,
0.00444405572488904,
-0.04766232520341873,
-0.011564020998775959,
0.01729677803814411,
0.029754847288131714,
-0.013282377272844315,
-0.016947170719504356,
-0.0015873254742473364,
0.0036255286540836096,
-0.011986253783106804,
0.04757582023739815,
-0.07629843801259995,
0.028656860813498497,
-0.052450209856033325,
-0.007251296658068895,
-0.02383066527545452,
0.016371970996260643,
-0.05100465938448906,
0.01362596731632948,
0.012056774459779263,
0.0076528931967914104,
0.02711273357272148,
0.05828101933002472,
-0.026915229856967926,
-0.032683879137039185,
0.03631487861275673,
0.003387369913980365,
-0.050452783703804016,
0.04394960403442383,
0.0224917009472847,
-0.023421309888362885,
-0.031272631138563156,
0.03809288144111633,
-0.05341864377260208,
0.007656009402126074,
-0.05377546325325966,
-0.07175889611244202,
0.05511396750807762,
0.022354912012815475,
0.004949313122779131,
0.03466570004820824,
-0.03128755837678909,
-0.041308797895908356,
0.0026766580995172262,
-0.005088033154606819,
-0.04826739430427551,
0.014878159388899803,
-0.031108252704143524,
0.008608746342360973,
-0.017831336706876755,
0.04555130377411842,
-0.009453875944018364,
0.00401736656203866,
0.011878540739417076,
0.002704471116885543,
0.03371436521410942,
-0.05744564160704613,
-0.0021483066957443953,
-0.035362958908081055,
0.004032141529023647,
-0.03630523383617401,
0.0164544265717268,
-0.01660582423210144,
0.047552742063999176,
-0.05595491826534271,
0.01226495485752821,
0.011365472339093685,
-0.002502040471881628,
-0.0747830793261528,
-0.026399368420243263,
0.02907435968518257,
0.03267104923725128,
0.05421476811170578,
-0.0625883936882019,
0.06424757838249207,
-0.0020963866263628006,
-0.032077688723802567,
0.052921608090400696,
-0.0020778290927410126,
0.02747093327343464,
-0.007944724522531033,
-0.023194581270217896,
0.0025956749450415373,
0.02816903404891491,
-0.003006506245583296,
0.05256086215376854,
0.0018006796017289162,
-0.0056746299378573895,
-0.003941047471016645,
-0.010203692130744457,
-0.018915805965662003,
0.055097658187150955,
0.02444123849272728,
-0.039023224264383316,
0.08487391471862793,
0.008739571087062359,
-0.02497768960893154,
0.018301865085959435,
0.01669357530772686,
0.017112968489527702,
-0.031187932938337326,
0.002752843778580427,
0.01359936036169529,
0.030517376959323883,
0.030609218403697014,
-0.05455804616212845,
0.0016106500988826156,
-0.0030814683996140957,
-0.001705432077869773,
0.024921178817749023,
0.018844524398446083,
0.015259230509400368,
-0.013123882934451103,
-0.0539013110101223,
-0.04038292169570923,
0.02949228696525097,
-0.018804222345352173,
-0.02898520603775978,
0.0069120810367167,
-0.027226660400629044,
0.017421215772628784,
0.010017754510045052,
0.013895089738070965,
-0.03634630888700485,
-0.014295530505478382,
0.042041290551424026,
0.005218437872827053,
-0.027754005044698715,
0.039805151522159576,
0.024737127125263214,
-0.029613152146339417,
0.021062351763248444,
0.058627981692552567,
0.012044504284858704,
-0.02730719745159149,
-0.021352732554078102,
-0.029276160523295403,
0.012568878009915352,
-0.00811260286718607,
-0.032821930944919586,
-0.035980720072984695,
0.03230210766196251,
-0.004932016599923372,
0.027784140780568123,
-0.006426145788282156,
-0.012787156738340855,
0.00878014974296093,
-0.026209305971860886,
0.031370893120765686,
-0.006444557569921017,
0.0498746857047081,
0.02412199042737484,
0.00887987855821848,
0.015955865383148193,
-0.023415694013237953,
0.0364336334168911,
0.0027188656385987997,
-0.04961131513118744,
0.03596534952521324,
0.012569286860525608,
0.004162674769759178,
-0.03332221508026123,
0.012367085553705692,
-0.004669550806283951,
0.00004982969767297618,
-0.02378768101334572,
0.0058076754212379456,
-0.04548225179314613,
0.016266584396362305,
0.01341315172612667,
-0.011852191761136055,
0.00331594655290246,
-0.009474342688918114,
-0.018094724044203758,
0.04736632853746414,
0.01259421557188034,
-0.002704950049519539,
0.04496171325445175,
0.006964360363781452,
0.05500778555870056,
0.042331043630838394,
-0.03416537120938301,
-0.008011773228645325,
0.05247390270233154,
-0.02833039127290249,
-0.053601983934640884,
0.022515233606100082,
0.010545047000050545,
0.01445244811475277,
-0.02864229492843151,
-0.01955297403037548,
0.05177292972803116,
-0.0226238165050745,
-0.02851763740181923,
0.02987857349216938,
-0.0014292908599600196,
0.028785424306988716,
0.04411390423774719,
0.016027653589844704,
0.02060426026582718,
0.0060248286463320255,
0.021724078804254532,
0.04112996906042099,
0.007665109820663929,
-0.021043164655566216,
0.012507864274084568,
-0.0006462152814492583,
-0.03447083756327629,
-0.018174072727560997,
0.008527671918272972,
0.035080451518297195,
-0.03265269473195076,
0.028778957203030586,
0.0155781339854002,
0.023529071360826492,
0.02072305977344513,
-0.01996813714504242,
-0.00712296599522233,
0.0678342804312706,
-0.008722502738237381,
-0.006580859888345003,
-0.017702164128422737,
0.011215941980481148,
0.01565377414226532,
0.00932867731899023,
0.01220768503844738,
0.0631217360496521,
0.005514136981219053,
0.02597675658762455,
-0.049767471849918365,
0.013038801029324532,
0.009947706013917923,
-0.049352969974279404,
-0.010944221168756485,
0.005209827329963446,
-0.017841607332229614,
0.01773398369550705,
-0.025414548814296722,
-0.00006158904579933733,
-0.043558552861213684,
0.005325443111360073,
0.01944097876548767,
0.02858414314687252,
-0.0050783343613147736,
-0.026834623888134956,
-0.025929123163223267,
0.04389447346329689,
-0.01613643206655979,
0.032292354851961136,
-0.022388065233826637,
-0.005561676807701588,
0.00465070316568017,
-0.008122740313410759
] |
<p>Reading a french article talking about a <em>recycling unit of rare earth from energy saving light bulbs</em> near Lyon - France (here is the <a href="http://www.solvay.com/EN/NewsPress/20120927_Coleopterre.aspx" rel="nofollow">official press release of the Salvay company</a>), I was wondering :</p>
<ul>
<li>where is rare earth used in energy saving light bulbs ?</li>
<li>what advantages does it provide ?</li>
<li>why don't we use them in regular light bulbs ?</li>
</ul> | 1,410 | [
-0.05549538508057594,
-0.04294450581073761,
0.028480330482125282,
-0.0272396057844162,
0.036044906824827194,
0.022825507447123528,
-0.048548925668001175,
-0.04093794897198677,
0.00946411956101656,
-0.011253955774009228,
0.004785397555679083,
0.06497108936309814,
0.05425762012600899,
0.020138511434197426,
0.021529052406549454,
0.03047766350209713,
0.029915550723671913,
-0.030329495668411255,
0.00012044175673509017,
-0.061496153473854065,
-0.0022045907098799944,
-0.028691159561276436,
-0.021654995158314705,
0.023326890543103218,
-0.0005587782943621278,
0.006224061828106642,
-0.005347950849682093,
-0.009960958734154701,
0.023969653993844986,
0.049016423523426056,
0.037247445434331894,
-0.03451327234506607,
-0.005444146227091551,
0.024932337924838066,
0.010775106027722359,
-0.008291308768093586,
-0.026591463014483452,
-0.017025964334607124,
0.008492902852594852,
0.015262320637702942,
-0.04907430708408356,
-0.012136876583099365,
0.03478790819644928,
0.028330309316515923,
0.008972332812845707,
0.034735798835754395,
0.007863340899348259,
-0.04406755790114403,
0.03958653658628464,
-0.06581303477287292,
0.039336856454610825,
0.0006432370864786208,
-0.00970324408262968,
0.026648223400115967,
-0.015351607464253902,
0.02502685971558094,
0.04110318422317505,
0.04748629778623581,
-0.00886467844247818,
-0.047451213002204895,
-0.0027202621567994356,
0.010631456971168518,
-0.0020631300285458565,
-0.021122006699442863,
-0.03285021334886551,
0.010754113085567951,
-0.010804424062371254,
0.007287502288818359,
0.04944886267185211,
0.012105817906558514,
0.03814973309636116,
0.027984419837594032,
0.012581891380250454,
-0.0005429750890471041,
0.01123511791229248,
-0.043196503072977066,
0.013104484416544437,
0.003928694408386946,
0.03185738995671272,
0.006992711219936609,
0.0033673769794404507,
-0.013589643873274326,
0.03870486095547676,
-0.0017971961060538888,
-0.04683849588036537,
0.01057566236704588,
0.052415285259485245,
-0.025144852697849274,
0.029156146571040154,
-0.02176704816520214,
0.06637551635503769,
0.03775783255696297,
0.06793202459812164,
0.02544509246945381,
-0.017561061307787895,
0.016479497775435448,
-0.016638176515698433,
0.006355651654303074,
0.0033076051622629166,
-0.012285424396395683,
0.025340238586068153,
0.02545338124036789,
0.08020973950624466,
0.07308708876371384,
-0.014344699680805206,
-0.04213482141494751,
0.01761002093553543,
-0.0032495977357029915,
0.03104582615196705,
0.01309039443731308,
-0.0637955367565155,
-0.017650391906499863,
0.012858672998845577,
0.015223990194499493,
0.0379130057990551,
-0.03168635442852974,
-0.014186362735927105,
0.00880205724388361,
0.0714481920003891,
0.06134693697094917,
0.028208844363689423,
-0.011951766908168793,
0.0019023050554096699,
-0.016291825100779533,
-0.05746566504240036,
0.0534839928150177,
-0.02138560079038143,
0.012305865064263344,
-0.0241171196103096,
0.0441339835524559,
-0.024864183738827705,
-0.020286278799176216,
-0.0053276605904102325,
-0.011025635525584221,
0.023278210312128067,
-0.02229292131960392,
-0.09390724450349808,
-0.03247154504060745,
0.021300848573446274,
0.010904279537498951,
-0.015064455568790436,
-0.06303514540195465,
0.0034967882093042135,
-0.04123939946293831,
0.05886390060186386,
0.005326948594301939,
-0.031006183475255966,
-0.011144074611365795,
0.03947149217128754,
-0.006304219365119934,
-0.023881468921899796,
-0.038904108107089996,
0.024371080100536346,
-0.027460405603051186,
0.03632332384586334,
-0.04336309805512428,
0.02024664357304573,
0.06036686897277832,
0.017255032435059547,
-0.05650535970926285,
0.052053626626729965,
0.0064234319142997265,
-0.027054710313677788,
0.0005931177292950451,
-0.0013371520908549428,
-0.05157008767127991,
0.0639628991484642,
-0.012105570174753666,
0.025899678468704224,
0.03653210774064064,
0.028315123170614243,
0.06114165112376213,
0.03721308335661888,
0.019305292516946793,
0.005507176276296377,
-0.02525242790579796,
-0.015826059505343437,
-0.03910859301686287,
0.042655184864997864,
-0.015955498442053795,
-0.07528819888830185,
-0.007049789652228355,
0.017145683988928795,
-0.050050634890794754,
0.03958094120025635,
0.05447341501712799,
0.005702124908566475,
-0.01943192072212696,
0.04760993272066116,
-0.08457767963409424,
-0.021538764238357544,
-0.058111079037189484,
0.004301036708056927,
-0.025499824434518814,
-0.017089491710066795,
-0.022017991170287132,
-0.001708640600554645,
0.02551054023206234,
0.020221756771206856,
0.009587925858795643,
-0.02018299698829651,
-0.04047776386141777,
0.017328351736068726,
-0.006234908010810614,
0.018688401207327843,
0.02392282895743847,
0.025458022952079773,
0.0045562502928078175,
0.022679053246974945,
-0.043752510100603104,
-0.03906698897480965,
-0.03246342018246651,
0.005256520584225655,
0.015970630571246147,
0.013582104817032814,
-0.07865643501281738,
-0.01970295049250126,
-0.009323137812316418,
-0.029946263879537582,
0.02445068024098873,
-0.01209129299968481,
0.04976532608270645,
0.03255561739206314,
-0.008208401501178741,
0.022787323221564293,
0.014020172879099846,
0.007633970119059086,
0.05768788233399391,
0.012113125994801521,
-0.030480703338980675,
-0.07751980423927307,
-0.006994491443037987,
0.060383062809705734,
0.04278866946697235,
-0.07763750106096268,
0.027091115713119507,
0.0069844163954257965,
0.03758438676595688,
0.018767111003398895,
0.010882781818509102,
-0.04070710018277168,
-0.039042018353939056,
0.01999669522047043,
0.032109785825014114,
0.01921628788113594,
0.018774738535284996,
-0.002901835599914193,
0.02796218916773796,
0.027167847380042076,
-0.016570311039686203,
-0.004417779389768839,
0.05183587595820427,
-0.008696923032402992,
0.014888790436089039,
0.00677540572360158,
-0.017822472378611565,
0.06221172958612442,
-0.06283219158649445,
0.0158228799700737,
0.00045582771417684853,
0.0071982345543801785,
0.03966021537780762,
-0.004188879858702421,
-0.043848540633916855,
0.005434937309473753,
0.020130205899477005,
-0.03419269993901253,
-0.014259140938520432,
0.01812438853085041,
-0.019268518313765526,
0.02771630696952343,
-0.03397348150610924,
0.0200642179697752,
-0.02249034494161606,
-0.0028655631467700005,
-0.019418658688664436,
0.009545142762362957,
0.0014189305948093534,
-0.012874681502580643,
-0.051543012261390686,
-0.02654108963906765,
-0.015483425930142403,
-0.018287628889083862,
0.05720531567931175,
-0.01445281133055687,
0.03436332941055298,
0.012384752742946148,
-0.0008142362930811942,
0.036731570959091187,
-0.0007168246665969491,
0.022643515840172768,
0.018678732216358185,
0.016169758513569832,
-0.057556603103876114,
0.011006616987287998,
0.0216387752443552,
0.029077421873807907,
0.005171056836843491,
-0.022397805005311966,
0.03816176578402519,
-0.01572990231215954,
-0.046826329082250595,
-0.011696340516209602,
-0.07538573443889618,
-0.02992558851838112,
-0.01633950136601925,
0.0008314396836794913,
-0.020810618996620178,
-0.030476655811071396,
-0.007100862450897694,
-0.004316633101552725,
-0.02092777192592621,
-0.009578750468790531,
-0.025608977302908897,
-0.06617376953363419,
0.0032802936621010303,
0.011714504100382328,
0.046226825565099716,
-0.012654662132263184,
0.011638171970844269,
0.08041736483573914,
0.03839618340134621,
-0.04488120973110199,
-0.055770404636859894,
-0.04693533852696419,
-0.02158399671316147,
-0.035924237221479416,
-0.001780403428710997,
0.043911147862672806,
-0.006190874148160219,
0.04754617437720299,
0.012524068355560303,
0.03481636941432953,
0.002704982878640294,
0.025748511776328087,
-0.004519728012382984,
-0.006845142692327499,
0.007142350543290377,
-0.010783961042761803,
0.03757518157362938,
-0.022894257679581642,
-0.00864508468657732,
0.007856156677007675,
-0.012272708117961884,
0.05568371340632439,
0.0012156541924923658,
-0.0414421483874321,
0.019975077360868454,
-0.01085834763944149,
-0.013600479811429977,
-0.05247142165899277,
0.015055698342621326,
-0.000004560559773381101,
-0.023076782003045082,
0.0033763840328902006,
-0.009095837362110615,
0.06963424384593964,
-0.015037168748676777,
-0.013612359762191772,
0.02958899363875389,
0.06975175440311432,
0.002596271224319935,
-0.01020814199000597,
-0.00298750470392406,
-0.020357541739940643,
0.011333771049976349,
0.0075077274814248085,
0.006181211210787296,
0.03531551733613014,
0.023039693012833595,
0.012645787559449673,
0.0026417660992592573,
-0.022934356704354286,
0.002342749387025833,
-0.06593585759401321,
-0.023065390065312386,
-0.010706149972975254,
0.04746956005692482,
-0.01038517989218235,
0.06372567266225815,
0.01559619139879942,
-0.010111584328114986,
-0.02280961163341999,
-0.03835558891296387,
-0.07700532674789429,
0.019046725705266,
-0.022317713126540184,
0.06742743402719498,
-0.017234645783901215,
0.03280571103096008,
0.0015217303298413754,
-0.0128591638058424,
-0.0333956815302372,
-0.061782464385032654,
0.0026800911873579025,
-0.0156644806265831,
0.009134454652667046,
-0.0008856055210344493,
-0.05142400786280632,
0.015654781833291054,
0.030973613262176514,
0.008893697522580624,
0.014778753742575645,
0.013601976446807384,
0.0013007947709411383,
-0.03228335827589035,
-0.005076567642390728,
-0.00045427074655890465,
-0.02135549858212471,
0.03735747188329697,
0.02599472552537918,
0.041888970881700516,
0.04856681451201439,
-0.00933756958693266,
-0.005770586896687746,
0.03319447487592697,
0.004571819212287664,
-0.012478439137339592,
-0.023962024599313736,
-0.034334152936935425,
0.015172121115028858,
0.009237424470484257,
0.026109497994184494,
0.023291025310754776,
-0.011934409849345684,
0.03178015351295471,
0.001449881005100906,
0.0135000329464674,
-0.018347177654504776,
-0.04654547572135925,
0.004122329410165548,
-0.023159755393862724,
-0.01565934717655182,
-0.055545080453157425,
0.0005075481603853405,
-0.027527321130037308,
0.02027622051537037,
0.03305594623088837,
0.01099243015050888,
-0.029720474034547806,
-0.010604104027152061,
0.030713550746440887,
0.046533577144145966,
-0.009346215054392815,
0.033893898129463196,
0.03952142223715782,
0.017487386241555214,
0.03489280864596367,
-0.026167839765548706,
0.008447205647826195,
0.010098041035234928,
0.03176502138376236,
0.007359218318015337,
-0.0011486089788377285,
-0.06268451362848282,
0.018861116841435432,
0.0678248479962349,
0.08060362935066223,
-0.03844333067536354,
0.017745161429047585,
-0.059103235602378845,
0.0042776730842888355,
0.011709400452673435,
-0.02487659454345703,
0.0011817687191069126,
-0.03972733020782471,
-0.02027292177081108,
-0.013329562731087208,
-0.045799318701028824,
0.031404417008161545,
-0.008310983888804913,
0.01600671373307705,
0.03665648028254509,
-0.0027031973004341125,
-0.05410236120223999,
-0.018267164006829262,
0.041487161070108414,
0.007435925304889679,
0.04170534759759903,
0.0033208150416612625,
-0.0011169599601998925,
-0.006712556350976229,
0.01095775980502367,
0.01381323579698801,
-0.04819992557168007,
0.014243846759200096,
0.012003798969089985,
-0.03247940540313721,
0.0566394068300724,
-0.03446559980511665,
-0.08414410799741745,
0.023079078644514084,
0.03559944033622742,
0.014502303674817085,
-0.0026222222950309515,
-0.03164208307862282,
-0.0008034906350076199,
0.05377569422125816,
0.032745230942964554,
0.01946953684091568,
0.036639485508203506,
-0.018314361572265625,
0.011159385554492474,
-0.01531862560659647,
0.036840833723545074,
-0.02030811458826065,
0.025539986789226532,
0.015628475695848465,
-0.008727786131203175,
-0.012196213006973267,
0.017338786274194717,
0.011122040450572968,
0.031349267810583115,
0.010115447454154491,
-0.020587338134646416,
-0.014538425020873547,
0.04647655785083771,
-0.007506043184548616,
-0.030387800186872482,
-0.0410584919154644,
0.05043697729706764,
-0.019024226814508438,
-0.0192894097417593,
0.02406548336148262,
-0.028410643339157104,
0.026021504774689674,
0.014431951567530632,
-0.011574309319257736,
0.012440450489521027,
-0.045263562351465225,
0.0036180829629302025,
0.014989720657467842,
-0.014182141050696373,
0.032170619815588,
0.0056110345758497715,
0.021250829100608826,
0.06937968730926514,
-0.06100316345691681,
-0.020133312791585922,
-0.008009666576981544,
-0.026340598240494728,
0.005714687053114176,
-0.061491742730140686,
0.02985565736889839,
0.005873634945601225,
-0.010725708678364754,
-0.07634952664375305,
-0.03618159890174866,
0.021691102534532547,
-0.01026204414665699,
-0.0240588691085577,
-0.06147356703877449,
-0.002177843824028969,
-0.005801033694297075,
-0.014302506111562252,
-0.015071379952132702,
0.04556186497211456,
-0.028090672567486763,
0.0009546718210913241,
0.020529504865407944,
-0.018705740571022034,
0.07820414751768112,
-0.006167488172650337,
-0.010503674857318401,
0.022710472345352173,
0.009257867000997066,
0.021276991814374924,
-0.058831918984651566,
0.02263912744820118,
-0.013376054354012012,
-0.03758244961500168,
-0.00188187207095325,
0.002735280664637685,
0.01805715262889862,
-0.007896291092038155,
-0.008626136928796768,
0.05699806287884712,
0.0345948226749897,
-0.0271723922342062,
0.002874951343983412,
0.032217707484960556,
0.0020078495144844055,
0.018604639917612076,
0.013276343233883381,
0.017496159300208092,
0.0027674040757119656,
0.020756766200065613,
0.04851951077580452,
-0.015405640006065369,
0.006304353009909391,
-0.005656803492456675,
0.04021712392568588,
0.008801604621112347,
0.021382510662078857,
0.06138061732053757,
-0.006700959522277117,
0.01826060749590397,
-0.01770847663283348,
0.035250406712293625,
-0.024240434169769287,
0.0012685947585850954,
-0.03286733850836754,
-0.05042766407132149,
-0.00940551608800888,
-0.009651086293160915,
0.03706102445721626,
-0.026229942217469215,
0.0284712016582489,
0.013189834542572498,
-0.02076038159430027,
-0.000347709545167163,
-0.04601592943072319,
-0.0112460320815444,
0.041523952037096024,
-0.06064700707793236,
0.022379828616976738,
0.01439628191292286,
0.0055994512513279915,
0.0004891596618108451,
0.04125763848423958,
0.001448526862077415,
0.010248646140098572,
0.05407053977251053,
0.05164822190999985,
-0.0002596312842797488,
-0.010335428640246391,
-0.024257641285657883,
0.0035736418794840574,
-0.016592485830187798,
0.03944402188062668,
0.012737666256725788,
-0.02870905213057995,
0.06397351622581482,
-0.013195155188441277,
-0.008002047426998615,
-0.0507100485265255,
-0.013332348316907883,
-0.06127530708909035,
0.03479856252670288,
0.03746379539370537,
-0.02523719146847725,
-0.00649815471842885,
0.013715730980038643,
-0.024991674348711967,
0.007701847702264786,
0.008486071601510048,
-0.011011683382093906,
-0.0548429861664772,
-0.015468459576368332,
-0.007075858768075705,
-0.03734469786286354,
0.028163043782114983,
-0.008870230056345463,
-0.021647483110427856,
-0.03691556677222252,
-0.047324828803539276,
0.0077456641010940075,
0.01426259707659483,
0.037782762199640274,
0.025967733934521675,
0.05097728967666626,
0.008640334941446781,
0.04524562507867813,
-0.01877387799322605,
-0.011967531405389309,
0.13629639148712158,
-0.018317582085728645,
-0.005915279034525156,
-0.050317294895648956,
-0.020285222679376602,
0.01601865142583847,
0.011306585744023323,
-0.024205166846513748,
-0.011115034110844135,
-0.024830585345625877,
0.035533808171749115,
0.038796041160821915,
0.04703541100025177,
-0.01614484190940857,
0.007680840790271759,
0.04225359112024307,
-0.029036283493041992,
-0.010167050175368786,
0.037454552948474884,
0.004752395674586296,
-0.04734596982598305,
-0.010844637639820576,
-0.06095065549015999,
-0.024894526228308678,
-0.005142591893672943,
-0.0273197703063488,
-0.0159812793135643,
-0.03180210664868355,
0.040189698338508606,
0.0003517009608913213,
0.009049900807440281,
-0.002288089133799076,
0.008700908161699772,
0.012715360149741173,
-0.013403115794062614,
0.015949919819831848,
0.02742292918264866,
-0.01835901476442814,
0.009684935212135315,
0.003606933867558837,
0.048500243574380875,
-0.03302522003650665,
-0.014557252638041973,
0.01389342825859785,
-0.06220481917262077,
-0.030454780906438828,
-0.015709418803453445,
-0.00020146011956967413,
-0.028441108763217926,
-0.014811442233622074,
0.017199885100126266,
-0.00006487419159384444,
0.03303563594818115,
-0.02881399542093277,
-0.025458548218011856,
-0.011381915770471096,
0.04531354457139969,
0.014673613011837006,
-0.028231527656316757,
-0.02392226830124855,
0.01464352197945118,
-0.02595314010977745,
0.04101713001728058,
-0.0243203304708004,
0.004363513085991144,
0.029157452285289764,
-0.02563820406794548,
-0.03884042426943779,
-0.011253375560045242,
-0.0268880445510149,
-0.04865008965134621,
-0.006728109437972307,
0.0002309273841092363,
-0.009875724092125893,
-0.002179439179599285,
-0.007349968422204256,
0.04950354993343353,
-0.004353960044682026,
-0.02921590581536293,
-0.019557667896151543,
-0.0691431313753128,
0.06598973274230957,
0.005192920099943876,
-0.0668296217918396,
-0.029320038855075836,
0.026941701769828796,
0.01912851817905903,
0.019445866346359253,
-0.0023019742220640182,
0.010883948765695095,
-0.010633209720253944,
0.0020719661843031645,
0.012319467961788177,
0.0012855468085035682,
-0.017230812460184097,
0.01859055832028389,
-0.018456242978572845,
-0.009924156591296196,
-0.03472234308719635,
0.023060644045472145,
0.006282047834247351,
0.007722354028373957,
0.05952053144574165,
-0.0029430193826556206,
-0.03744380176067352,
-0.021688146516680717,
0.020476557314395905,
-0.039844270795583725,
-0.019779343158006668,
-0.01805286854505539,
-0.01280207373201847,
-0.010322658345103264,
-0.03368237242102623,
-0.04494849219918251,
-0.008879086934030056,
-0.03253695368766785,
0.05033821612596512,
0.012650718912482262,
-0.0026752257253974676,
-0.02967788279056549,
0.04574975743889809,
-0.018816061317920685,
-0.011410551145672798,
-0.0566423274576664,
-0.015560220927000046,
0.008452649228274822,
-0.004855825565755367,
0.006182375829666853,
0.025634104385972023,
0.030393989756703377,
0.029138529673218727,
0.031957466155290604,
0.004970979411154985,
-0.018545683473348618,
0.0189231988042593,
-0.0019073892617598176,
0.02812223881483078,
0.04240233078598976,
-0.053287215530872345,
0.010718237608671188,
0.05499774590134621,
-0.024045458063483238,
-0.03495404124259949,
-0.021450486034154892,
-0.0058979010209441185,
0.006209016311913729,
0.01956833153963089,
0.05584375560283661,
-0.0013770926743745804,
0.06824658811092377,
0.0060988436453044415,
-0.01579110510647297,
-0.0020963018760085106,
0.0005296534509398043,
0.04879209026694298,
0.02943112701177597,
-0.03749195486307144,
-0.04181722179055214,
-0.0070246257819235325,
0.03971482440829277,
0.05941130593419075,
0.0001210126793012023,
-0.010732772760093212,
-0.02786971442401409,
-0.021499108523130417,
-0.006181062664836645,
-0.016322851181030273,
0.005705582443624735,
0.02200680412352085,
0.0328180231153965,
-0.03675973415374756,
0.054466262459754944,
0.012209547683596611,
-0.05270729586482048,
-0.03697684779763222,
-0.013890765607357025,
-0.0191164780408144,
-0.03957408666610718,
-0.008147615939378738,
-0.023368138819932938,
0.05388060212135315,
0.022869395092129707,
-0.07801805436611176,
0.05170561373233795,
0.005180050618946552,
-0.07800297439098358,
-0.03570069000124931,
0.006810052786022425,
-0.03116496093571186,
0.040825843811035156,
0.0377601683139801,
0.027732858434319496,
0.04312174394726753,
0.016023710370063782,
0.048214446753263474,
-0.030236823484301567,
0.025816915556788445,
0.04582727327942848,
-0.041892074048519135,
-0.008232556283473969,
0.07752794772386551,
-0.022375527769327164,
-0.012669318355619907,
0.01341971755027771,
0.019019152969121933,
-0.0015657045878469944,
-0.00599465100094676,
-0.005648549646139145,
-0.05421823263168335,
0.010147685185074806,
0.04158788546919823,
0.02307416871190071,
-0.0789949968457222,
-0.004087179899215698,
0.057321611791849136,
-0.007633262313902378,
-0.013129067607223988,
0.007045827805995941,
0.02165231667459011,
-0.022543085739016533,
-0.009928525425493717,
0.018414467573165894,
0.024005332961678505,
0.004872542340308428,
0.05353017523884773,
0.01136105228215456,
-0.011414517648518085,
-0.010143594816327095,
-0.038933951407670975,
-0.015347402542829514,
-0.02477540448307991,
-0.0017074983334168792,
-0.008906502276659012,
0.022049229592084885,
0.03569506108760834,
-0.011250858195126057,
-0.045302461832761765,
0.011783071793615818,
0.006485949736088514,
-0.050154488533735275,
-0.04370575770735741,
0.020315272733569145,
0.033592719584703445,
-0.006373279262334108,
-0.009875367395579815,
-0.003521113423630595,
-0.061692409217357635,
0.01422949694097042,
0.0016959431814029813,
0.027297915890812874,
0.0036847288720309734,
-0.05691578611731529,
0.0039039424154907465,
-0.04391717165708542,
0.053206104785203934,
0.003331821644678712,
-0.052498120814561844,
-0.03997744619846344,
-0.058929700404405594,
-0.007239621132612228,
0.030911885201931,
0.04863594099879265,
-0.002104121958836913,
-0.015027079731225967,
0.00067553436383605,
-0.0027295509353280067,
0.02317054010927677,
-0.036994922906160355,
0.06473534554243088,
0.03424682095646858,
-0.014064858667552471,
0.0069089531898498535,
0.023681096732616425,
-0.019706910476088524,
0.0016088522970676422,
0.05984114855527878,
0.016679883003234863,
-0.035701241344213486,
-0.03877986967563629,
-0.0072010778822004795,
0.02437734417617321,
0.02721215970814228,
-0.016218723729252815,
0.056238554418087006,
-0.04125368967652321,
0.004000995773822069,
-0.005736973136663437,
-0.028993908315896988,
-0.04458973929286003,
0.02945292554795742,
-0.0004784819611813873,
-0.011416605673730373,
0.026699865236878395,
-0.018238015472888947,
0.07323384284973145,
-0.054427649825811386,
-0.008589745499193668,
0.03091183304786682,
-0.01285732164978981,
-0.03718406334519386,
0.023094817996025085,
0.007604454644024372,
0.014023816213011742,
0.020541710779070854,
-0.00009707507706480101,
-0.0387132354080677,
0.04044166952371597,
0.0016036854358389974,
0.06546469032764435,
-0.012762884609401226,
-0.019804202020168304,
0.009387046098709106,
0.009563989005982876,
-0.006528027821332216,
-0.01790759339928627,
0.025721577927470207,
0.03250053524971008,
-0.03728584572672844,
0.00424558250233531,
0.024537870660424232,
-0.00824443157762289,
-0.020395198836922646,
0.033905066549777985,
-0.0015144959324970841,
0.08684590458869934,
-0.017217325046658516,
0.013011970557272434,
-0.01862003654241562,
0.026672454550862312,
-0.008109532296657562,
0.01733463816344738,
0.002374443458393216,
0.0065058027394115925,
-0.000910377420950681,
0.03649687394499779,
-0.004910626448690891,
-0.005142589565366507,
0.015970727428793907,
-0.004705364350229502,
0.04234357178211212,
-0.030866771936416626,
-0.026601601392030716,
-0.0032368178945034742,
0.009991955943405628,
-0.0019133253954350948,
-0.05034131556749344,
-0.00543951103463769,
0.032766878604888916,
0.03017602115869522,
0.014447844587266445,
-0.022592244669795036,
0.0019481308991089463,
0.019806718453764915,
-0.044398270547389984,
-0.024052245542407036,
-0.002675918862223625,
-0.02252202481031418,
-0.029920758679509163,
0.0003286316932644695
] |
<p>In <a href="http://en.wikipedia.org/wiki/Homebrewing" rel="nofollow">homebrewing</a> on of the key steps when brewing with <a href="http://brewwiki.com/index.php/Extract_Brewing" rel="nofollow">extract</a> is to rapidly chill the wort from boiling temperatures to about 80F in 30 min. This is needed to reduce risk of environmental contamination, oxidation, and control of formation of <a href="http://beersmith.com/blog/2012/04/10/dimethyl-sulfides-dms-in-home-brewed-beer/" rel="nofollow">Dimethyl Sulfide</a> This isn't too hard for small batches of beer, and most people use ice baths for their brew pots, however, as you get to larger sized batches, most people resort to <a href="http://morebeer.com/search/102202" rel="nofollow">wort chillers</a> run from tap water to reduce temperature. Usually this works great from getting from boiling to 90F, but the temperature gradient usually is too low to allow for rapid chilling from 90F to 80F. In order to optimize this process, one might like a nice set of physical equations for modeling heat exchange rather than some rule of thumb engineering models for heat exchangers. If one were to model this process from a physicists point of view, what would be the resulting set of equations? </p> | 1,411 | [
-0.019296452403068542,
-0.01695794239640236,
-0.023672906681895256,
0.009785114787518978,
0.015053823590278625,
-0.043866220861673355,
-0.035085223615169525,
0.005491646006703377,
0.03235503286123276,
-0.029899369925260544,
0.019177941605448723,
0.05059855803847313,
0.03236997500061989,
0.036497775465250015,
0.02122194692492485,
0.017342010512948036,
0.041435159742832184,
-0.047163110226392746,
-0.006230324972420931,
0.027127863839268684,
-0.04208923131227493,
0.05050218105316162,
-0.020889507606625557,
-0.0007645674631930888,
-0.0073755644261837006,
-0.0006122251506894827,
0.009905228391289711,
0.007406509481370449,
-0.02610829845070839,
0.0002624182961881161,
0.01746731996536255,
-0.041238635778427124,
0.01616259664297104,
0.04869849607348442,
0.03332365304231644,
-0.0018775246571749449,
-0.010490539483726025,
-0.04225202277302742,
0.004639860242605209,
-0.031889092177152634,
-0.062289759516716,
0.0023550859186798334,
-0.011901737190783024,
0.0028316418174654245,
-0.044588468968868256,
-0.004091807175427675,
0.008096182718873024,
-0.029858268797397614,
0.05206751823425293,
-0.03813755139708519,
-0.0013212885241955519,
0.0008030622266232967,
0.03376040980219841,
0.0372437983751297,
0.0008249530801549554,
0.04174921289086342,
0.05492813512682915,
0.030751293525099754,
-0.0026615592651069164,
-0.06293430179357529,
-0.023444287478923798,
-0.024284139275550842,
-0.050820980221033096,
0.005053896456956863,
-0.018594792112708092,
0.022138686850667,
0.017794175073504448,
0.016879204660654068,
0.024985969066619873,
0.016141964122653008,
0.026239318773150444,
-0.003850208828225732,
0.03175642341375351,
-0.005674822721630335,
0.013772675767540932,
-0.011501665227115154,
-0.030130166560411453,
-0.00787848699837923,
0.009081690572202206,
0.04731877148151398,
-0.041675519198179245,
0.02742833085358143,
0.006145595107227564,
0.04778491333127022,
0.016557127237319946,
-0.016722258180379868,
0.05828624218702316,
-0.033988408744335175,
-0.0017780811758711934,
0.05664529651403427,
0.010877661406993866,
0.06183444708585739,
0.049768827855587006,
0.007341527380049229,
0.020008251070976257,
0.007986612617969513,
-0.003185503650456667,
0.06480887532234192,
-0.02926047332584858,
-0.03963812440633774,
0.023531043902039528,
-0.016692981123924255,
-0.008125360123813152,
0.1015341505408287,
0.015691038221120834,
-0.017887841910123825,
-0.03341399133205414,
0.015619710087776184,
-0.013285694643855095,
-0.019052788615226746,
-0.056402646005153656,
-0.0028146638069301844,
-0.007340287324041128,
0.002024770248681307,
-0.024411289021372795,
-0.03988197445869446,
-0.0076460642740130424,
-0.017771132290363312,
0.030405037105083466,
0.04361807182431221,
0.022234177216887474,
-0.034049566835165024,
0.027113478630781174,
-0.011430198326706886,
-0.03966158628463745,
0.04815912991762161,
0.014115857891738415,
0.0038869990967214108,
-0.04503071680665016,
-0.007276193238794804,
-0.011919367127120495,
-0.012480532750487328,
-0.016196690499782562,
-0.01154810469597578,
0.00007893193105701357,
-0.013189663179218769,
-0.07695124298334122,
-0.056985266506671906,
-0.001484732492826879,
-0.010627669282257557,
0.013774196617305279,
-0.07034182548522949,
-0.012464627623558044,
-0.0001226076710736379,
0.07716142386198044,
-0.005874852184206247,
-0.002971227513626218,
-0.052836012095212936,
-0.028629224747419357,
-0.009711002930998802,
-0.030811745673418045,
-0.007867095060646534,
-0.00627508107572794,
-0.013698369264602661,
-0.019418001174926758,
-0.0384194515645504,
0.024090543389320374,
0.0673258900642395,
-0.026834528893232346,
0.001243678038008511,
0.02039124071598053,
0.010449348017573357,
-0.04279942438006401,
0.013427309691905975,
-0.006193776614964008,
-0.05240091308951378,
0.0573749877512455,
-0.048009730875492096,
0.0596703365445137,
0.009693557396531105,
-0.01756305620074272,
0.033568963408470154,
0.010895062237977982,
-0.012752502225339413,
0.016655592247843742,
0.0022060906048864126,
0.009809071198105812,
0.0008140570134855807,
-0.007305824663490057,
0.038254011422395706,
-0.0017331225099042058,
0.004256080370396376,
-0.00843032170087099,
-0.000882950029335916,
0.027422809973359108,
0.018902035430073738,
-0.009146369993686676,
0.01899821311235428,
0.029744870960712433,
-0.03510947898030281,
-0.006934842560440302,
-0.11457489430904388,
0.0406954400241375,
-0.01319302711635828,
0.039475973695516586,
-0.024437453597784042,
0.011438899673521519,
0.054364562034606934,
-0.016851402819156647,
-0.053140789270401,
0.030996428802609444,
0.014901170507073402,
0.04771876707673073,
0.02821178175508976,
0.03334978222846985,
0.05735737085342407,
0.04410413280129433,
-0.03404194116592407,
0.024313589558005333,
-0.02832331694662571,
-0.03724455460906029,
-0.009945784695446491,
-0.04599554464221001,
-0.003984538838267326,
0.006780772935599089,
-0.026831233873963356,
0.028700681403279305,
-0.02535860799252987,
0.017705276608467102,
-0.01468217745423317,
-0.023669429123401642,
0.07440250366926193,
0.047160811722278595,
0.03810935467481613,
0.027407953515648842,
0.004891746211796999,
0.03523099422454834,
0.03800622746348381,
0.02439873479306698,
-0.04199318587779999,
-0.03364879637956619,
0.001725211855955422,
0.058063723146915436,
0.01883993297815323,
-0.047617945820093155,
0.0202582236379385,
-0.002886663656681776,
0.04639880359172821,
0.0451507531106472,
0.020586783066391945,
-0.01164940930902958,
0.012849275022745132,
0.050957996398210526,
0.027014348655939102,
0.009087287820875645,
0.023119982331991196,
0.04467032849788666,
0.005573933478444815,
-0.00301388674415648,
0.015616891905665398,
-0.010692582465708256,
0.020746013149619102,
0.059532348066568375,
-0.02139865979552269,
-0.003599603194743395,
-0.03235117346048355,
0.020075220614671707,
-0.02658659592270851,
0.010390609502792358,
0.02079923078417778,
0.015811504796147346,
0.05734473094344139,
0.013729169964790344,
-0.025731032714247704,
0.00539396470412612,
0.03641407936811447,
-0.0028917507734149694,
-0.016259001567959785,
0.024054449051618576,
-0.08640500158071518,
0.01243890542536974,
-0.06633730232715607,
0.023105911910533905,
-0.020496856421232224,
-0.0012588865356519818,
0.006429396569728851,
0.026403453201055527,
0.0003638611815404147,
0.00535390293225646,
-0.01464640162885189,
-0.013032902032136917,
-0.015151869505643845,
-0.005904755555093288,
0.008042719215154648,
-0.037871669977903366,
-0.006691840011626482,
-0.006925148423761129,
-0.019170714542269707,
0.045067910104990005,
-0.009967902675271034,
0.0023438085336238146,
-0.02258368581533432,
0.025516880676150322,
-0.06460462510585785,
-0.030305765569210052,
0.010655350051820278,
-0.0008098608232103288,
0.0016844474012032151,
-0.006060013081878424,
0.018601082265377045,
-0.012405884452164173,
-0.032105453312397,
0.033565156161785126,
-0.026052065193653107,
-0.029315834864974022,
-0.02038593590259552,
0.041939377784729004,
0.009962167590856552,
0.004723414313048124,
0.03611680120229721,
-0.0032495150808244944,
-0.013228349387645721,
-0.015951357781887054,
-0.07769934833049774,
-0.07950145751237869,
-0.009518030099570751,
0.03264481946825981,
0.047259263694286346,
0.006695427931845188,
0.0005278978496789932,
0.047174956649541855,
-0.00785848218947649,
-0.059674233198165894,
-0.0057102530263364315,
-0.04231391102075577,
0.01790444366633892,
-0.059743430465459824,
-0.048871010541915894,
0.026929156854748726,
-0.029868993908166885,
0.0002561977016739547,
0.016713779419660568,
0.039051324129104614,
0.0675390288233757,
0.008445808663964272,
-0.02395559474825859,
-0.011045961640775204,
-0.008240874856710434,
-0.0009390626801177859,
0.02513972669839859,
-0.0071766856126487255,
-0.022472888231277466,
0.039288535714149475,
-0.019682293757796288,
0.05373089388012886,
0.028953487053513527,
-0.07084748148918152,
0.009225952439010143,
0.0005454112542793155,
-0.026989076286554337,
-0.024029262363910675,
-0.013851364143192768,
-0.015564456582069397,
-0.038323137909173965,
0.04011144861578941,
0.005890135653316975,
0.036635469645261765,
-0.013781742192804813,
0.01756615750491619,
-0.0020795930176973343,
0.05746244266629219,
-0.01502753235399723,
0.003620672505348921,
-0.04653409495949745,
-0.026598483324050903,
-0.004897576291114092,
-0.019736915826797485,
0.05014890804886818,
0.04865647107362747,
-0.002913777017965913,
0.02219395712018013,
0.001838241470977664,
-0.030831411480903625,
0.020735692232847214,
-0.10793523490428925,
-0.0026082706172019243,
0.009524966590106487,
0.054165344685316086,
0.010755487717688084,
0.043446436524391174,
0.02913779206573963,
0.01829921267926693,
0.0007858099997974932,
0.02545507624745369,
-0.08668777346611023,
0.05468181520700455,
-0.0162418894469738,
-0.03322937339544296,
0.0019427776569500566,
-0.017267689108848572,
0.009740473702549934,
-0.0017139676492661238,
0.006208071950823069,
-0.02279932051897049,
0.03586636111140251,
-0.041703883558511734,
0.01343563199043274,
-0.011152822524309158,
-0.061681315302848816,
-0.020936118438839912,
0.01721891388297081,
0.016340114176273346,
-0.023315342143177986,
-0.0031171853188425303,
0.009967416524887085,
0.008073866367340088,
-0.0016977438936010003,
-0.02039300836622715,
0.012654155492782593,
0.004077430348843336,
0.038211263716220856,
0.027429617941379547,
0.006831959821283817,
-0.008620375767350197,
-0.00900973193347454,
0.03914017230272293,
0.03774314001202583,
-0.02552393078804016,
0.00498576695099473,
-0.04645805060863495,
-0.0399516262114048,
0.017086593434214592,
0.03942697122693062,
0.03474865108728409,
-0.016559774056077003,
0.03239014744758606,
0.01752646639943123,
-0.015809034928679466,
-0.029960094019770622,
0.033943917602300644,
0.05246763676404953,
-0.007028975058346987,
-0.047966618090867996,
-0.02832728438079357,
-0.04411556199193001,
-0.018549636006355286,
0.03003641776740551,
0.030687913298606873,
0.04071556031703949,
0.00936855562031269,
0.008560002781450748,
0.013282106257975101,
-0.023271767422556877,
-0.0007957663619890809,
0.03843102604150772,
0.039277005940675735,
0.07045657187700272,
-0.0184653140604496,
0.01460080873221159,
-0.02577052265405655,
0.062345147132873535,
0.024939846247434616,
-0.056025538593530655,
0.008247008547186852,
-0.08580271154642105,
0.003094315528869629,
0.028447069227695465,
0.07844159007072449,
-0.008940505795180798,
0.04340844973921776,
-0.019630009308457375,
-0.02960909716784954,
0.025689968839287758,
-0.025699343532323837,
0.021379215642809868,
-0.019377946853637695,
-0.011374210007488728,
-0.004548787139356136,
-0.036713629961013794,
-0.01591600477695465,
0.013607551343739033,
-0.02343992330133915,
0.02069575898349285,
0.015089775435626507,
-0.015045278705656528,
-0.0034773435909301043,
0.030784273520112038,
0.007339403498917818,
0.033858880400657654,
-0.021803727373480797,
-0.007933864369988441,
-0.0062605529092252254,
0.031220028176903725,
-0.005498095881193876,
-0.0492420457303524,
-0.001440341817215085,
-0.008932988159358501,
-0.02204967476427555,
0.014956805855035782,
-0.032783132046461105,
-0.04281478747725487,
0.03061501681804657,
0.03234327957034111,
0.00836031511425972,
-0.009712259285151958,
-0.014372294768691063,
0.03169539198279381,
0.059693556278944016,
0.01514151506125927,
0.0680321455001831,
0.024285322055220604,
-0.06061548367142677,
-0.012415112927556038,
-0.04046904668211937,
0.01525636576116085,
-0.025568131357431412,
-0.03158215060830116,
-0.03697221353650093,
-0.005092161241918802,
-0.04302498325705528,
0.026984142139554024,
-0.047973424196243286,
0.03026171401143074,
-0.06218565255403519,
-0.0452004037797451,
0.0011783394729718566,
0.028926949948072433,
-0.009359262883663177,
-0.02991867996752262,
0.03453622758388519,
0.020095784217119217,
-0.003630934515967965,
0.0010617104126140475,
0.019451197236776352,
-0.0015665318351238966,
0.019196730107069016,
-0.010945203714072704,
-0.03425190970301628,
0.026035718619823456,
-0.027196524664759636,
0.002793875988572836,
0.02200019359588623,
-0.0300691369920969,
0.06588639318943024,
0.002627839334309101,
0.009234026074409485,
0.015492049045860767,
-0.03136613219976425,
0.02353278174996376,
-0.001012530643492937,
0.007297183852642775,
-0.019250525161623955,
-0.0245356522500515,
0.010265436954796314,
-0.01323567982763052,
0.021299388259649277,
-0.0550948865711689,
-0.038722846657037735,
0.05186091363430023,
-0.01676560938358307,
0.001340844901278615,
-0.03462472930550575,
-0.026722637936472893,
-0.017711615189909935,
-0.03858441114425659,
0.004138142801821232,
0.0574759878218174,
0.0005244130734354258,
0.0005396338528953493,
0.0023361125495284796,
0.018054751679301262,
0.04190251603722572,
0.01888766512274742,
0.019453825429081917,
0.007451656274497509,
0.0005993279628455639,
-0.009789696894586086,
0.019614635035395622,
0.01805725134909153,
-0.046701330691576004,
-0.0031585998367518187,
-0.002779671223834157,
0.0029334581922739744,
0.052995674312114716,
0.011869508773088455,
-0.017071161419153214,
0.013329914771020412,
0.017865626141428947,
-0.017837312072515488,
-0.027100365608930588,
0.02829093299806118,
0.01448794361203909,
0.04127867892384529,
0.0069253044202923775,
-0.000794537307228893,
0.0004598227678798139,
0.0032842496875673532,
-0.02932305634021759,
0.009540002793073654,
-0.0048597026616334915,
-0.003135859267786145,
0.04961799085140228,
-0.0066961972042918205,
0.02599547803401947,
0.0425121895968914,
0.0018251516157761216,
0.06110590696334839,
0.007500017993152142,
0.013961633667349815,
0.0012085030321031809,
-0.006586994975805283,
-0.010014492087066174,
-0.022952059283852577,
-0.04941447079181671,
-0.012922290712594986,
0.06584944576025009,
0.009497687220573425,
0.03673311322927475,
0.021749556064605713,
-0.007953881286084652,
-0.002073339419439435,
-0.028301402926445007,
-0.015524694696068764,
0.04376286268234253,
0.018830997869372368,
0.04390878975391388,
0.012810432352125645,
-0.0015744057018309832,
0.017507405951619148,
0.0287526436150074,
-0.003416672581806779,
0.004855482839047909,
0.04052186384797096,
-0.010236925445497036,
-0.023653171956539154,
-0.0733327567577362,
-0.02164868451654911,
0.015598410740494728,
-0.07961415499448776,
0.009405702352523804,
0.040242813527584076,
0.0004816694709006697,
0.06592655181884766,
0.00016734685050323606,
-0.03312673047184944,
-0.07773464918136597,
-0.004974560346454382,
-0.03692741319537163,
0.019900023937225342,
0.004167620092630386,
-0.01505238562822342,
0.016214441508054733,
0.018723394721746445,
0.010801458731293678,
-0.008096586912870407,
-0.010056755505502224,
-0.013271608389914036,
-0.008277337066829205,
0.033960361033678055,
0.013743673451244831,
-0.046335358172655106,
0.01653480716049671,
0.007475811988115311,
-0.002692104782909155,
-0.02749716117978096,
-0.003146722912788391,
0.043280523270368576,
-0.006880659610033035,
0.010117748752236366,
-0.01396704837679863,
0.06793806701898575,
0.009350650012493134,
-0.022143833339214325,
0.0413617305457592,
0.015623127110302448,
0.13346059620380402,
0.04799063876271248,
0.02011861838400364,
-0.06414590030908585,
0.003251317422837019,
0.014838670380413532,
-0.019963674247264862,
0.012612511403858662,
-0.02024809643626213,
-0.01163315586745739,
0.03624516725540161,
0.01600106619298458,
0.04361818730831146,
0.007454784121364355,
0.02889000065624714,
0.03348222002387047,
-0.05380857735872269,
-0.02968498505651951,
0.03227045387029648,
0.020528899505734444,
0.007922696880996227,
0.02040814608335495,
-0.04477960243821144,
0.02674497663974762,
-0.0010688601760193706,
0.020988041535019875,
-0.023691104725003242,
-0.04420933499932289,
0.014277910813689232,
-0.005581021774560213,
-0.050205688923597336,
0.015147451311349869,
-0.022459864616394043,
-0.0029644325841218233,
0.011508590541779995,
0.024026766419410706,
0.05645497515797615,
-0.03965115174651146,
0.027766849845647812,
-0.0029741430189460516,
0.02146235853433609,
0.03304154425859451,
0.022014332935214043,
0.03351479023694992,
-0.04286286234855652,
0.005115721374750137,
-0.03412867709994316,
0.00744601059705019,
-0.01813063584268093,
-0.07154686003923416,
-0.014453141950070858,
-0.05860988423228264,
0.04137164354324341,
-0.0373072512447834,
-0.025378968566656113,
0.012890619225800037,
0.013939372263848782,
0.014190681278705597,
-0.07142088562250137,
-0.05099036172032356,
0.04574252665042877,
0.006241023074835539,
0.0064886813051998615,
-0.002694876631721854,
-0.008419251069426537,
-0.02414657175540924,
0.014678426086902618,
0.07766680419445038,
0.016760919243097305,
-0.007066888269037008,
-0.06350214779376984,
0.005191135220229626,
-0.046158090233802795,
-0.02005503699183464,
0.014933670870959759,
0.04251275211572647,
0.025422120466828346,
-0.01045575924217701,
-0.016490306705236435,
-0.019980398938059807,
-0.04744180291891098,
-0.006096665747463703,
0.03085312806069851,
0.006153147201985121,
-0.03117782436311245,
-0.0008402001112699509,
-0.019820427522063255,
0.048619531095027924,
-0.016026625409722328,
0.011154400184750557,
-0.003519998863339424,
0.021353239193558693,
0.04702276736497879,
-0.008860384114086628,
-0.01907307282090187,
-0.011040044017136097,
-0.07719381153583527,
-0.04546944424510002,
0.013017307966947556,
0.10346461087465286,
0.010771668516099453,
-0.008735661394894123,
0.017951099202036858,
-0.018870104104280472,
-0.02685745619237423,
0.020786136388778687,
0.02716904878616333,
-0.04607740044593811,
0.0002569126372691244,
0.013714795932173729,
-0.025550656020641327,
-0.02295556664466858,
-0.021549250930547714,
-0.027957459911704063,
0.0033056188840419054,
-0.024781210348010063,
0.018878741189837456,
-0.0339740514755249,
0.02809336967766285,
-0.012036086991429329,
0.025517893955111504,
-0.025032157078385353,
0.007203224115073681,
-0.06097957119345665,
-0.022759323939681053,
-0.0020072697661817074,
0.02008482813835144,
0.026984065771102905,
0.014393417164683342,
-0.00958253163844347,
-0.004789210855960846,
-0.01090750191360712,
0.03940608352422714,
0.011318568140268326,
-0.02043488621711731,
-0.014006322249770164,
0.0013275789096951485,
0.036330435425043106,
-0.07324691116809845,
-0.04788542166352272,
0.0010100676445290446,
-0.06173793599009514,
0.0056931632570922375,
-0.015461122617125511,
-0.027711492031812668,
0.013908302411437035,
0.016676634550094604,
-0.03203355520963669,
0.005826887208968401,
0.04399116337299347,
-0.0037771956995129585,
0.010604677721858025,
-0.010716267861425877,
-0.0005006571300327778,
0.03461247310042381,
0.014715311117470264,
0.0029244516044855118,
-0.03557179868221283,
0.013417878188192844,
0.02675643004477024,
0.0246055219322443,
0.020511629059910774,
-0.005073233973234892,
-0.012205544859170914,
0.01002974808216095,
-0.004673771094530821,
-0.0057144551537930965,
-0.006536334753036499,
-0.008640127256512642,
0.04972964525222778,
-0.06336868554353714,
0.028320610523223877,
-0.0018255201866850257,
-0.01767958328127861,
-0.11154444515705109,
0.033449310809373856,
-0.016067292541265488,
0.014891194179654121,
-0.01573522761464119,
-0.024213092401623726,
0.0334288589656353,
0.01371542178094387,
-0.08623233437538147,
0.019593818113207817,
-0.03205738216638565,
-0.0023960936814546585,
-0.01897377148270607,
0.026629196479916573,
-0.016140779480338097,
0.0220346637070179,
0.012266745790839195,
0.0007770360098220408,
0.030638711526989937,
-0.026428766548633575,
-0.0005226766807027161,
-0.021662570536136627,
0.04140140861272812,
0.0011510594049468637,
0.025413531810045242,
-0.0012916360283270478,
0.02786591462790966,
-0.038062676787376404,
-0.028637560084462166,
0.019446227699518204,
-0.027052411809563637,
-0.005036710761487484,
0.0016060679918155074,
0.013784394599497318,
-0.018993837758898735,
0.031006230041384697,
0.027059080079197884,
-0.01090920064598322,
-0.0021551584359258413,
0.01480311993509531,
0.03464531525969505,
0.07799147814512253,
-0.004963547922670841,
0.02799723483622074,
0.05306525155901909,
-0.004984467290341854,
-0.05562744289636612,
0.02973048761487007,
-0.03686385601758957,
-0.01521260291337967,
0.035948630422353745,
-0.006196705158799887,
0.030261484906077385,
-0.034462712705135345,
0.002442331751808524,
-0.06357213854789734,
-0.027959249913692474,
0.04831929877400398,
-0.012212783098220825,
0.0237446092069149,
0.005644951947033405,
-0.015856988728046417,
-0.02249591052532196,
-0.01101220864802599,
-0.028712254017591476,
-0.04311389476060867,
-0.01169247180223465,
-0.026974769309163094,
0.016056790947914124,
0.007484015543013811,
-0.05970728024840355,
-0.003702305955812335,
-0.006905390881001949,
0.07864353805780411,
-0.031947869807481766,
0.03426128998398781,
0.013545717112720013,
-0.031168237328529358,
-0.0024798589292913675,
-0.024818599224090576,
0.01983572728931904,
-0.008206048980355263,
-0.00869772583246231,
-0.05763443931937218,
-0.02817186713218689,
0.006192116532474756,
-0.005495721474289894,
0.04993849992752075,
0.0016256999224424362,
-0.053168028593063354,
0.018008483573794365,
0.0442405641078949,
0.02461652085185051,
-0.03239196911454201,
0.04177669808268547,
0.023939713835716248,
-0.005987546872347593,
-0.004292719531804323,
-0.015130777843296528,
-0.019508322700858116,
0.03389441594481468,
0.03435300290584564,
0.006306407041847706,
0.0318169891834259,
0.05197681859135628,
-0.016769442707300186,
0.006793867330998182,
-0.010296761058270931,
0.007822715677320957,
0.055064793676137924,
-0.044267844408750534,
-0.024523887783288956,
0.051863618195056915,
-0.032602593302726746,
0.015754908323287964,
0.05311411991715431,
-0.019044416025280952,
0.036325421184301376,
-0.003333519911393523,
-0.03401889652013779,
-0.01212188508361578,
-0.05149068683385849,
0.0195584986358881,
0.03510074317455292,
-0.02865689992904663,
0.000034663258702494204,
0.007313884794712067,
0.011782077141106129,
0.0327933169901371,
-0.0025877589359879494,
-0.02780497446656227,
-0.030903410166502,
0.01539954636245966,
-0.03975784778594971,
0.039228521287441254,
0.035273827612400055,
0.0009677894995547831,
0.02856151945888996,
0.03291826695203781,
-0.01860811375081539,
0.04842276871204376,
0.062427423894405365,
0.012234151363372803,
-0.0014196831034496427,
-0.033613428473472595,
0.02290486916899681,
-0.001418949686922133,
-0.014723798260092735,
0.017299750819802284,
-0.03798329457640648,
0.046252042055130005,
0.006184710655361414,
0.011794285848736763,
-0.049073126167058945,
-0.009473022073507309,
-0.04749365895986557,
0.006504795514047146,
-0.015518249943852425,
0.04603709280490875,
-0.02025875262916088,
-0.002749472390860319,
-0.006010995712131262,
0.005869734566658735,
-0.01857674866914749,
-0.001715342397801578,
0.04005592316389084,
-0.03136434033513069,
-0.01270890049636364,
-0.0013089858694002032,
-0.019320519641041756,
-0.019005782902240753,
-0.061168864369392395,
0.03302861377596855,
0.021723370999097824,
0.0200906191021204,
0.021424809470772743,
-0.007808282505720854,
0.02266787737607956,
0.05477837100625038,
-0.061288438737392426,
-0.019968969747424126,
0.005404910538345575,
-0.00492766173556447,
-0.03187787905335426,
-0.004241595510393381
] |
<p>Show that the Hamiltonian operator $\hat{H}= (\hat{p}^2/2m)+\hat{V}$ commutes with all three components of $\vec{L}$, provided that $V$ depends only on $r$. (Thus $H$,$L^2$, $L_z$ are mutually compatible observables).
($\vec{L}$ is $\langle L_x, L_y, L_z\rangle$.)</p> | 1,412 | [
-0.04526238888502121,
0.02180006541311741,
0.026457834988832474,
0.007210003677755594,
0.011215531267225742,
0.001851451932452619,
-0.01710912585258484,
-0.02118983305990696,
0.013651527464389801,
-0.020444002002477646,
0.009622176177799702,
0.022849448025226593,
0.05245036631822586,
0.04320913925766945,
0.02152547612786293,
-0.008088436909019947,
-0.009671281091868877,
-0.015778152272105217,
-0.006717588286846876,
-0.03086574375629425,
-0.027750711888074875,
0.0255579873919487,
0.029323410242795944,
-0.017733225598931313,
-0.007696771062910557,
0.04227696359157562,
0.033187270164489746,
-0.023346256464719772,
0.027913423255085945,
0.07280393689870834,
-0.059303201735019684,
-0.004423444624990225,
-0.0022202543914318085,
0.0492776520550251,
0.0022027678787708282,
0.023074747994542122,
-0.04086348041892052,
-0.006340639665722847,
0.01201857440173626,
0.0065244948491454124,
-0.07972194254398346,
-0.005400983616709709,
0.011717544868588448,
0.056979116052389145,
0.001412897720001638,
0.0027558908332139254,
-0.02111394703388214,
0.016002414748072624,
0.04143786430358887,
-0.04228359833359718,
0.08583994209766388,
0.028320636600255966,
0.018924390897154808,
-0.003489903174340725,
-0.03671213239431381,
-0.0021667552646249533,
0.026101235300302505,
0.09053449332714081,
0.02667173743247986,
-0.03102218359708786,
-0.007184562738984823,
-0.04613038897514343,
-0.014897901564836502,
-0.018960149958729744,
-0.04056889936327934,
0.022518711164593697,
0.04940398409962654,
0.009909109212458134,
0.02133549377322197,
-0.00023756385780870914,
-0.038278136402368546,
-0.02204904332756996,
0.037369903177022934,
-0.0327545702457428,
0.038176581263542175,
0.010746899992227554,
-0.009892893955111504,
0.04155373573303223,
0.022280165925621986,
-0.011280380189418793,
0.013516812585294247,
0.01615186221897602,
0.02200760878622532,
0.0237069483846426,
0.025769082829356194,
-0.006722519639879465,
0.07130543887615204,
0.02774866297841072,
0.017537159845232964,
0.02617800608277321,
0.011512348428368568,
0.0017381792422384024,
0.03229368478059769,
0.011043126694858074,
-0.012150894850492477,
0.06266167759895325,
0.0029249086510390043,
0.06545037776231766,
0.002529553137719631,
-0.019791672006249428,
0.0004381382022984326,
-0.02340736798942089,
0.006935246754437685,
0.05261515825986862,
0.010966910049319267,
-0.015943290665745735,
-0.006077323108911514,
0.016284199431538582,
-0.04103808104991913,
-0.02230444923043251,
-0.03527938202023506,
0.017997730523347855,
0.007395488675683737,
0.010167531669139862,
-0.012747520580887794,
-0.03693884238600731,
0.01004874799400568,
-0.017874963581562042,
0.044791996479034424,
0.062229420989751816,
-0.015336431562900543,
-0.023508640006184578,
-0.02641848661005497,
-0.03515014424920082,
-0.0722133219242096,
0.004818292334675789,
0.03212516009807587,
-0.021490318700671196,
-0.021838799118995667,
0.028565598651766777,
0.04184659942984581,
-0.03746507689356804,
-0.004486784338951111,
-0.007931661792099476,
-0.008024157024919987,
-0.030620824545621872,
-0.1110154539346695,
-0.012103228829801083,
0.01168917864561081,
-0.004207628779113293,
-0.03370248153805733,
-0.04433131963014603,
0.007953439839184284,
0.0775429904460907,
0.09596136212348938,
-0.026587126776576042,
0.006285840645432472,
0.027476198971271515,
0.037003207951784134,
0.0013728655176237226,
0.003413872327655554,
-0.021876178681850433,
0.003914667759090662,
-0.03442556411027908,
-0.03476462885737419,
-0.05363389477133751,
0.009999003261327744,
0.035463154315948486,
0.001644566422328353,
-0.0058478121645748615,
0.07114800810813904,
-0.025080233812332153,
-0.007746694143861532,
0.009383583441376686,
0.008137986995279789,
-0.03263005614280701,
0.05433802679181099,
-0.0019025696674361825,
0.02994207665324211,
-0.01758560538291931,
0.006266141775995493,
0.02362581342458725,
-0.006111885886639357,
0.036930814385414124,
0.01270865835249424,
-0.02606484480202198,
-0.052180055528879166,
-0.011960422620177269,
0.009775299578905106,
-0.016334541141986847,
-0.027393236756324768,
-0.04655950516462326,
-0.010054466314613819,
0.015523860231041908,
-0.013073477894067764,
0.03154011443257332,
0.01808781921863556,
0.0034878540318459272,
0.0035141664557158947,
-0.02920595183968544,
0.030656136572360992,
-0.05009511485695839,
0.01478075236082077,
0.0029943925328552723,
-0.05039500817656517,
0.0744030773639679,
0.024069570004940033,
-0.009844071231782436,
0.017570234835147858,
-0.058341704308986664,
-0.004369039088487625,
0.01705910451710224,
-0.005282929632812738,
-0.0011177778942510486,
0.011758693493902683,
0.011464995332062244,
0.0744786262512207,
0.024710707366466522,
0.019281266257166862,
-0.03252570331096649,
-0.035264745354652405,
0.028194433078169823,
0.02077053114771843,
0.007752311881631613,
0.03782004490494728,
0.01901756040751934,
-0.009979307651519775,
0.0023979514371603727,
-0.021989258006215096,
0.031925611197948456,
-0.029224716126918793,
0.04112958535552025,
0.06839874386787415,
-0.0265666414052248,
-0.0038197063840925694,
0.02867654524743557,
0.022810323163866997,
0.04945901408791542,
-0.01856766641139984,
0.003849146654829383,
-0.04545456916093826,
-0.018142294138669968,
0.033435843884944916,
0.04460005462169647,
-0.040710628032684326,
0.031292837113142014,
0.013043808750808239,
0.06289250403642654,
0.014950312674045563,
0.0301349014043808,
-0.029560955241322517,
-0.020182309672236443,
0.05182765796780586,
-0.003396555781364441,
-0.0027758765500038862,
-0.019421065226197243,
0.015129524283111095,
0.017745109274983406,
0.040136635303497314,
0.031031567603349686,
-0.04196867346763611,
0.05686892569065094,
-0.03323962911963463,
0.018410686403512955,
0.016980614513158798,
-0.034881215542554855,
0.01231513824313879,
-0.014758544974029064,
0.039596572518348694,
0.024622885510325432,
-0.026190897449851036,
-0.010336354374885559,
-0.011201347224414349,
-0.023659728467464447,
0.002454860135912895,
-0.01216390822082758,
-0.03857201710343361,
-0.007565199863165617,
0.02807137556374073,
-0.028971683233976364,
-0.016447197645902634,
0.0019982752855867147,
-0.019418176263570786,
-0.006722389720380306,
0.0021083548199385405,
0.012497656978666782,
0.004799063317477703,
0.018100403249263763,
-0.05366384610533714,
-0.04250165447592735,
-0.010716041550040245,
-0.029709510505199432,
0.036772921681404114,
-0.004677973687648773,
-0.03648151457309723,
-0.004690189380198717,
-0.031807929277420044,
-0.010620662942528725,
0.024561205878853798,
0.015253518708050251,
0.017475422471761703,
-0.00019152234017383307,
-0.008388107642531395,
-0.05042138695716858,
-0.008890463039278984,
-0.01526035089045763,
0.030793463811278343,
-0.050125375390052795,
0.013129519298672676,
0.019367819651961327,
-0.004473045468330383,
-0.05402155965566635,
-0.02201949805021286,
0.001397258136421442,
-0.02608105167746544,
0.022032279521226883,
-0.05301683023571968,
-0.016012120991945267,
-0.007710007019340992,
0.02830764465034008,
0.027753809466958046,
-0.03550911694765091,
-0.01869533769786358,
-0.07788000255823135,
-0.055864088237285614,
0.011922240257263184,
0.0448320247232914,
0.027592170983552933,
-0.015261874534189701,
-0.007856655865907669,
0.06364769488573074,
0.05241776257753372,
-0.028189251199364662,
0.008715885691344738,
0.030673621222376823,
-0.022898485884070396,
-0.051229216158390045,
0.052816856652498245,
0.020018495619297028,
-0.01203901693224907,
0.07228632271289825,
0.02131708711385727,
-0.012748540379106998,
0.02805287018418312,
0.023238549008965492,
0.0035099019296467304,
0.027325356379151344,
0.008321177214384079,
0.01128197181969881,
0.04059310257434845,
0.013266751542687416,
-0.023719480261206627,
0.010460897348821163,
0.025745879858732224,
-0.004373814444988966,
0.013907092623412609,
-0.06974702328443527,
0.06334235519170761,
-0.018612274900078773,
0.0170705895870924,
-0.0052945176139473915,
0.04235953465104103,
0.02645309455692768,
-0.012041901238262653,
-0.018614254891872406,
0.003244456835091114,
0.02635686658322811,
-0.016708487644791603,
-0.003703588852658868,
0.04987740516662598,
-0.010845594108104706,
-0.002674785675480962,
-0.034251999109983444,
0.0001293313252972439,
-0.02013716846704483,
0.03654185310006142,
-0.001496487995609641,
-0.030325904488563538,
0.018769191578030586,
0.009197765961289406,
-0.003011318389326334,
-0.017347214743494987,
-0.03839189559221268,
-0.015356048941612244,
-0.05303181707859039,
0.013576196506619453,
-0.032882578670978546,
0.015151130966842175,
-0.00021704199025407434,
0.08620928227901459,
0.03871772065758705,
0.0009466103510931134,
0.02297825925052166,
0.0028390681836754084,
-0.06162920594215393,
0.012306557036936283,
-0.010741516016423702,
-0.011229924857616425,
0.008498674258589745,
-0.03252553567290306,
0.018783653154969215,
-0.022009851410984993,
-0.026300083845853806,
-0.03411933779716492,
-0.02493755705654621,
-0.044799111783504486,
0.03389495611190796,
-0.021092643961310387,
-0.04974236711859703,
-0.008745002560317516,
0.03545758128166199,
0.037272531539201736,
0.025263521820306778,
0.03070043958723545,
0.059284746646881104,
-0.03777052089571953,
0.03386940434575081,
-0.02222898043692112,
0.0016704582376405597,
0.003737778402864933,
0.034499965608119965,
0.021534889936447144,
0.022220660001039505,
0.032316990196704865,
-0.0031256990041583776,
-0.022471386939287186,
0.05148381367325783,
0.02261745184659958,
-0.001159951090812683,
0.021382613107562065,
-0.04100004956126213,
-0.029902171343564987,
-0.0012630822602659464,
0.07572413235902786,
-0.019933149218559265,
-0.003310863161459565,
0.046641990542411804,
0.013310518115758896,
-0.018287276849150658,
0.014267833903431892,
0.02136165089905262,
0.030056182295084,
-0.021207746118307114,
-0.033194057643413544,
0.0025459309108555317,
-0.015956174582242966,
-0.0022377409040927887,
0.013487108051776886,
-0.02037990093231201,
-0.0060205296613276005,
-0.010285085998475552,
0.014360416680574417,
0.058566536754369736,
-0.004418067634105682,
0.005064314231276512,
-0.000608914764598012,
0.04746285825967789,
-0.024027973413467407,
-0.016036877408623695,
-0.012720339931547642,
0.047976646572351456,
0.0034920526668429375,
-0.002204751130193472,
-0.0075919134542346,
-0.031203797087073326,
0.018348515033721924,
0.02156304195523262,
0.04072781279683113,
-0.00865545030683279,
0.00016084261005744338,
-0.011350124143064022,
-0.018774306401610374,
0.05528591200709343,
-0.0061729950830340385,
0.03915552422404289,
0.010084991343319416,
-0.011390144936740398,
-0.04120751470327377,
-0.05051777884364128,
-0.052195630967617035,
0.006376250181347132,
-0.02814946509897709,
0.01623135432600975,
-0.06539382040500641,
-0.03605913743376732,
-0.017961369827389717,
-0.008188387379050255,
0.05570607632398605,
0.05544373765587807,
0.051948025822639465,
-0.0006511704414151609,
-0.035765547305345535,
0.03780623525381088,
-0.025571724399924278,
-0.08183873444795609,
-0.02561476081609726,
0.04111715778708458,
-0.005712463520467281,
0.0383557453751564,
-0.0544428676366806,
-0.037705518305301666,
0.03026811219751835,
0.014947635121643543,
0.014548364095389843,
0.05315789207816124,
-0.017553359270095825,
0.06990597397089005,
0.03404306247830391,
0.004991812165826559,
0.05622372403740883,
-0.028685716912150383,
0.013758525252342224,
-0.02462053671479225,
-0.013803779147565365,
-0.014174004085361958,
-0.032618340104818344,
0.01650136150419712,
-0.009437663480639458,
0.01600639708340168,
-0.012564967386424541,
0.04040111228823662,
-0.023973217234015465,
-0.007167650852352381,
-0.017684752121567726,
-0.014975306577980518,
-0.03950261324644089,
0.027156585827469826,
-0.060023147612810135,
-0.019788097590208054,
-0.006464330479502678,
-0.00023275415878742933,
0.029666835442185402,
-0.016692129895091057,
0.018106861039996147,
-0.0056391991674900055,
0.020984038710594177,
0.012582216411828995,
-0.004559869412332773,
0.05953555926680565,
-0.05258464440703392,
0.009207917377352715,
-0.01183073315769434,
-0.04369140416383743,
0.0151571836322546,
-0.02139349654316902,
0.03891560807824135,
0.015005596913397312,
0.006532972678542137,
-0.047002553939819336,
0.023828396573662758,
-0.02920876443386078,
0.01993587426841259,
-0.04335341975092888,
-0.023817146196961403,
0.000728755840100348,
-0.01405841764062643,
-0.04869643598794937,
-0.037624530494213104,
0.000635311531368643,
0.03566563129425049,
-0.0013465306255966425,
0.00013351607776712626,
0.007934743538498878,
-0.022470438852906227,
-0.03181750327348709,
0.004303568974137306,
0.02893420122563839,
-0.05673442780971527,
-0.010015919804573059,
-0.01039011962711811,
0.017805064097046852,
0.04652470722794533,
-0.024481363594532013,
0.008934445679187775,
0.005268546286970377,
-0.04631255567073822,
0.01641485095024109,
-0.000026581432393868454,
0.04177282750606537,
0.0037910386454313993,
-0.05114465206861496,
-0.0005009904270991683,
-0.027191471308469772,
0.058685943484306335,
-0.015280584804713726,
-0.04061048477888107,
0.040467288345098495,
0.0009577579912729561,
-0.040506500750780106,
-0.00035993847995996475,
0.00007592159818159416,
-0.01525680162012577,
0.010117112658917904,
0.006177758798003197,
-0.0015455370303243399,
-0.05241212621331215,
-0.050382308661937714,
0.00706506660208106,
-0.008323119953274727,
-0.03030451200902462,
-0.05024203658103943,
0.09092872589826584,
0.02528805285692215,
0.03826075792312622,
0.0063210236839950085,
-0.010144981555640697,
-0.02318001538515091,
-0.0435049869120121,
0.02210202068090439,
-0.005041534546762705,
0.006771657150238752,
-0.02935211919248104,
-0.028568055480718613,
-0.05273876339197159,
0.035688430070877075,
0.07160274684429169,
-0.00398443266749382,
0.05875958129763603,
0.05800775811076164,
-0.0001570811728015542,
-0.01728585734963417,
0.0035648022312670946,
-0.014404709450900555,
0.016669774428009987,
-0.0002534640661906451,
0.029633546248078346,
-0.01966225542128086,
0.012502877973020077,
0.028574097901582718,
0.01827527955174446,
-0.008647373877465725,
-0.019723843783140182,
0.02075008489191532,
0.023809410631656647,
0.017429832369089127,
-0.024292856454849243,
-0.04473166540265083,
0.0417204387485981,
-0.015360080637037754,
0.029247956350445747,
-0.004986938089132309,
-0.029730552807450294,
0.01602715626358986,
0.039645079523324966,
-0.012285617180168629,
-0.016573656350374222,
-0.028498023748397827,
-0.040748339146375656,
0.04128013178706169,
0.02572573907673359,
0.007560617756098509,
0.027239417657256126,
0.015081203542649746,
0.04591650143265724,
-0.0040389904752373695,
0.028614042326807976,
-0.023143479600548744,
-0.040938910096883774,
0.002901824191212654,
-0.01073870062828064,
-0.02131921984255314,
0.0303241778165102,
0.002616921905428171,
-0.0016836434369906783,
-0.003529901150614023,
-0.01061057485640049,
0.009489133954048157,
0.019795654341578484,
0.036333803087472916,
-0.005827093031257391,
0.03518456593155861,
0.005794632714241743,
0.03522443026304245,
-0.013602028600871563,
0.02580956183373928,
0.13872092962265015,
0.020352330058813095,
0.05095120519399643,
-0.06099717691540718,
0.017149517312645912,
-0.0038970913738012314,
-0.004757151938974857,
-0.05023584142327309,
0.04435436427593231,
-0.026036174967885017,
0.009767226874828339,
-0.033248960971832275,
0.04671959951519966,
-0.031620778143405914,
0.0006328057497739792,
0.04570823907852173,
-0.05006417632102966,
-0.02037542685866356,
-0.031056756153702736,
0.008590293116867542,
0.0071363733150064945,
-0.014384391717612743,
-0.048454370349645615,
0.012190950103104115,
-0.06667649745941162,
-0.013286133296787739,
-0.04163293540477753,
-0.05315510183572769,
0.034861255437135696,
-0.03304611146450043,
-0.009134405292570591,
0.026198333129286766,
0.006450651213526726,
-0.025389812886714935,
-0.0231462549418211,
0.019085660576820374,
0.03292899206280708,
0.005172133445739746,
0.04015535116195679,
0.0401306189596653,
-0.005697800777852535,
-0.016434617340564728,
-0.01328323408961296,
0.004583792295306921,
-0.0413983054459095,
-0.011109611950814724,
-0.026771513745188713,
0.08891452103853226,
0.0021525826305150986,
0.0033460347913205624,
0.022300051525235176,
-0.0111920777708292,
-0.027589101344347,
-0.03864356875419617,
0.018875278532505035,
0.01786671206355095,
0.033391982316970825,
-0.025352468714118004,
0.016808195039629936,
-0.0263192281126976,
-0.012864074669778347,
-0.014856155961751938,
-0.0067087155766785145,
-0.03322647884488106,
0.006052404176443815,
-0.009170455858111382,
0.014521769247949123,
0.01587926596403122,
0.013820383697748184,
-0.020189551636576653,
-0.028308069333434105,
-0.02808506414294243,
-0.02088269591331482,
-0.028026705607771873,
0.007613908965140581,
0.014188231900334358,
0.04383651167154312,
0.0327528640627861,
-0.015766896307468414,
-0.03136780112981796,
-0.12356165796518326,
0.0064367810264229774,
0.004833457060158253,
-0.03220789134502411,
-0.008750411681830883,
-0.015758519992232323,
0.0548325814306736,
0.045467738062143326,
0.00587279349565506,
0.009703611955046654,
0.0008070349576883018,
0.043235745280981064,
0.025872472673654556,
-0.022894643247127533,
-0.033139318227767944,
0.02205137349665165,
-0.045359157025814056,
0.025859907269477844,
0.020639803260564804,
-0.007122604176402092,
0.028391731902956963,
0.029279423877596855,
-0.02432861179113388,
0.051006365567445755,
-0.0025448251981288195,
-0.0102560268715024,
0.01954546384513378,
0.007274360861629248,
0.0018326106946915388,
0.03583689033985138,
0.03935401141643524,
-0.035089511424303055,
-0.02504199743270874,
-0.01746903359889984,
-0.02093290165066719,
0.00026654708199203014,
-0.041313670575618744,
-0.0052915047854185104,
-0.00008824226097203791,
0.004629019182175398,
0.035581912845373154,
-0.027801157906651497,
0.013737978413701057,
-0.03619854152202606,
0.0006587163079530001,
-0.009665641002357006,
-0.0003036628768313676,
-0.011315609328448772,
0.03256009519100189,
-0.006611659657210112,
-0.03384532034397125,
0.020802903920412064,
0.048311129212379456,
-0.02613215520977974,
-0.01016785018146038,
0.010154356248676777,
0.014588692225515842,
0.01657624915242195,
0.008886788040399551,
-0.021182755008339882,
0.02164529077708721,
-0.04443063959479332,
0.009429954923689365,
-0.002627474954351783,
0.008141836151480675,
0.0490722693502903,
0.011571492068469524,
-0.033158667385578156,
-0.005711140111088753,
0.02507014386355877,
-0.009161699563264847,
-0.01992064341902733,
0.01173266302794218,
-0.044294148683547974,
-0.02827920950949192,
0.009571773000061512,
0.028873849660158157,
-0.006197975482791662,
0.01211011316627264,
0.029737256467342377,
0.04316677525639534,
-0.022636160254478455,
0.038990363478660583,
-0.010405059903860092,
0.012751858681440353,
0.03837989270687103,
0.008309626020491123,
-0.028720228001475334,
0.06552056223154068,
0.038888197392225266,
-0.037284642457962036,
0.04959918558597565,
0.018574250862002373,
-0.009812245145440102,
-0.11820778995752335,
-0.01737949252128601,
-0.018245643004775047,
-0.0077520329505205154,
0.06196955218911171,
-0.0629890039563179,
0.014097968116402626,
0.04094359278678894,
-0.07087716460227966,
0.024075621739029884,
-0.020063703879714012,
0.015297124162316322,
-0.030172280967235565,
-0.002562369918450713,
-0.03728688508272171,
0.06308601796627045,
-0.02035835199058056,
0.032720837742090225,
0.012637386098504066,
0.04896946996450424,
-0.003770578885450959,
-0.023741403594613075,
-0.050234004855155945,
0.011866443790495396,
-0.003346651792526245,
-0.0319155715405941,
0.05242101475596428,
-0.03710668534040451,
0.01714859902858734,
-0.007009973283857107,
-0.022352665662765503,
0.0033722640946507454,
-0.04493768885731697,
0.021799743175506592,
-0.0054862829856574535,
0.03727084770798683,
0.00804014690220356,
-0.006311853416264057,
-0.013975477777421474,
-0.02627241611480713,
0.027948465198278427,
0.018389999866485596,
-0.032135870307683945,
-0.022364893928170204,
-0.006897077430039644,
-0.06854872405529022,
-0.049832724034786224,
0.028164247050881386,
0.016500623896718025,
0.026094546541571617,
0.02130625583231449,
-0.014573062770068645,
-0.000914554635528475,
-0.041090622544288635,
0.013547034934163094,
-0.046106062829494476,
0.00035810910048894584,
0.009694886393845081,
0.01586461067199707,
-0.018305588513612747,
-0.006504119839519262,
-0.03523978218436241,
-0.04273000359535217,
0.011804454028606415,
-0.0010287459008395672,
-0.018533846363425255,
-0.07342905551195145,
-0.002184667158871889,
0.019514145329594612,
-0.0030668482650071383,
0.009711053222417831,
-0.039358947426080704,
-0.06475565582513809,
0.007340227719396353,
-0.008221155032515526,
0.02383950911462307,
-0.04076308757066727,
-0.014417415484786034,
-0.03356274962425232,
-0.027044257149100304,
0.03469153866171837,
0.06741929054260254,
-0.024472257122397423,
-0.030143538489937782,
-0.0361352413892746,
-0.0025794783141463995,
0.01672498695552349,
0.050803180783987045,
0.016920194029808044,
-0.014633442275226116,
0.019002825021743774,
0.007272318005561829,
0.004047570284456015,
-0.0522427037358284,
0.013354726135730743,
-0.04160810634493828,
0.0020007232669740915,
0.0131955211982131,
-0.0016747944755479693,
0.0095724081620574,
-0.0039499904960393906,
0.003662962233647704,
-0.014691120013594627,
0.012321318499743938,
0.013451600447297096,
-0.04946668818593025,
0.03375163674354553,
-0.034866709262132645,
-0.009542054496705532,
0.06575051695108414,
0.03133544325828552,
0.011734291911125183,
0.042146120220422745,
-0.026733888313174248,
-0.052972305566072464,
0.01368984766304493,
-0.052595287561416626,
-0.018624255433678627,
-0.008651556447148323,
0.010653574019670486,
0.0025811076629906893,
-0.0324651263654232,
0.014753174036741257,
0.015167796052992344,
-0.0381428562104702,
-0.0338565818965435,
0.03509601578116417,
-0.01681685447692871,
0.04397677257657051,
0.0336885042488575,
0.02048414573073387,
0.02320900373160839,
0.0049080983735620975,
0.04095609486103058,
0.04436461627483368,
0.03375645726919174,
-0.010811924934387207,
-0.01254198607057333,
0.04739396274089813,
-0.027128499001264572,
0.02711661346256733,
0.030470194295048714,
0.014455324970185757,
-0.03719593212008476,
0.009365524165332317,
0.05255938321352005,
-0.014294839464128017,
0.01063932478427887,
-0.00543648935854435,
-0.001930589322000742,
0.054340582340955734,
-0.0342048779129982,
-0.0006898902938701212,
-0.06213049218058586,
0.006165743805468082,
-0.032115865498781204,
0.01850506104528904,
0.0034839047584682703,
0.04765017703175545,
-0.015710391104221344,
0.01725776307284832,
-0.058459848165512085,
-0.010780992917716503,
0.003291509347036481,
-0.038671694695949554,
0.026346785947680473,
0.0052566262893378735,
-0.02690071240067482,
-0.013049262575805187,
-0.034210965037345886,
0.007523092441260815,
-0.033732108771800995,
0.006779186427593231,
0.0694645345211029,
0.015472953207790852,
-0.01464085467159748,
0.019204558804631233,
-0.05699876695871353,
0.04452519863843918,
-0.049323126673698425,
-0.036109451204538345,
-0.0217154398560524,
0.03554614633321762,
0.003673248691484332,
0.023717869073152542
] |
<p>Before the discovery of neutrino mass, how did people aware electron and muon neutrinos are different?</p> | 1,413 | [
-0.02180134877562523,
-0.03349459543824196,
-0.0036543430760502815,
-0.03289815038442612,
0.02851802483201027,
0.0149439861997962,
-0.00623884703963995,
-0.011235377751290798,
0.004816978704184294,
0.005483548156917095,
0.047079574316740036,
0.003316764486953616,
0.032236263155937195,
-0.03744933009147644,
0.02381506934762001,
0.02472735568881035,
-0.016576625406742096,
0.007995843887329102,
-0.022598596289753914,
-0.012693542055785656,
-0.0185043066740036,
-0.008605096489191055,
-0.01878395304083824,
0.015514595434069633,
-0.02509833127260208,
0.034401047974824905,
0.02908475138247013,
0.040309321135282516,
0.0312136672437191,
0.03395770490169525,
0.031025022268295288,
-0.039775650948286057,
0.05443592742085457,
-0.008846315555274487,
0.020651860162615776,
-0.02061866596341133,
0.011573825031518936,
-0.03111514449119568,
-0.0017487541772425175,
0.02831765078008175,
-0.02640478126704693,
-0.05129573866724968,
-0.0006473471294157207,
-0.0054598962888121605,
-0.07841642200946808,
0.020257214084267616,
0.0031860102899372578,
-0.023232044652104378,
0.059388671070337296,
-0.05000210925936699,
0.03392058610916138,
0.012782540172338486,
0.03785586357116699,
0.026632273569703102,
-0.0068487985990941525,
0.010379322804510593,
0.06358197331428528,
0.03835143893957138,
-0.015791526064276695,
-0.0658809244632721,
-0.020751673728227615,
-0.052890174090862274,
0.028713714331388474,
-0.008769464679062366,
-0.03010198473930359,
0.04035815969109535,
-0.026361819356679916,
-0.026352321729063988,
0.008790426887571812,
0.022241245955228806,
0.0033267142716795206,
0.0299998726695776,
0.0003189466369803995,
0.04993261769413948,
0.015178740955889225,
-0.030046483501791954,
-0.0112961670383811,
-0.017456375062465668,
0.019043931737542152,
0.03703225404024124,
-0.030580364167690277,
0.03482794016599655,
0.04222123324871063,
0.02804500050842762,
-0.0032574976794421673,
-0.01623416878283024,
0.07620880752801895,
-0.00663275271654129,
-0.023517945781350136,
0.03877400979399681,
-0.0056886738166213036,
0.0008380915969610214,
0.036842409521341324,
-0.03118065558373928,
-0.007104089017957449,
0.029465854167938232,
0.006578126922249794,
-0.005630156956613064,
0.027852868661284447,
-0.02454141527414322,
0.06160767748951912,
0.005903160665184259,
0.018069801852107048,
0.07415073364973068,
0.015295087359845638,
-0.03269011527299881,
-0.04233064502477646,
0.001908540609292686,
-0.04701627045869827,
-0.018584031611680984,
-0.007595889735966921,
0.009976554661989212,
-0.020950790494680405,
0.009100631810724735,
0.014316441491246223,
0.0043711294420063496,
-0.0066235605627298355,
-0.0466221459209919,
0.09752099215984344,
0.06606584042310715,
0.015261214226484299,
0.011962637305259705,
0.015520421788096428,
-0.02717185765504837,
-0.061712946742773056,
-0.005118845030665398,
0.02538769505918026,
-0.005514997057616711,
-0.003280875040218234,
0.012401210144162178,
-0.009630803018808365,
-0.0072168889455497265,
-0.0028406751807779074,
-0.005216762889176607,
0.025839736685156822,
0.023269781842827797,
-0.07192236185073853,
-0.06988935172557831,
0.07666300237178802,
0.0034516609739512205,
-0.045007891952991486,
-0.06968111544847488,
-0.0026881867088377476,
0.0020427138078957796,
0.06370216608047485,
0.022736258804798126,
-0.003368868725374341,
-0.020650532096624374,
0.03240141272544861,
-0.00498940609395504,
0.003566837403923273,
-0.006377174984663725,
-0.0038389237597584724,
0.028722478076815605,
0.012704135850071907,
-0.03926902264356613,
-0.019149545580148697,
0.019062446430325508,
-0.024294087663292885,
-0.023671332746744156,
0.08148449659347534,
-0.017917035147547722,
-0.0006874004611745477,
-0.007833531126379967,
-0.005234535317867994,
-0.040717389434576035,
0.10109124332666397,
0.010300534777343273,
-0.02113249897956848,
0.04686601832509041,
-0.022811274975538254,
0.0520283505320549,
0.03679637238383293,
0.025886166840791702,
0.03536352515220642,
-0.0353357270359993,
-0.030714068561792374,
0.013279130682349205,
0.020288709551095963,
-0.011496721766889095,
-0.04377846419811249,
-0.020584655925631523,
0.008939436636865139,
0.012752224691212177,
-0.01272023469209671,
0.0708543211221695,
-0.02414894662797451,
-0.035804878920316696,
0.037204138934612274,
-0.06582314521074295,
-0.03739054873585701,
-0.05420801416039467,
-0.016907665878534317,
-0.004756598267704248,
-0.007326629478484392,
0.01939399726688862,
-0.014394299127161503,
-0.0005013555055484176,
-0.02588574029505253,
-0.026671811938285828,
-0.0037351425271481276,
0.06456980854272842,
0.028390562161803246,
0.0051298560574650764,
0.008945561945438385,
0.03637848421931267,
0.028784004971385002,
-0.026961738243699074,
-0.006478908006101847,
-0.011398080736398697,
-0.010079222731292248,
0.02338235080242157,
-0.01844094879925251,
-0.00046167170512489974,
-0.003019595518708229,
0.014616603963077068,
-0.0384647436439991,
-0.024634545668959618,
-0.026522887870669365,
0.0773656889796257,
-0.003010933054611087,
0.06421352922916412,
-0.016056574881076813,
-0.020736167207360268,
0.017618127167224884,
0.03947366029024124,
0.037790291011333466,
0.027051487937569618,
0.003977003041654825,
-0.03489416465163231,
-0.0623624362051487,
-0.03278099000453949,
0.0525103323161602,
0.010911603458225727,
-0.04532374441623688,
0.006716364994645119,
-0.006657499819993973,
0.05637110397219658,
0.01563851349055767,
0.04740450903773308,
-0.022859642282128334,
-0.050089020282030106,
-0.012590962462127209,
0.010451705195009708,
-0.02844775654375553,
0.03370216116309166,
0.035555992275476456,
0.02073536440730095,
-0.00982381496578455,
-0.01863163337111473,
-0.02663050964474678,
0.01622598059475422,
-0.020133912563323975,
-0.023318253457546234,
0.007002013269811869,
-0.03725968673825264,
0.015668563544750214,
-0.0422288179397583,
-0.011328979395329952,
-0.020301438868045807,
-0.023945504799485207,
-0.0004753598477691412,
-0.012494096532464027,
-0.0074475607834756374,
0.02747151255607605,
0.002452546963468194,
0.01166390161961317,
0.0016592054162174463,
0.03444318100810051,
-0.036802396178245544,
0.020750559866428375,
-0.03197174519300461,
-0.03130326047539711,
0.0037026687059551477,
0.0019416187424212694,
0.026029637083411217,
0.013933055102825165,
0.00611448846757412,
-0.03560391440987587,
-0.05576278269290924,
-0.002702431520447135,
-0.014020679518580437,
0.02033323049545288,
0.06409256160259247,
-0.011421565897762775,
0.034121353179216385,
-0.03589900583028793,
-0.03437216207385063,
0.010577701963484287,
0.03883902356028557,
0.02725592441856861,
0.008340532891452312,
-0.01732817105948925,
-0.012014159001410007,
-0.01805829629302025,
-0.012943404726684093,
-0.009980075992643833,
0.013980136252939701,
0.0034934920258820057,
0.04011785611510277,
-0.009695637039840221,
0.00020062319526914507,
-0.0081581249833107,
-0.03449278697371483,
-0.03022785857319832,
-0.0024978111032396555,
-0.024384725838899612,
-0.017781201750040054,
-0.04702572152018547,
0.013962593860924244,
0.002322474494576454,
-0.06284894794225693,
-0.013142222538590431,
-0.016599679365754128,
-0.029259521514177322,
0.02561204321682453,
0.001488343346863985,
0.031535714864730835,
0.01409144140779972,
-0.017292030155658722,
0.0602492094039917,
0.0021612674463540316,
-0.012286156415939331,
-0.04391849786043167,
0.007442099042236805,
-0.034207358956336975,
-0.028238607570528984,
-0.0023779254406690598,
0.03896120935678482,
0.0011158514535054564,
0.03198602423071861,
0.027720797806978226,
0.018981628119945526,
-0.016031624749302864,
0.02438187412917614,
-0.009993529878556728,
-0.036076758056879044,
-0.022881275042891502,
-0.011470971629023552,
0.03140359744429588,
0.00579240033403039,
-0.012952414341270924,
0.03381998836994171,
0.019690541550517082,
0.058817021548748016,
0.003932209685444832,
-0.0015262772794812918,
0.06430542469024658,
0.009572852402925491,
-0.001350783510133624,
-0.03632037341594696,
0.009120248258113861,
-0.0006181937642395496,
-0.0067154960706830025,
-0.0012474632821977139,
-0.011429625563323498,
0.01826399751007557,
-0.013734196312725544,
-0.023469651117920876,
0.03206748515367508,
0.018020449206233025,
-0.026600521057844162,
-0.028421206399798393,
-0.014887828379869461,
0.03599848225712776,
0.04176170006394386,
-0.020475171506404877,
-0.010407144203782082,
0.03162035718560219,
0.021210215985774994,
0.012218359857797623,
-0.025471491739153862,
-0.023366384208202362,
-0.02814961038529873,
-0.05154552310705185,
0.015550335869193077,
0.022941963747143745,
-0.010690619237720966,
-0.015252592042088509,
0.050958868116140366,
0.020160185173153877,
-0.016376016661524773,
-0.019198453053832054,
-0.021469540894031525,
-0.08461200445890427,
0.02921050414443016,
-0.09782503545284271,
-0.004683232866227627,
-0.029366308823227882,
-0.009774885140359402,
-0.025943687185645103,
0.009064409881830215,
-0.01991187036037445,
-0.047413893043994904,
-0.01210490521043539,
-0.039565421640872955,
0.042862776666879654,
-0.012762997299432755,
-0.03171778470277786,
-0.034710727632045746,
0.05278930440545082,
0.009476764127612114,
0.03073892556130886,
-0.01114528626203537,
0.020406275987625122,
-0.01845717802643776,
0.019599566236138344,
-0.02144688367843628,
0.031620513647794724,
0.011488660238683224,
-0.006918686907738447,
0.031132474541664124,
0.0072535197250545025,
-0.06388358771800995,
-0.010688473470509052,
0.03241374343633652,
0.08035677671432495,
0.019117338582873344,
-0.002555258572101593,
-0.03509588539600372,
-0.049454186111688614,
-0.0009115655557252467,
0.004906876012682915,
0.04265573248267174,
-0.02069895900785923,
0.024555856361985207,
0.010021465830504894,
-0.0006094960845075548,
-0.011475294828414917,
0.06511656939983368,
0.05370168760418892,
-0.003483763663098216,
-0.04335297271609306,
-0.008711924776434898,
0.020877165719866753,
-0.005124161951243877,
0.023216065019369125,
0.01679069548845291,
0.03509941324591637,
-0.007527734152972698,
-0.0334894023835659,
0.022164473310112953,
-0.010161913000047207,
-0.023910559713840485,
-0.017491832375526428,
-0.011098144575953484,
0.027072723954916,
-0.004181849770247936,
0.010509447194635868,
-0.04350580275058746,
0.015842756256461143,
0.03450838103890419,
-0.04662127420306206,
-0.033069029450416565,
-0.05371507629752159,
-0.010737389326095581,
0.02275203913450241,
0.029497433453798294,
-0.004790362901985645,
-0.0034041660837829113,
-0.07463482022285461,
0.005763686262071133,
0.04234043136239052,
-0.014952002093195915,
0.024797793477773666,
-0.026851674541831017,
0.03645801916718483,
-0.02964637614786625,
-0.012449725531041622,
0.011956020258367062,
0.05930117517709732,
-0.0024578673765063286,
0.03857903182506561,
-0.04307803884148598,
-0.005690427962690592,
-0.020756471902132034,
0.004992105066776276,
0.034504424780607224,
0.05503401532769203,
0.025334838777780533,
0.0332610122859478,
-0.003970489837229252,
0.0030669330153614283,
-0.02371812053024769,
-0.10111193358898163,
0.001147515489719808,
0.013997632078826427,
-0.0028682344127446413,
0.024329883977770805,
-0.043123409152030945,
-0.06531371176242828,
0.008591330610215664,
0.008655468001961708,
0.0019207802833989263,
-0.03360620513558388,
-0.06516680866479874,
0.004166002385318279,
0.030568568035960197,
-0.02122858352959156,
0.056612398475408554,
-0.0023144108708947897,
-0.017386460676789284,
0.008279777131974697,
-0.02644452080130577,
0.021964600309729576,
-0.04339220002293587,
0.0019273279467597604,
0.015159565024077892,
0.02277490869164467,
-0.02775425836443901,
0.08856169134378433,
0.032125040888786316,
0.05835239589214325,
0.01061828713864088,
-0.04649531841278076,
-0.04127717390656471,
0.02916490100324154,
0.004410094115883112,
-0.020300962030887604,
-0.002391711575910449,
0.0017604157328605652,
-0.009224527515470982,
-0.024286620318889618,
0.019972607493400574,
-0.00987748522311449,
0.010742257349193096,
-0.013242672197520733,
0.009639370255172253,
0.030879192054271698,
-0.058115776628255844,
-0.039421215653419495,
0.05304534360766411,
-0.06132093444466591,
0.03784351050853729,
-0.013914049603044987,
-0.009854127652943134,
0.018722960725426674,
-0.08604352176189423,
-0.0371147021651268,
0.024340642616152763,
-0.001488400623202324,
0.08509383350610733,
-0.046229153871536255,
0.04832833632826805,
0.0195595882833004,
0.018128126859664917,
-0.07269378006458282,
-0.010077581740915775,
0.012608722783625126,
0.013595289550721645,
0.03257050737738609,
0.012836185283958912,
-0.01172642782330513,
-0.048589468002319336,
-0.007158467546105385,
0.026706170290708542,
0.041163839399814606,
-0.02029496431350708,
-0.02175268344581127,
-0.03681508079171181,
0.028736989945173264,
0.0760350376367569,
-0.030128059908747673,
-0.021471016108989716,
-0.010296541266143322,
-0.012862651608884335,
0.013694160617887974,
0.005592661909759045,
0.05024795979261398,
0.00047483897651545703,
-0.035856034606695175,
-0.0021799795795232058,
0.001641431706957519,
0.033967792987823486,
-0.018825378268957138,
0.02285175770521164,
0.06929906457662582,
0.015745246782898903,
-0.03645355626940727,
0.00320126349106431,
0.02737090364098549,
-0.04347696900367737,
0.04661118984222412,
0.0008836191263981164,
-0.011401508934795856,
-0.006227359641343355,
-0.029974766075611115,
0.07947981357574463,
0.007895519025623798,
0.03240013122558594,
-0.01711847074329853,
0.021851828321814537,
0.020471883937716484,
-0.027939829975366592,
0.012395006604492664,
-0.030066220089793205,
0.03331206366419792,
-0.04039052128791809,
0.044157762080430984,
0.01059540081769228,
0.026256214827299118,
-0.0016358218854293227,
-0.01953725516796112,
-0.03492724150419235,
-0.029063256457448006,
0.07537383586168289,
-0.03411969542503357,
0.050369780510663986,
-0.003468907903879881,
-0.021258512511849403,
0.014179958961904049,
-0.03344184160232544,
0.003084375988692045,
-0.01557188667356968,
-0.0029785477090626955,
0.03572647646069527,
-0.019544532522559166,
0.021731369197368622,
0.020377397537231445,
0.03652225807309151,
0.0051861838437616825,
0.028831083327531815,
0.03139602765440941,
0.05728592723608017,
-0.0012427277397364378,
0.016025684773921967,
-0.020649516955018044,
0.018331686034798622,
-0.01950923353433609,
-0.009567712433636189,
-0.02098342590034008,
-0.012244125828146935,
0.01638798974454403,
-0.03573375567793846,
-0.02473052777349949,
0.023688090965151787,
-0.0013201216934248805,
-0.04290603846311569,
0.022960180416703224,
0.02414163202047348,
0.015036171302199364,
-0.009508004412055016,
0.008702629245817661,
0.03239305689930916,
-0.02844531461596489,
0.010925380513072014,
-0.007927360944449902,
-0.04905327409505844,
-0.0018997223814949393,
-0.05355990305542946,
-0.03832055628299713,
0.03077586740255356,
-0.025135770440101624,
-0.03957720473408699,
-0.004727649036794901,
0.010939267463982105,
0.017355559393763542,
0.025396138429641724,
0.019160114228725433,
-0.04142997786402702,
0.02102959156036377,
-0.0672813430428505,
0.02741498313844204,
-0.008375929668545723,
-0.010567082092165947,
0.12605857849121094,
0.04307568445801735,
0.025180712342262268,
-0.06413213908672333,
0.04960688576102257,
-0.0323537141084671,
-0.00031497509917244315,
-0.01784912683069706,
0.03981117904186249,
-0.009183347225189209,
0.04373491182923317,
-0.04140245169401169,
0.07159937173128128,
0.06552069634199142,
0.024667879566550255,
0.040939003229141235,
0.006800816860049963,
-0.056210633367300034,
0.01803586073219776,
0.0407402366399765,
0.00769805209711194,
0.02063768543303013,
-0.05476149544119835,
0.051183827221393585,
-0.02331412024796009,
0.01484057866036892,
-0.013533600606024265,
-0.03959069773554802,
0.029525235295295715,
-0.012026726268231869,
-0.05899893119931221,
0.031655315309762955,
0.04242424666881561,
-0.017822805792093277,
-0.023483572527766228,
0.0009861321887001395,
0.03601456433534622,
-0.0014160254504531622,
0.05413787439465523,
-0.003461382584646344,
0.04746150225400925,
-0.001679426059126854,
-0.030513830482959747,
0.02102896384894848,
-0.08868975937366486,
0.024623071774840355,
-0.0042906892485916615,
0.020024320110678673,
-0.00023925660934764892,
-0.006686164066195488,
0.01767403446137905,
0.014605004340410233,
-0.04187240079045296,
-0.03185707703232765,
-0.047760818153619766,
-0.018830440938472748,
0.0064718700014054775,
-0.03810349106788635,
0.020007777959108353,
-0.008964034728705883,
0.025664757937192917,
-0.01648261398077011,
0.03885848447680473,
-0.009832184761762619,
0.019768116995692253,
-0.0030958654824644327,
0.003836163319647312,
-0.06132031977176666,
-0.00764917116612196,
-0.02727069891989231,
-0.00861786212772131,
-0.028854748234152794,
-0.04393823444843292,
-0.016329636797308922,
0.016049858182668686,
0.030657360330224037,
0.04675603657960892,
0.03941597044467926,
-0.01047990471124649,
-0.03349355235695839,
-0.05185610428452492,
0.04105183482170105,
0.0005180534208193421,
0.009632713161408901,
0.009031170979142189,
-0.015321663580834866,
0.010488907806575298,
0.01586194708943367,
-0.04036129638552666,
0.0098627470433712,
-0.025530505925416946,
-0.010801061987876892,
0.004148497246205807,
-0.03388788178563118,
0.013230778276920319,
0.005827911198139191,
-0.0273769348859787,
-0.013586901128292084,
-0.06818736344575882,
0.019953453913331032,
0.049930673092603683,
-0.004045548848807812,
0.0223375391215086,
0.03380075842142105,
0.0015917080454528332,
-0.037479598075151443,
0.0112524488940835,
-0.035879045724868774,
-0.006580526474863291,
0.006784746423363686,
0.034601252526044846,
-0.01667337864637375,
-0.028985606506466866,
-0.05165816843509674,
0.031201722100377083,
0.021083401516079903,
0.016352372244000435,
0.01600150391459465,
0.03429440036416054,
-0.045904528349637985,
0.04168276488780975,
-0.005629219114780426,
-0.03298669680953026,
-0.02162889577448368,
0.016910500824451447,
0.004481869749724865,
-0.03624647483229637,
-0.0016433077398687601,
0.019860543310642242,
-0.00041733391117304564,
-0.000842076085973531,
0.004784077405929565,
0.015977971255779266,
-0.027116684243083,
-0.012203115969896317,
-0.0010553733445703983,
-0.01435134094208479,
0.03048953413963318,
-0.017641765996813774,
-0.008169510401785374,
0.01654193550348282,
-0.004772807937115431,
-0.056048423051834106,
0.02168024145066738,
-0.019172267988324165,
0.017421294003725052,
0.03668087720870972,
-0.04298723116517067,
0.028809983283281326,
0.06733924150466919,
-0.07780805975198746,
-0.014193772338330746,
0.021629350259900093,
0.004072142764925957,
-0.04728483036160469,
-0.003387470729649067,
0.02803710103034973,
-0.020623017102479935,
-0.0024999200832098722,
0.0735132023692131,
0.02382661961019039,
0.014320220798254013,
-0.006478222087025642,
-0.027168691158294678,
-0.03690016642212868,
0.05743144825100899,
0.00979797262698412,
0.0145687535405159,
0.0036125928163528442,
0.04932403936982155,
-0.03706469014286995,
0.023275325074791908,
0.0035238610580563545,
0.009314476512372494,
-0.08576469123363495,
-0.0008946045418269932,
0.0009185757953673601,
-0.005720214918255806,
0.033059097826480865,
-0.012417263351380825,
0.027690956369042397,
0.0457395538687706,
-0.03607333078980446,
-0.015495192259550095,
-0.03695209324359894,
-0.05915296450257301,
0.004163509234786034,
-0.02621440589427948,
-0.005661251023411751,
0.03358231112360954,
0.017847219482064247,
0.04887709021568298,
0.02523285709321499,
0.03257695958018303,
-0.01920693926513195,
-0.016341732814908028,
-0.006751897279173136,
-0.0027683801017701626,
0.03791922703385353,
-0.00563833536580205,
0.036163330078125,
-0.02275218442082405,
0.007035612128674984,
0.0550224743783474,
-0.0021842357236891985,
-0.020144212990999222,
0.00018633918080013245,
0.024003751575946808,
0.021773524582386017,
0.031915146857500076,
0.00828575436025858,
-0.03232651576399803,
-0.014041343703866005,
0.04000205174088478,
0.0010529602877795696,
0.03681333363056183,
0.006021301727741957,
-0.014998228289186954,
0.010283537209033966,
-0.01515229046344757,
-0.0364653617143631,
0.0005096489912830293,
-0.030371733009815216,
-0.06340614706277847,
0.0143742011860013,
0.004618942271918058,
0.024897312745451927,
-0.049937956035137177,
0.01254943199455738,
-0.017768753692507744,
-0.017036840319633484,
0.018114792183041573,
0.025252029299736023,
0.018654635176062584,
0.04218440130352974,
0.005656218621879816,
-0.03157574683427811,
-0.007007251493632793,
0.0069841123186051846,
-0.0015663711819797754,
-0.04181881994009018,
0.0012835863744840026,
0.025460537523031235,
0.033887382596731186,
-0.002802554750815034,
-0.08960968255996704,
-0.05101707950234413,
0.023546431213617325,
-0.00029997900128364563,
0.024865232408046722,
-0.019530732184648514,
-0.04667854309082031,
0.0014839667128399014,
-0.03415330871939659,
0.024279408156871796,
-0.009909524582326412,
0.0370149165391922,
-0.04758838191628456,
-0.0030721588991582394,
-0.014064785093069077,
0.01269980613142252,
0.05169455334544182,
0.03859031945466995,
-0.007451533805578947,
0.0323466919362545,
0.029773833230137825,
-0.017323842272162437,
-0.03487424552440643,
0.019622039049863815,
-0.007126140873879194,
-0.024134479463100433,
0.005050601903349161,
0.00825063418596983,
-0.004408406093716621,
0.03066345304250717,
0.006056454498320818,
0.03698579967021942,
-0.036773212254047394,
-0.009264030493795872,
0.01643979735672474,
0.06624523550271988,
0.02623230218887329,
-0.04063892364501953,
0.04276597127318382,
-0.012144969776272774,
0.02098892256617546,
0.02267462946474552,
-0.00525416387245059,
-0.022766390815377235,
0.04028032347559929,
0.006808657664805651,
0.016722247004508972,
0.020480485633015633,
-0.02570318430662155,
-0.005817932076752186,
-0.048928599804639816,
-0.0063378592021763325,
0.03640934079885483,
-0.01113343145698309,
-0.005705758463591337,
0.018621055409312248,
0.03609180450439453,
0.037287112325429916,
0.031602561473846436,
-0.008476119488477707,
0.024401361122727394,
0.012948580086231232,
0.008832840248942375,
0.05490880087018013,
0.032290808856487274,
0.032832469791173935,
0.013502590358257294,
0.02736372873187065,
-0.007107098586857319,
0.022739291191101074,
-0.018398467451334,
0.03857017681002617,
0.0017708593513816595,
-0.051431551575660706,
-0.0037506078369915485,
-0.03634752705693245,
-0.02399434521794319,
0.02825743891298771,
-0.010558169335126877,
0.09298253804445267,
-0.02754254639148712,
0.008393548429012299,
0.013908776454627514,
-0.011433827690780163,
-0.005640770774334669,
0.013146039098501205,
0.007794555276632309,
-0.00806386023759842,
-0.013547083362936974,
0.010309217497706413,
-0.03629348799586296,
-0.004266939125955105,
0.025907842442393303,
-0.03418021276593208,
0.027577746659517288,
0.022703135386109352,
0.017026200890541077,
-0.01691637560725212,
-0.025986071676015854,
-0.006788056343793869,
-0.01819431595504284,
0.00997384823858738,
0.01707831397652626,
0.027521735057234764,
-0.03198329731822014,
-0.04701099917292595,
-0.04179806634783745,
0.012846799567341805,
-0.05157346650958061,
0.000056383887567790225,
-0.030749088153243065,
0.002618679078295827,
-0.03047128953039646,
-0.0063529061153531075
] |
<p>We've been using EMF to transmit energy (information) for over a century.
I was wondering is there any other way to send a message on long distances, even faster than EMF waves can travel? For example there are particles that travel faster than C. Or as another example I have heard the Quantum Entanglement can be useful in this case.</p> | 1,414 | [
0.009653612039983273,
-0.03976069390773773,
-0.019914012402296066,
-0.04402698576450348,
0.0403423048555851,
0.006985980551689863,
-0.008401283994317055,
-0.0266592875123024,
0.02938399277627468,
-0.014628942124545574,
0.015557033009827137,
0.06012725457549095,
0.02278718538582325,
0.005111767444759607,
0.03352322429418564,
0.0016796962590888143,
0.005008883308619261,
0.016976207494735718,
0.012549180537462234,
-0.028324894607067108,
0.010625007562339306,
0.004317657556384802,
-0.02701789326965809,
-0.00868838932365179,
0.024843959137797356,
0.019931400194764137,
0.03301749378442764,
-0.0047288015484809875,
0.022124163806438446,
0.044666141271591187,
0.03500329330563545,
-0.02255352959036827,
-0.006523448973894119,
0.03184404969215393,
0.021446246653795242,
-0.020010028034448624,
-0.043016355484724045,
-0.0596943125128746,
0.018313033506274223,
-0.014000863768160343,
-0.0314088799059391,
-0.04606214538216591,
0.012262145057320595,
0.05833785608410835,
-0.04745905473828316,
0.009277835488319397,
0.02775106392800808,
-0.04663218930363655,
0.020060023292899132,
-0.061337895691394806,
0.046506237238645554,
-0.021553097292780876,
0.015713732689619064,
-0.047773778438568115,
0.019513171166181564,
0.012688720598816872,
0.09731080383062363,
0.058032311499118805,
0.008381293155252934,
-0.032279256731271744,
-0.0009164558723568916,
0.011294449679553509,
-0.005958826281130314,
-0.04816459119319916,
-0.03842145949602127,
0.026777783408761024,
-0.03717871382832527,
-0.013150341808795929,
0.028334088623523712,
0.011822111904621124,
-0.0100869694724679,
0.02771691046655178,
0.05806518346071243,
0.043485790491104126,
0.00758287264034152,
-0.026345137506723404,
-0.017326530069112778,
-0.007017668802291155,
0.05027231201529503,
0.059134628623723984,
-0.02473076619207859,
-0.014788873493671417,
0.012072005309164524,
0.03681632876396179,
-0.015914181247353554,
-0.014120952226221561,
0.03668869659304619,
-0.00999089702963829,
-0.004568692296743393,
0.03719160705804825,
-0.0443824827671051,
-0.021233510226011276,
0.018423505127429962,
0.012632114812731743,
-0.019626131281256676,
-0.0004686284519266337,
-0.0019296081736683846,
0.03429195657372475,
0.027517549693584442,
-0.04550036042928696,
0.03791041299700737,
-0.01769430562853813,
0.016458578407764435,
0.08693097531795502,
0.026821328327059746,
-0.030184879899024963,
-0.03519674018025398,
-0.006200442556291819,
-0.008181205950677395,
0.039955899119377136,
-0.022009352222085,
-0.012080958113074303,
0.007776301354169846,
0.0020595991518348455,
0.014188885688781738,
-0.025643646717071533,
-0.003070130944252014,
-0.042802006006240845,
0.0632375106215477,
0.08422093093395233,
0.04129119962453842,
-0.03703276813030243,
0.06098848953843117,
-0.018964234739542007,
-0.03776593133807182,
0.008014627732336521,
0.009129045531153679,
0.02236439473927021,
-0.011053257621824741,
0.0244846623390913,
0.0017217884305864573,
-0.02139638550579548,
-0.000024258968551293947,
-0.03396566957235336,
0.04387511685490608,
-0.023789631202816963,
-0.12833259999752045,
-0.06536656618118286,
0.05720429867506027,
-0.0022601583041250706,
-0.0009553155396133661,
-0.0750897228717804,
0.0424397774040699,
0.034216031432151794,
0.06926138699054718,
0.03251853957772255,
-0.0029136650264263153,
-0.04211314767599106,
0.048780880868434906,
0.02850317396223545,
0.0017064387211576104,
-0.03545330464839935,
0.010747410356998444,
-0.01977580599486828,
0.05015983060002327,
-0.04458967596292496,
0.004632005468010902,
0.0264019463211298,
0.0018759113736450672,
-0.02390160597860813,
0.08227873593568802,
-0.01970124989748001,
0.0246433075517416,
0.013353122398257256,
-0.020427558571100235,
-0.02686421386897564,
0.10704118758440018,
0.030737154185771942,
-0.008319668471813202,
0.027589421719312668,
0.014485489577054977,
0.029107989743351936,
0.02426004596054554,
-0.021259821951389313,
0.017713651061058044,
-0.05463472753763199,
0.0059119523502886295,
0.00780462147668004,
-0.00932884681969881,
-0.015997933223843575,
-0.020114731043577194,
-0.036829568445682526,
0.03212856501340866,
0.04022151604294777,
-0.0018689013086259365,
0.03282603248953819,
-0.03743164986371994,
-0.016461949795484543,
0.033608369529247284,
-0.055013131350278854,
0.0013503112131729722,
0.0047898502089083195,
0.05763785168528557,
0.022339221090078354,
0.02016870304942131,
0.03191523998975754,
-0.004131460562348366,
0.014918265864253044,
-0.04420848190784454,
-0.034164369106292725,
-0.01135155837982893,
0.04280573129653931,
0.023959212005138397,
-0.004420748446136713,
-0.005706401076167822,
0.060458727180957794,
0.03024049662053585,
-0.016001634299755096,
0.0087815560400486,
0.010660857893526554,
-0.05493524670600891,
-0.025676550343632698,
0.004169658292084932,
0.043286629021167755,
0.024824194610118866,
0.004458467476069927,
0.020737620070576668,
0.0071161226369440556,
-0.03125179931521416,
0.01703324168920517,
-0.022230369970202446,
0.0651913583278656,
0.0004536895430646837,
0.030159756541252136,
-0.01797827146947384,
0.03778582438826561,
0.040671516209840775,
0.0033222471829503775,
-0.007080193608999252,
-0.06454099714756012,
-0.09285544604063034,
-0.01782224327325821,
0.03207091614603996,
0.007785098627209663,
-0.045464541763067245,
0.003563879756256938,
0.03436065465211868,
0.07433290034532547,
0.03616359457373619,
0.03295699506998062,
-0.033669427037239075,
-0.028873326256871223,
0.020484846085309982,
0.042374446988105774,
-0.009231015108525753,
0.03306286409497261,
0.04758401960134506,
0.00664322916418314,
-0.023939520120620728,
0.0025490091647952795,
-0.03732621297240257,
0.008587147109210491,
-0.021026942878961563,
-0.004050614777952433,
-0.0031975985039025545,
-0.043397918343544006,
0.006573887076228857,
-0.06280336529016495,
-0.0028162789531052113,
-0.018054338172078133,
0.0011113270884379745,
0.006824546959251165,
0.016732100397348404,
-0.02262420766055584,
-0.003972726408392191,
-0.01155233383178711,
-0.036973126232624054,
-0.010312865488231182,
0.03469277545809746,
-0.048048410564661026,
0.03487681597471237,
-0.02048100158572197,
0.004284439142793417,
-0.02334444969892502,
-0.0007265390595421195,
0.04123450070619583,
0.004945082124322653,
0.052193816751241684,
-0.013931608758866787,
-0.06604129821062088,
0.002823415445163846,
-0.08314478397369385,
-0.006120301317423582,
0.009850121103227139,
-0.031045924872159958,
0.0328800193965435,
-0.027085185050964355,
-0.06245584785938263,
0.04854736477136612,
-0.0426645502448082,
0.013448410667479038,
-0.011094539426267147,
-0.0383056215941906,
-0.03769645839929581,
-0.008255266584455967,
-0.01975383423268795,
0.012669664807617664,
-0.028257951140403748,
0.024456964805722237,
0.06251396983861923,
-0.014190804213285446,
-0.03946799784898758,
-0.0369136817753315,
-0.04945733770728111,
-0.043729666620492935,
-0.0205056294798851,
-0.016279716044664383,
0.02131432481110096,
-0.06421656161546707,
0.03836249187588692,
-0.007918629795312881,
-0.050876639783382416,
0.013297861441969872,
-0.04529711604118347,
-0.04790882766246796,
0.0721004456281662,
-0.008454066701233387,
0.023666968569159508,
-0.01119739655405283,
-0.008233330212533474,
0.04150184616446495,
0.03473110496997833,
-0.0385008305311203,
-0.0034350764472037554,
-0.032826319336891174,
-0.002834390150383115,
-0.028531454503536224,
-0.00815536268055439,
0.04837969318032265,
-0.01375456340610981,
0.025256220251321793,
0.06249697133898735,
-0.0371595174074173,
0.0018679735949262977,
-0.001484390813857317,
-0.03651869669556618,
-0.0183576587587595,
0.005503825843334198,
0.005977990105748177,
0.07265380024909973,
0.03270576894283295,
-0.07129938155412674,
0.03058646246790886,
0.02553677372634411,
0.009559777565300465,
-0.0011651567183434963,
-0.03267979994416237,
0.013748224824666977,
0.026631882414221764,
0.032102104276418686,
0.0017370906425639987,
0.028910525143146515,
-0.002499090740457177,
0.00865098088979721,
0.002365633612498641,
0.04500226303935051,
0.039835695177316666,
-0.01616705022752285,
0.0013437395682558417,
0.027904627844691277,
0.05125872790813446,
-0.02886304259300232,
-0.029435090720653534,
-0.029548289254307747,
0.015094499103724957,
-0.014422688633203506,
0.012117375619709492,
-0.04456126317381859,
0.016325591132044792,
0.026485083624720573,
0.014913776889443398,
0.027326220646500587,
0.00037595015601255,
-0.0022335005924105644,
-0.03236141428351402,
0.025312775745987892,
0.013425360433757305,
0.03741033747792244,
0.02958168275654316,
0.0570143386721611,
0.04349992051720619,
-0.01804378628730774,
0.018804140388965607,
-0.010868671350181103,
-0.09735039621591568,
0.03280225023627281,
-0.017317593097686768,
-0.01240170281380415,
0.009514054283499718,
-0.029516039416193962,
-0.02731790952384472,
-0.0028032457921653986,
-0.05117158591747284,
-0.00896832998842001,
-0.018816811963915825,
-0.058637719601392746,
-0.028548356145620346,
-0.017112383618950844,
-0.051599327474832535,
-0.02455936372280121,
-0.00233855820260942,
0.0007737232954241335,
-0.01949065364897251,
-0.010921180248260498,
0.04669027402997017,
-0.04266461357474327,
-0.004380401223897934,
0.004494585562497377,
-0.009059046395123005,
0.014829238876700401,
0.004045337438583374,
0.02662479504942894,
0.00345685426145792,
-0.05790600925683975,
-0.004483119584619999,
0.02431774139404297,
0.03587871417403221,
-0.01056017354130745,
-0.007098295260220766,
-0.04071410000324249,
-0.03785422444343567,
-0.012204375118017197,
-0.009504018351435661,
0.05991329252719879,
0.010419322177767754,
0.011858795769512653,
0.02854916825890541,
-0.009130796417593956,
-0.020217860117554665,
0.006206796504557133,
0.03980964794754982,
0.008020725101232529,
-0.036831729114055634,
-0.014022819697856903,
-0.04268653318285942,
-0.002756238915026188,
-0.019349070265889168,
0.02204299345612526,
-0.008501874282956123,
-0.004772441927343607,
-0.001129895099438727,
0.02967425063252449,
0.01039478462189436,
-0.022474508732557297,
-0.010355264879763126,
0.006861266680061817,
-0.012718861922621727,
0.007250747177749872,
-0.0052265929989516735,
-0.0440496988594532,
0.002156689064577222,
0.03248921036720276,
0.010185847990214825,
-0.013424615375697613,
-0.09046521037817001,
0.023409510031342506,
0.0390922948718071,
0.04178214818239212,
-0.004986962303519249,
-0.004591620527207851,
-0.06916140764951706,
-0.017537876963615417,
0.03578382357954979,
-0.030651133507490158,
0.02114352583885193,
-0.019604884088039398,
-0.01730319857597351,
-0.006811902392655611,
-0.019571464508771896,
0.016159506514668465,
0.030707571655511856,
0.0040889885276556015,
-0.023726608604192734,
-0.001557813840918243,
0.0004534738545771688,
0.01441243663430214,
0.01973574236035347,
0.055228814482688904,
0.056986238807439804,
0.02726472169160843,
0.0009961697505787015,
0.015552771277725697,
0.026165468618273735,
-0.02400786802172661,
-0.0720675140619278,
0.002668229164555669,
0.02738099731504917,
-0.039025574922561646,
0.019539492204785347,
-0.012869857251644135,
-0.042446691542863846,
0.010426909662783146,
0.007754889782518148,
-0.002435758477076888,
-0.02498975396156311,
-0.027742711827158928,
0.02492714487016201,
0.017007943242788315,
-0.0013607997680082917,
0.034043360501527786,
0.04239761456847191,
-0.02604200504720211,
0.02252286858856678,
0.0034914410207420588,
0.062030717730522156,
-0.027642058208584785,
0.016705233603715897,
0.012224012054502964,
0.03430632874369621,
-0.0358344167470932,
0.031517378985881805,
-0.013849169947206974,
-0.019861068576574326,
-0.01606067270040512,
-0.051231253892183304,
-0.03197284787893295,
0.03460878133773804,
-0.005851562134921551,
-0.007044519763439894,
-0.028143638744950294,
0.022723756730556488,
-0.012640953995287418,
-0.02022174745798111,
0.019912494346499443,
0.008766899816691875,
-0.017424816265702248,
0.006797337904572487,
0.005692041479051113,
-0.004108157474547625,
-0.04699759557843208,
0.008891507051885128,
0.01881449669599533,
-0.07079464942216873,
0.03938814997673035,
0.003493634983897209,
-0.014100981876254082,
0.01762726902961731,
-0.06121157109737396,
-0.04381516948342323,
0.044905342161655426,
-0.018944116309285164,
0.026114508509635925,
-0.0414249412715435,
0.014125213027000427,
-0.030324939638376236,
-0.01651853136718273,
-0.0545886754989624,
-0.03783673048019409,
0.031201111152768135,
0.012168689630925655,
0.004914911463856697,
-0.04032034054398537,
-0.017565326765179634,
-0.045959439128637314,
-0.00748917693272233,
-0.02026171050965786,
0.04331739991903305,
-0.012824315577745438,
0.008549490943551064,
0.028161393478512764,
-0.015766730532050133,
0.017429988831281662,
-0.0009937266586348414,
-0.046528711915016174,
0.020302236080169678,
0.016247309744358063,
0.03206527605652809,
-0.025888746604323387,
0.027876686304807663,
-0.03549269214272499,
-0.01324059721082449,
0.004029992967844009,
-0.006128683220595121,
0.0006553310086019337,
-0.024517733603715897,
0.006058801431208849,
0.05357328802347183,
0.028858011588454247,
-0.013320820406079292,
0.022815953940153122,
0.03726732358336449,
0.013350185006856918,
-0.009689015336334705,
-0.02774130180478096,
0.015491233207285404,
-0.03732561320066452,
-0.050128303468227386,
0.03629215434193611,
0.020037034526467323,
0.025410564616322517,
-0.023549439385533333,
0.025368735194206238,
0.015401484444737434,
-0.007872945629060268,
0.006606344599276781,
0.0034335122909396887,
0.011608771048486233,
-0.03470778465270996,
0.00398284662514925,
-0.009152557700872421,
0.030261188745498657,
0.004414415452629328,
-0.02054215595126152,
0.011640466749668121,
-0.038810111582279205,
0.055158890783786774,
-0.026705022901296616,
0.034167420119047165,
0.0038912876043468714,
0.012584127485752106,
-0.011206072755157948,
0.007409999147057533,
-0.04335616156458855,
0.028124669566750526,
-0.013108004815876484,
0.014427169226109982,
0.011993080377578735,
-0.007096451707184315,
0.024816708639264107,
0.06578166782855988,
0.01653345301747322,
0.007203561719506979,
0.027573082596063614,
0.05637998506426811,
0.008494354784488678,
-0.024060742929577827,
-0.03980037197470665,
0.025748789310455322,
-0.06268338114023209,
0.027250811457633972,
-0.005546239670366049,
-0.029181810095906258,
0.034524016082286835,
-0.012937207706272602,
0.007283239159733057,
-0.004246360622346401,
-0.026064591482281685,
-0.03622257709503174,
0.03191755712032318,
0.02432633750140667,
0.009103349409997463,
0.003919506911188364,
-0.0007841828046366572,
0.02684599906206131,
-0.002340733539313078,
0.007475411519408226,
0.003180011175572872,
-0.11952503025531769,
-0.05839936062693596,
-0.017674477770924568,
-0.042576372623443604,
0.049747854471206665,
0.028400972485542297,
-0.019882474094629288,
-0.003072419436648488,
-0.010299407877027988,
0.03980972245335579,
0.006346698384732008,
-0.0009714190964587033,
-0.017102055251598358,
0.05282308906316757,
0.003963877912610769,
0.029952332377433777,
-0.0009145162766799331,
-0.01156699936836958,
0.08004200458526611,
0.030535273253917694,
-0.0027373749762773514,
-0.051069390028715134,
0.03567919135093689,
-0.03941962122917175,
0.03291003406047821,
-0.0770447626709938,
0.022738207131624222,
-0.03005816973745823,
0.03462303429841995,
0.02961389161646366,
0.0474320612847805,
-0.02340518683195114,
0.00838400050997734,
0.07397186756134033,
-0.04163356497883797,
-0.04293934255838394,
-0.002628725953400135,
0.024395501241087914,
0.002675113268196583,
-0.0016634598141536117,
-0.041441235691308975,
0.021662637591362,
-0.058024030178785324,
-0.019789284095168114,
-0.007253945339471102,
-0.023048749193549156,
0.058845505118370056,
-0.0017574079101905227,
-0.02652927301824093,
-0.03637068718671799,
0.0030274412129074335,
-0.010730311274528503,
-0.019495893269777298,
0.019664831459522247,
0.04048421233892441,
0.020411528646945953,
0.0003448595816735178,
0.006319263018667698,
0.03544226661324501,
-0.01648373156785965,
0.0013623108388856053,
-0.014287995174527168,
-0.05206521227955818,
0.0071365381591022015,
-0.017722662538290024,
0.012697222642600536,
-0.024971559643745422,
0.01086911465972662,
0.02605907991528511,
0.03752439469099045,
-0.004462717566639185,
-0.009556409902870655,
-0.03305777534842491,
0.015804840251803398,
0.020088234916329384,
-0.008666237816214561,
0.008712491020560265,
-0.02473730407655239,
0.0439380407333374,
-0.018970981240272522,
0.00971502996981144,
-0.007929859682917595,
0.003609834471717477,
-0.0005879451055079699,
-0.018045632168650627,
-0.00010443211067467928,
-0.03815430775284767,
-0.060093652456998825,
-0.011214007623493671,
0.009245825000107288,
-0.02415969967842102,
-0.0024215425364673138,
0.024511955678462982,
0.037211496382951736,
-0.017710955813527107,
-0.002244452480226755,
-0.024370741099119186,
-0.020350387319922447,
-0.02422460727393627,
0.032746557146310806,
-0.019284117966890335,
-0.004204365890473127,
0.020181816071271896,
-0.012990107759833336,
0.04546283185482025,
0.022680208086967468,
-0.012392152100801468,
0.02538486383855343,
-0.032663024961948395,
-0.01213407889008522,
0.055256325751543045,
-0.025917110964655876,
-0.02393414080142975,
-0.026740316301584244,
-0.023212874308228493,
0.003447495633736253,
-0.02998369373381138,
0.01175356563180685,
0.06493125110864639,
-0.013615871779620647,
0.00035304398625157773,
0.00019614350458141416,
-0.028676837682724,
-0.004478571005165577,
0.01553424634039402,
-0.02209494076669216,
-0.009092393331229687,
0.0015307000139728189,
0.04660161957144737,
0.012327685952186584,
-0.051599256694316864,
-0.025717662647366524,
0.000056360997405136004,
-0.01394177321344614,
0.03214222937822342,
-0.0097952326759696,
0.023416301235556602,
-0.0038673160597682,
0.02312427945435047,
-0.0415363535284996,
0.02078455314040184,
-0.043199002742767334,
-0.01938280463218689,
-0.031493593007326126,
-0.032858509570360184,
-0.02125699818134308,
0.029785512015223503,
-0.04946017265319824,
0.022077029570937157,
0.012399556115269661,
0.013757873326539993,
-0.009352773427963257,
0.012102309614419937,
0.03217479959130287,
0.02020176872611046,
0.04937588423490524,
-0.02977501042187214,
-0.02875330112874508,
0.05037003755569458,
-0.039118535816669464,
-0.03972925990819931,
0.0481109544634819,
-0.02412475273013115,
0.018977269530296326,
0.03831908106803894,
-0.01296770665794611,
-0.008689513429999352,
0.06224989891052246,
0.025469301268458366,
0.013675807043910027,
0.016664210706949234,
-0.024608170613646507,
-0.018732905387878418,
0.01461953017860651,
-0.0011791349388659,
-0.020201904699206352,
-0.01780514419078827,
0.02155369147658348,
0.026321351528167725,
0.04329599812626839,
0.03132898733019829,
0.0016974532045423985,
-0.01909187249839306,
0.02778714708983898,
0.03822527453303337,
-0.01443421933799982,
0.043622925877571106,
0.05526706948876381,
-0.017782030627131462,
0.02839585579931736,
0.03415533900260925,
0.025354688987135887,
-0.07914666831493378,
0.03016139194369316,
0.014793787151575089,
0.009054199792444706,
0.056330908089876175,
-0.036848340183496475,
0.041010692715644836,
0.004877080675214529,
-0.07833230495452881,
0.03216966241598129,
-0.04528145492076874,
0.0011910605244338512,
-0.012441663071513176,
0.041302308440208435,
-0.029597342014312744,
0.06242983788251877,
0.04411416873335838,
0.03470374643802643,
0.0012082819594070315,
0.02281709760427475,
-0.013497604057192802,
-0.025292834267020226,
-0.024976788088679314,
0.016584716737270355,
0.02088826149702072,
0.02713814750313759,
0.08870362490415573,
-0.025882821530103683,
0.00529223307967186,
0.02393663488328457,
-0.0017813927261158824,
0.04158326983451843,
-0.001679117209278047,
0.000036978475691284984,
0.027043938636779785,
0.016580557450652122,
-0.023985546082258224,
-0.027058912441134453,
-0.011419362388551235,
0.012018092907965183,
-0.006347418297082186,
0.022728141397237778,
0.003363215597346425,
-0.005474425852298737,
-0.010456381365656853,
-0.02593347802758217,
-0.016216469928622246,
0.021636782214045525,
-0.03676987811923027,
-0.03417377173900604,
0.00815696269273758,
0.010790343396365643,
0.05112376809120178,
-0.035056017339229584,
-0.017293410375714302,
-0.055436015129089355,
-0.018283097073435783,
0.0012612619902938604,
-0.005472270771861076,
-0.012537089176476002,
0.014903445728123188,
-0.012098309583961964,
-0.020035095512866974,
0.028542054817080498,
0.016552075743675232,
0.03603019192814827,
-0.04147011786699295,
-0.034706566482782364,
-0.013868343085050583,
0.03646117076277733,
0.00477786036208272,
-0.04155373200774193,
-0.025388803333044052,
0.052196212112903595,
-0.0025250690523535013,
0.04370701313018799,
0.03043627180159092,
0.020664403215050697,
-0.009384936653077602,
-0.03169959783554077,
0.01835843175649643,
-0.011658390052616596,
0.05169157683849335,
-0.043594613671302795,
-0.04754873365163803,
0.010648518800735474,
0.009732997976243496,
0.09845506399869919,
-0.010928301140666008,
0.022425394505262375,
0.027901997789740562,
0.005356424488127232,
0.01041021291166544,
-0.026472190394997597,
-0.0026991269551217556,
-0.022708715870976448,
-0.058145035058259964,
-0.04394824057817459,
-0.007052401080727577,
-0.007385591976344585,
-0.00576609605923295,
0.00989367812871933,
0.015661440789699554,
0.01637755148112774,
-0.02211882546544075,
-0.023829825222492218,
0.042046789079904556,
0.03493613004684448,
-0.020290661603212357,
0.021897951140999794,
-0.01810508593916893,
0.010777219198644161,
-0.014219716191291809,
-0.03911270201206207,
-0.03020378388464451,
0.0377681739628315,
-0.027244072407484055,
0.029702072963118553,
-0.016396915540099144,
0.034358516335487366,
0.007242935709655285,
-0.05950058251619339,
-0.0056500802747905254,
0.03565095365047455,
-0.043308891355991364,
0.013478436507284641,
0.0669899582862854,
-0.0033574928529560566,
0.0065582566894590855,
0.006967602763324976,
0.028441527858376503,
-0.00935992132872343,
0.023313939571380615,
-0.039185989648103714,
0.04881121963262558,
0.01284737791866064,
-0.023030241951346397,
0.049788251519203186,
0.012852792628109455,
-0.00008417260687565431,
0.02663501538336277,
-0.002403016434982419,
0.0028558841440826654,
-0.032671812921762466,
0.001989397220313549,
0.003776493715122342,
0.0037224905099719763,
-0.014825548976659775,
0.04087059199810028,
-0.03321045637130737,
0.08411633223295212,
-0.053437504917383194,
0.015048729255795479,
0.008068112656474113,
-0.0004927380941808224,
-0.0016733065713196993,
0.01174214482307434,
-0.022668417543172836,
0.03717867657542229,
-0.021598121151328087,
0.014315379783511162,
-0.0021172515116631985,
-0.012078278698027134,
0.01571434922516346,
-0.0501520037651062,
0.0062225074507296085,
-0.0165863037109375,
-0.016273409128189087,
-0.011214732192456722,
-0.018646126613020897,
-0.011436969973146915,
-0.001651728875003755,
0.012363639660179615,
0.03938228636980057,
-0.005062119569629431,
-0.014793685637414455,
-0.012731673195958138,
0.02179890312254429,
0.05227117985486984,
-0.03255240619182587,
0.03803286328911781,
-0.029194876551628113,
0.019710196182131767,
-0.018919285386800766,
0.030024895444512367
] |
<p>It is said <a href="http://en.wikipedia.org/wiki/Introduction_to_general_relativity#Experimental_tests" rel="nofollow">in this wikipedia article</a> (in the 7th paragraph) that where there exists huge masses and very large gravitational forces (like around binary pulsars), general relativistic effects can be observed better:</p>
<blockquote>
<p>By cosmic standards, gravity throughout the solar system is weak. Since the differences between the predictions of Einstein's and Newton's theories are most pronounced when gravity is strong, physicists have long been interested in testing various relativistic effects in a setting with comparatively strong gravitational fields. This has become possible thanks to precision observations of binary pulsars.</p>
</blockquote>
<p>But <a href="http://whystringtheory.com/motivation/gravity/#" rel="nofollow">here in whystringtheory.com </a> (in the last paragraph), it is said that </p>
<blockquote>
<p>For small spacetime volumes <strong>or large gravitational forces Einstein has little to offer</strong></p>
</blockquote>
<p>I know that in singularities, GR fails and this is a motivation for quantum gravity theories. But the second quote above says in small spacetime volumes <strong>or</strong> large gravitational forces.</p>
<p>Is there any problem with general relativity in conditions with very large gravitational forces (in big enough volumes of spacetime)?</p> | 1,415 | [
-0.025262169539928436,
-0.02403523214161396,
-0.0022433025296777487,
-0.055107660591602325,
0.04139897972345352,
0.0348861999809742,
-0.028903892263770103,
-0.05203845724463463,
-0.0009479505242779851,
-0.026188116520643234,
0.008815346285700798,
0.03334694728255272,
0.05806534364819527,
0.024876657873392105,
0.027025433257222176,
0.019913800060749054,
-0.020220955833792686,
-0.029794052243232727,
0.0004185581055935472,
-0.02690133824944496,
0.0007942730444483459,
0.03681560605764389,
-0.00012736808275803924,
0.0033582390751689672,
-0.002736875554546714,
-0.0013090460561215878,
0.010830376297235489,
0.013417765498161316,
0.02482473850250244,
0.05162012577056885,
-0.004940366838127375,
0.0019256866071373224,
-0.021018140017986298,
0.04513716325163841,
0.023454321548342705,
0.018453754484653473,
-0.03636446222662926,
-0.002474127570167184,
0.008657923899590969,
-0.006815582979470491,
-0.038337185978889465,
-0.026505110785365105,
-0.00982383918017149,
0.06181786581873894,
-0.029057517647743225,
0.03238333761692047,
0.040185995399951935,
-0.019200699403882027,
0.05790148302912712,
-0.059630416333675385,
0.017217865213751793,
0.02486724779009819,
0.04175438731908798,
0.03252111375331879,
-0.02348768711090088,
-0.00042257242603227496,
0.07591462880373001,
0.08340658992528915,
-0.050385795533657074,
-0.0558309480547905,
-0.021968116983771324,
0.00881886575371027,
-0.016118405386805534,
-0.021048398688435555,
-0.028210174292325974,
0.05823429673910141,
-0.025980843231081963,
-0.03235148265957832,
0.015675345435738564,
0.015096613205969334,
-0.003636804409325123,
0.04184367507696152,
0.015562678687274456,
0.0355459563434124,
-0.01240540575236082,
-0.010976440273225307,
0.023949958384037018,
-0.028313545510172844,
0.028679676353931427,
0.04980294406414032,
-0.03954986855387688,
0.010766172781586647,
0.035708315670490265,
0.02162744477391243,
0.01114066131412983,
0.006529643200337887,
0.07936812192201614,
-0.012877514585852623,
0.0038643185980618,
0.025918642058968544,
-0.02426820807158947,
-0.004009532276540995,
0.009805034846067429,
0.008805998601019382,
-0.04543206840753555,
0.014917165040969849,
0.0019198738737031817,
0.05194474756717682,
-0.019823042675852776,
-0.0035719170700758696,
-0.005568501073867083,
-0.011640259064733982,
0.003431493416428566,
0.07002592086791992,
0.009431787766516209,
-0.03763190284371376,
-0.038758523762226105,
0.016355259343981743,
-0.004976131021976471,
-0.0125004006549716,
-0.016061410307884216,
-0.015890637412667274,
-0.00400151452049613,
-0.029804708436131477,
0.009919276461005211,
-0.04247702658176422,
-0.011086752638220787,
-0.023578105494379997,
0.06354562938213348,
0.06123119965195656,
0.05907334387302399,
-0.010740388184785843,
0.014775502495467663,
-0.06363996118307114,
-0.05199515447020531,
0.04872976616024971,
0.05291956290602684,
-0.03679182380437851,
-0.0479554757475853,
0.030520347878336906,
0.011163915507495403,
0.019185032695531845,
-0.04184558242559433,
-0.002752683823928237,
0.05591558665037155,
-0.017226753756403923,
-0.11959361284971237,
-0.04602592810988426,
0.06877976655960083,
0.017459560185670853,
0.012088236398994923,
-0.03902879357337952,
0.01163408812135458,
0.030719324946403503,
0.07488550990819931,
0.0005320232594385743,
0.030179671943187714,
-0.0003995912557002157,
0.024352731183171272,
-0.0013048090040683746,
-0.04549958556890488,
0.025239247828722,
0.006105971056967974,
-0.03349883854389191,
-0.012715885415673256,
-0.10708830505609512,
-0.011271236464381218,
0.030744118615984917,
0.035270072519779205,
-0.04387758672237396,
0.07563193142414093,
-0.03833136335015297,
0.010285386815667152,
-0.004247830715030432,
-0.0028136952314525843,
0.004003478679805994,
0.08990999311208725,
0.03301496058702469,
0.026589807122945786,
0.06999236345291138,
0.012842989526689053,
0.04700113460421562,
0.015556758269667625,
-0.005909349303692579,
0.020218433812260628,
-0.0608491376042366,
-0.0036670928820967674,
-0.0008451585890725255,
0.00595338037237525,
-0.00922336895018816,
-0.029358647763729095,
-0.008488678373396397,
-0.011932622641324997,
-0.03382117673754692,
-0.0205156821757555,
0.0460224375128746,
-0.010511700995266438,
0.004709896631538868,
-0.007012339308857918,
-0.001529353903606534,
-0.01220097579061985,
-0.04606839641928673,
-0.000043916596041526645,
-0.01006248313933611,
0.0006783156422898173,
0.015602599829435349,
0.012271234765648842,
0.023612411692738533,
-0.03292090818285942,
-0.03128815442323685,
-0.017073284834623337,
0.027652055025100708,
-0.058279864490032196,
0.020029524341225624,
0.020208299160003662,
0.038088053464889526,
0.022354084998369217,
-0.021909553557634354,
0.013414341025054455,
0.014150228351354599,
-0.005504955537617207,
0.055188942700624466,
0.019848830997943878,
0.004591690376400948,
0.006697798613458872,
-0.009737434796988964,
0.00870426557958126,
0.02541297860443592,
0.0015064760809764266,
0.0455775186419487,
-0.042421627789735794,
0.07193553447723389,
0.008134964853525162,
0.016076162457466125,
-0.0010400431929156184,
0.03016854077577591,
0.016210587695240974,
0.005889777094125748,
0.008758319541811943,
0.00328205362893641,
-0.06354369968175888,
0.01874615252017975,
0.028664760291576385,
0.02947031706571579,
-0.04109855368733406,
0.040711238980293274,
0.05128507688641548,
0.034337349236011505,
-0.0251405481249094,
0.02220340259373188,
-0.02367044985294342,
-0.05031193420290947,
0.02525944449007511,
0.021014543250203133,
0.02674264833331108,
0.04769264534115791,
0.02040713280439377,
0.042189180850982666,
0.007935487665235996,
-0.015783170238137245,
-0.010633465833961964,
0.020176764577627182,
-0.013963819481432438,
0.006534040439873934,
0.030923934653401375,
-0.02826518565416336,
0.03505678474903107,
-0.008003927767276764,
0.00841628760099411,
0.017222696915268898,
0.016975635662674904,
0.003797439392656088,
-0.08034347742795944,
-0.008383823558688164,
0.020619485527276993,
0.00996389426290989,
-0.02076801471412182,
-0.00374539359472692,
0.004909004084765911,
-0.06109242141246796,
-0.021037645637989044,
-0.02037140354514122,
0.011344115249812603,
-0.04285520687699318,
0.020164072513580322,
0.017559709027409554,
0.004178918898105621,
0.02890678122639656,
-0.022924242541193962,
-0.024019284173846245,
-0.002259722677990794,
-0.03270780295133591,
-0.013086199760437012,
0.016542671248316765,
-0.01686473749577999,
0.036345094442367554,
-0.025908339768648148,
-0.02963583916425705,
0.037637077271938324,
-0.033158447593450546,
0.05727016553282738,
-0.001476817298680544,
-0.002673243870958686,
-0.015774693340063095,
-0.017332179471850395,
-0.03686252236366272,
0.019107932224869728,
-0.004467197228223085,
-0.019332127645611763,
0.07773223519325256,
0.01799815520644188,
-0.05093944072723389,
-0.005531652364879847,
-0.03285329416394234,
-0.03467472642660141,
-0.009424087591469288,
0.00440807593986392,
-0.01770980842411518,
-0.042759787291288376,
0.03071356751024723,
0.014160627499222755,
-0.06280913949012756,
-0.04521055147051811,
-0.045562490820884705,
-0.028853045776486397,
0.04367793723940849,
-0.010859111323952675,
0.04379342123866081,
-0.02281769923865795,
-0.01887914165854454,
0.045482344925403595,
0.008500236086547375,
-0.01864982582628727,
-0.048566412180662155,
0.000020177934857201762,
-0.027261067181825638,
0.00018957733118440956,
-0.010566046461462975,
0.0006449237116612494,
0.03147904947400093,
0.006671723909676075,
0.026368191465735435,
0.02660905383527279,
-0.022462384775280952,
0.021538378670811653,
-0.02275138348340988,
-0.02450370043516159,
0.019277498126029968,
-0.037026964128017426,
0.020621174946427345,
0.03522386774420738,
-0.03068850003182888,
-0.030189096927642822,
-0.004492823500186205,
0.021538259461522102,
-0.00004142849502386525,
-0.0461542122066021,
0.029672883450984955,
-0.0059898169711232185,
0.03666848689317703,
0.014107320457696915,
-0.0013785071205347776,
-0.015291565097868443,
-0.0026270034722983837,
0.04088595509529114,
0.0010014793369919062,
0.05719097703695297,
0.008821441791951656,
-0.03657585754990578,
-0.017707647755742073,
0.042795583605766296,
-0.032334014773368835,
-0.03959326446056366,
0.004285701084882021,
-0.01829187013208866,
0.04646948352456093,
-0.008362889289855957,
0.00880404282361269,
0.060914378613233566,
0.0274966973811388,
0.04170330613851547,
-0.01727329194545746,
-0.03590169548988342,
0.013428233563899994,
-0.05464240908622742,
-0.002316599478945136,
0.00993870198726654,
0.06134366989135742,
0.02313038893043995,
0.013430805876851082,
0.08136541396379471,
-0.006716728676110506,
-0.0012941529275849462,
-0.010364850051701069,
-0.09757158160209656,
0.017643248662352562,
-0.026517361402511597,
-0.02596200630068779,
0.0517008900642395,
-0.025249307975172997,
-0.02469370700418949,
-0.013220374472439289,
0.00571847427636385,
-0.020170575007796288,
0.008316965773701668,
-0.052709829062223434,
0.006691774353384972,
-0.022674916312098503,
-0.03538079932332039,
0.006188170984387398,
0.03488597646355629,
0.036900781095027924,
-0.004555962514132261,
0.000048271835112245753,
-0.00022805249318480492,
-0.030759621411561966,
-0.020266475155949593,
0.01005516480654478,
0.02695719711482525,
0.025681020691990852,
0.042239367961883545,
-0.00553473923355341,
0.03639307990670204,
-0.00776071147993207,
0.003850893583148718,
0.05862872675061226,
0.03846970945596695,
-0.0075972662307322025,
0.005097032058984041,
-0.01703164353966713,
-0.032454218715429306,
-0.018533144146203995,
-0.015297429636120796,
0.05993155390024185,
0.006926363334059715,
-0.015627479180693626,
-0.018596313893795013,
0.002408892149105668,
0.0014661084860563278,
0.04471539705991745,
0.045696649700403214,
-0.012119381688535213,
-0.026105383411049843,
-0.010354675352573395,
-0.05895450711250305,
-0.053190600126981735,
-0.01660841703414917,
0.052591949701309204,
-0.0015033396193757653,
-0.09214979410171509,
-0.0003246982232667506,
0.016980625689029694,
0.027829669415950775,
-0.05341627448797226,
-0.006270702462643385,
-0.020377079024910927,
0.009957819245755672,
-0.03190777823328972,
0.020608318969607353,
-0.007899009622633457,
0.006690346170216799,
0.05659235641360283,
0.0039007500745356083,
-0.02977757528424263,
-0.06088469177484512,
0.016889723017811775,
0.04963849484920502,
0.020771440118551254,
0.008019392378628254,
-0.010285981930792332,
-0.05275195837020874,
-0.015003954991698265,
0.032977838069200516,
-0.0739571824669838,
0.016163567081093788,
-0.010579111985862255,
0.029512636363506317,
-0.05128852277994156,
-0.036633484065532684,
0.002017541788518429,
0.003226050641387701,
-0.05628684535622597,
0.0024653621949255466,
-0.012773636728525162,
0.0004760882875416428,
-0.0015734913758933544,
0.010675838217139244,
0.006978832650929689,
0.04464571923017502,
0.03917378559708595,
-0.002862401306629181,
-0.011018683202564716,
0.0035215518437325954,
-0.061294279992580414,
-0.07667755335569382,
0.007477221544831991,
-0.02723323553800583,
-0.016093801707029343,
0.05197465419769287,
-0.044777631759643555,
-0.05215366557240486,
0.03563661500811577,
-0.0009542024927213788,
-0.01812703348696232,
0.015884194523096085,
-0.03897997736930847,
0.004837679676711559,
0.014052221551537514,
0.0022127083502709866,
0.03291460499167442,
0.0023672496899962425,
-0.023700157180428505,
0.0017454286571592093,
-0.022251766175031662,
0.014954457059502602,
-0.060342784970998764,
-0.029342427849769592,
0.01705804467201233,
-0.0012106038630008698,
-0.030080219730734825,
0.04814579337835312,
-0.020352637395262718,
-0.006998491007834673,
-0.008116560988128185,
-0.03736836835741997,
-0.012728477828204632,
0.021562784910202026,
0.030786361545324326,
0.005797855090349913,
0.007592673879116774,
0.027422960847616196,
0.009857532568275928,
-0.025274889543652534,
0.013987647369503975,
0.005389505065977573,
-0.006998138967901468,
0.055399101227521896,
-0.029241684824228287,
0.009882684797048569,
0.012713988311588764,
-0.0008705819491297007,
0.024512674659490585,
-0.04762077331542969,
0.04084862396121025,
-0.0058624898083508015,
-0.017829524353146553,
0.021214520558714867,
-0.03501865640282631,
-0.02265525795519352,
-0.009492715820670128,
-0.014701115898787975,
0.022866925224661827,
-0.046516966074705124,
0.01871410757303238,
0.01717139407992363,
0.027330204844474792,
-0.09328474849462509,
-0.03901713341474533,
0.05569857731461525,
0.01596883125603199,
-0.009962397627532482,
0.0028681603725999594,
0.001171802170574665,
-0.056268610060214996,
0.009553185664117336,
-0.05668725445866585,
0.03641835227608681,
-0.02311122417449951,
-0.029034718871116638,
-0.008084602653980255,
0.00826429296284914,
0.05362998694181442,
-0.013970725238323212,
0.0031550154089927673,
0.00622560502961278,
0.0028820487204939127,
0.019109057262539864,
0.0012075870763510466,
0.01692473143339157,
-0.013852549716830254,
-0.0659865215420723,
-0.028868164867162704,
0.013508765958249569,
-0.015008237212896347,
0.00027985137421637774,
-0.006433860398828983,
0.07055608183145523,
-0.008253464475274086,
0.0008003979455679655,
-0.02078293077647686,
0.025543637573719025,
0.0003293540794402361,
-0.0014339382760226727,
-0.02715124376118183,
-0.0077260942198336124,
-0.014431052841246128,
-0.032428547739982605,
0.04397615045309067,
-0.017051873728632927,
-0.0010867721866816282,
0.0015717470087110996,
0.06950833648443222,
0.0022134126629680395,
-0.015373891219496727,
0.001255369745194912,
-0.033794403076171875,
0.021160505712032318,
0.008477168157696724,
0.00040270446334034204,
0.015381218865513802,
0.02529565431177616,
-0.0016632062615826726,
-0.03284529969096184,
-0.0044082277454435825,
0.011982482858002186,
0.060324717313051224,
0.005847935099154711,
0.02627159282565117,
0.03735095262527466,
-0.021588163450360298,
-0.01652573049068451,
-0.02200792357325554,
-0.0188557431101799,
0.007220039609819651,
0.016585294157266617,
0.011670970357954502,
-0.005234431009739637,
0.01715809479355812,
0.04187146574258804,
0.040673498064279556,
-0.010153376497328281,
0.0007537833298556507,
0.046354543417692184,
0.042565807700157166,
-0.0004998433287255466,
-0.018078478053212166,
-0.014787141233682632,
0.06963811814785004,
-0.038926832377910614,
0.030246322974562645,
0.010276060551404953,
0.008122636936604977,
-0.0007271667709574103,
-0.01242882665246725,
0.0202768687158823,
-0.03679225221276283,
-0.039089590311050415,
-0.029123757034540176,
0.025047173723578453,
0.015743279829621315,
-0.0007747854688204825,
-0.011328102089464664,
0.014360175468027592,
-0.0016564300749450922,
0.03345710039138794,
0.02451113983988762,
-0.0019821696914732456,
-0.0826483890414238,
-0.03645290434360504,
-0.03120254911482334,
-0.05091353505849838,
0.043834373354911804,
0.013748201541602612,
-0.03163643181324005,
0.020471105352044106,
-0.035089656710624695,
0.013461326248943806,
0.045799620449543,
0.0456371046602726,
-0.04691911116242409,
0.03953082114458084,
0.003687842981889844,
-0.020519182085990906,
0.005473522003740072,
-0.0037049634847790003,
0.12055668979883194,
0.04141370952129364,
-0.027288932353258133,
-0.0576658621430397,
0.05119289457798004,
0.0012446136679500341,
0.02433236502110958,
-0.03864734247326851,
0.0048755984753370285,
-0.011886782012879848,
0.009927722625434399,
0.024618161842226982,
0.058869585394859314,
-0.008185391314327717,
-0.017449183389544487,
0.05880174785852432,
-0.03925793617963791,
-0.047074370086193085,
0.015691936016082764,
0.04407206177711487,
0.006296980194747448,
-0.004220730159431696,
-0.009791026823222637,
0.027327654883265495,
-0.0218452550470829,
-0.007432245649397373,
-0.003875317284837365,
-0.009228742681443691,
0.013175803236663342,
0.026354031637310982,
-0.06089283153414726,
0.03035968542098999,
0.002314751036465168,
-0.04151959344744682,
-0.03254453092813492,
-0.006395142991095781,
0.04012694209814072,
-0.0012058934662491083,
-0.010584428906440735,
0.02635306306183338,
-0.03867055103182793,
-0.008739280514419079,
-0.022232860326766968,
0.03449755162000656,
-0.052575256675481796,
0.002726280130445957,
-0.020588790997862816,
0.08032671362161636,
-0.0341445654630661,
0.0017095600487664342,
0.00542854331433773,
-0.023259291425347328,
-0.011130611412227154,
-0.029662074521183968,
-0.007847282104194164,
-0.002795078558847308,
0.001935271080583334,
-0.01750912517309189,
-0.043857380747795105,
-0.017460742965340614,
0.029802173376083374,
0.01157709676772356,
0.03497288003563881,
-0.011459936387836933,
-0.0028217474464327097,
0.008521543815732002,
-0.015182338654994965,
0.03827862814068794,
-0.03399566188454628,
0.019997838884592056,
-0.013644075952470303,
-0.022737544029951096,
-0.04631195589900017,
-0.002852819627150893,
0.023683752864599228,
0.03650815039873123,
0.024151189252734184,
0.005096024367958307,
0.0008247607038356364,
-0.0024972446262836456,
-0.03174871206283569,
0.011172267608344555,
-0.04311121627688408,
-0.03802734240889549,
-0.04127711430191994,
0.019315356388688087,
-0.0007193980272859335,
0.04069676250219345,
0.02180713601410389,
-0.03481201454997063,
0.011144548654556274,
0.02131514437496662,
0.007504296489059925,
-0.018842225894331932,
-0.020881257951259613,
-0.02297324128448963,
-0.02187092788517475,
-0.025803158059716225,
-0.002269760239869356,
0.0005019353120587766,
0.018051791936159134,
0.0024761375971138477,
0.028622040525078773,
0.024384796619415283,
-0.032334789633750916,
-0.007163636386394501,
0.02728315256536007,
-0.009833678603172302,
-0.02937381900846958,
0.017142243683338165,
0.02144727110862732,
-0.053389228880405426,
-0.030663734301924706,
-0.02348075807094574,
0.01505953073501587,
0.008241157978773117,
0.04306875169277191,
-0.030361348763108253,
0.06853744387626648,
-0.006096762605011463,
0.021693961694836617,
-0.06747701019048691,
-0.008385918103158474,
-0.04360261932015419,
-0.00027973990654572845,
-0.009562958031892776,
-0.01780509203672409,
-0.02712029591202736,
0.015030506998300552,
-0.01920793019235134,
-0.026250502094626427,
0.02614547125995159,
0.013448589481413364,
-0.027691971510648727,
0.04305613785982132,
0.031228579580783844,
-0.003034653840586543,
0.0451064258813858,
0.0020169587805867195,
-0.03219177573919296,
0.0564909428358078,
-0.0443539097905159,
-0.060065656900405884,
0.03393951803445816,
-0.05378912761807442,
0.01624467968940735,
0.010829504579305649,
-0.026326313614845276,
-0.013822870329022408,
0.07101352512836456,
0.005534616764634848,
0.014965270645916462,
0.007867896929383278,
-0.006121110636740923,
-0.008190826512873173,
0.01940528117120266,
0.024264279752969742,
-0.019427139312028885,
-0.009811945259571075,
0.02114684320986271,
0.02403288520872593,
0.01616220735013485,
-0.01885698176920414,
0.0069510797038674355,
0.006192592438310385,
-0.003399585373699665,
0.014326312579214573,
-0.01651707850396633,
0.02708350121974945,
0.04975514858961105,
-0.08864548057317734,
0.02537921629846096,
0.014973481185734272,
0.01369514036923647,
-0.09182605892419815,
0.00014332799764815718,
0.004295740742236376,
0.004666055087000132,
0.030182257294654846,
-0.019412247464060783,
0.021843668073415756,
0.017582323402166367,
-0.0680072233080864,
0.015245028771460056,
-0.030844587832689285,
-0.0042635295540094376,
-0.00954088568687439,
-0.013955577276647091,
-0.026968641206622124,
0.0411720834672451,
0.028113307431340218,
0.04672348126769066,
-0.011749188415706158,
-0.0006856769323348999,
0.014874285086989403,
-0.018508918583393097,
-0.013698269613087177,
0.03590155392885208,
-0.045582111924886703,
0.01190317701548338,
0.09021702408790588,
-0.013845034874975681,
-0.03817348927259445,
0.0375269390642643,
-0.00017579220002517104,
0.011930711567401886,
0.003182078478857875,
-0.011037197895348072,
-0.0010033564176410437,
0.018900280818343163,
0.03750056400895119,
0.0059699080884456635,
-0.006783633027225733,
0.008705180138349533,
-0.041433319449424744,
0.04958253726363182,
0.02231900580227375,
-0.0029132962226867676,
0.024267157539725304,
-0.046031370759010315,
-0.015187873505055904,
0.022979505360126495,
-0.020649848505854607,
-0.001591729698702693,
-0.01018674299120903,
0.047877464443445206,
0.011283940635621548,
-0.031231939792633057,
-0.0016528596170246601,
-0.06261981278657913,
0.011402632109820843,
0.0032531199976801872,
0.008386798202991486,
-0.0014570632483810186,
0.025202803313732147,
0.00020180181309115142,
-0.0003657297056633979,
-0.0014149356866255403,
-0.03390596807003021,
0.006463255267590284,
-0.03372564539313316,
0.02718281000852585,
-0.01562846265733242,
0.03165852651000023,
0.0016766497865319252,
-0.050653669983148575,
-0.02187560871243477,
0.0756789892911911,
0.019618475809693336,
0.0001216841337736696,
-0.026036322116851807,
0.019192559644579887,
-0.01093041431158781,
-0.10404551029205322,
0.020778529345989227,
-0.004222292453050613,
0.009098496288061142,
-0.026965146884322166,
-0.015596725046634674,
-0.007808240130543709,
0.02109268680214882,
0.016360076144337654,
-0.018930498510599136,
-0.020073894411325455,
0.032966624945402145,
-0.02638324163854122,
0.008393495343625546,
-0.037786394357681274,
-0.01310804020613432,
-0.014680273830890656,
-0.05534215644001961,
0.006455614697188139,
-0.014247192069888115,
-0.0003410890931263566,
0.01118481531739235,
0.0071657090447843075,
-0.01742100901901722,
0.06283482909202576,
0.003297206247225404,
-0.018014676868915558,
0.07070373743772507,
0.020516004413366318,
0.008192348293960094,
0.06762930750846863,
-0.018822787329554558,
0.04936247691512108,
0.008831252343952656,
-0.0049872025847435,
-0.010582774877548218,
0.008486263453960419,
-0.038622088730335236,
-0.01728956401348114,
0.011234410107135773,
-0.013414064422249794,
-0.0056279744021594524,
0.009016860276460648,
0.003943145740777254,
0.04492558166384697,
-0.035844627767801285,
-0.0077779898419976234,
0.013022487983107567,
0.025434810668230057,
0.03887278586626053,
-0.011620864272117615,
0.005562046077102423,
0.019887205213308334,
-0.019650448113679886,
-0.028840824961662292,
0.06283308565616608,
0.03410714864730835,
0.03858356550335884,
0.024695735424757004,
0.04041678085923195,
0.004300672560930252,
-0.007423255126923323,
0.02933001145720482,
0.06268762052059174,
-0.03788185492157936,
-0.002185752848163247,
0.0007850474794395268,
-0.01598554104566574,
0.0067254467867314816,
0.025569692254066467,
-0.009388281032443047,
0.07536866515874863,
-0.01162206381559372,
-0.018442640081048012,
0.0013330747606232762,
-0.024355078116059303,
0.0037365059833973646,
0.05009045824408531,
0.009605406783521175,
0.04574153572320938,
0.020930279046297073,
0.014825697056949139,
-0.008536272682249546,
-0.010926331393420696,
0.024305325001478195,
-0.0034721477422863245,
-0.004393793176859617,
-0.008702930994331837,
0.0024816610384732485,
-0.010615937411785126,
0.003335457993671298,
-0.029801825061440468,
-0.007793285418301821,
0.01636199653148651,
0.012550771236419678,
0.027345307171344757,
-0.06527300179004669,
0.004565733019262552,
-0.0035891791339963675,
0.04537317156791687,
-0.09892153739929199,
0.014221605844795704,
-0.004709097556769848,
-0.000007875971277826466,
-0.019595151767134666,
-0.006479681935161352
] |
<p>Up to now, nothing else than one Standard Model (SM) Higgs boson-like resonance has been found at the LHC while many predictions based on effective theories using supersymmetry require several Higgs scalars and needs an entourage of sparticles close in mass to tame its quantum instabilities (I borrow more or less from <a href="http://books.google.fr/books?id=kKKAfrfCofcC&pg=PA58&lpg=PA58&dq=james%20wells%20predictions%20based%20on%20effective%20theories%20%20require%20that%20the%20Higgs%20boson%20needs%20an%20entourage%20of%20particles%20close%20in%20mass%20to%20tame%20its%20quantum%20instabilities&source=bl&ots=VpWPssqr1d&sig=vKIWPRLTI7dgfH0bZuzWSXfwvIU&hl=fr&sa=X&ei=XvzLUYTuGcO2hAeRiYHwBg&ved=0CCwQ6AEwAA#v=onepage&q=james%20wells%20predictions%20based%20on%20effective%20theories%20%20require%20that%20the%20Higgs%20boson%20needs%20an%20entourage%20of%20particles%20close%20in%20mass%20to%20tame%20its%20quantum%20instabilities&f=false" rel="nofollow">James D. Wells</a>). </p>
<p>On the other hand, the spectral and almost-commutative extension of the SM by <a href="http://arxiv.org/abs/1208.1030" rel="nofollow">Chamseddine and Connes</a>, expects only one Higgs boson without other particles in the TeV range. In this noncommutative approach spacetime appears as the product (in the sense of fibre bundles) of a continuous manifold by a discrete space and it has been proved by <a href="http://arxiv.org/abs/hep-th/0104108" rel="nofollow">Martinetti and Wulkenhaar</a> that under precise conditions, the metric aspect of ”continuum × discrete” spaces reduces to the simple picture of two copies of the manifold. </p>
<p><strong>Could it be that this picture of a two-sheets spacetime helps to overcome the technical naturalness issue related to the standard model Higgs (<em>replacing temptatively a low energy supersymmetry by a new geometric framework</em>) and has to be taken seriously in order to progress in the understanding of physics beyond the SM?</strong> </p>
<p>To ask it differently:</p>
<p><strong>Reminding that the Standard model like Higgs boson is a <em>natural</em> consequence of the noncommutative geometric framework, could it be that the <em>discreteness of space-time</em> usually expected at the Planck scale from quantum gravity already shows up <em>at the electroweak scale</em> through the very existence of the already discovered Higgs boson?</strong>
(this formulation could require a new, yet to be defined, heuristic meaning for the term: <em>naturalness</em>)</p>
<p>Last but not least, it is worth noting that to postdict the correct mass of the Higgs boson detected at LHC8, the last version of the spectral model relies on a weak coupling with another scalar that shows up "naturally" in the spectral action just like the Higgs. This "<a href="http://books.google.fr/books?id=1d2Dm4C3nSMC&pg=PA196&lpg=PA196&dq=big%20broson%20connes&source=bl&ots=vOYNMuyTuH&sig=kYYq_fYp5TWsvNghgqzglUGz_p8&hl=fr&sa=X&ei=XODVUeCyF8KlPYG8gYgJ&ved=0CEgQ6AEwBA#v=onepage&q=big%20broson%20connes&f=false" rel="nofollow">big brother</a>" from the Higgs boson is expected to acquire a vev generating a mass scale above $10^{11}GeV$ for right-handed Majorana neutrinos. It could thus be responsible for a type I see-saw mechanism explaining the neutrino phenomenology beyond the minimal SM. </p>
<p><em>May be noncommutative geometry can help to make effective theories more alive and kicking!
In memoriam Ken Wilson</em></p>
<p><em>To celebrate the 4th of July "IndependentHiggsday", I wish a happy birthday to the lightest scalar field of the Standard Model and I congratulate experimentalists who work hard to prove physics is alive (and <a href="http://www.physicstoday.org/resource/1/phtoad/v53/i7/p15_s1?bypassSSO=1" rel="nofollow">not ordered</a> by theories ;-)!</em></p>
<p>EDIT : The title of the question has been changed in an attempt to improve clarity (after reading <em><a href="http://indico.cern.ch/getFile.py/access?contribId=27&sessionId=3&resId=0&materialId=slides&confId=239571" rel="nofollow">The Higgs: so simple yet so unnatural</a></em>); the former title was: </p>
<blockquote>
<p>Doubling the number of elementary particles or "doubling space-time"
to accommodate Higgs boson phenomenology at 8TeV?</p>
</blockquote> | 1,416 | [
0.002231890568509698,
-0.04717714712023735,
0.042330313473939896,
-0.05065518617630005,
0.05738798528909683,
0.031097427010536194,
-0.016562609001994133,
-0.05678769201040268,
-0.013679630123078823,
-0.0400446355342865,
0.05012839287519455,
0.010589352808892727,
0.07001856714487076,
0.011187465861439705,
-0.012664396315813065,
-0.000599724124185741,
-0.006749565713107586,
-0.01678483746945858,
-0.019241254776716232,
-0.0038262747693806887,
0.023132221773266792,
0.04920075461268425,
-0.011171192862093449,
0.025636151432991028,
-0.0095762237906456,
-0.0005542141734622419,
0.04407189041376114,
0.021407412365078926,
0.007044848054647446,
0.054254453629255295,
-0.057681240141391754,
-0.04193011671304703,
-0.002648780355229974,
0.03130488470196724,
0.0055282567627727985,
0.018807727843523026,
0.047586437314748764,
-0.0676061287522316,
0.00813143327832222,
0.016468461602926254,
-0.05722935497760773,
-0.02278505265712738,
-0.03252510353922844,
0.04731464758515358,
-0.03778634965419769,
-0.018509699031710625,
-0.022929148748517036,
0.016480760648846626,
0.09242100268602371,
-0.064420185983181,
0.07691183686256409,
0.01972263865172863,
0.027723968029022217,
0.02039581723511219,
-0.01135075744241476,
-0.005349643528461456,
0.031279318034648895,
0.04791005700826645,
0.01739475317299366,
-0.055782075971364975,
-0.050460707396268845,
-0.040831174701452255,
0.005878585856407881,
-0.01988617330789566,
-0.03927457332611084,
0.037868816405534744,
0.001252578105777502,
-0.00812593661248684,
0.021683208644390106,
-0.005136086139827967,
0.026206061244010925,
-0.004689882509410381,
0.006152408197522163,
-0.0008860497619025409,
0.04006166756153107,
-0.021935204043984413,
-0.005270204972475767,
-0.00711510144174099,
0.02883172407746315,
0.04547961428761482,
0.01331392116844654,
-0.004463301971554756,
-0.002576385624706745,
0.007395319174975157,
0.022044619545340538,
-0.03334344923496246,
0.07105018943548203,
-0.03332352265715599,
-0.011174648068845272,
0.012604068033397198,
-0.0246070995926857,
-0.0054776896722614765,
0.10018441826105118,
-0.03006899729371071,
-0.022174909710884094,
0.0069707478396594524,
0.02782602794468403,
0.03898560628294945,
-0.048702750355005264,
-0.004345311317592859,
-0.011868258938193321,
0.00046260992530733347,
-0.010296735912561417,
0.07865023612976074,
0.03239477798342705,
-0.04587710276246071,
-0.02599816396832466,
-0.03155037760734558,
-0.05804028734564781,
-0.03639987111091614,
-0.018207130953669548,
0.01086656004190445,
-0.0032582206185907125,
-0.0022855494171380997,
-0.02989218570291996,
-0.04130850359797478,
0.0011427029967308044,
-0.041889458894729614,
0.09960593283176422,
0.052761856466531754,
0.05063280090689659,
-0.030519556254148483,
0.0074052331037819386,
-0.019497456029057503,
-0.0716041550040245,
0.016245488077402115,
0.05163238197565079,
-0.015122790820896626,
-0.06499292701482773,
0.025656847283244133,
0.011273616924881935,
-0.016435746103525162,
-0.0036165749188512564,
0.024402428418397903,
0.042376089841127396,
-0.048497844487428665,
-0.11725997179746628,
-0.05419188365340233,
0.08420147001743317,
-0.019977571442723274,
-0.012246927246451378,
-0.03004334308207035,
-0.02688858099281788,
0.054637834429740906,
0.09763427823781967,
-0.016467442736029625,
-0.002163609489798546,
0.013965184800326824,
0.018592193722724915,
0.004414397291839123,
0.0011711285915225744,
-0.015890000388026237,
-0.004012659192085266,
0.0061975340358912945,
-0.045883577316999435,
-0.054077353328466415,
0.03533614054322243,
0.04168010875582695,
-0.006244188640266657,
0.03793971985578537,
0.07334015518426895,
0.00734495697543025,
0.0012380753178149462,
0.022086599841713905,
0.02591654285788536,
-0.03848937526345253,
0.05216413363814354,
-0.003615932073444128,
0.019609637558460236,
0.0303112231194973,
-0.021808208897709846,
-0.01666255109012127,
0.019036611542105675,
0.024944452568888664,
-0.010874471627175808,
-0.03028605878353119,
-0.003251579822972417,
-0.025478022173047066,
-0.014281866140663624,
-0.02326536737382412,
-0.04872458428144455,
-0.036885835230350494,
-0.031329195946455,
0.0010075063910335302,
0.030358323827385902,
0.04390629008412361,
-0.020303158089518547,
-0.007139489520341158,
0.001560449367389083,
-0.051465678960084915,
-0.02995167300105095,
-0.06221085041761398,
-0.05184971168637276,
0.024136986583471298,
-0.02385876514017582,
0.05818382650613785,
-0.007995100691914558,
0.007111996412277222,
-0.0330418199300766,
-0.008756603114306927,
0.01293852087110281,
0.039734385907649994,
0.032394230365753174,
0.023096738383173943,
0.0202797781676054,
0.05974660813808441,
0.04405434429645538,
-0.015612623654305935,
0.03017279878258705,
-0.007771418429911137,
-0.07429003715515137,
0.002234561135992408,
-0.0215742364525795,
0.001076622400432825,
0.0010961880907416344,
0.010864892974495888,
0.024601655080914497,
-0.025751134380698204,
-0.010510802268981934,
0.00669051380828023,
-0.0319845974445343,
0.027754327282309532,
-0.009893221780657768,
0.010942433029413223,
-0.01460462436079979,
0.03122875839471817,
0.0013772688107565045,
0.02898699790239334,
-0.03500107303261757,
-0.0016306453617289662,
-0.053996313363313675,
0.0008327052346430719,
0.00024754295009188354,
0.05341638997197151,
-0.02211582660675049,
0.04123622924089432,
0.04009367153048515,
0.032708991318941116,
0.05961661413311958,
0.03223465755581856,
-0.03895477578043938,
-0.04592789337038994,
0.034123774617910385,
0.025519374758005142,
0.022337766364216805,
0.022841574624180794,
0.023807819932699203,
0.005850109737366438,
0.016242029145359993,
0.006295493803918362,
-0.02355172298848629,
0.015978224575519562,
0.007050930988043547,
-0.03625454008579254,
-0.011910485103726387,
-0.03517024219036102,
0.015795765444636345,
-0.001096824067644775,
0.03453114628791809,
0.018126584589481354,
-0.002729931380599737,
-0.00009687121928436682,
0.0031979456543922424,
-0.03492629900574684,
0.009744546376168728,
-0.014783050864934921,
-0.020991159602999687,
-0.016908476129174232,
0.01821986585855484,
-0.04675021767616272,
0.03668894246220589,
-0.02845899946987629,
0.0017503536073490977,
-0.009464866481721401,
-0.015081663616001606,
0.02954842895269394,
-0.007036952767521143,
0.03155595436692238,
-0.049930475652217865,
-0.009489357471466064,
0.04936705902218819,
-0.016936270520091057,
0.023798737674951553,
0.01691441796720028,
-0.046803928911685944,
-0.029612265527248383,
-0.07278310507535934,
-0.01713631860911846,
0.035335641354322433,
-0.01712263561785221,
-0.01862414740025997,
0.0044828238897025585,
-0.003585833590477705,
-0.062274787575006485,
-0.03404628485441208,
-0.00032581749837845564,
0.013992276042699814,
-0.024890722706913948,
-0.002229014877229929,
0.04105735570192337,
0.022159403190016747,
-0.06824634224176407,
0.018866989761590958,
0.005259588826447725,
-0.007463124580681324,
-0.023257721215486526,
-0.006249006371945143,
-0.021248040720820427,
-0.055893491953611374,
0.06155279651284218,
0.04933667927980423,
-0.015910567715764046,
0.0077749816700816154,
-0.057628463953733444,
-0.0184062160551548,
-0.01912548765540123,
-0.030226407572627068,
0.04933398589491844,
-0.007679451256990433,
-0.03303876519203186,
0.08196616917848587,
0.008930248208343983,
-0.002447844250127673,
-0.007823795080184937,
0.003073250176385045,
-0.02689295820891857,
-0.05229361727833748,
0.012374116107821465,
0.03261713683605194,
0.010200995951890945,
0.01316475123167038,
0.04024576023221016,
0.02352156676352024,
0.02276517078280449,
0.0026099339593201876,
-0.0266704224050045,
0.007307522930204868,
-0.021832257509231567,
0.000831657787784934,
0.03841555491089821,
-0.006319532636553049,
-0.01844855397939682,
-0.013484355062246323,
-0.0037659641820937395,
0.017785027623176575,
-0.01831653341650963,
-0.044208452105522156,
0.059541329741477966,
0.0048586102202534676,
0.03557980805635452,
0.0043817609548568726,
0.012038707733154297,
0.022390510886907578,
-0.05806316062808037,
-0.0027897825930267572,
-0.004638431128114462,
0.009456572122871876,
-0.010840018279850483,
0.0276636965572834,
0.005524982698261738,
0.03404146432876587,
-0.029312441125512123,
-0.02669603005051613,
-0.001011953572742641,
-0.03708269074559212,
0.014162877574563026,
-0.01465493906289339,
-0.04101626202464104,
0.021912986412644386,
0.033116262406110764,
-0.012045384384691715,
-0.01248150784522295,
0.004726058803498745,
-0.025521831586956978,
-0.03240332007408142,
-0.022492147982120514,
-0.016305556520819664,
0.03372325003147125,
-0.010816631838679314,
0.020839080214500427,
0.009908024221658707,
0.008541002869606018,
-0.034654200077056885,
-0.03112269751727581,
-0.07908877730369568,
0.028252892196178436,
-0.03472694754600525,
0.002661044243723154,
0.018516087904572487,
-0.03691034018993378,
-0.030062193050980568,
0.024839896708726883,
-0.031978294253349304,
-0.044186148792505264,
0.015146767720580101,
-0.03772498667240143,
0.014822596684098244,
-0.029613807797431946,
-0.025152835994958878,
-0.019775515422225,
0.006260689347982407,
0.054060593247413635,
-0.03697876259684563,
-0.008067924529314041,
-0.006990678608417511,
-0.06154990941286087,
-0.02184445597231388,
0.011213988065719604,
0.051265615969896317,
0.006696324795484543,
0.00829269178211689,
0.048331957310438156,
0.005605238024145365,
-0.09128774702548981,
-0.012874591164290905,
0.05944965407252312,
0.042380012571811676,
0.018257074058055878,
-0.009828340262174606,
0.02107834815979004,
-0.03566297888755798,
-0.017610132694244385,
0.04649672284722328,
0.06570129096508026,
-0.0057680788449943066,
-0.012156931683421135,
0.03389247506856918,
0.0067437272518873215,
-0.019274787977337837,
0.07082339376211166,
0.034966304898262024,
-0.012126311659812927,
-0.025229977443814278,
-0.030060699209570885,
0.022107427939772606,
-0.001743639586493373,
-0.00032601793645881116,
0.011655584909021854,
-0.009550667367875576,
-0.018982883542776108,
-0.008327377028763294,
0.005870441440492868,
0.04882516339421272,
-0.054677654057741165,
-0.0010921481298282743,
0.010211577638983727,
0.018885543569922447,
-0.031572047621011734,
-0.008043363690376282,
-0.007557507138699293,
0.039541590958833694,
0.04101729765534401,
0.005842110142111778,
0.02138848975300789,
-0.09261363744735718,
-0.019353795796632767,
0.04911167174577713,
0.027440853416919708,
-0.023794125765562057,
-0.010884945280849934,
-0.03631185367703438,
-0.01507987268269062,
0.05729587376117706,
-0.04950494319200516,
0.028397532179951668,
0.02571938931941986,
-0.005380197893828154,
-0.02107846364378929,
-0.005156373605132103,
-0.0032634029630571604,
0.030927475541830063,
0.0033691043499857187,
0.02397352270781994,
-0.0019233168568462133,
-0.015804903581738472,
-0.03327829763293266,
0.013232477009296417,
0.014914491213858128,
0.00040281101246364415,
0.01642487198114395,
0.010141698643565178,
0.014763233251869678,
0.013728835619986057,
-0.006905481219291687,
-0.12574291229248047,
0.00665225088596344,
0.006477206014096737,
-0.04937710985541344,
0.02688644640147686,
-0.022204086184501648,
-0.04826163128018379,
0.028467385098338127,
0.030848609283566475,
0.01612040400505066,
-0.03046923689544201,
-0.05766865983605385,
0.019415458664298058,
0.019770938903093338,
0.008982847444713116,
0.03569798544049263,
0.025578198954463005,
-0.05119721218943596,
-0.0026498448569327593,
-0.021509191021323204,
-0.0023481857497245073,
-0.021894775331020355,
-0.006123356055468321,
-0.04120246693491936,
-0.004255127627402544,
-0.06495020538568497,
0.06159864738583565,
-0.01682264544069767,
0.0012245465768501163,
0.005043793469667435,
-0.0007943933014757931,
-0.007284231949597597,
0.037537336349487305,
0.009251410141587257,
-0.0013107858831062913,
-0.00812025461345911,
0.05223317816853523,
-0.015293166972696781,
-0.009849131107330322,
0.06238315626978874,
0.001327422447502613,
0.007493471726775169,
0.0020629039499908686,
-0.019326334819197655,
0.010054913349449635,
-0.0050215162336826324,
-0.01350132655352354,
0.022422095760703087,
-0.05716446042060852,
0.0528261698782444,
-0.015386971645057201,
0.030891479924321175,
0.0007432684651575983,
-0.015590699389576912,
-0.027189819142222404,
0.032589782029390335,
-0.001593532389961183,
-0.024784548208117485,
-0.00594342453405261,
0.0063642701134085655,
0.026472968980669975,
-0.0061965323984622955,
-0.07889349013566971,
0.00005959045665804297,
-0.0033038409892469645,
0.014674128033220768,
-0.030189795419573784,
-0.003716265084221959,
0.010807867161929607,
-0.048207879066467285,
-0.004555755294859409,
-0.0371275432407856,
0.017243610695004463,
-0.07087880373001099,
0.03785385563969612,
0.01435071136802435,
0.03145410493016243,
0.009945760481059551,
0.01419136393815279,
0.022635284811258316,
0.018765630200505257,
0.0049884687177836895,
0.00535466568544507,
-0.015230031684041023,
0.027605393901467323,
-0.0038487708661705256,
-0.03878124803304672,
-0.02987762913107872,
-0.006262659095227718,
0.012804468162357807,
-0.018838854506611824,
0.013876458629965782,
0.05591989681124687,
0.018254965543746948,
0.03551284968852997,
-0.021573858335614204,
0.01940327137708664,
0.001101388013921678,
0.017743626609444618,
0.015106048434972763,
-0.006785923149436712,
0.01693100668489933,
-0.034312762320041656,
0.027132248505949974,
0.0023776728194206953,
-0.01730889268219471,
-0.009896918199956417,
0.02962435968220234,
0.0014734489377588034,
-0.00854793656617403,
0.010282536968588829,
-0.033172138035297394,
0.017453400418162346,
-0.014893796294927597,
0.04810595139861107,
-0.018679099157452583,
-0.005851087160408497,
0.00947278831154108,
-0.05166645348072052,
-0.03181848302483559,
-0.027344929054379463,
0.04247215762734413,
0.015308327041566372,
0.010477621108293533,
0.006805102806538343,
-0.036365099251270294,
0.007294133305549622,
-0.029101217165589333,
-0.01004874799400568,
-0.001089146244339645,
0.03916753828525543,
-0.0009611299028620124,
-0.038344867527484894,
-0.011175519786775112,
0.042318738996982574,
0.013183774426579475,
-0.013051311485469341,
0.01823321357369423,
0.03290727362036705,
0.03649898245930672,
-0.0053284368477761745,
-0.014614688232541084,
0.01843804307281971,
0.06364167481660843,
-0.0420617014169693,
0.026780733838677406,
0.027998793870210648,
-0.009689105674624443,
0.02901589311659336,
0.007699986454099417,
0.007834761403501034,
-0.010777120478451252,
-0.018562085926532745,
-0.0408434197306633,
0.05455425754189491,
0.03026389703154564,
0.009739684872329235,
-0.005521252751350403,
0.022442497313022614,
0.0039918674156069756,
0.02745213732123375,
0.03852878510951996,
-0.00833872426301241,
-0.07930532097816467,
-0.04131900891661644,
-0.0371977761387825,
-0.029617637395858765,
0.053996145725250244,
-0.015914523974061012,
-0.039650700986385345,
0.009971880353987217,
0.001464165630750358,
0.04856362193822861,
-0.014065639115869999,
0.028650358319282532,
-0.004105038940906525,
0.001109787728637457,
-0.016108743846416473,
0.019400257617235184,
-0.039503201842308044,
0.010554535314440727,
0.16594147682189941,
0.06521373987197876,
0.025589577853679657,
-0.0678592324256897,
0.014062964357435703,
-0.008348304778337479,
-0.0017019492806866765,
-0.03574754670262337,
0.012994254007935524,
-0.019667362794280052,
-0.00833185389637947,
0.009774813428521156,
0.04183055832982063,
0.009876154363155365,
-0.006773106288164854,
0.015139400959014893,
-0.04049046337604523,
-0.036248233169317245,
-0.0357939638197422,
0.028209269046783447,
-0.0018233212176710367,
-0.0021289896685630083,
-0.009409859776496887,
0.033364199101924896,
-0.020117489621043205,
0.023336701095104218,
-0.019405487924814224,
-0.03647877275943756,
0.011046141386032104,
-0.009945311583578587,
-0.013346468098461628,
-0.03403649479150772,
0.00018018673290498555,
0.00017647846834734082,
-0.0028982984367758036,
0.02368144504725933,
0.010242214426398277,
-0.011834426783025265,
0.022869465872645378,
0.045427192002534866,
0.020095620304346085,
-0.01191946305334568,
0.02387477271258831,
0.03448040038347244,
-0.05127124860882759,
-0.023952776566147804,
-0.011762159876525402,
0.0625670850276947,
0.013659985736012459,
-0.018659498542547226,
-0.0028673859778791666,
-0.006684459745883942,
-0.009974072687327862,
0.003781515872105956,
-0.026783790439367294,
-0.026822753250598907,
0.021952582523226738,
-0.032598432153463364,
-0.0118314353749156,
0.004599025472998619,
0.022317873314023018,
0.016317712143063545,
0.03059324063360691,
0.013933447189629078,
0.0019192827166989446,
-0.038513850420713425,
0.00854481104761362,
0.026744168251752853,
0.026707101613283157,
0.004259155131876469,
-0.033410608768463135,
0.026180148124694824,
-0.02519087679684162,
-0.0048682475462555885,
0.009871394373476505,
0.018855039030313492,
0.03979911282658577,
0.015238242223858833,
-0.001216304604895413,
-0.04234956577420235,
-0.013986947014927864,
0.056760307401418686,
-0.001066921278834343,
-0.002484197961166501,
-0.009608025662600994,
-0.01988033764064312,
0.00951510202139616,
0.011423695832490921,
-0.04697825014591217,
0.0032792589627206326,
0.0000025787180675251875,
0.04270647466182709,
0.023394562304019928,
-0.03406611457467079,
-0.008296281099319458,
-0.009416612796485424,
-0.031908147037029266,
0.010087640956044197,
0.014073299244046211,
0.04089934751391411,
-0.0033672316931188107,
0.02024485357105732,
0.006448554806411266,
0.08194585889577866,
-0.010112838819622993,
-0.02839803881943226,
0.03172372281551361,
-0.022561440244317055,
-0.004829280078411102,
0.05409747362136841,
0.050946060568094254,
-0.011533497832715511,
-0.0440848283469677,
-0.0038771508261561394,
-0.005380263086408377,
0.026785921305418015,
0.004575253929942846,
-0.048209965229034424,
0.008840368129312992,
-0.00267717894166708,
0.05039353668689728,
-0.0023309628013521433,
-0.029707400128245354,
-0.017460083588957787,
0.005425552371889353,
-0.026064589619636536,
-0.0018908942583948374,
0.010026652365922928,
0.036141637712717056,
-0.017095865681767464,
-0.007256318815052509,
0.014797281473875046,
0.011247430928051472,
-0.03163185715675354,
-0.0063194772228598595,
0.009750659577548504,
0.012800922617316246,
0.039157938212156296,
0.004114367067813873,
-0.035101231187582016,
0.01829691417515278,
-0.02449582889676094,
-0.07287593930959702,
0.03117426484823227,
0.010132568888366222,
-0.007248258218169212,
0.020842235535383224,
-0.023207206279039383,
-0.04472190514206886,
0.04565361514687538,
-0.0338270403444767,
-0.02096375823020935,
0.015052590519189835,
0.0012419045669957995,
-0.034689970314502716,
0.00914990808814764,
-0.016924535855650902,
0.02336074225604534,
-0.006217306479811668,
0.0164208821952343,
0.030825920403003693,
0.002696226816624403,
-0.03239510953426361,
-0.015639157965779305,
-0.017286937683820724,
0.056657034903764725,
-0.021306876093149185,
0.02957605943083763,
-0.00614661630243063,
0.022129639983177185,
-0.04143427312374115,
0.016171541064977646,
0.02542426995933056,
-0.008837446570396423,
-0.08876614272594452,
-0.029861334711313248,
-0.001003332668915391,
0.031319450587034225,
0.050088271498680115,
-0.035805851221084595,
0.03603899106383324,
0.043054431676864624,
-0.039504267275333405,
0.025868449360132217,
-0.03700091317296028,
-0.026826750487089157,
-0.012356670573353767,
0.005489376373589039,
-0.028790775686502457,
0.07055622339248657,
-0.0076293679885566235,
0.04323681816458702,
-0.02774187922477722,
-0.012999760918319225,
0.014772284775972366,
-0.012042058631777763,
-0.04824884608387947,
0.0005304156802594662,
0.0018742537358775735,
-0.02490171045064926,
0.053502172231674194,
0.0160815566778183,
-0.009685933589935303,
0.055509474128484726,
0.04814251884818077,
0.022143524140119553,
-0.019269175827503204,
0.045124005526304245,
0.01660834066569805,
0.011802947148680687,
0.032400086522102356,
-0.016277162358164787,
0.0002122537262039259,
-0.005829790607094765,
-0.011534393765032291,
0.051867686212062836,
0.018246179446578026,
0.01364970114082098,
0.006386346649378538,
-0.06560017168521881,
-0.025388069450855255,
0.0044397031888365746,
-0.02692175842821598,
0.005087064113467932,
0.0026853415183722973,
0.010423061437904835,
-0.024162156507372856,
-0.011086167767643929,
0.024641824886202812,
-0.06669603288173676,
0.025894436985254288,
0.04122094810009003,
0.028089500963687897,
0.01989896222949028,
0.046193450689315796,
-0.007295625749975443,
0.01892169937491417,
0.0234207920730114,
0.01957279071211815,
-0.02397126331925392,
-0.04631644859910011,
-0.010833368636667728,
-0.0005278928438201547,
0.05336903780698776,
0.01880936697125435,
-0.0013387731742113829,
-0.03766077384352684,
0.035822175443172455,
0.008288726210594177,
0.05700032785534859,
-0.020709482952952385,
-0.016088904812932014,
-0.0098623838275671,
-0.031243113800883293,
0.06298515200614929,
0.014454041607677937,
0.005809282884001732,
-0.03453834727406502,
-0.02854287065565586,
0.036249008029699326,
0.011696888133883476,
0.04227849096059799,
-0.01224641501903534,
-0.026256399229168892,
0.04302698373794556,
0.02643326297402382,
0.007685219869017601,
-0.025352805852890015,
-0.026064056903123856,
0.012386901304125786,
0.004948130343109369,
-0.00021638075122609735,
-0.017372209578752518,
-0.0033028502948582172,
0.049858808517456055,
0.03289271146059036,
0.002000859472900629,
0.024752536788582802,
0.01807267777621746,
-0.038355693221092224,
0.04734829440712929,
-0.0011665987549349666,
-0.04190904274582863,
0.0575125627219677,
0.00715324142947793,
0.013102523051202297,
0.020294105634093285,
-0.012145917862653732,
0.004467481281608343,
0.02607625722885132,
-0.024750303477048874,
-0.006701123435050249,
-0.00319498754106462,
-0.021045364439487457,
-0.00011014002666343004,
-0.04509541764855385,
-0.0002520805282983929,
0.03532424941658974,
-0.020222947001457214,
0.004431253299117088,
0.05322035029530525,
-0.0011134605156257749,
0.003953767940402031,
0.058326419442892075,
-0.012519314885139465,
-0.006423295475542545,
-0.010764560662209988,
0.028884027153253555,
0.03070816770195961,
0.02099316380918026,
0.011753545142710209,
0.0031623798422515392,
-0.0020037111826241016,
0.007497536018490791,
0.02851947769522667,
0.015875615179538727,
0.014835277572274208,
-0.022649819031357765,
-0.005823848303407431,
0.02150680497288704,
0.0006909776129759848,
-0.005783083848655224,
0.00981287844479084,
-0.01660373993217945,
0.0905979722738266,
-0.06656509637832642,
-0.01983731985092163,
-0.03266669809818268,
-0.028017809614539146,
0.0250836294144392,
0.013696280308067799,
-0.01608734019100666,
0.04181012511253357,
-0.03099641390144825,
-0.03177005425095558,
0.05086759477853775,
0.019569752737879753,
0.00797383114695549,
-0.07339589297771454,
-0.013146128505468369,
-0.006003157701343298,
-0.01507407333701849,
-0.007493187207728624,
-0.0019364195177331567,
-0.0035393841098994017,
0.0025340691208839417,
0.012833621352910995,
-0.001882394659332931,
0.014842156320810318,
0.00636319862678647,
-0.026759451255202293,
-0.020502684637904167,
0.014051780104637146,
-0.02448204532265663,
-0.005381768569350243,
-0.024818893522024155,
0.022333165630698204,
-0.05707256495952606,
-0.00903263222426176
] |
<p>In Feynman diagrams, fermionic loops are drawn like this:</p>
<p><img src="http://i.stack.imgur.com/JkPkc.png" alt="enter image description here"></p>
<p>While scalar loops are drawn as tadpoles:</p>
<p><img src="http://i.stack.imgur.com/kOKCX.png" alt="enter image description here"></p>
<p>I assume the difference comes from the scalar not having an anti-particle. But how should one imagine such a tadpole diagram? I can imagine the fermionic loop as creation of particle and antiparticle, but I am at loss to only get a faint idea what the scalar loop should illustrate.</p> | 1,417 | [
-0.01687491126358509,
-0.025017039850354195,
-0.007717901840806007,
0.003992672543972731,
0.015770629048347473,
0.02050109952688217,
0.021701185032725334,
-0.027376733720302582,
-0.01940407045185566,
-0.017233343794941902,
0.04042007401585579,
-0.011567946523427963,
0.05228257551789284,
-0.005023237783461809,
0.022990064695477486,
0.03362434357404709,
-0.012590091675519943,
-0.040560152381658554,
0.017445934936404228,
-0.047221384942531586,
-0.009992130100727081,
0.03154328837990761,
-0.007233551237732172,
0.029744194820523262,
-0.012138985097408295,
0.04443180933594704,
0.047582101076841354,
0.030198343098163605,
0.0011109584011137486,
0.05231882631778717,
-0.04175480827689171,
-0.05965610593557358,
0.017411494627594948,
0.007201963569968939,
0.0208373311907053,
0.0006046129856258631,
-0.011350789107382298,
-0.04146864265203476,
-0.008353566750884056,
0.01468516793102026,
-0.0126644941046834,
-0.007532823830842972,
-0.03816995769739151,
0.04490489885210991,
-0.039138223975896835,
-0.012389391660690308,
-0.042958468198776245,
0.01369057409465313,
0.08133641630411148,
-0.06941419839859009,
0.03285176679491997,
0.042120859026908875,
0.0371878445148468,
0.015736078843474388,
0.004320147447288036,
-0.0007413236307911575,
0.05433167889714241,
0.04883120581507683,
-0.025160014629364014,
-0.0510101392865181,
-0.030676675960421562,
-0.046333689242601395,
-0.03363489732146263,
-0.015196884982287884,
0.007142309565097094,
0.033833421766757965,
-0.012716635130345821,
0.002972907153889537,
-0.006534752435982227,
0.036336205899715424,
0.010069448500871658,
0.01506275124847889,
0.003055943176150322,
0.003311754669994116,
0.01980886422097683,
-0.03398122638463974,
0.012511328794062138,
0.020472705364227295,
0.042288888245821,
0.059336528182029724,
-0.035971544682979584,
0.046606119722127914,
0.0013490425189957023,
0.03803541138768196,
-0.00040872025419957936,
-0.01593327708542347,
0.048762205988168716,
-0.027529506012797356,
-0.0461178719997406,
0.04154427722096443,
-0.008750646375119686,
0.012193613685667515,
0.050755664706230164,
-0.0008828096324577928,
-0.0677313357591629,
0.010684698820114136,
0.009940046817064285,
0.032445281744003296,
0.024999376386404037,
-0.02402437850832939,
-0.023394158110022545,
-0.009720982052385807,
0.02805495262145996,
0.0876399576663971,
0.002457439200952649,
-0.019045038148760796,
-0.05901859700679779,
0.034982722252607346,
-0.023565124720335007,
0.004296033177524805,
-0.053315430879592896,
0.017973463982343674,
0.0013986033154651523,
0.03186092525720596,
0.032492924481630325,
-0.062029413878917694,
-0.016829537227749825,
-0.015983855351805687,
0.053415827453136444,
0.04231499135494232,
0.03228069096803665,
-0.03817823901772499,
0.06975478678941727,
-0.02211209200322628,
-0.09057752043008804,
0.00610530748963356,
0.02243448793888092,
-0.0056274509988725185,
-0.0033664449583739042,
0.02134721167385578,
-0.012923805974423885,
0.010235733352601528,
0.038760535418987274,
0.0095932362601161,
0.0607573427259922,
-0.01994703896343708,
-0.07540012896060944,
-0.049672845751047134,
0.024596093222498894,
-0.036298830062150955,
-0.004885918460786343,
-0.08654612302780151,
-0.02262607030570507,
0.01661669835448265,
0.07636485248804092,
-0.013385082595050335,
-0.02926582656800747,
0.0015602372586727142,
0.005233799573034048,
0.013062669895589352,
-0.0017959551187232137,
-0.006410359404981136,
-0.0232018381357193,
-0.040274329483509064,
-0.015512240119278431,
-0.04207736626267433,
0.04600659757852554,
0.014202713966369629,
-0.023432528600096703,
0.006618674844503403,
0.05813119560480118,
-0.03082333132624626,
0.03972248733043671,
0.012025733478367329,
-0.029007138684391975,
0.0017351947026327252,
0.08135813474655151,
0.007700685411691666,
-0.05482114851474762,
0.049752190709114075,
-0.04162955656647682,
0.0006061587482690811,
-0.017972784116864204,
0.030262067914009094,
0.06633435934782028,
-0.03735438361763954,
-0.028752192854881287,
0.004352862946689129,
0.021751822903752327,
-0.01372551266103983,
-0.0253659226000309,
-0.02531210146844387,
-0.03046489879488945,
-0.008606018498539925,
-0.01585070602595806,
0.05833347514271736,
-0.009999060072004795,
-0.011090372689068317,
0.004779472481459379,
-0.06606215238571167,
-0.04318564757704735,
-0.06302248686552048,
-0.014249715022742748,
0.03364335000514984,
-0.0311043169349432,
0.06590462476015091,
0.019336484372615814,
0.008928182534873486,
-0.020996257662773132,
-0.05301080271601677,
-0.04059495031833649,
0.06158200651407242,
-0.00043968207319267094,
0.013001776300370693,
-0.010358774103224277,
0.023046554997563362,
0.031555842608213425,
0.0008540329872630537,
0.019374607130885124,
-0.031184429302811623,
-0.0016982208471745253,
-0.038817740976810455,
-0.0162851270288229,
-0.01130277942866087,
0.027866587042808533,
-0.013807203620672226,
-0.00627340842038393,
0.0031968425028026104,
-0.010535378009080887,
0.047028008848428726,
-0.016481533646583557,
0.050287920981645584,
0.03477323427796364,
0.01840793527662754,
-0.029742853716015816,
0.010725713334977627,
0.02213991805911064,
0.005816534161567688,
-0.0048948414623737335,
-0.0007235252414830029,
-0.01808895729482174,
-0.019628724083304405,
0.046962983906269073,
0.008628644049167633,
-0.031806670129299164,
0.002362878993153572,
0.011111557483673096,
0.009962216950953007,
0.01630062609910965,
0.056784775108098984,
-0.03323189914226532,
-0.026623142883181572,
0.03152485191822052,
0.026346692815423012,
0.02554016187787056,
-0.014817995950579643,
0.06417151540517807,
-0.010920158587396145,
-0.002704240381717682,
-0.02750764600932598,
-0.02337251603603363,
0.03051314316689968,
-0.042949363589286804,
0.0057205939665436745,
0.011167884804308414,
-0.02337930165231228,
0.02800368145108223,
0.01602758839726448,
0.03474537283182144,
0.030021442100405693,
-0.030448203906416893,
-0.014770682901144028,
-0.029464973136782646,
-0.009799770079553127,
0.013507487252354622,
0.01049276813864708,
-0.01608550176024437,
-0.007824063301086426,
0.01979369856417179,
-0.020911911502480507,
0.03923846036195755,
-0.0048721847124397755,
-0.010145868174731731,
-0.03833255171775818,
0.008012840524315834,
0.05024171620607376,
-0.03278646245598793,
0.01834389567375183,
-0.01964290253818035,
-0.05033266916871071,
0.0055500054731965065,
-0.0006275043706409633,
0.022703832015395164,
0.0488152913749218,
-0.04032374545931816,
0.01232973113656044,
-0.060379788279533386,
-0.045264601707458496,
0.03202427551150322,
-0.0042528570629656315,
-0.012360019609332085,
-0.0018004708690568805,
-0.0322042852640152,
-0.02807612344622612,
-0.012447241693735123,
-0.013408745639026165,
0.038151033222675323,
-0.008692160248756409,
-0.0035885092802345753,
0.03851713240146637,
-0.009624146856367588,
0.006632143631577492,
0.016069158911705017,
-0.05776733532547951,
-0.054693613201379776,
-0.010558867827057838,
-0.008685348555445671,
0.017936836928129196,
-0.029189802706241608,
0.0410618893802166,
0.0344216451048851,
-0.05172628536820412,
0.025116950273513794,
-0.07275506854057312,
-0.014323404990136623,
-0.022945675998926163,
0.01330973207950592,
-0.013697285205125809,
-0.020961716771125793,
-0.06014808639883995,
0.07540520280599594,
0.018118612468242645,
-0.02617519721388817,
-0.014176130294799805,
0.011345881968736649,
-0.01980000175535679,
-0.0425640307366848,
0.013001902028918266,
0.025412505492568016,
-0.00947494525462389,
0.042706187814474106,
0.034048762172460556,
0.06693442910909653,
0.03267193213105202,
0.021370727568864822,
-0.029049914330244064,
-0.0069692060351371765,
-0.0250641368329525,
-0.014739801175892353,
0.04351522773504257,
-0.03327272832393646,
-0.034688107669353485,
0.014825766906142235,
0.019691117107868195,
0.024172460660338402,
0.015399113297462463,
-0.0019356426782906055,
0.04119149595499039,
0.038698792457580566,
0.02783186547458172,
-0.02104300446808338,
0.03461090847849846,
-0.01902463659644127,
-0.021272750571370125,
-0.010073629207909107,
0.018668100237846375,
0.04256021976470947,
-0.03758851811289787,
0.0004274844832252711,
0.027222387492656708,
0.04807112738490105,
-0.05209827423095703,
-0.011925351805984974,
-0.003517218865454197,
-0.017251821234822273,
0.0029599142726510763,
-0.02419024519622326,
-0.013575895689427853,
0.02003890462219715,
0.03756634518504143,
-0.020308544859290123,
0.017937876284122467,
-0.02026141807436943,
0.00019128949497826397,
-0.02297074720263481,
-0.014426708221435547,
0.0005462912959046662,
0.04315284639596939,
0.014939707703888416,
0.05004907771945,
-0.027059247717261314,
0.028376661241054535,
0.009132915176451206,
-0.024477891623973846,
-0.07882367819547653,
0.028242750093340874,
-0.05803157016634941,
-0.030598323792219162,
-0.02241835929453373,
-0.01720600388944149,
0.0015653499867767096,
-0.03222101554274559,
-0.02650577947497368,
0.007612235844135284,
-0.004680200479924679,
-0.038814038038253784,
0.009998008608818054,
-0.030197514221072197,
-0.000030049897759454325,
-0.045000024139881134,
0.02692960388958454,
0.029838385060429573,
-0.010860427282750607,
0.0269489586353302,
0.03972238674759865,
-0.04697832465171814,
0.01919586770236492,
-0.022196365520358086,
0.02016478218138218,
-0.006783005315810442,
-0.004852415528148413,
0.08350932598114014,
0.008260195143520832,
-0.05011499673128128,
-0.013585650362074375,
0.053267549723386765,
0.057593733072280884,
0.03338385000824928,
-0.018243832513689995,
0.02399313636124134,
-0.07382304221391678,
-0.022859392687678337,
-0.012766217812895775,
0.06500951945781708,
-0.00923862960189581,
0.04659233242273331,
0.023973161354660988,
0.027589790523052216,
-0.010752581059932709,
0.055366434156894684,
0.06981026381254196,
0.0009783486602827907,
-0.014397378079593182,
-0.049312569200992584,
0.007374103181064129,
-0.007190266624093056,
-0.00397303095087409,
0.010952906683087349,
0.01494727935642004,
-0.007633838336914778,
0.005358556751161814,
0.0335916206240654,
-0.010055704973638058,
-0.040900927037000656,
0.011428662575781345,
-0.011419927701354027,
0.028644297271966934,
-0.015865538269281387,
-0.01481524109840393,
0.004166501108556986,
0.06347526609897614,
0.017136843875050545,
0.03517039865255356,
-0.013868583366274834,
-0.04846212640404701,
-0.031499672681093216,
0.05416719242930412,
0.024055738002061844,
0.0056663514114916325,
-0.0221205223351717,
-0.04771696776151657,
0.006591458804905415,
0.09893255680799484,
-0.03318554535508156,
0.021280517801642418,
-0.029317036271095276,
-0.004074368160218,
-0.010669326409697533,
-0.01315563078969717,
-0.024648332968354225,
0.04178474098443985,
-0.012853696011006832,
0.0089262081310153,
-0.03854990005493164,
-0.022970104590058327,
0.008512018248438835,
0.0038161519914865494,
-0.027697626501321793,
0.02936501055955887,
0.02689945138990879,
0.029531946405768394,
0.02567887306213379,
0.043886225670576096,
0.01057419739663601,
-0.09196878224611282,
0.02760111726820469,
0.0005199256702326238,
-0.010971920564770699,
0.023408856242895126,
-0.030818743631243706,
-0.025516316294670105,
-0.00008996531687444076,
0.0006274271872825921,
0.009767185896635056,
0.001991948578506708,
-0.08379577100276947,
0.02218024432659149,
0.04009509086608887,
-0.013678347691893578,
0.02185044065117836,
0.028437260538339615,
-0.02558562159538269,
-0.010605958290398121,
-0.0191621333360672,
0.014315676875412464,
-0.018666794523596764,
0.028249133378267288,
-0.0456271730363369,
0.005928002763539553,
-0.01886630617082119,
0.07228322327136993,
-0.04436947777867317,
0.022448532283306122,
-0.0048524970188736916,
-0.03990955650806427,
-0.0291002094745636,
-0.01364725548774004,
0.01565001904964447,
-0.03222754970192909,
-0.017725035548210144,
-0.011486446484923363,
-0.010356864891946316,
-0.028579430654644966,
0.0041317446157336235,
-0.0250129085034132,
-0.001695759128779173,
0.027261676266789436,
-0.0005755041493102908,
0.04220675677061081,
-0.009388727135956287,
-0.04811737313866615,
0.03975452110171318,
-0.06408374011516571,
0.02390463836491108,
-0.006798029877245426,
-0.005292109213769436,
0.005680403672158718,
-0.07914038002490997,
-0.015236951410770416,
0.00800386257469654,
-0.015933074057102203,
-0.012168865650892258,
-0.06776989996433258,
0.054604966193437576,
0.024711383506655693,
0.01637502759695053,
-0.07769917696714401,
-0.06609409302473068,
0.028575098142027855,
-0.03506547585129738,
-0.04869411513209343,
-0.006176742725074291,
-0.012735494412481785,
-0.009719542227685452,
-0.052952416241168976,
0.013513977639377117,
0.047561824321746826,
-0.05753028765320778,
-0.03519075736403465,
-0.012070540338754654,
0.03218458965420723,
0.049980614334344864,
0.01712464541196823,
0.028986752033233643,
0.004304856061935425,
-0.05138802155852318,
0.006711393594741821,
0.014298290945589542,
0.052253808826208115,
0.004102698992937803,
-0.017197206616401672,
0.012860924936830997,
-0.01446116529405117,
0.041499651968479156,
-0.021894438192248344,
0.011646712198853493,
-0.003119315020740032,
0.03450208529829979,
0.017072735354304314,
-0.011478575877845287,
-0.011752927675843239,
-0.01616925746202469,
0.04310799390077591,
0.005536912940442562,
-0.006438047159463167,
0.0030766651034355164,
-0.04220980033278465,
0.045207660645246506,
0.02082393690943718,
-0.009950194507837296,
-0.013185671530663967,
0.03217096999287605,
-0.011950711719691753,
0.004718357231467962,
0.020835094153881073,
-0.03319085016846657,
0.016414986923336983,
-0.02410290576517582,
0.041292570531368256,
0.040884830057621,
0.024879375472664833,
-0.0016776217380538583,
-0.002772141480818391,
-0.01417653076350689,
-0.0028694961220026016,
0.04968953877687454,
-0.0037192488089203835,
0.011865179054439068,
0.04113561660051346,
0.004312650300562382,
0.027980703860521317,
-0.03571925684809685,
-0.004722453188151121,
0.01039683073759079,
0.005771365016698837,
0.03376579284667969,
-0.06285136938095093,
0.011391508392989635,
0.023380335420370102,
0.042495712637901306,
-0.01651817373931408,
0.017495376989245415,
0.0463983416557312,
-0.003649865509942174,
0.02589869685471058,
0.028157319873571396,
-0.029839571565389633,
0.03587156906723976,
0.00016708974726498127,
0.030277695506811142,
-0.0011344201629981399,
-0.020120695233345032,
0.04768720269203186,
0.0046493797563016415,
0.02184116281569004,
0.019394004717469215,
-0.017145385965704918,
-0.03086381033062935,
0.0026345474179834127,
-0.001920910901390016,
-0.013147152028977871,
-0.032420311123132706,
0.002636872697621584,
0.0665031149983406,
0.013891313225030899,
0.018372023478150368,
-0.01859174482524395,
-0.07542453706264496,
-0.04166537895798683,
-0.028079841285943985,
-0.005786266177892685,
0.08929050713777542,
0.012245150282979012,
-0.03629220277070999,
0.024855690076947212,
-0.008871727623045444,
-0.0033039944246411324,
-0.014568262733519077,
0.020824477076530457,
-0.03316940367221832,
0.04138481616973877,
-0.024795755743980408,
0.034302517771720886,
0.0009431016515009105,
0.011173454113304615,
0.10466927289962769,
0.04261596128344536,
-0.009343676269054413,
-0.07847287505865097,
0.030797438696026802,
-0.03336634859442711,
-0.008443841710686684,
-0.021324196830391884,
0.057506199926137924,
0.010875188745558262,
0.026832737028598785,
0.026500336825847626,
0.04642431437969208,
-0.01963193342089653,
0.01938667707145214,
0.05970548465847969,
-0.03115045092999935,
-0.024167653173208237,
-0.009830953553318977,
0.03408162295818329,
-0.03361505642533302,
-0.006326186005026102,
-0.08458465337753296,
0.015546662732958794,
0.006675300188362598,
0.0265489611774683,
-0.048730961978435516,
-0.025152988731861115,
0.04269437491893768,
0.026075435802340508,
-0.04372560977935791,
-0.02778293937444687,
-0.00573983509093523,
-0.021992050111293793,
-0.025118010118603706,
-0.004930152092128992,
0.011361862532794476,
-0.038735225796699524,
0.04567057266831398,
0.05466760694980621,
0.04068303480744362,
-0.019792035222053528,
0.007159312721341848,
0.01450218167155981,
-0.014579611830413342,
-0.013566216453909874,
-0.02935704216361046,
0.0677008107304573,
0.006049968767911196,
-0.007271936163306236,
-0.02205100655555725,
0.04057125374674797,
0.04382968321442604,
-0.033969759941101074,
-0.021308641880750656,
-0.03289495408535004,
0.031162044033408165,
-0.008621873334050179,
-0.000975696777459234,
-0.01047433726489544,
0.008347876369953156,
-0.006099408958107233,
0.00041661097202450037,
-0.006075946148484945,
-0.025694498792290688,
0.020240630954504013,
-0.020407814532518387,
0.012850072234869003,
0.005895424634218216,
-0.013892341405153275,
-0.010687283240258694,
0.0017674819100648165,
-0.045985788106918335,
0.01284798514097929,
0.04286202788352966,
0.02055688574910164,
0.04538832604885101,
0.016261635348200798,
-0.0020481909159570932,
0.012854951433837414,
-0.022003138437867165,
0.05442827194929123,
-0.014547383412718773,
-0.01832597330212593,
0.0007614976493641734,
-0.021308962255716324,
0.03518574312329292,
0.012452163733541965,
-0.007377956062555313,
0.022240037098526955,
0.002069368027150631,
0.030987350270152092,
0.026245512068271637,
-0.024709058925509453,
-0.015457971021533012,
0.003306458704173565,
-0.03373689576983452,
-0.029032111167907715,
-0.022144267335534096,
-0.022205553948879242,
0.0006884517497383058,
-0.0014514406211674213,
-0.01931908167898655,
0.038808830082416534,
0.005387711804360151,
-0.007899725809693336,
0.023999536409974098,
-0.008353947661817074,
-0.00006106460932642221,
0.01024780422449112,
0.013831189833581448,
-0.03817315772175789,
-0.011407935060560703,
0.004400710575282574,
-0.013077090494334698,
0.01235403586179018,
0.0049079530872404575,
-0.027358731254935265,
-0.006606266833841801,
-0.04684528708457947,
-0.00011092792556155473,
-0.01508086547255516,
0.000530652585439384,
-0.07781169563531876,
0.02428578771650791,
0.0037662372924387455,
-0.006714178249239922,
-0.03886845335364342,
0.05862490460276604,
0.0013743710005655885,
-0.0072510079480707645,
0.0009108393569476902,
0.023357147350907326,
-0.01538072805851698,
0.005498364567756653,
0.03458750247955322,
0.015086774714291096,
0.004009732976555824,
0.005090042948722839,
-0.02915031649172306,
0.04703805223107338,
-0.03336651623249054,
-0.04867693409323692,
0.034609388560056686,
0.016263321042060852,
0.0302621778100729,
-0.008786802180111408,
-0.026748230680823326,
-0.0014872621977701783,
0.017214512452483177,
-0.01785355806350708,
-0.015667172148823738,
-0.005667818244546652,
-0.03863890469074249,
-0.009850353933870792,
-0.04389108344912529,
-0.017841491848230362,
0.0210568904876709,
0.0020883099641650915,
-0.011227870360016823,
0.03578044846653938,
-0.04141250625252724,
-0.0202327873557806,
-0.006272041704505682,
-0.002358222845941782,
0.02578117698431015,
-0.0065317219123244286,
0.01938614435493946,
-0.007288034539669752,
0.029506562277674675,
-0.0009701387607492507,
0.01960340328514576,
0.012565587647259235,
-0.0028628106229007244,
-0.10133367776870728,
-0.018206128850579262,
0.002213425235822797,
0.00009951419633580372,
-0.005398519802838564,
-0.03508482873439789,
-0.02140006422996521,
0.029961111024022102,
-0.048102423548698425,
-0.006586316041648388,
-0.029750371351838112,
-0.01095061656087637,
-0.02545524574816227,
-0.03567054122686386,
-0.003648969577625394,
0.08176633715629578,
0.022118769586086273,
0.025397108867764473,
0.009245472028851509,
-0.01723102107644081,
-0.04372141882777214,
-0.026816045865416527,
-0.01974906213581562,
0.018889978528022766,
0.00716507900506258,
-0.03569910302758217,
0.05258716642856598,
-0.016891540959477425,
0.012356667779386044,
0.03236791864037514,
0.024235166609287262,
-0.013842002488672733,
0.0004300283908378333,
-0.013196026906371117,
-0.01393869798630476,
0.020769447088241577,
0.004768905695527792,
0.01234309934079647,
-0.02194843627512455,
0.05166037380695343,
0.046606630086898804,
-0.000384532700991258,
0.01588754542171955,
0.013512520119547844,
-0.026824573054909706,
-0.02815774828195572,
-0.017834249883890152,
0.050953883677721024,
-0.011600448749959469,
-0.02878025732934475,
-0.024604978039860725,
0.008440443314611912,
0.04488277807831764,
0.0013662256533280015,
0.022243879735469818,
-0.06183015927672386,
-0.005862251855432987,
0.04088413342833519,
0.006176451686769724,
0.011165985837578773,
0.0284989383071661,
-0.013678036630153656,
-0.02473163604736328,
0.020210133865475655,
0.009027249179780483,
-0.002164470963180065,
-0.043587442487478256,
-0.002638343721628189,
-0.027484958991408348,
0.023217763751745224,
0.02283347398042679,
-0.038553398102521896,
-0.02836524322628975,
0.053274016827344894,
0.008293886668980122,
0.0290511567145586,
-0.0007638419629074633,
-0.05070861801505089,
-0.002289408817887306,
-0.01905454881489277,
0.02427733689546585,
0.001923635951243341,
-0.01375055406242609,
-0.018267787992954254,
-0.006117803510278463,
0.012514453381299973,
0.05308326333761215,
0.03722678869962692,
0.009261383675038815,
-0.030592966824769974,
0.03251129016280174,
0.012077966704964638,
0.029420357197523117,
-0.054680779576301575,
0.004688115790486336,
0.026350991800427437,
-0.0010530680883675814,
0.009912952780723572,
0.036629557609558105,
-0.011777806095778942,
0.036142393946647644,
0.048233699053525925,
0.008292712271213531,
-0.018274860456585884,
-0.021633174270391464,
-0.04457881674170494,
0.03964776173233986,
-0.014185293577611446,
-0.002141486154869199,
0.0767047330737114,
-0.0075387596152722836,
0.01267024502158165,
0.044446587562561035,
-0.007308298256248236,
0.003561001503840089,
0.06027153879404068,
-0.013408270664513111,
0.01873946376144886,
-0.013706819154322147,
-0.04299376904964447,
0.008764357306063175,
-0.07556477934122086,
-0.007664939388632774,
0.006779318675398827,
-0.008861320093274117,
-0.022830259054899216,
0.0510723814368248,
0.009857779368758202,
0.02314390242099762,
-0.0022995262406766415,
0.024266742169857025,
-0.018427960574626923,
0.03694883733987808,
0.0020552652422338724,
0.04926160350441933,
0.006660618353635073,
0.05222352221608162,
0.01827089488506317,
0.021565623581409454,
-0.008737601339817047,
0.06486448645591736,
-0.008739011362195015,
0.04040098935365677,
-0.015374001115560532,
0.00902493204921484,
0.041882120072841644,
-0.03193579241633415,
0.047877464443445206,
0.029360294342041016,
-0.011660078540444374,
0.07475271821022034,
-0.06701326370239258,
0.015680940821766853,
-0.00579538568854332,
-0.02107011340558529,
-0.045367009937763214,
0.014654824510216713,
-0.0037523978389799595,
0.03866275027394295,
-0.037641946226358414,
-0.046706583350896835,
-0.01805136911571026,
0.003990159370005131,
0.01244294922798872,
-0.043845560401678085,
-0.0051796697080135345,
0.002982627833262086,
-0.014967590570449829,
-0.02247992344200611,
0.023896295577287674,
-0.005329265724867582,
0.005370594561100006,
0.035684604197740555,
0.039067067205905914,
0.008982669562101364,
0.015556449070572853,
-0.02692950889468193,
-0.001479767612181604,
0.01691487617790699,
-0.05531638115644455,
-0.04861404374241829,
-0.004535313695669174,
0.033845048397779465,
-0.012823924422264099,
0.019891032949090004
] |
<p>Suppose to have a system $S$ immersed in an enviroment; the pure states are elements of $H_S \otimes H_E$, where $H_S$ is the hilbert space of the system and $H_E$ is the hilbert space of the enviroment.</p>
<p>The density matrix for the total system $\rho_{S+E}$ evolves according to the Von Neumann equation
$$
i \frac{d\rho_{S+E}}{dt} = [H,\rho_{S+E}].
$$</p>
<p>If we're interested only in $S$, we can trace over the degrees of freedom of the enviroment and use the reduced density matrix formalism
$$
\rho_S = Tr^E[\rho_{S+E}]
$$</p>
<p>What we want to do now is to find a time evolution operator $\Gamma_t$ for the reduced density matrices such that
$$
\rho_s(t) = \Gamma_t[\rho_S(0)].
$$</p>
<p>Now, during one lesson, one professor said that if we want the evolution operator to be linear, we <strong>MUST</strong> chose a nonentangled state (i.e. $\rho_{S+E} = \rho_S \otimes \rho_E$). While it can be easily proven that if the initial state is not entangled, the operator $\Gamma_t$ is linear, I don't see why, <strong>in general</strong>, the evolution operator for a reduced density matrix of an entangled state cannot be a linear operator.</p> | 1,418 | [
-0.013690966181457043,
-0.012300822883844376,
0.003714904887601733,
-0.026480911299586296,
0.0028165248222649097,
0.003357452806085348,
-0.04884754493832588,
0.0009505141642875969,
0.056863874197006226,
-0.03561774268746376,
0.003031987464055419,
0.017672061920166016,
0.062390122562646866,
0.025766341015696526,
0.01516992598772049,
-0.02442215196788311,
-0.02361435443162918,
0.0070159416645765305,
-0.04527074843645096,
-0.01454456988722086,
0.015289138071238995,
0.017827287316322327,
-0.0010703389998525381,
-0.01385137252509594,
0.00691484659910202,
0.023012999445199966,
0.023364689201116562,
-0.005987111944705248,
0.036506351083517075,
0.06199083849787712,
-0.026095328852534294,
-0.022078240290284157,
0.012246345169842243,
0.010817412286996841,
0.010243233293294907,
-0.03978850692510605,
-0.06783250719308853,
-0.03011094033718109,
0.006497871596366167,
0.013032715767621994,
-0.027994273230433464,
-0.0014934837818145752,
-0.010585514828562737,
0.04767915606498718,
-0.00941875297576189,
0.03348986431956291,
0.031989604234695435,
-0.020861448720097542,
0.0514942966401577,
-0.047051314264535904,
0.04682013764977455,
-0.00428741006180644,
0.0017831282457336783,
0.00868951715528965,
-0.007690060418099165,
0.035617027431726456,
0.021558457985520363,
0.04115503653883934,
0.01607290841639042,
-0.02098604291677475,
-0.022135674953460693,
-0.01820811815559864,
-0.0029974747449159622,
-0.04548228532075882,
0.01338987797498703,
-0.009833930991590023,
0.044161561876535416,
-0.003518894547596574,
0.03877662867307663,
-0.032035987824201584,
-0.01631740666925907,
0.003704383270815015,
0.0511874295771122,
-0.02028363198041916,
0.020634725689888,
-0.03702984377741814,
0.037070367485284805,
0.005431379657238722,
0.029688512906432152,
0.022285722196102142,
0.006485587917268276,
0.006388464011251926,
0.015808606520295143,
0.007412230130285025,
-0.027023211121559143,
-0.01135884877294302,
0.055034540593624115,
-0.029529966413974762,
0.015957828611135483,
0.07190012186765671,
0.020817868411540985,
0.030981911346316338,
0.029917830601334572,
0.028893014416098595,
-0.0068051922135055065,
0.0038229553028941154,
-0.009688662365078926,
0.08480259776115417,
0.023567410185933113,
-0.03925500437617302,
-0.020690089091658592,
-0.07110117375850677,
0.01065449882298708,
0.03952423110604286,
0.021931976079940796,
0.009872390888631344,
-0.0393315926194191,
0.0034085612278431654,
-0.009168758057057858,
-0.03134729340672493,
-0.04357518255710602,
0.010455949231982231,
0.01563166454434395,
0.03724413737654686,
-0.03629286587238312,
-0.04261887073516846,
0.014689882285892963,
-0.015282053500413895,
0.07779315114021301,
0.07527534663677216,
0.01830955781042576,
-0.014486974105238914,
0.029266832396388054,
-0.03783838078379631,
-0.06554443389177322,
0.04570060595870018,
0.01398830208927393,
-0.004614761099219322,
-0.06614228338003159,
0.01864142343401909,
0.00006964699423406273,
0.010423433035612106,
-0.0008801944204606116,
-0.01637720689177513,
0.024256138131022453,
-0.06751694530248642,
-0.12408383935689926,
-0.08292187750339508,
0.012817313894629478,
0.007984812371432781,
-0.002748154103755951,
-0.08307310193777084,
0.004752588924020529,
0.040249112993478775,
0.1036970317363739,
-0.030952000990509987,
0.017277754843235016,
0.01592704840004444,
-0.013123850338160992,
0.01949603110551834,
-0.00447373790666461,
-0.03228399157524109,
-0.0017104059224948287,
-0.0372341088950634,
0.012972217984497547,
-0.03672726824879646,
0.0732230395078659,
0.020794842392206192,
-0.020033936947584152,
0.006608760915696621,
0.08748108148574829,
-0.014085255563259125,
0.0012501261662691832,
0.018667858093976974,
-0.01658906601369381,
-0.05863099545240402,
0.09214426577091217,
0.007652290165424347,
0.04141004756093025,
0.000604220200330019,
0.022493448108434677,
0.008840708062052727,
0.012631461955606937,
0.044286731630563736,
0.03068273700773716,
-0.03228747472167015,
-0.027966409921646118,
0.009847399778664112,
-0.023949742317199707,
0.011832180432975292,
-0.0030188076198101044,
-0.025018004700541496,
-0.003044130513444543,
0.02056959830224514,
-0.008659396320581436,
-0.006173925008624792,
-0.014452468603849411,
-0.011116658337414265,
-0.007428365759551525,
-0.012796108610928059,
-0.013937374576926231,
-0.0558912418782711,
0.02323008142411709,
0.03983131796121597,
0.008616268634796143,
0.05010004714131355,
0.014823205769062042,
-0.000841593137010932,
-0.005981782916933298,
-0.05206133797764778,
-0.02212001569569111,
0.036015044897794724,
0.04629155248403549,
-0.025826359167695045,
0.01747152768075466,
0.014789612032473087,
0.046341363340616226,
0.0053009758703410625,
0.007772688753902912,
-0.018102210015058517,
-0.03596918657422066,
-0.005234651733189821,
0.024840442463755608,
0.006169826257973909,
0.022544147446751595,
0.015651067718863487,
-0.02545551396906376,
0.0030274216551333666,
-0.004345220047980547,
-0.00935477577149868,
-0.0567406602203846,
0.030135581269860268,
0.07534134387969971,
0.0018893057713285089,
0.023005910217761993,
0.018770918250083923,
-0.0008322146022692323,
0.0018561239121481776,
-0.007820738479495049,
-0.03502340614795685,
-0.035216331481933594,
0.01946296915411949,
-0.00003732384357135743,
0.01986735314130783,
-0.029665790498256683,
0.03860177844762802,
0.019593385979533195,
0.005724603775888681,
0.04138082638382912,
0.018753424286842346,
-0.02669111080467701,
0.004394077695906162,
-0.0008300695335492492,
-0.0111915348097682,
0.006436709314584732,
0.01724780537188053,
-0.006927472539246082,
-0.003708192612975836,
0.0032923154067248106,
-0.00741299893707037,
0.006065772846341133,
0.038513001054525375,
-0.0313008688390255,
0.02091679908335209,
0.005539576057344675,
-0.017821017652750015,
0.026558073237538338,
-0.020610282197594643,
0.03804432600736618,
0.01854577846825123,
-0.0257798433303833,
0.0023532353807240725,
-0.014697382226586342,
-0.04024322330951691,
0.019621018320322037,
-0.021764755249023438,
-0.016035759821534157,
-0.007028560154139996,
0.028879990801215172,
-0.04181703180074692,
-0.011426320299506187,
-0.028982803225517273,
0.004191241227090359,
-0.015980733558535576,
0.02001275308430195,
0.07246793806552887,
-0.017735200002789497,
-0.013578622601926327,
-0.04152572527527809,
-0.006505082827061415,
-0.028806233778595924,
-0.03876858577132225,
0.022392189130187035,
0.042578719556331635,
-0.04946248605847359,
0.019126107916235924,
-0.07294357568025589,
-0.006079913582652807,
0.007026717998087406,
-0.010940239764750004,
0.010479011572897434,
0.025342000648379326,
-0.007046840153634548,
-0.05949690565466881,
-0.07064975053071976,
-0.01860041543841362,
0.009390974417328835,
-0.025030730292201042,
0.0117368558421731,
0.04864947870373726,
-0.016116350889205933,
-0.04556281864643097,
0.01573975756764412,
-0.04671439900994301,
-0.044246554374694824,
-0.011421533301472664,
-0.04406719654798508,
0.020788269117474556,
-0.02705243229866028,
0.021195370703935623,
0.06763868778944016,
0.008213300257921219,
-0.010206841863691807,
-0.08150871098041534,
-0.07067571580410004,
-0.009292902424931526,
0.03260837867856026,
0.017275875434279442,
0.042245641350746155,
-0.04480547085404396,
0.059600282460451126,
0.054669998586177826,
-0.008628061972558498,
-0.009998969733715057,
0.0001453567820135504,
0.008241668343544006,
-0.031718652695417404,
0.018040599301457405,
-0.02088942378759384,
-0.0032009140122681856,
0.005405524279922247,
-0.017149077728390694,
0.00623396597802639,
0.059039484709501266,
-0.0048631043173372746,
0.009112300351262093,
0.014682149514555931,
0.017006784677505493,
0.01897423528134823,
0.05851632356643677,
-0.02753465063869953,
-0.011235269717872143,
0.020589537918567657,
-0.0011497532250359654,
0.021271727979183197,
-0.03781816363334656,
-0.05420181155204773,
0.04168248921632767,
0.007913801819086075,
0.010136781260371208,
0.00988486222922802,
0.023144986480474472,
-0.020995646715164185,
0.004099847283214331,
-0.004820880014449358,
0.021490275859832764,
-0.0067838383838534355,
-0.02574741654098034,
0.00682467594742775,
0.014562280848622322,
0.008418554440140724,
-0.016844116151332855,
-0.019629910588264465,
-0.0012223251396790147,
0.0023444273974746466,
0.01834021881222725,
0.006871641147881746,
-0.012879460118710995,
0.041714977473020554,
0.012189432047307491,
0.01926085352897644,
-0.02781960926949978,
-0.023527752608060837,
-0.053057704120874405,
-0.05133247748017311,
0.030272312462329865,
0.03331363946199417,
0.05207275599241257,
0.01744864322245121,
0.0238485224545002,
0.011731334961950779,
0.02524598129093647,
0.021120764315128326,
-0.01642439514398575,
-0.06078043580055237,
0.025984179228544235,
-0.020544296130537987,
-0.0431029349565506,
0.013985799625515938,
-0.009048783220350742,
0.01053058821707964,
-0.057994358241558075,
-0.0705217495560646,
0.007161536253988743,
-0.024728454649448395,
-0.07119467109441757,
0.0050094397738575935,
-0.026460720226168633,
-0.04356471076607704,
-0.014950156211853027,
0.022517884150147438,
0.02897600643336773,
-0.012482182122766972,
0.007509590592235327,
0.039101939648389816,
0.004169667139649391,
0.043989162892103195,
-0.014270505867898464,
0.0026315993163734674,
0.01620103046298027,
0.012146854773163795,
0.025058437138795853,
0.026612302288413048,
-0.016512848436832428,
0.014317869208753109,
0.005741608329117298,
0.04847361892461777,
-0.0180934090167284,
0.013586853630840778,
0.001900068367831409,
0.00045063518336974084,
-0.012817122042179108,
0.007297973148524761,
0.022170525044202805,
0.01580236293375492,
0.040053773671388626,
0.02636718563735485,
0.04579148069024086,
-0.0012580567272379994,
0.02789773792028427,
0.03486644849181175,
-0.021410351619124413,
0.003564521437510848,
-0.015172689221799374,
0.021957244724035263,
-0.017565326765179634,
-0.0017206365009769797,
-0.009490268304944038,
0.009502222761511803,
0.01399622205644846,
0.014338506385684013,
0.02000763639807701,
0.019629688933491707,
-0.0049266451969742775,
-0.0012940795859321952,
-0.005956553854048252,
-0.005901406053453684,
0.0036410605534911156,
0.0029051480814814568,
0.01581336371600628,
0.03803802654147148,
0.030084894970059395,
-0.00418271915987134,
0.013112091459333897,
-0.04717397689819336,
-0.03797866404056549,
0.005164113361388445,
0.02581411972641945,
0.000367234752047807,
-0.007475241087377071,
-0.03676679730415344,
-0.04794339835643768,
0.025291958823800087,
-0.017840147018432617,
0.03929777815937996,
-0.00022180502128321677,
-0.025670237839221954,
-0.012769673950970173,
-0.03444211557507515,
-0.019330695271492004,
0.04305038973689079,
0.02495053969323635,
0.02088533155620098,
-0.0029730587266385555,
0.002984832040965557,
-0.0034849673975259066,
-0.005666528828442097,
-0.01771685481071472,
0.05044753849506378,
0.007587254047393799,
-0.024584714323282242,
0.00519583560526371,
0.062335994094610214,
-0.03478729724884033,
-0.08777963370084763,
0.03375265374779701,
-0.018349837511777878,
-0.009608680382370949,
0.012644837610423565,
-0.02226489968597889,
-0.04664265736937523,
0.005908438470214605,
0.009621904231607914,
-0.012356286868453026,
0.027819130569696426,
-0.05731825530529022,
0.06302343308925629,
0.024317661300301552,
-0.010158088058233261,
0.03276319056749344,
0.030418869107961655,
-0.02746718004345894,
-0.0035028052516281605,
-0.053855862468481064,
0.029006298631429672,
-0.063300222158432,
0.07328250259160995,
-0.0448092520236969,
-0.002500607632100582,
-0.011856562457978725,
0.04849463701248169,
-0.011481042020022869,
0.009158357977867126,
0.020574901252985,
-0.059983011335134506,
0.009417656809091568,
0.04390280693769455,
-0.05910905450582504,
-0.005883052945137024,
-0.0052694291807711124,
0.002530894009396434,
-0.006300800014287233,
-0.009580470621585846,
-0.003952651284635067,
0.0006794747314415872,
0.01844344660639763,
0.07704221457242966,
-0.020642157644033432,
0.06324876844882965,
-0.03721372410655022,
-0.022552039474248886,
0.0005935763474553823,
-0.05604788661003113,
0.04298552870750427,
0.00035895282053388655,
-0.00002234214116469957,
0.012794534675776958,
-0.006490052677690983,
0.001952409977093339,
-0.00596744054928422,
-0.024845700711011887,
-0.029527198523283005,
-0.03925235569477081,
0.02203686162829399,
0.008687534369528294,
-0.01812577247619629,
-0.08640176057815552,
-0.054023467004299164,
-0.022833077237010002,
0.030196379870176315,
0.010737785138189793,
-0.043561697006225586,
0.021239399909973145,
-0.022157108411192894,
0.0038597395177930593,
-0.03443498536944389,
0.0606766939163208,
-0.0060586524195969105,
-0.003446625778451562,
0.051123227924108505,
0.05352190136909485,
0.03111582249403,
-0.030345527455210686,
0.026428362354636192,
0.02414499968290329,
-0.011228471994400024,
0.0004966068081557751,
-0.035288985818624496,
0.060129035264253616,
-0.021351298317313194,
-0.035056523978710175,
-0.009171659126877785,
-0.0064131710678339005,
0.05745365098118782,
-0.012118065729737282,
-0.019688259810209274,
0.03697870671749115,
-0.008067507296800613,
0.012742745690047741,
-0.012557822279632092,
0.00992131233215332,
0.0006650318391621113,
0.003701417939737439,
0.040107838809490204,
0.005741858389228582,
0.002073008567094803,
-0.029167359694838524,
0.020424749702215195,
-0.014420325867831707,
-0.0053847786039114,
-0.0026046063285320997,
0.06198102608323097,
0.011935272254049778,
0.024025561287999153,
0.07402165234088898,
-0.021359877660870552,
0.017596837133169174,
0.013128708116710186,
0.002989246277138591,
0.012830029241740704,
-0.00874133687466383,
-0.04542980715632439,
-0.03839050233364105,
-0.057888370007276535,
0.05261370167136192,
0.029826683923602104,
-0.00711172865703702,
0.004243430215865374,
-0.004510161932557821,
-0.0035488589201122522,
0.001304740086197853,
-0.011324182152748108,
-0.024396831169724464,
0.017262419685721397,
-0.02014751359820366,
0.05906818062067032,
-0.006829022895544767,
0.01540987566113472,
0.013452131301164627,
0.06475970149040222,
-0.036601532250642776,
0.05275965481996536,
0.01536648254841566,
0.00024300100631080568,
0.04544064402580261,
-0.0004756007983814925,
-0.03011288121342659,
0.03560155630111694,
-0.024344762787222862,
0.01321751531213522,
0.007717250846326351,
-0.021077292039990425,
0.014610420912504196,
0.014768927358090878,
0.02301090955734253,
-0.046480488032102585,
-0.024239996448159218,
-0.05988122150301933,
0.029533836990594864,
-0.04021381959319115,
-0.0038779466412961483,
0.038224734365940094,
0.019379159435629845,
0.02927890233695507,
0.010323992930352688,
0.02324216440320015,
-0.012816663831472397,
-0.04796775430440903,
0.022534329444169998,
-0.03878525272011757,
-0.016441337764263153,
0.025074664503335953,
0.00417527137324214,
-0.008284910582005978,
0.040057823061943054,
-0.020337456837296486,
0.038861505687236786,
-0.004962138831615448,
0.03190106898546219,
0.006036079488694668,
0.03609026223421097,
0.031432848423719406,
-0.000453598506283015,
-0.004643602296710014,
0.031569138169288635,
0.13989683985710144,
0.06823743134737015,
0.015353680588304996,
-0.05875905975699425,
-0.022639084607362747,
0.002426130697131157,
0.0022668687161058187,
-0.0005393587634898722,
0.04052224010229111,
0.004907388240098953,
0.030262766405940056,
-0.0627584457397461,
0.03577856346964836,
0.030793888494372368,
-0.028326280415058136,
0.024312496185302734,
-0.05357766151428223,
-0.03270565718412399,
0.011016836389899254,
-0.004795558750629425,
-0.023372454568743706,
-0.027341773733496666,
-0.041226208209991455,
0.00004674092269851826,
0.0022148294374346733,
-0.00019795411208178848,
-0.007614643778651953,
-0.0496731661260128,
0.020580384880304337,
-0.011533599346876144,
-0.036556802690029144,
0.028147367760539055,
-0.00907027069479227,
0.010023629292845726,
-0.0364764966070652,
0.039482682943344116,
0.007702629081904888,
0.021742941811680794,
0.046384260058403015,
0.023798419162631035,
0.013441509567201138,
-0.03577281907200813,
0.030284356325864792,
0.005988174118101597,
-0.01999070681631565,
0.021992318332195282,
-0.04059026017785072,
0.09002134203910828,
-0.03182186186313629,
-0.02216636762022972,
0.00009318048978457227,
-0.05820898711681366,
-0.005109474528580904,
-0.051009222865104675,
0.012431311421096325,
-0.020135095342993736,
0.04438663274049759,
0.027429495006799698,
-0.008111484348773956,
-0.014560876414179802,
-0.03641309589147568,
-0.009820224717259407,
0.013889306224882603,
0.008594686165452003,
-0.0038524316623806953,
0.025820137932896614,
0.01631055399775505,
0.021368570625782013,
-0.0038159091491252184,
-0.011520647443830967,
-0.05920194834470749,
-0.003686300478875637,
-0.030849672853946686,
-0.02691444382071495,
0.060769546777009964,
-0.003286529565230012,
0.06490057706832886,
-0.006606551352888346,
0.0013375648995861411,
-0.00019143731333315372,
-0.06943615525960922,
0.013085159473121166,
0.025123821571469307,
-0.037025272846221924,
0.0038328671362251043,
0.025094393640756607,
0.00682878540828824,
0.06890268623828888,
-0.014630689285695553,
-0.014593742787837982,
0.03216049075126648,
-0.011392632499337196,
0.0008607814670540392,
-0.0128242839127779,
-0.004453515168279409,
0.034127574414014816,
-0.016367584466934204,
0.01918848231434822,
-0.028041576966643333,
-0.013750829733908176,
0.0017840712098404765,
0.02836012654006481,
-0.03304009512066841,
0.03895076736807823,
0.006911460775882006,
-0.005190916825085878,
0.020830268040299416,
-0.007856256328523159,
0.007091455161571503,
0.0023996992968022823,
0.02673381008207798,
-0.05460512638092041,
-0.038338735699653625,
-0.04269834980368614,
0.02780376747250557,
-0.003917854744940996,
0.006129690445959568,
-0.05143796280026436,
-0.010107595473527908,
-0.03845318779349327,
0.044966112822294235,
-0.031349606812000275,
0.01629134826362133,
0.002266760217025876,
0.01604095660150051,
0.026500556617975235,
0.014670087955892086,
0.005912099499255419,
0.023624153807759285,
0.002514591673389077,
-0.04271353781223297,
0.03653830289840698,
0.05076638236641884,
0.03465983271598816,
-0.03198060393333435,
-0.010374998673796654,
0.007864885963499546,
0.016016503795981407,
-0.01544194109737873,
-0.0077744778245687485,
0.026369651779532433,
-0.03744281828403473,
0.020950166508555412,
-0.011923003941774368,
0.03822850063443184,
0.0203095730394125,
0.01418351847678423,
-0.012915766797959805,
0.00429541477933526,
0.021446432918310165,
-0.034922633320093155,
0.033867575228214264,
-0.004380661528557539,
-0.02786562591791153,
-0.01964694820344448,
-0.014125179499387741,
-0.010234348475933075,
0.032315898686647415,
-0.00938707496970892,
0.012542822398245335,
0.007516901474446058,
-0.0055610318668186665,
0.0032129341270774603,
-0.008230562321841717,
0.03536257892847061,
0.02496979758143425,
0.02494531311094761,
-0.003044885816052556,
0.017934482544660568,
0.050585854798555374,
-0.03685903176665306,
0.019783129915595055,
0.02688528224825859,
-0.0034866814967244864,
-0.09321137517690659,
0.014448095113039017,
-0.007285796571522951,
-0.01776804029941559,
0.01577155478298664,
-0.05260072275996208,
0.01264624111354351,
0.011724635027348995,
-0.07092393934726715,
0.02949042245745659,
-0.0093101030215621,
0.0023047644644975662,
-0.0025576648768037558,
0.02961517684161663,
-0.07134895771741867,
0.05284014716744423,
0.025580674409866333,
0.023430269211530685,
0.02418375015258789,
-0.013928159140050411,
0.001491266069933772,
-0.014557816088199615,
-0.016937388107180595,
0.010245689190924168,
0.008508470840752125,
-0.0382341630756855,
0.08338388800621033,
-0.043799784034490585,
-0.05269992724061012,
-0.006644125562161207,
-0.0325792096555233,
0.007887477986514568,
-0.020897159352898598,
0.03437238186597824,
0.011626600287854671,
0.00882226787507534,
0.06024309992790222,
-0.068459153175354,
0.010512614622712135,
0.020683905109763145,
-0.006840301677584648,
0.02998567558825016,
-0.013263959437608719,
-0.03848099336028099,
-0.010270885191857815,
-0.014852596446871758,
-0.04313080757856369,
0.03408952057361603,
-0.009504048153758049,
-0.014728601090610027,
0.007928085513412952,
-0.043112657964229584,
-0.031544506549835205,
0.0046914867125451565,
0.014867343008518219,
-0.02659454755485058,
-0.019792063161730766,
0.027649110183119774,
0.018297692760825157,
-0.029922515153884888,
0.02598589099943638,
-0.06339593976736069,
-0.0867626965045929,
0.008852703496813774,
-0.0005660835886374116,
-0.011622074991464615,
-0.06849568337202072,
-0.023403581231832504,
0.013932242058217525,
-0.006874605547636747,
-0.029428597539663315,
-0.0024928099010139704,
-0.04772030562162399,
0.0482451468706131,
0.007255224511027336,
0.0683431625366211,
-0.006984731648117304,
-0.05780370905995369,
-0.0014333651633933187,
-0.0294761024415493,
0.03974691405892372,
0.01630638912320137,
0.004480613861232996,
-0.0500500351190567,
-0.007381926290690899,
-0.012983678840100765,
0.03764600679278374,
0.04747562110424042,
-0.010340387001633644,
-0.0301502775400877,
0.0010066888062283397,
0.023335155099630356,
0.008877201937139034,
-0.002261319663375616,
0.024729248136281967,
-0.015926554799079895,
0.015454304404556751,
0.00950081367045641,
0.01784348301589489,
-0.04035111516714096,
0.001591685228049755,
0.0038591986522078514,
0.0006551708793267608,
-0.043936170637607574,
0.00438400125131011,
-0.04553546756505966,
0.05863295868039131,
-0.003936569206416607,
-0.0011284281499683857,
0.0434739887714386,
-0.0007504408131353557,
0.02911856584250927,
0.027959642931818962,
-0.012740807607769966,
-0.025576254352927208,
0.01860867440700531,
-0.04818219318985939,
-0.04688076302409172,
-0.01060407143086195,
-0.026190832257270813,
0.041258927434682846,
-0.009874129667878151,
0.003171473043039441,
0.021849825978279114,
-0.02803250029683113,
-0.016970744356513023,
0.032187823206186295,
-0.01661778800189495,
0.02071712352335453,
0.024693310260772705,
0.05436243116855621,
0.033996909856796265,
0.014780732803046703,
-0.01472367625683546,
0.05344753339886665,
0.023562470450997353,
-0.017739055678248405,
0.010691492818295956,
-0.0026947306469082832,
-0.036164943128824234,
0.027125481516122818,
0.04040445759892464,
0.011675266548991203,
-0.02344387397170067,
0.025324184447526932,
0.04680122062563896,
-0.014106526039540768,
-0.021922431886196136,
-0.025258438661694527,
-0.03227944299578667,
0.0840737521648407,
-0.03734568879008293,
0.024414505809545517,
-0.015861786901950836,
0.020311517640948296,
-0.031361810863018036,
0.022614195942878723,
0.009333565831184387,
0.06578559428453445,
-0.03194868564605713,
0.029204631224274635,
-0.03140344098210335,
-0.04034319892525673,
0.05017942562699318,
-0.037769611924886703,
-0.023158898577094078,
0.0042678904719650745,
-0.05338048189878464,
0.005751944612711668,
-0.04505746439099312,
0.015350270085036755,
-0.027079327031970024,
0.008836972527205944,
0.013096965849399567,
-0.006780728697776794,
-0.03685561940073967,
-0.035714007914066315,
-0.0002696237061172724,
0.03716868907213211,
-0.04569768160581589,
-0.0023631046060472727,
-0.005395288113504648,
0.021747030317783356,
-0.007400101982057095,
0.0021648823749274015
] |
<p>Can a negative charge ionize air? Adding to this question, I have studied that positive charge ionizes air but never studied that negative charge ionize air. If possible, please explain how does it ionize air?</p> | 1,419 | [
-0.04009174555540085,
-0.016119224950671196,
-0.018272165209054947,
0.014154167845845222,
0.031583502888679504,
-0.002094034804031253,
-0.03068150393664837,
-0.028463071212172508,
0.004698175936937332,
-0.03527400642633438,
0.04904317110776901,
0.060767315328121185,
0.04109939560294151,
-0.01620662212371826,
-0.00092550169210881,
-0.005285574588924646,
-0.015232804231345654,
-0.026868415996432304,
0.007515887264162302,
0.010067461058497429,
0.01600651443004608,
0.0072550224140286446,
0.0019026589579880238,
0.053131043910980225,
-0.040671635419130325,
0.025973886251449585,
0.036977801471948624,
-0.018073296174407005,
0.043294940143823624,
0.02999139577150345,
-0.019805477932095528,
0.0221172533929348,
0.014833744615316391,
0.03827587887644768,
0.026749497279524803,
-0.009904214181005955,
-0.026232155039906502,
-0.025467948988080025,
-0.043046265840530396,
0.019741764292120934,
-0.005237367935478687,
-0.049807108938694,
0.01588037610054016,
0.02227042429149151,
-0.06564471125602722,
0.003962617367506027,
-0.0019309447379782796,
-0.022592520341277122,
0.049512773752212524,
-0.09866350889205933,
0.05497549846768379,
-0.03341475501656532,
0.06307542324066162,
0.031166231259703636,
0.0010758049320429564,
0.0002721700875554234,
0.10885235667228699,
0.0791172981262207,
-0.0044861361384391785,
-0.01935453712940216,
-0.01592676341533661,
-0.029641011729836464,
-0.023790273815393448,
-0.011257367208600044,
-0.02780604362487793,
0.019184747710824013,
0.0020002711098641157,
-0.036746907979249954,
0.014652193523943424,
0.006416535936295986,
0.01414143294095993,
0.01621084287762642,
-0.004221279174089432,
-0.011865824460983276,
0.006915710866451263,
-0.020724810659885406,
0.03780076280236244,
-0.017538832500576973,
0.0462147481739521,
0.05438752844929695,
-0.04694542661309242,
-0.005267276894301176,
0.008608819916844368,
0.015544158406555653,
-0.010205485858023167,
-0.026440057903528214,
0.09685717523097992,
-0.02476617321372032,
0.03892912715673447,
-0.006629826035350561,
-0.0023998464457690716,
-0.02780015394091606,
0.006751636974513531,
0.006152212154120207,
0.0013964679092168808,
0.022814176976680756,
-0.00791864562779665,
0.07930496335029602,
0.033915724605321884,
-0.018856724724173546,
0.012303806841373444,
0.03320134058594704,
0.05746116489171982,
0.05453953519463539,
0.01070421002805233,
-0.021767379716038704,
-0.034787289798259735,
0.011252003721892834,
0.00504553085193038,
-0.01434461958706379,
-0.04780701547861099,
-0.00039586788625456393,
-0.014356020838022232,
-0.052832674235105515,
0.025606218725442886,
-0.018353678286075592,
0.01772887445986271,
-0.025228841230273247,
0.036270301789045334,
0.05396473407745361,
0.03508564457297325,
-0.021823996677994728,
0.048000212758779526,
-0.013770739547908306,
-0.03830137848854065,
-0.02253016084432602,
-0.0017467422876507044,
0.019222473725676537,
-0.00641810055822134,
-0.015421288087964058,
-0.01311354711651802,
-0.02885378897190094,
0.014600287191569805,
0.003418408101424575,
0.05061129853129387,
-0.03473004326224327,
-0.1131356805562973,
-0.06388574838638306,
0.009415892884135246,
0.005222734529525042,
0.0060991630889475346,
-0.06879910826683044,
-0.006501269992440939,
0.018537256866693497,
0.031180156394839287,
0.005493073258548975,
-0.027522528544068336,
-0.019714057445526123,
0.01897597126662731,
0.015727577731013298,
-0.006503649055957794,
0.017826130613684654,
0.0007677102694287896,
-0.021384092047810555,
-0.021390650421380997,
-0.05157206207513809,
0.012443523854017258,
0.02460496872663498,
0.009576734155416489,
-0.031250447034835815,
0.049955785274505615,
-0.002817166969180107,
0.013815244659781456,
0.021353663876652718,
-0.0009251421433873475,
-0.025850703939795494,
0.05522686615586281,
0.029901498928666115,
-0.03557261824607849,
0.04623003304004669,
0.017073240131139755,
0.07793261110782623,
0.0036815297789871693,
0.03383554145693779,
0.06799329072237015,
-0.0439915768802166,
-0.028347745537757874,
-0.07457593083381653,
0.07873771339654922,
-0.036431312561035156,
-0.04942277446389198,
-0.0006314778001978993,
-0.006960543803870678,
0.009223473258316517,
-0.003920366521924734,
0.04030924662947655,
-0.017320938408374786,
-0.011788305826485157,
0.001961949747055769,
-0.06480816751718521,
-0.016153620555996895,
-0.05022825300693512,
0.03537975996732712,
-0.002289606025442481,
-0.019666027277708054,
0.030065452679991722,
-0.004719123709946871,
0.059550851583480835,
-0.0563129223883152,
-0.002867596223950386,
0.009685294702649117,
0.04043189808726311,
-0.005781644023954868,
-0.02127164602279663,
0.02333013154566288,
0.05003060773015022,
0.016312677413225174,
0.008064611814916134,
0.03329570218920708,
-0.0009390617487952113,
0.013587902300059795,
-0.005853170063346624,
0.005016699433326721,
0.008737056516110897,
0.02843024954199791,
-0.003197397803887725,
0.0438985601067543,
0.0015514936530962586,
-0.0012570118997246027,
0.04737992212176323,
-0.011211683042347431,
0.08174315840005875,
0.04659978300333023,
0.0186111219227314,
0.009016860276460648,
0.034029360860586166,
0.03610038757324219,
-0.02341536059975624,
0.019405711442232132,
-0.022606341168284416,
-0.03189888224005699,
-0.005610954016447067,
0.06287079304456711,
0.022875631228089333,
-0.04352693632245064,
0.0018879943527281284,
0.014388489536941051,
0.03287206217646599,
0.03404068574309349,
0.052409496158361435,
-0.014986102469265461,
-0.025302942842245102,
0.005722008179873228,
0.014786632731556892,
0.029162699356675148,
0.0029012917075306177,
0.0586404912173748,
0.01759718358516693,
0.04884503781795502,
0.012144281528890133,
-0.013132473453879356,
0.042683202773332596,
-0.030289679765701294,
0.024016058072447777,
0.007091720588505268,
-0.03008543886244297,
0.026162557303905487,
-0.03493623435497284,
0.027168020606040955,
0.003036380745470524,
-0.012228532694280148,
0.016878345981240273,
-0.004725430626422167,
0.015517259016633034,
0.0213331151753664,
0.004302533343434334,
0.01828633062541485,
0.014628161676228046,
0.027986451983451843,
-0.06831146031618118,
0.04163627699017525,
0.0020406621042639017,
0.007109982892870903,
-0.017713703215122223,
0.011826850473880768,
0.026916583999991417,
0.020396452397108078,
0.04235094413161278,
-0.02212032489478588,
-0.06760153919458389,
-0.040774278342723846,
-0.040186941623687744,
-0.009147287346422672,
0.045924898236989975,
0.0079276654869318,
0.008110958151519299,
-0.06474320590496063,
-0.020073169842362404,
0.05156288295984268,
-0.03032512776553631,
-0.023981017991900444,
0.021229224279522896,
-0.024358859285712242,
-0.030157675966620445,
0.01715298555791378,
-0.0330764576792717,
0.009180592373013496,
-0.0207551009953022,
-0.01018308475613594,
0.05913224816322327,
0.0033921829890459776,
-0.019639894366264343,
0.034548498690128326,
-0.05475359037518501,
-0.04084695503115654,
-0.012882164679467678,
0.00026283226907253265,
0.04537086561322212,
-0.041275616735219955,
0.02254302240908146,
0.015119515359401703,
-0.05242134630680084,
0.012133930809795856,
-0.007043951656669378,
-0.004005987197160721,
0.022059887647628784,
0.01203963439911604,
0.008423556573688984,
-0.014275696128606796,
-0.05296370014548302,
0.036651287227869034,
-0.00870130117982626,
-0.019403398036956787,
0.0006341717089526355,
-0.054986920207738876,
-0.061291590332984924,
-0.018902232870459557,
-0.012513276189565659,
0.018149903044104576,
-0.0034745719749480486,
0.009039169177412987,
0.03777983412146568,
0.0308783371001482,
0.0010212109191343188,
0.01979082077741623,
-0.037676043808460236,
0.009085563011467457,
0.01181669533252716,
0.03554419055581093,
0.015113447792828083,
0.0016267055179923773,
-0.008153239265084267,
0.039075370877981186,
0.029308734461665154,
0.007246812805533409,
0.0323173888027668,
-0.012572871521115303,
0.03507546707987785,
-0.0060508535243570805,
0.029213739559054375,
-0.04702570289373398,
0.02612290531396866,
-0.024457518011331558,
0.010655359365046024,
0.003988682758063078,
0.02410612627863884,
0.026557497680187225,
0.001978036481887102,
0.0040671331807971,
0.007735881954431534,
0.06797154992818832,
-0.03802744299173355,
-0.031319040805101395,
0.008678498677909374,
-0.023129263892769814,
0.02514004521071911,
0.020740048959851265,
-0.00030951088410802186,
0.024053849279880524,
0.020121607929468155,
0.02312631905078888,
0.0009013484814204276,
-0.024961257353425026,
0.026823237538337708,
-0.04289377108216286,
0.0026624794118106365,
-0.01719145104289055,
0.008985060267150402,
-0.014194578863680363,
0.07519715279340744,
0.0013181385584175587,
0.03894950449466705,
0.013962607830762863,
-0.001988322241231799,
-0.05706125870347023,
0.019159911200404167,
-0.025835299864411354,
-0.004493871238082647,
-0.026875214651226997,
-0.02467901073396206,
-0.017787368968129158,
-0.013038295321166515,
-0.009558308869600296,
-0.013887058943510056,
-0.027205757796764374,
-0.029067501425743103,
0.014348823577165604,
-0.007984325289726257,
0.008349570445716381,
-0.03654159978032112,
0.052602965384721756,
0.011802086606621742,
0.006074737757444382,
-0.002016837941482663,
0.02749890834093094,
-0.022646674886345863,
0.0050754668191075325,
-0.014910497702658176,
0.012067711912095547,
0.007745735812932253,
0.008567014709115028,
0.003368174657225609,
0.003748747054487467,
-0.0014060345711186528,
-0.0008294177241623402,
-0.0010369038209319115,
0.03866761922836304,
-0.015679245814681053,
-0.0030914489179849625,
-0.040217865258455276,
-0.06896993517875671,
-0.029755305498838425,
-0.013177604414522648,
0.04215356335043907,
-0.0005118033150210977,
0.04773872718214989,
0.007992719300091267,
-0.005569825880229473,
-0.008215694688260555,
0.03626198694109917,
0.038678210228681564,
0.019394507631659508,
-0.009527062065899372,
-0.03961348161101341,
-0.013713822700083256,
-0.04292776808142662,
0.01655121147632599,
0.010719556361436844,
-0.015698276460170746,
-0.046648334711790085,
-0.005896993912756443,
0.021547365933656693,
0.007509660441428423,
-0.022236241027712822,
0.00871352944523096,
0.012463287450373173,
-0.008509518578648567,
-0.04263802617788315,
0.0019242959097027779,
0.009484004229307175,
0.012277164496481419,
0.01790071651339531,
0.01659877598285675,
-0.03630128502845764,
-0.11244302242994308,
0.020675253123044968,
0.04511693865060806,
0.034419700503349304,
-0.00603710301220417,
-0.010828212834894657,
-0.04934759438037872,
-0.007276935037225485,
0.03638013079762459,
-0.024485858157277107,
0.01526755653321743,
-0.04899878799915314,
0.024217313155531883,
-0.00577491894364357,
-0.008721569553017616,
-0.013161000795662403,
0.017809666693210602,
0.036550261080265045,
-0.013632572256028652,
-0.003565591759979725,
-0.010781723074615002,
-0.014245782978832722,
0.044827427715063095,
0.0504324696958065,
0.07845589518547058,
0.006562271621078253,
0.01545049250125885,
-0.013777650892734528,
0.007369165308773518,
-0.03373577818274498,
-0.07166514545679092,
-0.00942320842295885,
0.026273449882864952,
-0.015541820786893368,
0.056320637464523315,
-0.01653650403022766,
-0.038789376616477966,
0.0048893289640545845,
0.001135304686613381,
-0.0004771843377966434,
-0.038848020136356354,
-0.03911146521568298,
0.005819949321448803,
0.0248731542378664,
-0.0009764280985109508,
0.04072805866599083,
0.037997759878635406,
-0.034368790686130524,
0.020168347284197807,
-0.03147244453430176,
0.08319243788719177,
-0.023820018395781517,
-0.021957198157906532,
-0.007753403391689062,
0.03531713783740997,
0.007934164255857468,
0.054608821868896484,
-0.013997513800859451,
0.014530176296830177,
-0.014027219265699387,
-0.03620852157473564,
0.0029985676519572735,
0.015118100680410862,
0.011687999591231346,
-0.013588751666247845,
-0.027099965140223503,
0.01783910021185875,
0.014246025122702122,
-0.03804181516170502,
-0.015160080045461655,
-0.018328364938497543,
-0.0026011557783931494,
0.018686695024371147,
-0.03393681347370148,
-0.014224511571228504,
-0.016119368374347687,
-0.002761691343039274,
0.02821051888167858,
-0.06162203848361969,
0.04435257986187935,
0.017997803166508675,
-0.08749353140592575,
0.010780194774270058,
-0.10188502073287964,
-0.02414695918560028,
0.06565944850444794,
0.004841807764023542,
0.05503227189183235,
-0.03949017822742462,
0.06073349714279175,
0.008556844666600227,
0.007692199200391769,
-0.08015137910842896,
-0.059728994965553284,
0.009319388307631016,
0.01417404692620039,
-0.0028907465748488903,
-0.03606553003191948,
-0.04005873203277588,
-0.005550514906644821,
-0.024001240730285645,
0.004356942139565945,
0.059292178601026535,
-0.04329017922282219,
-0.007663142401725054,
0.030187875032424927,
-0.009859715588390827,
0.03221362084150314,
-0.01701761968433857,
-0.004882287234067917,
0.01779838651418686,
-0.02643531933426857,
-0.026990700513124466,
-0.0011777743929997087,
0.01990753971040249,
-0.021679697558283806,
-0.041708774864673615,
0.003974269609898329,
-0.017341947183012962,
0.021522363647818565,
-0.04903267323970795,
-0.01208703126758337,
0.032271258533000946,
0.03208395838737488,
0.01655990071594715,
-0.00901769008487463,
0.0381975919008255,
-0.0006068013608455658,
0.026106519624590874,
-0.006320519372820854,
-0.015078765340149403,
-0.07204316556453705,
-0.020237745717167854,
0.0421348437666893,
0.026847349479794502,
0.007235766388475895,
0.019924674183130264,
0.03975248709321022,
-0.023053959012031555,
-0.005161056760698557,
0.012107739225029945,
-0.02137984149158001,
0.026476075872778893,
-0.0092101925984025,
-0.008602410554885864,
0.04375804215669632,
0.026023833081126213,
-0.013467147015035152,
-0.02935866266489029,
-0.017680399119853973,
-0.008998063392937183,
0.054612986743450165,
0.014467949979007244,
0.029667025431990623,
0.0015493128448724747,
-0.0006103717023506761,
-0.030052050948143005,
-0.0236407108604908,
0.012898516841232777,
0.021302081644535065,
-0.011685533449053764,
-0.0012092465767636895,
-0.0006391844362951815,
0.07179645448923111,
-0.004834409337490797,
0.028139567002654076,
0.010954121127724648,
0.0031629034783691168,
0.02937191165983677,
0.02539592981338501,
0.030399858951568604,
-0.004446415696293116,
-0.05219579115509987,
0.04436226934194565,
-0.06356538087129593,
0.030613625422120094,
0.023365145549178123,
-0.028971752151846886,
0.02877696231007576,
-0.027673110365867615,
-0.00316551118157804,
-0.060310132801532745,
0.0004603753623086959,
-0.033406808972358704,
0.02529224380850792,
-0.00574595807120204,
0.016497556120157242,
-0.023627934977412224,
0.019552171230316162,
0.045879509299993515,
-0.011791439726948738,
-0.0029133688658475876,
0.03461337834596634,
-0.057860467582941055,
-0.02381570264697075,
-0.01701033115386963,
-0.031863097101449966,
0.02375635877251625,
-0.007852387614548206,
-0.0341707319021225,
-0.0003695433842949569,
-0.026463458314538002,
0.050486017018556595,
-0.0011697025038301945,
0.038885731250047684,
0.010115942917764187,
0.01929520070552826,
0.0016469290712848306,
0.015973031520843506,
0.010426279157400131,
0.013668359257280827,
0.10229922831058502,
0.07093494385480881,
-0.011140866205096245,
-0.08244042843580246,
-0.03478316217660904,
-0.02623927779495716,
0.005118952598422766,
-0.03372809663414955,
0.0024687135592103004,
-0.022804012522101402,
0.01886250451207161,
-0.00006562978524016216,
0.05164889618754387,
-0.003932328429073095,
0.012473497539758682,
0.04548332840204239,
-0.018059836700558662,
-0.05206504464149475,
-0.0012296545319259167,
0.013204011134803295,
-0.01708950102329254,
0.047996897250413895,
-0.047238364815711975,
0.027571579441428185,
-0.07534261792898178,
0.000697353680152446,
-0.03122836910188198,
-0.004682663828134537,
0.0495094358921051,
0.012373924255371094,
-0.04411323741078377,
-0.032461605966091156,
0.013794546015560627,
-0.0018055704422295094,
-0.03777711093425751,
-0.015747785568237305,
0.0064986879006028175,
0.027856994420289993,
-0.006592719350010157,
0.017416121438145638,
0.024333028122782707,
0.0005949741462245584,
-0.011242887936532497,
0.030715923756361008,
-0.056861214339733124,
0.0022789931390434504,
0.00979295652359724,
0.0020489345770329237,
-0.02329198084771633,
0.012074469588696957,
-0.02008017711341381,
0.030274927616119385,
-0.0001983963156817481,
-0.03758881986141205,
-0.06128370389342308,
-0.02292523719370365,
0.03703263774514198,
-0.023100372403860092,
-0.013851533643901348,
-0.06723135709762573,
0.03316085785627365,
-0.0014086650917306542,
-0.001000387710519135,
-0.017315812408924103,
0.02495550736784935,
0.01553574949502945,
0.005498544778674841,
0.01621262915432453,
-0.02669479325413704,
-0.04562939330935478,
-0.02895778976380825,
-0.01955123245716095,
-0.03192926570773125,
-0.03220878541469574,
0.04453666880726814,
0.06538805365562439,
0.07307194173336029,
0.018945980817079544,
0.02871996909379959,
-0.018729757517576218,
-0.053131069988012314,
0.040696319192647934,
-0.001285193138755858,
-0.02343927137553692,
-0.00216089328750968,
-0.03457135707139969,
0.0007912880973890424,
0.03536567464470863,
-0.0519389808177948,
0.0378282405436039,
-0.007610843982547522,
0.021975282579660416,
0.01357522513717413,
-0.028635980561375618,
-0.023643117398023605,
0.016772029921412468,
-0.05513210594654083,
0.032192815095186234,
-0.024602031335234642,
0.041917603462934494,
-0.016239216551184654,
0.005291313398629427,
0.016881227493286133,
0.011670615524053574,
-0.05350443348288536,
-0.01020099874585867,
0.04254411906003952,
-0.002606078749522567,
0.0012181849451735616,
0.008892158046364784,
0.012689891271293163,
-0.021110141649842262,
-0.008458463475108147,
-0.039961423724889755,
0.010868620127439499,
0.01842811331152916,
0.0527384988963604,
0.014790715649724007,
0.0399051196873188,
-0.003972011152654886,
0.008547654375433922,
-0.04313003644347191,
-0.02863435633480549,
-0.07973957061767578,
0.04312950372695923,
-0.021047882735729218,
-0.004818781744688749,
0.008539904840290546,
-0.018087314441800117,
-0.026683872565627098,
0.013005677610635757,
0.06402788311243057,
0.04772159084677696,
-0.02127194218337536,
-0.005805773660540581,
0.021665001288056374,
-0.032222095876932144,
0.05486780032515526,
-0.0001240618439624086,
-0.012582389637827873,
0.05142483860254288,
-0.046721599996089935,
-0.03135718032717705,
0.004143234342336655,
-0.017891328781843185,
0.01481096725910902,
0.03027399256825447,
-0.006912935059517622,
0.00603665504604578,
0.06746485084295273,
-0.0034916140139102936,
-0.010263334959745407,
0.010845350101590157,
-0.023837940767407417,
-0.012248414568603039,
0.009440885856747627,
0.012989785522222519,
-0.04185859113931656,
-0.009123744443058968,
0.03468535095453262,
0.012006633915007114,
0.019035914912819862,
0.001942209666594863,
0.02413848787546158,
-0.015774203464388847,
0.031226826831698418,
0.04381508007645607,
-0.000016403164408984594,
-0.007043119985610247,
0.036872610449790955,
-0.018451008945703506,
0.03182252123951912,
-0.0017224637558683753,
-0.02129555679857731,
-0.10193730890750885,
0.008565133437514305,
0.03436878323554993,
-0.01862758956849575,
0.01129577960819006,
-0.052513618022203445,
-0.0010826613288372755,
0.02691400796175003,
-0.060323238372802734,
-0.028769340366125107,
-0.026080729439854622,
-0.0024817781522870064,
-0.03273114562034607,
0.003128832671791315,
0.0019381903111934662,
-0.004684312269091606,
0.025599248707294464,
0.0579400397837162,
0.003388188546523452,
-0.0028698542155325413,
-0.009844431653618813,
-0.007091297768056393,
-0.007490294054150581,
0.020421454682946205,
0.02069266326725483,
-0.02322106808423996,
0.04856085404753685,
-0.04291880130767822,
0.015783965587615967,
0.024106550961732864,
-0.010039719752967358,
-0.009516177698969841,
-0.006557590328156948,
0.029901301488280296,
0.002383060986176133,
0.038234032690525055,
0.013118153437972069,
0.0037029164377599955,
-0.009508132003247738,
0.051013581454753876,
0.01750197820365429,
0.007568208035081625,
-0.005236376076936722,
-0.007256539538502693,
0.001121382461860776,
-0.0168220903724432,
-0.03717733174562454,
0.046594053506851196,
0.0014189338544383645,
-0.028338905423879623,
-0.025210926309227943,
0.0005994964740239084,
0.021586978808045387,
-0.005596236325800419,
-0.031093278899788857,
-0.04705693572759628,
0.0029906693380326033,
0.028511300683021545,
0.0046338303945958614,
-0.007658261805772781,
0.016207972541451454,
-0.011016239412128925,
-0.017975570634007454,
0.03303922340273857,
-0.011580309830605984,
0.025849474593997,
-0.04699705168604851,
-0.0047003477811813354,
0.009326343424618244,
0.0011452608741819859,
-0.008200456388294697,
-0.05060553550720215,
-0.04463871195912361,
0.022683631628751755,
-0.011171326041221619,
0.01956065185368061,
0.03218713030219078,
-0.07815276831388474,
-0.008915710262954235,
-0.05215043947100639,
0.016750868409872055,
-0.039394453167915344,
0.020515043288469315,
-0.049297574907541275,
-0.0436956025660038,
0.010176063515245914,
0.02297891303896904,
0.07042649388313293,
-0.017502134665846825,
-0.03855028375983238,
0.004877456929534674,
-0.007126233074814081,
0.016563156619668007,
-0.0318116620182991,
-0.0028794973623007536,
0.005662485025823116,
-0.04978539049625397,
0.004450895823538303,
-0.02064260095357895,
-0.03772791475057602,
0.04766631871461868,
-0.001971252029761672,
0.008737996220588684,
-0.010067986324429512,
-0.04393762722611427,
-0.034695062786340714,
0.0743120014667511,
0.027928225696086884,
-0.00589150283485651,
0.07640198618173599,
0.008412862196564674,
0.022909117862582207,
0.009579984471201897,
-0.019090158864855766,
-0.0118368836119771,
0.01191259641200304,
-0.018862979486584663,
-0.012835944071412086,
-0.0008284158539026976,
-0.008255232125520706,
0.019566845148801804,
-0.02162611298263073,
0.0019852176774293184,
0.01766357570886612,
-0.03114233911037445,
-0.007153572980314493,
0.03151760622859001,
0.010485506616532803,
0.024591192603111267,
-0.0028994823805987835,
0.0015528915682807565,
0.047048646956682205,
0.04524347931146622,
-0.033004291355609894,
0.06945565342903137,
0.01991337165236473,
-0.02685457281768322,
0.0026849526911973953,
-0.0018881482537835836,
0.015793131664395332,
0.00558119872584939,
0.03999488055706024,
0.05949094519019127,
0.009023001417517662,
-0.012025812640786171,
0.012492122128605843,
0.016415631398558617,
0.019283786416053772,
-0.001857204013504088,
-0.05010423809289932,
0.055508848279714584,
-0.03942714259028435,
0.018194301053881645,
-0.004117479082196951,
-0.0030417433008551598,
-0.02019510045647621,
0.023479368537664413,
-0.005726402159780264,
0.04324106127023697,
0.003052774118259549,
-0.04888234660029411,
-0.020194506272673607,
-0.010764514096081257,
0.002449235413223505,
-0.05998297035694122,
0.015813272446393967,
-0.023838656023144722,
0.03258795291185379,
-0.05715029686689377,
-0.006501543335616589,
-0.032107558101415634,
-0.021743210032582283,
-0.006563907954841852,
0.033568911254405975,
0.0415378175675869,
0.014781267382204533,
0.0020676248241215944,
-0.03216712549328804,
0.039205748587846756,
-0.04607900604605675,
-0.021670585498213768,
-0.013038412667810917,
-0.006068355869501829,
-0.020341290161013603,
0.009533198550343513
] |
<p>Is there a database (or any other source) of graphs of average transparency of various materials (cardboard, concrete, gypsum etc.) as a function of wavelength?</p> | 1,420 | [
-0.017710885033011436,
-0.045995209366083145,
-0.003338903421536088,
-0.042432744055986404,
0.018406320363283157,
0.03136494755744934,
-0.00556224025785923,
-0.010217573493719101,
-0.014062922447919846,
-0.0547725148499012,
0.04795584827661514,
0.030854972079396248,
0.05363835021853447,
0.03511480614542961,
-0.0027705207467079163,
-0.014837479218840599,
-0.027952302247285843,
0.001191071467474103,
-0.005850479006767273,
-0.053205911070108414,
0.020330702885985374,
0.011459510773420334,
-0.019839290529489517,
0.004389400593936443,
-0.04125121235847473,
0.03890399634838104,
0.015206505544483662,
0.019191982224583626,
0.02496384270489216,
0.05722985044121742,
-0.0233595073223114,
-0.007962160743772984,
-0.0043127029202878475,
0.06168820336461067,
0.03012893721461296,
0.002323538064956665,
-0.02187282219529152,
-0.0428239144384861,
-0.035757601261138916,
0.0022257359232753515,
-0.005828451830893755,
-0.007682345807552338,
-0.009908215142786503,
0.028558319434523582,
0.001246819505468011,
0.01090812124311924,
0.024591729044914246,
-0.030311288312077522,
0.0344952754676342,
-0.06591661274433136,
0.08484677225351334,
-0.03940955549478531,
0.04832349345088005,
0.01398684736341238,
-0.0090279346331954,
-0.00035823555663228035,
0.0564948171377182,
0.07023173570632935,
0.00831415131688118,
-0.018410449847579002,
-0.01788642443716526,
0.00572643568739295,
-0.01143223699182272,
-0.015030520968139172,
-0.045204903930425644,
0.030261503532528877,
-0.01581610180437565,
-0.04574368894100189,
0.035924579948186874,
-0.007068044971674681,
-0.04912884160876274,
0.004735594615340233,
0.06430303305387497,
-0.0007650211919099092,
-0.005438350141048431,
-0.023946257308125496,
0.00035840016789734364,
0.04987595975399017,
-0.0062742894515395164,
0.032423511147499084,
-0.04042382910847664,
-0.03124760091304779,
-0.006979175377637148,
-0.005290063563734293,
-0.026213187724351883,
-0.01891973242163658,
0.09863295406103134,
-0.03598909452557564,
-0.03407152369618416,
0.005347592756152153,
-0.0009662917582318187,
-0.05112013593316078,
0.035976592451334,
0.04636053368449211,
-0.03740876540541649,
-0.02761140465736389,
-0.02726569026708603,
0.0382542610168457,
-0.011264123022556305,
-0.004650004208087921,
0.04410123452544212,
-0.012649506330490112,
0.03175421804189682,
0.05254190415143967,
-0.0217158030718565,
-0.017881063744425774,
-0.016970716416835785,
-0.007682386320084333,
0.036066677421331406,
0.01729530841112137,
0.009484708309173584,
-0.0018572505796328187,
0.016474615782499313,
0.005231431685388088,
-0.01564311422407627,
-0.01839691586792469,
0.04129532724618912,
-0.01379657443612814,
0.04047060385346413,
0.0784619078040123,
0.03160412982106209,
-0.016804339364171028,
0.04271254315972328,
-0.014037834480404854,
-0.037281181663274765,
0.022346029058098793,
0.0387970469892025,
-0.040712639689445496,
-0.052353303879499435,
0.040953006595373154,
0.014724452048540115,
-0.05573660880327225,
0.05318506062030792,
-0.05274806544184685,
0.050142113119363785,
-0.0285476166754961,
-0.052289143204689026,
-0.079815573990345,
0.01900053769350052,
0.018961023539304733,
-0.025570020079612732,
-0.054080523550510406,
0.006695800460875034,
0.004497263114899397,
0.018256893381476402,
0.029765073210000992,
0.042393602430820465,
-0.015946529805660248,
0.04364510998129845,
-0.011185655370354652,
-0.04158977046608925,
-0.00027973734540864825,
0.048742782324552536,
-0.027731766924262047,
0.015160657465457916,
-0.06839071959257126,
-0.007039316464215517,
0.04407081380486488,
-0.018638867884874344,
-0.03443325683474541,
0.06413691490888596,
0.010070325806736946,
0.009781391359865665,
0.043910376727581024,
-0.0011086005251854658,
-0.05129573866724968,
0.06353799253702164,
-0.007304284255951643,
0.029336802661418915,
-0.02136114425957203,
0.0016364154871553183,
0.011550036258995533,
0.04341371729969978,
0.01630907505750656,
0.006276976782828569,
0.0033299848437309265,
-0.006120959762483835,
0.01357109472155571,
0.034774623811244965,
0.005409693345427513,
-0.04342804476618767,
0.0014751246199011803,
-0.008271406404674053,
0.0011301666963845491,
0.006070014089345932,
0.015520740300416946,
-0.002869895426556468,
-0.038773637264966965,
0.03006894141435623,
-0.07776013761758804,
0.005274725146591663,
-0.014196966774761677,
0.031016770750284195,
0.019250668585300446,
-0.0036530473735183477,
-0.008270069025456905,
0.02955845557153225,
-0.014660394750535488,
0.014304173178970814,
-0.015939101576805115,
0.009390338324010372,
0.002749113133177161,
0.03283774480223656,
-0.023582611232995987,
-0.0035241167061030865,
0.04233602061867714,
0.05548553168773651,
-0.023781321942806244,
0.006468585226684809,
-0.051855169236660004,
-0.025451119989156723,
-0.0008754855371080339,
-0.03358108550310135,
0.04711245745420456,
-0.0378895103931427,
0.002733692293986678,
-0.0076787094585597515,
0.009974861517548561,
-0.004839860834181309,
0.01759934425354004,
-0.04437563195824623,
0.024707650765776634,
0.03764372318983078,
0.02303898334503174,
-0.015227355062961578,
0.005739231128245592,
-0.03576953709125519,
0.016676481813192368,
-0.01071846578270197,
-0.01973317377269268,
-0.04015308618545532,
-0.0011522662825882435,
0.035878852009773254,
0.004672513343393803,
-0.04445479065179825,
-0.0036537772975862026,
0.00021915300749242306,
0.049559976905584335,
0.05659438669681549,
0.02399544045329094,
-0.012870592065155506,
-0.04489278793334961,
-0.012106895446777344,
0.004189581144601107,
0.029393402859568596,
0.014463009312748909,
-0.011913308873772621,
0.03634585812687874,
0.027914024889469147,
0.004205354489386082,
-0.01038385834544897,
0.024455755949020386,
-0.016312625259160995,
0.012206428684294224,
-0.0034406904596835375,
-0.019916178658604622,
0.028026795014739037,
-0.04475655406713486,
-0.023362938314676285,
0.018446320667862892,
-0.019475238397717476,
-0.008234107866883278,
-0.016431616619229317,
-0.016851136460900307,
0.052917879074811935,
0.001014360343106091,
-0.029919752851128578,
0.007900986820459366,
0.011671877466142178,
0.003956484608352184,
0.03522367402911186,
-0.028836477547883987,
0.02006874606013298,
-0.04662906005978584,
0.0029784946236759424,
0.006194127723574638,
0.025611354038119316,
0.060255493968725204,
-0.04399881139397621,
-0.02062046341598034,
-0.0193672776222229,
0.01040091272443533,
0.008841700851917267,
0.009999841451644897,
-0.017851291224360466,
-0.01181808952242136,
-0.028964821249246597,
-0.05353335291147232,
0.046808838844299316,
-0.0469692200422287,
-0.04311065003275871,
0.05119914561510086,
0.012667170725762844,
-0.028577370569109917,
0.015901215374469757,
0.002853624289855361,
0.017912359908223152,
-0.06532657891511917,
0.010735148563981056,
-0.007524800021201372,
0.00843078177422285,
-0.06216351315379143,
0.016550716012716293,
-0.03544201701879501,
-0.05669046938419342,
-0.00008195634291041642,
-0.005305652040988207,
-0.037239640951156616,
-0.047041505575180054,
-0.011352600529789925,
0.02396949753165245,
-0.04154116287827492,
0.012259612791240215,
-0.019886627793312073,
-0.04467723146080971,
0.02722734957933426,
-0.010977238416671753,
0.05683932453393936,
0.009241425432264805,
0.015455810353159904,
0.05152333900332451,
0.02725444920361042,
-0.017043083906173706,
-0.03588392958045006,
-0.029186677187681198,
0.04070302098989487,
-0.05507056787610054,
0.013286764733493328,
0.03996136784553528,
-0.010939457453787327,
0.01539807952940464,
0.008763722144067287,
-0.004762656986713409,
0.04636107757687569,
0.01586066000163555,
0.018528318032622337,
0.010444054380059242,
-0.0053182984702289104,
-0.062459733337163925,
0.03353165090084076,
0.08891591429710388,
-0.03268985077738762,
0.01914001628756523,
-0.010856241919100285,
0.05127179995179176,
0.0421498604118824,
-0.03349188342690468,
0.03948246315121651,
-0.013671941123902798,
-0.005376772023737431,
-0.004714488983154297,
-0.007027719169855118,
-0.0014977585524320602,
0.03655845671892166,
-0.05308566242456436,
0.039178311824798584,
0.008717235177755356,
0.036620330065488815,
-0.010099228471517563,
0.025082053616642952,
0.053821079432964325,
-0.015723969787359238,
0.005934929009526968,
0.0160108283162117,
0.015858381986618042,
0.03556526079773903,
-0.014800039120018482,
-0.017942842096090317,
0.07290244102478027,
0.028944512829184532,
0.02638605609536171,
0.014843922108411789,
-0.016561785712838173,
0.014737708494067192,
-0.05377471074461937,
-0.003253212431445718,
-0.04094066098332405,
0.03029021993279457,
0.021236952394247055,
0.03719031438231468,
0.01117234118282795,
0.012919878587126732,
0.03296782821416855,
0.02794717438519001,
-0.057141102850437164,
-0.017282037064433098,
-0.06628283858299255,
0.024246707558631897,
-0.032917384058237076,
0.0004425114020705223,
-0.0027989428490400314,
0.007791757117956877,
-0.02806977741420269,
0.0010504508391022682,
0.017548607662320137,
-0.031980961561203,
-0.011297961696982384,
0.0016830492531880736,
-0.005579384509474039,
-0.01943603716790676,
0.040146857500076294,
-0.02177581377327442,
0.013661585748195648,
0.005873602349311113,
-0.009358769282698631,
-0.022211752831935883,
-0.004910740535706282,
0.008033402264118195,
0.03861327841877937,
0.01497816015034914,
0.03245369717478752,
0.04164249077439308,
0.01676889695227146,
-0.04712316766381264,
-0.0010090365540236235,
-0.019229954108595848,
0.025827407836914062,
-0.004586485214531422,
-0.012587856501340866,
0.0017832883168011904,
-0.04946017265319824,
0.0050570047460496426,
-0.005942066200077534,
0.023454271256923676,
-0.040355101227760315,
0.02042314223945141,
0.0385926216840744,
-0.0043949950486421585,
-0.05306055769324303,
0.035289570689201355,
0.027016330510377884,
-0.026928378269076347,
-0.009321975521743298,
-0.014756202697753906,
-0.0038999621756374836,
-0.0027757855132222176,
0.008795781061053276,
-0.0038519178051501513,
0.06800834834575653,
0.0074924286454916,
0.011586742475628853,
0.019974272698163986,
0.02820657752454281,
-0.01935110241174698,
-0.017680540680885315,
0.004574163816869259,
0.0031099123880267143,
-0.017591973766684532,
0.008945216424763203,
0.016388200223445892,
0.04920056834816933,
0.021210474893450737,
0.016885695978999138,
-0.028440555557608604,
-0.07615987956523895,
0.024714935570955276,
0.02570539526641369,
0.01389356330037117,
0.008277582004666328,
-0.01758888177573681,
-0.029405413195490837,
-0.002317697275429964,
0.05366690084338188,
0.03542831540107727,
0.007709898985922337,
-0.023851078003644943,
0.01968526653945446,
-0.06551720947027206,
-0.005310723092406988,
0.02291915938258171,
0.004504390526562929,
0.04169590026140213,
0.006052997894585133,
-0.00663743307814002,
0.013334762305021286,
-0.020044362172484398,
0.0451776348054409,
0.03480013832449913,
0.07032831758260727,
-0.018987469375133514,
0.017531046643853188,
-0.011682930402457714,
0.0047017550095915794,
-0.028147175908088684,
-0.048233672976493835,
-0.009680129587650299,
0.005688379984349012,
-0.0034003970213234425,
0.06470595300197601,
-0.011993497610092163,
0.0048221200704574585,
0.053835488855838776,
0.04720112308859825,
-0.020267285406589508,
-0.00392009224742651,
-0.05007806420326233,
0.041644319891929626,
0.03214239329099655,
-0.0179497878998518,
0.06563334167003632,
0.057573094964027405,
-0.007868641056120396,
0.0052524288184940815,
-0.019515134394168854,
0.06144566833972931,
-0.023980632424354553,
0.0034263129346072674,
-0.0022970938589423895,
-0.0061779143288731575,
-0.03770047053694725,
0.010896367020905018,
0.02217159979045391,
0.0651833564043045,
-0.005528213456273079,
-0.04390815645456314,
-0.002807625336572528,
0.014498009346425533,
-0.013829397037625313,
0.012864162214100361,
-0.0033271063584834337,
0.011117051355540752,
-0.0067986901849508286,
-0.050533704459667206,
0.010799504816532135,
0.003508320776745677,
0.013779466971755028,
0.01701345294713974,
0.00596063444390893,
0.010628663934767246,
-0.10482898354530334,
0.0087669026106596,
-0.015190428122878075,
-0.00394392479211092,
0.050017207860946655,
-0.004479486029595137,
0.053497064858675,
0.07606251537799835,
-0.04508287459611893,
-0.0009816203964874148,
0.03988730534911156,
-0.02501007355749607,
0.044548194855451584,
-0.042859744280576706,
0.022656213492155075,
-0.019046641886234283,
0.03256767615675926,
-0.050453029572963715,
-0.026351723819971085,
0.03953862190246582,
0.03391296789050102,
-0.03835749998688698,
-0.01980380341410637,
0.014259373769164085,
-0.02816404402256012,
-0.022613966837525368,
0.02423780970275402,
0.04743035510182381,
-0.018165001645684242,
0.007734053768217564,
-0.019379286095499992,
-0.001931025879457593,
0.05032894015312195,
-0.03986744582653046,
-0.040741924196481705,
-0.016049066558480263,
-0.011426088400185108,
-0.034446071833372116,
-0.013411701656877995,
0.027251964434981346,
-0.0226086787879467,
0.000718754599802196,
-0.015175417065620422,
-0.013885468244552612,
0.039313480257987976,
-0.05194903910160065,
-0.00001459993018215755,
0.04090076684951782,
0.03294987976551056,
-0.017355240881443024,
-0.03531692549586296,
0.028094787150621414,
-0.04099702462553978,
-0.020570101216435432,
-0.026208940893411636,
-0.03384362906217575,
-0.019109675660729408,
-0.0325436070561409,
-0.013940722681581974,
0.023807762190699577,
-0.014540399424731731,
0.017853226512670517,
0.06954482197761536,
-0.002916651079431176,
-0.041904281824827194,
-0.01831403374671936,
-0.05199974775314331,
-0.011252190917730331,
-0.03603433817625046,
0.0036242289934307337,
0.00768004497513175,
-0.024784013628959656,
-0.013711623847484589,
-0.07548069953918457,
-0.01982216350734234,
-0.01266320887953043,
0.02616872265934944,
-0.03512202203273773,
0.04369964450597763,
0.045785047113895416,
-0.008258160203695297,
-0.015446189790964127,
-0.0046424162574112415,
-0.003276792587712407,
0.030424943193793297,
0.006810988765209913,
0.05591454729437828,
-0.012373224832117558,
-0.0025049205869436264,
-0.02425534836947918,
0.02412986569106579,
-0.01674743928015232,
0.026384413242340088,
0.0038375721778720617,
0.008177777752280235,
0.02404269389808178,
-0.05297573283314705,
-0.015129385516047478,
0.028812294825911522,
-0.07256211340427399,
0.04718080535531044,
0.0332789421081543,
-0.031619951128959656,
0.020470870658755302,
-0.01321523915976286,
-0.00966060720384121,
-0.010205336846411228,
-0.018637439236044884,
-0.02788478694856167,
0.013029592111706734,
0.028292475268244743,
0.03047371841967106,
-0.011336500756442547,
0.0018647437682375312,
0.0122151467949152,
-0.013466437347233295,
0.01623501442372799,
0.0003853750240523368,
-0.08760096877813339,
-0.04294067993760109,
-0.04316238313913345,
-0.06983628869056702,
0.015196052379906178,
0.02018607035279274,
-0.02768872305750847,
0.04214482381939888,
-0.044890787452459335,
0.01489689014852047,
-0.031015343964099884,
0.03719380497932434,
0.0174647718667984,
0.031434349715709686,
-0.033671747893095016,
0.02870596945285797,
-0.01295834593474865,
-0.035072196274995804,
0.12040575593709946,
0.08201264590024948,
0.014597035013139248,
-0.03384214639663696,
-0.003977106884121895,
-0.009280087426304817,
-0.003454765537753701,
-0.04274577647447586,
0.055825237184762955,
0.00011535412340890616,
-0.011093760840594769,
-0.016208847984671593,
0.06028759479522705,
0.015680376440286636,
-0.0071981907822191715,
0.03223951533436775,
-0.0030650256667286158,
-0.0025204813573509455,
0.058369603008031845,
0.05329061672091484,
-0.02955651842057705,
0.03321857005357742,
-0.04713834822177887,
0.0445675253868103,
0.0037086273077875376,
-0.02567492425441742,
-0.014682885259389877,
-0.056131381541490555,
0.04868268221616745,
-0.041241466999053955,
-0.010499496012926102,
0.0057115135714411736,
0.03121263161301613,
-0.006070626899600029,
-0.02557520940899849,
0.00878725666552782,
0.0395703986287117,
-0.008539637550711632,
-0.0013109680730849504,
0.009869709610939026,
0.02662288211286068,
0.018727635964751244,
0.011142801493406296,
-0.003427180228754878,
-0.04505970701575279,
-0.005098413210362196,
-0.01816488429903984,
-0.014547635801136494,
-0.002434961963444948,
0.00009434342791792005,
0.013394941575825214,
0.014832379296422005,
-0.024530082941055298,
-0.026817230507731438,
-0.016050728037953377,
0.008873588405549526,
0.03733965754508972,
-0.031238451600074768,
0.0051784212701022625,
0.02383299358189106,
0.013559862971305847,
-0.013801430352032185,
0.011679613031446934,
-0.008896736428141594,
-0.022749196738004684,
-0.021107142791152,
-0.012700495310127735,
0.037836119532585144,
0.014692881144583225,
-0.05317346379160881,
-0.001951777026988566,
-0.026995481923222542,
-0.00895564816892147,
-0.05105200782418251,
-0.021416185423731804,
0.03594745323061943,
0.051648564636707306,
-0.015190175734460354,
-0.017401281744241714,
-0.0036194263957440853,
-0.04719056189060211,
0.017761703580617905,
-0.038692817091941833,
-0.01958754099905491,
-0.018687529489398003,
-0.020598556846380234,
0.06433550268411636,
0.003736416809260845,
-0.008048968389630318,
0.0005804964457638562,
-0.004995604511350393,
0.005996711552143097,
0.05705801770091057,
-0.040706928819417953,
0.011442584916949272,
0.024470945820212364,
-0.03938865289092064,
0.024141715839505196,
0.00022892905690241605,
0.06153121590614319,
-0.020822463557124138,
0.020229579880833626,
0.036500077694654465,
0.020825054496526718,
-0.015297108329832554,
0.00045319070341065526,
-0.030620813369750977,
-0.07609360665082932,
0.013847406022250652,
0.015836963430047035,
-0.006966535467654467,
-0.03045860305428505,
-0.026049209758639336,
-0.03523344174027443,
-0.018173616379499435,
0.030898448079824448,
0.017254013568162918,
-0.014912367798388004,
0.006096843164414167,
-0.021358445286750793,
-0.009162123315036297,
-0.0008366168476641178,
-0.020488910377025604,
-0.02953660488128662,
-0.0340021550655365,
-0.01978888548910618,
-0.004995451774448156,
0.003804570296779275,
0.0184895358979702,
0.007417780812829733,
-0.001187322661280632,
0.027506045997142792,
0.011865772306919098,
0.016240861266851425,
-0.02012200653553009,
0.01199732068926096,
-0.0026563601568341255,
0.04647863656282425,
0.0018865360179916024,
-0.04202565550804138,
0.03480924293398857,
-0.020222747698426247,
-0.052599065005779266,
0.036426570266485214,
-0.02638120763003826,
0.026637675240635872,
-0.0014251717366278172,
-0.0014306269586086273,
-0.012762460857629776,
0.09886208921670914,
-0.026242412626743317,
-0.017044011503458023,
-0.005056692752987146,
-0.0057817972265183926,
0.05135974660515785,
-0.013162223622202873,
0.025757208466529846,
-0.015686919912695885,
-0.0027042278088629246,
0.04531704634428024,
-0.007388632744550705,
0.017523188143968582,
0.01655854657292366,
-0.00038612866774201393,
-0.04439524561166763,
-0.027707595378160477,
0.005857998505234718,
0.013933143578469753,
0.00914954673498869,
0.007942845113575459,
-0.008329997770488262,
0.04943309351801872,
0.05342146009206772,
0.010082410648465157,
-0.05974521487951279,
0.011862141080200672,
0.002391632879152894,
0.0536147765815258,
0.036874011158943176,
-0.06898767501115799,
0.05244431644678116,
0.03655989468097687,
-0.080281563103199,
0.035474225878715515,
0.0015339691890403628,
-0.06100068613886833,
-0.050476931035518646,
0.016191227361559868,
-0.012347489595413208,
-0.014362876303493977,
0.023200420662760735,
0.04962467402219772,
0.01971500925719738,
0.05259713530540466,
-0.03376718610525131,
0.01212206482887268,
0.01648278720676899,
0.028088388964533806,
0.02634740248322487,
-0.003401417750865221,
0.0067943064495921135,
0.018917793408036232,
0.0021237782202661037,
-0.0031854668632149696,
-0.0007244390435516834,
0.00013623893028125167,
-0.050151046365499496,
0.022779060527682304,
-0.013521634042263031,
0.034040823578834534,
0.02945755422115326,
0.018912799656391144,
-0.0320807583630085,
-0.04304470121860504,
0.02465594746172428,
0.02732536569237709,
-0.024665670469403267,
0.03175963833928108,
0.017081530764698982,
-0.03828268498182297,
-0.04159075394272804,
-0.015080097131431103,
0.011550946161150932,
0.006710669491440058,
-0.027699477970600128,
-0.019826285541057587,
0.0646796002984047,
-0.02002481184899807,
0.0007770041702315211,
-0.06840942800045013,
-0.026495471596717834,
0.018324758857488632,
0.023434197530150414,
-0.0037573266308754683,
0.030668973922729492,
0.0023943602573126554,
-0.04189202934503555,
-0.030118994414806366,
0.025464529171586037,
0.016172822564840317,
-0.027563821524381638,
-0.022339554503560066,
-0.028448937460780144,
-0.012408510781824589,
0.006861611735075712,
-0.016453932970762253,
-0.06997913867235184,
-0.012317251414060593,
0.0010906080715358257,
-0.017700472846627235,
0.04011022672057152,
-0.01545426994562149,
-0.006661213468760252,
-0.032597195357084274,
0.04311079531908035,
-0.0002692496054805815,
0.00027126140776090324,
-0.017240388318896294,
0.02909092605113983,
0.00018311508756596595,
0.032815828919410706,
0.046947408467531204,
-0.04481639713048935,
-0.035497717559337616,
-0.04599406570196152,
0.004606824833899736,
0.014748994261026382,
-0.02784736268222332,
0.0061664823442697525,
-0.010374913923442364,
-0.047782573848962784,
-0.04872380197048187,
-0.008223024196922779,
0.011426759883761406,
0.01731618121266365,
0.03696519136428833,
-0.004558558110147715,
-0.0007299595163203776,
-0.01322717685252428,
-0.020355086773633957,
0.04162144288420677,
0.04789891839027405,
-0.04682613164186478,
0.07373551279306412,
-0.0032219321001321077,
0.0005220943130552769,
0.02806984633207321,
0.007194063160568476,
-0.07324926555156708,
0.07689140737056732,
0.016879934817552567,
-0.027695991098880768,
0.0017927598673850298,
0.009013095870614052,
0.01960604451596737,
-0.05535527318716049,
0.006952648516744375,
0.030188504606485367,
-0.05477452278137207,
-0.007937588728964329,
0.06413033604621887,
-0.0004666142340283841,
0.010083314031362534,
0.004437613766640425,
0.02357935905456543,
0.013598254881799221,
-0.016315849497914314,
-0.0037241997197270393,
0.012519488111138344,
0.002634715288877487,
0.007206953130662441,
0.025156289339065552,
0.016289498656988144,
-0.00423298729583621,
0.02888455055654049,
0.023674484342336655,
0.03106311336159706,
-0.012236714363098145,
-0.031011447310447693,
-0.00004698221891885623,
0.006166238337755203,
0.022913070395588875,
0.0479402132332325,
-0.030290871858596802,
0.07920718193054199,
-0.03251107037067413,
0.010822592303156853,
-0.03870529681444168,
-0.015045353211462498,
-0.014374994672834873,
0.01336843241006136,
0.026726320385932922,
-0.005282325204461813,
-0.029736777767539024,
-0.0015454974491149187,
-0.007544976193457842,
0.023683883249759674,
0.031834252178668976,
-0.07315871119499207,
0.030836427584290504,
-0.00493657449260354,
-0.014600604772567749,
0.006055861711502075,
0.012367960065603256,
0.0022793374955654144,
-0.007216950878500938,
0.015978442505002022,
0.018207961693406105,
-0.022957582026720047,
-0.006642749533057213,
0.004005763214081526,
-0.01686137169599533,
0.024715974926948547,
-0.08961855620145798,
0.021783016622066498,
-0.02195128984749317,
0.027474485337734222,
-0.029175741598010063,
0.013978974893689156
] |
<p>I am interested in understanding how and whether the transformation properties of a (classical or quantum) field under rotations or boosts relate in a simple way to the directional dependence of the radiation from an oscillating dipole. </p>
<p>For example, the EM field from an oscillating electric dipole $\mathbf{d}(t) = q x(t) \hat{\mathbf{x}}$ pointing along the $x$-axis vanishes in the x-direction (in the far-field). On the other hand, the sound radiating from a similar acoustic dipole vanishes in the $y-z$ plane (in the far-field). This result makes total sense classically because EM radiation consists of transverse waves while acoustic radiation is carried by longitudinal waves (try drawing a picture if this is not immediately obvious). The same holds true even if the fields and dipoles under consideration are treated quantum mechanically.</p>
<p>Now, the acoustic (displacement) field is represented by a scalar field, while the EM field is a (Lorentz) vector field. This leads me to wonder if one can draw some more general conclusions about multipole radiation, based on the transformation properties of the field in question.</p>
<p><strong>Given a tensorial or spinorial field of rank <em>k</em>, and a multipole source of order <em>l</em>, what is the asymptotic angular dependence of the resulting radiation?</strong></p>
<p><strong>In particular, how does the radiation from a "Dirac" dipole look, assuming such a thing can even make sense mathematically?</strong></p>
<p>By the latter I mean writing the classical Dirac equation</p>
<p>$$ (\mathrm{i}\gamma^{\mu}\partial_{\mu} - m)\psi(x) = J(x), $$</p>
<p>for some spinor-valued source field $J(x)$ corresponding to something like an oscillating dipole. (I understand that in general this term violates gauge invariance and so is unphysical, but I am hoping this fact doesn't completely invalidate the mathematical problem.)</p>
<p>Apologies to the expert field theorists if this is all nonsense :)</p> | 1,421 | [
-0.025264155119657516,
0.009543342515826225,
0.02083744667470455,
-0.05343087017536163,
0.04520021006464958,
0.04400312900543213,
-0.0010502021759748459,
-0.01540630403906107,
0.026749778538942337,
-0.03311106190085411,
0.031743038445711136,
0.0071734157390892506,
0.059530969709157944,
0.0030301485676318407,
0.005648838821798563,
0.018290815874934196,
-0.04722389578819275,
0.015462293289601803,
0.003035333240404725,
-0.03620810806751251,
0.010400872677564621,
0.06375976651906967,
-0.011782118119299412,
0.02720767632126808,
-0.021915974095463753,
0.012353019788861275,
-0.006812798324972391,
0.02269909903407097,
-0.014440652914345264,
0.04269738122820854,
-0.021948952227830887,
-0.0324733667075634,
0.002009135438129306,
0.015762435272336006,
-0.0018931215163320303,
-0.01352741476148367,
-0.02226901985704899,
-0.008833339437842369,
0.03630859777331352,
0.020813727751374245,
-0.051412638276815414,
-0.029038337990641594,
-0.026483558118343353,
0.01898573525249958,
-0.015928350389003754,
0.00916608888655901,
-0.0251925066113472,
-0.006281259935349226,
0.06112050637602806,
-0.04963363707065582,
0.06653168797492981,
0.011851157061755657,
-0.005304770078510046,
0.02382388338446617,
-0.020878314971923828,
-0.008922220207750797,
0.058412086218595505,
0.07753554731607437,
0.0019346207845956087,
-0.0557047538459301,
0.017313411459326744,
-0.011551844887435436,
-0.00454058637842536,
-0.023224670439958572,
-0.009901318699121475,
0.025866178795695305,
0.012944252230226994,
0.013759461231529713,
0.04113199934363365,
-0.00837118923664093,
0.021145235747098923,
0.022875679656863213,
0.026254987344145775,
-0.020792843773961067,
-0.008528975769877434,
-0.010330439545214176,
0.00814297329634428,
0.02007763460278511,
0.03646685183048248,
-0.007459480781108141,
0.0001455317687941715,
0.008722573518753052,
-0.0004471456923056394,
0.015236042439937592,
0.0026576176751405,
0.006253762636333704,
0.047414422035217285,
-0.009402845054864883,
-0.000035001739888684824,
0.03708281368017197,
0.021050671115517616,
-0.028807666152715683,
0.007178397849202156,
0.004094448406249285,
-0.024716174229979515,
0.023985907435417175,
-0.0269316453486681,
0.01353779062628746,
0.020792407914996147,
-0.01793503947556019,
-0.005895789247006178,
-0.01897723786532879,
-0.006613242439925671,
0.05625199154019356,
-0.00788341648876667,
0.007247702218592167,
-0.002295879414305091,
0.019708124920725822,
-0.06733804941177368,
-0.021613428369164467,
-0.050300441682338715,
0.005502515006810427,
-0.044821690768003464,
-0.012769021093845367,
-0.014885729178786278,
-0.03881216049194336,
-0.018030688166618347,
-0.03342216834425926,
0.04747424274682999,
0.08390448987483978,
0.03323143720626831,
-0.05031729117035866,
-0.003137320978567004,
-0.05419837683439255,
-0.07363928109407425,
-0.005263267084956169,
0.0365021713078022,
0.013961060903966427,
-0.08145631104707718,
0.011120671406388283,
-0.018373603001236916,
-0.012966286391019821,
0.014276627451181412,
0.0015257030026987195,
0.0024898729752749205,
-0.05417991429567337,
-0.07651805877685547,
-0.054571062326431274,
0.01686706766486168,
-0.016145531088113785,
-0.00239160330966115,
-0.0710969790816307,
-0.019125351682305336,
0.040294405072927475,
0.08044818043708801,
-0.008786460384726524,
0.009972727857530117,
-0.003592605469748378,
0.07605616748332977,
0.014790934510529041,
-0.021481867879629135,
-0.005420555826276541,
-0.04271054267883301,
-0.04361267015337944,
-0.006720943842083216,
-0.03689824417233467,
0.029188062995672226,
0.03657270595431328,
0.01902056112885475,
-0.014385851100087166,
0.07239523530006409,
-0.005468631628900766,
-0.020143507048487663,
0.027299290522933006,
-0.00789683312177658,
-0.0024484777823090553,
0.06123419851064682,
0.05216576159000397,
-0.019758999347686768,
0.023256314918398857,
-0.009176339954137802,
-0.01485713105648756,
0.009142073802649975,
0.022467289119958878,
0.0011006076820194721,
-0.06864024698734283,
-0.01960853300988674,
-0.020941942930221558,
-0.0139717236161232,
-0.00836920365691185,
-0.05631037801504135,
-0.014770583249628544,
-0.033712565898895264,
-0.034896790981292725,
-0.019456366077065468,
0.04963194206357002,
-0.0013382765464484692,
-0.0009246231056749821,
-0.014492729678750038,
-0.06710891425609589,
0.003086555516347289,
-0.029949607327580452,
0.02863539569079876,
-0.02870357222855091,
-0.0104791559278965,
0.0570019893348217,
0.016083186492323875,
0.003951378166675568,
0.002689654240384698,
-0.01773931458592415,
0.03280289098620415,
0.0007649708422832191,
0.001665693474933505,
0.011082575656473637,
0.02081022597849369,
0.032860323786735535,
-0.008749262429773808,
0.009118308313190937,
0.005375970155000687,
0.005932079628109932,
-0.032875608652830124,
0.03468844294548035,
-0.027134964242577553,
0.0010733753442764282,
0.029484998434782028,
0.03386227414011955,
-0.006064265500754118,
-0.030157791450619698,
-0.02915751188993454,
-0.002576276892796159,
-0.024707166478037834,
0.05835951119661331,
0.02222033590078354,
-0.027384579181671143,
0.006344837602227926,
0.07962071895599365,
0.0011714308056980371,
0.0058135068975389,
-0.03448595851659775,
-0.02857460267841816,
-0.039571166038513184,
0.02922392077744007,
0.06513041257858276,
0.028637412935495377,
-0.07149949669837952,
0.07002081722021103,
0.01708870381116867,
0.029342046007514,
0.04776247218251228,
0.032518647611141205,
-0.04902622848749161,
-0.05527397617697716,
0.005225778557360172,
-0.015719201415777206,
0.01129962969571352,
0.0028501381166279316,
0.008555482141673565,
-0.014717668294906616,
-0.0007091428269632161,
-0.0013408182421699166,
-0.019216926768422127,
0.009389935992658138,
0.0021456636022776365,
-0.020140519365668297,
-0.011921055614948273,
-0.035913363099098206,
0.05888817831873894,
-0.03706325963139534,
0.029956147074699402,
0.0194746982306242,
-0.02761819213628769,
0.006421814672648907,
-0.02237623929977417,
0.037195660173892975,
0.03155580163002014,
-0.03624242544174194,
-0.002206268487498164,
0.005284364800900221,
0.03135918825864792,
-0.029598582535982132,
0.020681092515587807,
-0.03781641647219658,
-0.014290808700025082,
0.015165599063038826,
-0.031084129586815834,
0.02627401240170002,
0.016135361045598984,
0.010031870566308498,
0.0026697246357798576,
-0.029539048671722412,
0.011967266909778118,
-0.023862425237894058,
0.011406614445149899,
0.07027340680360794,
-0.03367343917489052,
-0.011234250850975513,
-0.07333938777446747,
-0.0015465369215235114,
0.047072313725948334,
-0.02922467514872551,
-0.008141220547258854,
0.0007299880380742252,
-0.006562132388353348,
-0.08372100442647934,
-0.055280834436416626,
-0.016070494428277016,
0.01482774131000042,
-0.04359535872936249,
0.01668820157647133,
0.06288598477840424,
-0.04223739355802536,
-0.016932684928178787,
-0.002747337333858013,
-0.018802957609295845,
-0.026950698345899582,
-0.015722235664725304,
-0.00474611995741725,
0.016620546579360962,
-0.04081445932388306,
0.013979007489979267,
0.030050093308091164,
-0.05313602834939957,
-0.014890988357365131,
-0.035065703094005585,
-0.016060471534729004,
0.041322410106658936,
0.0019663888961076736,
0.07563509047031403,
0.023227861151099205,
-0.031725358217954636,
0.07868839800357819,
0.025766432285308838,
-0.04414719343185425,
-0.04668360576033592,
0.0058141713961958885,
-0.0009824702283367515,
-0.056419920176267624,
-0.006228009704500437,
0.06056952103972435,
-0.0015918540302664042,
0.05211205780506134,
0.03017091006040573,
0.009880551137030125,
-0.03732820600271225,
0.02836727909743786,
-0.03690037876367569,
-0.0014020606176927686,
0.008895174600183964,
0.02664329670369625,
0.03355094790458679,
0.013435077853500843,
-0.042880184948444366,
-0.012131236493587494,
-0.0035995994694530964,
0.011619141325354576,
0.0034579248167574406,
-0.059214040637016296,
0.050469767302274704,
0.0065511371940374374,
-0.011962546966969967,
-0.03906037285923958,
0.03947684168815613,
0.020140783861279488,
-0.023148590698838234,
-0.0030141433235257864,
0.025289170444011688,
0.020578790456056595,
-0.024414436891674995,
0.005483062006533146,
0.03539660573005676,
0.023563748225569725,
-0.012005702592432499,
-0.008410892449319363,
-0.0033703783992677927,
-0.012274717912077904,
0.035218920558691025,
-0.0573856458067894,
-0.0021248646080493927,
0.029747657477855682,
0.014184092171490192,
0.009612329304218292,
0.002502202522009611,
-0.030836928635835648,
0.06118188425898552,
0.00285702315159142,
0.03002144768834114,
-0.010247602127492428,
0.040546711534261703,
0.03310200199484825,
0.08942817151546478,
0.0077218832448124886,
0.0009629520936869085,
0.01689118519425392,
0.0024775282945483923,
-0.05992355942726135,
0.018745597451925278,
-0.010689767077565193,
0.013344814069569111,
0.019057705998420715,
-0.02706846594810486,
-0.0036705832462757826,
-0.016130730509757996,
-0.04757212847471237,
-0.029619144275784492,
0.007331058848649263,
-0.053170640021562576,
0.056618351489305496,
-0.03488946706056595,
-0.06741489470005035,
-0.06374963372945786,
0.06605805456638336,
0.05125879868865013,
-0.03253559395670891,
0.018428340554237366,
0.025268780067563057,
-0.05727316811680794,
0.05692816898226738,
-0.001762499799951911,
0.03694891184568405,
0.007744168397039175,
0.0239738579839468,
0.04328146576881409,
-0.01981707476079464,
-0.04176337644457817,
0.008723425678908825,
0.01714332029223442,
0.05720085650682449,
-0.000798353343270719,
-0.026334965601563454,
-0.007189010735601187,
-0.04034857824444771,
-0.009922384284436703,
-0.0067980485036969185,
0.0775221586227417,
0.0008199600270017982,
-0.001008535735309124,
0.03234310448169708,
-0.002316045109182596,
0.009362748824059963,
0.027942419052124023,
0.00020272475376259536,
0.012075669132173061,
-0.006430100183933973,
-0.04856658726930618,
0.03438172861933708,
0.018071575090289116,
0.021556058898568153,
-0.03857554867863655,
-0.030325008556246758,
0.00022937162430025637,
-0.005369207821786404,
0.015503710135817528,
0.04336364194750786,
-0.02574971690773964,
0.020253514871001244,
0.025730881839990616,
-0.011351877823472023,
0.015500820241868496,
0.013190769590437412,
-0.0106873270124197,
0.040375713258981705,
0.06856788694858551,
-0.00465371273458004,
-0.015969036146998405,
-0.05530861020088196,
-0.013027544133365154,
0.05010518431663513,
0.01247045025229454,
0.03068574145436287,
0.0216843169182539,
-0.004662578925490379,
-0.014230772852897644,
0.022388610988855362,
0.0011053300695493817,
0.045814149081707,
0.0013990039005875587,
-0.009309246204793453,
0.02039007842540741,
-0.055145569145679474,
-0.04992149770259857,
0.04725352302193642,
-0.010948496870696545,
-0.022974617779254913,
-0.049188029021024704,
-0.03633907809853554,
-0.0011041368125006557,
0.008404399268329144,
0.013688638806343079,
0.028274502605199814,
0.020576419308781624,
-0.003389091929420829,
0.008003580383956432,
0.042945969849824905,
0.022223325446248055,
-0.09461472183465958,
0.029343923553824425,
0.024537455290555954,
-0.010789095424115658,
0.055539581924676895,
-0.03611192852258682,
-0.02635345607995987,
0.014820218086242676,
0.004445172380656004,
0.0018001237185671926,
0.04045068472623825,
-0.02895914390683174,
0.043038006871938705,
-0.003560842713341117,
0.020941684022545815,
0.029749669134616852,
0.04224047064781189,
-0.03396579623222351,
-0.019260238856077194,
0.012151950970292091,
0.002056334400549531,
-0.024761386215686798,
0.004381037317216396,
-0.039586011320352554,
0.03581095486879349,
-0.0186880212277174,
0.07761579006910324,
-0.02295011654496193,
-0.00881353672593832,
0.012081420049071312,
-0.017930256202816963,
-0.006375892087817192,
0.02764108218252659,
-0.04923124983906746,
-0.00629933038726449,
-0.025385767221450806,
0.043493401259183884,
-0.000596115889493376,
-0.013972013257443905,
0.021220030263066292,
-0.0017997018294408917,
0.013859369792044163,
0.07757903635501862,
-0.03274139389395714,
0.014685031957924366,
-0.004718608222901821,
-0.024529676884412766,
0.0024979813024401665,
-0.019510775804519653,
0.04374304413795471,
-0.020980864763259888,
-0.0018807186279445887,
0.03925678879022598,
-0.05489833652973175,
-0.021102452650666237,
0.04638401418924332,
0.0031598899513483047,
0.030062004923820496,
-0.03296200558543205,
-0.0503753200173378,
0.03227594494819641,
0.0027927954215556383,
-0.06455285102128983,
-0.00827535055577755,
0.0027459345292299986,
0.03785516321659088,
-0.011571086011826992,
-0.006732444278895855,
-0.031858205795288086,
-0.04568248242139816,
-0.0392121821641922,
0.029407404363155365,
0.013157486915588379,
-0.0326521135866642,
0.007434405852109194,
0.014195269905030727,
0.03281846269965172,
0.030142301693558693,
-0.043058302253484726,
0.009040266275405884,
0.018220823258161545,
-0.016728168353438377,
0.016517091542482376,
0.030580662190914154,
0.03677797317504883,
0.00341247720643878,
-0.018992016091942787,
-0.035618171095848083,
-0.0007162787951529026,
0.011007820256054401,
-0.03224916011095047,
-0.026024606078863144,
0.03687652572989464,
-0.002329700393602252,
-0.020352233201265335,
-0.0071945409290492535,
-0.013554364442825317,
-0.0071396068669855595,
0.035858433693647385,
-0.014505001716315746,
-0.028192540630698204,
-0.0579947866499424,
-0.028502468019723892,
0.011111908592283726,
-0.0055871750228106976,
0.039408497512340546,
0.0037892134860157967,
0.019482141360640526,
-0.019229896366596222,
-0.007438491564244032,
0.0085622388869524,
-0.006121357902884483,
0.01873534359037876,
0.0029786392115056515,
0.023908276110887527,
-0.012841167859733105,
0.009854289703071117,
-0.016266683116555214,
-0.04973549768328667,
-0.02139684371650219,
0.007037018425762653,
0.07440701872110367,
0.02434893324971199,
0.018313255161046982,
0.04022977128624916,
-0.02115459367632866,
-0.030721677467226982,
-0.0166864562779665,
-0.014673370867967606,
0.010974857024848461,
-0.013426610268652439,
0.01719949208199978,
-0.027072878554463387,
-0.00646620150655508,
0.027251286432147026,
0.04269449785351753,
-0.030788343399763107,
0.003977809567004442,
0.029432231560349464,
0.024276869371533394,
0.017504282295703888,
-0.019806645810604095,
-0.033652838319540024,
0.027067936956882477,
-0.03824419528245926,
0.005205177236348391,
0.027981257066130638,
0.03698405623435974,
0.011975903064012527,
0.07801128178834915,
0.029168331995606422,
-0.03204125165939331,
-0.0024479315616190434,
-0.07836916297674179,
-0.005967940203845501,
-0.0016807779902592301,
0.01184522733092308,
0.023866355419158936,
0.025385648012161255,
0.05960613861680031,
-0.017090197652578354,
0.010963696986436844,
-0.010736373253166676,
-0.03185572102665901,
0.0016308928607031703,
0.017023684456944466,
-0.031842995434999466,
0.05843844637274742,
-0.019449763000011444,
-0.025483233854174614,
0.04168371111154556,
-0.046156130731105804,
0.03895948827266693,
0.016564691439270973,
0.05602579563856125,
-0.00392972631379962,
0.03027665987610817,
-0.012283289805054665,
-0.009733106940984726,
-0.024288136512041092,
-0.03876844421029091,
0.1538582593202591,
0.043426718562841415,
0.05481690913438797,
-0.046843793243169785,
-0.017245503142476082,
-0.027293888852000237,
0.01577703468501568,
0.006179951597005129,
-0.024683142080903053,
-0.016725005581974983,
0.0001597866794327274,
-0.004407471977174282,
0.0751643031835556,
0.02100047655403614,
-0.016957679763436317,
0.03157486021518707,
-0.055070918053388596,
-0.008339555002748966,
-0.00471661938354373,
0.03999265283346176,
-0.003730821656063199,
0.009507651440799236,
-0.07244647294282913,
-0.013003116473555565,
-0.019986014813184738,
0.008667860180139542,
0.0059393360279500484,
-0.0446985699236393,
0.0011493124766275287,
-0.0451115220785141,
-0.051036182790994644,
0.018408311530947685,
-0.018572602421045303,
-0.025174472481012344,
-0.06576696783304214,
0.024628089740872383,
0.022256391122937202,
-0.008698583580553532,
0.007850619032979012,
0.010337487794458866,
0.02448028326034546,
-0.009629065170884132,
0.04383963719010353,
0.005224318243563175,
-0.0039161392487585545,
0.015386313199996948,
-0.028597485274076462,
0.037551745772361755,
0.018970049917697906,
-0.005399226676672697,
-0.0033135474659502506,
-0.013367450796067715,
0.025494664907455444,
-0.050619784742593765,
0.006928437855094671,
0.00022229137539397925,
0.03031712956726551,
0.0023553723003715277,
-0.01235178578644991,
0.0022619788069278,
0.028535595163702965,
0.02255028858780861,
-0.016633613035082817,
-0.022419704124331474,
-0.037027087062597275,
-0.005408855155110359,
0.0027887679170817137,
0.040104325860738754,
0.023501046001911163,
-0.030079251155257225,
-0.006274953950196505,
-0.012388745322823524,
-0.030081486329436302,
-0.005414704326540232,
-0.003926584497094154,
-0.005087789613753557,
0.0589839406311512,
0.012791883200407028,
-0.0070643373765051365,
-0.023998534306883812,
-0.08738958835601807,
-0.008180595003068447,
0.007529370486736298,
-0.05316822603344917,
0.007563278079032898,
0.006856816355139017,
-0.00045939520350657403,
0.062024086713790894,
-0.02121526002883911,
-0.0332389771938324,
-0.0006447258056141436,
0.007498555816709995,
0.03133980557322502,
-0.03014691174030304,
-0.02441764995455742,
0.007428484503179789,
-0.031054852530360222,
-0.013800541870296001,
-0.001914582564495504,
-0.010168810375034809,
0.024352533742785454,
0.02027737908065319,
-0.022119376808404922,
0.0430460162460804,
-0.024534745141863823,
-0.008805853314697742,
0.03345594182610512,
-0.024835413321852684,
0.02050042152404785,
0.006569344084709883,
0.00027863073046319187,
-0.045385148376226425,
-0.019809458404779434,
-0.027764497324824333,
0.007631309330463409,
-0.012250632978975773,
-0.02098117396235466,
-0.02356860600411892,
0.034787617623806,
-0.009417940862476826,
0.02441769652068615,
-0.006725257728248835,
0.0006349299219436944,
-0.0035871057771146297,
0.027223573997616768,
0.016294024884700775,
0.0060043600387871265,
0.028008311986923218,
0.059667836874723434,
-0.022854145616292953,
-0.031515758484601974,
0.014342513866722584,
0.04802580550312996,
-0.03504885733127594,
0.02163372002542019,
0.022660648450255394,
0.029019365087151527,
0.004401301499456167,
0.03562261536717415,
-0.0017693547997623682,
0.0006447809864766896,
-0.02699599415063858,
-0.0499909482896328,
0.03515578806400299,
-0.001338148140348494,
0.0066892472095787525,
0.028502948582172394,
0.004936512093991041,
-0.044796377420425415,
0.02934722602367401,
0.027362408116459846,
-0.009892851114273071,
-0.02148290164768696,
-0.02679680846631527,
0.022489424794912338,
-0.037263721227645874,
0.052651770412921906,
0.002735688118264079,
0.001425937400199473,
0.02921762876212597,
0.015526284463703632,
-0.03180960565805435,
-0.001499483361840248,
0.0039682285860180855,
-0.007269340567290783,
-0.004454754758626223,
0.009457250125706196,
0.01805081218481064,
0.03324691206216812,
0.07012949138879776,
-0.041802048683166504,
0.02827674336731434,
0.0412273146212101,
0.02048313245177269,
-0.11712914705276489,
-0.008993055671453476,
0.03399839997291565,
0.0011070802574977279,
0.033197011798620224,
-0.04785862937569618,
0.02729162573814392,
0.04937424138188362,
-0.09299556910991669,
0.004522957373410463,
-0.008572527207434177,
-0.012702148407697678,
0.023673346266150475,
-0.022485001012682915,
0.001939235720783472,
0.03438711166381836,
-0.0077208345755934715,
0.04842546209692955,
0.012903081253170967,
0.018652120605111122,
-0.019154421985149384,
-0.04091998189687729,
-0.04938328266143799,
0.010562757030129433,
0.0202235858887434,
-0.009186307899653912,
0.1032029464840889,
-0.023144163191318512,
-0.014263194054365158,
0.0314641036093235,
-0.008377925492823124,
-0.0006324090645648539,
-0.015045306645333767,
0.00347808375954628,
0.006518780719488859,
0.021158363670110703,
-0.00953486654907465,
-0.027303339913487434,
0.012363525107502937,
0.015385802835226059,
-0.0008975460077635944,
0.01411365158855915,
-0.04276358708739281,
0.023193862289190292,
-0.021725820377469063,
-0.04455695301294327,
-0.014666909351944923,
0.02011577971279621,
-0.014573122374713421,
-0.02322893962264061,
0.029634810984134674,
0.031048618257045746,
-0.015527303330600262,
0.009545168839395046,
0.057434067130088806,
-0.035534992814064026,
-0.006744150072336197,
-0.00013290924835018814,
0.039279449731111526,
0.015992868691682816,
0.03203556686639786,
-0.0014639273285865784,
-0.02838483452796936,
-0.00734756700694561,
0.0070546711795032024,
-0.0006559699540957808,
-0.0761694461107254,
0.005181481596082449,
-0.026409117504954338,
0.02440141700208187,
0.017070498317480087,
-0.012111538089811802,
-0.06677179038524628,
0.020101025700569153,
-0.007346984930336475,
0.04245888069272041,
-0.030254116281867027,
0.0025868879165500402,
-0.011095253750681877,
-0.08855349570512772,
0.000012812882232537959,
0.033803604543209076,
-0.007247040513902903,
-0.012082166969776154,
-0.034419674426317215,
0.03138064220547676,
0.02840547077357769,
0.07214447110891342,
0.0229710191488266,
-0.049821097403764725,
0.03324705362319946,
-0.02796010673046112,
-0.005105260759592056,
-0.03046778403222561,
-0.0175425186753273,
-0.014693080447614193,
0.026808978989720345,
-0.010762096382677555,
0.012414243072271347,
-0.028405319899320602,
0.0039544543251395226,
-0.0024375515058636665,
0.006277371663600206,
0.02358483336865902,
0.0012312338221818209,
-0.027437563985586166,
0.04589739441871643,
-0.0011772610014304519,
-0.03194127604365349,
0.020145200192928314,
0.01285271905362606,
-0.014417367987334728,
0.033234644681215286,
-0.06043306738138199,
-0.03420312702655792,
0.025843363255262375,
-0.022487549111247063,
-0.0179204773157835,
-0.02594883181154728,
0.009562014602124691,
0.04231753200292587,
0.002731363521888852,
-0.0022387190256267786,
0.0500214546918869,
-0.04055126756429672,
-0.018724702298641205,
0.053531475365161896,
0.013524188660085201,
0.0021116186399012804,
0.026201557368040085,
0.0030228709802031517,
0.02704695798456669,
-0.033704280853271484,
0.010764993727207184,
0.022358521819114685,
0.0025895468425005674,
0.031896788626909256,
-0.0005252001574262977,
0.03011402115225792,
0.0004971195594407618,
0.010291309095919132,
0.021697161719202995,
-0.0017633677925914526,
-0.03266410529613495,
0.025454817339777946,
0.03269056975841522,
-0.004522537812590599,
-0.014622318558394909,
0.022950537502765656,
-0.020577581599354744,
0.03347402438521385,
-0.011716404929757118,
0.00043651857413351536,
-0.05032607913017273,
-0.007435206323862076,
0.013442641124129295,
0.006571651436388493,
-0.013886895962059498,
0.026083379983901978,
-0.03141427040100098,
0.012748707085847855,
-0.007518867030739784,
-0.048781681805849075,
0.010835962370038033,
-0.04304955154657364,
-0.03301357850432396,
0.033298879861831665,
0.0017017428763210773,
0.016146916896104813,
-0.017358163371682167,
0.016141360625624657,
-0.030881637707352638,
0.020084256306290627,
0.026302849873900414,
0.022940490394830704,
-0.014841747470200062,
-0.008189952932298183,
-0.038168396800756454,
0.02247321791946888,
-0.0711597427725792,
0.005517374258488417,
-0.007002342026680708,
0.027896933257579803,
0.0361771397292614,
0.017501315101981163
] |
<p>Here is a small experiment my tutor once told us for just amusement. It works for myopic people at least, and can be a good check to see if you have myopia. </p>
<blockquote>
<p>With your naked eye, ("remove the spectacles" for myopic spectacle
wearers) see a considerably distant object (a few meters). It should
be a bit blurred and unclear if you have myopia. Then, using your
two thumbs and first fingers of both hands, create a tiny square in
between. Using a single eye, look through the square. For a large
square, the image is still blurred. But as you purse your fingers
tightly and reduce the dimensions of the space between, you will
eventually reach a point when the image comes in perfect focus. The
image is perfectly clear as you would see it with spectacles. For an object 1-2m away, the square needs to be much smaller than that in the picture.</p>
</blockquote>
<p><img src="http://i.stack.imgur.com/8Vw2e.jpg" alt="Not my hands"><img src="http://i.stack.imgur.com/rWO8M.jpg" alt="Not my hands"></p>
<p>This works for almost any myopic person. Why does it work? Does diffraction come into play? If it does, I don't see how that can adequately refract rays to act as a lens?</p> | 1,422 | [
0.0027224081568419933,
-0.022854657843708992,
0.02578737959265709,
-0.018570248037576675,
0.009676722809672356,
0.002943025901913643,
-0.030187679454684258,
-0.025027047842741013,
-0.008329065516591072,
-0.003631511004641652,
0.06191638484597206,
0.05835181102156639,
0.03210886940360069,
-0.006859913468360901,
-0.005018129013478756,
-0.006787784863263369,
-0.020260322839021683,
-0.012879920192062855,
-0.015327485278248787,
-0.025008467957377434,
-0.03708465397357941,
0.037516038864851,
-0.0296663548797369,
-0.004836547654122114,
-0.06854531913995743,
0.002473921747878194,
0.01432445552200079,
-0.01952957734465599,
0.035529255867004395,
0.04848247766494751,
-0.013713781721889973,
0.015390167944133282,
-0.004402849357575178,
0.01910264603793621,
-0.0018162355991080403,
0.00576943950727582,
-0.013615460135042667,
0.013287910260260105,
0.0026178781408816576,
-0.007565739098936319,
0.030509954318404198,
0.01595247909426689,
0.00786791555583477,
0.0575704462826252,
-0.05368651822209358,
0.018962537869811058,
-0.008518531918525696,
-0.04360015690326691,
0.014421910047531128,
-0.028527893126010895,
0.04853913187980652,
-0.0017173028318211436,
0.05392390489578247,
0.05478520318865776,
0.01306298840790987,
0.012864802964031696,
0.06665162742137909,
0.049024466425180435,
-0.020445596426725388,
-0.0363951101899147,
0.004595005884766579,
0.013146578334271908,
-0.03542231395840645,
-0.0025868851225823164,
-0.005332497414201498,
-0.01725492812693119,
-0.019605815410614014,
-0.006333653815090656,
0.016034536063671112,
-0.03495077043771744,
0.022300750017166138,
0.022087106481194496,
0.05625969171524048,
0.012163261882960796,
0.009068408980965614,
-0.05564263463020325,
0.0023102709092199802,
0.022417038679122925,
0.024766070768237114,
0.01978418044745922,
-0.004767012782394886,
0.008331608027219772,
0.01673765853047371,
0.032535940408706665,
0.07261120527982712,
-0.03565824031829834,
0.09193994104862213,
-0.03304088115692139,
-0.006737693678587675,
0.006586733739823103,
-0.017998890951275826,
-0.03488355129957199,
0.026329081505537033,
-0.010232592932879925,
0.0034582051448524,
0.02825121395289898,
-0.04021558538079262,
0.0405164510011673,
-0.004619312006980181,
-0.016650591045618057,
-0.02518169768154621,
0.010882026515901089,
0.018786795437335968,
0.0461968295276165,
-0.03307582065463066,
-0.0443187952041626,
-0.0032795891165733337,
0.0285186730325222,
-0.011854521930217743,
0.01658504642546177,
-0.04897573962807655,
0.0048209140077233315,
-0.01210163626819849,
0.03297248110175133,
0.038518741726875305,
-0.026157546788454056,
0.003956666681915522,
-0.0170326866209507,
0.060126565396785736,
0.10534143447875977,
0.04895037040114403,
-0.02676975540816784,
-0.003584526712074876,
-0.02960066869854927,
-0.058161646127700806,
0.048845142126083374,
0.009151989594101906,
-0.0004071082512382418,
-0.009694255888462067,
-0.015330920927226543,
0.002321346662938595,
0.002765880199149251,
0.033822279423475266,
0.009957869537174702,
0.015671486034989357,
0.016587404534220695,
-0.11440114676952362,
-0.02892264537513256,
0.04952416941523552,
0.021413343027234077,
-0.029998643323779106,
-0.04617159441113472,
0.031210169196128845,
0.04633244127035141,
0.06536027789115906,
0.03337923437356949,
0.024854036048054695,
-0.04344213381409645,
0.03367997705936432,
-0.028423210605978966,
-0.05141865462064743,
0.013858313672244549,
0.0006664064712822437,
-0.01931505650281906,
0.006216981448233128,
-0.06868363916873932,
0.03938345983624458,
0.03581113740801811,
0.016178255900740623,
-0.062196385115385056,
0.0746617317199707,
0.005587934982031584,
0.013112097978591919,
-0.0030002975836396217,
-0.02082635834813118,
-0.06241751089692116,
0.09882102906703949,
-0.00441189156845212,
0.027206938713788986,
0.01197865977883339,
0.0009476623963564634,
0.07985610514879227,
0.008858070708811283,
-0.010611729696393013,
0.008920389227569103,
0.0031709533650428057,
0.01263472344726324,
-0.0000641426959191449,
-0.001157825579866767,
0.019155295565724373,
-0.01033191941678524,
0.00490387761965394,
-0.011945259757339954,
-0.016973217949271202,
0.019250264391303062,
0.05435182526707649,
0.006781730335205793,
-0.014368310570716858,
0.009101093746721745,
-0.06874927878379822,
-0.019997743889689445,
-0.04785781726241112,
0.008874062448740005,
-0.004458235111087561,
-0.002768592443317175,
-0.013326478190720081,
-0.01515648141503334,
0.004006941802799702,
0.0036081871949136257,
-0.03664997220039368,
-0.026150789111852646,
0.02579004503786564,
0.03823917359113693,
0.03137044608592987,
0.02067723497748375,
0.06546549499034882,
0.0637463927268982,
0.0020957724191248417,
-0.009518123231828213,
-0.01153868343681097,
0.004974969197064638,
0.022596843540668488,
-0.020866135135293007,
0.019747639074921608,
0.01189500093460083,
0.012968768365681171,
0.021293098106980324,
0.04217591509222984,
0.014792549423873425,
0.007848669774830341,
-0.030654385685920715,
0.07018612325191498,
0.002428893931210041,
0.0022918677423149347,
0.03395630419254303,
0.019424742087721825,
0.0034147934056818485,
0.00009195231541525573,
0.017689833417534828,
-0.020631173625588417,
-0.048125021159648895,
-0.01759556122124195,
0.010803641751408577,
0.01581849530339241,
-0.035206589847803116,
0.01051903422921896,
0.004875917918980122,
0.04187392443418503,
0.014441491104662418,
0.0569240003824234,
0.0034094802103936672,
0.0000873986937222071,
-0.029340572655200958,
0.023665260523557663,
0.03109860233962536,
0.03279414400458336,
-0.01018068753182888,
0.008422743529081345,
-0.0021971683017909527,
-0.0022956684697419405,
0.019687635824084282,
0.003824796061962843,
-0.0014143893495202065,
0.0025988295674324036,
-0.015907250344753265,
0.011021901853382587,
-0.010659902356564999,
0.013535209000110626,
-0.046623483300209045,
0.014053262770175934,
-0.01523570716381073,
-0.013028500601649284,
-0.06909636408090591,
-0.00698678195476532,
0.025974854826927185,
0.039492055773735046,
-0.04456496611237526,
0.04081298038363457,
0.025541219860315323,
-0.07306651771068573,
-0.034039389342069626,
-0.02007800154387951,
-0.0010304347379133105,
-0.028010066598653793,
-0.00007314694084925577,
-0.01156296581029892,
0.071745865046978,
0.042488325387239456,
-0.03173588216304779,
-0.05281122773885727,
-0.015795059502124786,
-0.018520798534154892,
0.026759587228298187,
-0.014210422523319721,
-0.027860689908266068,
0.004469654057174921,
-0.00704535748809576,
0.0076530403457582,
0.04625900462269783,
0.02451731264591217,
0.00959304254502058,
-0.030405648052692413,
0.0003004419559147209,
-0.02595415897667408,
-0.008047426119446754,
-0.007668791338801384,
0.006023614201694727,
-0.01872914284467697,
0.011891371570527554,
0.0202690027654171,
0.020873578265309334,
-0.07412540167570114,
0.004782532807439566,
-0.05150526016950607,
-0.061803221702575684,
0.0015417734393849969,
0.04841093719005585,
0.011087246239185333,
-0.04016321897506714,
-0.009697613306343555,
-0.009221142157912254,
-0.01389315165579319,
0.03654536232352257,
-0.06827002018690109,
-0.06481514126062393,
0.03213193267583847,
0.03171023726463318,
0.027692584320902824,
-0.004313869867473841,
-0.0035832482390105724,
0.06878744810819626,
0.015447797253727913,
-0.01338919997215271,
-0.040077630430459976,
-0.012339078821241856,
-0.017729470506310463,
-0.015894690528512,
-0.007278572767972946,
0.03846144676208496,
-0.011090312153100967,
0.03200138732790947,
0.01586216501891613,
0.03482302278280258,
0.05368693917989731,
0.06340345740318298,
0.009053737856447697,
-0.046103619039058685,
-0.0039954897947609425,
-0.07295206934213638,
0.04910561814904213,
0.020503167062997818,
-0.07282135635614395,
-0.007250107824802399,
-0.020393462851643562,
0.047840915620326996,
0.0045263497158885,
-0.057755474001169205,
0.028217719867825508,
-0.03692130371928215,
0.03148699179291725,
0.013952174223959446,
0.016940616071224213,
0.02810153178870678,
0.019566332921385765,
-0.017350930720567703,
0.011159167625010014,
0.04644295200705528,
0.00039555030525662005,
-0.015532984398305416,
0.023141169920563698,
0.033071812242269516,
0.006720059551298618,
-0.027099335566163063,
-0.018828285858035088,
0.018160900101065636,
0.026986097916960716,
-0.021451743319630623,
0.0007440836634486914,
0.033898789435625076,
0.0020919630769640207,
0.005181291606277227,
0.0011444196570664644,
-0.003260647878050804,
-0.005723603069782257,
-0.04081292077898979,
0.014851567335426807,
-0.026195824146270752,
0.00876295194029808,
0.03057105652987957,
0.030390115454792976,
0.02141292206943035,
0.016679110005497932,
-0.015621769241988659,
0.030166994780302048,
-0.0661441758275032,
0.024317359551787376,
0.002541355788707733,
-0.05086473003029823,
-0.027302211150527,
-0.00739356828853488,
-0.008168612606823444,
-0.010120881721377373,
0.0048011536709964275,
-0.014410382136702538,
0.0049669090658426285,
-0.015970677137374878,
-0.004663508385419846,
0.02475779317319393,
-0.02325521595776081,
-0.0320628359913826,
0.01672534830868244,
0.02344823256134987,
0.016699889674782753,
0.010267545469105244,
0.018635669723153114,
-0.0042167468927800655,
0.007031209301203489,
-0.0030564069747924805,
-0.022274300456047058,
0.01944102719426155,
0.022201554849743843,
0.0021173094864934683,
0.04464348405599594,
-0.036776915192604065,
0.02582242712378502,
0.01674836501479149,
0.03261978551745415,
-0.005528708919882774,
-0.0018198954639956355,
-0.03886742889881134,
-0.03693357855081558,
-0.07042372226715088,
-0.010024799033999443,
0.03100045770406723,
-0.02541607804596424,
-0.009143718518316746,
0.01672503724694252,
0.013768552802503109,
-0.028372403234243393,
0.014242623932659626,
0.04771634191274643,
-0.0016570466104894876,
-0.03087233565747738,
-0.07694979757070541,
-0.033840496093034744,
-0.02256924845278263,
0.03313286975026131,
0.05926690250635147,
0.01887999288737774,
-0.0030930908396840096,
-0.06720487773418427,
0.04430868849158287,
0.004752629436552525,
-0.005925378762185574,
0.059209976345300674,
-0.021168068051338196,
-0.01813913881778717,
-0.012935527600347996,
0.05237748846411705,
0.02183634601533413,
0.044268086552619934,
0.02202589437365532,
-0.015442627482116222,
-0.03946324810385704,
-0.06368813663721085,
0.012462432496249676,
0.02386883832514286,
0.07774431258440018,
0.018731286749243736,
0.007431455887854099,
-0.038188636302948,
-0.04070344939827919,
0.023847898468375206,
-0.048144593834877014,
0.040898267179727554,
-0.046281371265649796,
0.014398775063455105,
-0.029090793803334236,
-0.0026911073364317417,
-0.039106715470552444,
-0.009597052820026875,
-0.03673133626580238,
-0.03898164629936218,
0.002103238133713603,
-0.009639093652367592,
-0.02791517600417137,
0.011980123817920685,
-0.007755944039672613,
0.06713294982910156,
0.011621549725532532,
-0.01776031404733658,
-0.010811839252710342,
-0.04700951278209686,
-0.058643799275159836,
-0.04081842675805092,
0.021895719692111015,
0.015418262220919132,
-0.054448410868644714,
0.05677002668380737,
-0.010710972361266613,
-0.0365770161151886,
0.03488806262612343,
0.006179430987685919,
-0.02828884869813919,
0.0356011688709259,
-0.03728500381112099,
-0.02082732878625393,
0.0411396361887455,
0.012315000407397747,
0.04613381624221802,
0.054487720131874084,
-0.009604561142623425,
0.02234809845685959,
-0.04927723482251167,
0.03295550495386124,
0.001338651985861361,
-0.0167890265583992,
0.00752120791003108,
0.01122523657977581,
-0.04834487661719322,
0.041139788925647736,
-0.012868276797235012,
0.03487003222107887,
0.012881680391728878,
-0.021004609763622284,
-0.006851616315543652,
0.04253194481134415,
0.008604448288679123,
0.025044262409210205,
0.028287215158343315,
-0.011121452786028385,
0.040855180472135544,
-0.01182490959763527,
0.015536039136350155,
0.011491761542856693,
0.010786867700517178,
0.028035350143909454,
-0.006436631083488464,
0.01702021434903145,
-0.044315535575151443,
0.005240563303232193,
-0.017792101949453354,
-0.046737801283597946,
0.04807356745004654,
-0.03675294294953346,
0.013220582157373428,
0.04744194075465202,
-0.04703257605433464,
-0.026027865707874298,
0.007821928709745407,
-0.030748335644602776,
0.0597575344145298,
-0.015294820070266724,
0.008859299123287201,
0.03756282851099968,
-0.00892642978578806,
-0.03608103096485138,
-0.02356034889817238,
0.023995576426386833,
0.036786794662475586,
0.007510121446102858,
-0.03371456637978554,
-0.015026315115392208,
0.017541714012622833,
-0.05369240790605545,
-0.019286364316940308,
0.027927998453378677,
-0.02233589068055153,
-0.014230991713702679,
0.00911888387054205,
-0.02290773205459118,
0.07634907960891724,
0.015164759941399097,
-0.058847516775131226,
0.0064495522528886795,
-0.05515934154391289,
-0.008592464029788971,
0.015906130895018578,
0.045392680913209915,
-0.046561554074287415,
-0.05859934538602829,
-0.028459522873163223,
-0.00956947822123766,
-0.0011800911743193865,
0.0010835027787834406,
-0.012911575846374035,
0.0013333873357623816,
0.003070349805057049,
0.0007619070820510387,
-0.032571058720350266,
0.03558681532740593,
-0.040872395038604736,
-0.011558705009520054,
-0.005337215960025787,
-0.0018037378322333097,
-0.017162930220365524,
-0.030680598691105843,
0.041652578860521317,
-0.003670664504170418,
-0.007154899649322033,
-0.031046448275446892,
0.057826343923807144,
-0.010700787417590618,
0.03578769415616989,
0.021957529708743095,
-0.0002550474018789828,
0.01607796922326088,
-0.011188183911144733,
0.015397355891764164,
-0.0034337439574301243,
0.04918520897626877,
-0.049188487231731415,
-0.0015197070315480232,
-0.029056034982204437,
-0.012173565104603767,
0.07976080477237701,
-0.028500819578766823,
0.05460185930132866,
0.026638522744178772,
-0.036214858293533325,
0.020027615129947662,
0.0022016617003828287,
0.012660399079322815,
-0.017270315438508987,
-0.023643238469958305,
0.04371454194188118,
-0.013987835496664047,
0.030143579468131065,
0.0004473006702028215,
0.043341200798749924,
0.03525150194764137,
0.006258403416723013,
0.050582144409418106,
0.05973852425813675,
0.016697648912668228,
-0.03562777489423752,
-0.021036002784967422,
-0.00004167489896644838,
-0.08058842271566391,
0.00962408073246479,
0.011503446847200394,
-0.022524774074554443,
0.0184031929820776,
-0.030199451372027397,
0.016342075541615486,
-0.024482443928718567,
-0.0062511214055120945,
-0.018814021721482277,
-0.003258847165852785,
-0.003164369612932205,
0.015911148861050606,
-0.012120774015784264,
-0.0628223568201065,
-0.005393689498305321,
0.021611230447888374,
0.05518490821123123,
-0.030387094244360924,
-0.06948745995759964,
-0.0012840019771829247,
-0.04018842801451683,
-0.037751901894807816,
0.06544069945812225,
0.019045894965529442,
-0.046281419694423676,
0.015852065756917,
-0.02995394729077816,
0.03557225689291954,
0.03663719445466995,
0.006252822000533342,
-0.02529066428542137,
0.004428306128829718,
-0.005228063557296991,
0.01491233054548502,
-0.00184888846706599,
-0.011928016319870949,
0.11041680723428726,
0.02679445780813694,
-0.015039080753922462,
-0.022062741219997406,
0.014681614935398102,
-0.04104318842291832,
-0.0006799887050874531,
-0.0298242699354887,
0.027959033846855164,
-0.04208766669034958,
0.02097977325320244,
0.02533898688852787,
0.04542728140950203,
0.035122618079185486,
-0.0108076436445117,
0.04013585299253464,
-0.019330326467752457,
-0.04046051949262619,
0.015118535608053207,
-0.005422741174697876,
0.025592364370822906,
0.025293800979852676,
-0.03948938474059105,
0.027193116024136543,
-0.01688859798014164,
-0.02366919443011284,
0.0021341631654649973,
-0.02438308671116829,
0.053110092878341675,
0.03144111484289169,
-0.04522315040230751,
-0.0023615036625415087,
0.009336375631392002,
-0.036523379385471344,
0.0012967607472091913,
0.007067128550261259,
0.028220515698194504,
-0.030852366238832474,
0.005178519058972597,
0.020308854058384895,
0.006542057264596224,
0.005417049862444401,
0.011377759277820587,
0.0012659949716180563,
-0.026637867093086243,
0.004970420151948929,
-0.029674218967556953,
0.025509579107165337,
-0.009807274676859379,
0.006810387596487999,
-0.01861889474093914,
-0.0195479653775692,
-0.0073652807623147964,
-0.06427837908267975,
-0.019750669598579407,
0.03529512882232666,
-0.0021048288326710463,
0.003448316128924489,
-0.04936056211590767,
0.009532008320093155,
0.02976936288177967,
0.01082442607730627,
-0.005603030789643526,
0.002254834631457925,
0.03898852691054344,
-0.03673894330859184,
0.005082222633063793,
0.02126440592110157,
-0.009928997606039047,
-0.030628185719251633,
-0.048114240169525146,
-0.007110456936061382,
0.001596051617525518,
-0.0016810102388262749,
-0.00976505409926176,
0.03350917994976044,
0.0328659787774086,
-0.004397931508719921,
-0.033457059413194656,
-0.011906487867236137,
-0.037852611392736435,
0.02035660482943058,
-0.0630694106221199,
0.013640419580042362,
-0.032338183373212814,
0.0006095845601521432,
0.03362523019313812,
0.03602778539061546,
0.0040719229727983475,
0.0012822347925975919,
0.002669125096872449,
0.04742371290922165,
0.018940899521112442,
-0.009339851327240467,
-0.06258869916200638,
0.0070929559879004955,
-0.0008030841127038002,
0.008197544142603874,
-0.008197983726859093,
0.02767646685242653,
0.015984322875738144,
0.04322497919201851,
0.029967471957206726,
-0.019015423953533173,
-0.06306055933237076,
0.02756037376821041,
-0.011085659265518188,
-0.05173185467720032,
0.01855396293103695,
-0.005641803611069918,
-0.006680277641862631,
-0.001359984278678894,
0.007130705751478672,
-0.006987712346017361,
0.0034478965681046247,
-0.0025572404265403748,
0.0370379313826561,
0.014109021984040737,
0.0001096933483495377,
0.005710193421691656,
0.016791436821222305,
-0.039381466805934906,
-0.044320885092020035,
-0.049386247992515564,
-0.012155735865235329,
-0.03024628758430481,
-0.010718271136283875,
-0.006434799637645483,
0.034721311181783676,
0.0064324443228542805,
-0.011091459542512894,
0.02153785526752472,
-0.004741741809993982,
0.0011742243077605963,
0.036726728081703186,
0.03224509209394455,
0.002981798257678747,
0.009378046728670597,
0.0017750256229192019,
0.018612971529364586,
0.048072509467601776,
-0.044064510613679886,
-0.014788379892706871,
-0.011466916650533676,
-0.012771210633218288,
0.02670309878885746,
0.007149183191359043,
-0.027166424319148064,
0.018120475113391876,
0.07307683676481247,
-0.01461268961429596,
-0.05321492627263069,
-0.0017548243049532175,
0.007801062893122435,
0.04891045391559601,
0.004508793819695711,
0.00034601680818013847,
-0.020195072516798973,
-0.05596799775958061,
0.06970144063234329,
-0.018494557589292526,
0.046324942260980606,
-0.007909807376563549,
0.02212446928024292,
-0.0289907269179821,
-0.042695268988609314,
-0.07041513174772263,
-0.009585545398294926,
0.007503512781113386,
0.02562563307583332,
-0.02373071387410164,
0.06415588408708572,
0.01609441079199314,
0.019691674038767815,
-0.0858425721526146,
0.00106274604331702,
0.023056985810399055,
0.052295953035354614,
0.07552585750818253,
-0.05576540529727936,
0.023315340280532837,
0.029088368639349937,
-0.052616942673921585,
-0.023295624181628227,
-0.007758540101349354,
-0.03469527140259743,
-0.04001772403717041,
0.017366457730531693,
-0.005559800658375025,
-0.002474028617143631,
-0.0016822111792862415,
0.05626443773508072,
0.025327341631054878,
0.011676134541630745,
-0.04845155030488968,
0.01849469356238842,
0.027026263996958733,
0.033670056611299515,
-0.018805265426635742,
0.016628647223114967,
0.054059747606515884,
-0.01929132640361786,
-0.020236553624272346,
-0.00043692783219739795,
-0.026142356917262077,
0.02632199600338936,
0.008744041435420513,
0.02862413413822651,
0.00414220942184329,
0.0304685328155756,
0.009661884978413582,
0.0215209499001503,
-0.016724389046430588,
-0.0009965532226487994,
0.01927940919995308,
0.044328294694423676,
-0.04123269021511078,
-0.010173308663070202,
0.07166224718093872,
-0.028489429503679276,
-0.03829701617360115,
0.028283340856432915,
0.02177058905363083,
-0.009474575519561768,
0.02504032850265503,
0.011505821719765663,
0.026454666629433632,
-0.01800808310508728,
-0.0003481925232335925,
-0.04595612734556198,
-0.002928053727373481,
0.016901206225156784,
-0.01712649129331112,
-0.04512915015220642,
0.027656568214297295,
-0.04237046092748642,
-0.041280824691057205,
0.010799229145050049,
-0.009189325384795666,
-0.02640894614160061,
-0.007695198990404606,
-0.012305721640586853,
0.03483719006180763,
0.035924628376960754,
0.03178595006465912,
-0.012830190360546112,
0.004602036438882351,
0.017035434022545815,
0.019551265984773636,
0.006425624247640371,
0.034886009991168976,
-0.026981845498085022,
-0.04542901739478111,
-0.0587477833032608,
0.020740419626235962,
-0.007783637847751379,
-0.02382725290954113,
-0.0658433735370636,
-0.027775077149271965,
-0.026491977274417877,
0.030689625069499016,
0.041931334882974625,
-0.0072697727009654045,
0.008506149053573608,
-0.012089977040886879,
0.018988801166415215,
-0.01268981583416462,
-0.0626075491309166,
-0.022922802716493607,
0.00461302837356925,
-0.01778975874185562,
-0.03221036121249199,
0.011370097286999226,
-0.03328222781419754,
0.021905427798628807,
0.019848553463816643,
0.002009490504860878,
0.021748576313257217,
0.012770963832736015,
-0.04451806843280792,
0.03198165073990822,
0.008916061371564865,
-0.04111068695783615,
0.027475187554955482,
-0.007580054923892021,
-0.02621435932815075,
-0.00017527809541206807,
-0.04378630220890045,
-0.04717833921313286,
0.02720051445066929,
-0.06718605011701584,
0.0013213984202593565,
-0.008386852219700813,
0.0018951997626572847,
0.03125528618693352,
-0.024309782311320305,
-0.019953027367591858,
-0.014790231361985207,
-0.016614144667983055,
-0.03836726397275925,
0.06184559315443039,
0.023593783378601074,
0.0047769383527338505,
-0.019711295142769814,
0.026538530364632607,
0.003235709620639682,
-0.05939734727144241,
-0.0022670419421046972,
0.04818528890609741,
-0.004323331639170647,
-0.024433527141809464,
0.023232627660036087,
0.058517053723335266,
0.04153352230787277,
0.02003253810107708,
-0.028521066531538963,
0.05550958961248398,
0.0034045090433210135,
-0.04889895021915436,
-0.02095438539981842,
-0.02002011425793171,
0.00989165436476469,
0.025266220793128014,
0.019054323434829712,
0.063941590487957,
0.0004009915282949805,
-0.007639373652637005,
0.0006410505156964064,
0.006571419537067413,
-0.022359002381563187,
0.031771544367074966,
0.04884984344244003,
0.003148778574541211,
-0.010495680384337902,
-0.055136848241090775,
-0.007235519587993622,
-0.01192154549062252,
-0.00335532589815557,
-0.015434898436069489,
0.06484589725732803,
-0.0064051453955471516,
-0.02177588641643524,
-0.0033531442750245333,
0.00162033352535218,
-0.020856497809290886,
-0.02254900522530079,
0.039728835225105286,
0.01880413480103016,
-0.006345515605062246,
0.0013584867119789124,
-0.008786732330918312,
-0.009749301709234715,
0.05358109995722771,
-0.09270383417606354,
0.0008195488480851054,
0.009601684287190437,
0.021438932046294212,
0.008963363245129585,
-0.010016844607889652
] |
<p>The invariance under translation leads to the conserved energy-momentum tensor $\Theta_{\mu\nu}$ satisfying $\partial^\mu\Theta_{\mu\nu}=0$, from which we get the conserved quantity$$P^\nu=\int d^3\mathbf x\Theta^{0\nu}(x)$$But I cannot see explicitly <strong>how this quantity is a four-vector</strong> covariant under Lorentz transformation, since $d^3\mathbf x$ is part of the invariant $d^4x$, $\Theta^{0\nu}(x)$ is part of the covariant tensor $\Theta^{\mu\nu}(x)$, neither of which transforms covariantly.</p>
<p>So can someone show me how this becomes correct?</p>
<p>And generally, how to show that a Noether charge $Q$ corresponding to the Noether current $j^\mu$, $$Q=\int d^3\mathbf x j^0(x)$$ , is a <strong>Lorentz scalar</strong>?</p> | 1,423 | [
-0.04958409070968628,
-0.00151012372225523,
-0.019694358110427856,
-0.027535397559404373,
0.04712613299489021,
0.04297464340925217,
-0.016943272203207016,
-0.03199870511889458,
0.01654013991355896,
-0.04563435539603233,
0.07059129327535629,
0.010225741192698479,
0.0948709174990654,
0.0361139141023159,
0.0029750161338597536,
-0.0041814264841377735,
-0.008976542390882969,
0.0016830131644383073,
-0.01393767911940813,
-0.03706066682934761,
-0.016647733747959137,
0.0295848548412323,
-0.014271846041083336,
0.0014130381168797612,
0.011442868039011955,
-0.0046778395771980286,
0.005786484107375145,
-0.013720573857426643,
0.0008811127045191824,
0.06742966175079346,
-0.006075580604374409,
-0.026908384636044502,
0.008710693567991257,
0.03336134925484657,
0.005218635778874159,
0.027394037693738937,
-0.004239760804921389,
-0.025349076837301254,
0.04323451593518257,
0.006441142875701189,
-0.04186244308948517,
-0.014073041267693043,
-0.008940963074564934,
0.04273320734500885,
-0.017693061381578445,
0.01611054502427578,
0.005265748593956232,
0.01698645018041134,
0.07034303992986679,
-0.04309071600437164,
0.07563415914773941,
0.022954661399126053,
0.02238822542130947,
0.02393544279038906,
-0.03580480441451073,
-0.03555912524461746,
0.07800044119358063,
0.07198014110326767,
-0.009109591133892536,
-0.019779343158006668,
-0.051730528473854065,
-0.028313053771853447,
0.01655387319624424,
-0.017776556313037872,
-0.007479166612029076,
0.01846465654671192,
-0.00023079449601937085,
0.001129182637669146,
0.01544073224067688,
-0.0008082211716100574,
-0.005577469244599342,
0.018451247364282608,
0.003988305572420359,
-0.028446011245250702,
0.00821769516915083,
0.012323757633566856,
0.011647284030914307,
-0.0077672675251960754,
0.02940758690237999,
0.0219192486256361,
-0.0032889116555452347,
0.004600335378199816,
0.0017049750313162804,
0.0139375701546669,
0.0028972001746296883,
0.0016010473482310772,
0.0173037126660347,
-0.0030325038824230433,
-0.008932697586715221,
0.060022879391908646,
0.005325694568455219,
-0.03542047739028931,
0.006263618357479572,
-0.028194217011332512,
-0.028807666152715683,
0.028697310015559196,
-0.001976090483367443,
0.05871713161468506,
-0.023023061454296112,
-0.02832355722784996,
-0.015233895741403103,
-0.01566048339009285,
0.011431700550019741,
0.05638079345226288,
0.0159525815397501,
-0.011425157077610493,
-0.02278667874634266,
-0.007356300484389067,
-0.022540025413036346,
-0.015462018549442291,
-0.06554584950208664,
0.015040750615298748,
-0.024991275742650032,
-0.0027246742974966764,
0.02547788806259632,
-0.04053463786840439,
0.0018389150500297546,
-0.006345387548208237,
0.043022822588682175,
0.05471474304795265,
0.0249024648219347,
0.015758372843265533,
0.03599504381418228,
-0.0062864115461707115,
-0.1004883199930191,
0.013009496964514256,
0.015714243054389954,
0.008451517671346664,
-0.015629323199391365,
0.007744644768536091,
-0.0033916684333235025,
-0.010746646672487259,
-0.008927213959395885,
0.036551397293806076,
0.016287676990032196,
-0.04761480540037155,
-0.09779500216245651,
-0.05682726949453354,
0.005772424396127462,
0.0026032549794763327,
-0.024555185809731483,
-0.08855202049016953,
-0.021399829536676407,
0.0034493242856115103,
0.07635542750358582,
-0.03471415117383003,
0.013152464292943478,
0.0014378349296748638,
0.02040300890803337,
0.016897736117243767,
0.025555845350027084,
-0.003394919913262129,
-0.01780218817293644,
-0.021240022033452988,
-0.037517476826906204,
-0.059547968208789825,
0.039386529475450516,
0.013584424741566181,
0.02187870256602764,
-0.024790452793240547,
0.06905651092529297,
-0.01566983573138714,
0.004892714787274599,
0.007644515950232744,
0.0071808951906859875,
0.010268508456647396,
0.042096782475709915,
0.0009239785140380263,
0.012632930651307106,
-0.004913579672574997,
0.012044400908052921,
0.015741901472210884,
-0.023809529840946198,
0.06827109307050705,
0.04307851940393448,
-0.05295777693390846,
-0.02594144456088543,
0.0038304149638861418,
0.0016261658165603876,
-0.010268289595842361,
-0.02065643109381199,
-0.03977828845381737,
-0.006743863690644503,
-0.019171789288520813,
-0.010815159417688847,
0.015895957127213478,
-0.0002958643308375031,
-0.006209462881088257,
-0.014705152250826359,
-0.03025498241186142,
0.02467932179570198,
-0.05852058157324791,
0.027525633573532104,
0.021478768438100815,
-0.04937107115983963,
0.043936699628829956,
0.0025074041914194822,
0.03464752063155174,
-0.002963372739031911,
-0.019705990329384804,
-0.0030797349754720926,
0.05550990253686905,
-0.00085507205221802,
0.013641531579196453,
0.015005192719399929,
0.019959328696131706,
0.04047399014234543,
0.02496451698243618,
0.010965638794004917,
0.02639824151992798,
0.009019814431667328,
0.0011630688095465302,
0.005129908211529255,
-0.015468113124370575,
-0.002376152202486992,
-0.0023947327863425016,
0.010324429720640182,
-0.012497692368924618,
-0.010231830179691315,
0.06613069027662277,
-0.02470145747065544,
0.087062768638134,
0.03685417026281357,
-0.04366808384656906,
0.024663161486387253,
0.02448437735438347,
-0.03221329301595688,
0.03186381980776787,
-0.018551791086792946,
-0.044692084193229675,
-0.023127179592847824,
-0.003404121147468686,
0.013501926325261593,
0.03194461390376091,
-0.037946369498968124,
0.0035826072562485933,
0.012761075049638748,
0.043936632573604584,
0.0297740139067173,
0.005728255957365036,
0.0007567284628748894,
-0.06520405411720276,
0.01848583109676838,
0.021573234349489212,
-0.009117301553487778,
0.014525942504405975,
-0.020507123321294785,
-0.018072459846735,
0.03317064791917801,
-0.016903748735785484,
-0.022712212055921555,
0.03382057324051857,
-0.01697314716875553,
0.012899424880743027,
-0.01660657860338688,
-0.013874752447009087,
0.035362932831048965,
0.010342581197619438,
0.07319429516792297,
0.03809832036495209,
0.016021158546209335,
0.01750040054321289,
-0.002304806374013424,
-0.02001369744539261,
0.035147618502378464,
-0.02071055769920349,
0.01823362149298191,
-0.010160009376704693,
0.005007466301321983,
-0.02183232270181179,
0.023536065593361855,
-0.00039160402957350016,
-0.010908672586083412,
-0.004383156541734934,
-0.00441580917686224,
0.004892239812761545,
0.0066213589161634445,
0.011005089618265629,
-0.03254624083638191,
-0.01532372273504734,
0.00792005192488432,
-0.007324506528675556,
0.0005290762637741864,
0.057605158537626266,
-0.05812697857618332,
0.0011805059621110559,
-0.06782067567110062,
-0.00831011962145567,
0.043864451348781586,
0.024175623431801796,
0.027415646240115166,
0.03296234831213951,
-0.025213878601789474,
-0.0835416242480278,
-0.01049786526709795,
0.005493801552802324,
0.007987601682543755,
-0.05198987200856209,
0.01086354535073042,
0.05973383039236069,
-0.0229455828666687,
-0.046496469527482986,
-0.015876976773142815,
-0.021691778674721718,
-0.05554015561938286,
-0.005326093174517155,
-0.008061016909778118,
0.01183247845619917,
0.004417585674673319,
0.05186028033494949,
0.019972439855337143,
-0.021244576200842857,
-0.0303350817412138,
-0.053323399275541306,
-0.009528279304504395,
0.013635215349495411,
-0.007064402103424072,
0.003404109738767147,
0.007471955381333828,
-0.0665961429476738,
0.0701257735490799,
0.04656997695565224,
-0.007865593768656254,
-0.014262826181948185,
-0.012944750487804413,
-0.006493621040135622,
-0.05988090857863426,
-0.003282192861661315,
0.009064226411283016,
-0.00915119331330061,
0.0376022607088089,
0.02914719097316265,
0.028608696535229683,
0.0018493254901841283,
0.012243091128766537,
-0.011974592693150043,
0.027037959545850754,
0.004894305020570755,
0.009421897120773792,
0.053565263748168945,
0.020682761445641518,
-0.011514373123645782,
-0.015329846180975437,
-0.005343294236809015,
-0.00429720152169466,
0.009785533882677555,
-0.04729589447379112,
0.05278472229838371,
-0.0013291427167132497,
0.012308705598115921,
-0.03866907209157944,
0.042410604655742645,
0.019726373255252838,
-0.053277257829904556,
-0.019112475216388702,
0.04397687688469887,
0.016237178817391396,
-0.017515594139695168,
-0.011446884833276272,
0.033353425562381744,
-0.0026748075615614653,
-0.04096927493810654,
0.004458992276340723,
-0.0030554330442100763,
0.012859334237873554,
0.022801661863923073,
-0.01868285983800888,
0.012447645887732506,
0.015049637295305729,
0.028566468507051468,
0.03397311270236969,
0.016595767810940742,
-0.006837781984359026,
0.009776603430509567,
-0.03554201498627663,
-0.006532942410558462,
0.011542649939656258,
0.03776266425848007,
0.030117454007267952,
0.061598774045705795,
0.04289942979812622,
0.013868948444724083,
-0.023834625259041786,
0.013963083736598492,
-0.07900568097829819,
0.023988714441657066,
-0.03997045382857323,
-0.0008791720028966665,
-0.008428600616753101,
-0.051739174872636795,
-0.023444410413503647,
-0.028559761121869087,
-0.0071805440820753574,
-0.0428147092461586,
-0.023960024118423462,
-0.03162512183189392,
0.03227417171001434,
0.005472724791616201,
-0.03588515892624855,
-0.04404187202453613,
0.04782235622406006,
0.044375188648700714,
-0.050254445523023605,
-0.010349318385124207,
0.05393145605921745,
-0.055540282279253006,
0.019569961354136467,
-0.021393030881881714,
0.011773217469453812,
0.01739531010389328,
-0.002258804626762867,
0.02420455403625965,
-0.02277545817196369,
-0.02094389498233795,
-0.023074187338352203,
0.03258313238620758,
0.08601664006710052,
0.006351823918521404,
-0.023742422461509705,
-0.031074948608875275,
-0.030325673520565033,
-0.02421884797513485,
0.0014540675329044461,
0.06000707671046257,
0.030966928228735924,
-0.005558935459703207,
0.01762542501091957,
0.032800156623125076,
0.010854733176529408,
0.02829054743051529,
0.059135109186172485,
0.00761917931959033,
-0.005578175187110901,
-0.05408624932169914,
0.017063288018107414,
-0.02769574336707592,
0.0003588245017454028,
0.004201272502541542,
-0.005253316834568977,
-0.02729937434196472,
-0.028907526284456253,
0.014782944694161415,
0.004785717930644751,
0.0009711434249766171,
0.001128563191741705,
0.03967344015836716,
0.013267334550619125,
-0.01237818505614996,
0.013927873224020004,
-0.029094940051436424,
0.04820331931114197,
0.044399652630090714,
0.01199292205274105,
0.006185454782098532,
-0.05767374485731125,
-0.006645600311458111,
0.015126293525099754,
0.04434582591056824,
0.00546162948012352,
-0.012500199489295483,
-0.04763409495353699,
0.004628411494195461,
0.04560760781168938,
-0.020730257034301758,
0.02361551858484745,
0.019669434055685997,
-0.008142562583088875,
-0.008868402801454067,
-0.04506022855639458,
-0.03644490987062454,
0.031271956861019135,
-0.02688189409673214,
0.03076624684035778,
-0.033699121326208115,
0.0013685880694538355,
0.026729075238108635,
0.03487430140376091,
-0.007246270775794983,
0.015491871163249016,
0.018841257318854332,
0.007252042181789875,
-0.02313111536204815,
0.045349977910518646,
-0.04042193293571472,
-0.10265518724918365,
-0.01734630949795246,
0.017525075003504753,
-0.021161800250411034,
0.03945883363485336,
-0.03738851100206375,
-0.06907571107149124,
0.009820147417485714,
0.005306316073983908,
0.033724747598171234,
0.05445550009608269,
-0.07825101166963577,
0.039684440940618515,
0.013593703508377075,
0.0038974047638475895,
0.024052828550338745,
0.03777749091386795,
0.003358239307999611,
-0.004070215858519077,
-0.03226936236023903,
0.043814726173877716,
-0.04053415358066559,
-0.0006822093273513019,
-0.016354337334632874,
0.009534263052046299,
-0.03632446378469467,
0.058012206107378006,
-0.02807319164276123,
-0.003072484629228711,
-0.02339186891913414,
0.02100301906466484,
0.0017661146121099591,
0.010845734737813473,
0.02350875549018383,
-0.040433019399642944,
-0.02326500229537487,
0.0033968649804592133,
0.016165172681212425,
-0.030060840770602226,
0.032950423657894135,
0.006101210135966539,
-0.011465211398899555,
0.03843151405453682,
0.00909582432359457,
0.014347054064273834,
0.007865827530622482,
-0.04211372137069702,
0.0010379417799413204,
-0.007891517132520676,
0.009365411475300789,
-0.018442118540406227,
0.004804674070328474,
0.010763118043541908,
-0.050098221749067307,
-0.0440472848713398,
0.02503977157175541,
-0.010997005738317966,
0.019111208617687225,
-0.0626521110534668,
-0.007907695136964321,
0.03960217162966728,
0.034423500299453735,
-0.0850045382976532,
-0.05165906623005867,
0.0007372883264906704,
-0.007186741102486849,
-0.01289826724678278,
-0.0026022663805633783,
-0.010154557414352894,
-0.028892213478684425,
-0.06625978648662567,
-0.00914213340729475,
0.04427781701087952,
-0.06653273105621338,
0.008183663710951805,
-0.008480637334287167,
0.016745617613196373,
0.07187633961439133,
-0.05775946378707886,
0.004807949531823397,
0.005672074388712645,
-0.010288825258612633,
0.010868587531149387,
-0.004336623474955559,
0.018119515851140022,
0.003684265073388815,
-0.016378583386540413,
-0.025660639628767967,
0.001071471837349236,
0.022685792297124863,
0.015120831318199635,
-0.0127600422129035,
0.0342315137386322,
-0.013715352863073349,
-0.04029399901628494,
-0.039006613194942474,
-0.03438770771026611,
-0.00022440719476435333,
0.04934702441096306,
-0.016301032155752182,
-0.004619933664798737,
-0.04362858831882477,
-0.023933373391628265,
0.048948485404253006,
-0.00710720382630825,
0.027343636378645897,
-0.029549473896622658,
0.05073443055152893,
-0.018829142674803734,
0.016508348286151886,
0.02493433654308319,
0.003309270367026329,
-0.029142964631319046,
-0.015454044565558434,
0.0108862966299057,
-0.023825176060199738,
0.0018756608478724957,
-0.04049555957317352,
-0.01887218840420246,
-0.04551491513848305,
0.05219234526157379,
0.06547599285840988,
-0.012537145987153053,
0.033528801053762436,
0.027278203517198563,
-0.028117256239056587,
-0.01344066672027111,
0.01006281841546297,
-0.037663400173187256,
0.023028401657938957,
-0.005588910076767206,
0.006256814114749432,
0.01583767496049404,
-0.004615642596036196,
0.03125271946191788,
0.05442024767398834,
-0.050743669271469116,
0.026264414191246033,
0.030181819573044777,
-0.005316539667546749,
0.0002849889569915831,
0.004183458164334297,
-0.06488825380802155,
0.03393218293786049,
-0.01142260991036892,
0.059441156685352325,
-0.007196244318038225,
0.003792356699705124,
0.030424661934375763,
-0.004098151344805956,
0.008961976505815983,
-0.012125028297305107,
-0.03170410171151161,
-0.05100984871387482,
0.017135607078671455,
0.030276963487267494,
-0.01141004916280508,
-0.03316158801317215,
0.015210744924843311,
0.08630362898111343,
-0.019938522949814796,
0.005202136468142271,
-0.006150218192487955,
-0.06047506257891655,
-0.01233026571571827,
-0.02794557623565197,
-0.005398857872933149,
0.06827475875616074,
-0.013936499133706093,
-0.009774595499038696,
-0.030784744769334793,
-0.020266836509108543,
0.043802689760923386,
0.026227694004774094,
0.01770852319896221,
-0.05109043046832085,
0.04937567561864853,
-0.012396958656609058,
0.011652117595076561,
-0.007467169314622879,
0.0036870925687253475,
0.11024827510118484,
0.04336627200245857,
0.004087758716195822,
-0.06743046641349792,
0.0023463040124624968,
-0.027321288362145424,
0.01006356906145811,
-0.042091358453035355,
0.032447878271341324,
-0.015516388230025768,
-0.01062091812491417,
-0.024529699236154556,
0.02086895890533924,
-0.01659904606640339,
-0.000549134099856019,
0.039471860975027084,
-0.03325723856687546,
-0.03942377120256424,
0.011889045126736164,
0.03195932134985924,
0.003660600632429123,
-0.0034184332471340895,
-0.056082677096128464,
0.005838431883603334,
-0.029890714213252068,
0.008950263261795044,
-0.053609952330589294,
-0.048714540898799896,
0.04026823863387108,
-0.01115417666733265,
-0.040826357901096344,
0.022433040663599968,
0.010605154559016228,
-0.01515909656882286,
-0.04277462884783745,
-0.019955793395638466,
0.0178768839687109,
0.005014099180698395,
0.052267108112573624,
0.04814913123846054,
0.016991371288895607,
0.011770729906857014,
0.03774050250649452,
0.05227117985486984,
-0.04312463849782944,
0.0032240028958767653,
-0.044194795191287994,
0.056313641369342804,
-0.011896112933754921,
0.005821865051984787,
0.024973412975668907,
0.0077129690907895565,
0.008593883365392685,
-0.07055000215768814,
-0.024744030088186264,
-0.014645470306277275,
0.014986739493906498,
-0.00424916110932827,
-0.0077520799823105335,
0.012145830318331718,
0.012862137518823147,
0.0022010442335158587,
0.022239359095692635,
-0.04821338132023811,
0.004689855966717005,
0.02620994858443737,
-0.011328818276524544,
-0.006664483342319727,
0.0002884819987230003,
-0.015069032087922096,
-0.012698390521109104,
-0.028932563960552216,
-0.013088524341583252,
-0.028251681476831436,
0.019297126680612564,
0.03324011713266373,
0.03519484028220177,
0.002450913190841675,
-0.004316393751651049,
0.002296509686857462,
-0.07441442459821701,
0.01253083348274231,
-0.02575736679136753,
-0.007563222199678421,
-0.006129327695816755,
0.0346214585006237,
0.015987509861588478,
0.06275716423988342,
-0.03684813156723976,
0.00822711642831564,
0.029516959562897682,
0.038011584430933,
0.026831667870283127,
0.0020946490112692118,
-0.016746902838349342,
0.00011889806046383455,
-0.015339543111622334,
-0.02202444151043892,
-0.018543625250458717,
0.0001396363222738728,
0.03646369278430939,
0.0029951410833746195,
-0.00859432015568018,
0.06307201832532883,
0.00211370293982327,
-0.019950157031416893,
0.04436904191970825,
0.026290634647011757,
0.026016514748334885,
0.03692692145705223,
0.018151504918932915,
-0.03019980899989605,
0.0069044106639921665,
-0.028008125722408295,
0.009601104073226452,
0.026807479560375214,
0.010723836719989777,
-0.05672622472047806,
-0.04013817012310028,
-0.033508945256471634,
0.036712657660245895,
-0.012372603639960289,
-0.020292915403842926,
-0.03389928489923477,
0.03728998079895973,
0.008092012256383896,
-0.0012187843676656485,
-0.0073974900878965855,
0.056118547916412354,
-0.020443545654416084,
-0.021777475252747536,
0.03747464343905449,
0.026105038821697235,
-0.04174893721938133,
0.005866264458745718,
-0.005022573750466108,
0.035265691578388214,
0.024870220571756363,
0.023727819323539734,
-0.018903853371739388,
0.02615419588983059,
-0.03395805135369301,
-0.03744736313819885,
0.05824194848537445,
-0.004352022428065538,
-0.011701258830726147,
0.009118041954934597,
-0.0058158813044428825,
-0.029771825298666954,
-0.0011114550288766623,
-0.0031707554589957,
0.00176961999386549,
-0.007267348002642393,
-0.06429803371429443,
-0.01114547811448574,
-0.04157925769686699,
0.04179617017507553,
0.0038506337441504,
0.009613966569304466,
0.033122316002845764,
0.0041882749646902084,
0.01819482445716858,
0.00952406506985426,
-0.012239234521985054,
0.010148072615265846,
0.0066563705913722515,
0.02810807153582573,
-0.0033915149979293346,
0.0037772124633193016,
0.08010891824960709,
-0.022172531113028526,
0.027939794585108757,
-0.006910637486726046,
-0.0019502028590068221,
-0.12219595909118652,
-0.022117186337709427,
-0.001772483577951789,
0.018081407994031906,
0.04766389727592468,
-0.0777110904455185,
0.03042536787688732,
0.051472410559654236,
-0.05394624546170235,
0.025893045589327812,
-0.036629121750593185,
-0.02070029079914093,
0.012701751664280891,
-0.02339285798370838,
-0.016457049176096916,
0.10306088626384735,
0.03213264420628548,
0.02233869396150112,
0.013368172571063042,
0.04102513939142227,
-0.015335170552134514,
-0.050354719161987305,
-0.02694350853562355,
0.023042207583785057,
0.020861543715000153,
-0.016101809218525887,
0.06055409461259842,
0.006771882530301809,
-0.04927343502640724,
0.04842958599328995,
0.00031434980337508023,
-0.01197417639195919,
0.014550043269991875,
0.03172425180673599,
0.026825355365872383,
0.030836597084999084,
0.014556760899722576,
0.0019241120899096131,
0.01935531571507454,
0.0063464161939918995,
0.04303561896085739,
0.0398448221385479,
-0.014646593481302261,
-0.014768133871257305,
0.013157055713236332,
-0.05186963826417923,
-0.02509785257279873,
0.03567017987370491,
-0.014650619588792324,
-0.010194889269769192,
-0.005409951321780682,
-0.01847744919359684,
0.017072027549147606,
-0.02954602986574173,
-0.003559427335858345,
-0.059762682765722275,
-0.031955745071172714,
0.024204086512327194,
-0.0323750264942646,
0.037919968366622925,
0.00922248512506485,
-0.007301690056920052,
-0.003954088781028986,
0.03556956350803375,
0.0205185916274786,
0.014517059549689293,
-0.06400914490222931,
0.007701526395976543,
-0.009842699393630028,
-0.004921742249280214,
-0.01615852490067482,
-0.030179988592863083,
-0.043797414749860764,
0.009034267626702785,
0.004335805308073759,
-0.0022063981741666794,
-0.016434896737337112,
-0.030531099066138268,
-0.012094524689018726,
-0.058615658432245255,
0.0030585594940930605,
0.04167517274618149,
-0.037221699953079224,
-0.018944351002573967,
0.03446679562330246,
-0.016761990264058113,
0.03261268138885498,
0.045389603823423386,
0.0021277498453855515,
-0.03077668324112892,
0.05158253014087677,
-0.006975920870900154,
0.031851135194301605,
-0.06044850870966911,
0.02226312831044197,
0.003952512517571449,
0.023928068578243256,
0.03229663148522377,
0.016352539882063866,
-0.04046071320772171,
0.011189294047653675,
-0.025505393743515015,
-0.00612134812399745,
0.03996628522872925,
-0.004414058290421963,
-0.02976834587752819,
0.01886342652142048,
-0.00447341613471508,
-0.01740436442196369,
0.04501941055059433,
-0.0003118888125754893,
0.03507978469133377,
0.049933601170778275,
-0.0205864068120718,
-0.01728544756770134,
-0.018476923927664757,
-0.04858742281794548,
-0.026865264400839806,
-0.025687076151371002,
0.02064848132431507,
0.04260615259408951,
-0.04810313880443573,
-0.02441864088177681,
0.06215931102633476,
-0.0009294678457081318,
-0.03702053427696228,
0.07399606704711914,
0.02223322167992592,
0.011521653272211552,
0.03191748633980751,
0.0061772787012159824,
0.013006197288632393,
0.01856779307126999,
0.023438813164830208,
0.030841007828712463,
0.03376176208257675,
-0.014622124843299389,
-0.006687909830361605,
0.007364622317254543,
-0.012186207808554173,
-0.017186623066663742,
0.0070647504180669785,
0.036703549325466156,
-0.012228859588503838,
0.001790263457223773,
0.021801071241497993,
-0.02332986518740654,
0.04014679789543152,
0.005834393203258514,
-0.025963490828871727,
0.06772999465465546,
-0.04560864344239235,
-0.018812017515301704,
-0.01830572821199894,
0.010412130504846573,
-0.021162666380405426,
0.028421608731150627,
0.0226907916367054,
0.07275576889514923,
-0.041276026517152786,
-0.03082915022969246,
-0.04262140020728111,
-0.027333928272128105,
0.002300338353961706,
-0.05316483601927757,
0.00906370673328638,
-0.006236005108803511,
0.019088611006736755,
-0.021002426743507385,
-0.00766770588234067,
-0.034918490797281265,
-0.00019333165255375206,
0.01182539388537407,
-0.006868445314466953,
0.07674362510442734,
-0.018098199740052223,
-0.014625390991568565,
-0.04057453200221062,
0.04046980291604996,
-0.04767603427171707,
-0.02426164411008358,
0.006881323177367449,
-0.0008562110015191138,
0.01870104856789112,
0.0052833110094070435
] |
<p>It is known that for perfect blackbodies,
$$\lambda T= c$$
where $\lambda= \text{peak wavelength}$<br>
$T= \text{Absolute temperature}$<br>
$c= \text{Wien's constant}$ </p>
<p>But this is for perfect blackbodies only, which have no theoretical existence. Does a similar formula exist for real bodies, which expresses $\lambda T$ in terms of its emissitivity $\epsilon$? I googled it, but found no relevant results. </p> | 1,424 | [
0.005427053663879633,
-0.05606075003743172,
0.050199054181575775,
-0.052359070628881454,
0.005904237739741802,
-0.0007229827460832894,
-0.04151386022567749,
0.006244491785764694,
-0.032550107687711716,
-0.03621256723999977,
0.028045717626810074,
0.04023433104157448,
0.06034905090928078,
0.018540464341640472,
-0.021794555708765984,
-0.01694210059940815,
-0.010496663860976696,
-0.026280909776687622,
-0.04385779798030853,
0.001816946780309081,
0.04350024461746216,
0.025143545120954514,
-0.007987532764673233,
-0.008710012771189213,
-0.017781227827072144,
0.03421654924750328,
-0.015167910605669022,
0.019057944416999817,
-0.008833988569676876,
0.026919128373265266,
-0.017220713198184967,
-0.027122238650918007,
0.039902348071336746,
0.011264408007264137,
0.0025268441531807184,
0.015038853511214256,
0.010935114696621895,
-0.029064012691378593,
-0.037095390260219574,
0.03150644525885582,
-0.017907021567225456,
-0.020914997905492783,
0.0034166343975812197,
0.04817303270101547,
0.0069619351997971535,
-0.002229884034022689,
-0.000730586179997772,
-0.051407165825366974,
0.03045777603983879,
-0.0672270879149437,
0.06363353133201599,
0.0011711788829416037,
0.06490106880664825,
0.002911458956077695,
-0.01071937009692192,
-0.01607666164636612,
0.10736192017793655,
0.0326753668487072,
-0.015206483192741871,
-0.03477738797664642,
0.020826512947678566,
0.0031408595386892557,
-0.006209732498973608,
0.010142087005078793,
-0.02441990189254284,
0.017390569671988487,
-0.0004054246237501502,
-0.041138697415590286,
0.04819469153881073,
0.004783418495208025,
0.02456536516547203,
-0.0008308838587254286,
0.04093592241406441,
-0.026742929592728615,
-0.02098604291677475,
-0.031605131924152374,
0.015321245416998863,
0.06637457013130188,
0.02853773906826973,
0.030171582475304604,
-0.022988036274909973,
0.0019042777130380273,
0.05188458040356636,
0.04313655570149422,
-0.015326387248933315,
0.02206079289317131,
0.04453178495168686,
0.0009432784281671047,
0.02881511300802231,
0.03115612082183361,
-0.002537875436246395,
-0.007666622754186392,
0.05825988948345184,
-0.001247998559847474,
-0.007750967051833868,
-0.0007217747624963522,
-0.014693733304738998,
0.04993541166186333,
-0.018336553126573563,
-0.04978398606181145,
-0.003832936519756913,
0.02034170739352703,
-0.025198565796017647,
0.09407900273799896,
0.008387555368244648,
-0.03087553195655346,
-0.04870283603668213,
-0.023321887478232384,
-0.025376489385962486,
-0.02210885100066662,
-0.04579143226146698,
0.0102764330804348,
-0.003527548164129257,
-0.015314962714910507,
-0.02429111860692501,
-0.0048523866571486,
0.0606100857257843,
-0.06190274655818939,
0.011475726962089539,
0.044396333396434784,
0.011365040205419064,
0.018152715638279915,
0.004881054162979126,
-0.0033403062261641026,
-0.037743087857961655,
0.010963250882923603,
0.06713762879371643,
-0.006687483284622431,
-0.05671914666891098,
-0.02257371135056019,
-0.004035735037177801,
-0.026748446747660637,
0.026311777532100677,
-0.003133616177365184,
0.01585042104125023,
-0.009710925631225109,
-0.03744223713874817,
-0.058857012540102005,
-0.028188304975628853,
-0.004482550080865622,
-0.027044687420129776,
-0.05225295573472977,
0.013301349245011806,
0.06615090370178223,
0.0859973281621933,
0.017274556681513786,
-0.018321016803383827,
-0.03012290596961975,
0.012548900209367275,
0.002952000591903925,
0.0021878306288272142,
-0.043985214084386826,
0.018397411331534386,
-0.0542016439139843,
-0.03415204957127571,
-0.04808834195137024,
0.006993942894041538,
0.02935771830379963,
-0.013898462057113647,
0.0339457243680954,
0.056416962295770645,
-0.022317802533507347,
-0.003417795291170478,
0.0033268900588154793,
-0.0239531472325325,
-0.042487841099500656,
0.05150038003921509,
0.018936267122626305,
-0.001324901939369738,
-0.029342005029320717,
0.01053848396986723,
-0.012956362217664719,
0.025753604248166084,
0.030690154060721397,
0.009725188836455345,
-0.04496857896447182,
-0.008176942355930805,
-0.046774838119745255,
0.0265259500592947,
0.054810531437397,
-0.07438085228204727,
-0.04486865922808647,
0.016858486458659172,
0.006423107348382473,
0.012702998705208302,
0.045995231717824936,
0.009638980962336063,
0.012574510648846626,
0.03958823159337044,
-0.044574566185474396,
0.020718185231089592,
-0.02387506514787674,
0.042877063155174255,
0.041642166674137115,
-0.01833323948085308,
0.004696897696703672,
0.021105078980326653,
0.006158860400319099,
0.0010751269292086363,
-0.013879813253879547,
0.03562302514910698,
0.051279108971357346,
0.005971035920083523,
0.0008508614846505225,
0.03042079694569111,
0.049113910645246506,
0.06767722964286804,
0.01464118342846632,
0.0381961390376091,
-0.025523370131850243,
-0.03483198583126068,
-0.014365024864673615,
-0.04931611567735672,
0.04977115988731384,
-0.012591841630637646,
0.020849034190177917,
0.04174313694238663,
-0.01913224160671234,
-0.011517914943397045,
0.017671922221779823,
-0.042196277529001236,
0.03429047390818596,
0.013896794058382511,
0.03973021358251572,
0.011852878145873547,
0.04667183756828308,
-0.018893204629421234,
0.011532397009432316,
-0.040798868983983994,
-0.05115833878517151,
-0.013671129941940308,
-0.003026604885235429,
0.0347360298037529,
0.02100500836968422,
-0.04646749794483185,
-0.011076905764639378,
0.023864999413490295,
0.021638648584485054,
0.07056494802236557,
0.0326479971408844,
-0.03688237816095352,
-0.048090431839227676,
-0.005076245870441198,
-0.021244214847683907,
0.01672779768705368,
0.016726432368159294,
0.026121273636817932,
0.025172656401991844,
0.020379958674311638,
-0.021022088825702667,
0.006072574760764837,
0.0346917100250721,
0.0365653932094574,
-0.013811405748128891,
-0.009591745212674141,
-0.0035288669168949127,
0.03047076426446438,
-0.04556101933121681,
0.02332760952413082,
-0.007596889045089483,
-0.006782840471714735,
0.02464943565428257,
-0.05191716179251671,
-0.014279501512646675,
0.016475802287459373,
0.03839081898331642,
-0.012051569297909737,
0.028961779549717903,
0.015711860731244087,
-0.012251417152583599,
0.05135679617524147,
-0.05049194023013115,
-0.01041147019714117,
-0.026415683329105377,
-0.008339140564203262,
-0.005240955390036106,
0.04930460825562477,
0.02808169089257717,
-0.031730178743600845,
-0.049429863691329956,
-0.010942019522190094,
0.0001833510905271396,
0.03244169428944588,
0.026959847658872604,
-0.018088264390826225,
-0.04432347044348717,
-0.025527050718665123,
-0.0542672835290432,
0.028161874040961266,
-0.011875886470079422,
0.00016236973169725388,
0.01913221925497055,
-0.03133867308497429,
-0.06701187044382095,
0.017241617664694786,
0.013348142616450787,
-0.04167897254228592,
-0.0388743057847023,
0.051577258855104446,
0.0271651279181242,
-0.02789415419101715,
-0.04797084629535675,
-0.004276100546121597,
-0.01683005318045616,
-0.038526345044374466,
-0.029059577733278275,
-0.03212485834956169,
0.023570753633975983,
-0.021190060302615166,
0.05234688147902489,
0.052074264734983444,
-0.008887640200555325,
0.0057228500954806805,
-0.049909066408872604,
-0.044915903359651566,
0.07707483321428299,
-0.029044969007372856,
0.0396469421684742,
-0.0049497648142278194,
-0.005670814774930477,
0.06725499778985977,
0.002680601319298148,
-0.033349666744470596,
-0.02386353351175785,
0.018222317099571228,
0.02248341031372547,
-0.026354586705565453,
-0.01000799797475338,
0.006951956544071436,
-0.004634991753846407,
0.007494576275348663,
0.0003697996726259589,
0.004025137983262539,
0.021164629608392715,
0.0233077984303236,
-0.003986406605690718,
0.00026315043214708567,
0.006354901008307934,
0.026550840586423874,
0.04714173078536987,
-0.003541260724887252,
-0.013819979503750801,
0.054430730640888214,
-0.03534756600856781,
0.028170540928840637,
0.021361371502280235,
-0.06268543004989624,
0.030030593276023865,
0.02325875498354435,
0.021877160295844078,
-0.03544597327709198,
0.035025931894779205,
-0.019284499809145927,
-0.015310966409742832,
-0.07728435844182968,
0.10782137513160706,
0.009468058124184608,
0.009364580735564232,
-0.0009760558023117483,
0.02418949082493782,
0.045528341084718704,
-0.00035756194847635925,
-0.009078195318579674,
0.0032160496339201927,
-0.025748280808329582,
0.005113583989441395,
-0.009087777696549892,
-0.017208339646458626,
0.02342248521745205,
0.02941080741584301,
0.0409276969730854,
0.020541280508041382,
0.009233699180185795,
0.0008335526217706501,
-0.06131868436932564,
-0.07036617398262024,
-0.010503019206225872,
0.04579067975282669,
0.0090266652405262,
0.050615329295396805,
0.0302471574395895,
0.06130338832736015,
0.062266137450933456,
-0.002969497349113226,
-0.09270511567592621,
-0.0048687453381717205,
-0.026598801836371422,
-0.018658775836229324,
-0.013156996108591557,
-0.004250933416187763,
0.006426523439586163,
-0.02079339697957039,
-0.03962833434343338,
0.005643378011882305,
0.02293071709573269,
-0.06442367285490036,
0.04090767726302147,
0.001082044211216271,
-0.05170605331659317,
0.038470491766929626,
0.08820513635873795,
0.004687013570219278,
-0.03468360751867294,
-0.0001361355825792998,
-0.023934364318847656,
-0.025543948635458946,
0.000590279174502939,
-0.00046574705629609525,
0.007300399709492922,
-0.025397194549441338,
0.057738978415727615,
0.03916739299893379,
0.04138483479619026,
-0.040512219071388245,
0.01721670851111412,
0.02890262007713318,
0.021207578480243683,
-0.03809357061982155,
-0.016840387135744095,
-0.028455832973122597,
-0.06148090958595276,
-0.008061313070356846,
0.03307187929749489,
0.03876153752207756,
-0.011843797750771046,
-0.0023312438279390335,
0.016100941225886345,
-0.022525591775774956,
0.0021239917259663343,
-0.02180015854537487,
-0.014421443454921246,
0.01896425522863865,
0.0029907396528869867,
0.00025323033332824707,
0.02571791224181652,
-0.015996452420949936,
0.017058851197361946,
-0.011026883497834206,
0.009766509756445885,
-0.002916975412517786,
0.02193349041044712,
0.028804782778024673,
0.021279726177453995,
-0.02223242074251175,
-0.005911407060921192,
-0.01561715453863144,
0.03420768305659294,
-0.06023075804114342,
0.016931718215346336,
0.01039214339107275,
0.04921519011259079,
0.047265857458114624,
-0.01468090619891882,
-0.03309747949242592,
-0.07278997451066971,
-0.01874380372464657,
0.009783785790205002,
0.026297416538000107,
0.01840411312878132,
-0.029758388176560402,
-0.042585935443639755,
-0.020171646028757095,
0.08094914257526398,
0.024578964337706566,
0.03717881068587303,
0.004255440551787615,
-0.034692104905843735,
0.002971032401546836,
-0.028502022847533226,
0.021712835878133774,
0.027909893542528152,
-0.005223533138632774,
0.025454849004745483,
-0.019953269511461258,
0.007065478712320328,
0.06437218934297562,
0.07555548846721649,
0.03296399861574173,
0.06761550158262253,
-0.01105138473212719,
-0.03608367592096329,
0.017363350838422775,
-0.008584144525229931,
-0.01854706183075905,
-0.04249947890639305,
-0.027947111055254936,
0.004053744953125715,
0.016029460355639458,
0.0220403503626585,
-0.02473169006407261,
-0.015442553907632828,
0.011038966476917267,
0.029496386647224426,
-0.04737351834774017,
0.03637949004769325,
-0.030965449288487434,
0.04958208650350571,
-0.017398210242390633,
-0.01400637999176979,
0.042416758835315704,
0.05907592177391052,
0.013063743710517883,
-0.0025714803487062454,
-0.041843436658382416,
0.022682178765535355,
-0.014561892487108707,
-0.02768035978078842,
-0.016299385577440262,
-0.0018965890631079674,
-0.06955280900001526,
0.014404315501451492,
-0.025737226009368896,
0.007487208116799593,
-0.0038116921205073595,
-0.02093399688601494,
0.008237763307988644,
-0.005791709758341312,
-0.00038314503035508096,
0.020521536469459534,
-0.0028594715986400843,
0.049991294741630554,
0.023584000766277313,
-0.01256389170885086,
0.01938682235777378,
-0.021195750683546066,
-0.005427676718682051,
0.044606540352106094,
0.0008845442207530141,
0.05733140558004379,
-0.022603096440434456,
0.0191019456833601,
0.04268518090248108,
-0.03062986209988594,
0.02794233150780201,
-0.001152761746197939,
0.0003799786791205406,
0.018513623625040054,
-0.045841019600629807,
0.012614456936717033,
0.0008848100551404059,
0.009895985946059227,
0.031068960204720497,
-0.034125037491321564,
0.005660013295710087,
0.02841712348163128,
0.0218039657920599,
-0.03890041634440422,
0.017262792214751244,
0.031057890504598618,
-0.002501111011952162,
-0.02507556602358818,
-0.04139059782028198,
0.016673598438501358,
-0.024560842663049698,
-0.04883626475930214,
0.06204647570848465,
0.0033224322833120823,
-0.005820810794830322,
-0.015905767679214478,
-0.039139725267887115,
0.021587220951914787,
0.01599312573671341,
0.0030467859469354153,
-0.012156334705650806,
0.01688951626420021,
0.032613325864076614,
0.011824267916381359,
0.034505296498537064,
0.03941524028778076,
-0.020062237977981567,
-0.017239442095160484,
-0.021433617919683456,
0.01189440954476595,
0.019844582304358482,
0.04008781909942627,
-0.026785388588905334,
0.03556152060627937,
0.029520412907004356,
-0.009604404680430889,
-0.010333947837352753,
0.026035357266664505,
0.005926680751144886,
0.012231234461069107,
-0.023324184119701385,
-0.018001632764935493,
-0.049376461654901505,
0.004166576080024242,
0.024863915517926216,
-0.006922676227986813,
0.030212845653295517,
-0.01897786371409893,
0.04676037281751633,
0.010958262719213963,
-0.051719095557928085,
-0.0008470219327136874,
-0.02244965359568596,
-0.0038300943560898304,
0.010152465663850307,
-0.012622717767953873,
-0.006245496682822704,
0.0313691571354866,
0.003991629462689161,
-0.029079126194119453,
-0.05887976661324501,
0.0013186992146074772,
0.07199510931968689,
0.013724450021982193,
0.05971280485391617,
-0.006787964608520269,
-0.010842148214578629,
-0.005771176889538765,
-0.03447452932596207,
-0.04380017891526222,
0.024442482739686966,
-0.02450266294181347,
0.008321287110447884,
-0.027536150068044662,
0.007386677898466587,
0.018184537068009377,
0.0696878656744957,
-0.04439952224493027,
0.057507358491420746,
-0.014300704933702946,
0.012774555943906307,
-0.01930524967610836,
-0.0455629862844944,
0.01040600799024105,
0.05786661058664322,
-0.01483398862183094,
0.07479722052812576,
0.005026743281632662,
0.0398900993168354,
-0.006746223662048578,
-0.012745395302772522,
0.015280665829777718,
-0.058609120547771454,
-0.03316779434680939,
-0.04143441095948219,
0.04341534525156021,
0.04203823208808899,
0.0015704183606430888,
-0.005537716671824455,
-0.01235576905310154,
0.01647077687084675,
-0.02975989505648613,
0.006256042048335075,
-0.016482038423419,
-0.047024842351675034,
0.015821393579244614,
-0.030029218643903732,
-0.07533256709575653,
0.02242417261004448,
0.0009881502483040094,
0.002435859525576234,
0.013169856742024422,
-0.02614913322031498,
0.015924232080578804,
0.030315697193145752,
0.03198804706335068,
-0.00622601667419076,
0.04326571896672249,
-0.05496733635663986,
-0.015936274081468582,
-0.00971724558621645,
0.02165106125175953,
0.13110066950321198,
0.03129785880446434,
0.016817891970276833,
-0.057724736630916595,
-0.0021385273430496454,
-0.022112660109996796,
0.013780229724943638,
-0.02449738048017025,
0.007979932241141796,
-0.04611567407846451,
-0.023756537586450577,
0.02940901182591915,
0.07654642313718796,
0.00783747248351574,
-0.039641670882701874,
-0.01639365777373314,
-0.008481912314891815,
0.015670670196413994,
0.026045124977827072,
0.026748821139335632,
0.007790211588144302,
-0.00012222956866025925,
0.0002516711538191885,
-0.009524323977530003,
-0.008697506971657276,
0.0014596573309972882,
-0.02032550238072872,
-0.010833337903022766,
-0.010405783541500568,
0.001886047888547182,
-0.0456702783703804,
-0.000574301986489445,
0.0059780580922961235,
-0.020826250314712524,
-0.0005357817281037569,
-0.006842008791863918,
0.0381566658616066,
0.005357629153877497,
0.028813732787966728,
0.05050791800022125,
0.006824132986366749,
0.024129830300807953,
-0.003598300740122795,
0.019305530935525894,
-0.03136816993355751,
-0.01854570209980011,
-0.019296795129776,
0.020477693527936935,
-0.00842196773737669,
0.0024181040935218334,
0.010523361153900623,
-0.03813432157039642,
0.02592981606721878,
-0.012166786007583141,
-0.0004231697821523994,
-0.008778853341937065,
-0.0002428008010610938,
-0.04239518567919731,
-0.03338045999407768,
-0.030138790607452393,
0.025312498211860657,
0.02903924696147442,
-0.005712013226002455,
0.025748711079359055,
-0.006877622101455927,
-0.0035973237827420235,
-0.016568109393119812,
0.06694424152374268,
0.004242183640599251,
-0.012804733589291573,
-0.031160755082964897,
-0.04211725294589996,
-0.03240161016583443,
-0.036181092262268066,
-0.02536553330719471,
0.00175731279887259,
-0.0002562316367402673,
-0.004628357477486134,
0.003395645646378398,
-0.05833977833390236,
-0.07458444684743881,
-0.007683492265641689,
-0.019831784069538116,
-0.022646639496088028,
0.00000894743516255403,
-0.0180650744587183,
0.019530421122908592,
0.03258775174617767,
-0.01399947889149189,
0.00005358447742764838,
0.05612115189433098,
0.051265835762023926,
0.05243354290723801,
-0.043629951775074005,
0.008960225619375706,
-0.006417788099497557,
-0.020530149340629578,
0.026650676503777504,
0.02233019843697548,
0.01845984160900116,
0.02308819070458412,
0.02870805375277996,
-0.00455427635461092,
0.011165930889546871,
-0.029002515599131584,
-0.01580197550356388,
0.011657178401947021,
-0.03822854906320572,
-0.011572803370654583,
0.010059517808258533,
-0.01717005856335163,
-0.04516155645251274,
-0.042960796505212784,
-0.04223376139998436,
-0.00481390580534935,
-0.024069275707006454,
0.017637992277741432,
-0.0412936694920063,
0.007500901818275452,
0.026402922347187996,
-0.025390923023223877,
-0.045082565397024155,
-0.028814204037189484,
-0.015410415828227997,
0.009607596322894096,
0.018206534907221794,
0.04141700267791748,
-0.015990428626537323,
-0.0027566750068217516,
-0.01870765909552574,
-0.01861461251974106,
0.03824867308139801,
-0.0028127830009907484,
-0.01940631866455078,
-0.00904865749180317,
-0.014427676796913147,
-0.012284968979656696,
0.04573629051446915,
0.014854801818728447,
-0.02686345763504505,
0.007543847896158695,
-0.028329448774456978,
-0.026543131098151207,
0.007610013242810965,
-0.02482730895280838,
0.015902956947684288,
-0.006905336398631334,
0.006505738478153944,
-0.0055489735677838326,
0.058110542595386505,
0.014398008584976196,
-0.010634022764861584,
0.02372562326490879,
0.005930426064878702,
-0.017024291679263115,
-0.021718913689255714,
0.046026915311813354,
-0.004857548978179693,
0.00406115734949708,
0.03536925092339516,
-0.025320371612906456,
-0.039704032242298126,
0.018482999876141548,
0.009982909075915813,
-0.01066322810947895,
-0.02835853025317192,
0.01363452523946762,
0.041566766798496246,
0.020123768597841263,
0.017879566177725792,
-0.018517112359404564,
0.049757953733205795,
0.037711016833782196,
-0.002488392638042569,
-0.07980285584926605,
0.007191925309598446,
0.010747639462351799,
0.007779694627970457,
0.011092142201960087,
-0.0552038811147213,
0.030823728069663048,
-0.011526077054440975,
-0.07442928105592728,
0.0032467807177454233,
-0.024373555555939674,
0.024566901847720146,
-0.05581769719719887,
0.009313371032476425,
-0.02104446105659008,
-0.011328354477882385,
0.035565830767154694,
0.01229923963546753,
0.029776329174637794,
0.049370817840099335,
-0.020618317648768425,
-0.06719585508108139,
-0.01718955859541893,
0.035915225744247437,
0.003943629562854767,
-0.03216523304581642,
0.047222357243299484,
0.0031599069479852915,
0.010679800994694233,
0.020328951999545097,
-0.011030495166778564,
-0.01430651918053627,
-0.01504043024033308,
0.02927851490676403,
-0.036286432296037674,
0.0316392183303833,
0.0328853614628315,
-0.007336899172514677,
0.007320248056203127,
0.005864283069968224,
0.016592925414443016,
0.013525199145078659,
-0.0038847115356475115,
0.004403792787343264,
0.036319196224212646,
-0.0636223554611206,
-0.032624080777168274,
0.03178301453590393,
0.013049976900219917,
-0.007978243753314018,
0.01682235114276409,
0.009766832925379276,
0.01338063832372427,
-0.03902731090784073,
-0.0005361293442547321,
-0.078011654317379,
0.0014905240386724472,
0.017888955771923065,
0.021922564134001732,
0.01724056340754032,
-0.01600763201713562,
0.00624617887660861,
-0.02835080772638321,
0.03674692660570145,
0.02471388876438141,
-0.008230740204453468,
-0.0358055904507637,
-0.0327937938272953,
-0.015076106414198875,
0.016489088535308838,
-0.020338721573352814,
-0.04797139763832092,
-0.03880809620022774,
0.008809203281998634,
-0.008165732957422733,
0.03289979323744774,
-0.06222536042332649,
-0.018008792772889137,
-0.0264541357755661,
-0.0323195718228817,
-0.000701509474311024,
-0.023578818887472153,
0.020701879635453224,
-0.01255261991173029,
-0.03495368734002113,
0.024693381041288376,
0.0006223375676199794,
0.0497027151286602,
-0.021168122068047523,
-0.06163812428712845,
-0.02312285639345646,
-0.02486575022339821,
0.013841470703482628,
-0.031955212354660034,
0.00783029105514288,
-0.01011771522462368,
-0.04077613353729248,
-0.020040258765220642,
0.029031407088041306,
-0.011098075658082962,
0.04658464342355728,
0.04676678031682968,
-0.018066110089421272,
-0.011385390534996986,
-0.002220677211880684,
-0.013266761787235737,
0.051945481449365616,
0.041385095566511154,
-0.019819531589746475,
0.08760842680931091,
0.023386411368846893,
0.031143207103013992,
0.0009059916483238339,
-0.02142290398478508,
-0.03597705811262131,
-0.0053542302921414375,
0.01333693228662014,
-0.03923971578478813,
-0.00045821283129043877,
0.035805173218250275,
-0.019666630774736404,
-0.05327340215444565,
0.009480157867074013,
0.03813692927360535,
-0.006190504878759384,
-0.045731525868177414,
0.008448172360658646,
0.007596394047141075,
0.016708895564079285,
-0.009658541530370712,
0.03044167347252369,
0.007483105640858412,
-0.010569574311375618,
-0.006212952546775341,
0.06317786127328873,
-0.0027868892066180706,
-0.01038021594285965,
0.02774697169661522,
0.014254442416131496,
-0.01396083552390337,
0.03897104039788246,
-0.021451575681567192,
0.004760663956403732,
-0.0347500815987587,
-0.024445513263344765,
-0.0004333252727519721,
0.008008669130504131,
0.0335443913936615,
0.03690161556005478,
-0.036332353949546814,
0.10402422398328781,
0.004347506444901228,
0.013313810341060162,
-0.024273814633488655,
0.003912545274943113,
-0.013908542692661285,
0.016160549595952034,
0.02900608256459236,
0.037514980882406235,
-0.03214970603585243,
-0.014988656155765057,
0.01301672961562872,
0.002916945843026042,
-0.011346091516315937,
-0.0728420615196228,
-0.016272755339741707,
0.007709982339292765,
-0.0037413479294627905,
-0.01210115011781454,
-0.022055238485336304,
-0.022820662707090378,
-0.030704952776432037,
-0.005675506312400103,
0.04377851262688637,
0.014786078594624996,
0.026312261819839478,
-0.0033848416060209274,
-0.010139057412743568,
0.03682322055101395,
-0.08080911636352539,
-0.014564186334609985,
0.010701598599553108,
0.014264937490224838,
-0.0010111958254128695,
-0.04748144745826721
] |
<p>In Bose-Einstein condensate (BEC), people often say there is a well defined macroscopic phase. What exactly the macroscopic phase is? (a phase factor $\mathrm{e} ^{i\phi}$ in a many-body wavefuction?) Is the macroscopic phase the same as the coherent phase?</p> | 1,425 | [
-0.0012630694545805454,
-0.02036818116903305,
-0.01665586046874523,
-0.04619999974966049,
0.05576304346323013,
0.006699462421238422,
-0.01141429040580988,
-0.0558423213660717,
-0.02064364217221737,
-0.024537911638617516,
0.06143627688288689,
0.02263130247592926,
0.03280290588736534,
-0.02289481833577156,
0.027493678033351898,
0.007513340096920729,
0.004651160445064306,
0.011163901537656784,
-0.024144815281033516,
-0.013943924568593502,
-0.0037641844246536493,
0.013737963512539864,
-0.0006922832108102739,
-0.010350878350436687,
0.014234300702810287,
0.052627407014369965,
0.0056092445738613605,
0.02987269125878811,
0.0332375168800354,
0.015661248937249184,
0.02498554438352585,
-0.053460024297237396,
0.017488058656454086,
0.03474922850728035,
0.004716148599982262,
-0.0058477227576076984,
-0.056013207882642746,
-0.054536934942007065,
-0.01654311828315258,
0.0018806973239406943,
-0.0770326629281044,
-0.05430565029382706,
-0.014055144041776657,
0.03198597952723503,
-0.02171734720468521,
-0.007806157227605581,
0.013059580698609352,
-0.021105708554387093,
0.03590114042162895,
-0.07047101855278015,
0.022439081221818924,
0.014947176910936832,
0.03634095564484596,
-0.004858917091041803,
-0.022595999762415886,
-0.001546895713545382,
0.0662762001156807,
0.061453647911548615,
0.003209390677511692,
-0.050646621733903885,
-0.01499495655298233,
-0.013321184553205967,
-0.008966658264398575,
-0.05515061318874359,
-0.04528774693608284,
0.04967274144291878,
0.021762488409876823,
-0.029507393017411232,
0.00382543308660388,
0.014016587287187576,
-0.012097673490643501,
-0.025220364332199097,
0.045301299542188644,
-0.01580527238547802,
0.036971066147089005,
0.002468156162649393,
0.0075012738816440105,
-0.005923147778958082,
-0.002760194940492511,
0.05449359863996506,
-0.02344481088221073,
0.03711039945483208,
0.0034615101758390665,
-0.011144794523715973,
-0.010045504197478294,
-0.016227077692747116,
0.0676901564002037,
-0.0306505486369133,
0.0014773965813219547,
0.011848025023937225,
-0.02438182197511196,
0.022691136226058006,
0.04247188940644264,
-0.020595578476786613,
-0.020007161423563957,
-0.014271277002990246,
0.006382726598531008,
0.044842880219221115,
-0.03497283160686493,
-0.044407714158296585,
0.0010696358513087034,
-0.01700378954410553,
0.04598915949463844,
0.06893330812454224,
-0.010041184723377228,
-0.01172031182795763,
-0.04444587975740433,
0.01851727068424225,
-0.02146824449300766,
-0.030056167393922806,
-0.059975650161504745,
-0.01938452385365963,
-0.0024373698979616165,
-0.0034896519500762224,
-0.0037500427570194006,
-0.030539309605956078,
-0.01971975527703762,
-0.013037040829658508,
0.05333599075675011,
0.10603085905313492,
0.027783440425992012,
-0.03572684898972511,
0.023899493739008904,
-0.047324638813734055,
-0.06580539792776108,
0.00734492763876915,
0.048628780990839005,
0.02560964599251747,
-0.05634847655892372,
0.042174141854047775,
-0.010928334668278694,
0.028044477105140686,
0.03163163736462593,
0.011117939837276936,
-0.022652683779597282,
-0.027400735765695572,
-0.1105833351612091,
-0.018585938960313797,
0.03653484210371971,
-0.027720540761947632,
-0.04786309972405434,
-0.07214350253343582,
0.05747070163488388,
0.03432707488536835,
0.09743138402700424,
-0.010385625064373016,
-0.022068867459893227,
-0.029984327033162117,
0.02266339212656021,
0.028863484039902687,
-0.02312519960105419,
-0.010195545852184296,
-0.018969841301441193,
0.012491602450609207,
-0.010466528125107288,
-0.03993530198931694,
0.005928643513470888,
0.06059655547142029,
0.00101889215875417,
0.011631584726274014,
0.06265110522508621,
-0.00892180111259222,
-0.030622972175478935,
0.04311636835336685,
-0.019200485199689865,
-0.05650978162884712,
0.0804930180311203,
-0.0024738714564591646,
0.005374942906200886,
-0.0005065268487669528,
0.011316485702991486,
0.02974689193069935,
0.0016567776910960674,
0.042808789759874344,
0.012042625807225704,
-0.018922459334135056,
0.004343376029282808,
-0.011382285505533218,
0.018451476469635963,
-0.013045186176896095,
-0.017142584547400475,
-0.07345334440469742,
-0.007719571702182293,
0.0025520657654851675,
-0.041253358125686646,
0.0289191585034132,
-0.049618713557720184,
0.012990513816475868,
0.018519647419452667,
-0.08028951287269592,
-0.036503832787275314,
-0.05514508858323097,
0.014767248183488846,
0.019534079357981682,
-0.012049267999827862,
0.05385170876979828,
0.02075742557644844,
0.00881885550916195,
-0.010673652403056622,
-0.020773623138666153,
-0.04517023637890816,
0.07115612179040909,
-0.0023953004274517298,
0.0026553738862276077,
0.051669348031282425,
0.008723766542971134,
-0.00007760670268908143,
-0.008982452563941479,
0.012789912521839142,
-0.027748804539442062,
-0.055429138243198395,
-0.017385032027959824,
-0.015152163803577423,
0.05292685702443123,
-0.05772068724036217,
-0.03878435865044594,
-0.0071644531562924385,
0.01970091462135315,
-0.010614290833473206,
0.02487311139702797,
-0.019547181203961372,
0.06267953664064407,
0.06095794215798378,
0.008675935678184032,
0.014990227296948433,
0.04760538414120674,
0.010813681408762932,
-0.0025235600769519806,
-0.011486961506307125,
-0.009885016828775406,
-0.06103205680847168,
-0.00867248885333538,
0.039288438856601715,
0.055533267557621,
-0.020924927666783333,
0.02018659934401512,
0.0054723951034247875,
0.07490499317646027,
0.04603712633252144,
0.024665560573339462,
-0.03178514167666435,
-0.030394496396183968,
0.034384988248348236,
0.0015179754700511694,
-0.014756651595234871,
-0.010537669993937016,
0.03564699739217758,
0.039955880492925644,
-0.005959092173725367,
-0.0263653751462698,
-0.016971314325928688,
0.019624685868620872,
-0.03279479593038559,
-0.021695220842957497,
-0.04600735381245613,
-0.03717818111181259,
0.026166606694459915,
-0.00720521155744791,
0.025203224271535873,
-0.017058266326785088,
-0.019378235563635826,
-0.002554832026362419,
-0.030170463025569916,
-0.03499327972531319,
-0.008597522974014282,
-0.015210654586553574,
-0.0734160840511322,
-0.021265096962451935,
0.010922268033027649,
-0.03691694512963295,
0.01069622952491045,
0.000876172911375761,
0.037106890231370926,
-0.030623633414506912,
0.01947225071489811,
0.05865708738565445,
0.017728831619024277,
0.030923333019018173,
-0.0313485823571682,
-0.06514318287372589,
-0.0023808584082871675,
-0.04732324555516243,
-0.007459681015461683,
0.027544071897864342,
-0.048345256596803665,
0.008246581070125103,
-0.010237348265945911,
-0.012204509228467941,
0.027745051309466362,
-0.02448948472738266,
0.005573472939431667,
0.0059842574410140514,
-0.013817111030220985,
-0.034611210227012634,
0.010029612109065056,
0.0070699709467589855,
-0.025494489818811417,
-0.004278447944670916,
0.011850371956825256,
0.01622193120419979,
-0.01951296254992485,
-0.02794608660042286,
-0.0209332387894392,
-0.025725360959768295,
-0.031648557633161545,
-0.020342208445072174,
-0.011795957572758198,
0.021972747519612312,
-0.007995756343007088,
0.026634754613041878,
0.029602477326989174,
-0.054889604449272156,
-0.023419830948114395,
-0.04132577031850815,
-0.020067645236849785,
0.035124246031045914,
-0.016113361343741417,
0.04566417261958122,
0.002360295969992876,
-0.05002647638320923,
0.0633951798081398,
-0.005481685046106577,
-0.055419355630874634,
0.0012133022537454963,
0.000515023828484118,
-0.013753749430179596,
0.02034865878522396,
-0.01560538075864315,
0.02662738971412182,
0.009278828278183937,
0.03263779357075691,
0.022967195138335228,
0.02402636595070362,
0.033839210867881775,
0.021243752911686897,
-0.019183894619345665,
0.009535429067909718,
-0.012021618895232677,
-0.013041725382208824,
0.0282993633300066,
-0.013702033087611198,
0.00047096246271394193,
0.02048458717763424,
-0.007227705791592598,
-0.0053327023051679134,
0.021224679425358772,
-0.005719230975955725,
0.043978385627269745,
-0.011697028763592243,
-0.000851073011290282,
-0.03609601780772209,
0.028309816494584084,
-0.016547780483961105,
-0.0013566373381763697,
0.02382151037454605,
0.011404431425035,
0.03928809240460396,
-0.002546023577451706,
-0.007182329893112183,
0.05031173303723335,
0.007686207070946693,
-0.006925349123775959,
0.0012233378365635872,
0.006198721006512642,
-0.020942959934473038,
0.04522266238927841,
-0.028377985581755638,
-0.06641343235969543,
0.011211193166673183,
0.037078406661748886,
0.013905508443713188,
-0.050574589520692825,
-0.01381093729287386,
-0.01624351739883423,
-0.01330454833805561,
-0.01723795011639595,
-0.0006610390264540911,
0.03360963612794876,
0.011103796772658825,
0.06445193290710449,
0.0024176575243473053,
0.010517771355807781,
0.0026616097893565893,
-0.00022544109378941357,
-0.056647974997758865,
-0.015022145584225655,
-0.0472315214574337,
0.021601477637887,
0.015923870727419853,
0.014187786728143692,
0.033530596643686295,
-0.023397153243422508,
-0.036585599184036255,
-0.024712180718779564,
0.028890984132885933,
-0.024666542187333107,
-0.0046670581214129925,
-0.016504323109984398,
-0.013328487053513527,
-0.0288973618298769,
-0.00842041801661253,
0.013955934904515743,
-0.018658287823200226,
0.04354974627494812,
0.043135423213243484,
-0.04201964661478996,
0.026940038427710533,
0.017161142081022263,
0.00024318842042703182,
-0.006401519291102886,
0.03957897052168846,
0.052733637392520905,
0.0335783027112484,
-0.041828930377960205,
-0.02026371844112873,
0.05023377388715744,
0.05951118469238281,
0.019704140722751617,
-0.008430411107838154,
0.033045973628759384,
-0.04681742563843727,
-0.016168341040611267,
-0.01335511077195406,
0.06792742758989334,
0.010403087362647057,
0.010505418293178082,
0.02541719377040863,
0.014989305287599564,
-0.02812204882502556,
0.0830371156334877,
0.05499111860990524,
0.031070297583937645,
-0.002855554921552539,
-0.06508650630712509,
-0.008793783374130726,
-0.012084878981113434,
0.023609302937984467,
0.022558556869626045,
-0.01305502001196146,
-0.03381398320198059,
0.022328492254018784,
0.014583996497094631,
0.004144868813455105,
-0.03666209429502487,
-0.020892813801765442,
-0.01933259516954422,
-0.0014673490077257156,
0.0029880187939852476,
0.0020037502981722355,
-0.007599528878927231,
0.03279309719800949,
0.017606742680072784,
0.0015892467927187681,
-0.008615300059318542,
-0.05922946706414223,
-0.027339957654476166,
0.029993485659360886,
0.014431419782340527,
0.014934060163795948,
-0.0069389925338327885,
-0.04155734181404114,
-0.048541177064180374,
0.05658287927508354,
-0.017011065036058426,
-0.007207076530903578,
-0.019304806366562843,
-0.017605328932404518,
0.016460832208395004,
-0.027803579345345497,
0.003291465574875474,
0.04993089661002159,
0.0022803943138569593,
0.008025280199944973,
-0.04388130456209183,
-0.019277598708868027,
-0.002372409449890256,
0.03782402724027634,
-0.03055095672607422,
0.06784965097904205,
-0.01922193169593811,
-0.02029890939593315,
0.023781176656484604,
-0.007187331095337868,
-0.016180746257305145,
-0.05207689106464386,
0.0028941419441252947,
0.03742937743663788,
0.013927021995186806,
0.015913862735033035,
-0.02870013378560543,
-0.07333764433860779,
-0.008974185213446617,
0.032893888652324677,
0.008723249658942223,
-0.00032704026671126485,
-0.035169508308172226,
0.05226751044392586,
0.014535908587276936,
0.009307862259447575,
0.05609026551246643,
-0.013699468225240707,
-0.03098605014383793,
-0.0005103179719299078,
-0.02477390319108963,
0.06122291833162308,
-0.015634793788194656,
0.045345284044742584,
-0.006966172251850367,
0.02504667453467846,
-0.005612907465547323,
0.04821297526359558,
-0.02249813824892044,
0.026419024914503098,
0.016772106289863586,
-0.020847763866186142,
0.005153746344149113,
0.023327238857746124,
-0.026822490617632866,
-0.018992850556969643,
0.021153949201107025,
0.003551888046786189,
0.005390641745179892,
-0.05123615637421608,
-0.007764569483697414,
-0.008213935419917107,
0.029265232384204865,
-0.0010241697309538722,
0.01886543445289135,
0.02591659314930439,
-0.06619515269994736,
-0.020340828225016594,
0.004972383379936218,
-0.0517750009894371,
0.0195249542593956,
-0.00806727260351181,
-0.007166360504925251,
-0.00863255001604557,
-0.05411498621106148,
-0.009395476430654526,
-0.029717549681663513,
-0.012564556673169136,
0.012903720140457153,
-0.02266721986234188,
0.0220734141767025,
0.03890610486268997,
0.012952054850757122,
-0.06208018213510513,
-0.06877665221691132,
0.020676152780652046,
0.023671889677643776,
0.01300225593149662,
-0.015620069578289986,
0.017087457701563835,
-0.005600681994110346,
-0.010217994451522827,
-0.008050628937780857,
0.01147144939750433,
-0.021148767322301865,
-0.026068808510899544,
0.010506758466362953,
0.004945890046656132,
0.03350095450878143,
0.006747682113200426,
-0.025398170575499535,
-0.01418754830956459,
0.0017148994375020266,
0.00913546234369278,
0.04209872707724571,
0.04823446273803711,
-0.024767355993390083,
-0.056967973709106445,
0.007232640404254198,
-0.03377210721373558,
0.0367182157933712,
-0.0016184591222554445,
0.009292279370129108,
0.020886782556772232,
-0.04450658708810806,
0.00926895346492529,
0.0054750023409724236,
-0.012496871873736382,
0.0088401073589921,
0.03428592160344124,
-0.0007055752212181687,
-0.03201043978333473,
-0.023893257603049278,
-0.05691660940647125,
0.02398814633488655,
0.023025790229439735,
-0.029968274757266045,
0.017564842477440834,
0.02452039159834385,
-0.0016419865423813462,
0.022078827023506165,
-0.007413257844746113,
-0.022788409143686295,
-0.001561867306008935,
0.01487366110086441,
0.008526531979441643,
0.02542761154472828,
0.00703450059518218,
-0.013037404976785183,
-0.03552798554301262,
-0.051625680178403854,
0.012643760070204735,
0.06783756613731384,
-0.029782261699438095,
0.036193862557411194,
-0.01361294649541378,
-0.011842031963169575,
-0.010124912485480309,
-0.042704012244939804,
0.004675333853811026,
0.08692463487386703,
-0.023323234170675278,
0.01875428669154644,
-0.04038483649492264,
-0.025007136166095734,
0.00011761703353840858,
0.06699993461370468,
-0.047067709267139435,
0.030479442328214645,
0.04675759747624397,
0.05534593015909195,
0.022013461217284203,
-0.010750538669526577,
-0.0007261124555952847,
0.05002111196517944,
-0.05103655904531479,
0.018786510452628136,
-0.0212083887308836,
0.0007597610238008201,
0.030740996822714806,
0.017128130421042442,
0.009468303062021732,
-0.021855603903532028,
-0.019794758409261703,
0.0013392296386882663,
0.003997095860540867,
0.012576193548738956,
0.0016867183148860931,
0.04397618770599365,
0.020943157374858856,
0.015425637364387512,
0.032106056809425354,
0.007291899062693119,
0.014411172829568386,
-0.06360691040754318,
-0.01950998418033123,
0.011114881373941898,
-0.07155129313468933,
0.0010409326059743762,
-0.005715551786124706,
-0.012189983390271664,
0.00420693214982748,
-0.016300972551107407,
0.02256130427122116,
0.0066762943752110004,
0.006346207577735186,
-0.020987296476960182,
0.02762240543961525,
-0.009532428346574306,
0.04330173879861832,
0.045707933604717255,
0.03406840190291405,
0.12051305919885635,
0.07234769314527512,
0.022113775834441185,
-0.08766210079193115,
0.03964373469352722,
-0.006209251470863819,
0.02225896343588829,
-0.028112867847085,
-0.01611161045730114,
-0.014071250334382057,
0.0005574558163061738,
-0.012364821508526802,
0.07459541410207748,
0.040227584540843964,
0.013976147398352623,
0.02250678651034832,
-0.0476313978433609,
-0.04030808061361313,
0.015431514009833336,
0.013062804937362671,
-0.004845560993999243,
0.006617648992687464,
0.0058365510776638985,
-0.030408650636672974,
-0.015276430174708366,
-0.0143734784796834,
-0.05094175785779953,
-0.009009287692606449,
0.05298672616481781,
0.03234567865729332,
0.007657409179955721,
-0.008642734959721565,
-0.025456981733441353,
-0.005368366371840239,
-0.020147079601883888,
0.01263909600675106,
0.02627893164753914,
-0.017396729439496994,
0.017805369570851326,
0.006886058021336794,
-0.024710966274142265,
0.012371481396257877,
-0.005734959151595831,
-0.02383917197585106,
-0.027122322469949722,
0.004804236348718405,
-0.024016203358769417,
0.04184151068329811,
-0.04075575992465019,
0.011827442795038223,
-0.018154259771108627,
0.010041327215731144,
0.024803034961223602,
-0.016768433153629303,
-0.0019486553501337767,
-0.0008044650312513113,
0.0060155657120049,
-0.045726265758275986,
-0.06183573231101036,
-0.042736053466796875,
-0.002489314414560795,
-0.027631321921944618,
0.00993925891816616,
-0.02426915243268013,
-0.010406761430203915,
-0.013598223216831684,
0.0202957633882761,
0.016376521438360214,
0.020976094529032707,
-0.012550952844321728,
-0.03736156225204468,
0.03142165020108223,
-0.05827904865145683,
-0.016835642978549004,
0.05962257832288742,
0.017504654824733734,
0.028566306456923485,
0.008619600906968117,
-0.031069733202457428,
0.004430985543876886,
-0.0661180391907692,
0.0219646617770195,
-0.0086813410744071,
-0.051147233694791794,
0.01502275187522173,
-0.0005444568232633173,
0.03714379295706749,
0.04343573749065399,
-0.0363372340798378,
0.016727130860090256,
-0.01771942898631096,
0.0018740162486210465,
0.027115637436509132,
-0.016552016139030457,
0.006959825754165649,
-0.0013645726721733809,
-0.009524055756628513,
-0.004648088477551937,
-0.012472580187022686,
0.019404606893658638,
0.027364090085029602,
0.007585514336824417,
-0.012593956664204597,
0.02087034285068512,
-0.0030096187256276608,
-0.010226727463304996,
0.013049482367932796,
-0.03341471031308174,
0.006093344185501337,
0.03245210647583008,
0.008938468061387539,
-0.019566833972930908,
-0.05665145069360733,
-0.021386582404375076,
-0.006021999754011631,
0.014786544255912304,
0.0260901041328907,
-0.021067192777991295,
0.010242716409265995,
0.021026642993092537,
0.011267290450632572,
-0.07010184973478317,
-0.014417105354368687,
-0.04282159358263016,
0.021237270906567574,
0.0184820294380188,
0.011743842624127865,
-0.005461088381707668,
0.006363196298480034,
0.019032541662454605,
-0.01587361842393875,
0.006415842566639185,
0.03252134472131729,
-0.003927296958863735,
0.015643833205103874,
0.06258916854858398,
-0.030400710180401802,
0.04357254132628441,
0.006079504732042551,
-0.013956861570477486,
0.045171599835157394,
-0.047551222145557404,
-0.06024773791432381,
0.01309151854366064,
0.0007277645054273307,
0.02399054914712906,
0.0623682364821434,
0.0359703004360199,
-0.012931815348565578,
0.03012710064649582,
-0.019785990938544273,
0.024548208341002464,
0.003955764230340719,
-0.018388427793979645,
-0.016400421038269997,
0.022625230252742767,
-0.006438379641622305,
-0.031077371910214424,
-0.030343422666192055,
0.06847183406352997,
0.039699945598840714,
-0.003247310174629092,
0.001936948741786182,
-0.010472866706550121,
0.01968446560204029,
0.04655624181032181,
0.04511619359254837,
0.002248958684504032,
0.020065581426024437,
0.0526152178645134,
0.018690168857574463,
0.02725638449192047,
0.026092251762747765,
-0.011102823540568352,
-0.08406665921211243,
-0.01957901194691658,
0.012640156783163548,
0.021036947146058083,
0.02723635546863079,
0.006974549498409033,
0.015467901714146137,
0.031104620546102524,
-0.024558547884225845,
0.02395377866923809,
-0.005423431750386953,
0.017231298610568047,
-0.00731487013399601,
-0.004399173893034458,
-0.03795279189944267,
0.05868345499038696,
0.005756733939051628,
0.013260988518595695,
-0.00043939342140220106,
0.005498318001627922,
0.009822665713727474,
-0.0038852132856845856,
-0.000456754001788795,
0.03355022519826889,
0.006375346798449755,
-0.016491979360580444,
0.0630306676030159,
-0.03058009222149849,
-0.043454863131046295,
0.037238653749227524,
0.029186001047492027,
0.006361093372106552,
-0.010946100577712059,
-0.017566373571753502,
-0.0055765872821211815,
0.029073692858219147,
-0.00790207926183939,
-0.004884899128228426,
0.01598525047302246,
0.04954439774155617,
0.0013458955800160766,
0.030232762917876244,
-0.008860253728926182,
-0.013360991142690182,
0.04133186861872673,
-0.024415770545601845,
-0.026930663734674454,
0.05827750265598297,
-0.008352665230631828,
-0.0352223701775074,
-0.025461379438638687,
-0.016538236290216446,
0.008943597786128521,
-0.024661952629685402,
0.05400310829281807,
-0.05258834362030029,
-0.038556329905986786,
0.03220228850841522,
0.00017959826800506562,
-0.010691022500395775,
-0.020117999985814095,
0.043477557599544525,
-0.05897975713014603,
0.055926382541656494,
0.01871967874467373,
-0.015448635444045067,
-0.050130270421504974,
-0.024815695360302925,
-0.010784742422401905,
-0.017183123156428337,
0.033047981560230255,
-0.04245223104953766,
-0.042361315339803696,
0.008324782364070415,
-0.0015909287612885237,
0.019880224019289017,
-0.018747886642813683,
-0.06642909348011017,
-0.04226168990135193,
-0.053908977657556534,
0.02038668654859066,
0.023208023980259895,
0.017133962363004684,
-0.034963998943567276,
0.005626044236123562,
-0.011495454236865044,
0.0029469169676303864,
0.04287129268050194,
0.005479945335537195,
-0.005834511946886778,
0.025673650205135345,
0.008470389060676098,
-0.0003246379201300442,
-0.011927289888262749,
-0.025831189006567,
-0.02513900212943554,
0.005549752153456211,
-0.02834024839103222,
0.00891059823334217,
-0.015046005137264729,
0.037759359925985336,
0.011021806858479977,
0.0019927986431866884,
0.03756039962172508,
-0.008817841298878193,
-0.035757582634687424,
0.05264915153384209,
0.0015037350822240114,
0.014311528764665127,
0.06541319191455841,
-0.013972361572086811,
0.013966700062155724,
0.0020633884705603123,
-0.045049794018268585,
-0.029784195125102997,
0.01646687090396881,
-0.013557540252804756,
-0.0068802000023424625,
-0.017031870782375336,
0.011690412648022175,
-0.00752420024946332,
-0.01174874883145094,
0.014482562430202961,
0.01854838989675045,
-0.054022304713726044,
-0.005905963014811277,
0.06694989651441574,
-0.0019626321736723185,
0.04608779400587082,
0.013582409359514713,
-0.016451053321361542,
0.03995544835925102,
0.010681851767003536,
0.03232574090361595,
0.07978451997041702,
0.038363806903362274,
0.0185675248503685,
0.044018249958753586,
-0.008499729447066784,
-0.029972007498145103,
-0.016909249126911163,
0.014600030146539211,
0.031554967164993286,
-0.023374581709504128,
-0.01848084107041359,
0.05696382746100426,
0.0014828686835244298,
0.023740408942103386,
0.001769578317180276,
-0.029915086925029755,
0.10574561357498169,
-0.027877869084477425,
0.01326229888945818,
-0.03906713053584099,
0.0171666257083416,
-0.0327320471405983,
-0.001034367480315268,
0.021328266710042953,
0.07864813506603241,
-0.01110213901847601,
-0.000686596380546689,
-0.0412544384598732,
0.0011328868567943573,
0.032999470829963684,
-0.07762930542230606,
-0.013079752214252949,
0.015320900827646255,
0.017800699919462204,
0.0023295797873288393,
-0.01911667175590992,
-0.03451493754982948,
-0.04792635887861252,
0.014694561250507832,
0.009698857553303242,
0.04327983409166336,
0.02721673622727394,
0.02159871906042099,
0.003362125949934125,
0.06130442023277283,
-0.03408623859286308,
0.02718578837811947,
-0.03224823623895645,
0.018741454929113388,
-0.022032344713807106,
0.024129172787070274
] |
<p>Would a rocket burn more fuel to get from Earth's surface to Low Earth Orbit, or to get from LEO to Geosynchronous Earth Orbit?</p> | 1,426 | [
-0.019684476777911186,
-0.007426480762660503,
-0.03905251622200012,
0.034346453845500946,
0.011435396037995815,
0.02936440519988537,
-0.000895326491445303,
-0.04251975566148758,
0.05200425907969475,
-0.023316821083426476,
-0.013392966240644455,
0.052160896360874176,
0.02932557836174965,
0.0044280244037508965,
-0.0039814128540456295,
0.010321155190467834,
-0.020154273137450218,
0.029644496738910675,
0.0032862660009413958,
-0.013986114412546158,
0.009700261987745762,
-0.02364962548017502,
0.04827538877725601,
0.004072314593940973,
-0.025182701647281647,
0.014726749621331692,
0.03470887988805771,
-0.027790239080786705,
0.02244819514453411,
0.0419929064810276,
0.039404042065143585,
0.004229789599776268,
0.017524661496281624,
0.05710526555776596,
0.020341884344816208,
0.018879486247897148,
-0.031898919492959976,
-0.00888042151927948,
-0.03540052846074104,
0.027794377878308296,
-0.025288142263889313,
-0.03677240386605263,
-0.01796078309416771,
0.04955838620662689,
0.03153400868177414,
0.034300778061151505,
-0.026780961081385612,
-0.01386868767440319,
0.05738203227519989,
-0.06523146480321884,
0.029705101624131203,
-0.036059629172086716,
0.010654636658728123,
0.04254428297281265,
0.00126649031881243,
0.01321999728679657,
0.0829806700348854,
0.07642015814781189,
0.009263345040380955,
-0.005878273397684097,
-0.02085009776055813,
-0.009972471743822098,
0.006719738710671663,
-0.030469616875052452,
0.009925831109285355,
0.010246473364531994,
0.0004840390174649656,
-0.024997351691126823,
0.01242735330015421,
0.05145013704895973,
0.01252182200551033,
0.02184775099158287,
-0.011169462464749813,
-0.01895596832036972,
0.02412763237953186,
-0.03682904317975044,
0.016460442915558815,
0.03384339436888695,
0.059660207480192184,
0.04302452132105827,
-0.043861035257577896,
-0.015081614255905151,
0.03036019578576088,
0.05227728188037872,
0.004300088156014681,
0.06235099583864212,
0.049329694360494614,
0.024369142949581146,
-0.0061083040200173855,
0.020568182691931725,
0.012694071978330612,
0.01998514123260975,
0.011930788867175579,
-0.014735674485564232,
0.01948525942862034,
0.052215326577425,
-0.01336892880499363,
0.03174761310219765,
0.03248074650764465,
-0.02698119916021824,
0.03347919508814812,
-0.013403651304543018,
0.02627919241786003,
0.07825317233800888,
0.056705184280872345,
-0.015520093962550163,
-0.019121304154396057,
0.010651041753590107,
-0.02850201353430748,
-0.0004979657824151218,
-0.01679203473031521,
0.014131424948573112,
-0.006143597885966301,
0.0165864247828722,
0.014894744381308556,
-0.016595156863331795,
0.010539079084992409,
-0.04348348453640938,
0.0077097793109714985,
0.058605119585990906,
0.04884696006774902,
0.032254546880722046,
0.048747431486845016,
0.04178594425320625,
-0.008161387406289577,
0.015687663108110428,
0.01986992172896862,
-0.011597054079174995,
-0.01187452208250761,
0.0010103360982611775,
-0.034785717725753784,
-0.03574274107813835,
-0.018657509237527847,
-0.04237394034862518,
0.05120672658085823,
0.03007473051548004,
-0.07604242861270905,
-0.034750115126371384,
0.05882622301578522,
0.01777641661465168,
0.014405859634280205,
-0.06622854620218277,
0.006187807768583298,
-0.0037959658075124025,
0.04410336911678314,
-0.0049544465728104115,
-0.00288310251198709,
0.006225955206900835,
0.02329494245350361,
-0.034115828573703766,
-0.035467132925987244,
-0.018059127032756805,
-0.009782574139535427,
-0.08379193395376205,
0.056158389896154404,
-0.0428924560546875,
-0.008359791710972786,
0.03165736049413681,
-0.005131225101649761,
-0.0074831643141806126,
0.040985316038131714,
-0.02818475477397442,
0.009195191785693169,
-0.016444915905594826,
0.03867937996983528,
-0.0014904225245118141,
0.08952151983976364,
0.040753450244665146,
0.01993556320667267,
0.04646783694624901,
0.038149818778038025,
0.021124200895428658,
0.00429119449108839,
-0.0019606947898864746,
0.058644868433475494,
-0.05433480069041252,
0.0015460099093616009,
-0.06363570690155029,
0.004690981935709715,
0.004931959323585033,
-0.05726832151412964,
-0.03437535837292671,
0.0009005500469356775,
-0.02231631800532341,
0.018591267988085747,
0.058396946638822556,
0.008828011341392994,
0.016308259218931198,
0.0012573788408190012,
-0.020450733602046967,
-0.0351034477353096,
-0.0499664805829525,
0.0046121408231556416,
-0.009968370199203491,
0.006321213208138943,
0.002842828631401062,
0.023935707286000252,
0.020973699167370796,
-0.06460001319646835,
-0.021611513569951057,
0.017210720106959343,
0.040275610983371735,
-0.005313902627676725,
-0.01219182088971138,
0.014261382631957531,
0.09132411330938339,
0.01583726704120636,
-0.008060871623456478,
0.0006125418585725129,
-0.03102504462003708,
-0.047228049486875534,
0.002548288321122527,
-0.005478824954479933,
0.020420176908373833,
0.019435547292232513,
-0.020647039636969566,
0.012089166790246964,
0.019146835431456566,
-0.02863496169447899,
0.04195230081677437,
-0.020988238975405693,
0.07567039877176285,
0.040534187108278275,
0.03580278530716896,
0.01850365474820137,
0.0017435544868931174,
-0.009721213020384312,
-0.0001544725091662258,
0.00043937438749708235,
-0.05427040532231331,
-0.029451468959450722,
-0.02786976285278797,
0.05882943049073219,
-0.021792007610201836,
-0.02091997303068638,
0.008764694444835186,
0.03306480869650841,
0.011079865507781506,
0.03377678990364075,
0.022793876007199287,
-0.02498789317905903,
-0.02046636864542961,
0.03191940486431122,
0.043051280081272125,
-0.0014854180626571178,
0.02478678524494171,
0.022668685764074326,
0.020635100081562996,
-0.02996000275015831,
-0.010144122876226902,
-0.03153830021619797,
0.040410447865724564,
0.004363934509456158,
-0.0027365495916455984,
0.02536376751959324,
-0.0061063822358846664,
0.04636157304048538,
-0.053696803748607635,
0.02007378078997135,
0.010075382888317108,
-0.031043438240885735,
0.016709499061107635,
0.011237788945436478,
0.0003917927388101816,
-0.0005437004729174078,
0.015327063389122486,
-0.021919703111052513,
-0.0003689128498081118,
0.060539018362760544,
-0.05214399844408035,
0.043673086911439896,
-0.04159989580512047,
0.0036955783143639565,
-0.027516556903719902,
-0.002661782782524824,
0.019383884966373444,
-0.04675116389989853,
0.014227967709302902,
-0.0423295758664608,
-0.021585242822766304,
-0.03299620375037193,
-0.02455618605017662,
-0.0021175146102905273,
0.021399855613708496,
-0.02019686996936798,
0.019368622452020645,
-0.015107969753444195,
-0.02159612625837326,
0.04695238173007965,
0.02066969871520996,
0.011493856087327003,
0.046762168407440186,
-0.0019347277702763677,
-0.08478919416666031,
-0.012635848484933376,
-0.020215727388858795,
0.016841638833284378,
0.04183005541563034,
-0.006164907477796078,
0.065818652510643,
-0.03069566935300827,
-0.05589349940419197,
0.0025732589419931173,
-0.06389448046684265,
-0.05284954980015755,
-0.00948333740234375,
0.0057640718296170235,
-0.010503827594220638,
-0.03765849024057388,
0.04888191074132919,
0.002219586633145809,
-0.0694398283958435,
-0.00229285447858274,
-0.04961354658007622,
-0.03489882871508598,
0.03927048295736313,
-0.027311058714985847,
0.015157054178416729,
-0.02910587564110756,
-0.04510778561234474,
0.06861904263496399,
0.029596203938126564,
0.012344541028141975,
-0.04592430591583252,
-0.03389638662338257,
-0.012651373632252216,
-0.0039177327416837215,
-0.00806803535670042,
-0.00025044672656804323,
-0.01097213476896286,
-0.021414779126644135,
0.028165938332676888,
0.05463084205985069,
0.004467246122658253,
0.02444199100136757,
-0.00984175130724907,
-0.030498197302222252,
0.006954402197152376,
0.02358834631741047,
0.017001478001475334,
-0.004499491769820452,
-0.04471166804432869,
0.010429142974317074,
-0.029382891952991486,
0.042991142719984055,
-0.023820295929908752,
-0.05799049511551857,
0.048981472849845886,
-0.01380072720348835,
-0.01396887842565775,
0.004991931840777397,
0.044287342578172684,
0.03243696317076683,
0.004347542300820351,
0.013101328164339066,
0.010921534150838852,
0.055425796657800674,
0.01199622917920351,
-0.027716558426618576,
0.015202805399894714,
0.08128795772790909,
-0.04494515433907509,
-0.026157330721616745,
-0.002663156483322382,
0.004428793676197529,
0.008307664655148983,
0.026691719889640808,
-0.039020612835884094,
0.0371524840593338,
0.021780580282211304,
0.007330290973186493,
0.027039095759391785,
-0.028672805055975914,
-0.0017923868726938963,
-0.07942504435777664,
-0.020441323518753052,
-0.007940327748656273,
0.06778720766305923,
0.01429712027311325,
0.0385667085647583,
0.0052246772684156895,
0.010185915976762772,
0.003343885997310281,
0.01852552779018879,
-0.1023607850074768,
0.0466301403939724,
-0.05360661819577217,
-0.01922677829861641,
0.004184269811958075,
0.013910655863583088,
-0.020915091037750244,
-0.06086454540491104,
-0.04557844251394272,
-0.015563476830720901,
-0.007440515328198671,
-0.03667646273970604,
0.023484017699956894,
-0.03026166930794716,
-0.021659590303897858,
-0.012909768149256706,
0.0031630503945052624,
0.030416909605264664,
-0.03640363737940788,
-0.00493810186162591,
0.020804161205887794,
-0.009742658585309982,
-0.00462466012686491,
-0.023890038952231407,
0.020875494927167892,
-0.01987641118466854,
0.01110234297811985,
-0.03224869817495346,
0.018240798264741898,
0.013557346537709236,
0.0034543301444500685,
-0.009118576534092426,
-0.008861524052917957,
-0.028686678037047386,
-0.0014476630603894591,
-0.04380599036812782,
-0.05301347374916077,
0.006124792620539665,
0.03151393309235573,
0.01570831798017025,
0.001289250678382814,
0.010734695941209793,
0.036877021193504333,
-0.005651670042425394,
0.036865781992673874,
0.01667398400604725,
0.009113652631640434,
0.020321447402238846,
-0.002904928755015135,
-0.01343094278126955,
-0.03356843441724777,
-0.03534053638577461,
-0.00644682114943862,
0.047181516885757446,
-0.02369876764714718,
-0.030089853331446648,
0.001600796589627862,
0.014687084592878819,
0.006157909985631704,
-0.03679906949400902,
-0.010806091129779816,
0.04279903694987297,
0.028875866904854774,
0.010320891626179218,
-0.03192542493343353,
-0.005488868337124586,
0.020611951127648354,
0.045158617198467255,
-0.01173500344157219,
0.008857118897140026,
-0.09581480920314789,
-0.03443874418735504,
0.014065040275454521,
-0.012562313117086887,
-0.03168452903628349,
-0.03545917570590973,
-0.04022727534174919,
-0.00923769362270832,
0.019191250205039978,
-0.016149885952472687,
0.03658613562583923,
-0.038864798843860626,
0.019081231206655502,
-0.0039529986679553986,
-0.03538259118795395,
-0.012330288998782635,
0.018667234107851982,
0.03369104117155075,
-0.009824003092944622,
-0.02190823294222355,
-0.004757822956889868,
-0.012936440296471119,
0.03997799754142761,
0.018686268478631973,
0.05255284160375595,
0.026612401008605957,
0.033832255750894547,
-0.012735072523355484,
0.0023192684166133404,
-0.023038947954773903,
-0.06331957876682281,
-0.03420500084757805,
0.022750120609998703,
0.01276186853647232,
0.029050910845398903,
-0.023135362192988396,
-0.0686248242855072,
0.03909130021929741,
-0.014176847413182259,
-0.015811746940016747,
-0.0721956118941307,
-0.0426771380007267,
0.015849648043513298,
0.050839200615882874,
0.009365963749587536,
0.04344230890274048,
0.025177661329507828,
-0.00474135996773839,
-0.005474002566188574,
-0.023097068071365356,
0.042216021567583084,
-0.04657238721847534,
-0.039547134190797806,
0.030461281538009644,
-0.04122910276055336,
-0.014730062335729599,
0.018881509080529213,
-0.029635736718773842,
0.002744508907198906,
-0.009119650349020958,
-0.06632185727357864,
-0.011097709648311138,
0.005384697578847408,
-0.005444461479783058,
-0.008514191955327988,
0.02489486336708069,
0.04246499389410019,
-0.024289757013320923,
-0.031198827549815178,
0.00017467212455812842,
0.0042649745009839535,
0.005161359440535307,
-0.02047048695385456,
-0.026156261563301086,
-0.00042741827201098204,
-0.024623027071356773,
-0.003081832081079483,
0.04091436043381691,
-0.04139846935868263,
0.0692281499505043,
0.002519117435440421,
-0.04083208367228508,
0.050800591707229614,
-0.074867844581604,
-0.017183654010295868,
0.023424915969371796,
-0.0019964103121310472,
-0.0041440208442509174,
-0.015842881053686142,
0.023960214108228683,
0.005212446674704552,
-0.029234733432531357,
-0.07735998928546906,
-0.0418594554066658,
0.028140153735876083,
0.017427681013941765,
0.015956055372953415,
-0.02909141778945923,
-0.02115744724869728,
-0.03047857992351055,
-0.025179630145430565,
-0.005650410428643227,
0.044737521559000015,
-0.00619904138147831,
-0.02252691611647606,
0.0009176571038551629,
0.0005363129312172532,
0.042960941791534424,
-0.011052202433347702,
-0.02407696284353733,
-0.01654597371816635,
-0.0044133407063782215,
0.01769690029323101,
-0.05870639532804489,
0.05509524047374725,
-0.01719990186393261,
-0.040240101516246796,
-0.031178783625364304,
-0.0188591405749321,
0.002618773141875863,
-0.019666528329253197,
-0.009893982671201229,
0.08306669443845749,
-0.004915180150419474,
0.011097347363829613,
-0.0051698447205126286,
0.04033590853214264,
-0.005114735569804907,
0.032597582787275314,
0.012371104210615158,
0.0055029974319040775,
-0.001565334852784872,
0.02102719619870186,
-0.006178802810609341,
-0.00023247521312441677,
-0.01058222260326147,
0.022497430443763733,
0.08330381661653519,
-0.020736088976264,
-0.035039208829402924,
0.0417000874876976,
0.01469847746193409,
0.011151501908898354,
-0.019742844626307487,
0.010257667861878872,
0.01452036201953888,
-0.0005905760917812586,
-0.028550559654831886,
-0.04483366012573242,
-0.008295885287225246,
-0.03747269883751869,
0.028117969632148743,
-0.06428603827953339,
0.017315475270152092,
-0.001180234830826521,
-0.001595485140569508,
0.043292850255966187,
-0.023823782801628113,
-0.006054012104868889,
0.015546518377959728,
-0.00888688862323761,
0.015182757750153542,
-0.023450378328561783,
-0.016390513628721237,
0.04264844208955765,
0.04439258575439453,
-0.007120831869542599,
0.027290597558021545,
0.030298002064228058,
0.012896839529275894,
0.026858631521463394,
-0.027277052402496338,
-0.06231003999710083,
0.028725044801831245,
-0.0432899072766304,
0.042236339300870895,
-0.004498319700360298,
0.005256697069853544,
0.07078790664672852,
-0.0044220988638699055,
-0.03447351232171059,
-0.013053159229457378,
0.01304997131228447,
-0.06621137261390686,
0.03871507570147514,
-0.000752433086745441,
0.019272495061159134,
0.018966814503073692,
0.004585464484989643,
0.02312150038778782,
-0.0162473376840353,
0.006399569567292929,
0.022538967430591583,
-0.07431486994028091,
-0.01264817826449871,
0.010600282810628414,
-0.04146460443735123,
0.024932952597737312,
0.013608151115477085,
-0.030840907245874405,
0.023977084085345268,
-0.004903072025626898,
-0.01821652613580227,
0.018952319398522377,
0.05630675330758095,
-0.05298548564314842,
0.0634351298213005,
-0.011839652433991432,
0.012897524982690811,
-0.0030521054286509752,
0.03292739763855934,
0.12739449739456177,
0.04472886770963669,
0.008880935609340668,
-0.07820878177881241,
0.015602660365402699,
-0.04369668290019035,
0.0027859800029546022,
-0.015817267820239067,
0.006606000475585461,
0.025503870099782944,
-0.012820655480027199,
0.04085918888449669,
0.02082175388932228,
-0.028443342074751854,
-0.03611551597714424,
0.0600273534655571,
-0.022426441311836243,
0.007049066014587879,
0.02802889049053192,
0.022298229858279228,
-0.009830806404352188,
0.01663222536444664,
0.011332652531564236,
0.060790229588747025,
-0.03963442146778107,
-0.014768373221158981,
-0.03510546311736107,
-0.05378612503409386,
0.035081442445516586,
0.0034677963703870773,
-0.06414978206157684,
-0.00019854608399327844,
0.04259371757507324,
-0.02165025658905506,
-0.02823570743203163,
0.03221860155463219,
0.00013520868378691375,
0.005050766281783581,
0.017157644033432007,
0.03939395397901535,
0.01438323687762022,
0.0113959526643157,
0.0072259604930877686,
-0.0017511332407593727,
-0.06241321191191673,
0.05612591281533241,
-0.028311938047409058,
-0.02035566233098507,
0.011645231395959854,
0.008157944306731224,
-0.014647644013166428,
0.022162504494190216,
0.006824980489909649,
-0.04122210294008255,
-0.02126947045326233,
0.007030567154288292,
0.020862732082605362,
0.0015457700937986374,
-0.04867080599069595,
-0.02889275550842285,
0.002217169152572751,
0.001861749216914177,
0.02939540334045887,
0.03344216197729111,
0.007116710301488638,
0.03062804415822029,
-0.00968547910451889,
0.036569371819496155,
-0.01668550632894039,
-0.03254298120737076,
-0.04466106370091438,
0.005800137296319008,
-0.0369432233273983,
0.00805320218205452,
0.014218994416296482,
0.024777548387646675,
0.05010482668876648,
0.010475395247340202,
-0.009919323027133942,
-0.018983229994773865,
-0.05096421390771866,
0.04757121577858925,
0.024844281375408173,
0.00763573357835412,
-0.03681281581521034,
-0.02334589511156082,
0.03171643242239952,
0.019168565049767494,
0.02014284022152424,
0.03877691552042961,
-0.03209841996431351,
0.03030506893992424,
0.007182565983384848,
-0.053369227796792984,
-0.018314963206648827,
0.01724804751574993,
-0.022730093449354172,
-0.00799556728452444,
-0.05850224196910858,
0.026964765042066574,
0.02352035418152809,
-0.011558148078620434,
-0.03624442219734192,
-0.008433781564235687,
-0.029318546876311302,
0.016721487045288086,
0.021839667111635208,
-0.007693983148783445,
-0.04515782743692398,
0.03120863251388073,
-0.007649049162864685,
-0.004121460951864719,
-0.012635203078389168,
-0.030254893004894257,
-0.008929792791604996,
0.025740614160895348,
0.02544162981212139,
-0.008661095052957535,
0.06372785568237305,
-0.03944506496191025,
0.038099389523267746,
-0.03561984375119209,
0.01464881096035242,
-0.053380340337753296,
0.0013592223403975368,
-0.00034548339317552745,
-0.02293693833053112,
-0.0183453056961298,
0.04469895362854004,
-0.03850235790014267,
-0.010198299773037434,
0.025488844141364098,
0.018627095967531204,
0.004973047412931919,
0.0018923693569377065,
0.04221399128437042,
-0.019790036603808403,
0.048485755920410156,
-0.04568322002887726,
-0.022570449858903885,
-0.013055364601314068,
-0.01612350344657898,
-0.059715427458286285,
0.03187660127878189,
-0.04774058610200882,
0.07539670914411545,
0.019995421171188354,
-0.060069020837545395,
-0.0213333647698164,
0.0919300764799118,
-0.040444813668727875,
-0.007810167968273163,
-0.004112222231924534,
0.008334701880812645,
0.010650641284883022,
-0.0025038726162165403,
0.006675782147794962,
-0.0037391826044768095,
-0.0047851200215518475,
0.016023973003029823,
-0.012710225768387318,
-0.042172785848379135,
0.014675019308924675,
-0.03131253272294998,
-0.026480214670300484,
-0.01827438734471798,
0.011974846944212914,
-0.0110437897965312,
0.02373483218252659,
0.0006608027615584433,
-0.003987503703683615,
-0.002788284793496132,
0.03876124322414398,
0.006093400530517101,
-0.035566940903663635,
0.00719776377081871,
-0.047029104083776474,
-0.010604314506053925,
0.029081353917717934,
-0.024778641760349274,
0.04343698173761368,
0.04398095980286598,
-0.059266023337841034,
0.011626262217760086,
-0.00371653214097023,
-0.031592607498168945,
-0.07267960160970688,
-0.029004622250795364,
0.009343361482024193,
0.027694974094629288,
0.03883814066648483,
0.009045064449310303,
-0.03752606362104416,
0.015389194712042809,
0.0013326138723641634,
0.008494614623486996,
-0.01081974245607853,
0.009297248907387257,
-0.013351740315556526,
-0.004143114201724529,
0.043635834008455276,
-0.024053208529949188,
-0.023605067282915115,
0.041312605142593384,
0.0213537085801363,
0.0558207705616951,
0.0010258563561365008,
0.009975804947316647,
0.001071075676009059,
0.018808577209711075,
0.01310434564948082,
-0.020488332957029343,
-0.030712446197867393,
0.031723927706480026,
-0.006130227819085121,
0.004279635846614838,
-0.023507047444581985,
0.021262573078274727,
0.008280698210000992,
0.004459545016288757,
-0.007460010703653097,
0.0191037580370903,
0.0012786256847903132,
-0.003198280232027173,
0.01837349496781826,
-0.007192883640527725,
0.03602784126996994,
0.000002217308065155521,
-0.03995742276310921,
-0.030594253912568092,
-0.026045694947242737,
0.039220016449689865,
-0.022408850491046906,
-0.030231256037950516,
0.005885598715394735,
0.0014118870021775365,
0.010641142725944519,
0.005037699826061726,
-0.018231602385640144,
0.0008405515691265464,
-0.010774265974760056,
0.010678010992705822,
-0.008023449219763279,
-0.018411820754408836,
-0.028968054801225662,
-0.03996700793504715,
0.023080211132764816,
0.06204414367675781,
0.022777007892727852,
0.01393607072532177,
0.009659030474722385,
-0.036591172218322754,
-0.012499614618718624,
-0.02168131433427334,
0.013457153923809528,
0.002908759517595172,
-0.012899624183773994,
-0.031419795006513596,
-0.03847278654575348,
-0.01312835793942213,
-0.0025205765850842,
0.038618139922618866,
0.011622225865721703,
-0.0032248161733150482,
0.017435848712921143,
0.011691081337630749,
0.008046899922192097,
-0.06808656454086304,
0.0376582071185112,
0.013145118951797485,
-0.06140085682272911,
0.012095913290977478,
-0.03161366283893585,
-0.04264047369360924,
0.027469800785183907,
0.04570533707737923,
0.026251530274748802,
-0.008532417938113213,
-0.007686142344027758,
0.00036741417716257274,
0.06251739710569382,
0.04407928138971329,
0.005552341695874929,
0.07247820496559143,
-0.014671452343463898,
0.004652533680200577,
0.009412064217031002,
0.0020745520014315844,
-0.026087619364261627,
0.02627827599644661,
-0.022171135991811752,
0.020607110112905502,
-0.012848766520619392,
-0.03383041173219681,
0.04222205653786659,
-0.058505114167928696,
-0.0056852796114981174,
0.04919678345322609,
-0.008832622319459915,
0.01711064763367176,
0.009332682006061077,
0.020406698808073997,
0.03955668956041336,
-0.014814021997153759,
0.006931457202881575,
0.021751653403043747,
0.01682690531015396,
-0.02121349424123764,
0.010665666311979294,
0.0352260060608387,
-0.015347851440310478,
0.005810680333524942,
0.011570344679057598,
0.032719455659389496,
0.0050062136724591255,
0.026593228802084923,
0.027202723547816277,
-0.012492082081735134,
-0.022003939375281334,
0.056144680827856064,
0.004141532815992832,
-0.011664514429867268,
0.01650707982480526,
-0.002957556862384081,
0.05251728743314743,
-0.04830564931035042,
-0.018353097140789032,
-0.009857898578047752,
-0.025587396696209908,
0.00946565717458725,
0.013941014185547829,
-0.02424789033830166,
0.012276582419872284,
0.02759183943271637,
0.0002664501662366092,
-0.01885359175503254,
-0.0033272511791437864,
0.04259578138589859,
-0.028839977458119392,
0.04980039596557617,
-0.012749231420457363,
-0.01878376677632332,
-0.034578513354063034,
-0.045748937875032425,
-0.04727068915963173,
-0.02263590507209301,
0.04746270552277565,
0.057645611464977264,
0.021948108449578285,
0.003325566416606307,
-0.0386740081012249,
-0.033250484615564346,
0.025053516030311584,
-0.05655499920248985,
-0.03355734050273895,
-0.01568925939500332,
-0.00894670095294714,
0.018101561814546585,
-0.005561691243201494
] |
<p>I am working on a simple force problem involving inclines. I found a reference of $48^\circ$, in the third quadrant; now, to find the obtuse angle, do I subtract that value from $270^\circ$, or do I add it to $180^\circ$?</p> | 1,427 | [
-0.008873685263097286,
-0.0224585123360157,
-0.024586211889982224,
-0.00467516528442502,
0.054795216768980026,
0.05244677513837814,
-0.03197983652353287,
0.010141692124307156,
-0.012632746249437332,
-0.0004381931503303349,
-0.012387610040605068,
0.06696368753910065,
0.05593389645218849,
0.011355959810316563,
0.03231310471892357,
0.030959704890847206,
-0.025810586288571358,
-0.014221797697246075,
-0.022498395293951035,
-0.005659731570631266,
-0.04646087810397148,
0.0046911598183214664,
-0.015401066280901432,
-0.016364865005016327,
-0.0011039082892239094,
0.040400221943855286,
0.04692558944225311,
-0.020661337301135063,
-0.02517816051840782,
0.05571575462818146,
0.03238850086927414,
0.0007380470633506775,
0.0416574627161026,
-0.013637183234095573,
0.04858279228210449,
-0.003261963604018092,
0.009289896115660667,
-0.013168931007385254,
-0.03983771800994873,
0.05182843282818794,
-0.046355944126844406,
0.007167704403400421,
-0.03478129208087921,
0.04914078488945961,
-0.022550208494067192,
0.04175853729248047,
-0.012651484459638596,
-0.026293134316802025,
0.014861703850328922,
-0.03591329976916313,
0.05917816236615181,
-0.01376922894269228,
-0.02518034167587757,
0.03057735040783882,
0.0005193187389522791,
-0.021224645897746086,
0.06891844421625137,
0.026117248460650444,
-0.006757102906703949,
-0.011826355941593647,
-0.03223543241620064,
-0.004496469162404537,
0.008907937444746494,
-0.01989593729376793,
-0.030154285952448845,
0.017416372895240784,
-0.014569651335477829,
0.0007374802371487021,
0.023234235122799873,
-0.028040442615747452,
0.02217119000852108,
0.03984016180038452,
0.04808616265654564,
-0.02869672328233719,
-0.002161209937185049,
-0.04044342786073685,
0.036314353346824646,
0.04682295024394989,
0.018515029922127724,
0.01615622080862522,
-0.029727531597018242,
-0.02520471066236496,
0.05902782455086708,
0.06260561943054199,
0.005871412344276905,
-0.02698296681046486,
0.040518663823604584,
-0.011422878131270409,
0.02212105318903923,
0.021891143172979355,
-0.002997571136802435,
0.040233712643384933,
0.00015052167873363942,
-0.021591994911432266,
0.02312488667666912,
0.03561455383896828,
-0.057301368564367294,
0.04312463849782944,
0.0033519777934998274,
0.014721115119755268,
0.0006109607638791203,
-0.028706951066851616,
0.017717629671096802,
0.05334452539682388,
0.002500098431482911,
0.0022358058486133814,
0.004927766975015402,
0.03517213836312294,
-0.0029257258865982294,
-0.044878002256155014,
-0.009108715690672398,
0.02050679922103882,
-0.03811515495181084,
-0.005624770652502775,
0.03136249631643295,
-0.016357697546482086,
0.0008899988606572151,
0.00685852812603116,
0.050704363733530045,
0.0394459143280983,
0.051179829984903336,
-0.05309183523058891,
0.016889309510588646,
-0.048766981810331345,
-0.039576463401317596,
-0.011888687498867512,
0.032375823706388474,
-0.04119524359703064,
-0.02489309385418892,
0.011820939369499683,
0.05379224196076393,
-0.025433117523789406,
-0.016844864934682846,
-0.005308732856065035,
0.029499147087335587,
-0.026412272825837135,
-0.07704011350870132,
-0.09090370684862137,
0.05910351499915123,
-0.008683092892169952,
-0.013181332498788834,
-0.04212820529937744,
-0.009709562174975872,
0.049615245312452316,
0.016692552715539932,
0.018210485577583313,
0.023250725120306015,
0.039588380604982376,
0.016163572669029236,
-0.0027198935858905315,
0.007369746454060078,
-0.008369597606360912,
-0.018759887665510178,
-0.031896911561489105,
0.016586346551775932,
-0.03995382785797119,
0.030397964641451836,
0.005859926342964172,
0.0041863201186060905,
-0.05576324835419655,
0.03545167297124863,
-0.002916594035923481,
-0.006110073532909155,
0.0204948540776968,
-0.024519503116607666,
-0.05703480541706085,
0.10971707105636597,
0.004546070005744696,
-0.006304414477199316,
0.01705002225935459,
-0.00542044872418046,
0.027969686314463615,
-0.0005642562755383551,
-0.0076916455291211605,
0.07857996970415115,
-0.002470622770488262,
0.003918335773050785,
-0.05925140529870987,
0.011434413492679596,
0.0022083541844040155,
-0.034260887652635574,
-0.05680660903453827,
0.007445122115314007,
0.018247874453663826,
0.0025081024505198,
0.02609061822295189,
0.025126416236162186,
0.0273538026958704,
0.0641072690486908,
-0.06258964538574219,
0.02868189476430416,
-0.060448773205280304,
0.02761182002723217,
0.034175336360931396,
-0.030160151422023773,
0.013122080825269222,
0.01773117482662201,
0.03192092478275299,
0.009687083773314953,
-0.002925512148067355,
0.011037139222025871,
0.027336305007338524,
0.03268128260970116,
-0.05498591810464859,
0.04557465761899948,
0.03515961766242981,
0.019710341468453407,
0.024269718676805496,
0.006144511513411999,
-0.04262398183345795,
-0.013618207536637783,
0.020128697156906128,
-0.02576605975627899,
0.036010000854730606,
0.009741556830704212,
0.02143954113125801,
-0.04979673773050308,
-0.015002653934061527,
-0.011186118237674236,
0.03316659852862358,
-0.05444595590233803,
0.07035806775093079,
0.04699931666254997,
0.01597318984568119,
0.009967569261789322,
-0.011129196733236313,
-0.016304954886436462,
0.047254253178834915,
0.025280814617872238,
-0.038765184581279755,
-0.040720537304878235,
0.009150579571723938,
0.018584338948130608,
-0.013765163719654083,
-0.02764461375772953,
-0.005417263135313988,
0.01798628829419613,
0.010629749856889248,
0.019627230241894722,
0.020438140258193016,
-0.017993047833442688,
-0.026698440313339233,
-0.02922634594142437,
0.053757667541503906,
-0.024102726951241493,
0.02006116695702076,
-0.04586297273635864,
0.011817392893135548,
-0.008327656425535679,
0.024368833750486374,
-0.00007161252142395824,
0.0030466087628155947,
-0.013585341162979603,
0.04975439980626106,
0.017485233023762703,
-0.000198851092136465,
0.038244277238845825,
-0.02886492758989334,
-0.041889410465955734,
0.0391823947429657,
0.005415208637714386,
0.007331558968871832,
-0.02072060853242874,
-0.01843143254518509,
0.041750870645046234,
-0.033582545816898346,
-0.059640295803546906,
-0.0015993502456694841,
0.026174820959568024,
-0.042843885719776154,
-0.02432897873222828,
-0.07987038791179657,
-0.009341316297650337,
-0.001290249521844089,
-0.0046424721367657185,
0.0026238381396979094,
0.021101683378219604,
0.014376618899405003,
-0.026899386197328568,
-0.024612409994006157,
-0.04079962521791458,
-0.053989607840776443,
0.020636506378650665,
0.01926586776971817,
-0.021941857412457466,
-0.0038330615498125553,
-0.03993486613035202,
-0.03584038466215134,
0.04157228022813797,
0.024430079385638237,
-0.010203071869909763,
0.04030212387442589,
-0.0039723035879433155,
-0.022929616272449493,
-0.02627771720290184,
-0.016464976593852043,
0.03195207193493843,
-0.021625086665153503,
-0.024026252329349518,
0.04237624257802963,
-0.026165755465626717,
-0.008504285477101803,
0.03165823221206665,
-0.03459783270955086,
-0.045296769589185715,
0.009785265661776066,
-0.006111393682658672,
0.02273048646748066,
0.0075889271683990955,
-0.020948922261595726,
-0.009287208318710327,
-0.022294048219919205,
0.014392606914043427,
-0.06725802272558212,
-0.0625317394733429,
0.00915756169706583,
0.010960323736071587,
0.023844128474593163,
-0.0029443278908729553,
-0.03366369381546974,
0.0463033989071846,
0.008068717084825039,
-0.05973155423998833,
-0.0007970797596499324,
-0.004178276751190424,
0.008586195297539234,
-0.04348737746477127,
-0.011809560470283031,
0.03269166499376297,
0.006033069919794798,
0.034087006002664566,
0.021824460476636887,
0.046136002987623215,
0.05409274622797966,
0.06414104253053665,
0.0077520329505205154,
-0.016240887343883514,
-0.0038115771021693945,
-0.008441809564828873,
0.05079727619886398,
0.05170275643467903,
0.01290165726095438,
0.00501550268381834,
-0.03253408893942833,
0.0751648023724556,
0.018815763294696808,
-0.02098587155342102,
0.010574886575341225,
-0.020172014832496643,
0.009970955550670624,
-0.01953398436307907,
0.058998432010412216,
0.02475750632584095,
0.022961830720305443,
-0.015848085284233093,
0.02233901061117649,
0.01042102836072445,
-0.04300669953227043,
-0.009874161332845688,
0.01900823414325714,
0.010485048405826092,
-0.016247842460870743,
-0.04046841710805893,
0.01047114934772253,
0.0022062761709094048,
0.02307274378836155,
-0.007113650441169739,
0.01613948866724968,
0.06350400298833847,
0.0037915133871138096,
0.03084670379757881,
-0.008323482237756252,
-0.05034433305263519,
0.01982003264129162,
-0.04097690060734749,
-0.033792413771152496,
0.03807462379336357,
0.027632901445031166,
0.020975379273295403,
0.029871657490730286,
0.036928437650203705,
-0.0004901931388303638,
0.004692737944424152,
0.012191524729132652,
-0.052719052881002426,
0.036366190761327744,
-0.029452752321958542,
-0.02146180532872677,
0.011827634647488594,
-0.008626876398921013,
-0.0022492611315101385,
-0.020235251635313034,
-0.01432664692401886,
-0.021382221952080727,
-0.029493283480405807,
-0.02879352867603302,
0.03496565297245979,
-0.014608621597290039,
0.02471715211868286,
-0.008330699056386948,
0.01523598562926054,
-0.01339995488524437,
-0.06997524201869965,
0.02608945593237877,
0.039143845438957214,
0.020986028015613556,
-0.012447621673345566,
-0.00328081869520247,
0.027889609336853027,
-0.004354322329163551,
0.01003394927829504,
-0.0026293336413800716,
0.040410663932561874,
0.03218962624669075,
0.0054878839291632175,
-0.03988702595233917,
0.04667571187019348,
0.01558342482894659,
-0.012770070694386959,
-0.004014324396848679,
-0.049322739243507385,
-0.00628926046192646,
-0.016755301505327225,
0.05278850346803665,
-0.05329398810863495,
0.00004330908632255159,
0.0438501350581646,
0.0030100492294877768,
-0.0207899808883667,
0.050741326063871384,
0.03621978312730789,
0.041166797280311584,
-0.02732045389711857,
-0.0541430301964283,
-0.006771286483854055,
-0.02761995606124401,
-0.009061154909431934,
0.04771818965673447,
-0.02106759324669838,
0.0034079239703714848,
-0.05038399621844292,
0.043731849640607834,
0.011313901282846928,
0.000809458433650434,
0.02265857718884945,
-0.011586940847337246,
0.03664962574839592,
-0.019814835861325264,
-0.0006494493572972715,
0.057293523102998734,
0.03658159449696541,
0.03425128385424614,
0.01051461510360241,
-0.0026895119808614254,
-0.08477908372879028,
-0.00010161849058931693,
0.0385209359228611,
0.036200571805238724,
-0.02582583576440811,
0.029933983460068703,
-0.04926042631268501,
-0.006644746288657188,
0.0724741518497467,
-0.019070375710725784,
0.006041236221790314,
-0.05037717521190643,
0.04848501458764076,
-0.005593207664787769,
0.005223684012889862,
-0.047928400337696075,
0.021927721798419952,
0.020326552912592888,
0.03835688531398773,
0.009518677368760109,
-0.0014566965401172638,
0.008032972924411297,
0.018229573965072632,
0.023401962593197823,
0.03252265602350235,
0.013560136780142784,
-0.029348822310566902,
0.03361939638853073,
-0.004509508144110441,
-0.009904209524393082,
-0.05905107036232948,
-0.026385802775621414,
0.04580458998680115,
0.007059004623442888,
-0.02307049371302128,
0.009403733536601067,
-0.028924517333507538,
0.01488218642771244,
-0.020766574889421463,
0.0168404970318079,
0.027637826278805733,
-0.009547727182507515,
0.050891708582639694,
0.013918054290115833,
-0.012227354571223259,
0.062355246394872665,
0.033351242542266846,
0.00008360683568753302,
-0.02481222152709961,
-0.014618403278291225,
0.00976333487778902,
-0.00244902353733778,
-0.04008476436138153,
-0.028812101110816002,
0.021847344934940338,
-0.027277180925011635,
0.03341328352689743,
-0.020200690254569054,
0.038108255714178085,
-0.039940815418958664,
-0.03209108114242554,
-0.024850325658917427,
0.003406297182664275,
-0.0061583626084029675,
-0.002074922900646925,
0.04727146029472351,
0.016836777329444885,
-0.026282690465450287,
-0.014724728651344776,
0.033991292119026184,
-0.04475205019116402,
0.03776604309678078,
0.025195764377713203,
-0.016530491411685944,
0.014185328036546707,
-0.03075532056391239,
-0.02679123356938362,
-0.012956301681697369,
-0.04655557870864868,
0.062381256371736526,
-0.021580224856734276,
0.014703133143484592,
0.013230680488049984,
-0.006130146328359842,
-0.029247133061289787,
0.004323206841945648,
-0.02582961693406105,
0.053847577422857285,
-0.06118200346827507,
0.02749127522110939,
0.0035606722813099623,
0.016986599192023277,
-0.0016873701242730021,
-0.07150048017501831,
0.007960557006299496,
0.02038159780204296,
-0.0032544126734137535,
0.0061936029233038425,
-0.00929333921521902,
-0.015889279544353485,
-0.054726555943489075,
-0.01686505228281021,
0.07291468232870102,
-0.032155100256204605,
0.0005033834604546428,
-0.0007443727809004486,
-0.0009140491019934416,
0.04364094138145447,
-0.012011194601655006,
0.0000381990939786192,
0.009871348738670349,
0.006288115866482258,
-0.02606167457997799,
0.0036472263745963573,
0.03452521190047264,
-0.017629927024245262,
-0.01038195937871933,
-0.007403322029858828,
-0.025678616017103195,
0.0036956698168069124,
-0.024180127307772636,
0.009065558202564716,
0.03298897668719292,
0.023990968242287636,
-0.012118076905608177,
-0.023426683619618416,
0.0463549867272377,
-0.007578985765576363,
0.009359261021018028,
-0.01480715163052082,
0.003190422197803855,
0.005776987411081791,
-0.02179364114999771,
-0.019107172265648842,
0.0247871745377779,
-0.001952471793629229,
-0.0002651340328156948,
0.09056245535612106,
-0.050758328288793564,
0.015050800517201424,
0.01788862608373165,
0.012002686969935894,
0.008155868388712406,
0.02774824947118759,
-0.028953807428479195,
0.012191178277134895,
-0.006309534888714552,
-0.04407433792948723,
-0.020399967208504677,
-0.03651753067970276,
0.017312869429588318,
0.07825067639350891,
-0.06138100102543831,
0.039086710661649704,
0.04811881482601166,
0.028788672760128975,
0.01587865501642227,
0.005102523602545261,
-0.012499791570007801,
0.019815297797322273,
0.009626996703445911,
0.012497134506702423,
-0.018938282504677773,
0.023370075970888138,
0.008300069719552994,
-0.003221813589334488,
-0.00480186240747571,
0.0029715863056480885,
0.01551662664860487,
0.05044171214103699,
-0.007966860197484493,
-0.028622562065720558,
-0.043522998690605164,
0.005708927754312754,
0.009178475476801395,
0.04417574033141136,
-0.04937827214598656,
-0.04969332367181778,
0.05643843114376068,
-0.008290508762001991,
0.011135648936033249,
-0.026353444904088974,
-0.00772018963471055,
-0.033499572426080704,
-0.031139565631747246,
0.02581862546503544,
0.013700010254979134,
-0.05548228323459625,
0.0076714493334293365,
0.03377086669206619,
-0.0047138831578195095,
0.0392143577337265,
-0.05004891753196716,
-0.04532869532704353,
-0.009263518266379833,
0.000007592442671011668,
-0.04695781320333481,
0.010025318711996078,
-0.011222788132727146,
-0.030366282910108566,
0.03663244843482971,
-0.037818294018507004,
0.018540017306804657,
0.03498977795243263,
0.012130332179367542,
-0.013486060313880444,
0.06581494212150574,
-0.022953130304813385,
-0.017621595412492752,
0.012523413635790348,
-0.019553063437342644,
0.10355126857757568,
0.06996983289718628,
-0.006875921506434679,
-0.07479825615882874,
0.05778875946998596,
0.00656991358846426,
0.006439280230551958,
-0.037624210119247437,
0.021907702088356018,
-0.03162531554698944,
0.0020990255288779736,
-0.004322207532823086,
0.053099945187568665,
-0.0036668372340500355,
-0.022039806470274925,
0.05508299916982651,
-0.040328506380319595,
-0.07611992210149765,
-0.008402467705309391,
0.028486035764217377,
0.022269343957304955,
0.014449238777160645,
0.008325180038809776,
0.02102898806333542,
-0.025316912680864334,
-0.004979425109922886,
-0.047157201915979385,
-0.04200457036495209,
0.015373855829238892,
0.0211492907255888,
-0.05613026022911072,
0.032295871526002884,
0.026307908818125725,
-0.030616484582424164,
-0.03784491866827011,
0.05590798333287239,
0.015705598518252373,
-0.03582635894417763,
-0.0031881150789558887,
0.012313099578022957,
0.003154731821268797,
0.02002335898578167,
0.018786290660500526,
0.0025401634629815817,
-0.06345606595277786,
-0.00871962122619152,
-0.03530808538198471,
-0.00583075312897563,
0.012609070166945457,
0.010789608582854271,
-0.01473226211965084,
0.026645883917808533,
-0.02927722968161106,
-0.08377757668495178,
-0.02931320294737816,
-0.006406661123037338,
0.020352670922875404,
-0.024701299145817757,
-0.022820470854640007,
0.031899768859148026,
0.06745947897434235,
0.028545483946800232,
0.009564300999045372,
0.012977666221559048,
0.002531727310270071,
0.001115636434406042,
0.005009176209568977,
0.033246029168367386,
-0.005217031110078096,
-0.060937248170375824,
0.004779213108122349,
0.011051558889448643,
-0.028400475159287453,
0.009845279157161713,
-0.010356580838561058,
0.04070752486586571,
0.013327172957360744,
0.002251372905448079,
-0.019401509314775467,
-0.02872307039797306,
-0.000174888496985659,
0.023973869159817696,
0.011182356625795364,
-0.012923695147037506,
-0.03395194932818413,
-0.00130454171448946,
0.026978332549333572,
0.010855277068912983,
0.03488056734204292,
-0.013058256357908249,
0.021585717797279358,
0.03455478698015213,
0.013048231601715088,
-0.006797499023377895,
-0.04442001134157181,
0.045207828283309937,
-0.042687803506851196,
-0.0065160710364580154,
-0.03827715292572975,
0.022429412230849266,
0.05267958715558052,
0.03504576534032822,
0.0047382875345647335,
0.008242393843829632,
-0.008417537435889244,
-0.0005156746483407915,
0.0028733692597597837,
-0.027460098266601562,
0.006552450358867645,
0.025578636676073074,
-0.009703036397695541,
-0.09088484942913055,
-0.004269793163985014,
-0.03914053365588188,
0.010635093785822392,
-0.018440205603837967,
0.026123715564608574,
-0.01792583055794239,
0.011746624484658241,
-0.011484920978546143,
-0.008225901983678341,
-0.027245858684182167,
-0.03330621123313904,
-0.004189399071037769,
-0.03399788960814476,
-0.004553176462650299,
-0.01750366948544979,
-0.03598153218626976,
0.01661779172718525,
-0.02463950775563717,
-0.04720964655280113,
-0.007524379063397646,
0.02898762933909893,
0.03386801481246948,
-0.03698089346289635,
0.04683777689933777,
-0.030474241822957993,
0.03090261109173298,
-0.0270992461591959,
-0.00018593556887935847,
0.05003386363387108,
-0.037101369351148605,
-0.012780816294252872,
0.05247339978814125,
-0.0007484569796361029,
0.008617330342531204,
0.0168120376765728,
-0.025340646505355835,
0.011944582685828209,
0.02036369778215885,
-0.024644775316119194,
-0.005686314310878515,
-0.022312164306640625,
-0.03340083360671997,
0.003347494173794985,
-0.021690189838409424,
-0.005199533887207508,
-0.006125812418758869,
-0.0035442018415778875,
0.03595616668462753,
0.014340977184474468,
-0.03722143918275833,
-0.03975481912493706,
-0.01586291380226612,
0.007394333370029926,
-0.01123778522014618,
-0.0056567806750535965,
-0.014317057095468044,
0.013365570455789566,
0.02019302360713482,
-0.03316940739750862,
0.018992139026522636,
0.027749544009566307,
0.017747702077031136,
-0.09904075413942337,
-0.007671821396797895,
0.013296803459525108,
0.005889351479709148,
0.05177890881896019,
-0.07189540565013885,
0.03290162235498428,
0.05045009031891823,
-0.05110974982380867,
-0.008897928521037102,
-0.04769214987754822,
-0.008110289461910725,
-0.007847847416996956,
-0.0267481692135334,
0.019586391746997833,
0.04473993182182312,
0.0013560402439907193,
0.034247614443302155,
0.04591457545757294,
-0.005502624437212944,
-0.024539528414607048,
-0.04062844067811966,
0.05042393505573273,
0.0386732742190361,
0.026260599493980408,
-0.0030688096303492785,
0.04496951028704643,
0.013063658960163593,
-0.04024245962500572,
0.056941092014312744,
-0.03680596873164177,
0.07428149878978729,
-0.02533581852912903,
0.027850275859236717,
0.0028018844313919544,
0.054411739110946655,
-0.031340062618255615,
-0.007852541282773018,
-0.01727108843624592,
-0.01985931769013405,
0.004894785117357969,
0.040328387171030045,
-0.01264769397675991,
-0.0012182258069515228,
0.022558314725756645,
-0.005194272845983505,
-0.04025116562843323,
0.015350611880421638,
-0.01201540045440197,
0.034308869391679764,
-0.021185215562582016,
0.001632766448892653,
0.015256181359291077,
-0.04571707546710968,
-0.01197892613708973,
-0.01751181297004223,
0.020361023023724556,
0.044351715594530106,
-0.03643380105495453,
0.005040817428380251,
-0.02003822661936283,
-0.010849466547369957,
-0.044911906123161316,
-0.0009469189681112766,
-0.02334791235625744,
0.003527810564264655,
-0.06523464620113373,
-0.012249990366399288,
-0.03389838710427284,
-0.044952522963285446,
-0.020828768610954285,
-0.0006172964349389076,
-0.022531596943736076,
0.05699138343334198,
0.03952684625983238,
-0.014816216193139553,
-0.0003633013693615794,
-0.03135376796126366,
-0.05296981334686279,
-0.05601191893219948,
0.013643060810863972,
0.04734792187809944,
-0.048373110592365265,
-0.01792425848543644,
-0.019717290997505188,
0.003542527789250016,
0.015597281977534294,
0.02838166430592537,
-0.012056681327521801,
0.0017905912827700377,
-0.026631537824869156,
-0.01117231696844101,
-0.0225489791482687,
-0.02859756350517273,
-0.006697481498122215,
0.03375877067446709,
0.03138110041618347,
-0.006876801606267691,
0.0025503330398350954,
-0.003564765676856041,
-0.0068560498766601086,
-0.015211498364806175,
0.026477761566638947,
0.019693387672305107,
0.02694789320230484,
-0.015491198748350143,
0.01116248220205307,
0.02340264990925789,
-0.016187401488423347,
0.06110401824116707,
0.035188380628824234,
0.00816854927688837,
0.020473144948482513,
-0.047557104378938675,
-0.05483362078666687,
0.023136785253882408,
0.0069255344569683075,
0.008700697682797909,
0.006697274278849363,
-0.01201309822499752,
0.039356671273708344,
-0.04931485652923584,
-0.025519367307424545,
0.05304724723100662,
-0.07552428543567657,
0.02084093540906906,
0.018098266795277596,
0.04800565168261528,
0.05318271368741989,
-0.0018079974688589573,
0.04624286666512489,
0.047898635268211365,
-0.05544659495353699,
0.03460020199418068,
-0.017214875668287277,
0.03687727823853493,
0.01699388585984707,
-0.02030136249959469,
0.0317847914993763,
0.02758614905178547,
0.026780830696225166,
-0.0031023507472127676,
0.023911122232675552,
-0.03476758673787117,
-0.04839364066720009,
-0.021840810775756836,
-0.02699965238571167,
-0.006650891155004501,
0.009544404223561287,
-0.03079700842499733,
0.030686264857649803,
-0.04911958798766136,
0.01919158175587654,
-0.03486476093530655,
0.021861234679818153,
-0.031333085149526596,
-0.014812272042036057,
-0.01149734202772379,
0.009520475752651691,
-0.019856514409184456,
-0.06698480993509293,
-0.0046234941110014915,
-0.004864959511905909,
0.0415835902094841,
-0.0009730163146741688,
0.021843090653419495,
0.020137082785367966,
0.00718705914914608,
-0.012554454617202282,
-0.022595534101128578,
-0.08240485191345215,
0.0054089524783194065,
0.042333342134952545,
0.038031283766031265,
0.020779242739081383,
0.026267176494002342,
0.00516974413767457,
-0.026846928521990776,
0.04350084438920021,
-0.04748126119375229,
-0.014688795432448387,
-0.006142992060631514,
0.026777517050504684,
0.009105677716434002,
-0.017409222200512886
] |
<p>I'm trying to understand tension. So here it goes:</p>
<p>I'll start from the beginning.</p>
<p>Let's assume I'm in space and can move around and apply forces.</p>
<p>Let's say a rope is attached to a body(which is in space).</p>
<p>1) Let's say the body is immovable.
Then the force with which the rope is pulled will be the tension in the rope. Right?</p>
<p>2) Okay, now let's say the body has a mass M and I apply a force F.
The body will accelerate towards me with a acceleration F/M. Obviously, the rope will slacken, so to keep the tension in the rope constant, I will have to accelerate away from the body, maintaining my distance to still apply the force. (I just mentioned that because no one really talks about how one can apply a constant force without having to 'keep up' with the body to keep applying the force. I just wanted to make sure that that truly is the case.)</p>
<p>Now let's say, I pull the rope and then let it slacken i.e. not try to maintain a constant force, then if I was able to measure the acceleration of the body and if I know it's mass, I will be able to find the force I applied and hence, the tension (=force applied) for that period of time on the rope. Is that correct?</p>
<p>3) Okay.
Now, let's say I pull the <em>rope</em> with X newtons of force and another person holds the <em>body</em> and pulls it in the opposite direction with Y newtons of force, shouldn't be the tension in the rope now be (X+Y) newtons, even if the body accelerates in one direction?
If the person instead <em>pushes</em> the body with Y newtons then shouldn't be the tension (X-Y) newtons in the rope now?</p>
<p>4) Let's say the ends of the rope are attached to two bodies and the rope is currently slackened. I then give both the bodies some initial velocity in the opposite direction to each other. Hence, the rope at some point will become taut. Is it possible to tell the force, the two bodies will experience when the rope becomes taut and hence find the tension the string will experience?</p>
<p>Please correct me if I'm wrong in any of these.
I would really appreciate the help.</p>
<p>Thank you.</p> | 1,428 | [
-0.024657681584358215,
0.025557756423950195,
-0.02250158227980137,
-0.025744911283254623,
0.012204736471176147,
-0.01298652496188879,
-0.006229064427316189,
-0.001643724157474935,
0.0034246440045535564,
-0.02060198411345482,
0.014207517728209496,
0.06136346980929375,
0.032732389867305756,
0.009692471474409103,
0.018935777246952057,
-0.015726149082183838,
-0.00937882624566555,
-0.030452614650130272,
0.001472459058277309,
-0.019562499597668648,
-0.024278441444039345,
0.0024472777731716633,
0.01157350093126297,
0.02458224445581436,
-0.005603528115898371,
0.011022759601473808,
0.026930885389447212,
-0.03220614045858383,
0.02798234485089779,
0.06566330790519714,
-0.01633268967270851,
-0.010918901301920414,
-0.009963618591427803,
0.002389231463894248,
0.023668646812438965,
0.04715532809495926,
-0.053863659501075745,
-0.03770681470632553,
0.012813273817300797,
0.03310355171561241,
-0.01366377156227827,
0.0024412653874605894,
-0.020968325436115265,
0.039218321442604065,
-0.06727497279644012,
0.03392280265688896,
0.00742568913847208,
-0.013586711138486862,
0.07208886742591858,
-0.048087939620018005,
0.10138224065303802,
-0.017443964257836342,
0.040485840290784836,
0.021986650303006172,
-0.007111722137778997,
-0.036697130650281906,
0.049510322511196136,
0.02893788181245327,
-0.012830127961933613,
-0.03920067846775055,
-0.023430004715919495,
0.019522180780768394,
-0.043080806732177734,
-0.04835692420601845,
0.022749897092580795,
0.028255166485905647,
-0.01954885572195053,
0.0020491096656769514,
0.04600489139556885,
-0.0034674813505262136,
0.0010183613048866391,
-0.010507944971323013,
0.03023030422627926,
-0.021384282037615776,
-0.012251283042132854,
-0.016156384721398354,
0.03489711880683899,
0.029388414695858955,
0.04191725328564644,
0.06298045068979263,
-0.03411991894245148,
-0.0043878210708498955,
0.06988033652305603,
0.07687745988368988,
0.02520373836159706,
-0.03877837210893631,
0.048513635993003845,
0.014947331510484219,
0.013876528479158878,
0.025799168273806572,
0.022182462736964226,
-0.002868067938834429,
-0.019828705117106438,
-0.02278052270412445,
0.014331056736409664,
0.046139054000377655,
-0.020855063572525978,
0.020484821870923042,
0.02163248136639595,
0.007001611869782209,
-0.012575844302773476,
-0.02020660601556301,
0.0036939566489309072,
0.051266998052597046,
0.013762026093900204,
-0.016584647819399834,
-0.010634221136569977,
0.01552031934261322,
0.014437339268624783,
-0.017119260504841805,
-0.04593762382864952,
-0.02145734429359436,
0.0008506433223374188,
-0.04391299560666084,
-0.022524982690811157,
-0.015924768522381783,
0.006364748813211918,
-0.01238140556961298,
0.06668546050786972,
0.04944860562682152,
0.032538436353206635,
-0.0417194627225399,
0.02303178608417511,
-0.02226528339087963,
-0.025490034371614456,
-0.026434075087308884,
0.028924964368343353,
-0.033602192997932434,
0.0011081238044425845,
0.03500570356845856,
0.0284124705940485,
-0.04176045209169388,
-0.04048256576061249,
0.009988635778427124,
0.062350817024707794,
-0.006237385328859091,
-0.1247265636920929,
-0.07942362874746323,
0.027681130915880203,
0.030996574088931084,
-0.017164118587970734,
-0.06098596751689911,
0.000842916953843087,
0.02220769412815571,
0.07016410678625107,
0.02078433334827423,
0.0011171095538884401,
0.006316406186670065,
-0.002564273541793227,
0.00405993964523077,
-0.0016327165067195892,
-0.02590632438659668,
-0.009869089350104332,
-0.04715530201792717,
-0.032527174800634384,
-0.06520918011665344,
0.024374790489673615,
0.02525475062429905,
0.0019736720714718103,
-0.032000597566366196,
0.04954246059060097,
-0.011940806172788143,
0.026355503126978874,
0.04055411368608475,
-0.032651446759700775,
-0.02646223083138466,
0.07120948284864426,
0.013040466234087944,
0.007178634405136108,
0.028473198413848877,
0.03666853532195091,
0.02012479677796364,
-0.00798607524484396,
0.00018603123317006975,
0.02082992158830166,
-0.06222885102033615,
-0.05033522844314575,
-0.025593290105462074,
-0.024481983855366707,
0.006536227185279131,
-0.06618597358465195,
-0.07770957052707672,
0.007200006395578384,
0.008589902892708778,
0.002328836591914296,
0.05325387045741081,
0.050098299980163574,
0.009722687304019928,
-0.03429802507162094,
-0.01132765132933855,
0.0018448357004672289,
-0.07139812409877777,
0.047307927161455154,
-0.011713108979165554,
0.009154124185442924,
-0.023262204602360725,
0.016747886314988136,
0.024607622995972633,
-0.048165418207645416,
-0.003012134460732341,
0.007575349882245064,
0.04186137020587921,
0.0028360404539853334,
0.005551367998123169,
0.010433424264192581,
0.03717382252216339,
0.027751315385103226,
0.03699018806219101,
0.015537641942501068,
-0.008822556585073471,
-0.028102096170186996,
0.014715369790792465,
-0.05073898285627365,
0.03249988704919815,
0.027216440066695213,
0.02376331202685833,
0.041033219546079636,
-0.03844043239951134,
-0.025875968858599663,
0.03720471262931824,
-0.002934932243078947,
0.09537816047668457,
0.028097977861762047,
-0.002516412176191807,
0.012994305230677128,
0.022055117413401604,
0.0048290761187672615,
0.0016090249409899116,
-0.01462659239768982,
-0.053946495056152344,
-0.04086824133992195,
0.006251013837754726,
-0.00939818937331438,
0.024708839133381844,
-0.0445905402302742,
0.015550076961517334,
0.049280956387519836,
0.043355781584978104,
0.030361022800207138,
0.031175320968031883,
-0.018995532765984535,
-0.05325926095247269,
0.014396201819181442,
0.014930959790945053,
-0.0014464461710304022,
0.044597651809453964,
0.0410727858543396,
0.040295545011758804,
0.034041877835989,
0.003753483295440674,
0.008116858080029488,
0.03832631558179855,
0.009973516687750816,
0.0032887915149331093,
0.03213408216834068,
-0.05355166643857956,
0.04070541262626648,
-0.005055302754044533,
0.03619097173213959,
0.025743957608938217,
0.012454861775040627,
-0.002645710250362754,
-0.032833926379680634,
0.003469934221357107,
0.008234209381043911,
-0.01725315861403942,
-0.014250480569899082,
-0.03512619435787201,
0.014114401303231716,
-0.023348072543740273,
-0.0024192731361836195,
-0.025826070457696915,
0.010296004824340343,
-0.036481816321611404,
-0.01333292294293642,
-0.010256380774080753,
0.012503194622695446,
0.044280387461185455,
-0.03211371973156929,
-0.015394039452075958,
0.005843197926878929,
-0.06527362763881683,
0.042773112654685974,
-0.0066168708726763725,
-0.04256778582930565,
-0.018790030851960182,
-0.019051801413297653,
-0.038076650351285934,
0.08202878385782242,
0.01695396564900875,
0.006473503541201353,
0.03603567183017731,
-0.024761488661170006,
-0.01849660649895668,
-0.014519630931317806,
-0.008891685865819454,
0.005544830579310656,
-0.013087589293718338,
-0.0023406632244586945,
0.0650021955370903,
0.009974350221455097,
-0.005931692663580179,
0.05547073855996132,
-0.08531875163316727,
-0.04400252923369408,
-0.023655926808714867,
0.00704378355294466,
0.009498019702732563,
-0.015772951766848564,
-0.02791178971529007,
0.02702905423939228,
0.00154794380068779,
0.008273028768599033,
-0.04977026581764221,
-0.036221444606781006,
0.002389095025137067,
0.013823719695210457,
0.03123650699853897,
0.026590760797262192,
-0.05479344353079796,
0.09194420278072357,
0.02567165717482567,
-0.0072676558047533035,
-0.035722650587558746,
0.0046050893142819405,
-0.036454521119594574,
-0.037296686321496964,
0.01751234009861946,
-0.018519259989261627,
-0.03089888207614422,
-0.029306137934327126,
0.023754362016916275,
0.010511914268136024,
0.027322810143232346,
-0.0028618634678423405,
0.02948380820453167,
0.0005787971895188093,
0.01265503466129303,
0.001083715003915131,
0.09693541377782822,
0.02067643590271473,
-0.01624353416264057,
0.017192449420690536,
-0.009101126343011856,
0.04993775859475136,
-0.02483728900551796,
-0.05614662915468216,
0.036419861018657684,
-0.011620160192251205,
0.0071699232794344425,
-0.013460575602948666,
0.05276882275938988,
0.008066256530582905,
-0.043589040637016296,
0.012227417901158333,
-0.026327719911932945,
0.035769060254096985,
-0.013514154590666294,
-0.004666993394494057,
0.04421064630150795,
0.06016188859939575,
-0.016837522387504578,
-0.06542417407035828,
-0.002671718131750822,
0.01738576777279377,
0.044558510184288025,
-0.05349333956837654,
-0.02603178657591343,
0.012684163637459278,
0.015915442258119583,
0.025179577991366386,
-0.005968163255602121,
-0.02772383578121662,
0.0010004565119743347,
-0.04999719560146332,
-0.0010471149580553174,
0.022835751995444298,
0.04123334959149361,
0.008796676993370056,
0.08738695830106735,
0.0335378497838974,
0.06632810086011887,
0.042612817138433456,
0.021077586337924004,
-0.1115439236164093,
0.03361770138144493,
-0.04229149967432022,
-0.05749489739537239,
0.013651452958583832,
0.012881357222795486,
-0.04595369100570679,
-0.04455690458416939,
-0.01353400107473135,
-0.011929781176149845,
-0.016596738249063492,
-0.077907495200634,
0.019020624458789825,
-0.03235877677798271,
-0.03635143116116524,
0.005747845396399498,
0.02520664408802986,
0.0343111976981163,
-0.01041017659008503,
0.04393107071518898,
0.037650130689144135,
-0.00882430374622345,
-0.01242775283753872,
-0.021359505131840706,
-0.035984210669994354,
0.027120236307382584,
0.008839596062898636,
0.012468664906919003,
0.04818001762032509,
0.0014521230477839708,
0.026671377941966057,
-0.006742554716765881,
0.04063614457845688,
0.007785673253238201,
-0.00878563616424799,
-0.016472695395350456,
-0.06391507387161255,
-0.030758129432797432,
-0.011947372928261757,
0.04447213560342789,
0.012079265899956226,
-0.006521468050777912,
0.029648810625076294,
-0.0012968812370672822,
-0.01758095622062683,
0.03387941047549248,
0.048881951719522476,
-0.013441052287817001,
-0.01450930256396532,
-0.04428018629550934,
0.004667667672038078,
-0.02585526742041111,
-0.0002085880551021546,
-0.020684275776147842,
-0.0014784090453758836,
-0.0316421203315258,
-0.019597021862864494,
0.04222698137164116,
0.010143203660845757,
-0.009411729872226715,
0.005634602624922991,
-0.020851770415902138,
0.02431703358888626,
-0.0029849379789084196,
0.012381162494421005,
0.03420615568757057,
-0.0029078477527946234,
0.036926791071891785,
-0.03818546235561371,
-0.008466357365250587,
-0.07792909443378448,
-0.04712696000933647,
0.016095370054244995,
0.03197195380926132,
-0.02232067659497261,
0.01126289926469326,
-0.009720045141875744,
-0.038714293390512466,
0.021941618993878365,
-0.01864532008767128,
0.07682834565639496,
-0.021639177575707436,
0.013839105144143105,
0.009078673087060452,
-0.028618762269616127,
-0.04152010381221771,
-0.011221365071833134,
-0.05022791028022766,
0.016519930213689804,
-0.007536065299063921,
0.0039915707893669605,
-0.013263897970318794,
0.008184892125427723,
0.02483861893415451,
0.03005068190395832,
-0.015104164369404316,
-0.026187853887677193,
0.01090686209499836,
0.01295529119670391,
-0.03179130703210831,
-0.0755293071269989,
0.01316562108695507,
-0.004169867839664221,
-0.030337175354361534,
0.01227205153554678,
-0.02622225135564804,
-0.06946811079978943,
0.024154070764780045,
-0.013764430768787861,
0.010159745812416077,
0.039838653057813644,
-0.029496507719159126,
0.0005043986602686346,
0.04434376209974289,
-0.014527807012200356,
0.034477103501558304,
0.04651154950261116,
-0.031805410981178284,
0.0011966453166678548,
-0.019880767911672592,
0.009225437417626381,
0.008060697466135025,
0.0003832389775197953,
-0.025273418053984642,
0.00992740597575903,
-0.054541219025850296,
0.028343982994556427,
0.0090497937053442,
0.00021945421758573502,
-0.025154944509267807,
-0.02623123861849308,
0.008141392841935158,
0.029505522921681404,
0.02757124975323677,
0.014081827364861965,
0.0023927567526698112,
-0.008877253159880638,
-0.014458810910582542,
-0.019706152379512787,
-0.00569088663905859,
0.03182702139019966,
-0.008498466573655605,
0.020896591246128082,
0.018591390922665596,
-0.007119692396372557,
0.01936999149620533,
-0.019441360607743263,
0.01736089214682579,
-0.04176006093621254,
0.04768463969230652,
0.0069629051722586155,
0.0197867713868618,
0.005441518034785986,
-0.010321893729269505,
-0.03634483367204666,
-0.007276100572198629,
-0.029628118500113487,
0.010111408308148384,
-0.031761400401592255,
0.016261542215943336,
0.005279019940644503,
0.007143342401832342,
-0.030552901327610016,
-0.039761174470186234,
0.04477398842573166,
0.000415589427575469,
-0.021414758637547493,
0.005332624539732933,
0.015102542005479336,
-0.012842459604144096,
-0.02868078649044037,
-0.0038655761163681746,
0.05793311446905136,
-0.06081388145685196,
-0.00896734744310379,
0.03088245540857315,
0.0028854769188910723,
0.021467365324497223,
-0.005346083547919989,
-0.015128636732697487,
-0.03125661984086037,
-0.02109757997095585,
0.009915482252836227,
0.014957013539969921,
0.051339291036129,
-0.02491513080894947,
-0.03031061962246895,
-0.0061538731679320335,
0.006040578708052635,
0.0309843048453331,
-0.013525821268558502,
-0.01647352986037731,
0.04928966611623764,
0.029186248779296875,
-0.014514205045998096,
-0.011511283926665783,
0.049585357308387756,
0.020921410992741585,
0.02247467450797558,
-0.00994898285716772,
0.01762160286307335,
-0.018523914739489555,
-0.04645092412829399,
0.02489081397652626,
0.015128596685826778,
0.014110946096479893,
0.0026739640161395073,
0.0575319305062294,
-0.029456447809934616,
-0.016922153532505035,
0.027521591633558273,
0.02488281950354576,
0.04009034112095833,
-0.010502612218260765,
-0.04585247486829758,
0.02596733160316944,
0.007079781033098698,
-0.04039020091295242,
0.0027951993979513645,
-0.017692985013127327,
0.0128129618242383,
0.06523986160755157,
-0.033364810049533844,
0.06866177916526794,
0.01890147104859352,
0.024296309798955917,
0.02626020833849907,
0.01627708040177822,
-0.016418708488345146,
-0.0448252335190773,
0.003849521279335022,
-0.009924574755132198,
-0.03375401720404625,
0.004412681329995394,
0.048725102096796036,
0.031702637672424316,
-0.03603655844926834,
-0.013090969994664192,
0.028772179037332535,
0.003066916251555085,
0.026374367997050285,
-0.011075488291680813,
-0.0012650369899347425,
-0.007166748400777578,
0.014221536926925182,
0.054129209369421005,
0.0032743585761636496,
-0.05601975694298744,
0.045280057936906815,
0.0336441770195961,
0.015029488131403923,
-0.05888177454471588,
-0.015109744854271412,
-0.035535700619220734,
0.0002153016539523378,
0.02274913713335991,
0.004928255919367075,
0.02623109519481659,
0.011012746952474117,
0.0280319694429636,
-0.015409483574330807,
0.04066475108265877,
-0.017116835340857506,
-0.0346890427172184,
-0.029172392562031746,
-0.03661887347698212,
-0.03377654030919075,
0.059699803590774536,
0.03406333178281784,
-0.051863670349121094,
0.011203885078430176,
-0.014457753859460354,
0.02725967951118946,
0.029000476002693176,
0.036224979907274246,
-0.016814783215522766,
0.059048429131507874,
-0.036355502903461456,
-0.0023240873124450445,
-0.050347961485385895,
0.03850161284208298,
0.1175801232457161,
0.026750078424811363,
-0.004755136091262102,
-0.004531454294919968,
-0.008461122401058674,
-0.026544222608208656,
-0.02079814299941063,
-0.01872602105140686,
0.013573003001511097,
0.007225824519991875,
-0.010127685032784939,
-0.012000711634755135,
0.046150095760822296,
-0.019613055512309074,
-0.05068470165133476,
0.0627073124051094,
-0.026638632640242577,
-0.039749033749103546,
-0.021197468042373657,
0.0011134706437587738,
-0.004727676976472139,
0.02177688293159008,
-0.004854054655879736,
0.04850742220878601,
-0.011115523055195808,
0.0009988744277507067,
-0.027025403454899788,
-0.03564697131514549,
0.008168507367372513,
-0.006885246839374304,
-0.053404550999403,
0.0019512488506734371,
-0.021601101383566856,
-0.07109159231185913,
-0.03642438352108002,
0.05988941341638565,
0.018544863909482956,
-0.02295539900660515,
-0.0015736382920295,
0.031940966844558716,
0.016910186037421227,
0.013259907253086567,
0.010913451202213764,
-0.008519196882843971,
-0.05353696271777153,
-0.012535673566162586,
-0.02600925602018833,
0.05100277438759804,
0.035779424011707306,
0.027562929317355156,
0.047338880598545074,
-0.008666965179145336,
0.018055874854326248,
-0.06225946173071861,
0.00851116981357336,
-0.012476266361773014,
0.035297516733407974,
-0.012403354048728943,
0.016730325296521187,
0.004335657227784395,
0.023773757740855217,
0.02079441212117672,
-0.030708737671375275,
0.016310127452015877,
-0.004197541158646345,
0.00039534736424684525,
-0.0023995311930775642,
0.030080052092671394,
-0.04188847541809082,
-0.0020938999950885773,
-0.03166794404387474,
-0.025899959728121758,
-0.009211946278810501,
0.008673499338328838,
0.010343458503484726,
0.06572897732257843,
0.008579336106777191,
-0.02337857149541378,
0.0020357363391667604,
-0.02616198919713497,
-0.018128205090761185,
0.02955477312207222,
-0.0090671731159091,
-0.011356145143508911,
-0.043607719242572784,
-0.02695360966026783,
0.026089297607541084,
0.02810913883149624,
0.009730742312967777,
0.008769186213612556,
0.008134105242788792,
0.03698684647679329,
0.02667427808046341,
-0.01003778912127018,
-0.03476691246032715,
-0.0012074265396222472,
0.020345527678728104,
0.029970694333314896,
0.010396003723144531,
0.03192237764596939,
0.04931671917438507,
0.012824647128582,
-0.014681893400847912,
0.01583087630569935,
-0.024422796443104744,
-0.0008056652150116861,
0.037202659994363785,
-0.01752561889588833,
-0.005195437930524349,
0.013549390248954296,
-0.018181564286351204,
-0.052803345024585724,
-0.011374607682228088,
-0.023358995094895363,
-0.021405914798378944,
-0.007889344356954098,
0.01662570983171463,
-0.01649313047528267,
0.030222466215491295,
-0.007549874484539032,
0.02347438596189022,
-0.04808491840958595,
-0.0180047620087862,
-0.047159407287836075,
-0.03351176530122757,
-0.0027159121818840504,
-0.0037358878180384636,
-0.02387826517224312,
0.015538986772298813,
-0.0427914634346962,
-0.0004127471474930644,
0.0014700813917443156,
-0.029498111456632614,
-0.005278578959405422,
-0.038464803248643875,
0.023016391322016716,
-0.018015462905168533,
0.013038967736065388,
-0.01955416426062584,
-0.023533856496214867,
0.02162468247115612,
-0.012663830071687698,
-0.00668225297704339,
0.012344952672719955,
0.021483024582266808,
0.043038394302129745,
0.016246672719717026,
-0.03945079445838928,
-0.029765160754323006,
0.058781154453754425,
-0.019939567893743515,
0.007957770489156246,
-0.00012707742280326784,
-0.048548173159360886,
-0.06191648170351982,
-0.013463698327541351,
0.016157051548361778,
-0.006801262963563204,
0.02064327336847782,
0.004082410130649805,
0.010173821821808815,
0.002588823903352022,
0.002144020050764084,
0.03452044352889061,
0.0034769768826663494,
-0.02365899458527565,
0.03812650963664055,
-0.010274611413478851,
0.020495589822530746,
0.06491445004940033,
-0.01436048373579979,
0.029001299291849136,
0.010711630806326866,
-0.0034903958439826965,
-0.10433350503444672,
0.016218511387705803,
0.004492351319640875,
0.010380811057984829,
0.01736173778772354,
-0.04949196055531502,
-0.03241240605711937,
0.02447725273668766,
-0.06933656334877014,
0.006333217490464449,
-0.05708397552371025,
-0.01480838656425476,
0.018797753378748894,
0.023266024887561798,
0.016615282744169235,
0.025432437658309937,
0.016920551657676697,
0.04640001058578491,
0.0015741917304694653,
0.0301388930529356,
0.021157465875148773,
-0.019821172580122948,
-0.001843221834860742,
0.0367269292473793,
-0.0024960990995168686,
0.024164577946066856,
0.042343370616436005,
-0.014923317357897758,
0.0037697264924645424,
0.0159192755818367,
0.00468970974907279,
0.047301508486270905,
-0.005943621508777142,
0.037292271852493286,
-0.013026468455791473,
0.02156427875161171,
-0.018728919327259064,
-0.0019133409950882196,
-0.008038242347538471,
0.0399080365896225,
0.003942067734897137,
0.03218379616737366,
-0.030714645981788635,
-0.0072833769954741,
0.04437761753797531,
-0.05491682514548302,
-0.0002725011436268687,
0.026292022317647934,
-0.02816017158329487,
0.0021482447627931833,
0.01827229931950569,
-0.010653064586222172,
-0.027894379571080208,
-0.008018722757697105,
-0.024743737652897835,
-0.0016657302621752024,
0.012231392785906792,
0.03707804158329964,
-0.012346900999546051,
-0.0246579647064209,
0.027877094224095345,
-0.009774117730557919,
-0.0006774814100936055,
0.028118543326854706,
-0.009060213342308998,
0.00898390170186758,
-0.05811354145407677,
-0.005372336599975824,
0.023798596113920212,
-0.027388909831643105,
-0.0013892403803765774,
-0.04156694933772087,
-0.00968664325773716,
0.028642408549785614,
0.053023580461740494,
0.001843571662902832,
0.001724223606288433,
-0.04154222086071968,
-0.023070568218827248,
-0.10209829360246658,
0.046514347195625305,
0.03012753091752529,
-0.039058391004800797,
-0.06974489241838455,
0.008374200202524662,
-0.011437193490564823,
0.024806438013911247,
0.037346046417951584,
-0.018773946911096573,
-0.010871835984289646,
0.03457186743617058,
-0.007471064105629921,
-0.016165055334568024,
-0.01116978283971548,
0.00807558186352253,
-0.00015534466365352273,
-0.014078567735850811,
0.011223790235817432,
0.003046966390684247,
-0.01142386719584465,
-0.005193827208131552,
0.019841982051730156,
-0.013616817072033882,
0.032633066177368164,
-0.00026796504971571267,
-0.030697178095579147,
0.006960118189454079,
0.01782347448170185,
-0.035652678459882736,
0.04998383671045303,
-0.004904994275420904,
0.018632737919688225,
0.025164389982819557,
-0.02518322505056858,
-0.04748356714844704,
0.039913587272167206,
-0.04283566400408745,
0.02375263161957264,
-0.019760258495807648,
-0.03882038593292236,
0.03611037880182266,
-0.07417923957109451,
-0.007540680933743715,
0.03615434095263481,
-0.06371082365512848,
0.007966434583067894,
0.031449709087610245,
0.037897009402513504,
-0.011927569285035133,
-0.036468639969825745,
0.04184314236044884,
0.05363113060593605,
0.0026293296832591295,
0.01393634732812643,
0.009210256859660149,
0.05155430734157562,
-0.030523769557476044,
-0.009089197032153606,
0.0646357610821724,
0.007000175770372152,
0.034801989793777466,
-0.007406344637274742,
0.014561906456947327,
-0.022662531584501266,
-0.014167437329888344,
-0.03388313204050064,
-0.02395247109234333,
-0.0018626860110089183,
0.034877289086580276,
-0.025865407660603523,
0.05952532961964607,
-0.02433970756828785,
-0.003098580287769437,
0.05326618626713753,
0.012313863262534142,
-0.007307880092412233,
-0.009034555405378342,
-0.009461717680096626,
0.008942740969359875,
0.009386522695422173,
-0.024318501353263855,
-0.006284813396632671,
-0.022745542228221893,
0.019725611433386803,
-0.0063406312838196754,
0.02931748330593109,
0.02359588071703911,
-0.01267085038125515,
-0.014721665531396866,
-0.03796415403485298,
-0.054087113589048386,
-0.016487088054418564,
0.06001181900501251,
0.013811130076646805,
0.0025959964841604233,
-0.03797990456223488,
-0.00410033343359828,
0.00166445376817137,
0.03932373225688934,
-0.07012147456407547,
-0.02246840111911297,
-0.005880144890397787,
0.02474808506667614,
0.025019267573952675,
-0.029917750507593155
] |
<p>Here is an argument that I have with regard to entropic forces and how it can be linked to the other forces in nature. </p>
<ul>
<li><p>Gravitational: This is debated: whether gravity is entropic or not. I am going for the paper that says gravity is entropic. <a href="http://physics.stackexchange.com/questions/4289/is-gravity-an-entropic-force-after-all">Is Gravity an entropic force after all?</a> . Here is my argument for it. Do let me know if it makes any sense at all. If we launch a projectile, then it follows a parabolic path provided the angle of projection is not 90 or 0. According to the entropic theory, the projectile has a random trajectory. However, if the trajectories are averaged out, then the path obtained is parabolic. Therefore, gravity is entropic. (This argument is rather hand-wavy in nature, I agree. Are there <strong>any alternate arguments that you can provide?</strong>)</p></li>
<li><p>Coulombic: Both gravitational and coulombic laws have similar structures and assumptions, the only difference being that mass has no sign whilst charges do. But that is the tendency of matter. Both are central forces, so if we draw parallels, then shouldn't <strong>Coulombic forces also be entropic?</strong> (Again, hand-wavy)</p></li>
</ul>
<p>As for the other forces, I have some sort of intuition but I am not sure if it makes any sense mathematically. Like nuclear forces, beyond a certain range, they are repulsive in nature. But since it is a much stronger force than gravity, and if gravity is entropic, (and gases collide randomly) then in order for a gaseous system to 'defy' gravity, won't the <strong>nuclear force also have to be entropic ?</strong> And could the repulsion be because if the particles combine, then the <strong>entropy of the system decreases?</strong> I am not sure.</p>
<hr>
<p>The arguments are quite hand-wavy, but I couldn't think of other ways to imagine it. <strong>Are there any mathematical proofs for the same?</strong> </p> | 1,429 | [
-0.024086127057671547,
-0.003979401662945747,
0.023710673674941063,
-0.006382406689226627,
0.005838070064783096,
0.02092653140425682,
0.00026337135932408273,
-0.014278463087975979,
0.0027005276642739773,
-0.02558518573641777,
0.04636118933558464,
0.02841668576002121,
0.045629143714904785,
0.051132142543792725,
0.009582377970218658,
-0.022128107026219368,
-0.006041554734110832,
-0.018840286880731583,
0.003684265771880746,
-0.04477303475141525,
-0.012073538266122341,
0.026315271854400635,
0.0007772152312099934,
0.020239543169736862,
-0.026813287287950516,
0.0703277438879013,
0.03008766658604145,
-0.048545803874731064,
-0.005078897345811129,
0.07929054647684097,
-0.004985612817108631,
-0.03646523132920265,
0.02462628483772278,
0.02520928904414177,
0.030694270506501198,
-0.007720636203885078,
-0.026230856776237488,
-0.020585007965564728,
-0.021001629531383514,
0.00787914264947176,
-0.05584324896335602,
-0.029177114367485046,
-0.012031258083879948,
0.01482029166072607,
-0.0256631039083004,
0.03177957981824875,
0.0156524907797575,
0.02087310329079628,
0.0810013934969902,
-0.04148377850651741,
0.02613960951566696,
0.024680985137820244,
0.0012876659166067839,
0.008093830198049545,
-0.005722135305404663,
-0.044754158705472946,
0.06670746952295303,
0.08557696640491486,
0.006717782001942396,
-0.05154329165816307,
-0.004464063327759504,
-0.0015838169492781162,
-0.03424811363220215,
-0.010158471763134003,
0.01116712111979723,
0.05055758357048035,
0.0177012849599123,
-0.018950417637825012,
0.04435104876756668,
0.02366178296506405,
0.0007462932844646275,
-0.0239336509257555,
0.008243536576628685,
-0.01775304414331913,
0.004148376174271107,
0.009022059850394726,
0.009886990301311016,
0.00018168467795476317,
0.0191950760781765,
0.058047253638505936,
-0.026446739211678505,
-0.001177215832285583,
0.01269536092877388,
0.05404561385512352,
0.009292863309383392,
-0.00633349409326911,
0.0816587433218956,
-0.0551002100110054,
-0.009157833643257618,
0.048412881791591644,
-0.012961695902049541,
-0.007039644289761782,
0.025996118783950806,
0.020360084250569344,
-0.040705252438783646,
0.016399305313825607,
-0.006640910636633635,
0.014582081697881222,
-0.005494121462106705,
0.013839155435562134,
-0.02221779339015484,
-0.030171120539307594,
0.02756502851843834,
0.10541179031133652,
0.011337829753756523,
-0.00449293153360486,
-0.02675655670464039,
0.004259285517036915,
-0.012823930010199547,
-0.004592096898704767,
-0.018764538690447807,
0.009850818663835526,
0.005568415857851505,
-0.02127283252775669,
-0.020198578014969826,
-0.009650361724197865,
0.03442481532692909,
-0.01906415820121765,
0.06453370302915573,
0.06867966055870056,
0.03863443434238434,
-0.014595134183764458,
0.0034692438784986734,
-0.052638985216617584,
-0.05170659348368645,
-0.027536682784557343,
0.06672149151563644,
-0.001584240817464888,
0.024604598060250282,
0.021387098357081413,
0.013346465304493904,
-0.0009040614240802824,
-0.030335253104567528,
0.006008991971611977,
0.05171825364232063,
-0.005618157796561718,
-0.11532904207706451,
-0.05892827361822128,
0.04416634514927864,
0.0024405086878687143,
-0.005366801284253597,
-0.04313739761710167,
0.01330795232206583,
-0.0023352825082838535,
0.06166393309831619,
0.0012851202627643943,
-0.002259921282529831,
-0.01658814772963524,
0.06230771914124489,
0.0067429556511342525,
0.001512687187641859,
0.0194094218313694,
0.012133166193962097,
-0.016724472865462303,
-0.05101810768246651,
-0.09677175432443619,
0.04544315114617348,
0.029934344813227654,
0.010367019101977348,
0.008571301586925983,
0.027531927451491356,
-0.05453815311193466,
0.016363242641091347,
-0.03504668176174164,
0.008321736007928848,
-0.03892066702246666,
0.05216129124164581,
0.023383362218737602,
-0.0027084010653197765,
0.035444218665361404,
-0.0018219619523733854,
0.021592900156974792,
0.0013329536886885762,
-0.004505673889070749,
0.03736449033021927,
-0.06438640505075455,
-0.024812856689095497,
-0.02150336466729641,
-0.036110274493694305,
-0.0038083787076175213,
-0.004080981016159058,
-0.043697815388441086,
-0.027501007542014122,
0.00003670782098197378,
-0.013155885972082615,
-0.01723477430641651,
0.03850077465176582,
-0.014622841961681843,
-0.0005437685758806765,
-0.02267165668308735,
-0.019928917288780212,
-0.07476679235696793,
0.03468071296811104,
-0.017086589708924294,
-0.022593338042497635,
0.045298438519239426,
0.01545540802180767,
0.011014379560947418,
-0.02087654545903206,
-0.012937686406075954,
-0.023982837796211243,
0.041518501937389374,
-0.017180338501930237,
0.01123814657330513,
0.020183973014354706,
0.05211567133665085,
0.0033573401160538197,
0.0002183835895266384,
0.016817020252346992,
0.018369553610682487,
-0.057268060743808746,
-0.004975426476448774,
-0.027260547503829002,
-0.0036433779168874025,
0.00802821945399046,
-0.008199105970561504,
0.02651144750416279,
0.03294449299573898,
-0.0038155936636030674,
-0.00025062059285119176,
-0.034854065626859665,
0.04690615087747574,
0.005864486563950777,
0.01707007735967636,
-0.030107254162430763,
0.07125963270664215,
0.014412589371204376,
0.015292203985154629,
-0.01601550355553627,
-0.0160250011831522,
-0.054838262498378754,
-0.014883525669574738,
0.014221242628991604,
0.06508959084749222,
-0.01144850067794323,
0.024262642487883568,
0.01910306140780449,
0.018530191853642464,
-0.004879271145910025,
-0.009517854079604149,
-0.01333070918917656,
-0.06040508672595024,
0.03432990610599518,
-0.0119788171723485,
0.029931165277957916,
-0.0011630154913291335,
0.01808730699121952,
0.00285232812166214,
0.015383154153823853,
-0.002967200940474868,
-0.010054996237158775,
0.003067457117140293,
0.026280498132109642,
0.007969072088599205,
0.010430398397147655,
-0.027419056743383408,
0.06282909214496613,
0.030012261122465134,
0.03911738097667694,
0.014613833278417587,
-0.007452727761119604,
-0.01877923309803009,
-0.05929705128073692,
-0.008468085899949074,
-0.022614963352680206,
0.018224939703941345,
0.004185846541076899,
-0.018148116767406464,
0.005506463814526796,
-0.07696026563644409,
-0.021940231323242188,
0.03155028820037842,
0.01387588120996952,
-0.03405623883008957,
0.0048307874239981174,
-0.004803562071174383,
-0.0012857234105467796,
0.004972880706191063,
-0.011516306549310684,
0.002578467596322298,
0.016235923394560814,
-0.0072274114936590195,
-0.023997126147150993,
0.021662931889295578,
-0.04271097853779793,
0.009029466658830643,
-0.03779616579413414,
-0.01364368200302124,
0.042588140815496445,
0.0016477841418236494,
0.02016441337764263,
0.010973906144499779,
-0.03559504821896553,
-0.04263083264231682,
0.008296350948512554,
-0.023173777386546135,
0.022863369435071945,
-0.07452905923128128,
-0.017302853986620903,
0.05871196463704109,
-0.02672971971333027,
-0.061073556542396545,
0.008267877623438835,
-0.038355469703674316,
-0.07291337847709656,
0.007389674428850412,
-0.0013120424700900912,
-0.013542532920837402,
0.02421167492866516,
0.0006397012621164322,
0.0342656746506691,
-0.0016284642042592168,
-0.04720389097929001,
-0.07235798239707947,
-0.017517168074846268,
0.049792736768722534,
0.004003274254500866,
0.05646691098809242,
-0.010017136111855507,
-0.04254462942481041,
0.050364986062049866,
0.045561160892248154,
0.0052190818823874,
-0.020322147756814957,
-0.017700232565402985,
-0.02127203159034252,
-0.001609571510925889,
0.011399971321225166,
0.010836356319487095,
0.020174384117126465,
0.02380870282649994,
0.014072326943278313,
0.047387197613716125,
-0.020055806264281273,
-0.03360399231314659,
-0.015137542970478535,
0.028640659525990486,
0.009151765145361423,
-0.026862984523177147,
0.06422239542007446,
0.04234291613101959,
-0.010176761075854301,
0.019529087468981743,
0.004155023023486137,
0.031228845939040184,
-0.0036632693372666836,
-0.06322918087244034,
0.04518870636820793,
0.007691569160670042,
0.009818943217396736,
-0.045178163796663284,
0.030687818303704262,
-0.014949945732951164,
-0.03436211124062538,
0.020920829847455025,
0.03028201125562191,
0.06038054823875427,
0.015022072941064835,
0.010894312523305416,
0.021567855030298233,
0.07172033935785294,
-0.004136075731366873,
-0.03392918407917023,
-0.03352149948477745,
0.0011093763168901205,
0.021406935527920723,
-0.023395057767629623,
0.02762233465909958,
0.028263894841074944,
0.026242926716804504,
0.010273199528455734,
-0.003711463650688529,
-0.03634344041347504,
-0.007560128811746836,
-0.07534246891736984,
0.010852915234863758,
-0.006711399182677269,
0.05039656162261963,
0.005275579635053873,
0.07103487104177475,
0.026644332334399223,
0.005617314018309116,
-0.009854624047875404,
0.0152725949883461,
-0.10881521552801132,
0.05056938901543617,
-0.05791138857603073,
-0.01623125746846199,
-0.009290057234466076,
-0.0361187718808651,
-0.04322517290711403,
-0.027146676555275917,
-0.022541014477610588,
-0.030103465542197227,
0.01535042468458414,
-0.04405087232589722,
-0.0011161398142576218,
-0.051716819405555725,
-0.06043547764420509,
0.014019234105944633,
0.042293768376111984,
0.048740800470113754,
-0.031980887055397034,
0.03180066868662834,
0.023654218763113022,
-0.03228205442428589,
-0.0002319453051313758,
0.000768458703532815,
0.04015238955616951,
0.021813152357935905,
0.06414269655942917,
-0.02622337080538273,
-0.013652841560542583,
0.028301259502768517,
-0.038281891494989395,
0.006259979214519262,
0.015969958156347275,
0.01792176254093647,
-0.015458520501852036,
-0.015473106876015663,
-0.03189989924430847,
-0.03302035853266716,
0.011583724990487099,
0.03405161201953888,
-0.005604535806924105,
0.020330708473920822,
-0.004000524990260601,
0.013558819890022278,
0.014582891948521137,
0.044285450130701065,
0.038737934082746506,
0.003626707009971142,
-0.036205217242240906,
-0.008059444837272167,
-0.05200866237282753,
-0.014239397831261158,
-0.002810956910252571,
0.023655135184526443,
-0.0014378040796145797,
-0.025135431438684464,
0.002652652096003294,
-0.020499709993600845,
0.020231420174241066,
-0.02933523803949356,
-0.0200077872723341,
-0.036267995834350586,
0.021293126046657562,
-0.0504857562482357,
0.024427996948361397,
0.010379619896411896,
0.004905081354081631,
-0.006838622968643904,
0.02971774712204933,
0.003980214707553387,
-0.053508512675762177,
0.0007547064451500773,
0.061866432428359985,
0.024831833317875862,
-0.025384919717907906,
0.011068726889789104,
-0.051815006881952286,
-0.0343233123421669,
0.05701661482453346,
0.001257497351616621,
0.009650642983615398,
-0.012158708646893501,
0.02542947605252266,
0.032335080206394196,
-0.08014103770256042,
-0.021902432665228844,
0.012092567048966885,
-0.0044162520207464695,
-0.024824194610118866,
0.001788998139090836,
-0.012021084316074848,
0.0007701404392719269,
0.0025583908427506685,
0.031543321907520294,
0.03930480405688286,
-0.02254393696784973,
0.02336696907877922,
-0.003953584004193544,
-0.028683630749583244,
0.002751813502982259,
-0.12781059741973877,
0.025066573172807693,
-0.030429836362600327,
-0.03015500120818615,
0.01720033399760723,
-0.04908487945795059,
-0.019574178382754326,
0.03015805594623089,
-0.01951100490987301,
0.005878165829926729,
0.023604553192853928,
-0.041545648127794266,
0.06613026559352875,
0.05076988786458969,
-0.008756614290177822,
0.01370255183428526,
0.056452780961990356,
-0.030189676210284233,
0.004645724780857563,
-0.01990051008760929,
0.038966186344623566,
-0.046398237347602844,
-0.016499565914273262,
-0.06291931867599487,
0.014591439627110958,
-0.04107966646552086,
0.020422670990228653,
0.02706647478044033,
-0.013193318620324135,
0.01867731101810932,
-0.05488664656877518,
-0.017710771411657333,
0.004833327606320381,
-0.012562645599246025,
0.021766474470496178,
-0.0042155152186751366,
0.025774912908673286,
-0.0023457007482647896,
-0.006520019378513098,
0.021247832104563713,
0.015703892335295677,
0.006795512977987528,
0.013849597424268723,
-0.023492291569709778,
-0.042848795652389526,
-0.031485144048929214,
0.004162497352808714,
0.0012199366465210915,
-0.06493283808231354,
0.067207932472229,
-0.022722167894244194,
-0.011013521812856197,
0.03714940696954727,
-0.036390259861946106,
-0.05071570351719856,
0.028003208339214325,
-0.03413376584649086,
0.019544722512364388,
-0.017214464023709297,
0.014168788678944111,
-0.01663627289235592,
-0.01847490295767784,
-0.0437626838684082,
-0.0005947392201051116,
0.0074966587126255035,
-0.0025149888824671507,
-0.04503199830651283,
-0.028608165681362152,
-0.0033686284441500902,
-0.060119036585092545,
-0.013319974765181541,
-0.005615353584289551,
0.029563428834080696,
-0.02167266421020031,
0.009020653553307056,
0.0378718264400959,
-0.006999733857810497,
0.03759780898690224,
-0.03459450602531433,
-0.03334705904126167,
0.015244805254042149,
0.01276940293610096,
0.026549063622951508,
-0.012785707600414753,
0.019638527184724808,
-0.005532529205083847,
-0.03930011764168739,
0.034404635429382324,
-0.0024597877636551857,
0.009574607014656067,
-0.02329125627875328,
-0.007670837454497814,
0.0456901490688324,
-0.01639614813029766,
-0.026401933282613754,
-0.0068259472027421,
0.020302576944231987,
0.001623062533326447,
0.04234851896762848,
-0.01919672079384327,
0.034180328249931335,
-0.0035110164899379015,
-0.07100657373666763,
0.04940495267510414,
-0.0029058882500976324,
-0.010656100697815418,
0.02592805027961731,
0.04157989099621773,
0.02318619005382061,
-0.030694875866174698,
0.011295059695839882,
-0.013459829613566399,
0.02933899685740471,
-0.022969258949160576,
0.010880193673074245,
0.00732302013784647,
0.003290698165073991,
-0.018336428329348564,
-0.027485104277729988,
-0.04244731366634369,
0.004562053829431534,
0.061521016061306,
-0.0014512250199913979,
0.016511276364326477,
0.024455036967992783,
-0.011155153624713421,
-0.00627044728025794,
-0.03105791099369526,
0.022427678108215332,
0.015437222085893154,
0.0012899287976324558,
0.03329116851091385,
-0.01827133446931839,
-0.0004403844941407442,
0.035734061151742935,
0.049748603254556656,
-0.02832719497382641,
0.007447773590683937,
0.00047053192974999547,
0.009464081376791,
0.006695392541587353,
-0.01704602688550949,
-0.046016398817300797,
0.045711055397987366,
-0.0522131584584713,
0.044662296772003174,
0.02039390616118908,
-0.014822075143456459,
0.00951418187469244,
0.015127777121961117,
0.0024753836914896965,
-0.0583433136343956,
-0.03434166684746742,
-0.02899318002164364,
0.013931580819189548,
-0.0013664368307217956,
0.0008410504087805748,
-0.011372792534530163,
0.0031039142049849033,
0.04158201441168785,
0.002014974830672145,
-0.026086745783686638,
0.005062614101916552,
-0.06517469137907028,
0.024030856788158417,
-0.022228294983506203,
-0.03924012929201126,
0.02538866549730301,
-0.022755637764930725,
-0.03746972978115082,
0.030564656481146812,
-0.004108673892915249,
0.04389890655875206,
0.054661162197589874,
0.001906480174511671,
-0.0003449044597800821,
0.0829252153635025,
-0.004212707281112671,
-0.026197616010904312,
-0.06014297902584076,
0.0021155904978513718,
0.14134088158607483,
-0.0013827065704390407,
0.021780190989375114,
-0.004752228502184153,
-0.011659076437354088,
0.023343777284026146,
0.0154546108096838,
0.00327333714812994,
0.006040884647518396,
0.010054996237158775,
0.01388006005436182,
0.01806916855275631,
0.03039710968732834,
0.014338753186166286,
-0.04597010836005211,
0.03991307318210602,
-0.04852398484945297,
0.00737463403493166,
-0.027193734422326088,
0.00642126239836216,
0.008702741004526615,
0.037960898131132126,
-0.051102567464113235,
0.02666381374001503,
-0.030146123841404915,
0.013342350721359253,
-0.0365099273622036,
-0.04853607714176178,
0.007437195163220167,
0.009484774433076382,
-0.030275054275989532,
0.007407574448734522,
0.010030255652964115,
-0.052490703761577606,
0.0010299076093360782,
0.003707918804138899,
0.033624790608882904,
-0.027664465829730034,
0.0071438816376030445,
-0.0006773920613341033,
0.004023157991468906,
0.03479491546750069,
0.0008080089464783669,
-0.0023727258667349815,
-0.05198144167661667,
-0.00923948734998703,
-0.014068875461816788,
0.04133349657058716,
-0.030742844566702843,
0.008627180010080338,
0.009847890585660934,
0.00039960979484021664,
0.052230387926101685,
-0.02330394834280014,
0.009941150434315205,
-0.04062101989984512,
0.03603687137365341,
-0.002907278947532177,
-0.05290741100907326,
-0.022445382550358772,
0.02083001099526882,
-0.018413173034787178,
0.005786221940070391,
-0.03431601822376251,
0.022537020966410637,
-0.015704341232776642,
-0.005627327132970095,
0.023605166003108025,
-0.005838973913341761,
0.0047946833074092865,
-0.01662493124604225,
-0.0070358687080442905,
-0.07048550248146057,
-0.024127095937728882,
-0.01570555940270424,
0.026077311486005783,
-0.0031939842738211155,
0.0403229258954525,
0.014263918623328209,
-0.05458441004157066,
-0.04757804796099663,
0.061184000223875046,
-0.029061945155262947,
0.00035672291414812207,
-0.011890474706888199,
0.006027221214026213,
0.03289420157670975,
0.05465921759605408,
0.03035399504005909,
0.0030066838953644037,
0.0462920255959034,
0.0159054696559906,
0.006465081125497818,
-0.01647183485329151,
-0.014630378223955631,
0.021516017615795135,
-0.027484536170959473,
-0.028058895841240883,
0.027913110330700874,
-0.005126325413584709,
0.02807997725903988,
0.03872901573777199,
0.0001429172552889213,
0.010435765609145164,
0.004118235316127539,
0.006962848827242851,
0.03464752063155174,
0.001227853586897254,
-0.033194415271282196,
0.024632519111037254,
0.005897441878914833,
-0.02522984892129898,
-0.0028349831700325012,
-0.013384336605668068,
-0.0055218772031366825,
-0.012430962175130844,
0.039031416177749634,
-0.0004918602644465864,
-0.004878823179751635,
0.00041393673745915294,
0.049083366990089417,
-0.047820355743169785,
-0.002127662068232894,
-0.04695594683289528,
-0.005857276264578104,
0.007449786178767681,
0.005727595649659634,
-0.007560610771179199,
0.0351361483335495,
-0.02095457725226879,
-0.031175309792160988,
0.04455193132162094,
0.028604065999388695,
0.007075594272464514,
-0.001658982364460826,
0.045237038284540176,
-0.012236615642905235,
0.026097675785422325,
-0.0025993925519287586,
-0.0024400397669523954,
0.04365386813879013,
-0.020531687885522842,
-0.054450154304504395,
0.004779944196343422,
-0.03557400405406952,
0.009535379707813263,
0.04987664893269539,
-0.024823777377605438,
-0.0031894068233668804,
0.049172937870025635,
0.004708530846983194,
0.001868654158897698,
0.003279745578765869,
-0.04606019705533981,
0.013026800937950611,
-0.02272483892738819,
0.009993174113333225,
-0.020375732332468033,
0.0366036631166935,
0.035454560071229935,
0.02199365943670273,
0.014814093708992004,
0.012138004414737225,
0.032553717494010925,
-0.029893608763813972,
0.0010239146649837494,
0.01872703619301319,
-0.001564995152875781,
0.003655452514067292,
0.023279644548892975,
-0.018872970715165138,
0.062088269740343094,
0.029811332002282143,
0.02969205752015114,
-0.09501629322767258,
0.010625016875565052,
0.009583079256117344,
0.0030369337182492018,
0.015516187995672226,
-0.03146000951528549,
-0.0015446486650034785,
0.0004972090246155858,
-0.047634307295084,
0.032375581562519073,
-0.010392666794359684,
-0.018661310896277428,
0.005068886559456587,
0.018829287961125374,
-0.03977621719241142,
0.04703819379210472,
0.004001361317932606,
0.05932796001434326,
0.023030772805213928,
0.04809188097715378,
-0.02765537239611149,
-0.03894028067588806,
-0.037624556571245193,
0.011715119704604149,
0.008056307211518288,
0.03573639318346977,
0.08511489629745483,
-0.020240195095539093,
0.018150702118873596,
0.026917839422822,
-0.005387885496020317,
-0.018629424273967743,
-0.03807171806693077,
0.0036829065065830946,
0.0412479043006897,
0.040018558502197266,
-0.004396355245262384,
0.011634944938123226,
0.02021530456840992,
0.016212888062000275,
0.019914329051971436,
0.020532449707388878,
-0.01642117276787758,
-0.0024278704077005386,
0.025740398094058037,
-0.021646156907081604,
-0.025183238089084625,
0.012836586683988571,
-0.007176772225648165,
-0.004571117926388979,
-0.015951819717884064,
-0.003141846042126417,
0.004006850998848677,
0.004984303377568722,
-0.007111434359103441,
-0.044918809086084366,
0.015926919877529144,
0.016059063374996185,
0.011467540636658669,
-0.03918866068124771,
0.03952593728899956,
-0.00783590693026781,
-0.0017001249361783266,
-0.013270929455757141,
-0.020544620230793953,
0.01683717593550682,
-0.002761048497632146,
-0.0034393370151519775,
-0.002446345519274473,
0.0585564523935318,
-0.021594708785414696,
-0.03687811642885208,
-0.05440698564052582,
0.064691461622715,
0.03347482532262802,
0.03597795218229294,
-0.03796980902552605,
-0.0303825493901968,
0.0014764730585739017,
-0.07636727392673492,
-0.030635574832558632,
0.005880115088075399,
0.010756622068583965,
-0.06657353788614273,
-0.03851412609219551,
0.0270689707249403,
0.030649801716208458,
0.03187105804681778,
-0.006225387565791607,
-0.0058452533558011055,
0.042794037610292435,
0.006726054009050131,
0.03108644112944603,
-0.03983122482895851,
0.009019073098897934,
-0.008139478042721748,
-0.026943517848849297,
0.02625720389187336,
0.007260414306074381,
-0.032124120742082596,
0.012534738518297672,
0.043361883610486984,
-0.06048981100320816,
-0.00314275617711246,
-0.004769061226397753,
-0.04168795794248581,
0.06631312519311905,
-0.013437101617455482,
-0.04332829266786575,
0.041780002415180206,
-0.024035941809415817,
0.006802551914006472,
-0.023258564993739128,
-0.00671033700928092,
-0.022151965647935867,
0.03442107141017914,
-0.00035672273952513933,
-0.03936060518026352,
-0.023294303566217422,
-0.0010308627970516682,
0.013535621576011181,
-0.05158437788486481,
-0.007044222205877304,
0.03473253175616264,
-0.03968747332692146,
-0.009841987863183022,
0.06896601617336273,
-0.01684240996837616,
0.06486444920301437,
0.0016216369112953544,
0.022826939821243286,
0.004524125251919031,
0.0027070953510701656,
0.0034146993421018124,
0.043981052935123444,
0.06618256866931915,
0.018118511885404587,
-0.024252595379948616,
0.03351374343037605,
-0.009467695839703083,
0.03182946518063545,
0.03927060216665268,
-0.002854794031009078,
-0.039921119809150696,
-0.010243329219520092,
0.03219987452030182,
-0.007385197561234236,
0.017137279734015465,
0.018750598654150963,
-0.0072882287204265594,
0.09864326566457748,
-0.03344019129872322,
-0.004109358415007591,
-0.019894663244485855,
-0.010474090464413166,
0.008257458917796612,
0.02828669548034668,
0.0027117307763546705,
0.0356312170624733,
0.017302753403782845,
-0.02606908231973648,
-0.026628490537405014,
0.0047073764726519585,
0.011112828738987446,
-0.02475561387836933,
0.026195542886853218,
0.021872635930776596,
0.039942000061273575,
-0.03549406677484512,
-0.013750789687037468,
-0.03472095727920532,
-0.03971490636467934,
0.025276971980929375,
0.012975389137864113,
0.005977426189929247,
0.0034918973688036203,
0.009379813447594643,
0.004004713613539934,
0.06324458122253418,
-0.03508607670664787,
-0.004651079420000315,
-0.04027334600687027,
0.01630173996090889,
-0.008259515278041363,
-0.029268605634570122
] |
<p>Do the interiors of black-holes create gravitational waves and if so do these waves cause the radius of the event horizon to fluctuate as the waves pass the horizon ?</p> | 1,430 | [
-0.01775328256189823,
-0.018170377239584923,
0.020100224763154984,
-0.019564146175980568,
0.05363646522164345,
0.03968492150306702,
-0.075667604804039,
-0.07709170877933502,
-0.006082166451960802,
-0.023956941440701485,
0.007609021849930286,
0.022714778780937195,
0.04546813294291496,
0.007995754480361938,
-0.011700103990733624,
-0.009015459567308426,
-0.002793195890262723,
-0.003226466244086623,
-0.009009083732962608,
-0.05124492943286896,
-0.025360137224197388,
0.05144718661904335,
0.024263329803943634,
0.009078888222575188,
-0.04832839220762253,
0.024158218875527382,
0.03612423315644264,
0.00021427006868179888,
0.021087661385536194,
0.02738901786506176,
0.01496583316475153,
-0.007945436052978039,
-0.002916014287620783,
0.06792675703763962,
0.023478757590055466,
-0.039314236491918564,
-0.04807247221469879,
-0.011399413459002972,
-0.026405174285173416,
0.002359444508329034,
-0.025022955611348152,
-0.04239922761917114,
-0.0057276226580142975,
0.030708778649568558,
-0.006513216532766819,
-0.025839079171419144,
0.0164541807025671,
-0.018380334600806236,
0.028135664761066437,
-0.05848384276032448,
0.05537768453359604,
-0.003214535303413868,
0.02815130352973938,
0.027021532878279686,
-0.010679006576538086,
0.023245403543114662,
0.08068223297595978,
0.04887460172176361,
-0.027383500710129738,
-0.050933416932821274,
0.002690398832783103,
0.02097640559077263,
-0.027825545519590378,
-0.005992545746266842,
-0.02328363060951233,
0.04369959980249405,
-0.008281217887997627,
-0.019388223066926003,
0.024400262162089348,
-0.02163054794073105,
-0.00420181592926383,
-0.0000726773650967516,
-0.00917334109544754,
-0.0047682588919997215,
0.023744530975818634,
-0.021484509110450745,
0.0022641648538410664,
-0.0008066394948400557,
0.008809748105704784,
0.05725724250078201,
0.010809022933244705,
-0.02276015467941761,
0.05419493466615677,
-0.01116944570094347,
0.028186216950416565,
0.034301482141017914,
0.0801134929060936,
-0.01095384918153286,
-0.002290075644850731,
0.0127164451405406,
-0.027930717915296555,
-0.010850519873201847,
0.020662572234869003,
-0.029169749468564987,
-0.010480600409209728,
0.031241556629538536,
0.004426692146807909,
0.08637901395559311,
-0.004817078355699778,
-0.03742796182632446,
0.019060224294662476,
0.004063311964273453,
-0.004593708552420139,
0.07000875473022461,
0.02001735381782055,
-0.053459540009498596,
-0.055290792137384415,
0.03959951549768448,
-0.06742634624242783,
-0.02655523642897606,
-0.04511628299951553,
-0.012261210940778255,
-0.03605562448501587,
-0.028781531378626823,
0.03627726063132286,
-0.029820062220096588,
0.010440765880048275,
-0.02202201820909977,
0.02030710130929947,
0.08381126075983047,
0.034665945917367935,
-0.018461979925632477,
0.012279562652111053,
-0.03841918706893921,
-0.03793995454907417,
0.031180204823613167,
0.044899243861436844,
-0.0037993467412889004,
-0.05753142759203911,
0.014870338141918182,
-0.0337359793484211,
0.006458862219005823,
0.019788024947047234,
-0.012154873460531235,
0.04230794683098793,
0.008348718285560608,
-0.09510423988103867,
-0.07113678753376007,
0.045607611536979675,
-0.015757959336042404,
-0.021237386390566826,
-0.048501234501600266,
-0.022187938913702965,
0.049717240035533905,
0.08689849078655243,
-0.003591391257941723,
-0.021918820217251778,
0.021247778087854385,
0.04494376480579376,
-0.0003711958706844598,
-0.022514602169394493,
0.01796833612024784,
-0.009147673845291138,
-0.02191612496972084,
0.021646149456501007,
-0.10093564540147781,
-0.011369113810360432,
0.03331400454044342,
0.015756715089082718,
-0.01925347000360489,
0.0667787417769432,
-0.005467760376632214,
0.0250213872641325,
0.019972389563918114,
-0.002211261074990034,
-0.04345067963004112,
0.06553895026445389,
0.02413269877433777,
-0.018121084198355675,
0.05001114681363106,
0.021000130102038383,
0.011102602817118168,
0.023912910372018814,
-0.01572771929204464,
0.011431275866925716,
-0.03926648199558258,
-0.009881870821118355,
-0.01992694102227688,
0.02721189707517624,
0.013182582333683968,
0.01356550958007574,
-0.029398230835795403,
-0.025014908984303474,
-0.005959856323897839,
-0.007118158042430878,
0.03361252695322037,
-0.025229446589946747,
-0.024697527289390564,
-0.013186988420784473,
-0.049414217472076416,
0.028297098353505135,
-0.03544260933995247,
0.06583461165428162,
0.010238280519843102,
0.0402219258248806,
0.02825159952044487,
0.036039866507053375,
0.02637435309588909,
-0.055494677275419235,
-0.02390659600496292,
0.007442364003509283,
0.06196262687444687,
-0.0029251547530293465,
-0.013935904949903488,
0.0014302011113613844,
0.060669347643852234,
0.024667901918292046,
-0.0011068275198340416,
0.035239774733781815,
0.011630546301603317,
-0.006256576627492905,
0.012961331754922867,
0.0013379111187532544,
0.01381552405655384,
-0.0666191503405571,
-0.006360911298543215,
0.01409109216183424,
0.0260346457362175,
0.017162354663014412,
0.003981431946158409,
-0.0369589701294899,
0.06189553067088127,
0.03636007755994797,
0.01337470579892397,
0.007355810608714819,
0.031208373606204987,
0.027865834534168243,
0.03020605444908142,
0.006675677374005318,
-0.011377819813787937,
-0.0562511645257473,
-0.011422044597566128,
0.026654113084077835,
0.021603114902973175,
-0.013603445142507553,
0.01831558719277382,
0.05044415593147278,
0.02740488015115261,
0.03986838832497597,
0.026009658351540565,
-0.004988581407815218,
-0.019447343423962593,
0.012923642992973328,
0.022665105760097504,
0.014047832228243351,
0.0179189033806324,
0.05652446299791336,
0.01667308621108532,
0.01523501705378294,
-0.027933601289987564,
0.0036904513835906982,
-0.011448699980974197,
-0.03741740807890892,
0.01029982604086399,
0.00017137386021204293,
-0.029470691457390785,
0.0007017632015049458,
-0.01990417204797268,
0.00032222416484728456,
0.026407036930322647,
-0.009305746294558048,
-0.013412075117230415,
-0.022983035072684288,
-0.0013353823451325297,
-0.0052104066126048565,
0.019477350637316704,
-0.0016059462213888764,
-0.03367486223578453,
0.03875880315899849,
-0.055173128843307495,
0.02471388876438141,
-0.03495339676737785,
-0.00892462208867073,
-0.016810428351163864,
0.0035745606292039156,
0.037439703941345215,
0.024891741573810577,
0.0385032556951046,
-0.025822846218943596,
-0.037904977798461914,
0.040954455733299255,
-0.017823481932282448,
-0.02797718718647957,
0.02647547610104084,
-0.053066667169332504,
0.0531480498611927,
-0.026489410549402237,
-0.009275280870497227,
0.011617596261203289,
-0.0008839702350087464,
0.02933829091489315,
0.008381349965929985,
-0.038964398205280304,
-0.020373981446027756,
0.01047895010560751,
-0.0492219515144825,
0.00980316661298275,
-0.011071600019931793,
0.04552818462252617,
0.041867695748806,
-0.003919603768736124,
-0.005196965299546719,
0.020829619839787483,
0.02615782432258129,
-0.020878992974758148,
-0.003215440781787038,
-0.024282265454530716,
0.01010809000581503,
-0.03891183063387871,
0.017980633303523064,
0.024215910583734512,
-0.08704883605241776,
0.009676378220319748,
-0.04028453677892685,
-0.035784538835287094,
0.05123225599527359,
-0.031514815986156464,
0.012030013836920261,
-0.0049730632454156876,
-0.022122742608189583,
0.03824617713689804,
0.014171321876347065,
-0.0077401273883879185,
0.0017113219946622849,
-0.010657954961061478,
-0.0033387746661901474,
-0.02112157642841339,
0.01935562863945961,
0.032377585768699646,
0.008490340784192085,
-0.014448613859713078,
0.0429689884185791,
0.0357794426381588,
0.0184510238468647,
0.010815590620040894,
-0.016396917402744293,
0.011798233725130558,
0.005989888217300177,
0.013057391159236431,
0.04820308834314346,
0.004203496500849724,
0.00039915379602462053,
0.013598647899925709,
-0.003044483484700322,
0.023375622928142548,
-0.0015782490372657776,
-0.014755253680050373,
0.03245243802666664,
0.001435294863767922,
0.018117548897862434,
-0.004103431478142738,
0.012390979565680027,
-0.005331916734576225,
-0.002728051273152232,
-0.01414626743644476,
0.016042476519942284,
0.05741216614842415,
0.01634138450026512,
-0.004136370960623026,
0.006648694165050983,
0.03348210081458092,
-0.02642982453107834,
-0.018093306571245193,
0.027562852948904037,
-0.017629297450184822,
0.056930091232061386,
-0.007283650804311037,
-0.028210710734128952,
0.05816131457686424,
0.02512887679040432,
-0.004357637371867895,
0.003311444539576769,
-0.04437515139579773,
0.008884595707058907,
-0.06319519132375717,
-0.01804385893046856,
-0.013077338226139545,
0.0057686371728777885,
0.013560429215431213,
0.035208411514759064,
0.0489690862596035,
0.010511009953916073,
0.022075442597270012,
-0.02020995505154133,
-0.10066442936658859,
-0.003673517145216465,
-0.08050210773944855,
-0.02517644874751568,
-0.028430363163352013,
-0.027371279895305634,
-0.014186618849635124,
-0.012314439751207829,
-0.009116265922784805,
-0.02204136550426483,
-0.02759246900677681,
-0.06371887028217316,
-0.026074625551700592,
-0.019472531974315643,
-0.04542256146669388,
0.002671271562576294,
0.04390622302889824,
0.041164297610521317,
0.01676042750477791,
0.006115890108048916,
0.018989168107509613,
-0.011994254775345325,
-0.0019985376857221127,
0.018915334716439247,
0.012849007733166218,
-0.028181709349155426,
0.061273131519556046,
0.03264220058917999,
-0.013334065675735474,
-0.03698323294520378,
-0.012273541651666164,
0.06420530378818512,
0.02078988403081894,
-0.02109002135694027,
-0.03114534169435501,
-0.013551287353038788,
-0.041391171514987946,
-0.023106737062335014,
0.013678628019988537,
0.05466938763856888,
-0.02144382894039154,
-0.012033083476126194,
0.03532000631093979,
-0.03396374359726906,
-0.025471089407801628,
0.029053639620542526,
0.04711416736245155,
0.008273757994174957,
-0.03185204416513443,
-0.04348080977797508,
-0.015464258380234241,
-0.006493000313639641,
-0.017867689952254295,
-0.0060578309930861,
-0.026102058589458466,
-0.05968998000025749,
0.045247480273246765,
0.001819369732402265,
-0.017318176105618477,
-0.011382459662854671,
-0.045648008584976196,
0.016120394691824913,
0.02821514941751957,
-0.03623461723327637,
0.03158637508749962,
0.018327247351408005,
0.04291047528386116,
0.0554785318672657,
-0.0017621545121073723,
-0.01926710270345211,
-0.08759838342666626,
-0.020565159618854523,
0.03460874781012535,
0.01969710923731327,
0.015832655131816864,
-0.012208372354507446,
-0.061086174100637436,
-0.04347978159785271,
0.043991394340991974,
-0.0009381353156641126,
0.02046271227300167,
0.010037527419626713,
-0.0029849233105778694,
-0.00944888312369585,
0.0034241818357259035,
-0.0021907659247517586,
0.020576581358909607,
-0.03210833668708801,
0.0026677390560507774,
-0.04828604683279991,
0.03433343023061752,
-0.005523934960365295,
0.05516919121146202,
0.00979570485651493,
0.05525440350174904,
0.021397043019533157,
0.005937650799751282,
-0.022876063361763954,
-0.007828937843441963,
-0.020380781963467598,
-0.0834861546754837,
-0.01673777960240841,
0.023085828870534897,
-0.02368931472301483,
0.053990911692380905,
0.0063565317541360855,
-0.03268276900053024,
0.005007539410144091,
0.027545075863599777,
0.0036717054899781942,
0.019644277170300484,
-0.041167013347148895,
0.01299159973859787,
0.010010572150349617,
-0.014566033147275448,
0.024677876383066177,
0.035009101033210754,
0.008929538540542126,
-0.015862762928009033,
-0.02030409686267376,
0.06433259695768356,
-0.05395705997943878,
-0.032876260578632355,
0.0286105927079916,
-0.009309599176049232,
-0.04971775412559509,
0.06160282716155052,
0.003196973819285631,
0.00833126064389944,
0.007385970558971167,
-0.015513659454882145,
-0.016891179606318474,
0.056076422333717346,
-0.004043553024530411,
0.007874728180468082,
0.016499247401952744,
0.024253863841295242,
0.021522480994462967,
-0.03751951456069946,
0.010581471025943756,
-0.017976513132452965,
0.01256474107503891,
0.037757065147161484,
-0.0205087848007679,
-0.000013132023013895378,
-0.038097359240055084,
-0.0140085369348526,
0.047132305800914764,
-0.031941987574100494,
0.048505716025829315,
-0.0024236412718892097,
-0.024948302656412125,
0.02397792972624302,
-0.016932880505919456,
-0.009855225682258606,
-0.02881593629717827,
0.001238486380316317,
0.04836716875433922,
-0.04070517420768738,
0.06162353232502937,
0.0318828746676445,
0.022428050637245178,
-0.11351645737886429,
0.008841258473694324,
0.048967134207487106,
0.024822669103741646,
0.01659555919468403,
-0.016164379194378853,
0.03600873053073883,
-0.06256222724914551,
-0.005158301908522844,
-0.045512545853853226,
-0.004450663924217224,
-0.047125957906246185,
0.019039493054151535,
-0.006389444228261709,
0.007988044992089272,
0.06077125668525696,
0.008092887699604034,
-0.014652803540229797,
0.0206467118114233,
0.01027586031705141,
0.011920617893338203,
-0.010570870712399483,
0.03848686441779137,
-0.0050942739471793175,
-0.03746316581964493,
-0.02988801896572113,
-0.00034353663795627654,
0.009996474720537663,
-0.006719491444528103,
0.004480954725295305,
0.06739755719900131,
0.02362571842968464,
0.00950086209923029,
-0.011776353232562542,
0.01277671754360199,
-0.059133563190698624,
0.007650267798453569,
0.008019748143851757,
-0.017225921154022217,
0.013391952961683273,
-0.01775074563920498,
0.034504234790802,
0.006331237964332104,
-0.0209012720733881,
-0.0032307880464941263,
0.05793067812919617,
0.024399034678936005,
-0.02986590936779976,
-0.058921944350004196,
-0.03578425198793411,
0.007784842513501644,
-0.023804696276783943,
0.0037687437143176794,
0.03040049597620964,
0.03085700236260891,
0.0025228168815374374,
-0.050463754683732986,
-0.0394308865070343,
-0.007157181389629841,
0.09311603009700775,
-0.009967902675271034,
-0.005588008090853691,
0.02620353177189827,
0.0029728661756962538,
-0.0037806699983775616,
-0.06161656230688095,
0.02370646223425865,
0.027670932933688164,
-0.013252947479486465,
0.0002713081776164472,
-0.020338663831353188,
0.024233222007751465,
0.005006694234907627,
0.039821114391088486,
-0.011743063107132912,
0.005413382779806852,
0.011201689951121807,
0.05385235324501991,
-0.022944333031773567,
0.030200881883502007,
-0.06291760504245758,
0.03491244465112686,
-0.03135683014988899,
0.01973266899585724,
-0.013780349865555763,
0.02567494846880436,
0.018825894221663475,
0.010851074010133743,
0.04232718423008919,
0.009319113567471504,
-0.012640219181776047,
-0.04742300882935524,
-0.010650142095983028,
0.010216438211500645,
0.024216746911406517,
-0.016194168478250504,
0.021550124511122704,
0.015221908688545227,
0.006930648349225521,
-0.023268776014447212,
0.01026464905589819,
-0.07997433841228485,
-0.029419418424367905,
-0.040754202753305435,
-0.07044719159603119,
0.04745836183428764,
0.01593354530632496,
-0.02317056618630886,
0.06262034177780151,
-0.026517054066061974,
0.02455969527363777,
0.02632506936788559,
0.054882582277059555,
-0.01628638617694378,
0.055463094264268875,
-0.016841214150190353,
-0.02672899328172207,
-0.0464358776807785,
-0.010525096207857132,
0.10539153963327408,
0.05876407027244568,
0.03208264708518982,
-0.06753258407115936,
0.020969945937395096,
-0.008838345296680927,
-0.006807190366089344,
-0.032630886882543564,
0.011934270150959492,
-0.01242922805249691,
-0.007830769754946232,
0.039353158324956894,
0.050338733941316605,
0.0003923950716853142,
-0.029954101890325546,
0.06011546030640602,
-0.007539124693721533,
0.0010735489195212722,
0.009862443432211876,
0.039764177054166794,
0.01713612675666809,
0.03291700780391693,
-0.017634235322475433,
0.03836094215512276,
-0.04436350613832474,
-0.022691180929541588,
-0.05522119253873825,
-0.015177295543253422,
0.012831706553697586,
-0.028544962406158447,
-0.07112626731395721,
-0.016972223296761513,
0.009777487255632877,
-0.014366493560373783,
-0.013806198723614216,
0.03413045033812523,
0.007478194311261177,
-0.01686415635049343,
0.004867633804678917,
0.009923149831593037,
-0.005996922496706247,
0.00908742006868124,
-0.021048983559012413,
0.02954830415546894,
-0.06256099790334702,
0.006809934973716736,
0.010451634414494038,
0.00823462475091219,
0.00700119324028492,
0.011044182814657688,
-0.009880165569484234,
0.0033423423301428556,
0.010051493532955647,
-0.03730318695306778,
-0.014661447145044804,
-0.014526525512337685,
-0.024014996364712715,
-0.0025151001755148172,
-0.015437440946698189,
-0.009520865976810455,
0.015202725306153297,
0.008944204077124596,
0.03079308196902275,
0.006116841454058886,
0.005250649061053991,
0.006017270032316446,
-0.030843572691082954,
0.027978593483567238,
-0.024801839143037796,
-0.013825971633195877,
-0.03972027823328972,
0.005724893882870674,
-0.04793858900666237,
-0.0027266545221209526,
0.007568941917270422,
0.014168641529977322,
0.00981043092906475,
0.03883591294288635,
0.006302854511886835,
-0.022223422303795815,
-0.05832893028855324,
0.026115046814084053,
-0.0313597172498703,
-0.004959970247000456,
-0.03213513270020485,
0.029878562316298485,
0.024400200694799423,
0.012296435423195362,
-0.017146168276667595,
-0.02139153890311718,
-0.0032407306134700775,
0.009852792136371136,
-0.02424820326268673,
-0.022628827020525932,
-0.006409081164747477,
0.016143523156642914,
-0.025566620752215385,
-0.008136163465678692,
-0.013458660803735256,
0.02666294574737549,
0.005717485677450895,
0.004207644611597061,
0.019446635618805885,
0.02475699782371521,
-0.0304937232285738,
-0.0018192528514191508,
-0.0016669858014211059,
-0.02844945900142193,
0.00610094889998436,
0.010084817185997963,
0.03165798261761665,
-0.04041333124041557,
-0.04451052099466324,
-0.017100753262639046,
0.0007730858633294702,
-0.008874647319316864,
0.06409389525651932,
-0.018459200859069824,
0.04632602259516716,
0.013137457892298698,
-0.001210646703839302,
-0.05611932650208473,
-0.03217248246073723,
-0.050676215440034866,
-0.015380441211163998,
0.005798125173896551,
-0.05159354209899902,
0.01318960078060627,
0.00857218075543642,
-0.00897485762834549,
-0.03712870180606842,
0.013902523554861546,
0.027792267501354218,
-0.009684639982879162,
0.013965245336294174,
0.04926534742116928,
-0.006010426674038172,
0.026795241981744766,
0.022833429276943207,
-0.05841169133782387,
0.0381317175924778,
-0.034735288470983505,
-0.03704182431101799,
0.04843685030937195,
-0.013460044749081135,
0.004880645778030157,
0.011671354994177818,
-0.03245287388563156,
0.01950870268046856,
0.05050234496593475,
0.00786592811346054,
-0.022160906344652176,
-0.00213000294752419,
-0.0027491366490721703,
0.0007756161503493786,
0.029000677168369293,
0.039589229971170425,
-0.00737517885863781,
-0.00095985276857391,
0.04643772915005684,
0.023128023371100426,
-0.01596282236278057,
0.0016961876535788178,
0.022855551913380623,
-0.03428467735648155,
0.04008042439818382,
-0.007717774715274572,
-0.0023457719944417477,
0.033370357006788254,
0.032662421464920044,
-0.006195009686052799,
0.04398435354232788,
0.057970356196165085,
-0.0038060457445681095,
-0.11934930086135864,
-0.041104596108198166,
-0.010861205868422985,
0.025571350008249283,
0.039109352976083755,
-0.036943770945072174,
0.007205218076705933,
-0.005581628531217575,
-0.04726138338446617,
0.046985168009996414,
-0.013411772437393665,
-0.015247415751218796,
-0.03059670329093933,
-0.0027841725386679173,
-0.005702673923224211,
0.021597815677523613,
0.06104046851396561,
0.0445590540766716,
-0.024183083325624466,
-0.015813512727618217,
-0.01175504457205534,
-0.020362937822937965,
0.006569265853613615,
0.02590612880885601,
0.02985953539609909,
-0.014163950458168983,
0.04608847200870514,
-0.02459476701915264,
-0.013867917470633984,
0.017117474228143692,
0.00920996256172657,
-0.010249106213450432,
0.003562471829354763,
-0.009431364014744759,
0.03966644033789635,
0.03686809539794922,
0.03546212241053581,
-0.01642763800919056,
-0.0057375370524823666,
0.03300952911376953,
-0.012923158705234528,
0.011481769382953644,
-0.00940314494073391,
0.009288481436669827,
-0.0015790705801919103,
-0.06933742016553879,
0.005226048640906811,
0.024920180439949036,
-0.021543120965361595,
0.00043788281618617475,
-0.03334220498800278,
-0.0011990058701485395,
0.00590851902961731,
-0.029495947062969208,
0.020371505990624428,
-0.056540876626968384,
-0.01378109585493803,
0.007440824061632156,
0.02464199811220169,
-0.022455880418419838,
0.02450382150709629,
0.03335799649357796,
-0.013427753932774067,
-0.003977661021053791,
-0.012699656188488007,
0.016294820234179497,
-0.04775767773389816,
0.03536072373390198,
-0.030248550698161125,
0.00016595542547293007,
0.028449201956391335,
-0.05333531275391579,
-0.008643346838653088,
0.018286380916833878,
-0.018084298819303513,
0.025446482002735138,
-0.02978656254708767,
-0.05186194181442261,
-0.05132834613323212,
-0.08091280609369278,
0.021038701757788658,
-0.010892699472606182,
-0.0013375794515013695,
-0.05752554163336754,
-0.014784649945795536,
-0.009834099560976028,
0.006502949632704258,
0.029879774898290634,
-0.007331212051212788,
0.009271078743040562,
0.05500423535704613,
-0.004376852419227362,
0.004667418543249369,
-0.04482316970825195,
-0.016428455710411072,
-0.004484775010496378,
-0.030690187588334084,
-0.018385237082839012,
-0.0055471924133598804,
-0.007557011675089598,
0.033519014716148376,
0.03757503628730774,
0.015702541917562485,
0.06096649542450905,
-0.015913087874650955,
-0.019427495077252388,
0.06777915358543396,
0.033318616449832916,
-0.0015669551212340593,
0.08193503320217133,
-0.018939506262540817,
0.010150534100830555,
0.039469730108976364,
-0.01574055291712284,
-0.023574071004986763,
-0.0009926037164404988,
-0.008521245792508125,
-0.0014225586783140898,
0.009605877101421356,
-0.00491182180121541,
0.01108515728265047,
-0.008547607809305191,
-0.026792703196406364,
0.04155617207288742,
-0.060469530522823334,
-0.011916721239686012,
0.02726571075618267,
0.00790242850780487,
0.00346773280762136,
-0.005924916826188564,
-0.024505196139216423,
0.029545508325099945,
0.011880999431014061,
-0.031803179532289505,
0.06401188671588898,
0.04418070241808891,
0.018988318741321564,
-0.011230656877160072,
0.023162296041846275,
-0.007792327553033829,
-0.01287227962166071,
-0.009200051426887512,
0.02762259542942047,
-0.03237328305840492,
-0.0548003651201725,
0.023371782153844833,
-0.0332878902554512,
0.023950831964612007,
0.02269853837788105,
-0.0326252318918705,
0.04909370839595795,
0.009000309742987156,
0.01364702358841896,
-0.007306217681616545,
-0.031437914818525314,
0.0056931315921247005,
0.04030685871839523,
0.030846647918224335,
0.06790753453969955,
0.032995566725730896,
-0.02585943043231964,
0.004344734828919172,
-0.0037552358116954565,
0.0061844224110245705,
-0.0727127194404602,
-0.009175654500722885,
0.019740011543035507,
0.007290421985089779,
-0.005978567525744438,
-0.008048078045248985,
-0.043755486607551575,
-0.02732166461646557,
0.020359769463539124,
0.024262290447950363,
0.03885243833065033,
0.0028490296099334955,
-0.024551965296268463,
-0.05326373502612114,
0.03514242544770241,
-0.049667686223983765,
-0.0007799861487001181,
-0.012245564721524715,
0.027296017855405807,
-0.005386117845773697,
0.010227467864751816
] |
<p>Will the event horizons of a two black holes be perturbed or bent before a collision? What will the shape of the event horizon appear to be immediately after first contact?</p> | 1,431 | [
-0.008971075527369976,
-0.04982041195034981,
0.00932734552770853,
-0.010362595319747925,
0.03163359314203262,
0.018049174919724464,
-0.06469747424125671,
-0.03672274574637413,
-0.014245635829865932,
-0.00613264599815011,
0.025271570309996605,
0.04020499438047409,
0.036059942096471786,
0.03365371748805046,
0.009517946280539036,
0.00177978805731982,
-0.007382404990494251,
-0.02001422457396984,
-0.01663687638938427,
-0.023383211344480515,
0.03074169158935547,
-0.011735672131180763,
0.04770917445421219,
0.0007909194100648165,
-0.03375218063592911,
0.013051395304501057,
0.022263167425990105,
-0.040942493826150894,
0.018624475225806236,
0.06013518199324608,
-0.015523279085755348,
-0.0348961316049099,
0.0049429177306592464,
0.028010839596390724,
-0.01689126156270504,
-0.006244943011552095,
-0.013349343091249466,
-0.024853190407156944,
-0.037602826952934265,
0.0019692236091941595,
-0.03518529236316681,
-0.035405565053224564,
0.018186194822192192,
0.07378515601158142,
-0.029628196731209755,
-0.021806461736559868,
0.0012826601741835475,
-0.019303664565086365,
0.0311218723654747,
-0.06087987497448921,
0.04423695430159569,
-0.010500059463083744,
0.015916557982563972,
0.009281587786972523,
-0.012181967496871948,
-0.007784734945744276,
0.07885684818029404,
0.06505311280488968,
-0.006803461350500584,
-0.048851143568754196,
-0.0001768625370459631,
-0.0062684668228030205,
-0.0016348323551937938,
0.0036067424807697535,
-0.04036528244614601,
0.05741714686155319,
-0.050446152687072754,
-0.03520563989877701,
-0.008216677233576775,
-0.04889470338821411,
0.007295253686606884,
0.006832815706729889,
-0.00442659854888916,
0.0028567006811499596,
0.013338178396224976,
-0.03241344913840294,
-0.0028146428521722555,
-0.002672928385436535,
0.028393615037202835,
0.08194759488105774,
-0.019051048904657364,
-0.004396438132971525,
0.04781067743897438,
-0.0011600378202274442,
0.017723841592669487,
0.002841359470039606,
0.07683964818716049,
0.0038542011752724648,
0.027072392404079437,
0.018419863656163216,
-0.005713875871151686,
0.005914202891290188,
-0.0025398347061127424,
-0.08239976316690445,
0.016367129981517792,
0.01693739928305149,
-0.0005311488639563322,
0.06259489059448242,
-0.022468583658337593,
-0.04758033901453018,
-0.018478045240044594,
0.011518210172653198,
-0.010645486414432526,
0.038808029145002365,
0.030857093632221222,
-0.029129987582564354,
-0.062070462852716446,
0.043073009699583054,
-0.03437980264425278,
-0.03995697945356369,
-0.004212084226310253,
0.0218278206884861,
-0.038138311356306076,
-0.016063246876001358,
0.044831305742263794,
-0.03472019359469414,
0.014389976859092712,
-0.026552753522992134,
0.053361594676971436,
0.05309240520000458,
0.07171951979398727,
-0.01886516623198986,
0.0013176599750295281,
-0.01781073957681656,
-0.027581043541431427,
0.008677082136273384,
0.05405867472290993,
-0.00407019630074501,
-0.024274593219161034,
-0.03508273512125015,
-0.05159096047282219,
0.0017112642526626587,
-0.012037083506584167,
-0.00035860692150890827,
0.022207126021385193,
0.013610322959721088,
-0.0721677765250206,
-0.05954528599977493,
0.03656213730573654,
-0.039652034640312195,
-0.019904574379324913,
-0.06112039461731911,
0.01003224030137062,
0.050862159579992294,
0.08165540546178818,
-0.020342377945780754,
-0.001448573893867433,
0.02696213498711586,
0.06333288550376892,
-0.005418950691819191,
-0.019499944522976875,
0.0006265428382903337,
-0.004448206163942814,
-0.018741576001048088,
-0.015286732465028763,
-0.054714273661375046,
-0.017905471846461296,
0.04560678452253342,
0.024959363043308258,
-0.04891660809516907,
0.08562502264976501,
-0.022900234907865524,
-0.0025911431293934584,
0.019842874258756638,
0.005535528529435396,
-0.005559138488024473,
0.08308210223913193,
0.025895139202475548,
0.007248455658555031,
0.05429365858435631,
0.036881834268569946,
0.037553075700998306,
0.0003696022613439709,
-0.0047928825952112675,
0.016130652278661728,
-0.0227822195738554,
0.011438906192779541,
0.009363248944282532,
-0.007350646425038576,
-0.027179136872291565,
-0.01356196403503418,
-0.02644343674182892,
-0.017312174662947655,
-0.010240086354315281,
-0.020449822768568993,
0.036322250962257385,
-0.0042551737278699875,
-0.018359949812293053,
-0.014008117839694023,
-0.031237250193953514,
-0.02616630494594574,
-0.06867978721857071,
0.02595398761332035,
0.009403624571859837,
0.00073100789450109,
0.048865433782339096,
0.02928374521434307,
0.014225606806576252,
-0.04679270088672638,
-0.0439070425927639,
0.00259293126873672,
0.044610895216464996,
-0.010770021006464958,
-0.013167777098715305,
0.005477775353938341,
0.08703647553920746,
0.045060109347105026,
-0.028446901589632034,
-0.004048837348818779,
-0.008357060141861439,
-0.02967097982764244,
0.011737490072846413,
-0.013871423900127411,
0.023228345438838005,
-0.01930021494626999,
0.033589161932468414,
0.015910973772406578,
0.017937371507287025,
0.03998813405632973,
-0.005624981131404638,
-0.01960584707558155,
0.08507797867059708,
0.029038511216640472,
0.027146421372890472,
0.015742897987365723,
0.037578925490379333,
0.03559047356247902,
0.013796542771160603,
0.014743688516318798,
-0.015165742486715317,
-0.04770800471305847,
-0.024751391261816025,
0.02084321714937687,
0.028384674340486526,
-0.024779746308922768,
0.028511477634310722,
0.036658015102148056,
0.020075920969247818,
0.015379723161458969,
0.018688850104808807,
0.015772052109241486,
-0.029100937768816948,
0.015372809022665024,
-0.011473804712295532,
0.0032655182294547558,
0.0011301502818241715,
0.029841644689440727,
0.020400356501340866,
0.002016253536567092,
-0.013087308034300804,
-0.04106450825929642,
0.009614916518330574,
-0.018101409077644348,
0.010415619239211082,
-0.007179449778050184,
-0.03709855675697327,
0.02544218860566616,
-0.013875480741262436,
-0.007654751185327768,
0.00018169938994105905,
-0.002039205515757203,
-0.04293997958302498,
-0.03510397672653198,
0.025833414867520332,
-0.02690979838371277,
0.01800628751516342,
0.024394851177930832,
-0.0054398695938289165,
0.033562883734703064,
-0.06946680694818497,
0.03126916661858559,
-0.01607096754014492,
-0.014558251947164536,
-0.006293721962720156,
0.01759238913655281,
0.02216722071170807,
0.016168421134352684,
0.02197423204779625,
-0.02008020132780075,
-0.07043987512588501,
0.017097923904657364,
-0.021268358454108238,
-0.00889118853956461,
0.02323472872376442,
-0.07217009365558624,
0.05987824127078056,
-0.03330881521105766,
-0.013933147303760052,
0.01827927492558956,
0.001511288108304143,
0.018877757713198662,
0.031017262488603592,
-0.02073959819972515,
-0.03343646600842476,
-0.033653873950242996,
-0.012448659166693687,
-0.0033256446477025747,
-0.035272520035505295,
0.019365889951586723,
0.039141926914453506,
-0.011515653692185879,
-0.0028855607379227877,
0.030633166432380676,
0.00047902436926960945,
-0.006895582191646099,
-0.007250976748764515,
-0.00712811341509223,
0.014447357505559921,
-0.005331375636160374,
0.0010135198244825006,
0.04511605575680733,
-0.04887146130204201,
0.011145183816552162,
-0.04361419379711151,
-0.04726913571357727,
0.06631192564964294,
-0.047830697149038315,
0.007481660693883896,
-0.011881805956363678,
-0.016003578901290894,
0.04006987065076828,
-0.01557714119553566,
0.012853768654167652,
-0.04004500433802605,
-0.0009044783655554056,
-0.015447410754859447,
-0.0062117078341543674,
0.015452075749635696,
0.02592012658715248,
0.01263429131358862,
-0.009427724406123161,
0.04641814902424812,
0.027483493089675903,
0.028775295242667198,
0.02269679680466652,
0.013990631327033043,
-0.03117457777261734,
0.0028851707465946674,
-0.0025885701179504395,
0.004510359838604927,
0.002010693773627281,
-0.010853689163923264,
0.026582015678286552,
-0.0003078088629990816,
0.04500516876578331,
0.03593333438038826,
-0.016758324578404427,
0.03231049329042435,
-0.010647355578839779,
-0.00206969678401947,
0.00940803810954094,
0.05477834492921829,
-0.027524014934897423,
-0.017739657312631607,
-0.02689851075410843,
-0.0026660810690373182,
0.06342515349388123,
-0.0048329937271773815,
-0.009668438695371151,
0.0361301526427269,
0.030807718634605408,
-0.04290349781513214,
-0.025038020685315132,
0.006262669339776039,
-0.027053488418459892,
0.04673333093523979,
-0.010488184168934822,
-0.020623190328478813,
0.03299606963992119,
0.01944104954600334,
0.014539984054863453,
0.017665598541498184,
-0.01813868246972561,
-0.01669757254421711,
-0.09278271347284317,
-0.02347777783870697,
0.018594693392515182,
0.01512287650257349,
-0.0006757307564839721,
0.0576944425702095,
0.00839308463037014,
0.00668342737480998,
0.004189832601696253,
0.0020232966635376215,
-0.07776959240436554,
0.015870394185185432,
-0.06755256652832031,
-0.027684248983860016,
-0.0025487688835710287,
-0.0015617902390658855,
-0.012872720137238503,
-0.011617348529398441,
0.002559874439612031,
-0.013897417113184929,
0.002612923737615347,
-0.07710147649049759,
0.01755344495177269,
-0.06645975261926651,
-0.05543328449130058,
0.00874230545014143,
0.0696222111582756,
0.043181098997592926,
0.006109657231718302,
0.03657245263457298,
0.026242392137646675,
-0.033691905438899994,
-0.0016445554792881012,
0.02952013723552227,
0.021759437397122383,
-0.03718233108520508,
0.0669146329164505,
0.02107720449566841,
-0.020655304193496704,
-0.029001988470554352,
0.02087705209851265,
0.02204466052353382,
0.05316916108131409,
0.008145519532263279,
-0.010698559693992138,
-0.03101067803800106,
-0.04830534756183624,
-0.013682355172932148,
-0.040800705552101135,
0.0770854577422142,
-0.04778197035193443,
-0.005061653908342123,
0.009049501270055771,
-0.01808127388358116,
0.0022965953685343266,
0.028869252651929855,
0.0439949557185173,
0.06310228258371353,
-0.029834425076842308,
-0.03689923137426376,
-0.02923029288649559,
-0.022647811099886894,
0.0035578045062720776,
0.01649671606719494,
-0.0051392060704529285,
-0.0636492669582367,
0.018306633457541466,
-0.008188361302018166,
-0.0050846366211771965,
-0.042303428053855896,
-0.015331047587096691,
-0.021893896162509918,
0.012539229355752468,
-0.0022637350484728813,
0.03122127801179886,
0.010445483028888702,
0.0536455363035202,
0.0638507679104805,
-0.00716799683868885,
-0.010024434886872768,
-0.07213488966226578,
-0.0027971924282610416,
0.049019064754247665,
0.052273280918598175,
0.007001558318734169,
-0.04128608852624893,
-0.07027294486761093,
-0.008341718465089798,
0.07324820011854172,
-0.0005765384412370622,
0.010880596935749054,
-0.006241843570023775,
0.0008921465487219393,
-0.043949373066425323,
0.025204714387655258,
-0.02720308117568493,
0.0538921020925045,
-0.0016920396592468023,
-0.002708383137360215,
-0.006421429105103016,
0.015680376440286636,
0.0062698135152459145,
0.026285763829946518,
0.048502497375011444,
0.06187863275408745,
0.06099623069167137,
0.00434151291847229,
-0.012230725027620792,
-0.012519349344074726,
-0.0141909783706069,
-0.08850129693746567,
0.013305922038853168,
0.014192098751664162,
-0.04390110448002815,
0.05453339219093323,
-0.02107764035463333,
-0.008851597085595131,
0.04730207845568657,
-0.0052663967944681644,
-0.01200531329959631,
0.0028515567537397146,
-0.03464658185839653,
0.01144141424447298,
0.006570638157427311,
-0.00006785974255762994,
0.027644958347082138,
-0.0012989894021302462,
-0.012626949697732925,
-0.03189733624458313,
-0.025822434574365616,
0.04588674008846283,
-0.028574533760547638,
-0.002780334325507283,
0.011472618207335472,
-0.030000410974025726,
-0.06671574711799622,
0.033315740525722504,
-0.018690837547183037,
-0.008574460633099079,
-0.0014371569268405437,
-0.005802888423204422,
-0.026716800406575203,
0.043631356209516525,
0.010008233599364758,
0.019307198002934456,
0.0337844118475914,
0.006295669358223677,
-0.006163293030112982,
-0.026788847520947456,
0.026670493185520172,
-0.02358362078666687,
0.021515177562832832,
0.04017855226993561,
-0.03199160099029541,
0.026685014367103577,
-0.04338079318404198,
0.00006687048880849034,
0.01891670748591423,
-0.046294067054986954,
0.04899132251739502,
-0.0055383420549333096,
0.013379432260990143,
0.08588510006666183,
-0.03363450989127159,
-0.00698602432385087,
0.0020311519037932158,
-0.008194450289011002,
0.028676532208919525,
-0.051450636237859726,
0.0677172988653183,
0.048868097364902496,
0.011466646566987038,
-0.06924851983785629,
-0.024411099031567574,
0.04300306737422943,
0.009947197511792183,
-0.002687490312382579,
-0.016818339005112648,
0.02635970525443554,
-0.06028097867965698,
-0.022782055661082268,
-0.03243974968791008,
0.04027939587831497,
-0.015697728842496872,
0.008769466541707516,
-0.00017091937479563057,
-0.009217922575771809,
0.038318753242492676,
0.026991965249180794,
-0.009398742578923702,
0.00036756234476342797,
-0.0191807821393013,
0.027185553684830666,
-0.019817087799310684,
0.04648306593298912,
-0.011658337898552418,
-0.020542293787002563,
-0.06917610764503479,
-0.041844796389341354,
0.02110053040087223,
-0.022185886278748512,
0.040693968534469604,
0.02700187638401985,
0.012891150079667568,
-0.01367719192057848,
0.01063340064138174,
0.015569251030683517,
-0.06588815897703171,
0.021335413679480553,
-0.023569783195853233,
0.0060157026164233685,
0.018437575548887253,
-0.050213634967803955,
0.04465208575129509,
0.015255079604685307,
-0.040716007351875305,
-0.035548847168684006,
0.0608079694211483,
-0.0019469638355076313,
-0.04067917540669441,
-0.010866617783904076,
-0.022838903591036797,
0.02672305330634117,
-0.026919716969132423,
-0.024404266849160194,
0.0361020490527153,
0.0009091265965253115,
-0.028549786657094955,
-0.04555987939238548,
-0.017887596040964127,
-0.022130023688077927,
0.07275862246751785,
-0.02026083506643772,
0.04007841274142265,
0.011427202261984348,
0.004843017086386681,
-0.01629374921321869,
-0.02901044301688671,
0.023478219285607338,
0.008030521683394909,
-0.018869688734412193,
0.03086470626294613,
-0.024874372407794,
0.012307190336287022,
0.0024475178215652704,
0.06952200084924698,
-0.018650131300091743,
0.027895823121070862,
0.007644148077815771,
-0.00054357381304726,
0.021155675873160362,
0.011659597046673298,
-0.02432091347873211,
0.019351279363036156,
-0.03292073681950569,
0.023386860266327858,
-0.024006342515349388,
0.017640724778175354,
0.03724529594182968,
0.019005151465535164,
0.03853679820895195,
0.017896154895424843,
-0.019874142482876778,
-0.036206841468811035,
0.029944853857159615,
0.012643842026591301,
0.026638157665729523,
-0.007214901968836784,
0.02148059569299221,
0.02006259374320507,
-0.024999018758535385,
0.004642679821699858,
-0.024269241839647293,
-0.07028032839298248,
-0.02924710139632225,
-0.03617478534579277,
-0.04195215553045273,
0.06143428757786751,
0.027567697688937187,
-0.004532158840447664,
0.04842337220907211,
-0.02165132574737072,
0.03417930379509926,
0.025419030338525772,
0.027085954323410988,
-0.032089997082948685,
0.05539034679532051,
-0.009457742795348167,
0.01099414937198162,
-0.044293880462646484,
-0.017320768907666206,
0.12379305064678192,
0.06324629485607147,
0.021599572151899338,
-0.05379762873053551,
0.040428027510643005,
-0.0015327725559473038,
-0.017831474542617798,
-0.02392756938934326,
0.0310719795525074,
-0.010011197067797184,
0.024161214008927345,
0.040563810616731644,
0.038892414420843124,
0.013698402792215347,
-0.03197050839662552,
0.035068754106760025,
-0.043471526354551315,
-0.010817126370966434,
-0.03176633268594742,
0.014390016905963421,
-0.008005477488040924,
0.04749409109354019,
-0.0121947405859828,
0.03490070626139641,
-0.03163236752152443,
0.003271011868491769,
-0.05396435782313347,
-0.019641006365418434,
0.04447021335363388,
-0.008522260002791882,
-0.030225997790694237,
0.008355584926903248,
0.026879407465457916,
-0.026600202545523643,
-0.017253348603844643,
0.03768875449895859,
0.015091706067323685,
-0.01960594579577446,
0.025120140984654427,
0.02903740108013153,
-0.005669405683875084,
-0.00612636236473918,
-0.006295821163803339,
0.02436869964003563,
-0.07567259669303894,
0.0004447763494681567,
-0.011448713019490242,
0.05172808840870857,
-0.013374816626310349,
-0.012610851787030697,
-0.020360495895147324,
0.02212074212729931,
0.01847272366285324,
-0.052680909633636475,
-0.020608704537153244,
-0.012592035345733166,
-0.019772546365857124,
-0.009738307446241379,
-0.0177911389619112,
-0.010451255366206169,
0.05113164335489273,
0.006934695411473513,
0.03884337469935417,
0.005921964067965746,
0.01997627690434456,
-0.00018181366613134742,
-0.0367245152592659,
0.059921156615018845,
-0.025646571069955826,
-0.018672287464141846,
-0.05032097548246384,
-0.013645772822201252,
-0.05737975984811783,
-0.010011163540184498,
-0.007363466080278158,
0.041385870426893234,
0.01951412670314312,
0.01389176957309246,
0.0031469198875129223,
0.004647014196962118,
-0.0503365658223629,
0.03297066688537598,
-0.02291232906281948,
-0.0129030030220747,
-0.04896117001771927,
0.022406773641705513,
0.05919431149959564,
0.013574501499533653,
-0.0035793965216726065,
-0.0055947015061974525,
-0.007669145241379738,
0.027377499267458916,
0.012522289529442787,
0.017964353784918785,
0.006262307055294514,
0.01314591709524393,
-0.043379370123147964,
-0.0005412024329416454,
-0.049781717360019684,
0.029651440680027008,
0.016432572156190872,
-0.012419477105140686,
0.014025194570422173,
0.0050046443939208984,
-0.02901952899992466,
-0.002970698056742549,
0.008425635285675526,
-0.01064570527523756,
-0.0006455605616793036,
0.004403319675475359,
0.041970930993556976,
-0.01843046024441719,
-0.014597859233617783,
-0.03676469624042511,
-0.017778415232896805,
-0.009669759310781956,
0.028658999130129814,
-0.0040519158355891705,
0.05603433772921562,
0.009067527949810028,
0.026772156357765198,
-0.04956746846437454,
-0.029008619487285614,
-0.0475614033639431,
0.011331602931022644,
0.013732022605836391,
-0.017085347324609756,
0.028726311400532722,
0.019969254732131958,
-0.020918812602758408,
-0.0558912418782711,
0.0039132037200033665,
0.005492047872394323,
-0.001512790797278285,
0.007248520385473967,
0.04534251242876053,
-0.004077997989952564,
0.013964144513010979,
0.028426935896277428,
-0.05690653249621391,
0.00660748453810811,
-0.05513564124703407,
-0.04244742915034294,
0.013954667374491692,
-0.005243455991148949,
0.0548592247068882,
0.014184367842972279,
-0.039171043783426285,
0.012982022017240524,
0.0580090656876564,
-0.00968272052705288,
-0.03920041769742966,
0.016374211758375168,
-0.02713301032781601,
-0.034294601529836655,
0.024168696254491806,
0.04445900022983551,
-0.027493635192513466,
-0.026120536029338837,
0.04358317703008652,
-0.006104710511863232,
-0.020767422392964363,
0.004202243871986866,
-0.01862066239118576,
-0.00487873051315546,
0.03236113116145134,
0.008710329420864582,
-0.027418632060289383,
0.0222429521381855,
0.05697489157319069,
-0.01701594889163971,
0.04609902575612068,
0.05332700535655022,
0.0020990436896681786,
-0.0791785940527916,
-0.02220766246318817,
0.034010257571935654,
0.017172126099467278,
0.07176566869020462,
-0.06685133278369904,
0.048137158155441284,
0.04076767340302467,
-0.05268647521734238,
0.029997900128364563,
-0.009703929536044598,
-0.015555587597191334,
-0.017514942213892937,
0.018136464059352875,
0.002284806687384844,
0.028818370774388313,
0.05675460398197174,
0.02737284079194069,
-0.021564457565546036,
0.0007032598368823528,
-0.02491678297519684,
0.0045305285602808,
-0.02721819095313549,
0.009416473098099232,
-0.01632450520992279,
-0.0024969647638499737,
0.054640237241983414,
0.004548786208033562,
-0.005508881993591785,
0.02077619917690754,
0.020930679515004158,
-0.01740310899913311,
0.007047717459499836,
-0.01624409668147564,
0.049808673560619354,
-0.021875709295272827,
0.020851969718933105,
-0.025782320648431778,
-0.013163208961486816,
0.01998855732381344,
-0.017247790470719337,
-0.003827046835795045,
-0.013519625179469585,
-0.004474444314837456,
0.011099310591816902,
-0.012312830425798893,
-0.021937983110547066,
0.010616475716233253,
-0.02476269006729126,
-0.04447627067565918,
-0.034973423928022385,
0.016665153205394745,
0.003974699880927801,
-0.006852774415165186,
0.020915990695357323,
-0.027844266965985298,
-0.00033348481520079076,
0.013173201121389866,
0.0035326159559190273,
0.012179932557046413,
0.06039179116487503,
-0.023792656138539314,
-0.00860555749386549,
0.019727010279893875,
-0.031056702136993408,
0.022841833531856537,
-0.0565405935049057,
0.011360758915543556,
-0.022281555458903313,
0.0026652379892766476,
0.018235286697745323,
-0.04690326750278473,
0.020073257386684418,
0.027580080553889275,
0.0009526971844024956,
0.02870003692805767,
0.011475026607513428,
-0.07020309567451477,
-0.04044892638921738,
-0.05033343657851219,
0.004590066149830818,
-0.0342814065515995,
-0.012432417832314968,
-0.04372435063123703,
-0.010092945769429207,
-0.030057493597269058,
0.009093763306736946,
0.026251623407006264,
0.0039146761409938335,
-0.010389793664216995,
0.01526646502315998,
0.001350019359961152,
0.00004045924652018584,
-0.04134952649474144,
-0.02157645672559738,
-0.009057681076228619,
-0.03586438298225403,
0.003850080305710435,
-0.006893042009323835,
0.037001799792051315,
0.040544088929891586,
-0.008423218503594398,
-0.019078539684414864,
0.04016825929284096,
0.00878658052533865,
-0.013904377818107605,
0.05345212668180466,
0.02211116999387741,
0.0041282097809016705,
0.06085466966032982,
-0.0060166046023368835,
0.022044073790311813,
0.021369483321905136,
-0.029233697801828384,
-0.018057530745863914,
-0.0010230205953121185,
-0.031996794044971466,
-0.02766606956720352,
0.004948953166604042,
0.007803745102137327,
0.0013934809248894453,
-0.04412810131907463,
0.012370123527944088,
0.02195325307548046,
-0.028324460610747337,
-0.011978096328675747,
0.05178413540124893,
-0.01861642114818096,
0.031014224514365196,
-0.020281799137592316,
0.006025852635502815,
0.006157937925308943,
-0.02533567138016224,
-0.012418853119015694,
0.022061115130782127,
0.03481677919626236,
0.00505781127139926,
-0.00022776471450924873,
0.0011491533368825912,
-0.014198720455169678,
-0.005154396407306194,
-0.030916986986994743,
0.039045024663209915,
-0.014325124211609364,
-0.030518874526023865,
0.04430730640888214,
0.002081015845760703,
0.001975148217752576,
0.003923814278095961,
-0.006661456543952227,
0.04549742490053177,
-0.005690567661076784,
0.016597110778093338,
-0.019935468211770058,
-0.016224710270762444,
-0.02365678921341896,
0.03777093440294266,
0.035114917904138565,
0.06346195936203003,
0.02159273996949196,
0.0026441600639373064,
-0.00866835005581379,
0.002383808372542262,
0.03058999590575695,
-0.033902257680892944,
0.009549818001687527,
-0.009600253775715828,
0.010215960443019867,
-0.021499598398804665,
-0.009074846282601357,
-0.031138068065047264,
-0.02661862038075924,
0.028019987046718597,
0.02556436136364937,
0.024076251313090324,
-0.0071929339319467545,
0.016116663813591003,
-0.028572646901011467,
0.04598069190979004,
-0.08620992302894592,
-0.021667443215847015,
-0.03080490231513977,
0.006663674954324961,
-0.0017173606902360916,
0.007907603867352009
] |
<p>Does space have an elastic quality?</p>
<p>What I was thinking about was if space is expanding, is it being 'stretched', like a balloon being blown up, and if so, is this causing gravity to weaken? Imagine space as a 2 dimensional sheet (got this from one of Brian Greene's books) with planetary bodies resting on it and causing a depression in it, if you were pulling this sheet from all sides over a period of time, you would cause the depression of the planetary body to decrease and eventually become flat, which if we go back to reality, would mean that the gravitational 'constant' had changed to the point where the planetary body had no influence on those objects which were previously orbiting around it (or even residing on it's surface).</p>
<p>Is this the case in reality? Or does space not have an elastic quality? If not, can you explain to me what exactly it means for space to be expanding? </p>
<p>In case you didn't notice, I'm a layman (hence the Brian Greene books :p), so try to keep your answers/explanations conceptual if possible.</p> | 1,432 | [
-0.02445770986378193,
0.01486232504248619,
0.0003990028635598719,
-0.04382339492440224,
0.0502290278673172,
0.027965348213911057,
-0.02763153612613678,
-0.014863979071378708,
0.006253159139305353,
-0.053278449922800064,
-0.027072355151176453,
0.0081294234842062,
0.025264926254749298,
-0.0060776905156672,
0.014091940596699715,
-0.02600257098674774,
0.012702309526503086,
0.0014231812674552202,
-0.004742911551147699,
-0.022082068026065826,
0.008305189199745655,
0.005652748979628086,
0.030134567990899086,
0.00991626363247633,
-0.01996060088276863,
0.01603742130100727,
0.04410834237933159,
-0.013170597143471241,
0.03000391274690628,
0.05302470177412033,
-0.007613266818225384,
-0.006728975102305412,
-0.04424627497792244,
0.016118448227643967,
0.03018181212246418,
0.005133815575391054,
-0.04108763113617897,
-0.00212618475779891,
-0.00047619643737562,
0.023863423615694046,
-0.048111941665410995,
-0.010205411352217197,
-0.02657560631632805,
0.06136875972151756,
-0.02369684725999832,
0.0012486230116337538,
0.016759932041168213,
-0.006636248901486397,
0.048705413937568665,
-0.04976019635796547,
0.06280822306871414,
-0.004138387739658356,
0.03913167119026184,
0.03200986608862877,
0.00032354320865124464,
-0.018255550414323807,
0.08999563753604889,
0.0730791985988617,
-0.04583248496055603,
-0.030690129846334457,
-0.012708564288914204,
0.015759432688355446,
-0.022106394171714783,
-0.03139902278780937,
-0.026777958497405052,
0.0529511533677578,
-0.05581570044159889,
-0.005515648052096367,
0.05541132763028145,
0.010374263860285282,
-0.012212255969643593,
0.005465140100568533,
0.02033090963959694,
-0.020473090931773186,
0.01376896258443594,
-0.04352520406246185,
0.05286215618252754,
0.018886495381593704,
0.02347542718052864,
0.0473509319126606,
-0.005077678710222244,
-0.011369858868420124,
0.04891452565789223,
0.07287199050188065,
-0.0032868178095668554,
0.03527238965034485,
0.06394051015377045,
-0.028948284685611725,
0.024081742390990257,
0.029563363641500473,
0.01644504815340042,
-0.008829507976770401,
0.03171232342720032,
-0.040378279983997345,
-0.02105802856385708,
0.027118738740682602,
-0.0151966018602252,
0.06378517299890518,
-0.007414975669234991,
-0.0014100598637014627,
0.0020352371502667665,
0.015435053035616875,
-0.013466853648424149,
0.0687389001250267,
0.011490341275930405,
-0.025981327518820763,
-0.06476226449012756,
0.005435834173113108,
-0.0019010131945833564,
-0.024572014808654785,
-0.021932287141680717,
-0.019554488360881805,
-0.010226313956081867,
-0.023466240614652634,
0.04112159460783005,
-0.031037189066410065,
-0.0011594617972150445,
-0.027446990832686424,
0.01652757078409195,
0.0789654329419136,
0.06300536543130875,
-0.044290944933891296,
0.04853063076734543,
-0.010864428244531155,
-0.06642086803913116,
0.028640680015087128,
0.027988452464342117,
-0.03343978151679039,
-0.02656008116900921,
0.03183595836162567,
-0.01287137996405363,
0.013632334768772125,
-0.018886683508753777,
0.007752964738756418,
0.0638657659292221,
0.010980700142681599,
-0.09714251011610031,
-0.03543722257018089,
0.05060543492436409,
0.0091526685282588,
-0.006286507938057184,
-0.04227083921432495,
0.013310709968209267,
-0.004010303411632776,
0.07444792985916138,
0.017278552055358887,
-0.018200039863586426,
-0.000028706339435302652,
0.03754284232854843,
-0.003001792123541236,
-0.04488469660282135,
-0.013156513683497906,
-0.0022494459990411997,
-0.06157074123620987,
0.017818951979279518,
-0.08286993205547333,
-0.01492262352257967,
0.05657511204481125,
0.002605038695037365,
-0.054568812251091,
0.06789478659629822,
-0.005119872745126486,
-0.011009462177753448,
0.007436982821673155,
-0.0411669984459877,
-0.023029522970318794,
0.056379690766334534,
0.012984901666641235,
-0.0018490797374397516,
0.05083931237459183,
0.02676878497004509,
0.005371020175516605,
0.0280658770352602,
0.029063178226351738,
0.04198553040623665,
-0.05553844943642616,
-0.048571135848760605,
-0.037848100066185,
0.004237952176481485,
0.006596289109438658,
-0.03792884945869446,
-0.01980278454720974,
-0.02295752614736557,
-0.006119434256106615,
0.004409650340676308,
0.03995659574866295,
0.02810414880514145,
-0.00012512714602053165,
0.0041189962066709995,
-0.020946385338902473,
0.015160739421844482,
-0.06982678920030594,
0.010653644800186157,
-0.0012327989097684622,
0.0031830258667469025,
0.001853377791121602,
0.011429599486291409,
0.02195952832698822,
-0.035003673285245895,
-0.05489625781774521,
-0.0050681354478001595,
0.03840779885649681,
-0.04251658543944359,
-0.02412533015012741,
0.02590830810368061,
0.10254420340061188,
0.005898566916584969,
0.016605710610747337,
-0.020075902342796326,
-0.03049520030617714,
-0.028510594740509987,
0.01635356806218624,
-0.023901399224996567,
0.018725857138633728,
-0.03185725584626198,
0.007887515239417553,
0.007706365082412958,
-0.0017548007890582085,
0.02291504479944706,
0.02928314357995987,
-0.05787920579314232,
0.07398571819067001,
0.04308340698480606,
-0.03168788179755211,
0.024672886356711388,
0.04771853983402252,
-0.007340532261878252,
0.02567148767411709,
-0.011929675005376339,
-0.003027845872566104,
-0.05641906335949898,
-0.002595672383904457,
0.04839364439249039,
0.014968641102313995,
0.0006245819386094809,
0.02314317412674427,
0.024594290181994438,
0.01574336737394333,
0.005668074358254671,
0.005489082541316748,
-0.013778395019471645,
-0.022604569792747498,
-0.012768284417688847,
0.031349506229162216,
0.05833308771252632,
0.039956752210855484,
0.012894767336547375,
0.05038156360387802,
0.008820895105600357,
-0.024890242144465446,
0.00670934934169054,
0.01636127009987831,
0.025208519771695137,
0.013061520643532276,
0.0020374369341880083,
0.005528070963919163,
0.03833139315247536,
-0.017937520518898964,
0.02135966345667839,
0.039687201380729675,
-0.017054907977581024,
0.0023051295429468155,
-0.07678167521953583,
-0.019657326862215996,
0.008681479841470718,
0.02392236888408661,
-0.012426366098225117,
-0.06029031425714493,
0.017528565600514412,
-0.047535575926303864,
-0.009642519056797028,
0.031430453062057495,
-0.00540484394878149,
-0.007402317598462105,
-0.03582853451371193,
0.021565133705735207,
0.01907103694975376,
0.02339905872941017,
-0.014353319071233273,
-0.010930103249847889,
0.019601890817284584,
-0.048143189400434494,
-0.002778983674943447,
-0.00015404073928948492,
-0.04940922185778618,
0.0400223582983017,
0.00744965672492981,
-0.009408033452928066,
0.028837598860263824,
-0.016335804015398026,
0.012654170393943787,
0.02507086843252182,
-0.000986103666946292,
-0.0361357182264328,
0.0008329563424922526,
-0.06394199281930923,
0.007906858809292316,
-0.017930928617715836,
-0.004194023087620735,
0.0547938235104084,
-0.0022382575552910566,
-0.012853364460170269,
0.025601496919989586,
-0.05790041387081146,
-0.0303440410643816,
-0.04176897183060646,
-0.022143127396702766,
-0.004063853528350592,
-0.03521231561899185,
0.006927100475877523,
0.039247188717126846,
-0.030839383602142334,
0.0014840572839602828,
-0.03868993744254112,
-0.033766068518161774,
0.01572134904563427,
-0.04301072284579277,
0.018456416204571724,
-0.02908473275601864,
-0.06821777671575546,
0.10219632834196091,
0.017699824646115303,
-0.03192207217216492,
-0.025377945974469185,
-0.007273390889167786,
-0.005947897210717201,
-0.01969055086374283,
0.04228360578417778,
-0.012265762314200401,
0.027754684910178185,
-0.001418869011104107,
0.06818599253892899,
0.06310705095529556,
-0.013736488297581673,
0.020266899839043617,
-0.03214986249804497,
0.008578766137361526,
0.0033004512079060078,
-0.023217281326651573,
0.026233574375510216,
0.020075730979442596,
-0.016257941722869873,
-0.0210327859967947,
-0.0201675184071064,
0.05103614926338196,
0.04183691740036011,
-0.054783087223768234,
0.04929487407207489,
0.003742096247151494,
0.046775683760643005,
0.00932508148252964,
0.002730223350226879,
-0.015616645105183125,
-0.004740830045193434,
0.015308449976146221,
0.009606740437448025,
0.04522203281521797,
0.015839800238609314,
-0.012281432747840881,
0.02598273940384388,
0.04581226408481598,
-0.023205580189824104,
-0.01015727873891592,
0.052039969712495804,
-0.004200011491775513,
0.042468950152397156,
-0.019275708124041557,
-0.01814875192940235,
0.04719138517975807,
0.04016438126564026,
0.010329780168831348,
-0.0036929333582520485,
-0.06760544329881668,
0.04748101159930229,
-0.05248326435685158,
-0.0007556555210612714,
0.018421636894345284,
0.03177136555314064,
0.003781981533393264,
0.020645886659622192,
0.035952143371105194,
0.03030017949640751,
0.05143757909536362,
0.0034853327088057995,
-0.09687786549329758,
-0.0023700138553977013,
-0.031194744631648064,
-0.02121766097843647,
0.008733442984521389,
0.02378780022263527,
-0.03362927585840225,
-0.0241258442401886,
-0.02133171819150448,
-0.04134755954146385,
-0.01657913252711296,
-0.09826669096946716,
0.0014564951416105032,
-0.014774168841540813,
-0.015022932551801205,
-0.0032312076073139906,
0.03388505056500435,
0.026063980534672737,
-0.00861577782779932,
0.04330306500196457,
0.0492541640996933,
-0.013890979811549187,
-0.004813161212950945,
-0.009526622481644154,
0.004685195628553629,
0.0025553791783750057,
0.006190442480146885,
0.015723230317234993,
0.023845326155424118,
-0.010225888341665268,
0.01725924387574196,
0.01533836405724287,
0.008009209297597408,
-0.044116102159023285,
-0.004832984879612923,
-0.011045903898775578,
-0.039561036974191666,
-0.024703213945031166,
-0.016334088519215584,
0.03373678773641586,
0.02420860342681408,
0.0024411145132035017,
0.019695134833455086,
0.007273251190781593,
-0.02942589670419693,
0.052663665264844894,
0.06698901951313019,
-0.02357216365635395,
-0.030800752341747284,
-0.019541526213288307,
-0.036728620529174805,
-0.02611721120774746,
-0.025493094697594643,
0.01778341457247734,
-0.023747984319925308,
-0.06388332694768906,
0.01778803952038288,
-0.005753801204264164,
0.013283699750900269,
-0.004787427838891745,
-0.012539466843008995,
0.02120531164109707,
0.014496619813144207,
-0.02228151075541973,
0.002340784529224038,
0.026007147505879402,
0.038432326167821884,
0.05225570872426033,
-0.007048260886222124,
-0.02219795063138008,
-0.09368729591369629,
0.01778518036007881,
-0.0024296913761645555,
-0.004209069535136223,
-0.0013309635687619448,
-0.019596705213189125,
-0.04627789929509163,
-0.061302438378334045,
0.010377141647040844,
-0.0299017746001482,
-0.00796215794980526,
-0.021094148978590965,
0.014074603095650673,
-0.018307961523532867,
0.012773034162819386,
-0.00294407457113266,
-0.0005007380968891084,
-0.027444349601864815,
0.028649164363741875,
-0.0035865858662873507,
0.031736474484205246,
-0.016265038400888443,
0.03981547802686691,
-0.0026514343917369843,
0.04282425343990326,
0.026267368346452713,
-0.007784015033394098,
-0.02604265883564949,
0.02386770211160183,
-0.035347193479537964,
-0.04295092448592186,
0.01488464418798685,
0.01987864449620247,
-0.03647872060537338,
0.01738901436328888,
0.009408919140696526,
-0.019533226266503334,
0.026685431599617004,
-0.019264044240117073,
-0.009930199943482876,
0.0322028212249279,
0.012308543547987938,
0.025368697941303253,
0.0037696759682148695,
-0.008152087219059467,
0.03571655601263046,
0.048901598900556564,
0.0013527226401492953,
0.016069533303380013,
-0.026767082512378693,
0.03470248728990555,
-0.06598079949617386,
0.018760351464152336,
-0.02191244065761566,
-0.020622150972485542,
-0.05033945292234421,
0.043099019676446915,
0.0031257006339728832,
-0.010286631062626839,
-0.00020355549349915236,
-0.0445636548101902,
-0.006270657759159803,
0.04563487321138382,
0.015889685600996017,
0.012608896009624004,
0.005926231388002634,
0.03177761286497116,
-0.022648178040981293,
-0.0072211711667478085,
-0.017738008871674538,
0.013839219696819782,
-0.04866962134838104,
0.02300087735056877,
-0.01613401249051094,
0.008182888850569725,
0.01868145540356636,
-0.005840443540364504,
0.02624683640897274,
-0.026938891038298607,
0.05857863649725914,
-0.0048423572443425655,
0.001998273888602853,
0.01769837737083435,
-0.02528991550207138,
0.008331029675900936,
-0.001046256977133453,
-0.031328484416007996,
0.038765549659729004,
-0.020106391981244087,
0.010098205879330635,
0.001334909233264625,
0.028922639787197113,
-0.10069812089204788,
-0.03111547790467739,
0.03759877383708954,
0.018967388197779655,
-0.021397797390818596,
-0.016414377838373184,
0.0050552841275930405,
-0.04235317185521126,
-0.002044664928689599,
-0.014545866288244724,
0.023276321589946747,
-0.011065101251006126,
-0.015209569595754147,
0.015959953889250755,
-0.012236031703650951,
0.03052639774978161,
-0.004524941090494394,
-0.016154205426573753,
-0.0045944820158183575,
0.017905866727232933,
-0.015577631071209908,
-0.03381285443902016,
0.07546082139015198,
-0.01893250085413456,
-0.034475360065698624,
-0.026546385139226913,
0.00782073475420475,
0.0030762413516640663,
-0.02323530800640583,
-0.034206241369247437,
0.026209814473986626,
0.012513692490756512,
0.0165166687220335,
0.015174133703112602,
0.02583109214901924,
-0.047138117253780365,
0.017377082258462906,
-0.0069971391931176186,
0.010745462030172348,
-0.0013546992558985949,
-0.059270743280649185,
0.023858027532696724,
-0.010073636658489704,
0.013244873844087124,
0.029259882867336273,
0.07575535774230957,
0.0311660747975111,
-0.03376808762550354,
0.017861954867839813,
-0.020502593368291855,
0.02675212360918522,
-0.0025086659006774426,
-0.01514179166406393,
0.00657128170132637,
-0.0015663797967135906,
-0.0635736957192421,
-0.01726110838353634,
-0.003880214411765337,
0.0015483270399272442,
0.0713171735405922,
-0.03778940811753273,
0.010355020873248577,
0.007803036831319332,
0.0020529250614345074,
0.001114089391194284,
-0.05012492090463638,
-0.005965111311525106,
-0.004285764880478382,
-0.02679659239947796,
0.025032315403223038,
-0.06629925966262817,
0.005839389283210039,
0.025541046634316444,
0.027578847482800484,
-0.04659174010157585,
0.002099124016240239,
0.012827594764530659,
0.028121942654252052,
0.03474811464548111,
-0.006242852658033371,
-0.03499697148799896,
0.02774728462100029,
0.0033757584169507027,
0.021538348868489265,
0.018899936228990555,
0.009109335020184517,
0.03142249956727028,
0.018194811418652534,
0.03608502447605133,
0.0015605996595695615,
-0.020900342613458633,
-0.06381553411483765,
0.009183591231703758,
-0.011813085526227951,
0.0166727714240551,
0.020477771759033203,
0.00014870779705233872,
0.0009324125130660832,
-0.005142247769981623,
0.0058341133408248425,
-0.014132288284599781,
-0.07465952634811401,
-0.058840177953243256,
-0.027935408055782318,
-0.0279996357858181,
0.04144397750496864,
0.009303721599280834,
-0.03496980294585228,
0.014529755339026451,
-0.005998515989631414,
0.020703677088022232,
0.012132851406931877,
0.047341760247945786,
-0.0039212387055158615,
0.07279808819293976,
-0.03323754668235779,
0.02495778724551201,
-0.03569922223687172,
0.006709492765367031,
0.10317297279834747,
0.04070387780666351,
-0.017014088109135628,
-0.04750124365091324,
0.023189706727862358,
-0.019095029681921005,
-0.0167462807148695,
-0.03191477805376053,
0.005488994065672159,
-0.006577290594577789,
0.0025571328587830067,
0.005970865488052368,
0.09290523082017899,
0.005009213928133249,
-0.03197283670306206,
0.05801859498023987,
-0.03972036764025688,
-0.02249807119369507,
-0.04093386232852936,
0.011300821788609028,
-0.02174418605864048,
0.02672918513417244,
-0.04161819443106651,
0.03218216821551323,
-0.023054342716932297,
0.018770717084407806,
-0.04257829114794731,
-0.0016257960814982653,
0.008925463072955608,
-0.0075555769726634026,
-0.040078163146972656,
0.03481178730726242,
0.0018473173258826137,
-0.024523448199033737,
-0.06664776057004929,
0.017788873985409737,
0.005368994083255529,
-0.003145913826301694,
0.0014806882245466113,
0.014188955537974834,
-0.042180392891168594,
0.019520824775099754,
-0.019350938498973846,
0.02543092519044876,
-0.02269255742430687,
-0.010074294172227383,
-0.014043297618627548,
0.07415260374546051,
-0.0037399386055767536,
0.002181177493184805,
0.03696748986840248,
0.004568411968648434,
-0.007867857813835144,
-0.046143196523189545,
-0.017105719074606895,
-0.011278867721557617,
0.016198040917515755,
-0.005070823710411787,
-0.03387673199176788,
0.00643126992508769,
0.015076901763677597,
0.016872046515345573,
0.04946170747280121,
-0.0009529493981972337,
0.020719174295663834,
0.03542284667491913,
-0.008843147195875645,
0.07828044146299362,
-0.025081558153033257,
0.006925320718437433,
-0.041127223521471024,
-0.004162798170000315,
-0.03689699247479439,
0.001021346659399569,
0.031794045120477676,
0.054634373635053635,
0.027038469910621643,
-0.03828499838709831,
0.007883044891059399,
-0.017046719789505005,
-0.004397518467158079,
0.04288918152451515,
-0.028593214228749275,
0.000055610467825317755,
-0.04205118492245674,
0.012459691613912582,
0.007306488696485758,
0.00020571850473061204,
0.0038295539561659098,
-0.02037457562983036,
-0.030552184209227562,
-0.010883502662181854,
0.013877693563699722,
-0.008915726095438004,
-0.006491012871265411,
0.010018383152782917,
-0.010452407412230968,
0.000029083199478918687,
-0.0018511399393901229,
0.02866971865296364,
0.021837200969457626,
-0.018114596605300903,
-0.013424208387732506,
0.011945582926273346,
-0.02731972560286522,
-0.006745402701199055,
0.02648884989321232,
-0.02233893610537052,
0.014109281823039055,
-0.004249291028827429,
-0.0063126604072749615,
-0.03642670065164566,
0.004258953966200352,
-0.026279231533408165,
-0.010828705504536629,
-0.013902007602155209,
0.03792775049805641,
-0.0022703001741319895,
0.0779067650437355,
-0.008548666723072529,
0.008532004430890083,
-0.07734444737434387,
-0.00954931229352951,
-0.07312338054180145,
0.003243969287723303,
0.014746222645044327,
-0.015197611413896084,
0.033143509179353714,
0.01831347867846489,
-0.06333837658166885,
-0.04520422965288162,
0.0313376784324646,
-0.0025254383217543364,
-0.014275647699832916,
-0.012759010307490826,
0.039932675659656525,
-0.006779279559850693,
0.051311194896698,
0.011692449450492859,
-0.02500411495566368,
0.012681666761636734,
-0.049923766404390335,
-0.08560599386692047,
0.019169941544532776,
-0.01915617659687996,
0.0538816973567009,
0.021567557007074356,
-0.023908467963337898,
-0.03768317028880119,
0.08475076407194138,
0.010443828999996185,
0.01798536628484726,
-0.012414907105267048,
-0.010259011760354042,
-0.026250384747982025,
0.00317202671431005,
0.022878851741552353,
-0.032523538917303085,
0.008831228129565716,
0.027631113305687904,
-0.007038519252091646,
-0.03303326666355133,
0.003955508582293987,
0.02726783975958824,
-0.036745138466358185,
-0.014338186010718346,
-0.016055773943662643,
-0.0045044622384011745,
0.013992023654282093,
0.02649111859500408,
-0.027504395693540573,
0.023447275161743164,
0.06923627108335495,
-0.019771648570895195,
-0.08423610031604767,
0.0037104501388967037,
-0.015536487102508545,
-0.010951987467706203,
0.014318641275167465,
-0.028578929603099823,
0.02799673192203045,
0.007941397838294506,
-0.04150490462779999,
0.04642864316701889,
-0.03364219143986702,
0.019202591851353645,
0.0006840699352324009,
-0.01251245941966772,
-0.02750709280371666,
0.021455571055412292,
0.05420314520597458,
0.06188856065273285,
-0.03176562488079071,
0.008986830711364746,
-0.014393766410648823,
0.009438397362828255,
0.0077495817095041275,
0.013291419483721256,
-0.02214379608631134,
-0.0029389765113592148,
0.057334840297698975,
0.011974595487117767,
-0.010021509602665901,
0.015385735780000687,
0.023170093074440956,
0.03826108202338219,
-0.005527911242097616,
-0.01987847127020359,
0.042070481926202774,
0.004221978131681681,
0.007872079499065876,
-0.0212419256567955,
-0.022020190954208374,
0.06287042051553726,
-0.014224814251065254,
0.0007687249453738332,
0.0017143308650702238,
0.019056489691138268,
0.013348993845283985,
-0.07910294085741043,
0.0012293189065530896,
-0.004453983623534441,
-0.011004505679011345,
0.030620582401752472,
0.004122440703213215,
0.000029220886062830687,
0.008271737024188042,
0.012954797595739365,
0.005399813409894705,
-0.029958708211779594,
-0.016066204756498337,
0.015608258545398712,
-0.020088862627744675,
-0.04593421518802643,
0.04457645118236542,
-0.0023397328332066536,
0.012067114003002644,
0.005325241480022669,
-0.023009514436125755,
0.009741134941577911,
-0.055107299238443375,
-0.003387719625607133,
-0.0023931905161589384,
-0.006699386052787304,
0.00673545990139246,
-0.008641872555017471,
-0.04404163360595703,
0.04656584560871124,
0.0301828533411026,
0.015876909717917442,
-0.01797698624432087,
-0.039736002683639526,
-0.029714884236454964,
-0.08172429352998734,
0.037969447672367096,
-0.010930810123682022,
-0.00840695295482874,
-0.023937813937664032,
-0.00047264847671613097,
-0.013593431562185287,
0.020405510440468788,
0.05192425474524498,
-0.012128761038184166,
-0.015332052484154701,
0.003442626679316163,
0.018543506041169167,
0.009566846303641796,
-0.060333993285894394,
-0.013718297705054283,
0.039193522185087204,
-0.03399056941270828,
0.008655733428895473,
-0.01792036183178425,
-0.015460241585969925,
0.0026872733142226934,
0.026724709197878838,
-0.006341449450701475,
0.05757668986916542,
-0.010928553529083729,
-0.06298927217721939,
0.043580032885074615,
0.03438105434179306,
-0.009868903085589409,
0.07657420635223389,
-0.02896968647837639,
0.03773527219891548,
0.029009927064180374,
-0.012337619438767433,
-0.008814766071736813,
0.035032499581575394,
-0.035840895026922226,
0.002013229299336672,
-0.03332974761724472,
-0.000914111384190619,
-0.009048478677868843,
-0.023231759667396545,
-0.00814101379364729,
0.0629284679889679,
-0.050903595983982086,
0.012535525485873222,
0.025865938514471054,
-0.0024320497177541256,
0.008867884986102581,
-0.013085023500025272,
-0.01182862464338541,
0.03115903027355671,
-0.006522851530462503,
0.01767360046505928,
0.025551391765475273,
0.0488612987101078,
0.011259868741035461,
-0.00710180401802063,
0.01869509369134903,
0.00022807488858234137,
0.0077645014971494675,
0.025209885090589523,
0.055428873747587204,
-0.06366988271474838,
-0.01717275008559227,
0.0013453996507450938,
0.024979500100016594,
-0.004623002372682095,
0.05570739880204201,
-0.021808398887515068,
0.05750507488846779,
-0.002144566038623452,
0.025791360065340996,
-0.011570192873477936,
0.011511039920151234,
-0.027098240330815315,
0.037028200924396515,
0.012907926924526691,
0.018848208710551262,
0.031045356765389442,
-0.009184506721794605,
-0.029943766072392464,
-0.0004968070425093174,
0.018231332302093506,
-0.015239858999848366,
0.0031725321896374226,
-0.007012748159468174,
-0.027610957622528076,
0.022308656945824623,
0.009817693382501602,
-0.0502888560295105,
-0.007242782041430473,
0.05226131156086922,
0.010680211707949638,
0.026883741840720177,
-0.007012477144598961,
0.011227798648178577,
-0.03663010522723198,
0.04436856135725975,
-0.06937727332115173,
0.02248925156891346,
-0.006877614185214043,
0.01983216218650341,
-0.02261260338127613,
0.002142804441973567
] |
<p>I just don't understand how a object with 2 ends can be unidimensional.</p> | 1,433 | [
-0.024370986968278885,
-0.025302063673734665,
0.023337941616773605,
0.026080146431922913,
-0.012835162691771984,
-0.03669402748346329,
0.010514865629374981,
-0.025126317515969276,
-0.024853728711605072,
-0.024719903245568275,
0.0513022243976593,
0.026180246844887733,
0.02047080732882023,
0.07754901051521301,
0.007961616851389408,
-0.003993331454694271,
0.02552240714430809,
-0.0469970777630806,
0.018422266468405724,
-0.039924439042806625,
0.016550365835428238,
-0.02435341291129589,
-0.014045744203031063,
-0.009135923348367214,
0.02185090258717537,
0.006874653045088053,
0.04436101019382477,
-0.05121449753642082,
0.06337558478116989,
0.056310366839170456,
-0.01987912505865097,
-0.07173497974872589,
0.008922743611037731,
0.014902637340128422,
0.05801108106970787,
0.026716960594058037,
-0.033660948276519775,
-0.0012282998068258166,
-0.007502560503780842,
0.022481055930256844,
0.029726747423410416,
0.0013959170319139957,
-0.0876287892460823,
0.07860898226499557,
-0.02956489473581314,
0.03594037517905235,
-0.0015547601506114006,
-0.021009277552366257,
0.053963351994752884,
-0.0106374341994524,
0.09459768980741501,
0.025609102100133896,
0.032620929181575775,
-0.006170015316456556,
-0.044271521270275116,
0.043895456939935684,
0.0523868128657341,
0.0713958740234375,
0.011613002978265285,
-0.04001655802130699,
-0.035577643662691116,
0.009650581516325474,
0.029569178819656372,
0.011881746351718903,
4.121530992051703e-7,
0.00650892686098814,
0.022839682176709175,
-0.025968017056584358,
0.02726622484624386,
-0.011678561568260193,
0.0002303983928868547,
-0.0009859426645562053,
0.06230665370821953,
-0.0034646496642380953,
0.016251947730779648,
-0.03322749212384224,
0.027941696345806122,
0.020892076194286346,
0.03675573691725731,
0.011878637596964836,
-0.019313758239150047,
-0.014842764474451542,
0.026484986767172813,
-0.0051384130492806435,
0.018813546746969223,
-0.0026251894887536764,
0.06490957736968994,
0.0024460861459374428,
-0.003529124893248081,
0.04073810949921608,
-0.0048033688217401505,
-0.058185357600450516,
0.0777839869260788,
0.044407885521650314,
-0.015863455832004547,
0.03258585184812546,
0.017391817644238472,
0.050772618502378464,
0.02798493206501007,
0.03763042762875557,
-0.006022023502737284,
0.0014649698277935386,
0.0074967555701732635,
0.056593459099531174,
0.02338847517967224,
0.0050531718879938126,
-0.02601739391684532,
0.024580538272857666,
0.028604736551642418,
0.018398690968751907,
-0.018818970769643784,
0.014850364066660404,
0.007207442075014114,
0.02765141986310482,
0.003940633498132229,
0.004657710436731577,
-0.017644936218857765,
0.04442073777318001,
0.023770874366164207,
0.06311455368995667,
0.01249238383024931,
-0.00010084496170748025,
-0.0013039166806265712,
0.0016650218749418855,
-0.10059194266796112,
0.03431786224246025,
0.036360107362270355,
-0.0213068388402462,
-0.01931706815958023,
0.03996698185801506,
0.03971574455499649,
0.005460559856146574,
0.0008730132249183953,
0.025131605565547943,
0.0076941438019275665,
-0.016378602012991905,
-0.08946029096841812,
-0.07718686014413834,
0.024641381576657295,
0.03317992389202118,
-0.004976910073310137,
-0.0800202339887619,
0.046218059957027435,
0.018727969378232956,
0.08543283492326736,
-0.06810484081506729,
0.012909877113997936,
0.011287788860499859,
0.017698755487799644,
0.01872434839606285,
-0.007936744019389153,
-0.013954601250588894,
-0.03639477863907814,
-0.015764160081744194,
0.003209384623914957,
-0.0700034499168396,
0.00627242773771286,
0.05278493091464043,
0.019281310960650444,
-0.017369596287608147,
0.06407328695058823,
-0.03466402739286423,
0.018748998641967773,
-0.005475096870213747,
-0.03289639204740524,
-0.051785752177238464,
0.10331187397241592,
0.013835744000971317,
-0.02214951068162918,
0.024898508563637733,
0.004162333440035582,
0.04321688786149025,
0.00531869288533926,
0.03739266097545624,
0.019895190373063087,
-0.030043315142393112,
-0.021422164514660835,
-0.032563500106334686,
0.002532771322876215,
0.008209382183849812,
-0.038066357374191284,
-0.03266366943717003,
0.012488356791436672,
-0.003986936993896961,
-0.004425907973200083,
-0.015495202504098415,
-0.010206544771790504,
-0.010888412594795227,
0.021301181986927986,
-0.044191449880599976,
0.005722657311707735,
-0.07382845878601074,
-0.0062744286842644215,
0.02146741934120655,
-0.028118619695305824,
0.010043005459010601,
-0.03225007653236389,
-0.004968527238816023,
-0.038670048117637634,
-0.01284907665103674,
-0.035064298659563065,
0.05433514341711998,
0.026197534054517746,
-0.023591872304677963,
0.010128890164196491,
0.06932906061410904,
0.06651709228754044,
0.013338727876543999,
0.03975061699748039,
-0.020662538707256317,
-0.01690618321299553,
0.02036227285861969,
0.010020446963608265,
-0.03639213368296623,
-0.03602439910173416,
-0.00025852155522443354,
0.012033585458993912,
0.009730549529194832,
0.00920763611793518,
0.051126159727573395,
-0.02727024257183075,
0.07207009941339493,
0.058617278933525085,
-0.017898552119731903,
-0.007321882527321577,
0.016301846131682396,
0.012300031259655952,
0.015956846997141838,
-0.02373591996729374,
-0.024133043363690376,
-0.0029445954132825136,
0.009427367709577084,
0.010832038708031178,
0.019341040402650833,
-0.026929480955004692,
-0.003113917075097561,
-0.019304605200886726,
0.03166847303509712,
0.005030264612287283,
0.017504148185253143,
-0.012837820686399937,
0.011386130005121231,
0.001149471732787788,
-0.014837400056421757,
0.013206463307142258,
0.025691844522953033,
0.03238323703408241,
-0.009305126965045929,
0.016360314562916756,
0.015045790933072567,
-0.03946874663233757,
0.037307996302843094,
0.022936057299375534,
0.009903275407850742,
0.017100486904382706,
-0.006482068449258804,
0.03885795548558235,
-0.034242335706949234,
0.021795211359858513,
0.02659023180603981,
0.036958761513233185,
-0.042865604162216187,
-0.03499453142285347,
0.0093104038387537,
0.028074705973267555,
0.007181499619036913,
-0.03011058270931244,
-0.029338955879211426,
0.04740370810031891,
-0.012434222735464573,
-0.0037207570858299732,
-0.03214142471551895,
-0.025325212627649307,
-0.01651376113295555,
0.008734850212931633,
0.02448051981627941,
0.017702516168355942,
0.0511498898267746,
-0.03892679885029793,
-0.024432115256786346,
-0.029371334239840508,
-0.021590139716863632,
0.0005943047581240535,
-0.040230948477983475,
-0.05347524955868721,
0.034642841666936874,
-0.02504347637295723,
-0.028279626742005348,
0.03026035986840725,
0.049159035086631775,
0.004278514068573713,
0.032932527363300323,
-0.02209234982728958,
-0.015220201574265957,
-0.043381575495004654,
-0.006004245951771736,
0.0008587408228777349,
-0.046070922166109085,
0.003960011526942253,
0.019603481516242027,
0.015432067215442657,
-0.05620826780796051,
0.035976458340883255,
-0.04660635441541672,
-0.026992855593562126,
0.00037179747596383095,
-0.05745498463511467,
0.03814664110541344,
-0.022017264738678932,
-0.012523762881755829,
-0.019425945356488228,
0.007843894883990288,
0.01761738397181034,
-0.05955994501709938,
-0.0327497236430645,
-0.0070750038139522076,
-0.010364280082285404,
0.0341234989464283,
0.015141506679356098,
-0.008936895988881588,
0.04990439862012863,
-0.011624890379607677,
-0.058602944016456604,
-0.03796859458088875,
-0.011766212061047554,
0.0066848876886069775,
-0.05252886936068535,
0.019583746790885925,
0.0010831068502739072,
-0.011047285981476307,
0.026056844741106033,
0.01908089779317379,
0.01639171503484249,
0.05836636573076248,
0.0035547844599932432,
-0.004916885867714882,
0.031229494139552116,
0.008104863576591015,
-0.02684980072081089,
0.02071012370288372,
0.005282410886138678,
-0.007911964319646358,
0.046680983155965805,
-0.014871226623654366,
0.01577494665980339,
-0.0063733248971402645,
-0.02634691447019577,
0.019252009689807892,
-0.014905974268913269,
0.020002514123916626,
0.032740797847509384,
0.041867274791002274,
-0.004483959171921015,
-0.029882486909627914,
-0.03396575525403023,
0.014532078057527542,
0.0745353102684021,
-0.06516853719949722,
-0.013425582088530064,
0.05317830294370651,
0.03843571990728378,
-0.04359879717230797,
-0.029734883457422256,
0.029101882129907608,
0.06183338537812233,
0.0027489063795655966,
0.007987692952156067,
-0.06011413037776947,
0.045053478330373764,
0.021818732842803,
0.003956454340368509,
0.0290848296135664,
-0.027005283161997795,
-0.00010280891001457348,
-0.05919506400823593,
0.010473370552062988,
-0.01108470093458891,
0.001384118222631514,
0.012196321971714497,
0.03925032541155815,
0.006896540522575378,
0.046516768634319305,
-0.037667009979486465,
0.009402136318385601,
-0.0581941157579422,
-0.019179819151759148,
-0.029714560136198997,
0.0016021467745304108,
-0.0461699441075325,
-0.03403355926275253,
-0.03828985244035721,
-0.011395181529223919,
-0.02300483174622059,
0.01426602527499199,
-0.020564064383506775,
-0.07352252304553986,
0.005459397565573454,
-0.034850820899009705,
-0.03507402166724205,
0.028482487425208092,
0.046123381704092026,
0.04585863649845123,
-0.008659915998578072,
0.010995293036103249,
0.009027413092553616,
-0.014978422783315182,
-0.03578910231590271,
-0.04192912206053734,
-0.012551943771541119,
0.014955801889300346,
-0.002680201316252351,
-0.06292930245399475,
0.009052790701389313,
-0.03275354579091072,
-0.0004528033605311066,
-0.001731137977913022,
0.056485194712877274,
-0.015952304005622864,
-0.005571379326283932,
-0.0557074137032032,
-0.030207376927137375,
-0.024877609685063362,
-0.022511299699544907,
0.0775117352604866,
0.007754824589937925,
0.036094002425670624,
0.04426063969731331,
0.0330740325152874,
-0.02710862271487713,
0.006389130372554064,
0.023117130622267723,
0.03149433061480522,
-0.016134975478053093,
-0.0478503555059433,
-0.03681252896785736,
-0.010868203826248646,
-0.01615167036652565,
-0.020129816606640816,
-0.008502710610628128,
-0.06011030077934265,
-0.01793408766388893,
0.013086732476949692,
-0.002558470005169511,
-0.04918811470270157,
0.0036615999415516853,
-0.03886260837316513,
0.0184380691498518,
-0.04000796750187874,
0.01965114288032055,
0.037213265895843506,
0.024952445179224014,
0.03812123090028763,
0.028964975848793983,
-0.000015888314010226168,
-0.04567098990082741,
0.019935941323637962,
0.03906496614217758,
0.02078726887702942,
-0.03657449781894684,
-0.023496953770518303,
-0.013092837296426296,
-0.02257598750293255,
-0.00952816754579544,
-0.026281457394361496,
0.02114344760775566,
-0.01869206875562668,
0.0060185459442436695,
-0.0009971045656129718,
-0.02303173579275608,
-0.053441524505615234,
-0.021795906126499176,
-0.011113941669464111,
0.034935321658849716,
0.01997990906238556,
-0.020778313279151917,
-0.024027051404118538,
0.03271319344639778,
0.009132631123065948,
0.006962039042264223,
-0.020524701103568077,
0.005119640380144119,
0.016615791246294975,
0.03593426197767258,
-0.049565911293029785,
-0.07777708768844604,
0.013651974499225616,
-0.01778329908847809,
-0.011976383626461029,
0.024784641340374947,
-0.05052589997649193,
-0.04727213829755783,
-0.0011450996389612556,
-0.02465403452515602,
0.0021284124813973904,
0.026748301461338997,
-0.007295642048120499,
0.02619159407913685,
0.023903371766209602,
0.009918329305946827,
0.0013921468053013086,
0.004145564511418343,
0.00659190071746707,
-0.059271205216646194,
-0.04929758235812187,
0.022584442049264908,
-0.015498443506658077,
0.0042226011864840984,
-0.012123006395995617,
-0.017405617982149124,
-0.06648889183998108,
0.055762216448783875,
0.039305780082941055,
0.004427981097251177,
-0.026073414832353592,
-0.04719637706875801,
0.007267194800078869,
0.022076120600104332,
0.006652184296399355,
0.00013234466314315796,
-0.0059993695467710495,
-0.006316513288766146,
-0.021775104105472565,
-0.022105131298303604,
0.0023806693498045206,
-0.04267625883221626,
0.02704276703298092,
0.04625259339809418,
0.017381178215146065,
0.031861983239650726,
-0.029012776911258698,
-0.02012665942311287,
-0.021151024848222733,
-0.04870819300413132,
0.021470144391059875,
-0.02683054842054844,
-0.002097790827974677,
0.004482101183384657,
-0.06545865535736084,
-0.01535312831401825,
-0.00033379337401129305,
-0.024979526177048683,
-0.012869587168097496,
-0.010743416845798492,
0.039140280336141586,
0.06910061836242676,
-0.017191024497151375,
-0.0343024842441082,
-0.0316031388938427,
-0.009453372098505497,
0.01220005564391613,
0.01274279598146677,
-0.014440195634961128,
0.03207709267735481,
-0.0017971015768125653,
-0.05116907134652138,
-0.019341370090842247,
0.03575283661484718,
-0.015870671719312668,
0.01851160079240799,
0.030260050669312477,
0.01563960500061512,
0.0373682864010334,
0.008890802040696144,
0.030512485653162003,
-0.01309018675237894,
-0.00966336764395237,
0.003167326096445322,
-0.014913862571120262,
0.009696709923446178,
-0.027951521798968315,
-0.0310783963650465,
0.00902475044131279,
-0.0075379908084869385,
0.06102596968412399,
-0.03866637125611305,
-0.00013731791113968939,
0.03212845325469971,
-0.010980874300003052,
-0.023786015808582306,
-0.012932948768138885,
-0.0057409051805734634,
0.0005945039447396994,
0.0023341139312833548,
0.0002239459427073598,
0.014837320894002914,
-0.010738474316895008,
-0.03551185131072998,
-0.00933130830526352,
0.02402818389236927,
-0.011072191409766674,
0.024897512048482895,
0.032940831035375595,
-0.028876926749944687,
-0.004520987626165152,
0.008833418600261211,
-0.017144031822681427,
-0.0002547937328927219,
0.04477943480014801,
-0.020268218591809273,
0.055166807025671005,
0.025253545492887497,
-0.020335115492343903,
0.006138884928077459,
0.007073136046528816,
0.0457078292965889,
0.06941202282905579,
-0.027138760313391685,
0.04121715575456619,
0.02420423924922943,
-0.007551600690931082,
0.006907641422003508,
-0.021297335624694824,
-0.0026125339791178703,
-0.018383841961622238,
0.02297228015959263,
0.041616737842559814,
-0.09088011085987091,
-0.03863608464598656,
0.050465963780879974,
0.03554478660225868,
-0.013909009285271168,
0.017291327938437462,
0.040285419672727585,
0.010863660834729671,
-0.005363970994949341,
0.026751656085252762,
-0.01450361032038927,
0.01425014715641737,
-0.03177772834897041,
0.00670303450897336,
0.03980095684528351,
-0.010981314815580845,
0.0195380300283432,
-0.005866587162017822,
0.0023810057900846004,
-0.03985898941755295,
-0.030657896772027016,
-0.0421149805188179,
0.006951129995286465,
0.015898708254098892,
0.014377848245203495,
-0.012420876882970333,
-0.03691660612821579,
0.027086451649665833,
0.015183881856501102,
0.027143053710460663,
-0.03227628022432327,
-0.01755553111433983,
-0.01580059714615345,
-0.020982712507247925,
-0.01675323210656643,
0.05559207499027252,
-0.015382030978798866,
0.02120438776910305,
0.01888960786163807,
-0.020448116585612297,
-0.03921043127775192,
-0.012462964281439781,
0.08586357533931732,
-0.015114321373403072,
0.03438268229365349,
0.01229074690490961,
0.0085249412804842,
-0.047402676194906235,
-0.012390587478876114,
0.14960302412509918,
0.030115144327282906,
0.02266737073659897,
-0.04479247331619263,
-0.006362403277307749,
-0.010842190124094486,
0.008138860575854778,
-0.004646135028451681,
0.025047415867447853,
-0.0024700670037418604,
0.002666216343641281,
0.05135652795433998,
0.024704517796635628,
0.007728665601462126,
0.04334106296300888,
0.036776453256607056,
-0.03556439280509949,
0.005740238353610039,
0.008011499419808388,
-0.002117546508088708,
-0.03267258033156395,
-0.0315047949552536,
-0.025213513523340225,
0.030033692717552185,
-0.0013562319800257683,
0.0203228946775198,
-0.011339766904711723,
-0.01385581586509943,
0.04965484142303467,
0.028578173369169235,
-0.02625386416912079,
0.0035010685678571463,
0.04937189817428589,
-0.01701613888144493,
0.005038328934460878,
0.02757234126329422,
0.026290735229849815,
-0.013888777233660221,
-0.04584495723247528,
0.028018668293952942,
0.05653858557343483,
0.007919004186987877,
-0.007702804170548916,
-0.004294386133551598,
-0.01112861093133688,
-0.029453136026859283,
-0.010701918974518776,
-0.002243918599560857,
0.03098025918006897,
0.011941678822040558,
-0.005939745344221592,
-0.007770721800625324,
0.027163490653038025,
-0.04265206307172775,
-0.008358820341527462,
0.02649339661002159,
-0.022716466337442398,
0.012049876153469086,
0.01852821744978428,
0.022185008972883224,
0.013668247498571873,
-0.019869647920131683,
0.009516413323581219,
-0.026482101529836655,
0.008522368036210537,
0.001472937292419374,
-0.012525949627161026,
0.03903242200613022,
0.024534104391932487,
-0.039261095225811005,
-0.027681216597557068,
0.0037192755844444036,
-0.03829880803823471,
0.02969781868159771,
0.005501675419509411,
0.020568327978253365,
0.011660750955343246,
-0.025146417319774628,
-0.005312505643814802,
-0.024378955364227295,
0.00628315843641758,
0.02084122970700264,
0.009510984644293785,
-0.015924865379929543,
-0.014684407971799374,
0.0029565810691565275,
0.031320326030254364,
0.028239509090781212,
-0.048070527613162994,
0.014310777187347412,
-0.00735468277707696,
0.06061163544654846,
-0.017437774688005447,
-0.016348998993635178,
-0.04794900119304657,
0.0062537845224142075,
-0.03673023357987404,
0.015874644741415977,
-0.01001233235001564,
0.008330262266099453,
0.04317454248666763,
0.03158196806907654,
-0.015573862008750439,
0.012730419635772705,
-0.04958449676632881,
0.006849382072687149,
0.05892280861735344,
-0.04123452305793762,
-0.024723518639802933,
0.03998958319425583,
-0.033150993287563324,
-0.027620242908596992,
-0.04586731642484665,
-0.0036399592645466328,
-0.042752910405397415,
0.050712067633867264,
0.014363027177751064,
-0.040541745722293854,
-0.013597000390291214,
0.00099582364782691,
0.047396160662174225,
-0.021047955378890038,
0.00475682970136404,
-0.06014082953333855,
-0.049984440207481384,
-0.01860327087342739,
0.021030021831393242,
-0.0022063858341425657,
0.004560453351587057,
-0.023682253435254097,
-0.013207195326685905,
0.02337234653532505,
0.04186348244547844,
-0.019461266696453094,
-0.0377117395401001,
0.019702039659023285,
0.021268628537654877,
0.01182064414024353,
0.008035354316234589,
-0.03975243493914604,
-0.013203676789999008,
-0.05196251720190048,
0.007353360299021006,
-0.03239612653851509,
-0.01103239320218563,
0.03213810175657272,
-0.008957707323133945,
-0.00799343641847372,
-0.039155762642621994,
0.040204890072345734,
-0.04810978099703789,
-0.045478928834199905,
0.021280162036418915,
-0.03354135528206825,
0.0026012109592556953,
0.01745591126382351,
-0.011586225591599941,
-0.007410258986055851,
-0.05237845331430435,
0.015677455812692642,
-0.004600741900503635,
0.044823385775089264,
-0.024078642949461937,
0.013102548196911812,
0.03859681263566017,
0.016066445037722588,
0.014672238379716873,
-0.010317088104784489,
0.014672822318971157,
0.047992780804634094,
-0.02220015414059162,
0.03285519778728485,
-0.006409694906324148,
-0.0052544185891747475,
-0.036120958626270294,
-0.00982582662254572,
0.011478977277874947,
-0.020217660814523697,
0.019850200042128563,
-0.016756368800997734,
-0.009597460739314556,
-0.015147273428738117,
-0.03221069276332855,
0.014758586883544922,
-0.022090274840593338,
-0.06063275411725044,
-0.05211037024855614,
-0.00008967435860540718,
-0.048887450248003006,
0.050564300268888474,
-0.0028522200882434845,
0.047220490872859955,
-0.022495971992611885,
0.014738236553966999,
-0.04459862783551216,
-0.025860337540507317,
-0.004729068372398615,
0.029355140402913094,
-0.026179397478699684,
-0.01784111000597477,
0.07914930582046509,
-0.006798376329243183,
0.009366383776068687,
0.04445505514740944,
-0.024771837517619133,
0.0044867731630802155,
0.032428350299596786,
0.010193759575486183,
0.022926805540919304,
-0.023060781881213188,
0.008335733786225319,
-0.01870822347700596,
-0.04192870110273361,
0.014510187320411205,
0.00563999405130744,
-0.00516936182975769,
-0.018848204985260963,
-0.014062270522117615,
0.015444225631654263,
-0.01927630417048931,
-0.01901262067258358,
-0.0030524597968906164,
-0.05408326908946037,
0.009698488749563694,
-0.056784775108098984,
0.031794991344213486,
0.019103655591607094,
-0.05938400700688362,
0.020835962146520615,
-0.020884739235043526,
-0.016163216903805733,
0.055144116282463074,
0.004377846140414476,
-0.01243844535201788,
0.05768904834985733,
-0.007175405975431204,
-0.009213904850184917,
0.03155309706926346,
0.03076307661831379,
-0.025219881907105446,
-0.019460584968328476,
0.02522461488842964,
0.019785134121775627,
0.01840442605316639,
0.014541300013661385,
-0.0325113944709301,
-0.035812098532915115,
0.006188110448420048,
0.032192498445510864,
0.05363428592681885,
-0.025098025798797607,
-0.03376084193587303,
-0.0031443829648196697,
-0.06806404143571854,
0.07938668876886368,
0.0025624006520956755,
0.036525219678878784,
-0.045801084488630295,
-0.034493234008550644,
0.005068856291472912,
0.031295958906412125,
0.08361142128705978,
-0.03409988060593605,
-0.0076050469651818275,
-0.016409173607826233,
0.05980435758829117,
-0.000833216414321214,
0.006485222838819027,
-0.005603346042335033,
0.011762382462620735,
-0.01805826462805271,
0.023025663569569588,
-0.030510803684592247,
0.0027875674422830343,
0.011183662340044975,
0.014876565895974636,
-0.01738564297556877,
0.019877050071954727,
-0.008774376474320889,
-0.034251485019922256,
0.004517560824751854,
-0.01859540492296219,
-0.002518477849662304,
0.07257594168186188,
0.015520614571869373,
0.0015022201696410775,
0.01192263513803482,
-0.03352504223585129,
-0.030125200748443604,
0.040012214332818985,
-0.001965075032785535,
-0.008158865384757519,
-0.07665620744228363,
0.0028350655920803547,
0.04694323614239693,
-0.038554079830646515,
-0.011506916955113411,
-0.01648382842540741,
-0.0222596637904644,
-0.014053033664822578,
0.04326458275318146,
0.004151165951043367,
-0.007547674234956503,
-0.02070228010416031,
-0.004183188080787659,
0.007612921297550201,
-0.04469085857272148,
0.02842804044485092,
0.0061410763300955296,
0.019873306155204773,
0.019788894802331924,
-0.01254761591553688,
0.028605539351701736,
-0.033468447625637054,
0.04006946086883545,
-0.02765100635588169,
0.030555743724107742,
0.004348713904619217,
-0.004521594382822514,
-0.013635746203362942,
-0.017931988462805748,
0.046953942626714706,
0.031101670116186142,
-0.04871859773993492,
0.07180515676736832,
0.028232572600245476,
-0.0010580728994682431,
-0.022666361182928085,
0.018703768029808998,
0.02707516960799694,
-0.012771833688020706,
0.0674387663602829,
0.02816273272037506,
0.03096708469092846,
-0.002148107159882784,
-0.042561937123537064,
-0.006434047594666481,
0.06923808157444,
0.04948975518345833,
0.0187373086810112,
-0.006137327291071415,
0.01927945390343666,
-0.008513321168720722,
-0.0272729080170393,
-0.024404659867286682,
-0.03797703608870506,
0.0398162417113781,
-0.0008059543906711042,
0.014579291455447674,
0.002051427960395813,
-0.018638715147972107,
0.0011957132956013083,
0.025896690785884857,
-0.07481346279382706,
-0.005125583149492741,
-0.02089715376496315,
-0.005200328771024942,
0.023496314883232117,
0.033363934606313705
] |
<p>How do surfaces reflect certain colours and absorb the others?</p> | 1,434 | [
-0.05226779356598854,
-0.049572911113500595,
0.01436906959861517,
-0.001446818350814283,
0.026260729879140854,
0.020190158858895302,
-0.022711394354701042,
-0.007814054377377033,
-0.006648275535553694,
-0.02316158451139927,
0.024798953905701637,
0.04158269613981247,
0.040712326765060425,
0.024140218272805214,
0.016027212142944336,
0.005770387593656778,
0.017767636105418205,
-0.007905146107077599,
-0.026602676138281822,
-0.011190297082066536,
-0.0021641638595610857,
0.010480077937245369,
0.031496401876211166,
0.029996054247021675,
-0.04443691670894623,
0.0011501506669446826,
0.03137395903468132,
-0.00976170226931572,
0.047851257026195526,
0.03905387967824936,
0.004010795149952173,
-0.0050365799106657505,
-0.00411986093968153,
0.03141782432794571,
-0.003064436838030815,
-0.01792636141180992,
-0.01807466708123684,
-0.026513366028666496,
-0.04375132918357849,
0.0042214649729430676,
-0.006978084333240986,
-0.031192824244499207,
-0.011799564585089684,
0.028182685375213623,
0.008285378105938435,
-0.02229168266057968,
-0.03988579660654068,
-0.03459146246314049,
0.028719360008835793,
-0.08590821921825409,
0.04775502160191536,
0.002622210653498769,
0.055828455835580826,
0.03721274062991142,
-0.004985196050256491,
0.018426405265927315,
0.07348328828811646,
0.07724271714687347,
-0.02975447289645672,
-0.019761331379413605,
0.023051127791404724,
-0.0036991662345826626,
-0.028590574860572815,
-0.01029236614704132,
-0.04272682964801788,
0.02638869360089302,
0.022216729819774628,
-0.043762777000665665,
0.04241294041275978,
0.02925543487071991,
-0.009507003240287304,
0.015760233625769615,
0.02812810242176056,
-0.00814267247915268,
-0.0020941123366355896,
-0.05180210620164871,
0.01574627123773098,
0.03975251689553261,
0.044708412140607834,
0.014275428839027882,
0.019505642354488373,
0.009836304001510143,
-0.013948428444564342,
0.015262113884091377,
-0.005345884244889021,
-0.0016249482287093997,
0.08281872421503067,
-0.008442137390375137,
0.002593298675492406,
0.01745266653597355,
0.007677214685827494,
-0.0013243787689134479,
0.029504941776394844,
0.011093742214143276,
-0.010644570924341679,
-0.008057408034801483,
-0.02100607566535473,
0.04224955663084984,
-0.004605666268616915,
0.002666217042133212,
0.0021208846010267735,
0.015979118645191193,
0.018267828971147537,
0.04163629934191704,
0.011516522616147995,
0.007932175882160664,
-0.030628688633441925,
0.047604385763406754,
0.0274326354265213,
0.021606039255857468,
-0.01585460640490055,
0.006993875373154879,
-0.0026754499413073063,
-0.022988982498645782,
0.009992714039981365,
-0.01648172177374363,
0.025363557040691376,
-0.030704816803336143,
0.0527275949716568,
0.08838293701410294,
-0.03678106889128685,
-0.023548142984509468,
0.004661266226321459,
0.01212287787348032,
-0.08130274713039398,
0.055242154747247696,
0.022484639659523964,
-0.035069357603788376,
-0.02869112603366375,
-0.01569877751171589,
-0.017490413039922714,
-0.050373949110507965,
-0.0024940315634012222,
0.011646062135696411,
-0.026821739971637726,
-0.009436864405870438,
-0.11390504986047745,
-0.06355097144842148,
-0.001329303253442049,
-0.0019948116969317198,
-0.016847454011440277,
-0.04567281901836395,
-0.0011979863047599792,
0.034290723502635956,
0.07107645273208618,
-0.0052929832600057125,
-0.0032298893202096224,
0.013476460240781307,
0.010689878836274147,
-0.004626478999853134,
-0.0022833081893622875,
-0.0060460311360657215,
0.004454733803868294,
-0.020709186792373657,
0.011208910495042801,
-0.05417559668421745,
0.022038741037249565,
0.03275084123015404,
0.005025574006140232,
-0.038296326994895935,
0.047296300530433655,
-0.011353264562785625,
-0.003925886936485767,
0.03893924877047539,
0.012516760267317295,
-0.030864935368299484,
0.08106119185686111,
0.013350802473723888,
0.03329182043671608,
0.036883529275655746,
-0.019725680351257324,
-0.00027789335581474006,
0.0015069672372192144,
0.05983611196279526,
-0.001969598699361086,
-0.013890741392970085,
0.003133464138954878,
0.016933832317590714,
0.017184918746352196,
-0.017072366550564766,
-0.04081611707806587,
-0.03494282439351082,
0.021517878398299217,
0.029142672196030617,
0.038327060639858246,
0.04478513449430466,
0.004383980296552181,
-0.05136572942137718,
-0.013015317730605602,
-0.05404415726661682,
-0.01488738227635622,
-0.043512973934412,
0.029161741957068443,
-0.001829030574299395,
0.006851439364254475,
0.010296173393726349,
0.020104905590415,
-0.008213148452341557,
-0.028139643371105194,
-0.03441542387008667,
-0.009212857112288475,
0.014033114537596703,
0.04163442924618721,
-0.0014197303680703044,
-0.01674973964691162,
0.08304678648710251,
0.04209013655781746,
-0.0014991690404713154,
0.05339184030890465,
-0.04193887487053871,
-0.025047479197382927,
0.01201293058693409,
-0.004292335826903582,
0.04134949669241905,
-0.01579524576663971,
-0.03460693359375,
0.016642360016703606,
0.04482490196824074,
-0.044846780598163605,
0.023328937590122223,
-0.012730421498417854,
0.07517953217029572,
0.007289276458323002,
-0.019445158541202545,
-0.000797231390606612,
0.04028630629181862,
0.009024064987897873,
0.007704216055572033,
0.010650835931301117,
-0.032820168882608414,
-0.03911985456943512,
-0.022143324837088585,
0.02580120414495468,
0.012517789378762245,
-0.03272804990410805,
0.004732074216008186,
-0.015437936410307884,
0.0718533843755722,
0.03532879799604416,
0.021916184574365616,
-0.0020775680895894766,
-0.0016970837023109198,
0.020853569731116295,
-0.01599336601793766,
-0.002191553357988596,
0.020386528223752975,
0.0024089692160487175,
0.01939830742776394,
0.035220760852098465,
-0.04736129939556122,
-0.027637239545583725,
0.03687293827533722,
-0.0011135762324556708,
0.019746210426092148,
0.005762620363384485,
-0.019633138552308083,
0.004925582557916641,
-0.026330919936299324,
-0.01618708111345768,
0.007809516042470932,
0.011324812658131123,
-0.007004837039858103,
-0.021731441840529442,
-0.016744205728173256,
0.03194180876016617,
0.002727511804550886,
-0.010621313005685806,
0.017257532104849815,
0.041093192994594574,
-0.01893388107419014,
0.021991416811943054,
-0.008745674043893814,
-0.02301536127924919,
-0.030150383710861206,
-0.002863717032596469,
0.0025306104216724634,
-0.0003332415653858334,
0.034193068742752075,
-0.05847684293985367,
-0.05142206326127052,
-0.01520453579723835,
-0.01728604920208454,
-0.0021791383624076843,
-0.0047935969196259975,
-0.04350726306438446,
0.030202582478523254,
-0.04887370765209198,
-0.02406821772456169,
0.017422130331397057,
-0.03934983164072037,
-0.020705297589302063,
-0.009478773921728134,
-0.026154030114412308,
-0.03033410757780075,
-0.015915971249341965,
-0.002850896678864956,
0.007368287071585655,
-0.021345125511288643,
0.008157075382769108,
0.02748112753033638,
-0.006115039344877005,
-0.018505550920963287,
0.01861678436398506,
-0.013139348477125168,
-0.054241519421339035,
0.007071883417665958,
-0.015461702831089497,
0.008738846518099308,
-0.027972565963864326,
-0.03067627176642418,
0.052612513303756714,
-0.05806427448987961,
0.007073314394801855,
-0.0035203935112804174,
-0.03897508233785629,
0.01519996952265501,
-0.0038586196023970842,
0.047469884157180786,
-0.02804531529545784,
0.03770091012120247,
0.05201418697834015,
0.01630675606429577,
-0.001062197727151215,
-0.003063873155042529,
-0.015585724264383316,
-0.023957138881087303,
-0.038801610469818115,
0.055247917771339417,
0.057469286024570465,
-0.04311618208885193,
0.02720070444047451,
-0.009784418158233166,
-0.00831986777484417,
0.05938298627734184,
0.013887081295251846,
-0.029885167255997658,
-0.0030942584853619337,
-0.014417095109820366,
-0.0148425018414855,
0.013308536261320114,
0.03327257186174393,
-0.03672396019101143,
0.018194150179624557,
0.007200529333204031,
0.03323884308338165,
0.02073167823255062,
-0.023404711857438087,
0.061158474534749985,
-0.04010730981826782,
0.021264981478452682,
-0.029818464070558548,
0.06181004270911217,
0.003672022605314851,
-0.00009044485341291875,
-0.0015421333955600858,
0.026206398382782936,
0.05579571798443794,
-0.01592494733631611,
-0.017189353704452515,
0.04265708476305008,
0.056147489696741104,
-0.027266407385468483,
-0.010243125259876251,
-0.01390224788337946,
-0.01841709204018116,
0.03261410444974899,
-0.028468843549489975,
0.013398189097642899,
0.06803557276725769,
0.05938039347529411,
0.03534255176782608,
0.02455415576696396,
-0.03861040994524956,
-0.026680370792746544,
-0.09836412221193314,
0.016381438821554184,
0.008909137919545174,
0.04663081839680672,
-0.005651387386023998,
0.057908110320568085,
0.026287727057933807,
0.03288322687149048,
0.0041901422664523125,
0.025977108627557755,
-0.0788922980427742,
0.001485459040850401,
-0.01672375574707985,
0.0027764630503952503,
-0.05024555325508118,
-0.03991013020277023,
0.009619480930268764,
-0.02470833994448185,
-0.030999237671494484,
-0.027206527069211006,
-0.013405140489339828,
-0.033425167202949524,
0.007378981914371252,
-0.022227749228477478,
-0.057887159287929535,
-0.005518011748790741,
0.04549961909651756,
0.013633044436573982,
0.0010801964672282338,
0.03944046050310135,
0.02410910464823246,
-0.03172390162944794,
-0.00021743115212302655,
-0.015835659578442574,
0.02806236781179905,
0.027163460850715637,
0.0381765142083168,
0.013585131615400314,
0.033498264849185944,
-0.021948715671896935,
0.0027987754438072443,
-0.03867952525615692,
0.050341926515102386,
-0.005180681589990854,
-0.04061434790492058,
-0.0042077768594026566,
-0.06414283812046051,
-0.025140533223748207,
-0.010078766383230686,
0.052901335060596466,
-0.058059386909008026,
-0.008759334683418274,
0.023124970495700836,
0.003229164984077215,
-0.04516366869211197,
0.02153712697327137,
0.002298020990565419,
0.0345093235373497,
-0.028136184439063072,
-0.012094889767467976,
-0.0028241609688848257,
-0.04398315027356148,
0.03239389881491661,
0.0007166930590756238,
0.015218657441437244,
-0.020771300420165062,
0.017209157347679138,
0.02636696770787239,
-0.013877157121896744,
-0.021294424310326576,
-0.033945124596357346,
-0.005676069762557745,
0.0032139713875949383,
-0.024154899641871452,
0.0031947854440659285,
-0.01629713736474514,
0.044763967394828796,
0.03689025714993477,
-0.015604165382683277,
-0.033937614411115646,
-0.07862108945846558,
-0.02449093386530876,
0.034823451191186905,
0.004135125782340765,
-0.013711010105907917,
-0.01869218237698078,
-0.048612434417009354,
-0.003302992321550846,
0.03475254029035568,
-0.025560487061738968,
0.031838614493608475,
-0.03987126797437668,
-0.01239293534308672,
-0.061327967792749405,
0.005756792612373829,
0.005780603736639023,
0.034406065940856934,
0.008563226088881493,
0.018512113019824028,
0.0017553551588207483,
-0.004964013118296862,
-0.034275516867637634,
0.03998468816280365,
-0.0006651157746091485,
0.014366434887051582,
-0.014394351281225681,
0.027877502143383026,
-0.000528756296262145,
0.019178327172994614,
-0.04645741730928421,
-0.08209145069122314,
0.009742115624248981,
0.027042921632528305,
0.006640252657234669,
0.06537793576717377,
-0.021639196202158928,
-0.03170948475599289,
0.03383053466677666,
0.011169901117682457,
-0.019421566277742386,
-0.0075552696362137794,
-0.039677828550338745,
0.011311282403767109,
0.03825128450989723,
-0.016973624005913734,
0.06187098100781441,
0.03236550837755203,
-0.049053896218538284,
-0.021774381399154663,
0.0039525022730231285,
0.04856714978814125,
-0.026047805324196815,
-0.022268226370215416,
0.019113656133413315,
-0.02929014526307583,
-0.02794841304421425,
0.024545716121792793,
0.024825923144817352,
0.00243236031383276,
0.006957520730793476,
-0.08194202184677124,
-0.04155787080526352,
-0.0057340445928275585,
0.017817679792642593,
0.006680838298052549,
0.022449329495429993,
0.009499241597950459,
0.02833334170281887,
-0.005242600571364164,
0.031990718096494675,
0.016551779583096504,
-0.0071892039850354195,
-0.005225769244134426,
0.01172571163624525,
0.005797445308417082,
-0.059440191835165024,
-0.001842457801103592,
-0.02713288925588131,
-0.024456778541207314,
0.07605322450399399,
-0.01819385588169098,
0.03999468311667442,
0.034319423139095306,
-0.05941121652722359,
0.003396834945306182,
0.00043841745355166495,
-0.018401550129055977,
0.0371733196079731,
-0.0384327694773674,
0.05748991295695305,
0.03262592479586601,
-0.012112567201256752,
-0.06467046588659286,
-0.019512193277478218,
0.015795046463608742,
0.06439025700092316,
-0.010419822297990322,
-0.03390777111053467,
0.02195107750594616,
-0.009799774736166,
-0.03230924904346466,
0.013062626123428345,
0.004613874014467001,
-0.05283493921160698,
-0.00908700656145811,
0.00829438678920269,
0.003757802303880453,
0.050236549228429794,
-0.006037569604814053,
0.00035242195008322597,
0.0016081474022939801,
-0.049404166638851166,
-0.0009418679983355105,
-0.01879010535776615,
0.0271451473236084,
-0.01740034483373165,
-0.013523821718990803,
-0.009772776626050472,
0.025444189086556435,
0.05580679327249527,
-0.021872347220778465,
0.031170982867479324,
0.019396841526031494,
0.034360580146312714,
-0.04720081016421318,
-0.045379042625427246,
0.035204578191041946,
0.007156607694923878,
0.035419393330812454,
-0.006009203847497702,
0.002308009658008814,
-0.014891061931848526,
-0.01849057711660862,
0.03786351904273033,
-0.006396116688847542,
0.015328807756304741,
0.004488724749535322,
0.10355795174837112,
-0.032940544188022614,
0.00014597039262298495,
0.003125397954136133,
-0.027852831408381462,
0.023235490545630455,
-0.013936863280832767,
0.002351603005081415,
0.01759849488735199,
0.009190971031785011,
-0.002068666974082589,
-0.009988255798816681,
-0.011581605300307274,
-0.039242345839738846,
0.024320457130670547,
-0.03317384421825409,
0.06647810339927673,
0.029420318081974983,
-0.011590148322284222,
-0.013109915889799595,
-0.023036867380142212,
-0.02938919886946678,
-0.008743252605199814,
-0.014296375215053558,
0.054736893624067307,
-0.009521126747131348,
0.039687059819698334,
-0.018967105075716972,
0.04321125149726868,
0.01365644857287407,
0.009387897327542305,
0.02903890423476696,
0.03509565070271492,
0.01839018613100052,
-0.01683533564209938,
-0.037532296031713486,
0.030259549617767334,
-0.0347764752805233,
0.006009658798575401,
-0.0026085618883371353,
-0.024533702060580254,
0.04373561218380928,
-0.015301571227610111,
-0.0018544476479291916,
-0.02377721481025219,
-0.015728618949651718,
-0.02201729081571102,
0.008424034342169762,
0.00988202728331089,
0.04911654815077782,
-0.02078641951084137,
-0.007690215948969126,
0.007270541042089462,
0.00795533787459135,
0.010488790459930897,
-0.012336467392742634,
-0.06451859325170517,
-0.027378881350159645,
-0.04494804888963699,
-0.026497958227992058,
0.03995503485202789,
-0.009137118235230446,
-0.009754207916557789,
0.032752469182014465,
-0.061165641993284225,
0.021606016904115677,
-0.005888449959456921,
0.012953457422554493,
-0.03485725447535515,
0.007408662233501673,
0.013610517606139183,
0.03858619183301926,
0.0035277139395475388,
-0.007413817103952169,
0.116227887570858,
0.07636432349681854,
0.02207125723361969,
-0.074039027094841,
-0.008522714488208294,
-0.0250245314091444,
-0.010119855403900146,
-0.019499128684401512,
0.0408761203289032,
-0.018756819888949394,
0.057754822075366974,
-0.016854332759976387,
0.0391390398144722,
0.016042187809944153,
0.00257380330003798,
0.01889215223491192,
-0.03678888827562332,
-0.007332472130656242,
0.022994887083768845,
-0.022642772644758224,
-0.015852326527237892,
0.0587734580039978,
-0.06765686720609665,
0.005752929020673037,
-0.019844524562358856,
-0.010163813829421997,
-0.030577974393963814,
-0.0479801781475544,
0.016457198187708855,
0.01901628077030182,
-0.038515880703926086,
0.04190078005194664,
0.015855172649025917,
-0.011636868119239807,
-0.0321025587618351,
0.040037136524915695,
0.05752110108733177,
-0.007488594390451908,
0.015847699716687202,
-0.012591462582349777,
0.023146381601691246,
-0.0022001611068844795,
-0.0032482545357197523,
0.016313331201672554,
-0.059811804443597794,
0.004372823517769575,
-0.04702330380678177,
0.017500856891274452,
-0.049226563423871994,
0.017403194680809975,
-0.0009593887953087687,
-0.01077767089009285,
-0.014282787218689919,
-0.028301317244768143,
-0.015156678855419159,
0.0006983282510191202,
0.023823067545890808,
-0.020619282498955727,
-0.04299740865826607,
0.013634266331791878,
0.01840469054877758,
-0.021463245153427124,
0.015053593553602695,
0.02335994690656662,
0.001817982061766088,
0.010346774943172932,
-0.005613613408058882,
0.020924942567944527,
0.03914080560207367,
-0.050593528896570206,
-0.01460306067019701,
0.002972295507788658,
-0.024570444598793983,
-0.04312882199883461,
-0.004517680034041405,
0.031905364245176315,
0.019204625859856606,
-0.002558582928031683,
-0.029272858053445816,
-0.0177511814981699,
-0.08027084171772003,
0.047557976096868515,
-0.026014653965830803,
-0.007991212420165539,
-0.047458749264478683,
-0.027868151664733887,
0.06860989332199097,
0.004942313767969608,
-0.008464866317808628,
0.024977635592222214,
-0.028111113235354424,
0.010885175317525864,
0.010299552232027054,
-0.0012189343106001616,
-0.013874388299882412,
0.025789877399802208,
-0.03142150118947029,
-0.01683288998901844,
-0.0017655782867223024,
0.05503994971513748,
0.013813639059662819,
0.01383732259273529,
0.03517591580748558,
0.01892748847603798,
-0.04459156468510628,
-0.022604890167713165,
-0.015525002032518387,
-0.026978136971592903,
-0.0051792762242257595,
0.0008622657041996717,
-0.0007046379032544792,
-0.014769390225410461,
-0.042748063802719116,
-0.018870484083890915,
-0.02298213727772236,
0.029627161100506783,
0.036568187177181244,
0.023084554821252823,
-0.00710411136969924,
-0.007522206287831068,
0.04753733053803444,
-0.01931607723236084,
-0.02909468114376068,
-0.07455460727214813,
0.009656604379415512,
-0.01880263350903988,
-0.006646597757935524,
-0.022001367062330246,
0.022639360278844833,
-0.004590157885104418,
-0.006262950133532286,
0.02940862998366356,
0.015086822211742401,
0.01081984955817461,
0.023699941113591194,
0.028211236000061035,
0.00837286189198494,
0.05361063778400421,
0.002757900394499302,
-0.03733439743518829,
0.05206580087542534,
-0.03172807767987251,
-0.052279453724622726,
0.010524950921535492,
-0.038022950291633606,
0.04587317258119583,
0.016032082960009575,
0.0018886716570705175,
-0.006110808812081814,
0.023180736228823662,
-0.014295581728219986,
-0.04034581035375595,
-0.021305322647094727,
0.0011588726192712784,
0.04492073878645897,
0.001416657818481326,
0.02198146842420101,
-0.03475511074066162,
-0.016853487119078636,
0.056329820305109024,
-0.025545194745063782,
-0.01955977827310562,
0.017941951751708984,
-0.014822328463196754,
-0.025560088455677032,
0.030518783256411552,
0.038792163133621216,
-0.0282603669911623,
0.010369799099862576,
-0.00927239190787077,
-0.018189039081335068,
0.05227680876851082,
0.027965065091848373,
-0.03949160501360893,
-0.08094983547925949,
0.031850118190050125,
0.0007922768127173185,
-0.009751697070896626,
0.0581238828599453,
-0.055120620876550674,
0.05254339426755905,
0.04970371350646019,
-0.0973707064986229,
0.017820827662944794,
0.007545532193034887,
-0.03038679249584675,
-0.01508620660752058,
0.06186596304178238,
-0.008430222049355507,
0.01115687470883131,
0.009855348616838455,
0.039929989725351334,
0.018661845475435257,
0.0275711826980114,
-0.012704773806035519,
0.0009534199489280581,
-0.011229477822780609,
0.00825938768684864,
-0.022990185767412186,
-0.0065752482041716576,
0.05515875667333603,
0.008168221451342106,
0.0073451995849609375,
-0.002475823275744915,
-0.01509831752628088,
0.018257707357406616,
-0.013186020776629448,
-0.022091804072260857,
0.016883816570043564,
-0.016298219561576843,
0.0005647491780109704,
0.0021825158037245274,
-0.02435358799993992,
0.020174600183963776,
0.039515212178230286,
0.03769955411553383,
0.016847243532538414,
0.0036953396629542112,
0.011134197935461998,
-0.04965783283114433,
-0.027145961299538612,
-0.013063742779195309,
-0.005446135066449642,
-0.010823492892086506,
0.03511492908000946,
0.027035487815737724,
0.057399727404117584,
-0.0013960929354652762,
-0.01861228235065937,
-0.06771016120910645,
-0.006342810578644276,
-0.018497474491596222,
0.014139189384877682,
0.022775879129767418,
0.04600656405091286,
-0.020794972777366638,
-0.004319360014051199,
-0.022444000467658043,
0.012516901828348637,
0.004812703933566809,
0.0015417026588693261,
0.010511566884815693,
0.04759566858410835,
-0.010862440802156925,
-0.009738361462950706,
0.004509886261075735,
-0.043556902557611465,
0.00412323884665966,
0.010250400751829147,
0.010964732617139816,
-0.01379311177879572,
-0.09016978740692139,
-0.03326667472720146,
-0.03502494841814041,
0.061377283185720444,
-0.030428512021899223,
-0.04945617541670799,
-0.0392288975417614,
0.003917705733329058,
-0.013429270125925541,
0.05041418969631195,
0.0639658197760582,
-0.02607913315296173,
-0.029144233092665672,
-0.01959255151450634,
0.03635596111416817,
0.06914574652910233,
-0.015125048346817493,
0.04992061108350754,
-0.0008465473656542599,
-0.009614250622689724,
-0.022738009691238403,
-0.027701864019036293,
-0.001713588833808899,
0.02280338853597641,
0.012515151873230934,
-0.008001611568033695,
0.010215467773377895,
-0.004104111809283495,
-0.036373768001794815,
0.07587683945894241,
0.01673489436507225,
-0.042971182614564896,
0.06932837516069412,
-0.001106488169170916,
0.010551831685006618,
0.01805572398006916,
0.0031828635837882757,
-0.06368842720985413,
0.016902631148695946,
-0.025494791567325592,
-0.012802811339497566,
-0.015702104195952415,
-0.01889605075120926,
0.02632269077003002,
-0.03569837287068367,
0.03044656105339527,
0.01278667151927948,
-0.0020672567188739777,
-0.023238571360707283,
0.06615104526281357,
-0.016562072560191154,
0.021475227549672127,
-0.0026251671370118856,
0.006819528993219137,
0.011801585555076599,
-0.001007374026812613,
-0.048512887209653854,
0.03871767222881317,
0.016188759356737137,
0.004887139890342951,
0.014347659423947334,
0.049747928977012634,
0.005980122834444046,
0.01194662693887949,
0.012731747701764107,
0.027498751878738403,
-0.02181745506823063,
-0.006398462690412998,
0.01244848221540451,
0.0079067787155509,
-0.013980850577354431,
0.012581611052155495,
-0.019765574485063553,
0.11465199291706085,
-0.04006365314126015,
0.027700025588274002,
-0.01584658771753311,
0.009230013936758041,
-0.020983221009373665,
-0.008480515331029892,
0.04004870355129242,
0.032685309648513794,
0.0009644983219914138,
-0.03476335108280182,
-0.03894811123609543,
0.02538660354912281,
0.03544639050960541,
-0.03949340805411339,
0.06696956604719162,
0.001906110206618905,
-0.008619752712547779,
-0.0024585057981312275,
0.02478446066379547,
0.017139816656708717,
-0.009071877226233482,
0.0148641811683774,
0.029098503291606903,
-0.001716665574349463,
0.029891664162278175,
0.014148252084851265,
-0.03273748233914375,
0.038948170840740204,
-0.10044177621603012,
-0.032885946333408356,
0.0035582564305514097,
0.008486272767186165,
-0.012901314534246922,
-0.026279868558049202
] |
<p>Consider infinitely many distinguishable observers, no two of whom ever meet; and who generally "keep sight of each other", but not necessarily "each keeping sight of all others".<br>
How should they determine whether or not they can be described as being "defined on a Lorentzian manifold"?</p>
<p>[This question refers to terminology of <a href="http://en.wikipedia.org/wiki/Frame_fields_in_general_relativity" rel="nofollow">http://en.wikipedia.org/wiki/Frame_fields_in_general_relativity</a> and is meant as follow-up to <a href="http://physics.stackexchange.com/questions/69303/whats-a-noninertial-frame">that question</a>; in the attempt to ask perhaps more originally.]</p>
<p><strong>Edit</strong><br>
The phrase "defined on a Lorentzian manifold" appears a very general condition. </p>
<p>To be more specific consider instead the question:<br>
"How should the given observers determine whether or not some subset of the entirety of events in which they (separately) participated can be described as "open set of a 3+1 dimensional Lorentzian manifold"?</p> | 1,435 | [
-0.006286723539233208,
-0.00810396857559681,
0.009390773251652718,
-0.013647187501192093,
0.03826078772544861,
0.010415749624371529,
-0.043969254940748215,
-0.0342896394431591,
-0.013188465498387814,
-0.011657637543976307,
0.009390352293848991,
0.014109678566455841,
0.049247242510318756,
0.03224319592118263,
0.006685284432023764,
-0.027149073779582977,
0.007945659570395947,
0.013680092059075832,
-0.03098321333527565,
-0.08650472015142441,
0.03199353069067001,
0.01993371918797493,
0.02020123414695263,
-0.030138377100229263,
-0.057969238609075546,
0.015830913558602333,
0.005761692300438881,
-0.014250229112803936,
0.030960289761424065,
0.052920151501894,
-0.04633750021457672,
-0.04762189835309982,
-0.00522855669260025,
0.016749341040849686,
0.034104444086551666,
0.006513896863907576,
-0.044288668781518936,
-0.0013066205428913236,
0.01545743178576231,
-0.02295871637761593,
-0.04371242970228195,
-0.009985501877963543,
-0.027609819546341896,
0.04074779152870178,
-0.0357523076236248,
0.014343908987939358,
0.01246111374348402,
0.0007901671342551708,
0.05052856728434563,
-0.048124223947525024,
0.04151356965303421,
0.0006563757197000086,
0.03816314414143562,
-0.017385493963956833,
-0.01040611695498228,
-0.0006078536389395595,
0.05491321533918381,
0.07602694630622864,
-0.000040089540561893955,
-0.028948595747351646,
-0.039023060351610184,
0.0020704511553049088,
0.02562868595123291,
-0.012563323602080345,
0.0008651535608805716,
0.05190848186612129,
-0.0033078109845519066,
-0.0057839080691337585,
0.03026757575571537,
-0.015038604848086834,
-0.021407440304756165,
-0.004876077640801668,
0.02053629234433174,
-0.021280203014612198,
0.006725311744958162,
-0.006046418100595474,
0.016781847923994064,
-0.02028229460120201,
0.0422254353761673,
0.020994601771235466,
-0.006249719765037298,
-0.02658606693148613,
0.013756186701357365,
-0.016430336982011795,
0.036557696759700775,
-0.021684054285287857,
0.06214621663093567,
0.01634788326919079,
0.0013202157570049167,
0.03627325966954231,
0.00524326553568244,
-0.025761637836694717,
0.021877706050872803,
-0.010511049069464207,
-0.03744279593229294,
0.03700239211320877,
-0.020578697323799133,
0.03683428838849068,
0.002451537409797311,
-0.02179311215877533,
-0.02935841679573059,
-0.058936700224876404,
0.01908373273909092,
0.06173983961343765,
0.0030775878112763166,
0.009580147452652454,
-0.0297614187002182,
0.02295859530568123,
-0.03470276668667793,
-0.02432633377611637,
-0.03166056051850319,
0.050371769815683365,
0.006354534067213535,
0.02529112622141838,
0.0066694398410618305,
-0.030467655509710312,
0.006237782072275877,
0.0013765529729425907,
0.03736088052392006,
0.09507111459970474,
0.055564701557159424,
-0.015422787517309189,
-0.0422574058175087,
-0.014227431267499924,
-0.08106881380081177,
0.0377543568611145,
0.036743246018886566,
0.006101945880800486,
0.004068824462592602,
-0.007452039979398251,
-0.011844267137348652,
0.0012665529502555728,
0.016851991415023804,
0.029905501753091812,
0.013471134938299656,
-0.04705879092216492,
-0.11268147826194763,
-0.05780994892120361,
0.050989970564842224,
0.03605818375945091,
-0.024865875020623207,
-0.08078670501708984,
0.00017292395932599902,
0.03730062022805214,
0.066139355301857,
-0.022704144939780235,
-0.004884599708020687,
0.030186530202627182,
0.027104202657938004,
-0.012446848675608635,
-0.04840967804193497,
0.005902037490159273,
-0.03670259937644005,
-0.04507891461253166,
-0.006786417681723833,
-0.03339415043592453,
-0.0009242697851732373,
0.02403298392891884,
0.00156656582839787,
-0.028510600328445435,
0.07718291878700256,
0.03912445530295372,
0.023981209844350815,
0.01628170907497406,
0.015451034530997276,
-0.02618595026433468,
0.0876961350440979,
-0.00891636312007904,
0.03553922846913338,
0.0502479262650013,
0.04449015483260155,
0.031812578439712524,
-0.0344492644071579,
0.030235137790441513,
0.0376620888710022,
-0.04463499039411545,
-0.025240611284971237,
0.010082568973302841,
0.018409499898552895,
-0.003917049150913954,
0.0026594672817736864,
0.008664052933454514,
-0.007469175849109888,
-0.03793064504861832,
0.0035292059183120728,
0.019779276102781296,
0.01503551285713911,
0.0286842193454504,
0.01226460188627243,
-0.053006600588560104,
0.02088896371424198,
-0.052425362169742584,
-0.01986454799771309,
-0.001012062537483871,
-0.04258954897522926,
0.021006450057029724,
-0.009712078608572483,
-0.0007441660272888839,
-0.04468921199440956,
-0.020789219066500664,
-0.021896835416555405,
0.05555238574743271,
0.021976741030812263,
-0.015555686317384243,
0.008659899234771729,
0.02552463859319687,
0.07334455102682114,
-0.005432241130620241,
0.0012074722908437252,
0.007552214898169041,
-0.037557203322649,
0.0320211686193943,
0.01625688374042511,
0.029834924265742302,
0.02101745270192623,
-0.0034814043901860714,
-0.0110624423250556,
0.011427044868469238,
-0.03336203843355179,
0.03650182858109474,
-0.026356259360909462,
0.06002093479037285,
0.02325093001127243,
-0.0023971430491656065,
-0.03633669763803482,
0.013468449003994465,
0.01894444413483143,
0.018674297258257866,
-0.011356819421052933,
-0.008563118986785412,
-0.0700533390045166,
-0.013798432424664497,
0.05035269632935524,
0.036356646567583084,
-0.02295958250761032,
0.0058080218732357025,
0.018558813259005547,
0.02075180783867836,
-0.035983890295028687,
-0.00832288060337305,
-0.018030209466814995,
-0.031157074496150017,
0.00902625359594822,
-0.015517111867666245,
0.04678318649530411,
0.030915861949324608,
0.03259463980793953,
-0.004533234052360058,
0.017178716138005257,
-0.013099683448672295,
0.011707732453942299,
0.0755557268857956,
-0.03141707181930542,
0.01445361040532589,
-0.008895652368664742,
0.008696945384144783,
0.022876011207699776,
-0.013759041205048561,
0.04059654846787453,
0.013783421367406845,
0.00901825912296772,
-0.032201554626226425,
-0.0010736404219642282,
0.009557164274156094,
-0.003287844592705369,
0.0025191116146743298,
-0.061625272035598755,
-0.016965074464678764,
0.01442805677652359,
-0.05183875933289528,
-0.023411152884364128,
-0.007382961921393871,
-0.06634236872196198,
0.028851844370365143,
0.005325749516487122,
0.02916603907942772,
0.012944728136062622,
0.027507392689585686,
-0.05558403581380844,
-0.01673569157719612,
-0.01788744516670704,
-0.002610787283629179,
0.00946039892733097,
0.019896099343895912,
-0.04170827195048332,
0.04013326019048691,
0.005094085820019245,
-0.03888503834605217,
0.010236101225018501,
-0.01786665804684162,
0.03577538579702377,
0.028827982023358345,
-0.008823633193969727,
-0.04794685170054436,
-0.0032507525756955147,
-0.05208510905504227,
0.014908617362380028,
-0.015477348119020462,
0.0038160360418260098,
0.05300780385732651,
0.01092496607452631,
-0.04297296330332756,
-0.004472192842513323,
-0.03859146684408188,
-0.0406099297106266,
-0.0011341484496369958,
0.0124563779681921,
0.03306612744927406,
-0.035755470395088196,
0.038177862763404846,
0.031114686280488968,
-0.036799218505620956,
-0.027657190337777138,
-0.07110962271690369,
-0.08794187009334564,
-0.00604165019467473,
-0.009406931698322296,
0.026903612539172173,
0.01113496720790863,
-0.030745549127459526,
0.025333795696496964,
0.025787001475691795,
-0.02876395732164383,
-0.026225009933114052,
0.013598366640508175,
0.0015498396242037416,
-0.019561195746064186,
-0.030811477452516556,
-0.028593065217137337,
0.024509891867637634,
0.009521677158772945,
0.030253715813159943,
0.011346670798957348,
0.03092915751039982,
0.03635002300143242,
0.004135741852223873,
-0.02706688456237316,
0.009279108606278896,
0.000735824869479984,
0.030953967943787575,
0.050881680101156235,
-0.02186630666255951,
-0.01223822496831417,
-0.020529547706246376,
0.004300729837268591,
0.04492293298244476,
-0.04575368016958237,
0.029634281992912292,
0.013640633784234524,
-0.005305459722876549,
0.015598590485751629,
0.019924430176615715,
-0.007771172560751438,
0.015701424330472946,
0.0009061738383024931,
0.01756794936954975,
0.024442311376333237,
-0.008958671241998672,
-0.003836333053186536,
0.05189083144068718,
0.020980559289455414,
-0.04143639653921127,
-0.0358356311917305,
-0.02826698124408722,
-0.013496112078428268,
0.018314993008971214,
0.0040641832165420055,
-0.00819973275065422,
0.022733837366104126,
0.025088908150792122,
-0.015043342486023903,
0.029443422332406044,
0.010958832688629627,
-0.048617541790008545,
-0.07601282000541687,
-0.016450652852654457,
-0.0023508002050220966,
0.02060539834201336,
-0.0017140567069873214,
0.033649981021881104,
-0.003174691926687956,
-0.009493444114923477,
-0.0008729373221285641,
0.03256549313664436,
-0.04806938394904137,
0.005329647567123175,
-0.02522541582584381,
-0.012210859917104244,
0.008045829832553864,
-0.004243768285959959,
0.029481152072548866,
-0.034866925328969955,
-0.017199724912643433,
-0.01929030381143093,
-0.017905790358781815,
-0.0797184407711029,
0.022440243512392044,
-0.03493548184633255,
-0.06793707609176636,
-0.03108653798699379,
0.057633571326732635,
0.08536194264888763,
0.026027297601103783,
0.06126365065574646,
0.01379199605435133,
-0.03372544050216675,
-0.02105318382382393,
0.03833365440368652,
-0.0030151554383337498,
0.015727724879980087,
0.00931030698120594,
-0.00917540118098259,
0.01890745759010315,
-0.0280920322984457,
0.03625887632369995,
-0.02215592935681343,
0.039137568324804306,
-0.0007104827673174441,
-0.0008940461557358503,
-0.022827720269560814,
-0.013469829224050045,
-0.017673639580607414,
-0.0014561149291694164,
0.06696976721286774,
-0.03512420132756233,
-0.018715104088187218,
0.050952594727277756,
-0.0000681206292938441,
0.0014887625584378839,
0.012815618887543678,
0.04069345071911812,
0.010450571775436401,
-0.029076529666781425,
-0.0063411882147192955,
0.008860080502927303,
0.0003445721522439271,
0.006022755987942219,
-0.004273813217878342,
0.03851116821169853,
-0.0014642413007095456,
-0.008556120097637177,
0.005048995837569237,
-0.013291727751493454,
-0.016189469024538994,
0.015064120292663574,
-0.05139785632491112,
0.022096263244748116,
0.017715049907565117,
-0.020729869604110718,
-0.03187781199812889,
0.042266957461833954,
0.07426153123378754,
0.03240532800555229,
-0.0028584885876625776,
-0.07240766286849976,
-0.003892448963597417,
0.041168469935655594,
0.027596168220043182,
0.034445397555828094,
-0.03649652376770973,
-0.04838235676288605,
0.014111293479800224,
0.02369619347155094,
-0.051386814564466476,
0.002340783132240176,
-0.00042425625724717975,
-0.010485263541340828,
-0.05111774057149887,
-0.024126047268509865,
-0.03107248991727829,
-0.0031580126378685236,
-0.010472187772393227,
0.004333553370088339,
-0.016212869435548782,
0.06162417680025101,
0.0012828597100451589,
0.021477794274687767,
0.020585553720593452,
0.037547409534454346,
0.04354311525821686,
0.013819967396557331,
-0.016280101612210274,
-0.0025260041002184153,
-0.056043658405542374,
-0.03842431679368019,
0.04107172414660454,
0.04754538834095001,
-0.03700436279177666,
0.018804416060447693,
-0.03786478936672211,
-0.05971985682845116,
-0.020113958045840263,
-0.0018033593660220504,
0.009900011122226715,
0.049482107162475586,
-0.0638045147061348,
0.05581441894173622,
-0.0011603928869590163,
0.0016094435704872012,
0.02284042350947857,
0.02628372050821781,
0.011918499134480953,
0.004116436932235956,
0.0005237694713287055,
-0.0054909647442400455,
-0.04235751926898956,
0.005170072428882122,
-0.006172416266053915,
-0.01737200655043125,
-0.04923577979207039,
0.04801160469651222,
-0.03019534982740879,
-0.0020265919156372547,
0.020571764558553696,
-0.036072421818971634,
-0.0066359746269881725,
0.0035747867077589035,
0.008378648199141026,
0.04123414680361748,
-0.025530772283673286,
0.008502412587404251,
-0.008274903520941734,
0.0027905700262635946,
0.0451602041721344,
-0.012120502069592476,
0.03254000470042229,
0.06078321486711502,
-0.0004208648460917175,
0.018080268055200577,
-0.03176360949873924,
0.00764040881767869,
0.018615029752254486,
-0.0475834496319294,
0.06001899763941765,
-0.004912570584565401,
-0.0004941430524922907,
0.03054935485124588,
-0.016330432146787643,
-0.03753802552819252,
-0.0014033798361197114,
-0.018879162147641182,
0.03682737797498703,
-0.008399122394621372,
0.022388208657503128,
0.024576256051659584,
0.009840862825512886,
-0.08542674034833908,
-0.02899135835468769,
0.037501513957977295,
0.008169043809175491,
0.024258267134428024,
-0.02019524574279785,
0.054335035383701324,
-0.06866824626922607,
-0.001239392557181418,
-0.036707233637571335,
0.044711075723171234,
-0.03339111804962158,
-0.034470655024051666,
-0.004643585532903671,
0.049685537815093994,
0.02940535731613636,
-0.009474538266658783,
-0.010994824580848217,
0.010805610567331314,
-0.001637798734009266,
0.005264913197606802,
0.0010952354641631246,
0.008508452214300632,
-0.0053244722075760365,
-0.0506952665746212,
-0.03514273464679718,
0.0199603121727705,
-0.021491173654794693,
-0.03306682035326958,
0.013013897463679314,
0.03491254895925522,
-0.05623172968626022,
-0.009708071127533913,
-0.053652822971343994,
0.00683122081682086,
0.004285672679543495,
-0.0016517424955964088,
-0.028574084863066673,
0.010743618942797184,
0.031027235090732574,
-0.047961365431547165,
0.0349968783557415,
-0.01902453973889351,
-0.01823345758020878,
-0.022239437326788902,
0.022868139669299126,
-0.003142979461699724,
0.007782930973917246,
-0.0013008629903197289,
0.008501489646732807,
0.03740556538105011,
-0.06183210387825966,
0.008340194821357727,
-0.0042637367732822895,
0.02162368781864643,
-0.052619270980358124,
-0.03357558697462082,
-0.043218281120061874,
0.013775820843875408,
0.054552461951971054,
-0.013816237449645996,
0.00910680741071701,
0.04598574340343475,
-0.018013279885053635,
0.00780909787863493,
-0.025888461619615555,
0.04656318947672844,
-0.02958855591714382,
-0.013987736776471138,
0.05342622473835945,
-0.034775473177433014,
-0.014810114167630672,
0.04479594901204109,
0.05762113630771637,
-0.018329039216041565,
0.016308806836605072,
0.012462470680475235,
0.02116446942090988,
0.033227089792490005,
-0.009449148550629616,
-0.026982726529240608,
0.0027901006396859884,
-0.03367411717772484,
-0.015511898323893547,
0.028770843520760536,
-0.013882975094020367,
0.021598225459456444,
0.027552910149097443,
0.045649897307157516,
0.012665064074099064,
-0.016889503225684166,
-0.06896478682756424,
0.01202115137130022,
0.04544716700911522,
0.022199371829628944,
-0.012361625209450722,
-0.010868255980312824,
0.01785975694656372,
0.011174757964909077,
-0.002068126108497381,
0.006609955336898565,
-0.04570601508021355,
-0.0020334129221737385,
-0.08173125237226486,
-0.028967073187232018,
0.05437798425555229,
-0.010307597927749157,
-0.01266639307141304,
-0.01116271037608385,
-0.0010679293191060424,
0.00693519925698638,
0.042141832411289215,
0.0711718425154686,
-0.018401600420475006,
0.0557476170361042,
-0.011180640198290348,
0.03261130675673485,
-0.012548595666885376,
0.021558361127972603,
0.10713138431310654,
0.05490478500723839,
-0.00044664705637842417,
-0.05568355694413185,
0.006838434841483831,
0.014929077588021755,
-0.0021441832650452852,
-0.021689675748348236,
0.03331266716122627,
-0.013096651062369347,
0.0010269900085404515,
0.03069143369793892,
0.021248139441013336,
-0.015438220463693142,
-0.025276681408286095,
0.07341469079256058,
-0.050163015723228455,
-0.03869903087615967,
-0.0030945881735533476,
0.021148569881916046,
0.004948877729475498,
-0.023557094857096672,
-0.012236674316227436,
0.06497585028409958,
0.04378732666373253,
0.015512902289628983,
-0.011569583788514137,
-0.022036325186491013,
0.02745143137872219,
0.0215168297290802,
-0.043394990265369415,
0.010735580697655678,
-0.0050978269428014755,
-0.006554149091243744,
-0.04785938933491707,
0.00249744625762105,
0.02851022593677044,
-0.01823151670396328,
0.039876315742731094,
0.043571796268224716,
-0.004679951351135969,
0.0003534237330313772,
0.02263212390244007,
-0.0035976609215140343,
-0.012859745882451534,
-0.03963395953178406,
-0.025995323434472084,
0.05525574833154678,
0.002856950042769313,
-0.02763926237821579,
-0.007910341955721378,
-0.016054676845669746,
0.011692266911268234,
-0.09102363139390945,
-0.020877547562122345,
-0.0161917544901371,
0.012758797965943813,
-0.00016150657029356807,
-0.03395816683769226,
0.011886443011462688,
0.057840511202812195,
-0.0064096092246472836,
0.0005612740642391145,
-0.034813422709703445,
-0.016675332561135292,
-0.007615368813276291,
-0.01911359839141369,
0.03881608694791794,
0.040759190917015076,
-0.0015166111988946795,
-0.03473016992211342,
-0.05282063037157059,
-0.02434661239385605,
-0.014447723515331745,
0.012782002799212933,
0.008908314630389214,
0.04778058081865311,
0.014741424471139908,
0.03729927912354469,
0.020714828744530678,
-0.010218074545264244,
0.0028557213954627514,
-0.03932119160890579,
-0.03469381853938103,
-0.012566636316478252,
0.022214550524950027,
0.009271614253520966,
0.025917168706655502,
0.010808083228766918,
-0.008214260451495647,
0.010132143273949623,
0.03885823115706444,
-0.012306705117225647,
0.0004926117835566401,
0.012399994768202305,
0.027826067060232162,
-0.019709080457687378,
0.018267247825860977,
-0.05911571532487869,
0.02057674340903759,
0.04952830448746681,
0.029848940670490265,
0.017839832231402397,
0.044615183025598526,
0.004362380597740412,
0.010356486774981022,
0.03498951345682144,
-0.007132555358111858,
0.0038078997749835253,
0.022208252921700478,
0.016988802701234818,
-0.027689950540661812,
-0.04206903651356697,
-0.035487100481987,
-0.006172018591314554,
-0.0033974216785281897,
-0.011340689845383167,
-0.03175732493400574,
0.021581754088401794,
0.001992226578295231,
-0.0005073765642009676,
-0.014731728471815586,
-0.008122041821479797,
0.0039270371198654175,
0.010808522813022137,
0.0017892358591780066,
-0.002720948774367571,
-0.027957802638411522,
0.0051892464980483055,
-0.030110744759440422,
-0.031500443816185,
-0.017960531637072563,
-0.005087769124656916,
-0.036356598138809204,
-0.013069435954093933,
0.017757222056388855,
-0.019671814516186714,
0.019238168373703957,
0.030089963227510452,
-0.028712764382362366,
0.014793656766414642,
-0.031074732542037964,
-0.02295313961803913,
0.016382630914449692,
0.01444135420024395,
0.0489550419151783,
0.042287375777959824,
-0.039596449583768845,
-0.02316591702401638,
0.03345448151230812,
0.004633481148630381,
-0.004820472095161676,
0.03031237982213497,
0.007310120854526758,
-0.005971014034003019,
-0.008169419132173061,
0.03176336735486984,
0.012545168399810791,
-0.051821518689394,
-0.0006709914887323976,
0.0157930888235569,
0.0013898606412112713,
-0.016730083152651787,
0.01578737422823906,
0.0019469782710075378,
-0.042201220989227295,
0.00129529251717031,
-0.012152939103543758,
0.024475911632180214,
0.06061363220214844,
-0.040997132658958435,
0.034147609025239944,
0.018970130011439323,
0.01091645285487175,
-0.13408780097961426,
-0.018999017775058746,
0.0015561857726424932,
0.018749861046671867,
0.022034868597984314,
-0.042429935187101364,
-0.011811620555818081,
0.05695940554141998,
-0.06975122541189194,
0.008658197708427906,
0.02764659747481346,
-0.009711703285574913,
-0.04904588311910629,
0.04574361443519592,
-0.026162002235651016,
0.05096551775932312,
0.027098266407847404,
0.026004556566476822,
-0.005657562520354986,
0.025855982676148415,
-0.04531312733888626,
-0.03206101432442665,
-0.048520248383283615,
0.045579325407743454,
-0.03476931154727936,
-0.019493727013468742,
0.0864935889840126,
-0.006271256133913994,
-0.02033327892422676,
0.025060614570975304,
0.010175003670156002,
-0.017885813489556313,
0.0014638523571193218,
-0.004707932937890291,
0.013719907030463219,
0.029094839468598366,
0.03801218420267105,
0.0010968904243782163,
0.0039828745648264885,
0.008907672017812729,
-0.0038156467489898205,
0.00007369858212769032,
-0.0036971645895391703,
-0.04610982909798622,
0.009713234379887581,
-0.05030598118901253,
-0.054024357348680496,
0.05361637473106384,
-0.011525246314704418,
0.003272135043516755,
-0.01502403523772955,
0.0185342226177454,
-0.01230985764414072,
-0.021916527301073074,
-0.009465700946748257,
-0.05118541419506073,
-0.02219296060502529,
0.023679940029978752,
-0.0036359343212097883,
-0.01668972335755825,
0.0025624861009418964,
-0.041845615953207016,
-0.034341007471084595,
0.009676123969256878,
-0.014311418868601322,
0.01755147986114025,
-0.04696645215153694,
0.013499059714376926,
-0.004809497855603695,
-0.010838617570698261,
-0.0008850317681208253,
-0.041447170078754425,
-0.02430094964802265,
0.025163082405924797,
0.01629733480513096,
0.0035950648598372936,
0.00006603612564504147,
-0.03158525004982948,
-0.02464814856648445,
-0.10172060877084732,
0.03334394469857216,
0.05047351121902466,
-0.003568926127627492,
-0.06736218929290771,
-0.030436350032687187,
-0.01836523599922657,
0.03400316834449768,
0.06279637664556503,
0.011017968878149986,
-0.012874174863100052,
0.046262226998806,
0.004885146394371986,
0.006864710710942745,
-0.0310659259557724,
0.01709149032831192,
-0.023913098499178886,
-0.011873738840222359,
-0.011131959035992622,
-0.023740693926811218,
-0.011502258479595184,
0.018648624420166016,
0.04538195952773094,
0.00838556606322527,
0.031899966299533844,
0.005783255212008953,
-0.03532453253865242,
0.04243944212794304,
0.02874220348894596,
0.010488918051123619,
0.038547538220882416,
0.011774973943829536,
-0.003014916554093361,
0.045864447951316833,
-0.019208142533898354,
-0.05097530037164688,
-0.001344548538327217,
-0.018716491758823395,
-0.02739318460226059,
0.0032585198059678078,
0.010627237148582935,
0.016138216480612755,
-0.02368268556892872,
0.008277789689600468,
0.06718707829713821,
0.008321675471961498,
-0.009388422593474388,
0.026191003620624542,
0.0019441201584413648,
0.035442277789115906,
0.0035672748927026987,
0.0009160618064925075,
0.01963486149907112,
-0.027055714279413223,
0.011521177366375923,
0.02785564213991165,
0.05032414570450783,
0.004254004918038845,
-0.00047727907076478004,
0.03346392884850502,
-0.02308528870344162,
0.015429485589265823,
-0.009267611429095268,
0.05733538046479225,
-0.004309654235839844,
0.02476433664560318,
0.008706234395503998,
-0.0039005791768431664,
-0.006391705945134163,
0.03339613974094391,
0.012135527096688747,
0.08340513706207275,
0.006135078147053719,
-0.0038291963282972574,
-0.0007999981753528118,
0.02912256121635437,
-0.01134833600372076,
0.024090586230158806,
0.03392460569739342,
0.01782066747546196,
-0.019281666725873947,
0.015398170799016953,
-0.027564438059926033,
-0.02124863490462303,
0.01932831108570099,
-0.049905698746442795,
0.028704332187771797,
-0.0021568804513663054,
0.03311305120587349,
-0.009995591826736927,
-0.0010295446263626218,
-0.00751985888928175,
0.010035501793026924,
0.058003079146146774,
0.0036433516070246696,
0.04727783799171448,
-0.05368448793888092,
-0.01650426909327507,
-0.06128302589058876,
0.03748759254813194,
-0.08292139321565628,
0.018162047490477562,
-0.02418505772948265,
0.06870414316654205,
-0.02066894806921482,
0.0025074882432818413
] |
<p>If I'm running at say $400\: \mathrm{m/s}$ and a bullet travels at $400\: \mathrm{m/s}$ and I fire the gun, will I see the bullet leave the barrel? </p>
<p>I either see it stay in the barrel floating because we are moving at the same speed.
-- Or --
The bullet would move and have a speed of $800\: \mathrm{m/s}$. </p>
<p>What is the correct answer?</p> | 1,436 | [
-0.03354495391249657,
-0.011291280388832092,
-0.01210570428520441,
-0.027275847271084785,
0.025439418852329254,
0.004630201030522585,
-0.02321728691458702,
-0.03805847838521004,
0.021742984652519226,
0.01133028045296669,
0.07087648659944534,
0.03583446517586708,
0.05594906583428383,
0.016878850758075714,
0.025889169424772263,
0.03233950585126877,
-0.0086886091157794,
0.010822976939380169,
-0.004170533269643784,
-0.03200824558734894,
-0.017355911433696747,
-0.0032939608208835125,
0.03110240399837494,
0.0027340042870491743,
-0.031113987788558006,
0.013785777613520622,
0.04145454242825508,
0.008590388111770153,
0.0019862959161400795,
0.030662335455417633,
-0.034791819751262665,
-0.010967225767672062,
0.0250596571713686,
0.06023978814482689,
-0.006188885308802128,
0.03028830885887146,
-0.03802856430411339,
-0.025522159412503242,
-0.017222188413143158,
0.027470432221889496,
-0.010664350353181362,
0.0037644219119101763,
0.03342975303530693,
0.03551282733678818,
-0.024193650111556053,
0.023726115003228188,
-0.027156377211213112,
-0.02634267322719097,
0.05888201296329498,
-0.008303691633045673,
0.03789326921105385,
-0.019148878753185272,
0.023043593391776085,
0.023223111405968666,
0.011235173791646957,
-0.017120083793997765,
0.06445465236902237,
0.05207887291908264,
-0.020194344222545624,
-0.027686992660164833,
-0.01291624829173088,
-0.02311776578426361,
-0.020849747583270073,
-0.0049027311615645885,
-0.002594812773168087,
-0.014403468929231167,
-0.005719339475035667,
-0.029723430052399635,
0.019179120659828186,
-0.04617422819137573,
-0.008184598758816719,
-0.016525162383913994,
0.03619130700826645,
-0.029844051226973534,
0.045680176466703415,
-0.05657210573554039,
0.03901049494743347,
0.0613081119954586,
0.024881636723876,
0.0533369705080986,
-0.032946471124887466,
-0.039561137557029724,
0.033439330756664276,
0.03632594645023346,
0.025345956906676292,
-0.0475725419819355,
0.08458780497312546,
0.021313587203621864,
0.014239104464650154,
0.03806881979107857,
-0.0032763078343123198,
-0.018248669803142548,
0.005610673222690821,
-0.007992053404450417,
-0.004373731091618538,
0.049696337431669235,
0.00892726518213749,
0.024929044768214226,
0.05458918586373329,
-0.03845630958676338,
-0.027104511857032776,
-0.048843856900930405,
0.04477239027619362,
0.08471240848302841,
-0.0032985233701765537,
0.008072921074926853,
-0.01017392985522747,
0.003987689968198538,
-0.05107154697179794,
0.01374368742108345,
-0.03132930397987366,
-0.007723100017756224,
0.013206743635237217,
0.010117506608366966,
-0.031171131879091263,
-0.018537087365984917,
0.023898253217339516,
-0.013151389546692371,
0.03218074142932892,
0.02394699864089489,
0.04425087198615074,
-0.012964791618287563,
-0.011158348992466927,
0.0012523316545411944,
-0.0649934709072113,
-0.009900239296257496,
0.02188681997358799,
-0.01576213724911213,
-0.02635985054075718,
0.005559617653489113,
0.0008967667235992849,
-0.015095334500074387,
0.008680416271090508,
-0.0054477215744555,
0.03704273700714111,
0.007816523313522339,
-0.09970667958259583,
-0.04702726751565933,
0.06435411423444748,
0.01626831665635109,
-0.0049117798916995525,
-0.08814592659473419,
0.009683662094175816,
0.027266068384051323,
0.04860253259539604,
-0.027292849496006966,
-0.02151534892618656,
0.009332040324807167,
0.004963976331055164,
-0.02322150394320488,
-0.024262942373752594,
-0.004224928095936775,
-0.014870304614305496,
0.004056267905980349,
0.037205398082733154,
-0.03448222205042839,
-0.0038976192008703947,
0.03721395507454872,
0.009992670267820358,
-0.006816125474870205,
0.03117194026708603,
-0.014302308671176434,
-0.00854114443063736,
-0.015463422983884811,
0.021569499745965004,
-0.024177730083465576,
0.05923799052834511,
0.014360440894961357,
-0.007341396063566208,
-0.0011301669292151928,
0.031025057658553123,
0.011623180471360683,
-0.020945029333233833,
-0.01684957556426525,
0.00763886421918869,
-0.024491388350725174,
-0.027589524164795876,
0.0005823404644615948,
-0.03142969682812691,
0.003384424839168787,
-0.04947857931256294,
-0.04770280420780182,
-0.02514522150158882,
0.001109317410737276,
0.03229411691427231,
0.02034459263086319,
0.031059863045811653,
0.04123994708061218,
-0.008366481401026249,
-0.024370890110731125,
0.0010183524573221803,
-0.07932798564434052,
0.020275965332984924,
-0.0007972744642756879,
0.005436536390334368,
0.041823334991931915,
-0.009983671829104424,
-0.02434675395488739,
-0.0192178413271904,
0.024634912610054016,
-0.00007709873898420483,
0.04120608791708946,
-0.011971169151365757,
-0.01428158301860094,
0.008244561962783337,
0.08026014268398285,
0.030006766319274902,
0.030503686517477036,
-0.00597271928563714,
-0.011180208064615726,
-0.014497464522719383,
-0.02563319355249405,
-0.005722209811210632,
0.0024807860609143972,
0.007102056872099638,
-0.001329852850176394,
0.02115362510085106,
-0.010237437672913074,
0.021969251334667206,
0.006644267123192549,
-0.04074438288807869,
0.08305344730615616,
0.04375925660133362,
-0.06946514546871185,
-0.004123791120946407,
0.04121805727481842,
0.015026791021227837,
-0.022409362718462944,
-0.0010812224354594946,
-0.020272916182875633,
-0.03425069898366928,
-0.035724665969610214,
0.03097822703421116,
0.0023640126455575228,
-0.016348306089639664,
0.05601656436920166,
0.009358064271509647,
0.017360303550958633,
0.036010995507240295,
0.003992625046521425,
-0.045553725212812424,
-0.05796102061867714,
0.04467971622943878,
-0.02907167375087738,
0.01500325370579958,
-0.011944258585572243,
0.013362977653741837,
0.005819458048790693,
0.005545029882341623,
-0.03367530182003975,
-0.0005347034893929958,
0.03559350222349167,
0.03390728309750557,
0.02977779507637024,
0.014584369957447052,
-0.04328559711575508,
0.02959052100777626,
0.015970658510923386,
-0.011721556074917316,
-0.004126611165702343,
0.020031744614243507,
0.01943156309425831,
-0.051419395953416824,
-0.00041633573709987104,
-0.02827923372387886,
0.03975291550159454,
-0.008707924745976925,
-0.02115180529654026,
0.023776624351739883,
-0.049322836101055145,
0.019255949184298515,
-0.020476611331105232,
-0.02298477292060852,
-0.014869889244437218,
0.0012775168288499117,
0.047217365354299545,
0.03841438144445419,
0.013008123263716698,
-0.052125029265880585,
-0.03563181310892105,
-0.02148306928575039,
-0.04562566056847572,
-0.004905765410512686,
-0.014093407429754734,
-0.04287904500961304,
0.031795814633369446,
-0.03183921054005623,
-0.06397893279790878,
0.029901109635829926,
0.005059733521193266,
-0.011824218556284904,
0.0393744595348835,
-0.018384797498583794,
-0.07442470639944077,
-0.008973567746579647,
-0.035030290484428406,
-0.0013811822282150388,
-0.04520966857671738,
-0.0006255822954699397,
0.07215414941310883,
-0.005820386577397585,
-0.052185069769620895,
0.019588790833950043,
-0.025190306827425957,
-0.04495890811085701,
-0.025120899081230164,
0.0011293807765468955,
0.0349138118326664,
0.0006458561983890831,
0.02079150080680847,
0.0036590909585356712,
-0.010536613874137402,
0.002529110061004758,
-0.0656483992934227,
-0.021209558472037315,
0.03842078521847725,
-0.018876824527978897,
0.039964571595191956,
-0.0006735859205946326,
-0.00266846246086061,
0.07940197736024857,
0.028704868629574776,
-0.0008385646506212652,
-0.00631340267136693,
-0.036410704255104065,
0.03372582793235779,
-0.06345634907484055,
0.017590871080756187,
0.05892326682806015,
-0.00829878356307745,
0.01781318709254265,
-0.01920253224670887,
0.0619293637573719,
0.013239539228379726,
0.00597910163924098,
0.031115174293518066,
-0.008688987232744694,
0.002603261498734355,
0.018172793090343475,
0.040264494717121124,
0.023490464314818382,
-0.036104511469602585,
0.014563464559614658,
-0.010159752331674099,
0.05165981128811836,
0.03438618779182434,
-0.056366946548223495,
0.09522921591997147,
-0.0025510743726044893,
-0.06613858789205551,
-0.03245057165622711,
0.05925047770142555,
0.016933152452111244,
-0.019831379875540733,
-0.003688640659675002,
-0.000913288036826998,
0.04234188050031662,
0.018124936148524284,
0.028160661458969116,
0.0287349671125412,
0.02615085430443287,
-0.03385653346776962,
-0.017023254185914993,
-0.03582377731800079,
-0.017011912539601326,
0.041522055864334106,
-0.03380466252565384,
-0.030270220711827278,
0.009320923127233982,
0.033149801194667816,
0.003431821707636118,
-0.004501232877373695,
-0.02658497728407383,
-0.03478065878152847,
-0.03752954304218292,
0.009760101325809956,
-0.012744907289743423,
0.03732912614941597,
0.00013134028995409608,
0.08226718008518219,
0.0016230606706812978,
0.020293159410357475,
0.016576196998357773,
0.028200101107358932,
-0.04028914123773575,
0.0204155296087265,
-0.016398515552282333,
-0.01698903739452362,
-0.025633661076426506,
-0.005739483051002026,
-0.029996037483215332,
-0.01578420028090477,
-0.017920585349202156,
-0.025823766365647316,
-0.016791250556707382,
-0.0304286926984787,
-0.014639105647802353,
-0.02132384106516838,
-0.06347957253456116,
0.014823291450738907,
0.038735050708055496,
0.02442437969148159,
0.0036679329350590706,
0.04909341782331467,
0.02776596136391163,
-0.04111149534583092,
0.005506564863026142,
-0.0015463015297427773,
-0.0005906545557081699,
-0.00846277829259634,
0.04077563062310219,
0.003657757304608822,
-0.01100379228591919,
-0.026369409635663033,
0.007846287451684475,
0.021099144592881203,
0.02968563325703144,
-0.013965966179966927,
-0.022166097536683083,
-0.04006235674023628,
-0.05142117664217949,
0.01976468600332737,
-0.03468436375260353,
0.07863818109035492,
-0.03289470821619034,
-0.023058244958519936,
0.036881156265735626,
-0.005173335317522287,
0.008546213619410992,
0.07255211472511292,
0.04274144396185875,
0.022781018167734146,
-0.019877571612596512,
-0.0510091707110405,
-0.0229796152561903,
-0.02117658406496048,
-0.0005636463174596429,
0.0006076344288885593,
0.00024451574427075684,
-0.00028009561356157064,
-0.0057123564183712006,
0.01908259652554989,
0.04127778112888336,
0.0046173762530088425,
0.023605145514011383,
0.011792697012424469,
0.006263756658881903,
-0.0041987900622189045,
0.01693260297179222,
0.023941032588481903,
0.05172043293714523,
0.029116002842783928,
0.0029246907215565443,
-0.01310248114168644,
-0.06489892303943634,
-0.010579673573374748,
0.041383784264326096,
0.00936306081712246,
-0.022979840636253357,
0.006199568510055542,
-0.051586538553237915,
-0.038514163345098495,
0.026236621662974358,
-0.005559183191508055,
0.027739692479372025,
-0.012473277747631073,
0.0061645288951694965,
0.0069540031254291534,
-0.03615979477763176,
-0.03370629623532295,
0.0025637829676270485,
0.0329093411564827,
0.004538603127002716,
-0.03190784901380539,
0.006334891077131033,
0.01187283918261528,
0.0035223043523728848,
0.051651544868946075,
0.04864121973514557,
-0.028571641072630882,
0.028900915756821632,
-0.01210019737482071,
-0.038472577929496765,
-0.053012948483228683,
-0.06866922229528427,
0.0310615673661232,
-0.008037994615733624,
-0.007341359741985798,
0.022310972213745117,
0.014038593508303165,
-0.045187171548604965,
0.04354210942983627,
0.021930260583758354,
-0.007544989697635174,
0.027000678703188896,
-0.07422803342342377,
0.01469019427895546,
0.018212439492344856,
-0.02058873139321804,
-0.003571202978491783,
0.027986394241452217,
-0.02150505967438221,
-0.03644926846027374,
0.0036158778239041567,
0.012164236977696419,
-0.029599303379654884,
-0.020593024790287018,
-0.03128579258918762,
0.010280885733664036,
-0.04494175314903259,
0.024776043370366096,
-0.01380457915365696,
0.019232358783483505,
0.023504918441176414,
-0.024545297026634216,
-0.010502281598746777,
0.0049374885857105255,
0.02517414093017578,
0.011882374063134193,
-0.044273171573877335,
-0.004715512972325087,
-0.018108563497662544,
-0.004963109269738197,
0.021781910210847855,
0.009291308000683784,
-0.0029160703998059034,
0.03594795987010002,
-0.016673734411597252,
0.000020972793208784424,
-0.04754020646214485,
0.015038488432765007,
0.00909380055963993,
-0.024903280660510063,
0.06350622326135635,
0.0020635402761399746,
0.02079787291586399,
0.04878796637058258,
-0.04999933019280434,
-0.0784970298409462,
0.036760829389095306,
0.027922969311475754,
0.007992742583155632,
-0.04427007585763931,
0.06859086453914642,
0.01796337403357029,
-0.005588185042142868,
-0.04371623694896698,
-0.028611386194825172,
0.04386543110013008,
0.013445844873785973,
-0.02853427827358246,
-0.013082851655781269,
0.0015467238845303655,
-0.03498963639140129,
-0.04431368410587311,
0.01855289191007614,
0.0233346838504076,
0.006835850887000561,
-0.005854789633303881,
-0.0003346509183757007,
0.016143132001161575,
0.07656793296337128,
0.008054881356656551,
-0.01160779595375061,
-0.01859896630048752,
-0.00550798187032342,
-0.03515567630529404,
-0.008391598239541054,
0.07680387049913406,
-0.001806089305318892,
0.001307118684053421,
-0.01682121679186821,
-0.03957253694534302,
0.04232499748468399,
-0.009274438954889774,
0.03005228005349636,
0.03594082221388817,
-0.002755992580205202,
0.02287035994231701,
0.008291619829833508,
0.0027671358548104763,
0.01620100624859333,
0.05107782781124115,
-0.019907211884856224,
0.013101567514240742,
-0.017759021371603012,
-0.03851209953427315,
0.04418695345520973,
-0.0038795657455921173,
0.0017022175015881658,
-0.003483392531052232,
0.07045208662748337,
-0.033752866089344025,
0.01245206780731678,
0.031097838655114174,
0.042390283197164536,
0.04718434810638428,
-0.012189659290015697,
-0.03154636174440384,
-0.014886223711073399,
0.0119358841329813,
-0.010836287401616573,
-0.050407323986291885,
-0.005577622447162867,
-0.009040488861501217,
0.04915503412485123,
-0.013194725848734379,
0.048286162316799164,
-0.01065347995609045,
0.012903199531137943,
0.01688489504158497,
-0.032059069722890854,
0.016054024919867516,
-0.012956485152244568,
-0.008438734337687492,
0.01481752097606659,
-0.03270585462450981,
0.0003040031879208982,
0.04573489725589752,
0.03276406228542328,
0.0057088290341198444,
-0.013440300710499287,
0.0038581546396017075,
-0.027723276987671852,
-0.013769581913948059,
-0.04048875346779823,
-0.029254592955112457,
0.003712959587574005,
-0.06543906778097153,
0.04055510833859444,
-0.02120690420269966,
-0.0219767764210701,
0.06484142690896988,
0.023468784987926483,
-0.0008837533532641828,
-0.055998388677835464,
0.017195237800478935,
-0.059990882873535156,
-0.04029447212815285,
-0.007379984948784113,
0.011456488631665707,
-0.0029903806280344725,
-0.0040370989590883255,
0.04376297444105148,
-0.028791777789592743,
0.02543768100440502,
-0.03439141809940338,
-0.0441509447991848,
-0.020795123651623726,
-0.01914161443710327,
-0.006076537072658539,
0.06313415616750717,
-0.009025904349982738,
0.008962521329522133,
-0.003646984463557601,
-0.005725914612412453,
0.035328421741724014,
0.015518835745751858,
0.05000549927353859,
-0.051105789840221405,
0.05395742505788803,
-0.02568434737622738,
0.01587802916765213,
-0.03449433669447899,
0.024760007858276367,
0.11167210340499878,
0.044695571064949036,
0.03759947791695595,
-0.003543719882145524,
0.0018984007183462381,
0.0008360486826859415,
0.05663139745593071,
0.010289700701832771,
-0.0037896165158599615,
0.0127065759152174,
0.014423182234168053,
0.009106267243623734,
0.05261315777897835,
-0.004673512652516365,
-0.018213391304016113,
-0.0027834654320031404,
-0.0634969174861908,
0.025355299934744835,
-0.013428105972707272,
-0.0019405506318435073,
0.014680703170597553,
0.03094259649515152,
0.004489438608288765,
0.009212180972099304,
-0.029263900592923164,
-0.026211684569716454,
-0.04522424191236496,
-0.05511646717786789,
0.009482317604124546,
-0.022116249427199364,
-0.016168376430869102,
-0.02426437847316265,
0.01140060368925333,
-0.04339076206088066,
-0.021945960819721222,
0.005244215950369835,
0.014238225296139717,
-0.048610869795084,
0.017313389107584953,
0.02827855758368969,
0.02026212401688099,
0.009195134975016117,
-0.0072301458567380905,
0.011851399205625057,
-0.04065738618373871,
0.018324218690395355,
-0.036001015454530716,
0.013945277780294418,
-0.009297175332903862,
0.002160136355087161,
-0.01966833509504795,
-0.005815270822495222,
-0.006297965068370104,
-0.09088721126317978,
-0.026160456240177155,
0.02236947976052761,
0.0028337929397821426,
0.027098355814814568,
-0.017885558307170868,
-0.04191712290048599,
0.01903454400599003,
0.025681359693408012,
-0.014587919227778912,
-0.004370587877929211,
0.012004447169601917,
-0.03268904611468315,
0.020087003707885742,
0.04054093733429909,
-0.042995162308216095,
0.009307499043643475,
-0.0026476201601326466,
-0.015786385163664818,
-0.037516556680202484,
-0.014744003303349018,
0.03235362097620964,
0.04629289358854294,
0.007728157564997673,
0.023731203749775887,
-0.0015340325189754367,
-0.03806450963020325,
-0.09037957340478897,
0.04468059912323952,
0.01014684047549963,
0.03449593111872673,
-0.04775861278176308,
0.00035122846020385623,
0.03165501728653908,
0.03428397700190544,
-0.009808743372559547,
-0.012418611906468868,
-0.004330724943429232,
0.06766942143440247,
0.03647058084607124,
-0.002081198850646615,
-0.01716415211558342,
0.06706000119447708,
-0.009874116629362106,
0.06537832319736481,
-0.04722553864121437,
0.037417471408843994,
0.034834958612918854,
0.02690211683511734,
0.018161077052354813,
0.0010873876744881272,
-0.022380316630005836,
0.02335757575929165,
0.0245528444647789,
-0.03097243420779705,
-0.04466382414102554,
0.044457871466875076,
0.03442437946796417,
0.028096113353967667,
0.014912111684679985,
-0.020057817921042442,
-0.0193010363727808,
-0.006866338197141886,
-0.016344396397471428,
-0.008376219309866428,
0.020116643980145454,
-0.04389381781220436,
-0.026083700358867645,
-0.0753011703491211,
-0.0026695060078054667,
-0.03829317167401314,
0.01899995096027851,
0.03699174523353577,
-0.0033930910285562277,
-0.043939258903265,
0.003662420902401209,
-0.04113440960645676,
-0.026791682466864586,
0.010878131724894047,
-0.0037187261041253805,
0.0031285525765269995,
-0.029128042981028557,
0.013863318599760532,
0.0016450573457404971,
-0.0009750732569955289,
0.022086653858423233,
-0.00702122924849391,
0.045164935290813446,
0.001968705328181386,
-0.004966672509908676,
0.04071523994207382,
0.013737926259636879,
0.06286774575710297,
0.006267623044550419,
-0.011841132305562496,
0.020253527909517288,
0.06312166899442673,
-0.03293852508068085,
0.009332409128546715,
-0.034770023077726364,
-0.03875085711479187,
0.06488363444805145,
-0.033403292298316956,
0.04686088114976883,
-0.022219112142920494,
0.0020259609445929527,
0.040886323899030685,
0.01656724140048027,
-0.02029579132795334,
-0.00037092698039487004,
0.006322095636278391,
-0.005634671077132225,
-0.024433976039290428,
0.035488493740558624,
0.006286010146141052,
0.020735591650009155,
0.034173160791397095,
0.028062982484698296,
0.054232094436883926,
-0.0026074121706187725,
-0.016629157587885857,
-0.10638045519590378,
-0.0016727400943636894,
0.04051732271909714,
0.023035511374473572,
0.03590909019112587,
-0.057314418256282806,
-0.026029445230960846,
0.0361875556409359,
-0.07250633835792542,
-0.000897940481081605,
-0.03555717319250107,
0.0015780989779159427,
-0.04974839836359024,
0.005358383059501648,
-0.016630863770842552,
0.05407737195491791,
0.0062488773837685585,
-0.007241636980324984,
0.010125281289219856,
0.021760396659374237,
-0.00577498646453023,
-0.02747511863708496,
0.004513969644904137,
0.028810329735279083,
0.0037538649048656225,
-0.002542893635109067,
0.04402613639831543,
-0.03313359618186951,
0.051362697035074234,
0.00996139645576477,
0.002988652791827917,
0.0176108218729496,
-0.038664624094963074,
0.014494048431515694,
0.015957901254296303,
0.04088390991091728,
-0.009499546140432358,
-0.005791757255792618,
0.0027054587844759226,
0.023277778178453445,
0.001641455222852528,
0.03731545805931091,
-0.018889574334025383,
-0.022235579788684845,
-0.005048918537795544,
-0.04268094524741173,
-0.060271769762039185,
-0.006652375217527151,
-0.01786881498992443,
-0.016774842515587807,
0.035766396671533585,
0.016719326376914978,
0.023800279945135117,
0.006670610513538122,
-0.00040356584941037,
0.0008626272901892662,
0.0019891750998795033,
0.010888132266700268,
0.007889541797339916,
-0.014460793696343899,
0.039601683616638184,
-0.004372982773929834,
-0.04072555527091026,
0.013768184930086136,
-0.011879462748765945,
-0.006667271722108126,
-0.025328606367111206,
-0.026640795171260834,
0.024846820160746574,
0.006134558469057083,
0.004244152456521988,
-0.02928026020526886,
-0.005190780386328697,
0.004553352948278189,
0.014949486590921879,
0.03431582823395729,
-0.013938902877271175,
-0.0049433596432209015,
-0.0360579788684845,
-0.06273084133863449,
0.008160504512488842,
0.03320051357150078,
-0.021216746419668198,
-0.06278929114341736,
-0.0543336346745491,
-0.012812493368983269,
0.025992946699261665,
0.055967118591070175,
-0.024473687633872032,
-0.04215949773788452,
0.022425547242164612,
-0.059593360871076584,
0.0062257335521280766,
-0.04342871531844139,
-0.014366092160344124,
-0.032526638358831406,
-0.04634406417608261,
-0.04099826514720917,
0.03952879086136818,
-0.04961259290575981,
-0.0015448699705302715,
0.04560074582695961,
-0.011301065795123577,
-0.00011999991693301126,
-0.002915398683398962,
-0.01603548228740692,
0.04027625918388367,
0.04989186301827431,
-0.0005138335982337594,
0.05595845729112625,
0.02711479738354683,
-0.003929091617465019,
0.05400023236870766,
-0.038478244096040726,
-0.03623802959918976,
0.004719773773103952,
-0.026302732527256012,
-0.05208660662174225,
0.0341307558119297,
-0.008149419911205769,
-0.0046419864520430565,
-0.0506049208343029,
0.006107817869633436,
0.028949499130249023,
-0.011695144698023796,
-0.03291214257478714,
0.038474008440971375,
0.033691346645355225,
0.03981831297278404,
-0.03466895967721939,
0.04938608407974243,
0.036094773560762405,
-0.01680196262896061,
0.018264010548591614,
-0.0018169146496802568,
0.013426046818494797,
0.0007696541724726558,
0.009209283627569675,
0.04094616696238518,
0.018716581165790558,
0.01488968450576067,
0.01686498336493969,
0.0552050843834877,
-0.017511244863271713,
-0.008109308779239655,
0.03491905704140663,
-0.010687500238418579,
-0.012418319471180439,
0.036516640335321426,
-0.042812906205654144,
0.06467066705226898,
-0.03760689124464989,
0.01850758120417595,
-0.009773718193173409,
0.013446773402392864,
-0.03902152180671692,
0.029718363657593727,
-0.014940154738724232,
0.012913956306874752,
-0.013305400498211384,
-0.02395056188106537,
0.037622593343257904,
0.01076227705925703,
0.009716806001961231,
-0.031637415289878845,
-0.0002995375543832779,
0.011566697619855404,
-0.00844441819936037,
-0.03984883055090904,
0.006995826028287411,
-0.03519505634903908,
0.001064163283444941,
0.04198401793837547,
0.010146111249923706,
0.01984228380024433,
-0.014566429890692234,
-0.014061026275157928,
-0.04460828751325607,
0.03577585518360138,
-0.056118763983249664,
-0.02985103614628315,
-0.03437746316194534,
0.0342959463596344,
0.04061892256140709,
-0.008282812312245369
] |
<p>We speak of locality or non-locality of an equation in QM, depending on whether
it has no differential operators of order higher than two.</p>
<p>My question is, how could one tell from looking at the concrete solutions of the equation whether the equ. was local or not...or, to put it another way, what would it mean to say that a concrete solution was non-local?</p>
<p>edit: let me emphasise this grew from a problem in one-particle quantum mechanics. (Klein-Gordon eq.) Let me clarify that I am asking what is the <em>physical meaning</em> of saying a solution, or space of solutions, is non-local. Answers that hinge on the <em>form</em> of the equation are...better than nothing, but I am hoping for a more physical answer, since it is the solutions which are physical, not the way they are written down ....</p>
<p>This question, which I had already read, is related but the relation is unclear. <a href="http://physics.stackexchange.com/q/13624/6432">Why are higher order Lagrangians called 'non-local'?</a></p> | 1,437 | [
-0.033095404505729675,
0.0027583586052060127,
0.007126093842089176,
-0.022927578538656235,
0.005035671405494213,
0.03100389614701271,
-0.0416979156434536,
-0.02620622329413891,
0.02286566235125065,
-0.03474823758006096,
0.033634576946496964,
-0.005914443172514439,
0.05614210292696953,
0.036570459604263306,
-0.0046323188580572605,
0.03960312530398369,
-0.003385694231837988,
-0.008252101950347424,
-0.020868923515081406,
-0.02968534082174301,
0.027532849460840225,
0.007331885863095522,
0.0036551458761096,
-0.02292143926024437,
0.007928500883281231,
0.007239131256937981,
0.0020822540391236544,
0.012978853657841682,
0.010595432482659817,
0.05806805193424225,
-0.01959449052810669,
-0.03360193222761154,
0.0017674962291494012,
0.005974613130092621,
-0.008352910168468952,
0.01770138181746006,
0.0025348037015646696,
-0.024778466671705246,
0.022646961733698845,
-0.021553462371230125,
-0.04592205584049225,
-0.048555757850408554,
0.002057294826954603,
0.05802864953875542,
-0.045945536345243454,
0.03180308640003204,
0.045452781021595,
0.001229077228344977,
0.053687192499637604,
-0.030387764796614647,
0.08120164275169373,
0.006704416591674089,
-0.0203989390283823,
0.04090671241283417,
-0.03555644676089287,
0.014211846515536308,
0.06168382242321968,
0.05701391026377678,
-0.009506868198513985,
-0.05344034731388092,
-0.07139308750629425,
-0.04811515286564827,
0.04175668954849243,
-0.01966645009815693,
-0.005456890445202589,
0.03766454756259918,
0.05266125127673149,
0.007267018314450979,
-0.015519502572715282,
-0.0024292832240462303,
-0.0179746150970459,
-0.007027113810181618,
0.06057316064834595,
-0.0338401272892952,
0.026344917714595795,
-0.011633558198809624,
-0.002555564045906067,
0.0019392343237996101,
0.03184499964118004,
0.020578881725668907,
-0.028261786326766014,
0.03296830877661705,
0.015110202133655548,
-0.01965777762234211,
-0.010894589126110077,
-0.030456339940428734,
0.05862800031900406,
-0.0029852567240595818,
-0.003322228090837598,
0.03628523647785187,
0.009794443845748901,
0.035863474011421204,
0.04610246792435646,
-0.020494874566793442,
-0.023238971829414368,
0.01587662845849991,
0.04693058133125305,
0.04251519963145256,
-0.008352297358214855,
-0.018840983510017395,
-0.0022928009275346994,
-0.06610015779733658,
-0.021166613325476646,
0.08561577647924423,
0.007827263325452805,
-0.02391301654279232,
-0.061094388365745544,
0.040662311017513275,
-0.035890210419893265,
0.026508698239922523,
-0.012738259509205818,
0.04046383872628212,
-0.00015522998000960797,
0.022877883166074753,
0.006382927764207125,
-0.03330936282873154,
-0.016887586563825607,
-0.002751012099906802,
0.07131746411323547,
0.049401212483644485,
0.03459961339831352,
-0.02145291492342949,
0.017227962613105774,
-0.026162568479776382,
-0.045885052531957626,
0.015598663128912449,
0.0248432420194149,
0.006776805967092514,
-0.013179188594222069,
-0.016848383471369743,
0.0042928908951580524,
0.006976746488362551,
-0.0010426511289551854,
0.02255822904407978,
0.03830665349960327,
-0.017882389947772026,
-0.10105279833078384,
-0.06350406259298325,
0.0277419276535511,
0.051948290318250656,
0.00034742875141091645,
-0.057628877460956573,
0.009812976233661175,
0.006286735646426678,
0.09125781059265137,
-0.010841364040970802,
0.014670517295598984,
0.026360051706433296,
0.02304372377693653,
0.004817269276827574,
-0.012854653410613537,
-0.011517803184688091,
-0.020942125469446182,
-0.04414048790931702,
0.01044217124581337,
-0.036312252283096313,
0.013670709915459156,
0.003531389171257615,
0.024852929636836052,
-0.015905488282442093,
0.07557214051485062,
-0.03530501574277878,
0.020473472774028778,
0.017822133377194405,
0.006543673574924469,
-0.008127938024699688,
0.09495232999324799,
0.00861366931349039,
0.021486319601535797,
0.0455951914191246,
0.014034353196620941,
0.024829022586345673,
-0.002358705038204789,
0.009466427378356457,
0.05549358204007149,
-0.017758093774318695,
-0.0238625630736351,
0.004791686311364174,
0.020744789391756058,
-0.024717772379517555,
-0.02131630666553974,
-0.0058946129865944386,
-0.00721803167834878,
0.020766345784068108,
-0.03128783777356148,
0.042341042309999466,
0.001716631231829524,
0.02932875230908394,
0.029940979555249214,
-0.030659019947052002,
-0.02321968786418438,
-0.1014716848731041,
0.0011253185803070664,
0.06164627894759178,
-0.006879751104861498,
0.0521509163081646,
0.021273912861943245,
-0.01625070907175541,
-0.04457422345876694,
-0.036792442202568054,
-0.012199724093079567,
0.04265548661351204,
0.026876894757151604,
-0.01418278831988573,
0.025875549763441086,
0.028075693175196648,
0.030330821871757507,
-0.007718004286289215,
0.03354032710194588,
-0.02444065362215042,
-0.03898942098021507,
0.009526015259325504,
0.008492492139339447,
0.03939327597618103,
-0.017541205510497093,
-0.010509144514799118,
-0.007340469863265753,
-0.015956377610564232,
-0.029686560854315758,
0.027279261499643326,
-0.03424627706408501,
0.055832866579294205,
0.036758143454790115,
0.020364567637443542,
0.0018179320031777024,
0.017915701493620872,
-0.028761953115463257,
0.0224207304418087,
-0.0081193121150136,
-0.014336259104311466,
-0.049498770385980606,
-0.03673560172319412,
0.05113808810710907,
0.03656982257962227,
-0.040049195289611816,
-0.013820656575262547,
-0.0011305027874186635,
0.04088092967867851,
0.008568095043301582,
0.009937215596437454,
-0.04468805342912674,
-0.045640528202056885,
0.034719474613666534,
0.02568185329437256,
-0.0024465552996844053,
0.026581045240163803,
0.04795257747173309,
0.014085047878324986,
0.027554726228117943,
-0.0269971564412117,
-0.005875099916011095,
0.05099515616893768,
-0.055904097855091095,
0.019936921074986458,
-0.023614583536982536,
-0.02727893926203251,
0.062100850045681,
0.0007700849673710763,
0.030883977189660072,
-0.004062998108565807,
-0.0288811307400465,
0.003666854929178953,
-0.027554558590054512,
-0.0009409321937710047,
0.03593474626541138,
-0.007630351930856705,
-0.06174267455935478,
-0.004821429960429668,
0.019592592492699623,
-0.045768965035676956,
0.003677904140204191,
-0.024040723219513893,
-0.011960097588598728,
-0.013662905432283878,
0.020228995010256767,
0.04755169153213501,
-0.011799256317317486,
0.023721352219581604,
-0.012300251051783562,
-0.0430249460041523,
-0.015947196632623672,
-0.016229715198278427,
0.01944219134747982,
0.04911446571350098,
-0.032436903566122055,
0.03425070270895958,
-0.07833600789308548,
-0.00473075732588768,
0.034331031143665314,
0.0020180554129183292,
0.011553162708878517,
0.020382484421133995,
-0.030474897474050522,
-0.023287173360586166,
-0.027834061533212662,
-0.053983572870492935,
0.02250596694648266,
-0.026933293789625168,
0.015394305810332298,
0.05841083824634552,
-0.01717672497034073,
-0.024873552843928337,
-0.01547912135720253,
-0.03025772050023079,
-0.04957060515880585,
-0.0027894896920770407,
-0.006315997801721096,
0.056105852127075195,
-0.03774859756231308,
0.017198927700519562,
0.02618023380637169,
-0.020815031602978706,
0.015736738219857216,
-0.07052934169769287,
-0.06210586056113243,
-0.00879080779850483,
-0.0010842717019841075,
0.017088817432522774,
-0.029734622687101364,
-0.021225493401288986,
0.08417876809835434,
-0.00041765422793105245,
0.00122182653285563,
0.0022201277315616608,
0.006475516129285097,
0.007684113923460245,
0.023050932213664055,
0.0027101922314614058,
-0.012987243011593819,
-0.001938881236128509,
0.02254144847393036,
0.018959052860736847,
0.05942791327834129,
0.017557090148329735,
0.02792976424098015,
0.00042467957246117294,
-0.033894676715135574,
-0.023007838055491447,
-0.003981555346399546,
0.0568031407892704,
0.021012011915445328,
-0.04037432745099068,
0.008075994439423084,
-0.01339795719832182,
0.007631394080817699,
0.013156750239431858,
-0.04825616627931595,
0.031714797019958496,
0.02303844317793846,
-0.000474269938422367,
-0.011483787558972836,
0.040172796696424484,
-0.012075538747012615,
-0.050195880234241486,
-0.024627279490232468,
0.00321483938023448,
0.0005805171676911414,
0.0047852881252765656,
0.022542940452694893,
0.008435506373643875,
0.034705162048339844,
-0.04290756955742836,
0.0016993989702314138,
0.019783224910497665,
0.0007591110188513994,
0.0062459311448037624,
-0.005677766632288694,
-0.021305285394191742,
0.013894790783524513,
0.007607084698975086,
0.02190416119992733,
-0.0009244554676115513,
-0.03827594965696335,
0.013920385390520096,
-0.0363893024623394,
-0.014928784221410751,
-0.01370422262698412,
0.02672506496310234,
0.0063367183320224285,
0.04385904595255852,
0.003620120231062174,
0.0005211302195675671,
0.015162847004830837,
0.016131358221173286,
-0.05304128676652908,
0.010042880661785603,
0.005093373823910952,
-0.040458060801029205,
-0.010344015434384346,
-0.0019661628175526857,
0.005808765534311533,
-0.024080241098999977,
-0.021032853052020073,
0.03601850941777229,
0.015930738300085068,
-0.07614079862833023,
0.028473632410168648,
-0.0448182113468647,
-0.05184395983815193,
-0.03507270663976669,
0.005911292042583227,
0.030072690919041634,
-0.012045682407915592,
0.0012874896638095379,
0.02881607785820961,
-0.04032355546951294,
0.0042938124388456345,
-0.002107532462105155,
-0.012964146211743355,
0.07171647995710373,
-0.005394026171416044,
0.018329117447137833,
0.030491502955555916,
-0.021626146510243416,
0.020077763125300407,
0.04905670881271362,
0.06772033870220184,
-0.002049405127763748,
-0.047825608402490616,
0.003621612209826708,
-0.008498967625200748,
0.01822500489652157,
0.019248394295573235,
0.03720710799098015,
-0.003583490615710616,
0.019513456150889397,
0.02050267904996872,
0.025095535442233086,
0.007204831577837467,
0.02400883100926876,
0.028031278401613235,
0.024187292903661728,
-0.041263286024332047,
-0.03371873497962952,
-0.01113115530461073,
-0.011590481735765934,
-0.0038171005435287952,
-0.0035883737727999687,
-0.016419364139437675,
0.02687578834593296,
0.008942775428295135,
0.031597960740327835,
0.005412794649600983,
-0.022843070328235626,
-0.024344133213162422,
-0.03322108834981918,
-0.02137804590165615,
-0.04469537362456322,
0.007253875490278006,
-0.009597635827958584,
0.04733389988541603,
0.04443218186497688,
-0.018439073115587234,
-0.0016518259653821588,
-0.09283767640590668,
-0.021818876266479492,
0.04427390918135643,
0.024641530588269234,
0.004727024119347334,
-0.04858275502920151,
-0.04759382829070091,
-0.004199456889182329,
0.04798043891787529,
-0.03519994765520096,
0.02601824328303337,
0.013411890715360641,
0.009487491101026535,
-0.02440900169312954,
-0.028596127405762672,
-0.019364843145012856,
0.004524380899965763,
0.03779120370745659,
0.007105070631951094,
-0.040154192596673965,
0.020850995555520058,
-0.031782038509845734,
0.019548488780856133,
-0.0196904968470335,
0.05280236899852753,
0.002005389891564846,
0.008214686997234821,
-0.05138368159532547,
0.01359819807112217,
0.011561036109924316,
-0.064975805580616,
0.025655439123511314,
0.023999745026230812,
-0.01454060897231102,
0.03250882402062416,
-0.07347141951322556,
-0.07504246383905411,
0.0004342564498074353,
-0.026361385360360146,
-0.021208729594945908,
0.03609003499150276,
-0.06444431096315384,
0.04719133302569389,
0.006105875596404076,
0.06454788148403168,
0.051107537001371384,
0.016572454944252968,
0.007313987240195274,
-0.027899527922272682,
-0.028627939522266388,
0.020175760611891747,
-0.03190062567591667,
0.01675616018474102,
-0.0510893352329731,
0.005253341980278492,
-0.03331376984715462,
0.04166824743151665,
-0.028969448059797287,
0.013814503327012062,
-0.016190553084015846,
-0.04037785902619362,
-0.03289039060473442,
0.04256776347756386,
0.009749009273946285,
-0.02824980579316616,
-0.0122763030230999,
0.02407458983361721,
0.009482312947511673,
-0.04049387946724892,
0.020706119015812874,
-0.03175411373376846,
-0.02047562040388584,
0.07411643117666245,
-0.02161106839776039,
0.03701382130384445,
0.0003236884658690542,
-0.007646994199603796,
0.035968881100416183,
-0.03823602944612503,
0.010005982592701912,
0.041494861245155334,
-0.03699420019984245,
0.02009643241763115,
-0.05495193973183632,
-0.02933804877102375,
-0.012835009023547173,
-0.015765244141221046,
0.0228375606238842,
-0.028893301263451576,
0.0014339344343170524,
0.03527846932411194,
0.008600479923188686,
-0.07426610589027405,
-0.03802121430635452,
0.005657294765114784,
0.023341653868556023,
-0.03482791408896446,
-0.02144801802933216,
-0.01739353872835636,
-0.023197319358587265,
0.030652033165097237,
0.03343717381358147,
0.03711584210395813,
0.01074298657476902,
-0.009234977886080742,
0.03630461543798447,
0.0442214272916317,
0.03319995850324631,
-0.01082803588360548,
-0.00497042341157794,
-0.010241257958114147,
0.005727964919060469,
0.00950601790100336,
0.034608565270900726,
0.03761785477399826,
-0.022928934544324875,
-0.034518320113420486,
-0.03907245025038719,
-0.012792499735951424,
-0.0003031840897165239,
0.02117023803293705,
-0.02847435139119625,
0.04992198571562767,
-0.028779776766896248,
-0.0045721097849309444,
0.001893677283078432,
0.00013844874047208577,
-0.004223550204187632,
0.02676607482135296,
-0.00179608806502074,
0.004563930910080671,
0.01814766228199005,
-0.0014372633304446936,
0.0128746023401618,
-0.0099044693633914,
-0.03732359781861305,
0.02182031236588955,
0.013429039157927036,
-0.015167384408414364,
0.02075308747589588,
0.04776321351528168,
-0.0020831732545048,
0.014844530262053013,
-0.011923626065254211,
0.013741833157837391,
-0.009207818657159805,
0.030333947390317917,
-0.021576641127467155,
-0.02511521987617016,
0.001447272952646017,
0.04092589393258095,
0.04329674318432808,
0.007301996927708387,
0.03825846314430237,
0.019696714356541634,
-0.019515108317136765,
-0.009228783659636974,
0.00487767718732357,
0.0008913465426303446,
0.04250471666455269,
0.014136765152215958,
0.054194893687963486,
-0.03186926245689392,
-0.022731350734829903,
0.042043574154376984,
0.03681354224681854,
-0.03366391360759735,
0.0004492320877034217,
-0.00178006652276963,
0.03331715613603592,
-0.003585423342883587,
-0.017873158678412437,
-0.062133293598890305,
0.03383000195026398,
-0.02607758529484272,
0.0015713523607701063,
0.024835174903273582,
-0.02949145995080471,
0.042545344680547714,
-0.004867074079811573,
0.033430635929107666,
0.011184952221810818,
-0.002097098622471094,
-0.06378789246082306,
0.01590842381119728,
0.012954670935869217,
0.03591082990169525,
-0.004162339027971029,
0.00323169631883502,
0.03093782439827919,
0.015249159187078476,
-0.006510516162961721,
0.013220383785665035,
-0.05006687715649605,
-0.007078961469233036,
-0.0787140280008316,
-0.03511131927371025,
0.030878271907567978,
0.030885763466358185,
-0.002026189351454377,
-0.017791330814361572,
-0.031744394451379776,
0.009552976116538048,
0.010007538832724094,
0.02325729839503765,
-0.05197754502296448,
0.026577303186058998,
0.002859498141333461,
0.0005934083019383252,
0.00846618227660656,
-0.006792535074055195,
0.10048271715641022,
0.0630444660782814,
-0.003862862242385745,
-0.05743088200688362,
0.002335215453058481,
-0.03565379977226257,
0.008269349113106728,
-0.013257039710879326,
0.01472555473446846,
-0.008640849031507969,
-0.0262772124260664,
0.028240816667675972,
0.01211415696889162,
-0.0018886742182075977,
0.008998899720609188,
0.07948162406682968,
-0.0438997820019722,
-0.06919708102941513,
0.004092846531420946,
0.024708116427063942,
0.01637193001806736,
-0.016759365797042847,
0.007990865968167782,
0.03177288547158241,
-0.0029943000990897417,
0.04013771191239357,
-0.025002198293805122,
-0.031037606298923492,
0.027137983590364456,
0.013004569336771965,
-0.048689182847738266,
-0.011180257424712181,
-0.0052843899466097355,
0.009110180661082268,
-0.055228039622306824,
-0.005679184105247259,
0.048600487411022186,
-0.024835282936692238,
0.08050187677145004,
0.03028452955186367,
-0.023926813155412674,
0.005714903585612774,
0.007417506538331509,
0.03762084245681763,
-0.04425190016627312,
0.012981799431145191,
-0.00582166388630867,
0.032593734562397,
-0.024417521432042122,
0.005918187089264393,
-0.024602284654974937,
-0.011201361194252968,
0.00018841192650143057,
-0.04398497939109802,
-0.021254539489746094,
-0.00034999949275515974,
0.04106524586677551,
0.002064980799332261,
-0.0480659082531929,
-0.03265029564499855,
0.004167069680988789,
0.0008666576468385756,
-0.002018745755776763,
-0.0060613201931118965,
0.0080814054235816,
-0.00042104616295546293,
-0.01993495039641857,
0.01821483112871647,
0.02083263173699379,
-0.00577349029481411,
-0.06888340413570404,
-0.015920141711831093,
-0.033467162400484085,
-0.008512391708791256,
0.00014452991308644414,
0.01887112855911255,
0.031924545764923096,
0.014724872075021267,
-0.0050467862747609615,
-0.004793679341673851,
-0.04268801212310791,
-0.021431373432278633,
-0.01727822795510292,
0.011031410656869411,
-0.005942529067397118,
0.030191142112016678,
-0.006345158908516169,
0.0312555767595768,
-0.013630008324980736,
0.004690205678343773,
0.001194891519844532,
0.022854121401906013,
0.022339917719364166,
-0.012150974944233894,
-0.029314525425434113,
0.005669033620506525,
-0.06399339437484741,
-0.02583928592503071,
-0.00972604751586914,
-0.018457429483532906,
-0.00813594926148653,
0.008684705942869186,
0.03571165353059769,
0.022523202002048492,
0.0057465392164886,
-0.02786731719970703,
0.03561337664723396,
-0.00968211330473423,
0.005113994237035513,
0.040321655571460724,
0.022973662242293358,
-0.05937507748603821,
-0.011865603737533092,
-0.02327021397650242,
-0.0028194868937134743,
0.01897987723350525,
0.0593084916472435,
-0.02292398363351822,
-0.03715725243091583,
0.005570282693952322,
0.031794048845767975,
-0.04418892413377762,
0.02328086830675602,
-0.06093114614486694,
0.050262413918972015,
-0.012036170810461044,
-0.037495195865631104,
-0.017949603497982025,
0.022925270721316338,
0.006637304089963436,
-0.06317922472953796,
0.002289892639964819,
0.036748599261045456,
-0.028617478907108307,
-0.006300509907305241,
0.0011722658528015018,
0.007175952661782503,
0.05656956881284714,
0.012782875448465347,
-0.032637517899274826,
0.015708601102232933,
-0.030212383717298508,
-0.058688852936029434,
0.037305958569049835,
-0.02430742047727108,
0.006306047551333904,
0.07362023741006851,
-0.00027077391860075295,
-0.037198424339294434,
0.047145236283540726,
-0.05049145221710205,
0.012619633227586746,
-0.007572731468826532,
-0.021011902019381523,
-0.022315876558423042,
-0.02541068196296692,
-0.02802344225347042,
-0.007535523734986782,
0.006475167348980904,
0.010597056709229946,
0.015268786810338497,
0.01168700773268938,
-0.013491328805685043,
0.009689096361398697,
-0.0070370822213590145,
0.03202829882502556,
0.003450683318078518,
0.0035352229606360197,
-0.01300719752907753,
0.07675773650407791,
-0.046540070325136185,
0.014097570441663265,
0.01633373834192753,
0.03574976697564125,
-0.0957842543721199,
0.001734205987304449,
0.004732655826956034,
0.037254247814416885,
0.05362734571099281,
-0.03736414760351181,
0.01875471882522106,
0.015228575095534325,
-0.07878334075212479,
0.023997943848371506,
-0.025293640792369843,
-0.018401391804218292,
-0.02637646161019802,
0.01048489660024643,
-0.029712338000535965,
0.059495020657777786,
0.03601551428437233,
0.03611886501312256,
0.003656005719676614,
0.017952917143702507,
-0.01066885981708765,
-0.011438300833106041,
-0.0055706393904984,
0.027611931785941124,
-0.01991293951869011,
-0.0097585404291749,
0.07894548028707504,
-0.033917371183633804,
-0.031012745574116707,
0.05508692190051079,
-0.045939113944768906,
-0.04140984266996384,
-0.01342462282627821,
0.011699739843606949,
-0.0025222264230251312,
0.004005936440080404,
0.036021698266267776,
0.004601913504302502,
-0.036285649985075,
0.023157421499490738,
0.013931539840996265,
0.046216294169425964,
-0.006590557284653187,
0.0017263769404962659,
0.028815370053052902,
-0.013265330344438553,
-0.028637172654271126,
0.033975280821323395,
-0.027950963005423546,
0.008813805878162384,
0.017499729990959167,
0.008732977323234081,
0.015633834525942802,
0.016623230651021004,
0.023685378953814507,
-0.0026324333157390356,
0.0002863270929083228,
0.03972981497645378,
-0.002483274322003126,
-0.04365843906998634,
0.015188380144536495,
-0.02553928643465042,
-0.07065008580684662,
0.021130049601197243,
0.011431084014475346,
0.012264876626431942,
-0.055133502930402756,
-0.04329186677932739,
0.00623504351824522,
-0.027116481214761734,
-0.0022537684999406338,
-0.04196350276470184,
-0.0364154651761055,
0.03112206421792507,
0.00715922424569726,
0.0009188751573674381,
0.000883357017301023,
-0.005278551019728184,
-0.026759957894682884,
-0.0827251523733139,
0.029659444466233253,
0.012181947007775307,
-0.004779653158038855,
-0.03935578092932701,
-0.019598741084337234,
-0.02728644385933876,
0.022595062851905823,
0.02932046353816986,
0.030017191544175148,
-0.02063424326479435,
0.060546670109033585,
0.008087804540991783,
0.006892372388392687,
-0.009836607612669468,
-0.006763386074453592,
0.0030532071832567453,
0.0285654179751873,
-0.029229948297142982,
0.005374336615204811,
-0.018640348687767982,
0.03604774549603462,
0.05266997218132019,
0.008958259597420692,
-0.005242452025413513,
-0.028194304555654526,
-0.04998120293021202,
0.07972037047147751,
0.01419498585164547,
-0.008786190301179886,
0.06749536097049713,
-0.007546588312834501,
0.008342788554728031,
0.04368070140480995,
-0.02539839968085289,
-0.023639148101210594,
-0.02788202278316021,
-0.012162416242063046,
-0.010722185485064983,
0.009887193329632282,
-0.019951287657022476,
0.020881470292806625,
-0.013719637878239155,
-0.00009198114275932312,
0.0697420984506607,
-0.02674923464655876,
-0.024862084537744522,
0.03336296230554581,
0.02291826531291008,
0.030601903796195984,
0.0260264091193676,
-0.007774325553327799,
0.05763251334428787,
0.013301814906299114,
-0.040471043437719345,
0.059292957186698914,
0.042376864701509476,
0.022239599376916885,
0.018537010997533798,
0.022433893755078316,
-0.013202846050262451,
0.005781323183327913,
-0.016838334500789642,
0.0777655839920044,
-0.036991093307733536,
-0.0038273059763014317,
0.02027246728539467,
-0.015085350722074509,
-0.006717493757605553,
-0.014638958498835564,
-0.04465755447745323,
0.0838824138045311,
-0.0010198784293606877,
0.00942996796220541,
-0.039670802652835846,
0.042399339377880096,
0.0004690653004217893,
-0.01726648584008217,
0.009065937250852585,
0.059036947786808014,
-0.018208399415016174,
0.014416322112083435,
-0.02442319504916668,
-0.015212161466479301,
0.02743535488843918,
-0.049926772713661194,
-0.012456019409000874,
0.006592389661818743,
-0.0003211389121133834,
-0.006001529283821583,
-0.01335788145661354,
-0.013296266086399555,
0.008108080364763737,
0.024400608614087105,
-0.01071707159280777,
0.035351235419511795,
-0.04282880946993828,
-0.020853562280535698,
-0.05313880741596222,
0.028079528361558914,
-0.05116229131817818,
-0.026841476559638977,
-0.03811429813504219,
0.022490529343485832,
-0.028598923236131668,
-0.03603107109665871
] |
<p>Where can I find the base data for computing the energy release of nuclear decays and the spectra of the decay products?</p>
<hr>
<p>My immediate need is to find the energy release by the beta decay of Thorium to Protactinum upon receiving a neutron:</p>
<p>$$\mathrm{Th}02 + n \to \mathrm{Th}03 \to \mathrm{Pa} 13 + e^- + \bar{\nu}$$</p>
<p>The estimated amount of energy released from Beta decay is roughly 1eV.
Minus the neutrino loss, how much kinetic energy is released as heat?</p> | 1,438 | [
0.011239762417972088,
-0.04091986268758774,
-0.011606852523982525,
-0.008105692453682423,
-0.0012778498930856586,
0.04837813600897789,
-0.05388544499874115,
-0.010741044767200947,
0.044242873787879944,
-0.0536247119307518,
0.035219285637140274,
0.045310527086257935,
0.02235962636768818,
0.041533298790454865,
-0.014277440495789051,
0.005130450241267681,
-0.004788464866578579,
-0.016521373763680458,
-0.02225250005722046,
-0.05932004004716873,
0.026915235444903374,
-0.016382595524191856,
-0.0281671229749918,
0.0049558342434465885,
-0.06275252252817154,
0.06131907179951668,
0.022368064150214195,
0.025530841201543808,
0.02193489484488964,
0.06561257690191269,
-0.02440425008535385,
-0.07571069151163101,
0.006994050461798906,
0.00673424918204546,
0.0034226374700665474,
0.010372983291745186,
-0.03759399801492691,
-0.04254733771085739,
0.004666121676564217,
0.038117021322250366,
-0.026683999225497246,
-0.02889031358063221,
-0.018422024324536324,
0.03587207943201065,
-0.042636025696992874,
-0.017830587923526764,
0.009472244419157505,
0.012461427599191666,
0.022811725735664368,
-0.03528980165719986,
0.058332543820142746,
0.005185549613088369,
0.05070909485220909,
0.002392725320532918,
-0.013299007900059223,
0.012250043451786041,
0.02809039317071438,
0.08076612651348114,
0.027589967474341393,
-0.06403262913227081,
0.0021028672344982624,
-0.02616686187684536,
-0.03978375345468521,
0.015248635783791542,
-0.011523284949362278,
0.028210340067744255,
-0.016202017664909363,
-0.03138813376426697,
0.005762984976172447,
0.025228029116988182,
0.0769398882985115,
0.002917095785960555,
0.022713368758559227,
-0.004677291959524155,
0.02149062044918537,
-0.012865985743701458,
0.02059437334537506,
0.006886395160108805,
0.04164350777864456,
0.05920077860355377,
0.006948608905076981,
0.03193650394678116,
0.043295715004205704,
0.023267310112714767,
-0.03495848551392555,
0.000040744351281318814,
0.0748371109366417,
-0.008383626118302345,
0.003923278767615557,
0.02913166768848896,
0.02939877100288868,
0.01107113528996706,
0.0007233548094518483,
0.03070911392569542,
-0.037879426032304764,
0.017723077908158302,
0.005640022456645966,
0.06496378779411316,
-0.012724359519779682,
-0.02550325356423855,
0.05156482756137848,
0.0027349963784217834,
0.013981916010379791,
0.07568373531103134,
-0.013492398895323277,
0.0035012783482670784,
-0.005215862300246954,
-0.005151162855327129,
-0.019257396459579468,
-0.02394886687397957,
-0.029539596289396286,
-0.015603241510689259,
-0.013854792341589928,
0.035949867218732834,
-0.012653701938688755,
-0.04094544053077698,
0.0012394596124067903,
-0.023384172469377518,
0.04017471522092819,
0.009489036165177822,
0.0347164049744606,
-0.023145603016018867,
0.006180943455547094,
-0.03831397742033005,
-0.06274186819791794,
0.006112765986472368,
0.03662122040987015,
-0.010006322525441647,
-0.07455719262361526,
0.02833566628396511,
-0.017828328534960747,
-0.0377720482647419,
0.03256181627511978,
-0.03659295663237572,
0.01679365523159504,
0.006075856275856495,
-0.0837196558713913,
-0.0543832965195179,
0.014197498559951782,
0.0048500238917768,
-0.04322852939367294,
-0.041228532791137695,
0.0009168888791464269,
0.031153276562690735,
0.05417655035853386,
-0.006853312719613314,
0.008211608044803143,
-0.018081219866871834,
0.027530867606401443,
-0.026665346696972847,
-0.02519971691071987,
-0.008966909721493721,
-0.012332023121416569,
-0.030562469735741615,
-0.0473991259932518,
-0.050988804548978806,
0.02364213578402996,
0.007707081735134125,
-0.028760187327861786,
-0.0043074931018054485,
0.07503312081098557,
-0.0021792950574308634,
0.002564583672210574,
-0.002973702270537615,
0.018892960622906685,
-0.0349106602370739,
0.05967148020863533,
0.001997456420212984,
-0.023780545219779015,
0.011554963886737823,
-0.00539066456258297,
0.011064122430980206,
-0.027417922392487526,
0.023964272812008858,
0.07337817549705505,
-0.015347531996667385,
-0.039612337946891785,
-0.013917486183345318,
0.0009490865049883723,
0.02155158296227455,
-0.04676646366715431,
-0.03175180405378342,
0.004137814976274967,
-0.008005131036043167,
0.03962075710296631,
0.027271553874015808,
0.029037397354841232,
-0.04860542342066765,
0.015662694349884987,
-0.030015869066119194,
-0.031132198870182037,
-0.06295132637023926,
0.02672729827463627,
-0.026778921484947205,
-0.02374652959406376,
-0.03496910631656647,
0.0005305429804138839,
0.015943428501486778,
-0.006466816645115614,
-0.03098711557686329,
-0.005228491500020027,
0.004998259246349335,
0.018341263756155968,
-0.01096042338758707,
-0.01281864382326603,
0.03827530890703201,
0.04064079374074936,
-0.01619407907128334,
0.014232538640499115,
-0.01967557519674301,
-0.019993845373392105,
-0.02979285456240177,
-0.04835383966565132,
0.0023051314055919647,
0.012096202000975609,
0.006341856438666582,
-0.03914722055196762,
-0.027308326214551926,
0.00965412799268961,
-0.0031139731872826815,
-0.018260501325130463,
0.08363188803195953,
0.03954090178012848,
0.055617690086364746,
-0.0011387986596673727,
0.017222851514816284,
0.0027375048957765102,
0.01933218725025654,
-0.021521955728530884,
-0.01645023003220558,
-0.04432119429111481,
-0.026025384664535522,
0.021484272554516792,
0.013482505455613136,
-0.05112812668085098,
0.007059826515614986,
0.0458306185901165,
-0.00834780465811491,
0.028392303735017776,
0.01910596713423729,
-0.03369844704866409,
-0.034635208547115326,
-0.01874687895178795,
-0.018736131489276886,
-0.018429450690746307,
-0.009054108522832394,
0.019739819690585136,
0.06557385623455048,
0.004546732176095247,
-0.016290949657559395,
-0.0020174793899059296,
0.045787882059812546,
0.013642361387610435,
-0.011344716884195805,
-0.030464300885796547,
-0.07393624633550644,
0.062233325093984604,
-0.02701677195727825,
0.021421851590275764,
0.004774127155542374,
-0.001167233451269567,
0.036931995302438736,
0.00990256853401661,
-0.04047006368637085,
0.03960667923092842,
0.01974227838218212,
0.005067368503659964,
0.011421401984989643,
0.016486579552292824,
0.0027166707441210747,
0.06554272025823593,
-0.021805662661790848,
-0.05771953612565994,
-0.0017924944404512644,
0.020084410905838013,
0.027491584420204163,
-0.0055436319671571255,
0.03714881092309952,
-0.04585152864456177,
-0.023813491687178612,
0.006407447159290314,
-0.05320453643798828,
-0.02683122456073761,
0.04379197955131531,
-0.04822666943073273,
0.01821981556713581,
-0.0487443245947361,
-0.04023107513785362,
0.013478330336511135,
0.0014789720298722386,
-0.019897397607564926,
0.05860763415694237,
0.004945491906255484,
-0.07974855601787567,
-0.016376985237002373,
0.0011360769858583808,
-0.04068519175052643,
-0.014365633949637413,
0.026990335434675217,
0.04016929492354393,
0.00394717650488019,
-0.0220133438706398,
0.028498711064457893,
-0.05920569971203804,
-0.0007057505426928401,
-0.034620966762304306,
0.024645982310175896,
0.00855676643550396,
0.006808799225836992,
0.02289431542158127,
0.023636402562260628,
-0.019439080730080605,
-0.01563662476837635,
-0.061819836497306824,
-0.03990549594163895,
0.01043887622654438,
0.0018952824175357819,
0.056737080216407776,
0.026717200875282288,
-0.033531446009874344,
0.08432677388191223,
0.03929330036044121,
-0.042225949466228485,
-0.004345574416220188,
-0.008242620155215263,
0.02559000253677368,
-0.009525192901492119,
0.022765059024095535,
-0.0010812780819833279,
-0.010932130739092827,
0.0032686933409422636,
-0.032752007246017456,
0.013717610388994217,
0.05068892985582352,
0.02037050761282444,
-0.023226913064718246,
0.022685831412672997,
0.029267888516187668,
-0.01053717639297247,
0.03218459710478783,
0.002896343357861042,
-0.036409709602594376,
0.020568760111927986,
-0.002230987651273608,
0.03608895093202591,
0.013183961622416973,
-0.05642077326774597,
0.024581806734204292,
0.032216448336839676,
-0.012910858727991581,
-0.04737434163689613,
0.030971603468060493,
-0.005042641423642635,
-0.025415698066353798,
-0.0011230779346078634,
0.04248132184147835,
0.05181602016091347,
-0.010119754821062088,
0.008051585406064987,
0.007443107198923826,
0.05344749614596367,
0.0014243652112782001,
-0.05185472592711449,
-0.024133294820785522,
-0.01125016063451767,
-0.0012761172838509083,
-0.0029347508680075407,
0.034167394042015076,
0.04590398818254471,
0.04371672123670578,
0.04497252777218819,
-0.0007976389024406672,
-0.02750970795750618,
-0.04485873505473137,
-0.05572125315666199,
-0.0297870896756649,
-0.024823956191539764,
0.07916580140590668,
0.022116990759968758,
0.04641507565975189,
-0.01292754989117384,
-0.0006748656160198152,
0.04305519163608551,
-0.0036789034493267536,
-0.10206864029169083,
0.031089480966329575,
-0.040999289602041245,
-0.02104448899626732,
0.020153434947133064,
0.013887510634958744,
0.03480566665530205,
-0.00013553060125559568,
-0.05210939794778824,
0.001957047963514924,
-0.004556475207209587,
-0.03557625040411949,
0.0092008076608181,
-0.02786937914788723,
-0.039949528872966766,
-0.013101743534207344,
0.04246258735656738,
0.04244815558195114,
-0.009900311939418316,
-0.01851971633732319,
0.016564866527915,
-0.01636115089058876,
0.00511713745072484,
-0.007276918739080429,
0.024845775216817856,
-0.027969148010015488,
0.04661673307418823,
0.02724946290254593,
0.04282635822892189,
-0.01819787174463272,
0.01588943786919117,
-0.013464716263115406,
0.055003345012664795,
0.036822762340307236,
-0.03702278807759285,
-0.018156519159674644,
-0.010599731467664242,
0.02568972483277321,
0.05161573737859726,
0.03270162642002106,
0.0067282551899552345,
0.02402273193001747,
0.012350302189588547,
0.002845341106876731,
-0.02149089239537716,
0.03210132569074631,
0.06000897288322449,
-0.0014455338241532445,
-0.007236297242343426,
-0.0378669835627079,
0.014167984947562218,
0.009356040507555008,
-0.026111682876944542,
-0.05634380131959915,
0.029176482930779457,
-0.013462440110743046,
0.0022330963984131813,
0.010585715994238853,
0.016370851546525955,
-0.03094468265771866,
-0.002458483213558793,
0.026708045974373817,
0.0445169173181057,
-0.011208677664399147,
-0.02771454118192196,
0.03985927253961563,
0.020138153806328773,
0.027596205472946167,
-0.0019463945645838976,
0.045257121324539185,
-0.07307794690132141,
-0.0013233906356617808,
0.06254506856203079,
0.0601387694478035,
-0.005391315091401339,
-0.05700219050049782,
-0.04751553386449814,
0.013458733446896076,
0.05841705575585365,
-0.03319273144006729,
0.028845157474279404,
0.03132934495806694,
0.004972025286406279,
-0.04014125093817711,
-0.030268732458353043,
-0.007533233612775803,
0.03605608269572258,
0.013049808330833912,
0.03516208380460739,
-0.0374048687517643,
-0.003125361865386367,
-0.019845692440867424,
0.02591165341436863,
0.037243787199258804,
0.044192224740982056,
-0.009719430468976498,
0.007467356044799089,
0.0034646671265363693,
-0.0022308772895485163,
0.012881094589829445,
-0.053866855800151825,
-0.009416244924068451,
-0.0013336585834622383,
0.005215529352426529,
0.04013626649975777,
-0.03290338069200516,
-0.06452976167201996,
0.0037356603424996138,
0.039119698107242584,
0.002203631680458784,
-0.04651576280593872,
-0.06402198225259781,
0.05241181701421738,
0.042085837572813034,
0.003914861939847469,
0.07444001734256744,
0.0810699388384819,
-0.016551507636904716,
0.005645572207868099,
-0.04174095019698143,
-0.01053256168961525,
-0.023482443764805794,
0.012362262234091759,
-0.03729087859392166,
0.018222128972411156,
-0.012387612834572792,
0.01471736654639244,
-0.0044809263199567795,
0.01992885395884514,
0.0033215826842933893,
0.003042342606931925,
-0.03710002824664116,
0.03574489802122116,
-0.004560425411909819,
0.022897813469171524,
0.007289578206837177,
-0.005749884527176619,
-0.011051630601286888,
-0.007265096064656973,
0.0320560596883297,
0.025123972445726395,
-0.004401991609483957,
0.00970432534813881,
-0.03225705772638321,
0.02612634189426899,
-0.038994576781988144,
-0.03315484896302223,
0.03475133329629898,
-0.018678883090615273,
0.009663407690823078,
-0.017275337129831314,
0.031203893944621086,
0.05392817035317421,
-0.034917205572128296,
-0.02908046916127205,
0.012726212851703167,
-0.016398027539253235,
0.017549287527799606,
-0.04086608067154884,
0.03891555964946747,
-0.0007126815035007894,
0.021892568096518517,
-0.049051836133003235,
-0.002239496447145939,
0.02467643842101097,
-0.008213946595788002,
-0.04483937472105026,
-0.054017484188079834,
0.0039475662633776665,
-0.04110113903880119,
-0.01308745052665472,
0.0020075037609785795,
0.02734157256782055,
-0.025429842993617058,
0.010873490013182163,
0.00668971287086606,
0.0053731887601315975,
0.06377743184566498,
0.02317124605178833,
0.019664358347654343,
0.030484460294246674,
0.05088922008872032,
-0.03783212974667549,
0.0020383992232382298,
0.011226371861994267,
-0.011270610615611076,
-0.041332196444272995,
0.01054245512932539,
0.02144319750368595,
0.05690141022205353,
-0.010558610782027245,
0.008734134957194328,
0.04330088198184967,
0.022355347871780396,
-0.00498719047755003,
-0.022896192967891693,
0.031380388885736465,
0.01659248396754265,
0.039131250232458115,
-0.027678459882736206,
-0.03705456480383873,
-0.01539376750588417,
0.004188630264252424,
-0.02420666813850403,
-0.020375018939375877,
0.019527120515704155,
0.018576467409729958,
0.028079703450202942,
0.021280907094478607,
0.011425597593188286,
0.003948966506868601,
0.0010725900065153837,
0.017422933131456375,
-0.018164727836847305,
0.027504567056894302,
0.008335988968610764,
-0.03467625752091408,
-0.033184558153152466,
-0.03373922035098076,
-0.0685000866651535,
-0.015149986371397972,
0.03206048533320427,
0.012072490528225899,
0.05513497069478035,
0.015399189665913582,
0.0055192019790410995,
0.01650957204401493,
-0.01982215978205204,
-0.011030999943614006,
0.0184536874294281,
0.015440244227647781,
0.02522621862590313,
-0.005807089153677225,
-0.025151466950774193,
-0.013684064149856567,
0.026997743174433708,
-0.02501237392425537,
0.046837229281663895,
0.006711910013109446,
0.0233847014605999,
0.015631577000021935,
-0.06161521375179291,
-0.03742634505033493,
-0.004576613660901785,
-0.008590003475546837,
0.031176000833511353,
0.01707252860069275,
0.008954674005508423,
0.05487581342458725,
0.01838139444589615,
0.00829359795898199,
-0.06072166562080383,
-0.005573215428739786,
-0.041744109243154526,
0.004399430938065052,
0.029874123632907867,
-0.015542454086244106,
-0.02064170502126217,
0.024739746004343033,
0.021100059151649475,
-0.024730050936341286,
0.018981367349624634,
0.0036784245166927576,
-0.04624035581946373,
-0.0010289379861205816,
-0.03173298016190529,
-0.06816145032644272,
0.024396000429987907,
-0.026533465832471848,
-0.03457997739315033,
0.0042028105817735195,
-0.017681583762168884,
0.03776710107922554,
0.00589613476768136,
0.035909898579120636,
0.027310749515891075,
0.07374383509159088,
-0.038326703011989594,
-0.004111515358090401,
0.005332969129085541,
0.036766406148672104,
0.14090017974376678,
0.06445980817079544,
0.03375840187072754,
-0.056014906615018845,
-0.01871228963136673,
-0.00031923639471642673,
0.018885456025600433,
-0.011249897070229053,
0.012929871678352356,
-0.0062638442032039165,
0.013720918446779251,
0.03221319988369942,
0.04884723573923111,
0.004408720880746841,
0.014976748265326023,
0.025987759232521057,
-0.013870583847165108,
-0.024423999711871147,
0.05747368186712265,
0.006226558703929186,
-0.020470064133405685,
0.016535980626940727,
-0.040330711752176285,
0.0057991924695670605,
0.02211117371916771,
-0.03382842615246773,
-0.0494823083281517,
-0.03392456844449043,
0.020455285906791687,
0.010404492728412151,
-0.03238850086927414,
-0.03268419951200485,
0.006943637505173683,
0.04494231939315796,
0.01721002906560898,
0.01580638810992241,
0.007177174091339111,
0.003750898875296116,
0.0071409232914447784,
0.041955750435590744,
0.019675958901643753,
-0.014586725272238255,
0.023627249523997307,
0.03595537319779396,
-0.04913537576794624,
0.013150096870958805,
-0.020550154149532318,
0.05448853597044945,
-0.034695014357566833,
-0.011698043905198574,
-0.015468762256205082,
0.003004741622135043,
-0.00658026896417141,
-0.027922796085476875,
0.007355565205216408,
-0.012632202357053757,
-0.0026783873327076435,
-0.0580398328602314,
0.010857058688998222,
-0.03806930407881737,
0.0016077343607321382,
-0.013880651444196701,
0.03499647602438927,
0.003286314196884632,
-0.014646465890109539,
0.026553496718406677,
-0.025582488626241684,
0.0263187475502491,
-0.003101707436144352,
-0.003676614025607705,
-0.007194464094936848,
-0.01882840506732464,
-0.025756539776921272,
-0.022341420873999596,
0.015902217477560043,
0.0025855363346636295,
0.003906837198883295,
0.026039524003863335,
0.0025154268369078636,
-0.017464345321059227,
-0.04928768053650856,
0.058054160326719284,
-0.008427112363278866,
-0.033831384032964706,
-0.0184704028069973,
-0.002786048222333193,
-0.008497536182403564,
0.036192186176776886,
-0.011861312203109264,
0.019565090537071228,
0.015402638353407383,
-0.010722688399255276,
0.04825650900602341,
-0.04093148186802864,
-0.00628751190379262,
0.021118268370628357,
-0.04812461882829666,
-0.0008105008746497333,
-0.025911441072821617,
0.05088313668966293,
-0.005241950508207083,
0.010851151309907436,
0.062398653477430344,
0.018681704998016357,
-0.013224429450929165,
-0.02109382674098015,
-0.02460525557398796,
-0.05177123099565506,
0.016632145270705223,
-0.03835733234882355,
-0.007077214308083057,
0.0011821843218058348,
0.011627297848463058,
-0.028935713693499565,
-0.014782113023102283,
0.0167920533567667,
0.015244798734784126,
-0.02929716184735298,
0.04261912405490875,
-0.05916806682944298,
0.011023181490600109,
0.0067785861901938915,
0.03245658054947853,
0.012670195661485195,
0.0008536507957614958,
0.008260912261903286,
-0.002910513198003173,
-0.010145915672183037,
0.012273508124053478,
-0.00439969077706337,
0.0030919380951672792,
0.046543288975954056,
0.0005509181646630168,
-0.020716434344649315,
0.0006054722471162677,
0.018428592011332512,
-0.0034837268758565187,
0.05625510960817337,
0.009642907418310642,
-0.004162546247243881,
0.028727110475301743,
-0.007545505650341511,
-0.027123555541038513,
0.03321908041834831,
-0.004345008637756109,
0.010794825851917267,
0.03780727833509445,
-0.03326552361249924,
-0.03041987679898739,
0.07362206280231476,
-0.03744564205408096,
-0.028715960681438446,
0.04201384261250496,
0.008637583814561367,
0.011768507771193981,
0.013788928277790546,
0.009158466011285782,
0.0002636450226418674,
-0.018818898126482964,
0.007570995949208736,
0.007938926108181477,
-0.01675969734787941,
-0.009681589901447296,
-0.04774825647473335,
-0.0017611355287954211,
-0.026125876232981682,
0.01713545434176922,
0.009264295920729637,
0.028185024857521057,
0.06392528861761093,
-0.04497727379202843,
0.025400537997484207,
0.031380582600831985,
0.003753924509510398,
-0.10678191483020782,
-0.02419419400393963,
-0.03776964917778969,
0.025926677510142326,
0.011223582550883293,
-0.09799974411725998,
0.037267547100782394,
-0.0034746602177619934,
-0.03743966668844223,
-0.013793925754725933,
-0.011974825523793697,
-0.020565904676914215,
-0.012308558449149132,
0.0073334272019565105,
-0.005660373251885176,
0.04425443708896637,
0.04893212392926216,
0.06551478058099747,
0.03495541960000992,
0.007010262459516525,
-0.0033843987621366978,
-0.020238570868968964,
-0.051259372383356094,
-0.0045530423521995544,
-0.0002533598162699491,
-0.0294051393866539,
0.04353085905313492,
-0.014768649823963642,
-0.01037555281072855,
0.006561663467437029,
-0.017159512266516685,
-0.005501692648977041,
-0.018042882904410362,
-0.0034329667687416077,
-0.04056598246097565,
0.04493824392557144,
0.024150459095835686,
-0.008487619459629059,
-0.029221491888165474,
0.0009877703851088881,
0.004561800044029951,
0.034103408455848694,
-0.020827583968639374,
0.03647402673959732,
0.04566888511180878,
-0.02128012292087078,
-0.01510764379054308,
0.002623188542202115,
0.005451506935060024,
-0.029403598979115486,
-0.004092936869710684,
-0.01591523177921772,
-0.012105143629014492,
-0.024511143565177917,
-0.013502856716513634,
-0.02211260236799717,
0.012521318159997463,
0.018371595069766045,
0.01021056529134512,
0.03312103450298309,
0.006879741325974464,
0.001968791475519538,
-0.03757748380303383,
0.0019717691466212273,
0.016913510859012604,
-0.011768084019422531,
-0.038779400289058685,
0.02104489505290985,
0.016801053658127785,
0.0024320005904883146,
-0.009400934912264347,
-0.04175892844796181,
-0.08236261457204819,
0.011329910717904568,
0.004642506595700979,
0.011667263694107533,
-0.01650347001850605,
-0.03177553787827492,
0.016244078055024147,
-0.05247970297932625,
0.002132556401193142,
-0.008363574743270874,
-0.017677243798971176,
-0.03323986381292343,
0.0020206940826028585,
0.01329720113426447,
0.005288390442728996,
0.028729459270834923,
-0.008263755589723587,
-0.03274309262633324,
0.005048607010394335,
-0.05499172583222389,
0.012281244620680809,
-0.02789113111793995,
0.0409977100789547,
-0.016802377998828888,
-0.044773489236831665,
-0.006653151009231806,
-0.004956299439072609,
-0.021567171439528465,
0.04104863852262497,
0.03101922944188118,
0.034288134425878525,
-0.0191988293081522,
-0.020932981744408607,
0.017619827762246132,
0.07772961258888245,
0.0032374057918787003,
-0.015390114858746529,
0.09231451153755188,
-0.010053157806396484,
0.008841043338179588,
0.02741003967821598,
-0.025242293253540993,
0.0015549729578197002,
0.046154268085956573,
-0.02324601076543331,
-0.024025144055485725,
-0.005590404849499464,
-0.031460296362638474,
0.05837529897689819,
-0.04956572875380516,
-0.005810785572975874,
0.049779340624809265,
-0.038905560970306396,
-0.021623140200972557,
0.012827818281948566,
0.005491455085575581,
0.04164613410830498,
0.022343631833791733,
0.04688224196434021,
0.013987050391733646,
-0.006830398924648762,
0.024648517370224,
0.03244613856077194,
0.0058492133393883705,
0.0006543495110236108,
-0.0023098201490938663,
-0.01321806013584137,
-0.025491997599601746,
0.0053872535936534405,
0.0115371597930789,
0.0038161559496074915,
-0.038305312395095825,
-0.0630832239985466,
0.048264797776937485,
-0.006233806721866131,
-0.014929933473467827,
0.004854380153119564,
-0.05167647451162338,
0.09385783970355988,
-0.042131390422582626,
0.013605196960270405,
-0.051764655858278275,
-0.020198192447423935,
-0.0230224821716547,
0.02562602050602436,
-0.00574106490239501,
0.02315646968781948,
-0.0051908548921346664,
0.05022905021905899,
-0.0012693083845078945,
0.020745541900396347,
0.011548657901585102,
-0.059510793536901474,
-0.02831781841814518,
-0.009036888368427753,
-0.010331444442272186,
-0.0032301084138453007,
0.009421993978321552,
-0.009116529487073421,
-0.020647233352065086,
0.010696395300328732,
0.036047209054231644,
0.0066476366482675076,
-0.003898021299391985,
-0.027382154017686844,
-0.014889532700181007,
0.0593002550303936,
-0.02837495319545269,
-0.0051069073379039764,
-0.035977184772491455,
-0.0010486844694241881,
-0.05423670634627342,
-0.023302607238292694
] |
<p><strong>Problem/Solution</strong></p>
<p><img src="http://img832.imageshack.us/img832/1313/88791065.jpg" alt="">!</p>
<p><strong>Question</strong></p>
<p>What happened to the work done by friction BEFORE it touched the spring? Why was that neglected? Also they say there is no physical meaning behind the negative root, so what is the "unphysical" meaning behind the negative root? How are we supposed to know that the speed is constant before and just as it makes contact with the spring?</p>
<p><strong>@atomSmasher</strong></p>
<p><img src="http://img59.imageshack.us/img59/917/friclk.jpg" alt="">!</p>
<p>I am referring to the green region. Shouldn't it be</p>
<p>$E_i = \frac{1}{2}mv_A ^2 - f_k(x_b + x_{green distance})$</p>
<p>$E_f = \frac{1}{2}kx_B ^2$</p>
<p>I realize we would have two unknowns then. </p> | 1,439 | [
-0.004978576209396124,
-0.00034364123712293804,
-0.018139386549592018,
0.009596363641321659,
0.024780791252851486,
-0.013862949796020985,
-0.03335319831967354,
-0.02185962349176407,
-0.045834194868803024,
0.004021213389933109,
0.014365743845701218,
0.051385555416345596,
0.02941276505589485,
0.03103131428360939,
0.0408395454287529,
-0.013128071092069149,
0.007108085788786411,
-0.05733050778508186,
-0.008402238599956036,
-0.0213553998619318,
0.03685421869158745,
-0.020910050719976425,
0.017297739163041115,
0.006564869545400143,
-0.011915849521756172,
-0.01695822738111019,
0.008754363283514977,
-0.022877197712659836,
-0.0001465070090489462,
0.028741924092173576,
-0.0034148565027862787,
-0.03514501824975014,
-0.005051457788795233,
-0.025649771094322205,
0.015570237301290035,
0.04977978393435478,
-0.0406782440841198,
-0.017750956118106842,
-0.04794225096702576,
0.03210877627134323,
-0.0014666870702058077,
0.006069744937121868,
0.00022426726354751736,
0.027281323447823524,
0.005428472999483347,
0.014761829748749733,
0.042864035815000534,
-0.018087226897478104,
0.06437719613313675,
-0.044966936111450195,
0.04216008633375168,
-0.010376396588981152,
0.016256598755717278,
0.021519601345062256,
-0.04035162553191185,
-0.0509922094643116,
0.061709724366664886,
0.07475343346595764,
-0.0030325937550514936,
-0.05884270742535591,
0.00009659468923928216,
-0.002180177951231599,
-0.03120501898229122,
0.0021057589910924435,
-0.013942612335085869,
0.03963808715343475,
-0.0030348498839884996,
-0.013216705992817879,
0.025962360203266144,
0.0004365288477856666,
0.016382679343223572,
0.011940876953303814,
0.0358181893825531,
-0.0031306131277233362,
0.01499900408089161,
-0.01800333894789219,
0.0009676088229753077,
0.023361777886748314,
0.022632131353020668,
0.0297955684363842,
-0.042462658137083054,
0.0005641098250634968,
0.03176713362336159,
0.024344248697161674,
-0.014817689545452595,
-0.004307253751903772,
0.040887169539928436,
0.011782536283135414,
0.028864264488220215,
0.013747606426477432,
0.04487403482198715,
0.02593899704515934,
0.006250768434256315,
-0.022988740354776382,
0.01816413924098015,
0.03727440536022186,
0.024310506880283356,
0.031776174902915955,
0.012392363511025906,
-0.003763079410418868,
-0.021147629246115685,
-0.04367415979504585,
0.041194524616003036,
0.04866243153810501,
-0.012891334481537342,
-0.019805453717708588,
0.014308716170489788,
0.028074068948626518,
0.003557269461452961,
0.00941783282905817,
-0.03595227748155594,
0.006037836894392967,
0.014277273789048195,
-0.023425860330462456,
0.013927076943218708,
-0.04250848665833473,
-0.02470906637609005,
0.011616501957178116,
0.049309223890304565,
0.007493217475712299,
0.018704844638705254,
-0.017816059291362762,
0.02707132324576378,
0.0009072180837392807,
-0.01808895170688629,
-0.02272075042128563,
0.04492483288049698,
-0.012632114812731743,
-0.017946965992450714,
0.017920779064297676,
0.005085647106170654,
0.03075982630252838,
-0.008123897016048431,
0.0008462420664727688,
0.005498955491930246,
-0.007900998927652836,
-0.0996197909116745,
-0.09887153655290604,
0.05388110131025314,
0.0005439324886538088,
-0.032885096967220306,
-0.09640137851238251,
-0.014303096570074558,
0.037195660173892975,
0.05660718306899071,
0.012000001035630703,
-0.03185737133026123,
-0.011354172602295876,
0.03599177673459053,
0.007904727011919022,
0.01078030001372099,
-0.018051061779260635,
-0.008302695117890835,
-0.028178896754980087,
-0.00825655460357666,
-0.047469012439250946,
0.01376201119273901,
0.04250691831111908,
-0.021543163806200027,
-0.014583276584744453,
0.06390652060508728,
0.0011907587759196758,
0.0030190390534698963,
0.006270826328545809,
-0.026125511154532433,
-0.01372356154024601,
0.0500776469707489,
0.0379229374229908,
-0.008024407550692558,
0.025581132620573044,
0.014335095882415771,
0.023609858006238937,
-0.03262533247470856,
-0.012697677128016949,
0.014306440949440002,
-0.03523392230272293,
0.008379733189940453,
-0.013040128163993359,
0.04838459938764572,
-0.02202020213007927,
-0.0701407864689827,
-0.06226339563727379,
0.010888285003602505,
0.022856013849377632,
-0.02315184473991394,
0.05897391960024834,
-0.0027361628599464893,
0.0151410773396492,
0.02105550840497017,
-0.022869497537612915,
-0.0037928728852421045,
-0.046357639133930206,
0.023201901465654373,
0.015143001452088356,
-0.0424543134868145,
0.02919471636414528,
-0.011865024454891682,
0.043106935918331146,
-0.025448983535170555,
-0.014224440790712833,
0.04775276407599449,
0.03511592000722885,
0.02452859655022621,
-0.002395801478996873,
0.005751598626375198,
0.07774101197719574,
0.026706993579864502,
0.004617784172296524,
0.01936922036111355,
-0.028065944090485573,
-0.0031689687166363,
0.010490253567695618,
-0.061279959976673126,
0.010995933786034584,
0.026012159883975983,
-0.00330268032848835,
0.015499611385166645,
-0.010041855275630951,
0.008155242539942265,
-0.014735882170498371,
-0.024050725623965263,
0.06733978539705276,
0.08664512634277344,
-0.004903605207800865,
0.013950904831290245,
0.02498455159366131,
0.004463931079953909,
0.0627526342868805,
-0.02107708342373371,
-0.017442746087908745,
-0.054427385330200195,
-0.02935813181102276,
0.01970708929002285,
0.037808310240507126,
-0.030041947960853577,
-0.001683823182247579,
0.02946501038968563,
-0.008103792555630207,
0.010699664242565632,
0.011184541508555412,
-0.0008512168424203992,
-0.038905661553144455,
0.03176214173436165,
0.018001554533839226,
-0.016858534887433052,
0.023481693118810654,
0.028604963794350624,
0.013909649103879929,
0.03318589925765991,
-0.037712663412094116,
0.016333438456058502,
0.047483302652835846,
0.00597437983378768,
0.03549308702349663,
-0.003364963922649622,
-0.002299022627994418,
0.029271366074681282,
-0.010497748851776123,
0.04930305853486061,
0.011737165972590446,
-0.0190481748431921,
0.03277212753891945,
-0.01618335023522377,
-0.012752578593790531,
0.002263587899506092,
-0.02620047889649868,
-0.010912156663835049,
-0.011881551705300808,
0.03323724493384361,
-0.05060235783457756,
-0.011317740194499493,
-0.024293623864650726,
-0.021111762151122093,
0.01793493703007698,
-0.023153357207775116,
0.04868149757385254,
0.02412521280348301,
0.016661472618579865,
-0.013677638955414295,
-0.010085206478834152,
-0.002740587340667844,
-0.040283624082803726,
0.009018919430673122,
0.007219891529530287,
0.001999068306759,
0.009508172981441021,
-0.009887822903692722,
-0.0040418608114123344,
0.034767474979162216,
-0.005798382218927145,
-0.01226675882935524,
0.00615639379248023,
0.012499978765845299,
-0.03706519305706024,
-0.0013973742024973035,
-0.03140512853860855,
0.004627969115972519,
-0.05444476380944252,
-0.011528920382261276,
0.05034687742590904,
-0.03250056877732277,
-0.017387863248586655,
0.0221612136811018,
-0.03147027641534805,
-0.03214901313185692,
-0.03162042424082756,
-0.023407140746712685,
0.037984076887369156,
-0.008348595350980759,
0.017628682777285576,
-0.007127841934561729,
-0.015559641644358635,
-0.016551297158002853,
-0.052162282168865204,
-0.015300578437745571,
0.010695272125303745,
-0.01719866320490837,
0.07257018238306046,
-0.023951301351189613,
-0.006984819192439318,
0.11167099326848984,
0.06692366302013397,
-0.023464426398277283,
-0.03583712503314018,
-0.033656589686870575,
-0.051208630204200745,
-0.03933727741241455,
-0.025499826297163963,
0.05805385485291481,
-0.00019498885376378894,
0.054722342640161514,
-0.005242484621703625,
0.03096819669008255,
0.06228512153029442,
-0.008526794612407684,
-0.008356046862900257,
-0.0150901572778821,
-0.016111716628074646,
0.013257439248263836,
0.056369371712207794,
0.032584499567747116,
0.019747775048017502,
0.022296365350484848,
-0.004640142899006605,
0.028072956949472427,
0.04691903293132782,
-0.06735937297344208,
0.0458524152636528,
0.007711523678153753,
-0.00006333646160783246,
-0.03246355801820755,
0.02172320894896984,
-0.005014762282371521,
-0.01663224585354328,
-0.035229988396167755,
-0.02817787602543831,
0.03479243814945221,
0.0018925793701782823,
-0.007569611072540283,
0.027348050847649574,
0.029055535793304443,
-0.009376474656164646,
-0.06530758738517761,
-0.008182034827768803,
-0.0026321394834667444,
0.04714977368712425,
-0.001965401228517294,
-0.007204416673630476,
0.01724049635231495,
0.048234716057777405,
0.02553286962211132,
0.01876159757375717,
-0.06384988129138947,
-0.0401885025203228,
-0.05375029146671295,
-0.07092899084091187,
0.005250030662864447,
0.04715253412723541,
-0.00735804159194231,
0.042384978383779526,
0.008383963257074356,
0.019131958484649658,
0.01380692794919014,
-0.012916472740471363,
-0.1001710370182991,
0.026325419545173645,
-0.035952989012002945,
-0.04340425133705139,
-0.0035189364571124315,
0.011959505267441273,
0.028065448626875877,
-0.034756843000650406,
-0.0011052755871787667,
0.028182253241539,
0.03258579224348068,
-0.05635935068130493,
0.004399814177304506,
-0.019483566284179688,
-0.04737498611211777,
-0.03365200012922287,
-0.0008233509142883122,
0.06315900385379791,
-0.009001255966722965,
0.04333042353391647,
0.06492204964160919,
-0.042528215795755386,
0.014195905067026615,
-0.040074992924928665,
-0.02276628278195858,
0.021919816732406616,
0.03927982598543167,
0.006788084749132395,
0.006381590850651264,
0.029551876708865166,
0.012527555227279663,
0.029705481603741646,
0.040569569915533066,
0.00446460023522377,
0.01082376018166542,
-0.027554698288440704,
-0.03873128443956375,
-0.02037757821381092,
-0.024345576763153076,
0.07200326025485992,
-0.0584489107131958,
-0.003325844882056117,
-0.0058860378339886665,
0.007274176459759474,
-0.009923703037202358,
0.043735526502132416,
0.02533000521361828,
0.019992193207144737,
0.007851999253034592,
-0.07015921175479889,
-0.017504602670669556,
-0.0483257956802845,
-0.03245845064520836,
0.009295988827943802,
-0.017969030886888504,
-0.01797768659889698,
-0.012586748227477074,
0.04766617715358734,
0.04052756726741791,
0.007775587495416403,
0.043990615755319595,
-0.03198856860399246,
0.005308690946549177,
-0.026566453278064728,
-0.0127143245190382,
0.02574942633509636,
0.01989923231303692,
0.07587137073278427,
-0.009303196333348751,
-0.006862815003842115,
-0.07426834106445312,
-0.03964168578386307,
0.029750438407063484,
0.06166621670126915,
0.005715357605367899,
-0.0014755429001525044,
-0.054775021970272064,
-0.0501374825835228,
0.05238111689686775,
-0.033358316868543625,
0.038453109562397,
-0.0007857333403080702,
0.039203353226184845,
-0.03556956723332405,
-0.05653342232108116,
-0.03436234965920448,
0.012012801133096218,
-0.02210092358291149,
0.010711935348808765,
-0.007540772669017315,
-0.03291536122560501,
0.016901973634958267,
0.007473757956176996,
0.013654367998242378,
0.05579238757491112,
-0.02440473437309265,
-0.030603062361478806,
-0.012726940214633942,
-0.020639905706048012,
-0.02094481885433197,
-0.09929009526968002,
0.030703561380505562,
-0.014511816203594208,
-0.008014474995434284,
0.026368867605924606,
-0.040909264236688614,
-0.05500662326812744,
0.041488129645586014,
0.025492124259471893,
-0.007621008437126875,
-0.01028196420520544,
-0.022808067500591278,
0.04467349499464035,
0.05960273742675781,
-0.0027278733905404806,
0.02102750726044178,
0.00046620372449979186,
-0.03087998740375042,
0.03514718636870384,
-0.014915568754076958,
-0.014785676263272762,
-0.0007761734304949641,
0.025418948382139206,
-0.04602218419313431,
0.006773528642952442,
-0.03141484037041664,
0.027425937354564667,
-0.0032576052471995354,
0.02992110699415207,
-0.059036675840616226,
-0.04199981689453125,
0.008817655965685844,
0.011649107560515404,
-0.011160853318870068,
0.00028324269806034863,
-0.014878676272928715,
-0.0026951837353408337,
-0.0031058008316904306,
-0.05016684532165527,
-0.0030174297280609608,
0.025844000279903412,
0.01701887883245945,
0.04228535294532776,
0.006487634032964706,
-0.0022647548466920853,
-0.01582547277212143,
-0.01685415767133236,
0.00019484301446937025,
-0.04728216305375099,
0.02198498137295246,
0.0003875421534758061,
0.0014580696588382125,
0.005558056756854057,
-0.011127402074635029,
-0.027345387265086174,
-0.0006639870698563755,
-0.030123012140393257,
-0.012157567776739597,
-0.06966521590948105,
0.00002318999577255454,
0.04390463978052139,
-0.00781180988997221,
-0.030674053356051445,
-0.06079205125570297,
0.014621042646467686,
-0.009752105921506882,
-0.010289224795997143,
-0.0009452376398257911,
-0.01708647422492504,
0.015920352190732956,
0.009106053970754147,
0.030858302488923073,
0.025153517723083496,
-0.021646734327077866,
-0.02053091675043106,
0.047211773693561554,
0.04581919312477112,
0.03575965017080307,
0.0044590481556952,
-0.009625217877328396,
0.04252852872014046,
0.006830733269453049,
-0.05044499412178993,
0.01992603950202465,
0.035014815628528595,
-0.03340502828359604,
-0.033205296844244,
-0.0258677639067173,
-0.0006692089373245835,
0.00293306028470397,
0.013057073578238487,
-0.023955384269356728,
0.014905099757015705,
0.023698126897215843,
0.009061401709914207,
-0.029821082949638367,
0.014182663522660732,
0.022589199244976044,
0.030876226723194122,
0.007673527114093304,
-0.02005741186439991,
-0.0349309965968132,
-0.030228452757000923,
-0.007312987931072712,
0.01815982162952423,
-0.026265282183885574,
-0.009808938950300217,
0.07724763453006744,
-0.04978563264012337,
0.005183721426874399,
0.04117850586771965,
-0.024883978068828583,
0.03682208061218262,
-0.012205999344587326,
0.03908747062087059,
-0.011703668162226677,
0.004792075604200363,
-0.021479133516550064,
-0.026620084419846535,
-0.04750059172511101,
-0.013620814308524132,
0.05590562894940376,
-0.02384462207555771,
0.05766545981168747,
-0.008670472539961338,
-0.0015347906155511737,
-0.007354161702096462,
0.0005011178436689079,
-0.003625498153269291,
-0.02796916477382183,
-0.006422364618629217,
0.01771051622927189,
-0.02343054488301277,
0.020448917523026466,
0.046108003705739975,
0.02444439008831978,
-0.04877796024084091,
-0.03916574642062187,
0.009310688823461533,
0.040390364825725555,
0.028129171580076218,
-0.009111215360462666,
-0.029967717826366425,
-0.0034298072569072247,
0.0134396031498909,
0.07262559235095978,
0.0158239733427763,
-0.030273467302322388,
0.08798597753047943,
0.01892387494444847,
-0.011903616599738598,
-0.031003817915916443,
-0.004610223229974508,
-0.05476713553071022,
-0.00672442140057683,
-0.007735503371804953,
0.019115129485726357,
0.03809402510523796,
-0.006795939523726702,
-0.0004554114129859954,
0.01222566794604063,
0.03397683426737785,
-0.04628736153244972,
-0.03391031548380852,
-0.02941587008535862,
-0.038818515837192535,
-0.05761442333459854,
0.058583177626132965,
-0.01278921402990818,
-0.05278913304209709,
0.05166653171181679,
-0.06513579189777374,
0.03208424150943756,
0.04252461716532707,
0.018132366240024567,
-0.02422291226685047,
0.09077003598213196,
0.014223686419427395,
0.021310772746801376,
-0.010847276076674461,
0.012444600462913513,
0.1288333237171173,
0.05833306908607483,
0.008264313451945782,
-0.043559908866882324,
0.029642615467309952,
-0.01574089005589485,
0.008548867888748646,
-0.00976850651204586,
0.015217192471027374,
-0.04061189666390419,
0.033052511513233185,
0.006725167389959097,
0.04509919881820679,
-0.007862575352191925,
-0.014758007600903511,
-0.0006281888927333057,
-0.007722756359726191,
-0.03990694135427475,
-0.0003902299504261464,
-0.024269232526421547,
-0.032091476023197174,
-0.0051335725001990795,
0.004272070247679949,
0.03515659272670746,
-0.029056662693619728,
-0.0013889435213059187,
-0.015066522173583508,
-0.03512964025139809,
0.04115930199623108,
-0.008448249660432339,
-0.0008921081898733974,
0.07380417734384537,
0.022814331576228142,
-0.015001708641648293,
-0.01616753078997135,
0.02561117149889469,
0.03730686008930206,
0.00026865556719712913,
0.036643534898757935,
0.036551542580127716,
0.016808269545435905,
-0.024425985291600227,
0.012478210963308811,
0.002615126548334956,
-0.04814600944519043,
-0.015423660166561604,
-0.05999254807829857,
0.06260228902101517,
-0.016244852915406227,
-0.01631329208612442,
0.019289491698145866,
-0.019483445212244987,
0.006568084005266428,
-0.041934847831726074,
-0.017898477613925934,
0.010186202824115753,
0.03767414391040802,
-0.01673843339085579,
-0.018133757635951042,
0.012601101770997047,
0.03178514912724495,
0.008363621309399605,
-0.02141278050839901,
-0.005589162465184927,
-0.006780189462006092,
-0.012811914086341858,
0.03215329721570015,
0.055449895560741425,
-0.00583725655451417,
-0.0072684520855546,
-0.03351357579231262,
-0.016126373782753944,
-0.025615151971578598,
0.013294434174895287,
-0.011512205936014652,
0.02681780606508255,
0.030511684715747833,
-0.018360592424869537,
-0.01770871691405773,
-0.05668263882398605,
-0.023950913920998573,
0.0549103282392025,
0.01933560147881508,
-0.005244059953838587,
-0.02579645998775959,
0.014271430671215057,
0.0035747012589126825,
0.029536135494709015,
-0.014584487304091454,
0.011176864616572857,
0.012364063411951065,
0.04507995396852493,
0.01531925704330206,
-0.014059518463909626,
-0.02028724178671837,
0.009804829955101013,
-0.020109334960579872,
0.014019131660461426,
-0.001278234994970262,
0.020433610305190086,
0.0014858251670375466,
0.02482789009809494,
0.00141660135705024,
0.009238757193088531,
-0.025583907961845398,
0.006943803280591965,
0.011927193962037563,
-0.030786942690610886,
-0.008269602432847023,
0.030217569321393967,
-0.035544347018003464,
-0.054179947823286057,
-0.0005853131879121065,
-0.03414028510451317,
-0.011490259319543839,
0.034710947424173355,
0.04120362177491188,
-0.025115113705396652,
0.0250575989484787,
-0.04141635075211525,
0.025672229006886482,
-0.05812036991119385,
0.0030097216367721558,
-0.015185513533651829,
-0.014291890896856785,
0.0014304860960692167,
0.017402997240424156,
-0.023295670747756958,
0.03602156788110733,
-0.009015685878694057,
0.0049097854644060135,
-0.0006906752241775393,
0.05146912485361099,
0.011952998116612434,
0.02154773660004139,
-0.0011485611321404576,
0.001045391196385026,
0.00563703291118145,
0.004891789518296719,
-0.010619097389280796,
0.04508849233388901,
-0.0515553243458271,
-0.048425111919641495,
-0.0037579191848635674,
0.0355532243847847,
0.00902886688709259,
-0.006706443149596453,
-0.011793832294642925,
0.007559543941169977,
0.026181045919656754,
-0.03511533513665199,
0.018022757023572922,
-0.006715237628668547,
-0.0457848384976387,
-0.04655275121331215,
-0.027720561251044273,
0.02623605914413929,
-0.03069283440709114,
0.03154867887496948,
-0.0014567459002137184,
0.021813785657286644,
-0.032341040670871735,
-0.012240788899362087,
0.026482710614800453,
-0.010882525704801083,
-0.009222667664289474,
0.04878797009587288,
0.034005068242549896,
0.023212842643260956,
0.03724127262830734,
0.002327925758436322,
0.01765306666493416,
-0.02483074925839901,
0.02003638446331024,
-0.10772579163312912,
0.006105645559728146,
0.0004971800372004509,
0.014247335493564606,
-0.003099313471466303,
-0.045894984155893326,
-0.018468212336301804,
0.03835410997271538,
-0.07904490828514099,
0.02711002714931965,
-0.01851051300764084,
-0.025751128792762756,
-0.025868982076644897,
-0.021303286775946617,
-0.029142742976546288,
0.033271145075559616,
0.026187431067228317,
0.061682362109422684,
0.015564199537038803,
0.039414383471012115,
-0.012887432239949703,
-0.012671227566897869,
0.018965842202305794,
0.0231800377368927,
-0.00716999638825655,
0.0014052879996597767,
0.05542980134487152,
0.006156250834465027,
0.010817360132932663,
0.01681230589747429,
-0.03761099651455879,
-0.0018458093982189894,
0.005902544595301151,
0.002719000680372119,
0.028806030750274658,
0.052642788738012314,
0.029716357588768005,
-0.00008338737825397402,
-0.01680930331349373,
-0.03015691600739956,
-0.014795550145208836,
0.007136820815503597,
0.028517339378595352,
0.028752682730555534,
0.03977620601654053,
-0.013551618903875351,
-0.011704432778060436,
0.025956114754080772,
-0.058663561940193176,
0.0037822267040610313,
0.010161539539694786,
0.02583981864154339,
-0.01565154455602169,
-0.050929829478263855,
-0.039937444031238556,
-0.008199778385460377,
-0.016025329008698463,
0.0355212576687336,
0.0023915201891213655,
-0.0214788019657135,
0.023083198815584183,
-0.00126036093570292,
-0.05545498803257942,
0.009431549347937107,
-0.03327436372637749,
-0.013516129925847054,
-0.05891138315200806,
0.006622152868658304,
0.005227013491094112,
-0.03329436853528023,
-0.020693324506282806,
-0.014181451871991158,
-0.03731343895196915,
0.045126624405384064,
0.00837612897157669,
0.012388695031404495,
-0.0005278654862195253,
-0.01828697696328163,
-0.022780470550060272,
-0.11663657426834106,
0.02609105221927166,
0.01125582680106163,
-0.022729050368070602,
-0.007253569550812244,
-0.01962440274655819,
-0.0036891282070428133,
0.003910612314939499,
0.03135151043534279,
-0.015281789936125278,
-0.03612324967980385,
0.032844267785549164,
-0.02657315507531166,
0.04148980602622032,
-0.02421174943447113,
0.03067273274064064,
-0.017957940697669983,
0.02847392112016678,
0.019601264968514442,
0.00192152033559978,
-0.01602674275636673,
0.026992643252015114,
0.02875479869544506,
-0.024541523307561874,
0.001852159621194005,
0.00542646087706089,
-0.018343737348914146,
0.016107993200421333,
-0.02739478088915348,
-0.013922952115535736,
0.0702211856842041,
0.030582474544644356,
0.021619204431772232,
0.030697807669639587,
-0.03709174692630768,
-0.06361579895019531,
0.01629408821463585,
-0.042151130735874176,
-0.02146066352725029,
0.00042102098814211786,
-0.03600653260946274,
0.020548414438962936,
-0.07039611041545868,
-0.016449881717562675,
0.023896001279354095,
-0.05833042785525322,
-0.04505624622106552,
-0.005264165811240673,
-0.0006254224572330713,
0.03363099321722984,
0.0219286996871233,
0.03938045725226402,
0.017752742394804955,
-0.012874203734099865,
0.008283864706754684,
0.001839043339714408,
0.0313362181186676,
0.017508141696453094,
0.006990597117692232,
0.008542602881789207,
-0.007160620763897896,
0.05068877339363098,
0.011329472996294498,
0.024720782414078712,
-0.03132709860801697,
-0.01860000751912594,
0.03579006716609001,
0.018343007192015648,
-0.00330341886729002,
0.023773496970534325,
-0.00440108822658658,
0.0722903236746788,
-0.022661639377474785,
0.02339513972401619,
-0.008530736900866032,
0.028492435812950134,
-0.022237062454223633,
-0.024282680824398994,
0.037203896790742874,
0.008020548149943352,
-0.016360430046916008,
-0.01319494191557169,
-0.015567242167890072,
0.049931783229112625,
0.0009537679143249989,
-0.023763174191117287,
0.011917819269001484,
-0.0013930926797911525,
-0.028122156858444214,
0.03260491415858269,
-0.02034951001405716,
-0.03868841007351875,
-0.047788843512535095,
0.07900259643793106,
0.05962526425719261,
-0.014796601608395576,
-0.021503740921616554,
0.016714157536625862,
0.016346046701073647,
0.06612032651901245,
-0.03051002137362957,
0.008542959578335285,
0.01771610789000988,
-0.0008657555445097387,
0.014519767835736275,
-0.02711496874690056
] |
<p>I'm quite perplexed by the notion of 'observation' in regards to the collapse of a particle's probability wave. Does a particle's wave only collapse when it is involved in a strong interaction (such as a collision with another particle, like bouncing a photon off another particle to determine the other particle's position) or does any interaction with another particle or field also cause this collapse?</p>
<p>For example, I presume traditional detectors such as those mentioned when talking about the double slit experiment are devices that do exactly as I stated above and (in the case of the double slit) have a stream of photons (like a curtain) going from the top of the slit to the bottom which the electron (or particle being shot at the slits) has to pass through and therefore get smashed into by the photons. </p>
<p>So given an environment where there was no other gravitational or electromagnetic influence, or where the effects of such have been taken into account, what would happen if you had a region of space within which a massive neutral particle 'is' (ie, it's probability wave fills this volume), and then shot a beam of photons across the bow of this region (so as to pass nearby, but not intersect), and then have a photo-sensitive plate on the other side to see if the photons passed straight by, or were pulled towards one direction slightly by the warping of spacetime caused by the massive neutral particle (gravitational lensing on a mini scale)? Does this even make sense? And if the photons were being pulled slightly towards the massive neutral particle, would the waveform collapse at this point, since if the mass of the neutral particle was known, the amount by which the photons path had been bent could confirm it's position couldn't it?</p>
<p>Or perhaps take the above and use an electromagnetically positive particle as the target and an electromagnetically negative particle as the beam you shoot by it to see if it is effected by the electromagnetic field caused by the target particle if that makes more sense.</p>
<p>I might be making some silly errors or assumptions here, I'm only a layman with no formal education or in depth knowledge, so be gentle :)</p> | 1,440 | [
-0.03245100378990173,
-0.008996747434139252,
-0.0319649875164032,
-0.047301970422267914,
0.032149940729141235,
0.03303234651684761,
-0.018639078363776207,
-0.05387074500322342,
-0.0029422042425721884,
-0.008028050884604454,
0.00914879608899355,
0.03716527670621872,
0.023802243173122406,
0.009112429805099964,
-0.005981920752674341,
0.03245195373892784,
-0.011145909316837788,
0.006462815683335066,
-0.037781283259391785,
-0.09047100692987442,
-0.007595225237309933,
0.04580464959144592,
0.010524815879762173,
-0.011173141188919544,
-0.033485475927591324,
0.008832167834043503,
0.011828416958451271,
-0.015912316739559174,
0.03808945417404175,
0.03441236913204193,
-0.00691411504521966,
-0.014678829349577427,
-0.005332134198397398,
0.03973319008946419,
0.010822635143995285,
-0.002760208211839199,
-0.03435755521059036,
-0.037294141948223114,
0.03214119374752045,
-0.0015464382013306022,
-0.03471281751990318,
-0.010854083113372326,
-0.016019290313124657,
0.03769119828939438,
-0.061140768229961395,
-0.012014780193567276,
-0.0005353447631932795,
0.008716745302081108,
0.044195808470249176,
-0.06849473714828491,
0.061045221984386444,
-0.009282341226935387,
0.04082806035876274,
-0.00716954143717885,
-0.022010870277881622,
-0.03310317173600197,
0.07817506790161133,
0.08419203013181686,
-0.030269602313637733,
-0.033847954124212265,
-0.0014218665892258286,
-0.000977163901552558,
-0.04167421534657478,
-0.009115847758948803,
-0.012205333448946476,
0.046684812754392624,
-0.022778168320655823,
-0.005727631971240044,
0.025160353630781174,
0.01931558921933174,
0.002065388485789299,
0.02171894535422325,
0.012363117188215256,
0.03153088316321373,
-0.007492178585380316,
0.012208850122988224,
0.047974225133657455,
0.003495800541713834,
0.015717657282948494,
0.03060564026236534,
0.0077396961860358715,
0.0008209795341826975,
0.039401907473802567,
0.050725068897008896,
0.030733264982700348,
-0.022618623450398445,
0.07101798802614212,
-0.02518540993332863,
0.007377318572252989,
0.028451571241021156,
-0.02561734803020954,
0.01257795374840498,
0.02482348494231701,
-0.011495891027152538,
-0.06588621437549591,
0.029706139117479324,
-0.012220131233334541,
0.061802204698324203,
0.010688845999538898,
0.007813205942511559,
0.007834597490727901,
0.01174958422780037,
0.022654522210359573,
0.07817380875349045,
0.020987549796700478,
-0.04283488541841507,
-0.060244765132665634,
0.061660852283239365,
0.004428195767104626,
-0.010953553020954132,
-0.04683155566453934,
0.01469512190669775,
0.02438879944384098,
0.014177790842950344,
0.05455239117145538,
-0.03690261021256447,
-0.008046934381127357,
-0.03392847999930382,
0.07689730823040009,
0.045222725719213486,
0.017273643985390663,
-0.03268784284591675,
0.011859645135700703,
-0.055030494928359985,
-0.07965873926877975,
0.017200138419866562,
0.052705422043800354,
-0.013425235636532307,
0.01284719631075859,
0.020505391061306,
0.011613383889198303,
-0.02414238639175892,
0.03756310045719147,
-0.014978618361055851,
0.050810571759939194,
-0.008028211072087288,
-0.1005665510892868,
-0.08269096165895462,
0.020116545259952545,
0.002048037713393569,
-0.020579596981406212,
-0.0434882752597332,
-0.03274686634540558,
0.054760247468948364,
0.08010903000831604,
-0.00467715272679925,
0.010695816949009895,
-0.014763189479708672,
0.04038992151618004,
-0.0029194550588726997,
-0.017530318349599838,
-0.0022641606628894806,
-0.010811635293066502,
-0.019977232441306114,
-0.035732630640268326,
-0.04660504683852196,
0.016778282821178436,
0.031862519681453705,
-0.008151731453835964,
-0.040809739381074905,
0.0543338805437088,
-0.018742887303233147,
-0.008773603476583958,
-0.012986872345209122,
-0.007699599955230951,
-0.03980589658021927,
0.08093733340501785,
0.03410404548048973,
-0.010718939825892448,
0.026566844433546066,
0.0097594503313303,
0.04210784658789635,
-0.017026780173182487,
0.0003770983894355595,
0.015678782016038895,
-0.040149006992578506,
-0.01484645064920187,
-0.02806248515844345,
0.023711295798420906,
-0.040454816073179245,
0.010722815059125423,
-0.01803075335919857,
-0.018879778683185577,
0.02286827564239502,
0.011172381229698658,
0.047531768679618835,
0.00022438123414758593,
-0.01603451743721962,
-0.00808254536241293,
-0.05711369588971138,
-0.009542202576994896,
-0.03457367792725563,
-0.004579748027026653,
-0.0042917304672300816,
0.003716376842930913,
0.013133390806615353,
-0.012425409629940987,
0.04532244801521301,
-0.028348777443170547,
-0.03942176699638367,
-0.0010108796413987875,
0.03758440166711807,
-0.006734370719641447,
-0.006895552389323711,
0.009437274187803268,
0.045352958142757416,
0.009058741852641106,
0.01759665086865425,
-0.0006188025581650436,
-0.02062157541513443,
0.002690839348360896,
0.01549801416695118,
-0.003191043622791767,
0.0002914254437200725,
0.013698447495698929,
0.0013530731666833162,
0.010305941104888916,
-0.00201886473223567,
-0.012698699720203876,
0.0211464986205101,
-0.038820091634988785,
0.07126892358064651,
0.035736698657274246,
0.009085080586373806,
-0.030764587223529816,
0.05264974758028984,
0.024741629138588905,
-0.0027524118777364492,
0.011403354816138744,
-0.03449400141835213,
-0.05274595692753792,
-0.022878963500261307,
0.011849924921989441,
-0.011436347849667072,
-0.0240841805934906,
0.03865412622690201,
0.019839009270071983,
0.03085389733314514,
0.0196500476449728,
0.028066309168934822,
-0.012744029983878136,
-0.02266867458820343,
-0.021342096850275993,
0.027128851041197777,
-0.0026523026172071695,
-0.013919147662818432,
0.024053925648331642,
0.009022029116749763,
-0.01641629822552204,
-0.009368994273245335,
-0.010664073750376701,
-0.004255457315593958,
-0.009740862064063549,
0.03152388706803322,
-0.021191252395510674,
-0.01074400544166565,
0.012575464323163033,
0.0023968012537807226,
0.030596178025007248,
0.04054999351501465,
-0.02143317274749279,
-0.014612319879233837,
-0.0561566986143589,
-0.022540172562003136,
0.04282939434051514,
0.014916783198714256,
-0.015030375681817532,
-0.04265886917710304,
0.02570067159831524,
-0.05238873139023781,
0.007842903025448322,
0.010512703098356724,
-0.008324733003973961,
-0.00781146390363574,
-0.003192493226379156,
0.03706420212984085,
0.023851880803704262,
0.031939249485731125,
-0.04192506521940231,
-0.06973661482334137,
0.0006460795411840081,
-0.049812812358140945,
0.014901373535394669,
0.03616540506482124,
-0.04573830962181091,
-0.0045987581834197044,
-0.03117559663951397,
-0.04105277732014656,
0.0374533049762249,
-0.033365316689014435,
0.021788861602544785,
0.0038702324964106083,
-0.010427329689264297,
-0.03587891906499863,
-0.01531000155955553,
-0.027366722002625465,
-0.015089927241206169,
-0.02262619510293007,
0.012254036031663418,
0.06347198784351349,
0.03662659227848053,
-0.030109133571386337,
0.03208424150943756,
-0.013610953465104103,
-0.04313395917415619,
-0.02842787653207779,
-0.0030018712859600782,
-0.0007143821567296982,
-0.0189492329955101,
0.02570994570851326,
0.03513085097074509,
-0.04998422786593437,
0.026556244120001793,
-0.034827012568712234,
-0.0463956780731678,
0.022822679951786995,
-0.0052527133375406265,
0.011543083004653454,
-0.03155599161982536,
-0.008893820457160473,
0.0571281760931015,
0.06286954879760742,
-0.0190313458442688,
-0.028541164472699165,
0.023807043209671974,
0.008551917038857937,
0.024732545018196106,
-0.0008669096860103309,
-0.023942597210407257,
-0.005952212959527969,
0.047151561826467514,
0.03144703805446625,
0.033906858414411545,
0.011982937343418598,
0.04395020753145218,
-0.007916081696748734,
0.006868316326290369,
-0.02642274647951126,
-0.020858339965343475,
0.028469035401940346,
0.04194070026278496,
-0.021308187395334244,
0.01895788125693798,
0.005005653016269207,
-0.014949715696275234,
0.02651139721274376,
-0.032417114824056625,
0.06536106020212173,
0.02669447474181652,
0.01795613020658493,
-0.0005866275751031935,
0.00187886250205338,
-0.02678854390978813,
0.0016311492072418332,
-0.0066198427230119705,
-0.029109232127666473,
0.048547472804784775,
-0.003137613646686077,
0.003294635098427534,
0.008642216213047504,
0.020359797403216362,
-0.00014770368579775095,
-0.02908024564385414,
0.012283781543374062,
-0.011002513580024242,
0.030625974759459496,
-0.008730643428862095,
-0.027006277814507484,
0.08584045618772507,
0.05167204141616821,
0.02576502598822117,
-0.03553019091486931,
-0.01585417427122593,
-0.02050376683473587,
-0.0061464388854801655,
0.012831736356019974,
0.014570514671504498,
0.004138510208576918,
0.02988281100988388,
0.03957192227244377,
0.05805527791380882,
0.026535384356975555,
0.018435465171933174,
0.002723401878029108,
-0.09352587908506393,
0.0021874026861041784,
-0.03692987561225891,
-0.040917135775089264,
-0.025586795061826706,
0.0029995080549269915,
-0.007506290916353464,
0.0005323655786924064,
-0.00007345603808062151,
-0.02041623555123806,
0.002398994518443942,
-0.06863458454608917,
0.019291838631033897,
-0.011627552099525928,
-0.05155181139707565,
-0.015106741338968277,
0.06169206276535988,
0.037900544703006744,
0.00907385628670454,
-0.03389621153473854,
0.0003475756093394011,
-0.06408947706222534,
0.0009316836949437857,
0.010136918164789677,
0.011827332898974419,
0.007734100334346294,
0.04658311977982521,
0.030079703778028488,
0.021327272057533264,
-0.05283476412296295,
0.031008180230855942,
0.042875420302152634,
0.07568550854921341,
-0.00914391316473484,
-0.006482242606580257,
-0.01114602666348219,
0.00342847453430295,
-0.02545354701578617,
-0.017438765615224838,
0.05706910416483879,
0.006780415773391724,
-0.010238371789455414,
0.014092556200921535,
0.0274112019687891,
0.014887851662933826,
0.05112668499350548,
0.05410842224955559,
0.002189956372603774,
-0.00668942229822278,
-0.04652305692434311,
0.00020632482483051717,
-0.01802409254014492,
-0.006071257870644331,
0.02285352535545826,
0.016092564910650253,
-0.007860498502850533,
-0.0052563222125172615,
0.040062226355075836,
-0.003095620544627309,
-0.02035117894411087,
0.012108279392123222,
-0.03876396641135216,
-0.010471036657691002,
0.004730319604277611,
-0.0025122426450252533,
0.03563923016190529,
0.036567214876413345,
0.036845479160547256,
0.011253898963332176,
-0.007275912910699844,
-0.08208601921796799,
-0.014378197491168976,
0.05332765355706215,
0.021277032792568207,
-0.0028278157114982605,
0.005092682782560587,
-0.03510752320289612,
-0.021685773506760597,
0.054418083280324936,
-0.05220664665102959,
0.015185823664069176,
0.005080092698335648,
0.004245263058692217,
-0.015343240462243557,
-0.004892449826002121,
-0.019171010702848434,
0.023899905383586884,
-0.02641337737441063,
0.005802833009511232,
-0.008454883471131325,
-0.011111441068351269,
-0.01487923413515091,
0.0010365830967202783,
-0.0012868696358054876,
0.044089995324611664,
0.020087625831365585,
0.0016974336467683315,
0.02362188696861267,
-0.002161695621907711,
-0.035804618149995804,
-0.07343213260173798,
0.022718481719493866,
0.026033297181129456,
-0.022879917174577713,
0.0413944311439991,
-0.002699677599593997,
-0.024759074673056602,
0.01980246789753437,
-0.02040906436741352,
0.014459480531513691,
0.010945814661681652,
-0.028412293642759323,
0.041052307933568954,
0.030110284686088562,
0.006416019983589649,
0.04727793484926224,
0.008943388238549232,
-0.008058208040893078,
0.02130795642733574,
-0.018576422706246376,
0.01902111992239952,
-0.04826141148805618,
0.011963757686316967,
-0.024634910747408867,
0.01725625991821289,
-0.030694130808115005,
0.054541412740945816,
0.011150090023875237,
0.007189379073679447,
0.011371595785021782,
-0.033236049115657806,
-0.008131355978548527,
0.0009916258277371526,
-0.004177276510745287,
-0.010248715057969093,
-0.03965405747294426,
0.0022365087643265724,
0.009394899941980839,
-0.020475711673498154,
0.007751809433102608,
-0.004909077193588018,
-0.0025854308623820543,
0.016318634152412415,
-0.015311607159674168,
-0.009895692579448223,
-0.013820912688970566,
-0.007702475879341364,
0.05818062648177147,
-0.047205012291669846,
0.024333950132131577,
-0.020680321380496025,
-0.0058816708624362946,
0.07943147420883179,
-0.05009426921606064,
-0.04740741103887558,
0.0021134130656719208,
-0.03471561521291733,
0.026791423559188843,
-0.04107721522450447,
0.010896175168454647,
-0.014769735746085644,
0.04482220113277435,
-0.07955477386713028,
-0.012623404152691364,
0.021582573652267456,
-0.0038233594968914986,
-0.001642450224608183,
-0.007758037652820349,
-0.008017479442059994,
-0.035676226019859314,
0.00025830173399299383,
-0.04880335181951523,
0.004527278244495392,
-0.060963504016399384,
-0.005595447029918432,
0.0027745887637138367,
0.014906487427651882,
0.048423465341329575,
0.0050832717679440975,
-0.018199406564235687,
0.026272786781191826,
-0.017350325360894203,
-0.013554970733821392,
0.033157527446746826,
0.03768360987305641,
-0.02552085742354393,
-0.05847789719700813,
-0.024817343801259995,
-0.021698053926229477,
-0.004821562673896551,
-0.007921699434518814,
-0.008705596439540386,
0.04111577942967415,
0.03297409042716026,
0.0006607850082218647,
0.0014479439705610275,
0.015606120228767395,
-0.030276743695139885,
-0.013766790740191936,
0.022786440327763557,
-0.025403855368494987,
0.01680590771138668,
-0.054587189108133316,
0.08062976598739624,
0.009707195684313774,
-0.0021463739685714245,
0.02783440239727497,
0.02337689697742462,
0.010903670452535152,
0.0126030957326293,
0.025032568722963333,
-0.03376166522502899,
0.007803305983543396,
-0.024941710755228996,
0.00460943765938282,
0.03400883451104164,
-0.00016704552399460226,
-0.03003953956067562,
-0.017188936471939087,
-0.029369156807661057,
0.0041988142766058445,
0.06405733525753021,
-0.01268315501511097,
0.03466099873185158,
-0.01772785373032093,
-0.026617515832185745,
-0.013317584991455078,
-0.04599243775010109,
0.035318393260240555,
0.010268207639455795,
0.025565506890416145,
0.010386348702013493,
-0.04694255813956261,
0.014647415839135647,
0.022064033895730972,
0.04843605309724808,
-0.010233026929199696,
0.011866371147334576,
0.018255390226840973,
0.05313515290617943,
0.0583764873445034,
-0.01835692673921585,
-0.04110024496912956,
0.0027967020869255066,
-0.04478153958916664,
0.013809655793011189,
-0.0028605570551007986,
0.02120494842529297,
0.012917909771203995,
-0.001117785694077611,
0.025098035112023354,
-0.038696303963661194,
-0.029132848605513573,
-0.03615453839302063,
0.02710791677236557,
0.02372344397008419,
-0.0062509155832231045,
-0.00016156252240762115,
0.017641324549913406,
0.06175985559821129,
0.00863441452383995,
-0.004454006440937519,
-0.008913222700357437,
-0.0937952771782875,
-0.05663333088159561,
-0.06575458496809006,
-0.04677842929959297,
0.05877168849110603,
-0.031253114342689514,
0.006850284058600664,
0.011397427879273891,
-0.03641119971871376,
0.010519007220864296,
0.019180309027433395,
0.029605235904455185,
-0.043400343507528305,
0.0329386442899704,
-0.01361942384392023,
0.010810227133333683,
-0.02198815532028675,
-0.023895258083939552,
0.11543988436460495,
0.04390236362814903,
0.014905015006661415,
-0.054679304361343384,
-0.01337580755352974,
-0.018728289753198624,
0.027371490374207497,
-0.007217369507998228,
-0.0014183849561959505,
-0.026363728567957878,
-0.001803868100978434,
0.028826888650655746,
0.046701814979314804,
0.022844934836030006,
-0.00522093428298831,
0.06336580216884613,
-0.04541129618883133,
-0.06791248172521591,
0.0037901359610259533,
0.0021549153607338667,
0.004525201395153999,
0.01741928607225418,
-0.0335637629032135,
0.06234947219491005,
-0.05248619243502617,
0.0012717023491859436,
-0.02362479642033577,
-0.01961446925997734,
0.0032006078399717808,
0.009338073432445526,
-0.06401319056749344,
-0.01571301743388176,
-0.013058262877166271,
-0.05033084750175476,
-0.032189931720495224,
0.00020651707018259913,
0.031736019998788834,
-0.006958945654332638,
0.04248230159282684,
0.028142759576439857,
-0.005288539454340935,
0.0003071200626436621,
0.03228585422039032,
-0.003502826439216733,
-0.03264983370900154,
-0.005403690971434116,
0.015252946875989437,
0.08404868841171265,
0.008251986466348171,
-0.020105434581637383,
0.010716802440583706,
-0.03605997934937477,
0.0238371342420578,
-0.04378194361925125,
-0.0099329287186265,
-0.039966970682144165,
0.0007869255496188998,
0.0014916503569111228,
-0.00245250784792006,
0.04008669778704643,
0.05659180507063866,
0.03529518097639084,
0.0043918779119849205,
0.012096787802875042,
0.04602905735373497,
-0.003449253272265196,
-0.02667469158768654,
0.056860070675611496,
0.015147939324378967,
-0.025609934702515602,
-0.057881470769643784,
-0.009532303549349308,
-0.03885022550821304,
-0.02133825048804283,
0.05414745584130287,
0.020815808326005936,
0.015505352057516575,
-0.01807520166039467,
0.048331066966056824,
-0.005795673001557589,
-0.06636305898427963,
0.0442119725048542,
-0.043436698615550995,
-0.013484169729053974,
-0.02421208843588829,
0.0035801813937723637,
0.014507162384688854,
0.05903772637248039,
-0.01574462093412876,
-0.04484696686267853,
0.008227916434407234,
0.025863874703645706,
0.009364225901663303,
-0.04205170273780823,
-0.0528564415872097,
-0.014557193033397198,
0.011309402994811535,
-0.011357903480529785,
-0.05696834623813629,
0.003663219278678298,
-0.0033128508366644382,
-0.006592807359993458,
0.049283385276794434,
0.010435736738145351,
-0.014700481668114662,
-0.03425086289644241,
-0.025401804596185684,
-0.019850486889481544,
0.0067439270205795765,
0.006546946708112955,
0.06044229492545128,
-0.012455306947231293,
-0.01603405922651291,
-0.012493127956986427,
-0.02266109175980091,
0.0072538480162620544,
0.021046660840511322,
-0.02509186416864395,
0.0233450960367918,
0.02173847146332264,
0.024737315252423286,
-0.006427343934774399,
-0.011767417192459106,
-0.007668083067983389,
0.016514964401721954,
0.018881818279623985,
-0.044466532766819,
-0.005535870790481567,
0.02696884050965309,
0.014152472838759422,
-0.08438874036073685,
-0.012814600020647049,
0.03884062170982361,
-0.0506778247654438,
0.04065769538283348,
0.02983075939118862,
0.011018538847565651,
0.026254484429955482,
0.01503157988190651,
-0.0004332039679866284,
-0.010000379756093025,
-0.04662850499153137,
-0.048279762268066406,
0.07059236615896225,
0.014336144551634789,
0.04776018485426903,
0.016846850514411926,
-0.00802881084382534,
-0.01466918271034956,
0.05774485319852829,
-0.00008478201198158786,
-0.016496451571583748,
0.009807701222598553,
-0.055117953568696976,
0.006805066950619221,
0.00990945752710104,
0.032737404108047485,
-0.028795037418603897,
-0.00765629205852747,
0.049784671515226364,
0.020932668820023537,
0.0017741412157192826,
0.024080360308289528,
-0.003002568380907178,
-0.02900443971157074,
0.0034892780240625143,
-0.031569965183734894,
-0.018571626394987106,
-0.021276040002703667,
0.06725801527500153,
-0.061900608241558075,
0.022402390837669373,
0.04423372820019722,
0.021049074828624725,
-0.1259077787399292,
-0.009053082205355167,
0.032265521585941315,
0.005254960153251886,
0.05023719742894173,
-0.03534536063671112,
0.020838892087340355,
0.02661719359457493,
-0.03594547510147095,
0.0030450813937932253,
-0.007846027612686157,
-0.0401703342795372,
-0.028321459889411926,
0.004431682173162699,
-0.030417349189519882,
0.04648077115416527,
0.00913142692297697,
0.06167393550276756,
0.011889996938407421,
0.0031387247145175934,
-0.016315681859850883,
-0.02912210300564766,
0.0013374160043895245,
0.008140466175973415,
-0.005342054180800915,
-0.010845508426427841,
0.07240049540996552,
-0.025135494768619537,
0.005233634263277054,
0.032500363886356354,
-0.0029986766166985035,
0.026706401258707047,
0.0005187642527744174,
0.000828463351354003,
0.009676427580416203,
0.013506152667105198,
0.011446284130215645,
0.01693769544363022,
0.025506451725959778,
0.017359141260385513,
0.026886790990829468,
0.02756538614630699,
-0.002124316990375519,
-0.0021178051829338074,
-0.01617611013352871,
-0.060016993433237076,
-0.0198147501796484,
-0.007698265835642815,
0.013778949156403542,
-0.00031553758890368044,
0.011618100106716156,
0.016138840466737747,
0.004087659064680338,
-0.008386463858187199,
-0.005991596262902021,
-0.05617959052324295,
-0.011798818595707417,
0.03363804146647453,
0.036282945424318314,
-0.038370102643966675,
0.014450478367507458,
-0.02016765996813774,
-0.054148439317941666,
0.011195329949259758,
-0.012793503701686859,
0.016876935958862305,
-0.01824180781841278,
-0.001218676334246993,
-0.029761869460344315,
0.028040945529937744,
0.05591435357928276,
-0.029894957318902016,
-0.04296478256583214,
0.01824047788977623,
-0.023646892979741096,
0.034692272543907166,
0.012377660721540451,
-0.02157973311841488,
-0.0513736866414547,
-0.07971947640180588,
0.013547497801482677,
-0.0026388659607619047,
0.030539842322468758,
-0.038251642137765884,
0.005625918973237276,
-0.006124604027718306,
0.015088937245309353,
0.04668593406677246,
-0.005651877261698246,
-0.001976248575374484,
0.047086697071790695,
-0.048653118312358856,
0.009130352176725864,
-0.06197809427976608,
0.006564598996192217,
-0.006407567299902439,
-0.021380705758929253,
-0.0195282194763422,
-0.037076350301504135,
-0.007984626106917858,
0.028469715267419815,
0.03723350539803505,
0.02999122627079487,
0.022348735481500626,
-0.01833420805633068,
-0.002959669101983309,
0.021759510040283203,
0.010618490166962147,
0.025014670565724373,
0.05058855190873146,
0.002713930094614625,
0.008856747299432755,
0.02426489256322384,
-0.016517523676156998,
-0.04312985762953758,
-0.004950280766934156,
-0.016973013058304787,
0.004193556495010853,
-0.010090271942317486,
-0.003946828655898571,
0.0169487614184618,
-0.050261206924915314,
-0.036449700593948364,
0.003937745001167059,
-0.0408344566822052,
-0.017411284148693085,
0.06960505247116089,
-0.01645262911915779,
0.028804058209061623,
-0.011276493780314922,
0.010213281027972698,
0.030736062675714493,
0.013739843852818012,
-0.005709244403988123,
0.05599912628531456,
0.026921775192022324,
0.004064682871103287,
0.009864995256066322,
0.04994630068540573,
0.01095598191022873,
-0.010383746586740017,
0.004611095879226923,
0.05309576168656349,
-0.03991124406456947,
-0.011678160168230534,
0.03172600641846657,
0.00940778013318777,
-0.02523188851773739,
0.02648172341287136,
0.003071671584621072,
0.08667517453432083,
-0.0035207367036491632,
0.02380930259823799,
0.003998712636530399,
-0.008804285898804665,
0.006360167171806097,
0.037326227873563766,
0.01660763844847679,
0.020334532484412193,
0.01367653626948595,
0.008721794001758099,
-0.003276172559708357,
0.01663157530128956,
0.01429292093962431,
-0.05299101769924164,
-0.004770427476614714,
-0.0360499732196331,
-0.03192886710166931,
0.024245964363217354,
-0.026309311389923096,
-0.0370008759200573,
-0.043564073741436005,
-0.018401626497507095,
-0.001049716491252184,
0.00017595852841623127,
-0.009372140280902386,
0.031443700194358826,
-0.03979251906275749,
0.04877477139234543,
-0.047596223652362823,
-0.024052679538726807,
-0.018030771985650063,
0.025102559477090836,
-0.001620266935788095,
0.00967826321721077
] |
<p>I am curious whether the current <a href="http://en.wikipedia.org/wiki/Lambda-CDM_model" rel="nofollow">Lambda-CDM model</a> of cosmology matches well with observational data, especially expansion of the universe.</p>
<p>How well does Lambda-CDM defend its established status from other models, such as <a href="http://en.wikipedia.org/wiki/Quintessence_%28physics%29" rel="nofollow">quintessence</a> (quintessence can be said to extend Lambda-CDM, but there are some models against the standard model, I guess.)?</p> | 1,441 | [
-0.016575517132878304,
-0.017780473455786705,
0.009032215923070908,
-0.047386135905981064,
0.046105995774269104,
0.008828920312225819,
0.005911140702664852,
-0.021524490788578987,
0.013210248202085495,
-0.06302428245544434,
0.022056840360164642,
0.028192656114697456,
0.034759197384119034,
-0.00433914503082633,
0.02084844373166561,
-0.0026920619420707226,
0.009392687119543552,
-0.017894122749567032,
-0.014217347837984562,
-0.012590426951646805,
0.017792493104934692,
0.017735740169882774,
-0.022989768534898758,
0.008687962777912617,
-0.021267279982566833,
0.0372832715511322,
0.02632884867489338,
0.04049569368362427,
0.0218980610370636,
0.0779203474521637,
-0.010567598976194859,
-0.0027571970131248236,
-0.0013248308096081018,
0.05920456349849701,
0.0009752336773090065,
-0.0020640192087739706,
-0.008878668770194054,
-0.057009778916835785,
-0.017972532659769058,
0.0376625582575798,
-0.06379570811986923,
-0.026250535622239113,
0.013554277829825878,
0.07559730112552643,
-0.03780270367860794,
0.013299626298248768,
0.004157403949648142,
-0.002544649178162217,
0.07462303340435028,
-0.04399731382727623,
0.07216630131006241,
0.0202633049339056,
0.04394451901316643,
0.051909565925598145,
-0.008154680021107197,
-0.008108926005661488,
0.07206062972545624,
0.06422406435012817,
-0.006667149253189564,
-0.03785276040434837,
-0.029068225994706154,
-0.003455821191892028,
0.02120557799935341,
0.002905923407524824,
-0.033105865120887756,
0.0801323875784874,
-0.023498494178056717,
-0.010934618301689625,
0.0008888730662874877,
0.020044682547450066,
0.002271091565489769,
-0.010220879688858986,
0.02876468002796173,
0.012515008449554443,
0.022245939821004868,
-0.04382104054093361,
0.005222242325544357,
-0.007597947493195534,
0.022619398310780525,
0.03302926570177078,
0.0075052836909890175,
-0.006391868460923433,
0.026927944272756577,
0.0471157468855381,
0.0095390435308218,
-0.0003737749648280442,
0.05779169499874115,
-0.01435996312648058,
-0.00702782953158021,
0.03508452698588371,
-0.013198776170611382,
-0.004126220941543579,
0.014071115292608738,
-0.017417823895812035,
-0.026106959208846092,
0.05341769754886627,
0.007492765784263611,
0.04729727655649185,
-0.000659054727293551,
-0.002717198571190238,
-0.014253276400268078,
0.02676963247358799,
-0.00244512059725821,
0.06204346567392349,
0.016338352113962173,
-0.04077420011162758,
-0.0666000097990036,
0.0072306073270738125,
-0.039095018059015274,
-0.01204761490225792,
-0.04538536071777344,
0.013751070015132427,
0.0063265529461205006,
0.016228288412094116,
0.010956834070384502,
-0.03601425513625145,
0.017126234248280525,
-0.06255477666854858,
0.06130114197731018,
0.08521706610918045,
0.046159420162439346,
-0.014943107031285763,
0.014142347499728203,
-0.001223410596139729,
-0.020317381247878075,
-0.008351743221282959,
0.036982178688049316,
-0.035593416541814804,
-0.026162395253777504,
0.04048546776175499,
0.010381347499787807,
-0.020701207220554352,
-0.004633121658116579,
-0.006722331512719393,
0.05620858445763588,
-0.026965133845806122,
-0.06653370708227158,
-0.049125272780656815,
0.021637775003910065,
0.010046242736279964,
0.0023442604579031467,
-0.03770598769187927,
0.00414701271802187,
0.028537295758724213,
0.07284506410360336,
0.009584498591721058,
0.008374327793717384,
-0.010507548227906227,
0.05999146029353142,
-0.029161181300878525,
-0.028727075085043907,
-0.038008492439985275,
0.019725259393453598,
-0.06111352518200874,
-0.02474062703549862,
-0.1079922690987587,
-0.01876191422343254,
-0.00161214848048985,
0.01315995492041111,
-0.00576937198638916,
0.08802998811006546,
0.020802786573767662,
0.0028814945835620165,
-0.02609073556959629,
0.013215049169957638,
-0.020740075036883354,
0.06332012265920639,
-0.00000697206451150123,
0.021290328353643417,
0.034023500978946686,
-0.03355434909462929,
0.017924608662724495,
0.03243988752365112,
-0.009978747926652431,
0.01751919463276863,
-0.049997374415397644,
-0.00011475246719783172,
-0.04454991593956947,
0.016633430495858192,
-0.0006934590637683868,
-0.032724205404520035,
0.005564463324844837,
-0.022601481527090073,
0.01021761354058981,
0.011899081990122795,
0.03984779492020607,
-0.0177248977124691,
-0.012467371299862862,
0.020004943013191223,
-0.05890122801065445,
-0.03210931643843651,
-0.01770450547337532,
-0.008402034640312195,
0.0011733666760846972,
-0.0044851843267679214,
0.003917038440704346,
0.03478637710213661,
0.0014642516616731882,
-0.011173040606081486,
-0.007805912289768457,
-0.01305042952299118,
0.03308859467506409,
-0.004957953467965126,
0.023325933143496513,
0.03381015732884407,
0.048137884587049484,
0.05835453048348427,
-0.039143070578575134,
0.018048571422696114,
0.005023851525038481,
-0.061318814754486084,
0.008708970621228218,
-0.026238197460770607,
0.002052923431620002,
-0.01759614609181881,
0.0324268564581871,
0.039226237684488297,
0.01871311105787754,
0.004957274068146944,
0.07687576860189438,
-0.026641299948096275,
0.05070436745882034,
0.016381820663809776,
0.03154170885682106,
-0.010215316899120808,
0.03275163471698761,
-0.027830136939883232,
0.022555865347385406,
-0.0029957753140479326,
-0.021807730197906494,
-0.07784929126501083,
-0.014872589148581028,
0.037979744374752045,
0.026145407930016518,
-0.005989823490381241,
0.020481154322624207,
0.03533308580517769,
0.008204557001590729,
0.02139400690793991,
-0.022518185898661613,
-0.03180862218141556,
-0.05584819242358208,
0.0012124463682994246,
0.011007701978087425,
0.017996836453676224,
-0.004698135890066624,
0.020985979586839676,
-0.02627922035753727,
0.03674224764108658,
-0.03579502925276756,
-0.009098727256059647,
0.051645759493112564,
0.00521329278126359,
-0.023914391174912453,
-0.007963240146636963,
-0.019101403653621674,
0.05416788160800934,
-0.007029224187135696,
0.004639247432351112,
0.03833022713661194,
-0.011935791000723839,
0.04160362854599953,
-0.043295104056596756,
0.001806093379855156,
0.00669943168759346,
0.0077823675237596035,
-0.030866270884871483,
-0.01227017305791378,
0.010573900304734707,
-0.07269158959388733,
-0.010271490551531315,
-0.0657573789358139,
-0.0051664444617927074,
-0.058004360646009445,
-0.014383078552782536,
0.011786884628236294,
-0.008204499259591103,
0.025668293237686157,
-0.06010591611266136,
-0.05613028258085251,
0.025908337906003,
-0.0036459206603467464,
-0.015217913314700127,
0.022993270307779312,
-0.039197906851768494,
0.011138786561787128,
-0.021977337077260017,
-0.020714379847049713,
0.056340645998716354,
-0.013946808874607086,
0.023436956107616425,
-0.014595682732760906,
-0.014237421564757824,
-0.020359916612505913,
-0.019497359171509743,
-0.03311415761709213,
-0.0021785416174679995,
-0.013503074645996094,
-0.05173911154270172,
0.06814555823802948,
-0.004005627240985632,
-0.051881980150938034,
0.03596770390868187,
-0.05710190162062645,
-0.01546340063214302,
-0.019062725827097893,
0.03891746699810028,
0.0006591631099581718,
-0.023281889036297798,
0.06758762151002884,
0.025911670178174973,
-0.04852188751101494,
0.039657458662986755,
-0.058555975556373596,
-0.05795212462544441,
0.031916048377752304,
-0.04125788435339928,
0.030365008860826492,
-0.013163747265934944,
-0.023541050031781197,
0.04891090840101242,
0.04807458445429802,
-0.03504055738449097,
-0.02032255381345749,
0.01961582526564598,
-0.007306367624551058,
-0.021809903904795647,
0.001195202930830419,
-0.008014238439500332,
-0.02603740245103836,
0.03517599031329155,
0.006230100989341736,
0.035646285861730576,
-0.0010183732956647873,
0.014728902839124203,
-0.020604794844985008,
0.01869731768965721,
0.018996819853782654,
-0.005466500762850046,
0.04423447325825691,
0.024534255266189575,
-0.027424614876508713,
-0.003907297272235155,
-0.02628389000892639,
0.01794292964041233,
0.017241710796952248,
-0.044492293149232864,
0.05449598655104637,
-0.0011426976416260004,
-0.006958167999982834,
-0.01470264047384262,
-0.014872315339744091,
0.010505693033337593,
0.011891810223460197,
0.007729416247457266,
0.0233636312186718,
0.0038028054405003786,
0.02271896041929722,
0.02108192816376686,
0.022529901936650276,
0.025604482740163803,
-0.0201447531580925,
-0.0137826818972826,
-0.0005049406317993999,
0.005060252267867327,
-0.0029938537627458572,
-0.004663883708417416,
-0.024303013458848,
0.0604192353785038,
0.038904353976249695,
-0.0036608988884836435,
-0.018275707960128784,
-0.007347686681896448,
-0.005964065436273813,
-0.08363484591245651,
-0.008910543285310268,
-0.013166194781661034,
0.053912218660116196,
0.014842681586742401,
0.00013270071940496564,
0.026239484548568726,
-0.02759205549955368,
-0.01179675105959177,
0.01147689763456583,
-0.07121437042951584,
0.014599409885704517,
-0.040571387857198715,
0.004690167959779501,
-0.017893217504024506,
0.01569199562072754,
-0.007116395048797131,
0.020106351003050804,
-0.02230844832956791,
-0.062308818101882935,
-0.02012655697762966,
-0.03740911930799484,
0.02918790653347969,
-0.03924746438860893,
-0.04841625690460205,
0.025962315499782562,
0.008822566829621792,
0.03914452716708183,
-0.012408316135406494,
-0.0021564930211752653,
0.03423040360212326,
-0.029067113995552063,
-0.004601886961609125,
-0.007367134094238281,
0.03872857615351677,
-0.004435645416378975,
0.02754553034901619,
0.013950248248875141,
0.02472318895161152,
-0.05444091185927391,
0.030425990000367165,
0.018080735579133034,
0.01665612868964672,
0.020584458485245705,
0.009044413454830647,
-0.008515506982803345,
-0.06230790168046951,
-0.035510096698999405,
-0.00018514710245653987,
0.013042433187365532,
0.008424574509263039,
-0.008115403354167938,
0.05689562112092972,
0.0355139821767807,
-0.03155743330717087,
0.0361010804772377,
0.051146250218153,
-0.03408012166619301,
-0.016576433554291725,
-0.0324886254966259,
-0.026788847520947456,
-0.025533780455589294,
0.007803482934832573,
0.015447458252310753,
0.017892714589834213,
-0.02977849170565605,
0.04290449246764183,
-0.015120540745556355,
-0.009345153346657753,
-0.024427950382232666,
0.007153157144784927,
0.006652098149061203,
0.042052194476127625,
-0.04202815890312195,
-0.008382227271795273,
0.005604603327810764,
0.04812369868159294,
0.06274008005857468,
0.023577827960252762,
-0.012117675505578518,
-0.0698397308588028,
-0.010904951952397823,
0.040905099362134933,
0.01934392936527729,
-0.026923377066850662,
-0.048287637531757355,
-0.10990791022777557,
-0.027306783944368362,
0.054025739431381226,
-0.039040807634592056,
0.038330793380737305,
0.01231613289564848,
0.018840689212083817,
-0.009915722534060478,
0.012213467620313168,
0.015143160708248615,
0.016047431156039238,
-0.003115246305242181,
0.011690963059663773,
-0.025001736357808113,
0.031122898682951927,
-0.04619766026735306,
0.010031168349087238,
0.01176095474511385,
0.03411753103137016,
0.00859056506305933,
-0.019306493923068047,
0.038526009768247604,
-0.008747771382331848,
-0.0032791232224553823,
-0.05939379334449768,
0.009872286580502987,
0.015100513584911823,
-0.035230860114097595,
-0.010550604201853275,
-0.0036428829189389944,
-0.00461926031857729,
-0.032751407474279404,
0.030621705576777458,
-0.016151435673236847,
0.00593723775818944,
-0.03706404194235802,
0.047294847667217255,
0.008440895937383175,
-0.02780831977725029,
0.03886932507157326,
0.05001828446984291,
0.011842598207294941,
0.02229173853993416,
-0.00992275308817625,
0.008126889355480671,
-0.04810203239321709,
0.03593108430504799,
-0.02951139770448208,
-0.0014680741587653756,
-0.05637812241911888,
0.04240876063704491,
0.0014727931702509522,
0.033982206135988235,
-0.007581113837659359,
-0.013360138051211834,
0.00414316589012742,
0.013261307030916214,
-0.011546146124601364,
0.005974389147013426,
-0.0010277448454871774,
0.02949076145887375,
-0.009205872192978859,
-0.004597331862896681,
0.0397300198674202,
0.008326881565153599,
-0.021315891295671463,
-0.008678778074681759,
-0.021036626771092415,
0.04684688150882721,
0.03269901126623154,
-0.008121495135128498,
0.020930860191583633,
-0.026534777134656906,
0.04871674254536629,
0.0011164743918925524,
0.05307834595441818,
-0.011640931479632854,
-0.0743870884180069,
-0.01876509189605713,
0.026157991960644722,
-0.031167596578598022,
0.03572753444314003,
-0.023221731185913086,
0.022939002141356468,
0.013439117930829525,
-0.002501653041690588,
-0.08670719712972641,
-0.027066750451922417,
0.02594023384153843,
-0.012296080589294434,
-0.01817316748201847,
-0.0018942513270303607,
0.033141013234853745,
-0.03486436605453491,
-0.027571596205234528,
-0.010798999108374119,
0.06565753370523453,
-0.02034502476453781,
-0.004797088447958231,
-0.001773881260305643,
0.010223576799035072,
0.05485539883375168,
0.01397570688277483,
0.005803746171295643,
-0.010038310661911964,
0.0038802053313702345,
-0.037040162831544876,
-0.008942452259361744,
0.029235288500785828,
-0.02123725228011608,
-0.012964481487870216,
-0.032360345125198364,
0.006978320889174938,
0.004876383114606142,
-0.05319793522357941,
-0.02479633502662182,
0.04804489016532898,
-0.021757075563073158,
-0.015673086047172546,
-0.03438074141740799,
0.048003654927015305,
-0.03900301456451416,
0.004354896955192089,
-0.04646121710538864,
0.024862948805093765,
0.0162355974316597,
-0.05762402340769768,
0.05621952936053276,
-0.030408209189772606,
-0.011398128233850002,
-0.004978519398719072,
0.043147433549165726,
0.024751663208007812,
-0.01912294514477253,
0.006337006576359272,
-0.03298800811171532,
-0.010919901542365551,
-0.014652426354587078,
0.017701072618365288,
0.02669890597462654,
0.02225078083574772,
-0.03369754180312157,
-0.05356213450431824,
-0.008267445489764214,
0.009537260048091412,
0.053074777126312256,
-0.01657853089272976,
0.03246461600065231,
0.01877773180603981,
-0.002392199821770191,
-0.04207415133714676,
-0.026785535737872124,
-0.0136560732498765,
0.017391975969076157,
-0.018219532445073128,
0.025536229833960533,
-0.05159192159771919,
0.013940970413386822,
0.049468375742435455,
0.02869400382041931,
0.014896247535943985,
0.03735806792974472,
0.025203857570886612,
0.041699446737766266,
0.050695378333330154,
0.012550151906907558,
-0.06533928215503693,
0.04731620103120804,
-0.03260435163974762,
0.026852324604988098,
0.0006305202841758728,
-0.03772638365626335,
0.02286849357187748,
-0.004444811027497053,
0.014615283347666264,
0.0035656464751809835,
-0.020800966769456863,
-0.044232625514268875,
0.02877161279320717,
0.014995661564171314,
0.04637116566300392,
-0.0073748365975916386,
-0.018250418826937675,
0.024364903569221497,
0.007109427358955145,
0.041209153831005096,
-0.001643090508878231,
-0.11209587007761002,
-0.031767599284648895,
0.002634485950693488,
-0.037987492978572845,
0.0414188988506794,
-0.005516721401363611,
-0.05497606843709946,
-0.02746083401143551,
-0.02843993343412876,
0.006209125742316246,
0.004929503425955772,
0.019909100607037544,
0.0006786563899368048,
0.04488217085599899,
-0.06599711626768112,
0.01737651787698269,
-0.052482880651950836,
0.019115926697850227,
0.11149280518293381,
0.059070851653814316,
0.0046296510845422745,
-0.05068482086062431,
-0.007024941500276327,
0.00447801360860467,
0.015339057892560959,
-0.022756380960345268,
0.016212135553359985,
-0.009832632727921009,
0.007458835374563932,
0.013454308733344078,
0.05500955507159233,
-0.0066597964614629745,
-0.026837261393666267,
0.046427082270383835,
-0.019513707607984543,
-0.029020654037594795,
0.015847790986299515,
0.0034258821979165077,
0.0026948340237140656,
0.010373649187386036,
-0.03216271847486496,
0.020270509645342827,
-0.006292502861469984,
-0.006515726447105408,
-0.021206339821219444,
-0.01289732288569212,
-0.03236472234129906,
0.0011487138690426946,
-0.03659335523843765,
-0.0006846011965535581,
0.00031116875470615923,
-0.02182214893400669,
-0.03303408995270729,
0.00727094616740942,
-0.0010340857552364469,
-0.008744515478610992,
0.04403383284807205,
0.02291630394756794,
0.02281220071017742,
-0.00929064117372036,
-0.00021909094357397407,
0.03496851027011871,
-0.02544141747057438,
0.015402661636471748,
0.0028892839327454567,
0.031012054532766342,
-0.01091648917645216,
0.02675379067659378,
0.008932368829846382,
0.002757336711511016,
0.015312928706407547,
-0.017004599794745445,
-0.01987650617957115,
0.010752384550869465,
0.03047376312315464,
-0.023937050253152847,
-0.034215424209833145,
-0.03089572861790657,
0.039642464369535446,
-0.03677446022629738,
0.03526929393410683,
-0.015674477443099022,
-0.029608571901917458,
-0.015594213269650936,
-0.052949223667383194,
0.018134882673621178,
-0.021720852702856064,
0.0039149862714111805,
-0.033613983541727066,
-0.01971670612692833,
-0.0515282079577446,
0.01816372387111187,
0.009255698882043362,
0.024966906756162643,
0.051279108971357346,
0.0058853765949606895,
0.00451146112754941,
-0.008167257532477379,
-0.038633719086647034,
0.026776444166898727,
-0.006068192422389984,
0.0045259310863912106,
-0.021380608901381493,
-0.024223707616329193,
0.061907973140478134,
0.015588290058076382,
-0.04257020726799965,
0.025188827887177467,
-0.0022674179635941982,
-0.010797104798257351,
0.023598622530698776,
-0.03133659064769745,
-0.011999606154859066,
-0.025037294253706932,
-0.031750693917274475,
-0.021723978221416473,
-0.03186715766787529,
0.03721393644809723,
0.019343756139278412,
0.002184468787163496,
-0.003224046202376485,
0.022862493991851807,
0.01546464953571558,
0.031131016090512276,
0.008113585412502289,
-0.0526580885052681,
-0.014889420010149479,
-0.012477883137762547,
0.04525604471564293,
-0.03412395343184471,
-0.021975534036755562,
-0.052734680473804474,
-0.028040563687682152,
0.004829986486583948,
-0.008859317749738693,
-0.09275106340646744,
0.02652174048125744,
-0.009825254790484905,
0.0007195170037448406,
-0.04256201535463333,
-0.015452904626727104,
-0.028517773374915123,
-0.01835639588534832,
-0.01174512691795826,
-0.00829764548689127,
0.03583633527159691,
0.0339183434844017,
-0.03515424579381943,
-0.028986051678657532,
0.021144194528460503,
-0.015175306238234043,
-0.033902209252119064,
0.0314929336309433,
-0.016188763082027435,
0.029218386858701706,
0.04817507043480873,
-0.033162448555231094,
-0.011039444245398045,
0.06070438027381897,
-0.010265674442052841,
-0.05928545445203781,
0.02758832648396492,
-0.00938323512673378,
0.028741035610437393,
0.03132430091500282,
-0.01895720511674881,
-0.026952456682920456,
0.03808515891432762,
0.007788622286170721,
-0.004996088333427906,
0.03363707289099693,
-0.027005281299352646,
0.014354757964611053,
-0.00935114175081253,
-0.003099968656897545,
0.0004955926560796797,
-0.006949491798877716,
0.013531669043004513,
0.055043235421180725,
0.01512887328863144,
-0.006802886724472046,
0.0005047971499152482,
-0.0607103556394577,
-0.004004762973636389,
0.005134467501193285,
0.015777407214045525,
0.022718844935297966,
0.04224468022584915,
-0.053924717009067535,
0.06305241584777832,
0.04798328876495361,
0.015829090029001236,
-0.06666933745145798,
0.028307003900408745,
0.009663446806371212,
-0.008365643210709095,
0.036851704120635986,
-0.03294823691248894,
0.03358425572514534,
-0.0017414799658581614,
-0.03342540189623833,
0.023373642936348915,
-0.03843659907579422,
-0.016591453924775124,
-0.041921466588974,
-0.027724100276827812,
-0.0004619184765033424,
0.05628560855984688,
0.04085557162761688,
0.05247744545340538,
0.010332521051168442,
0.0024006085004657507,
0.02145690843462944,
0.029807262122631073,
-0.03919420763850212,
0.0032503094989806414,
-0.007498060818761587,
0.013982381671667099,
0.0477636456489563,
-0.024607937783002853,
-0.030570218339562416,
0.04427448660135269,
0.030418215319514275,
0.03208349272608757,
0.011310303583741188,
-0.003587141865864396,
0.016203461214900017,
0.0005493922508321702,
0.045022767037153244,
-0.007469972129911184,
0.008675727061927319,
0.053917866200208664,
0.01882759854197502,
0.025246581062674522,
0.016157418489456177,
-0.015802638605237007,
0.0011259560706093907,
-0.05203952267765999,
-0.013659698888659477,
0.01707485131919384,
0.03012387827038765,
0.013399932533502579,
-0.004715760238468647,
0.0053115421906113625,
0.011173015460371971,
0.019499637186527252,
0.012065314687788486,
-0.04435000941157341,
0.017176249995827675,
0.04366559907793999,
0.020053766667842865,
-0.038150809705257416,
0.026650814339518547,
0.007968285121023655,
-0.021313032135367393,
0.017344683408737183,
-0.005835640709847212,
0.029788333922624588,
-0.04267428442835808,
-0.0010075016180053353,
-0.019836511462926865,
0.0001421267370460555,
-0.013045777566730976,
-0.02068617381155491,
-0.032729487866163254,
0.05116717144846916,
-0.03101922757923603,
0.027777835726737976,
0.040614839643239975,
-0.04766065999865532,
-0.01092818658798933,
-0.06949669867753983,
0.05135389789938927,
-0.0006585654919035733,
0.014769085682928562,
0.010078102350234985,
-0.037269048392772675,
0.0028653049375861883,
-0.027000848203897476,
0.08133522421121597,
-0.023311618715524673,
-0.03645188733935356,
0.012994293123483658,
-0.003877543145790696,
-0.001570273656398058,
-0.06514532119035721,
-0.00015499541768804193,
0.005995575338602066,
-0.01673658937215805,
0.005360374227166176,
0.0036425990983843803,
-0.0029381371568888426,
0.014182742685079575,
0.05250784754753113,
-0.01487224455922842,
0.02050415612757206,
-0.001082747126929462,
-0.04421231150627136,
0.034496009349823,
0.007211180869489908,
-0.025438861921429634,
0.07538638263940811,
-0.006656626705080271,
0.01423471886664629,
0.024077190086245537,
-0.005056264344602823,
-0.037771597504615784,
0.032602421939373016,
-0.0372515544295311,
-0.022137194871902466,
0.016916001215577126,
0.01319874171167612,
-0.019900375977158546,
-0.03648177906870842,
-0.019297515973448753,
0.02408384531736374,
-0.029536208137869835,
0.0045386566780507565,
0.024959661066532135,
-0.014615744352340698,
0.06656984239816666,
-0.012701177038252354,
0.007756156846880913,
0.017854226753115654,
0.03719930723309517,
-0.015317021869122982,
0.03496134653687477,
0.05648345127701759,
0.020263532176613808,
0.027643058449029922,
-0.013016979210078716,
-0.023044578731060028,
0.023761292919516563,
-0.024201827123761177,
0.046967506408691406,
-0.0712735503911972,
-0.012836643494665623,
0.01364313904196024,
0.011378851719200611,
0.018754485994577408,
0.013042638078331947,
-0.015521274879574776,
0.06587950885295868,
-0.03025209717452526,
0.02860439568758011,
0.014540141448378563,
-0.027920778840780258,
-0.02960345521569252,
0.04052141681313515,
-0.0173228457570076,
0.04122243449091911,
0.0050626397132873535,
0.016117433086037636,
0.005108973011374474,
0.05312551558017731,
0.020335668697953224,
-0.01541596557945013,
-0.008106899447739124,
-0.0057584308087825775,
0.0032504943665117025,
-0.003577185794711113,
-0.016599951311945915,
0.004627194721251726,
-0.01635197177529335,
0.046253081411123276,
0.03944940119981766,
-0.009362814016640186,
-0.015390782617032528,
-0.014353842474520206,
-0.024263890460133553,
0.02844713255763054,
-0.0884968712925911,
0.0016671534394845366,
-0.03238021209836006,
-0.008489050902426243,
-0.0003059707523789257,
-0.04611384496092796
] |
<p>Some of us have been to those amusement park/carnival/theme park rides where you enter some capsule/machine, and you will float, etc.</p>
<p>There is also some other thing where you go inside a big room with normal gravity, and you are closed in and you start to float (i.e. no gravity), and the amount of gravity can be toggled by a person outside the room, or by some dial/switch, etc. It is like the picture I placed below.</p>
<p><img src="http://i.stack.imgur.com/y2NbX.jpg" alt="enter image description here"></p>
<p>I do not know what those things are called, and I will update accordingly when the names are presented, but what I am asking is how does that work?</p>
<p>How can the pull of gravity, result of the spacetime continuum affecting all bodies of mass, be artificially changed? If so, why don't we just alter gravity everywhere with these tools, and move giant, heavy objects easier and such?</p> | 1,442 | [
-0.031042538583278656,
-0.016543010249733925,
0.0004259608977008611,
-0.029406437650322914,
0.047621842473745346,
0.007073976099491119,
-0.014655365608632565,
-0.046272508800029755,
0.006253217812627554,
-0.04253345727920532,
-0.011819900944828987,
0.0672358050942421,
0.018124977126717567,
0.017245478928089142,
0.011616148985922337,
-0.0007563401013612747,
-0.00522473594173789,
0.01108454167842865,
0.015888765454292297,
-0.0647554025053978,
-0.044701483100652695,
0.029781151562929153,
-0.0320044569671154,
-0.0035205157473683357,
-0.031238548457622528,
0.0055062249302864075,
0.05129821598529816,
-0.011959901079535484,
-0.024776406586170197,
0.04185886308550835,
-0.03190220147371292,
-0.01979951001703739,
-0.02726517990231514,
0.015834854915738106,
0.03399144858121872,
0.00020926138677168638,
-0.06205945461988449,
-0.029720671474933624,
0.041780903935432434,
-0.00851564109325409,
-0.06235774978995323,
-0.010584449395537376,
-0.03860556706786156,
0.05042657628655434,
-0.03056979924440384,
0.005393041297793388,
-0.0081577617675066,
0.014304423704743385,
0.05992409214377403,
-0.08238842338323593,
0.04325351491570473,
0.013182717375457287,
0.028250446543097496,
0.04695870727300644,
0.03177044168114662,
-0.0005198335275053978,
0.05175584554672241,
0.02873116172850132,
-0.02014586329460144,
-0.03542044386267662,
-0.017602941021323204,
0.0008468469604849815,
-0.03843226283788681,
-0.0444583036005497,
-0.0019682375714182854,
0.0067208451218903065,
-0.027823491021990776,
0.018140632659196854,
0.028665641322731972,
-0.02976379357278347,
0.02157517522573471,
0.011956284753978252,
0.025269828736782074,
0.0027282454539090395,
0.016641484573483467,
-0.035832103341817856,
0.03305131196975708,
0.0018119252054020762,
0.02907354198396206,
0.03722737357020378,
0.018016966059803963,
-0.019757673144340515,
0.05876239016652107,
0.031069161370396614,
0.012802121229469776,
-0.027966536581516266,
0.06290670484304428,
-0.030818210914731026,
0.05172835290431976,
0.05130868777632713,
-0.021007772535085678,
-0.017633073031902313,
0.014485129155218601,
-0.002325465204194188,
-0.059834036976099014,
0.03360174596309662,
0.02215472050011158,
0.05669989064335823,
0.011322292499244213,
-0.04031742364168167,
-0.008427158929407597,
0.022906221449375153,
-0.01748618483543396,
0.057233795523643494,
0.00833801832050085,
-0.009051852859556675,
-0.03319515660405159,
0.00827878899872303,
-0.002227161545306444,
0.03525647148489952,
-0.042685575783252716,
-0.034342676401138306,
0.002502511953935027,
-0.05868884548544884,
0.03662944585084915,
-0.03512725606560707,
-0.006849033758044243,
-0.025360314175486565,
0.0363311804831028,
0.03526647016406059,
0.06362442672252655,
-0.023107903078198433,
0.014683160930871964,
-0.04511153697967529,
-0.039378754794597626,
0.02635267749428749,
0.0534980483353138,
0.005169957876205444,
-0.029434697702527046,
0.022336473688483238,
0.0037605296820402145,
-0.03551223501563072,
0.0055179777555167675,
0.0205415990203619,
0.042237911373376846,
0.007537952624261379,
-0.1170516163110733,
-0.061927709728479385,
0.0487753264605999,
0.03181082010269165,
0.001081304857507348,
-0.0553421825170517,
0.004350168164819479,
0.03592776134610176,
0.06968268752098083,
0.0372282974421978,
-0.008444120176136494,
0.016406012699007988,
0.02992229536175728,
0.03522951155900955,
0.004808051511645317,
0.027319109067320824,
0.0002505848533473909,
-0.04246140643954277,
-0.010079646483063698,
-0.08429230749607086,
0.031491465866565704,
0.05912209302186966,
0.006970488931983709,
-0.03911793977022171,
0.06776156276464462,
-0.016095491126179695,
0.002428238047286868,
-0.014654107391834259,
0.01072833500802517,
-0.008103806525468826,
0.09230455756187439,
0.014496364630758762,
-0.01912383735179901,
0.055847346782684326,
0.02784782089293003,
0.059535011649131775,
0.0004049914423376322,
0.046230532228946686,
0.01361320074647665,
-0.026640450581908226,
-0.006272484082728624,
-0.04211358353495598,
-0.0077816154807806015,
-0.029939061030745506,
-0.005739028099924326,
-0.003204287961125374,
-0.006933887954801321,
-0.019911127164959908,
0.015710374340415,
0.01935018040239811,
-0.019455425441265106,
-0.022653678432106972,
0.012570701539516449,
-0.025411197915673256,
0.0019651660695672035,
-0.07719099521636963,
0.019387036561965942,
-0.025657156482338905,
-0.010827727615833282,
0.0011445794953033328,
0.030208148062229156,
0.03449459373950958,
-0.037957482039928436,
-0.007388631347566843,
-0.013202491216361523,
0.032423801720142365,
0.01588977687060833,
-0.00012085106573067605,
-0.005999893415719271,
0.047114815562963486,
0.053006771951913834,
0.006085599306970835,
0.011913455091416836,
-0.010555092245340347,
-0.0422159843146801,
-0.024031314998865128,
0.0020987889729440212,
0.014495139010250568,
-0.005911002401262522,
0.009584913961589336,
0.04456409439444542,
0.03332380950450897,
-0.03025367669761181,
0.027004064992070198,
-0.03606932610273361,
0.09723279625177383,
0.034080974757671356,
-0.013572435826063156,
0.019736701622605324,
0.06401896476745605,
0.007606166414916515,
0.018932970240712166,
0.015313229523599148,
-0.026861010119318962,
-0.05325925722718239,
-0.02869781292974949,
-0.0040334779769182205,
0.018811888992786407,
0.000477741559734568,
0.0058031100779771805,
0.011011883616447449,
0.06269807368516922,
0.029478300362825394,
0.023649757727980614,
-0.012668880634009838,
0.0019987153355032206,
0.02759268879890442,
0.034180305898189545,
0.07237932085990906,
0.037757012993097305,
0.03974160924553871,
0.05394288897514343,
-0.02290395088493824,
-0.025418797507882118,
0.020006127655506134,
-0.004301905166357756,
0.005381484050303698,
-0.00039954952080734074,
-0.017189567908644676,
0.002281622961163521,
0.019020723178982735,
-0.025562353432178497,
0.009701942093670368,
0.026647882536053658,
0.01743386499583721,
-0.02878016047179699,
-0.06944197416305542,
-0.004578676540404558,
0.015569486655294895,
0.0381770022213459,
-0.012783811427652836,
-0.008061017841100693,
0.02628401480615139,
-0.03637117147445679,
0.028513459488749504,
-0.015212737955152988,
-0.0008326743263751268,
-0.03416914492845535,
0.017645977437496185,
0.001604375778697431,
0.02660282701253891,
0.034797340631484985,
-0.030935393646359444,
-0.024438615888357162,
-0.015860890969634056,
-0.01752912625670433,
-0.0101995337754488,
0.03963901102542877,
-0.06539040803909302,
0.04394051060080528,
-0.0263958852738142,
-0.034617986530065536,
0.08879581838846207,
-0.012848547659814358,
0.012923509813845158,
0.02466902881860733,
-0.006581742316484451,
-0.03059467487037182,
-0.00243398267775774,
-0.002322430955246091,
0.014581502415239811,
0.011815691366791725,
-0.02745732292532921,
0.07794483006000519,
0.03216272592544556,
-0.0660928264260292,
0.020553063601255417,
-0.05668824911117554,
-0.05235917493700981,
-0.02502558007836342,
0.02348794974386692,
-0.00693868612870574,
-0.05325565114617348,
-0.007534865289926529,
0.02520940825343132,
-0.049153268337249756,
0.005043154116719961,
-0.017593810334801674,
-0.05170911177992821,
-0.005136249121278524,
-0.04502618685364723,
0.032440364360809326,
0.00787536520510912,
-0.011283080093562603,
0.10553005337715149,
0.03415822237730026,
-0.03421149030327797,
-0.020501989871263504,
-0.004088400863111019,
0.014868231490254402,
-0.02123083546757698,
0.01068601943552494,
0.05060609430074692,
-0.0016689716139808297,
0.01225962769240141,
0.05096264183521271,
0.005184216424822807,
0.012420295737683773,
0.02779025211930275,
-0.024354053661227226,
0.01111077144742012,
0.015161524526774883,
0.005494034383445978,
0.05341877043247223,
0.007660976145416498,
-0.035321302711963654,
-0.012133816257119179,
-0.011885342188179493,
-0.00598455173894763,
0.007930795662105083,
-0.06832581758499146,
0.053377967327833176,
0.05563228577375412,
0.019214987754821777,
0.026406656950712204,
0.0016051477286964655,
-0.027082640677690506,
-0.02893657796084881,
0.003187044756487012,
0.005171953700482845,
0.028721744194626808,
-0.013537414371967316,
-0.017608007416129112,
0.010220571421086788,
0.08102280646562576,
-0.04864635318517685,
-0.025979258120059967,
0.029124082997441292,
0.018258225172758102,
0.02675255946815014,
-0.02288971282541752,
-0.015726175159215927,
0.04477107152342796,
0.04206692427396774,
0.04326745867729187,
-0.032886117696762085,
-0.015068267472088337,
0.014313111081719398,
-0.02508697472512722,
0.01407460868358612,
0.027177877724170685,
0.03393980860710144,
-0.020571917295455933,
0.025687336921691895,
0.018819505348801613,
0.03716062009334564,
0.011291008442640305,
-0.022571943700313568,
-0.10175814479589462,
0.047670818865299225,
-0.03600998967885971,
-0.024128077551722527,
0.01569986343383789,
0.029205363243818283,
-0.00008872248872648925,
-0.014474499970674515,
-0.028955502435564995,
-0.044475045055150986,
0.009043404832482338,
-0.0639960765838623,
-0.022598886862397194,
-0.005699423141777515,
-0.053106073290109634,
-0.007685504388064146,
0.020828669890761375,
0.01310903113335371,
0.000042488256440265104,
0.011067556217312813,
-0.021464325487613678,
-0.01879226416349411,
-0.0032821823842823505,
0.028017770498991013,
-0.013130273669958115,
0.04482289031147957,
0.027674738317728043,
0.019636981189250946,
0.034245431423187256,
-0.012978865765035152,
-0.01799715682864189,
0.010141689330339432,
0.015144743025302887,
-0.034653883427381516,
-0.00513520697131753,
-0.019717223942279816,
-0.056722018867731094,
-0.04950142651796341,
0.013125780038535595,
0.029190555214881897,
-0.0013820098247379065,
-0.0015124354977160692,
-0.004300948232412338,
0.0025687895249575377,
-0.027845896780490875,
0.010884378105401993,
0.05513499304652214,
0.014195745810866356,
-0.01933589018881321,
-0.03772676736116409,
-0.029703350737690926,
-0.03152823820710182,
-0.00911501795053482,
0.010976937599480152,
0.03519066423177719,
-0.04551432281732559,
0.021754715591669083,
0.03752552345395088,
0.01197702158242464,
-0.004465374164283276,
-0.018178729340434074,
-0.011173265054821968,
0.03157750144600868,
-0.009077104739844799,
0.033318452537059784,
0.022720802575349808,
0.01813766174018383,
0.04077315330505371,
-0.02478584088385105,
0.03564487397670746,
-0.09882424026727676,
-0.02992062084376812,
0.022390227764844894,
0.018963875249028206,
0.006685604341328144,
-0.01946243830025196,
-0.0441640242934227,
-0.05291515588760376,
0.018168572336435318,
-0.03786255791783333,
0.0029825379606336355,
0.001864577759988606,
0.011885656043887138,
0.0006441199802793562,
-0.012486853636801243,
-0.00014241831377148628,
0.005358448717743158,
-0.02595001459121704,
0.005350210703909397,
-0.010402394458651543,
0.018358802422881126,
0.034723736345767975,
0.010466726496815681,
-0.007434047758579254,
0.03650585934519768,
0.00927416980266571,
-0.00946845207363367,
0.010560577735304832,
-0.006850137375295162,
-0.06235739216208458,
-0.07676316052675247,
-0.04325335472822189,
0.039673835039138794,
-0.025414874777197838,
0.05108774080872536,
-0.03167835995554924,
-0.05277169868350029,
-0.0101856654509902,
-0.0023565436713397503,
0.04348212853074074,
0.027155132964253426,
-0.015084673650562763,
0.014980649575591087,
0.05903351306915283,
0.01615923084318638,
0.012149208225309849,
0.033882737159729004,
-0.04570848494768143,
0.0339776948094368,
-0.019746294245123863,
0.023928560316562653,
-0.01677374541759491,
-0.001283593475818634,
-0.012150872498750687,
0.0026291199028491974,
-0.026850931346416473,
0.04551628232002258,
0.004177034832537174,
-0.0005311958375386894,
0.02413167990744114,
-0.028527000918984413,
-0.014950686134397984,
0.06922250241041183,
0.022102894261479378,
-0.005122569389641285,
-0.0050577521324157715,
0.036082375794649124,
0.0087936632335186,
-0.042902614921331406,
0.00892073567956686,
0.031678423285484314,
-0.006457219831645489,
0.016240328550338745,
-0.018831584602594376,
0.004998669493943453,
-0.02027425542473793,
0.00867462158203125,
0.009981801733374596,
-0.06589847058057785,
0.08743419498205185,
-0.021753793582320213,
0.013143224641680717,
0.04648904874920845,
-0.04119786247611046,
-0.0400196835398674,
-0.04224501550197601,
-0.0365692600607872,
0.007707173470407724,
-0.030652081593871117,
0.020377978682518005,
0.03597741574048996,
0.04758426919579506,
-0.043622493743896484,
-0.05511878430843353,
0.049559179693460464,
-0.019959287717938423,
-0.007748046424239874,
-0.04905860871076584,
0.02830999530851841,
-0.047936465591192245,
-0.0392758809030056,
-0.023925721645355225,
0.01943138800561428,
-0.03465280309319496,
0.01753457821905613,
0.03238449618220329,
0.01311288308352232,
0.037752676755189896,
0.001359702437184751,
-0.06934467703104019,
0.002050654962658882,
-0.015146049670875072,
0.030945396050810814,
0.010862757451832294,
0.0399472676217556,
-0.03160636126995087,
-0.04195049777626991,
-0.0024526065681129694,
-0.001451800693757832,
0.0028762139845639467,
-0.009922669269144535,
0.031517673283815384,
0.04689439386129379,
0.023903537541627884,
0.019252343103289604,
-0.010689973831176758,
0.026485227048397064,
0.005819665268063545,
0.00464647077023983,
-0.01693795807659626,
0.023652054369449615,
0.026468276977539062,
-0.028861841186881065,
0.041448961943387985,
-0.006396419834345579,
-0.00941799022257328,
-0.004708427935838699,
0.05745885893702507,
0.009556122124195099,
-0.021777043119072914,
0.004911808762699366,
-0.02304021455347538,
0.030965682119131088,
-0.01804511621594429,
-0.008669110015034676,
0.025572996586561203,
0.0025951522402465343,
-0.005806395318359137,
-0.013337076641619205,
-0.03845153748989105,
-0.014997879043221474,
0.04398326575756073,
-0.026606081053614616,
0.08138121664524078,
0.0639149397611618,
-0.025706997141242027,
-0.011368495412170887,
-0.002541822148486972,
-0.0038319421000778675,
0.036649301648139954,
-0.014851421117782593,
0.012299023568630219,
0.002162133576348424,
0.011423150077462196,
0.019686641171574593,
0.04491930082440376,
-0.05274291709065437,
-0.008378676138818264,
0.03736502677202225,
0.014862343668937683,
0.011263102293014526,
-0.01773684099316597,
-0.0031024308409541845,
0.041016094386577606,
-0.012350176461040974,
0.057668231427669525,
-0.007312603294849396,
-0.003043191507458687,
0.008043495938181877,
0.008946811780333519,
0.00008647504728287458,
-0.026809515431523323,
-0.018299538642168045,
-0.053704921156167984,
-0.0052836304530501366,
0.0003117324667982757,
-0.01549107301980257,
-0.018009640276432037,
-0.02421901561319828,
0.04342672973871231,
-0.028786148875951767,
-0.026109764352440834,
-0.024825243279337883,
-0.06648682802915573,
-0.023856058716773987,
-0.0473167821764946,
-0.04063316434621811,
0.0447247251868248,
0.015762975439429283,
-0.031116481870412827,
0.026291443035006523,
-0.036400292068719864,
-0.012508713640272617,
0.03901305049657822,
0.03000013902783394,
-0.04060268774628639,
0.05490138381719589,
-0.016993990167975426,
0.007010150700807571,
-0.004065006505697966,
-0.029513459652662277,
0.10492981970310211,
0.004816688597202301,
-0.02421782724559307,
-0.04697420820593834,
-0.019188517704606056,
-0.031184768304228783,
-0.008011648431420326,
-0.026357751339673996,
0.0029341992922127247,
-0.0122215049341321,
0.031121915206313133,
-0.011053267866373062,
0.04331212118268013,
-0.008878305554389954,
0.0014221682213246822,
0.03520606830716133,
-0.052377015352249146,
-0.017697172239422798,
-0.007684648968279362,
-0.01608804054558277,
-0.037184689193964005,
0.01827363483607769,
-0.04743153601884842,
0.04730029031634331,
-0.019427279010415077,
0.009985282085835934,
-0.04547007381916046,
-0.042527683079242706,
-0.0016279371920973063,
0.011537675745785236,
-0.05110883340239525,
0.007800941821187735,
0.007294593378901482,
-0.04496098682284355,
-0.048678625375032425,
0.02996731363236904,
0.024333251640200615,
-0.03837873414158821,
-0.01654975302517414,
0.025454791262745857,
-0.015553971752524376,
-0.008971438743174076,
0.029191162437200546,
-0.017609763890504837,
-0.040571428835392,
0.012246343307197094,
-0.03633807227015495,
0.04407728090882301,
-0.027118077501654625,
0.01624409668147564,
0.004461168777197599,
-0.002022403758019209,
-0.021746693179011345,
-0.04072766751050949,
-0.018761156126856804,
-0.028655434027314186,
0.008363141678273678,
0.051131054759025574,
0.0015285700792446733,
0.013475765474140644,
0.02442873641848564,
0.019933518022298813,
0.003924075979739428,
-0.015870194882154465,
0.031224563717842102,
0.024315282702445984,
0.009594067931175232,
0.029325146228075027,
-0.02616576850414276,
0.015394148416817188,
-0.03718554228544235,
-0.003276791423559189,
-0.03708098083734512,
0.030565854161977768,
0.012810117565095425,
0.019736679270863533,
0.022615568712353706,
0.016655081883072853,
0.002496369881555438,
0.014257663860917091,
-0.007469134870916605,
0.027928093448281288,
-0.017371468245983124,
-0.01896863430738449,
-0.04381880164146423,
-0.01966235600411892,
-0.0054030329920351505,
0.03501707315444946,
0.030535215511918068,
-0.008172646164894104,
0.0077576483599841595,
0.0003753788478206843,
-0.0032595486845821142,
-0.02475271187722683,
-0.014779110439121723,
0.0256363395601511,
-0.025634456425905228,
-0.006814492866396904,
-0.003874929854646325,
0.038349367678165436,
0.01757242903113365,
-0.04602456092834473,
-0.0003755460202228278,
0.011884229257702827,
-0.02026907168328762,
0.009398609399795532,
0.030856357887387276,
-0.00020777933241333812,
-0.008682948537170887,
-0.02181653492152691,
0.009364851750433445,
-0.042866505682468414,
-0.02344108745455742,
-0.007711679209023714,
-0.022291526198387146,
-0.02747032791376114,
0.049552466720342636,
0.019844133406877518,
0.029093069955706596,
0.002521795453503728,
0.01919926330447197,
-0.016491182148456573,
0.013463825918734074,
-0.05942597985267639,
-0.020398933440446854,
0.0035712842363864183,
-0.002487799385562539,
-0.037655334919691086,
0.02557194046676159,
-0.02269093319773674,
-0.004899531602859497,
-0.0035025188699364662,
0.018950659781694412,
-0.022992586717009544,
0.008463218808174133,
0.021124862134456635,
-0.013153577223420143,
0.00858207419514656,
-0.006200691219419241,
-0.049143172800540924,
0.024287572130560875,
-0.026915792375802994,
-0.031181512400507927,
0.027131149545311928,
-0.015429064631462097,
0.041207391768693924,
0.0442761592566967,
-0.046876661479473114,
-0.010233191773295403,
0.037260640412569046,
-0.014475228264927864,
-0.022153250873088837,
-0.04512779414653778,
-0.007270227652043104,
-0.032434720546007156,
-0.004551497288048267,
0.023692790418863297,
-0.053964029997587204,
-0.04129726439714432,
0.002703647827729583,
0.018388183787465096,
-0.011573719792068005,
-0.0037243927363306284,
-0.010314149782061577,
-0.017369134351611137,
-0.0064166090451180935,
0.006606544833630323,
-0.00880685169249773,
0.03836280107498169,
0.04476740211248398,
-0.04498531296849251,
0.02141263708472252,
0.04292476549744606,
0.009191807359457016,
-0.08507765084505081,
-0.035839252173900604,
-0.0032323217019438744,
-0.0403713583946228,
0.04017183184623718,
-0.0240824893116951,
0.015895672142505646,
-0.008918133564293385,
-0.08964946120977402,
0.024627845734357834,
-0.046150870621204376,
-0.01339535228908062,
-0.0007210253970697522,
0.007406312040984631,
0.012389522977173328,
0.04791877418756485,
0.016783740371465683,
0.013699603267014027,
-0.014533850364387035,
-0.012912224046885967,
-0.02680984139442444,
-0.010347137227654457,
-0.0002554676902946085,
0.020106274634599686,
-0.013422323390841484,
0.007684162352234125,
0.058836158365011215,
-0.024337347596883774,
-0.014846247620880604,
0.012064064852893353,
0.02473105862736702,
-0.009591571986675262,
-0.028551995754241943,
-0.005901551339775324,
-0.012370464392006397,
0.01698176935315132,
0.009517152793705463,
0.022598447278141975,
-0.04384491592645645,
0.04931570962071419,
0.015059963800013065,
0.023257296532392502,
0.0010698245605453849,
-0.007757502142339945,
0.007192726247012615,
-0.037026744335889816,
0.015398074872791767,
0.011901017278432846,
-0.056176163256168365,
0.020464790984988213,
0.012728124856948853,
0.03654943034052849,
0.02659597061574459,
-0.014988777227699757,
-0.010446303524076939,
-0.023847734555602074,
0.018087215721607208,
0.01735086925327778,
-0.017292462289333344,
-0.008493868634104729,
0.02618340589106083,
-0.012959458865225315,
0.0029656311962753534,
0.02209133468568325,
-0.007479606196284294,
-0.053802672773599625,
-0.03421603515744209,
-0.009885177947580814,
-0.0034345989115536213,
-0.0004450816777534783,
0.03531934320926666,
-0.03953972086310387,
-0.015022112987935543,
0.029623541980981827,
0.04475103318691254,
0.004672546871006489,
-0.008557887747883797,
-0.03428945690393448,
-0.00114980130456388,
-0.0376507043838501,
0.04870279133319855,
0.006669178605079651,
-0.009720807895064354,
-0.013750230893492699,
-0.018593240529298782,
-0.007428934331983328,
0.036416660994291306,
0.06764242798089981,
0.0022970472928136587,
0.00943495612591505,
0.013683288358151913,
0.0007839932222850621,
0.03769966959953308,
-0.025835340842604637,
0.024218561127781868,
0.035154957324266434,
-0.08059319108724594,
0.003636928740888834,
0.03637215495109558,
-0.01486131176352501,
0.006397610530257225,
0.02021639421582222,
-0.02268289029598236,
0.056088462471961975,
-0.004627059679478407,
-0.007002420257776976,
0.01303884293884039,
0.02221342921257019,
-0.005270605441182852,
0.05403924733400345,
-0.003140880959108472,
0.027763504534959793,
0.035487301647663116,
-0.015758037567138672,
-0.009754616767168045,
0.04447140172123909,
-0.006739849224686623,
0.028582317754626274,
-0.04269156977534294,
-0.04796379804611206,
0.006829096935689449,
-0.003920745104551315,
0.022547584027051926,
0.011099736206233501,
-0.02603640966117382,
0.010601122863590717,
0.07478482276201248,
0.034620340913534164,
0.005907123442739248,
-0.015473773702979088,
0.0044146035797894,
-0.021539151668548584,
0.003125639632344246,
0.03658154606819153,
0.06520961970090866,
0.062059879302978516,
0.021912256255745888,
0.01158194337040186,
0.05425191670656204,
-0.015841981396079063,
0.024900052696466446,
0.015603836625814438,
0.024302145466208458,
-0.04398316144943237,
-0.008580749854445457,
-0.018631093204021454,
-0.007654169574379921,
-0.012433740310370922,
0.04918234795331955,
-0.022925183176994324,
0.051302678883075714,
-0.017906896770000458,
-0.0004654507793020457,
0.016437659040093422,
0.013129312545061111,
0.03864121064543724,
-0.012365378439426422,
-0.017515014857053757,
0.04653200879693031,
-0.0015879457350820303,
-0.04310358315706253,
-0.011446068063378334,
0.003765984671190381,
-0.016128215938806534,
0.040022678673267365,
0.054823558777570724,
0.012293100357055664,
-0.004723259713500738,
0.02270851470530033,
-0.023542890325188637,
-0.033172767609357834,
-0.057912033051252365,
0.025821750983595848,
0.01014226395636797,
0.029253002256155014,
-0.024737076833844185,
-0.023143038153648376,
-0.04608825594186783,
0.03796767070889473,
-0.06762176752090454,
-0.02974293939769268,
0.0022194210905581713,
0.05445089563727379,
-0.04695585370063782,
-0.007615519221872091
] |
<p>Recently I heard that there is some "alternate" equation for the Dirac one. It can be introduced if we refuse some properties of the theory describes the electron, which Dirac used in <a href="https://www.dropbox.com/s/vw8fa1s4rr32o85/Proc.%20R.%20Soc.%20Lond.%20A-1928-Dirac-610-24.pdf" rel="nofollow">his original article</a>. Then we will get theory with spin 1/2-particle and with modified (in compare with Dirac equation) mass. </p>
<p>I thought that it is connected with the invariance of theory under discrete Lorentz transformations. If we need it, we must to create theory which describes the sum of representations $\left(\frac{1}{2}, 0\right) + \left( 0, \frac{1}{2}\right)$ (because it is invariant under discrete transformations and as the consequence - under full Lorentz group transformations), so, finally, we will get the Dirac equation. But if we refuse the requirement of invariance under discrete transformations, we may describe two-component wave-function. Some analisys leads to the Klein-Gordon equation for it. But it has problems with propability density, so I think that the way of getting this alternate equation is another. </p>
<p>Can you help me?</p> | 1,443 | [
-0.0375220887362957,
0.01811271347105503,
0.01041797362267971,
-0.050293173640966415,
0.022429106757044792,
-0.002130014356225729,
-0.05881186202168465,
-0.02729959972202778,
-0.011067119427025318,
-0.05026094987988472,
0.030601516366004944,
-0.0015193112194538116,
0.05423664301633835,
0.036777716130018234,
0.00508895656093955,
0.031014788895845413,
-0.0032934858463704586,
0.018555786460638046,
-0.023971421644091606,
-0.04205607995390892,
0.01024228148162365,
0.023743659257888794,
0.031175820156931877,
-0.005940356757491827,
-0.002434457652270794,
0.01991007849574089,
-0.0013329698704183102,
0.009947946295142174,
-0.002031031996011734,
0.0406617745757103,
-0.013368582352995872,
-0.059010766446590424,
0.020433742552995682,
0.006303560454398394,
0.026500778272747993,
0.01080327108502388,
-0.009431722573935986,
-0.05503249913454056,
0.03140300139784813,
0.013111986219882965,
-0.029300004243850708,
-0.030655497685074806,
-0.005903384182602167,
0.02141055464744568,
-0.013715885579586029,
0.0364517979323864,
0.014433367177844048,
-0.018791183829307556,
0.057638153433799744,
-0.0733497366309166,
0.08712827414274216,
0.0020957975648343563,
0.01407632976770401,
-0.015527969226241112,
-0.026110656559467316,
-0.027796372771263123,
0.043490953743457794,
0.08433216065168381,
0.00397501653060317,
-0.04114214703440666,
-0.01335806306451559,
-0.031009862199425697,
0.0206924919039011,
-0.008849396370351315,
-0.004212712869048119,
0.028505921363830566,
0.023905552923679352,
-0.004910957533866167,
0.012722271494567394,
-0.008889952674508095,
0.017364690080285072,
-0.007447703741490841,
0.048022039234638214,
-0.00680547533556819,
0.04120374098420143,
0.01458978932350874,
0.018054574728012085,
-0.0009461615700274706,
-0.0018458805279806256,
0.018832450732588768,
0.008900663815438747,
0.03366478532552719,
0.014122147113084793,
0.0029669664800167084,
-0.02722259983420372,
-0.04764679819345474,
0.05410752445459366,
0.04363977164030075,
-0.011654007248580456,
-0.002169921062886715,
-0.015472226776182652,
-0.021453164517879486,
0.04807903245091438,
-0.020981566980481148,
-0.031078478321433067,
0.027386045083403587,
0.004600309766829014,
0.05946587771177292,
-0.015713954344391823,
-0.027771130204200745,
0.014896605163812637,
-0.026979370042681694,
-0.005367911420762539,
0.07355615496635437,
0.0098922373726964,
-0.0015639938646927476,
-0.05156616494059563,
-0.013181968592107296,
-0.01949554868042469,
-0.009401277638971806,
-0.01508172508329153,
0.033719953149557114,
-0.013136222958564758,
-0.003375477623194456,
-0.005210604052990675,
0.0017815836472436786,
-0.01425184030085802,
-0.012004196643829346,
0.062266722321510315,
0.11277904361486435,
-0.007840460166335106,
-0.014560762792825699,
0.027933618053793907,
-0.01901416853070259,
-0.06603066623210907,
-0.01870580017566681,
0.04396414756774902,
-0.004090988077223301,
-0.021984882652759552,
0.030957642942667007,
0.017748920246958733,
-0.012232622131705284,
0.02526680938899517,
0.025570467114448547,
0.038412779569625854,
-0.040893204510211945,
-0.08449321240186691,
-0.03387676924467087,
0.011977062560617924,
0.0011896109208464622,
-0.024420209228992462,
-0.05951207876205444,
0.02221679501235485,
0.01028124988079071,
0.08698322623968124,
-0.003353798994794488,
0.04219558462500572,
-0.002248283475637436,
0.01867450214922428,
0.003965987358242273,
0.0001715918624540791,
-0.023505911231040955,
0.012585800141096115,
-0.04211999475955963,
-0.02149629220366478,
-0.03250377997756004,
0.024303369224071503,
0.01270564366132021,
-0.0005443623522296548,
0.0008659074665047228,
0.06322738528251648,
-0.005738086067140102,
-0.02228420041501522,
0.0399482287466526,
0.010568316094577312,
-0.018324395641684532,
0.03926956653594971,
0.027216047048568726,
0.0032499281223863363,
0.047640517354011536,
0.014070173725485802,
0.015170454978942871,
0.0033134182449430227,
0.00830854196101427,
0.00885090697556734,
-0.051369983702898026,
-0.06775616854429245,
-0.01427442580461502,
-0.007788967341184616,
-0.008664966560900211,
-0.02573349140584469,
-0.018344318494200706,
-0.023180631920695305,
0.03293352201581001,
0.007245875429362059,
0.014932963997125626,
0.005095636006444693,
-0.005836109630763531,
0.0032528915908187628,
-0.0456916019320488,
0.0016085546230897307,
-0.0821322649717331,
-0.00425527710467577,
-0.03359280526638031,
0.023742100223898888,
0.02770022116601467,
0.015307423658668995,
-0.019450776278972626,
0.0068931858986616135,
-0.002199342707172036,
0.006565281189978123,
0.04307816922664642,
0.020895471796393394,
0.002764482516795397,
0.021259162575006485,
0.05619882047176361,
0.03152026608586311,
-0.005734439007937908,
-0.005160117521882057,
0.011979175731539726,
-0.01752672716975212,
0.01656283810734749,
-0.021623361855745316,
0.036514606326818466,
-0.012736411765217781,
0.000012801877346646506,
0.010417984798550606,
-0.005262379534542561,
-0.01036909967660904,
0.022428493946790695,
-0.015917005017399788,
0.05364593118429184,
0.027480753138661385,
-0.01868985965847969,
0.03128347545862198,
0.05103036016225815,
0.007432049605995417,
0.019536808133125305,
0.009035433642566204,
-0.0316624753177166,
-0.024983683601021767,
-0.005066603887826204,
0.05966939777135849,
0.052163682878017426,
-0.04012242704629898,
0.028475048020482063,
0.016944631934165955,
0.0333397313952446,
-0.0006436837138608098,
-0.00465574162080884,
-0.02993861585855484,
-0.08642002195119858,
0.021027015522122383,
-0.030014624819159508,
0.0009984023636206985,
-0.0041836220771074295,
-0.0014155263779684901,
-0.00628574937582016,
0.01660771854221821,
-0.02652118355035782,
-0.03033449500799179,
0.014031373895704746,
-0.0017945009749382734,
-0.0273290928453207,
-0.0122818723320961,
-0.04176315665245056,
0.029571112245321274,
-0.023997122421860695,
0.029370155185461044,
0.025887897238135338,
-0.034070033580064774,
-0.01025841012597084,
-0.031497448682785034,
-0.032648034393787384,
0.007683452684432268,
-0.011398045346140862,
0.001554623362608254,
-0.030620381236076355,
0.0006888076895847917,
-0.04385696351528168,
-0.0026775687001645565,
0.004104084335267544,
-0.031173333525657654,
0.0033871640916913748,
-0.011726138181984425,
0.02967662923038006,
0.04265521466732025,
0.0037175610195845366,
-0.0137696648016572,
-0.04229561984539032,
0.024023527279496193,
0.010934549383819103,
0.02090972661972046,
0.05001815780997276,
-0.0383199118077755,
-0.006470242515206337,
-0.06971082836389542,
-0.04216046258807182,
0.03629354387521744,
0.016389699652791023,
0.028523514047265053,
0.00277707795612514,
-0.006768960505723953,
-0.0762130469083786,
-0.028613846749067307,
-0.04491830989718437,
0.027309201657772064,
-0.048613257706165314,
-0.020407499745488167,
0.0505722239613533,
0.016468912363052368,
-0.022969504818320274,
-0.012450254522264004,
-0.014713326469063759,
-0.06982199847698212,
-0.011538597755134106,
-0.00879242829978466,
0.019445449113845825,
-0.02218686230480671,
0.04762730374932289,
0.004786874633282423,
-0.029203463345766068,
0.0015121542382985353,
-0.06470370292663574,
-0.02346332184970379,
0.00839188788086176,
-0.011980467475950718,
0.040561847388744354,
0.009320445358753204,
-0.04126540943980217,
0.08263307064771652,
0.015455835498869419,
-0.022313905879855156,
-0.024190979078412056,
0.011182704009115696,
0.0049918885342776775,
-0.039686914533376694,
-0.00821415614336729,
0.050976913422346115,
0.028856009244918823,
-0.00035626828321255744,
0.025673555210232735,
0.0075668818317353725,
0.013939379714429379,
0.0010922402143478394,
-0.034901559352874756,
0.043563518673181534,
0.01828243024647236,
0.0008827956044115126,
0.03805217891931534,
0.0013701904099434614,
-0.035159021615982056,
-0.004233688581734896,
-0.0006229283171705902,
0.0235711932182312,
0.013487783260643482,
-0.07270461320877075,
0.0270613394677639,
0.03667542710900307,
0.026691384613513947,
-0.00033823007834143937,
0.027872860431671143,
0.0051540229469537735,
-0.047257065773010254,
0.02827930636703968,
0.04644272103905678,
0.03374664485454559,
0.01976986601948738,
0.006572955287992954,
0.028955962508916855,
0.05069417878985405,
-0.03414790332317352,
-0.020307406783103943,
0.016092371195554733,
0.0019997672643512487,
0.02647862210869789,
-0.00733600277453661,
-0.014126518741250038,
0.04524579644203186,
0.019414937123656273,
0.04383646324276924,
-0.010915307328104973,
-0.010298850946128368,
0.017613152042031288,
-0.022183623164892197,
-0.002074248855933547,
-0.026902176439762115,
0.03490510955452919,
0.020640604197978973,
0.02159338817000389,
0.0345441997051239,
0.006496036890894175,
-0.0031120693311095238,
0.008960308507084846,
-0.08619231730699539,
-0.03897320106625557,
-0.000008599938155384734,
0.020233526825904846,
-0.03772537782788277,
0.005286617204546928,
0.027284355834126472,
-0.03147910535335541,
-0.04062904044985771,
-0.02543620765209198,
0.002951887436211109,
-0.02965550683438778,
0.04648619145154953,
-0.060327086597681046,
-0.02419712208211422,
-0.010161619633436203,
0.05772475525736809,
0.0366368442773819,
-0.004900485742837191,
-0.0038337837904691696,
0.042410314083099365,
-0.027760298922657967,
0.032873786985874176,
-0.02789285033941269,
-0.0044303275644779205,
0.008467690087854862,
0.0011586631881073117,
0.024789612740278244,
0.022868400439620018,
-0.020252825692296028,
-0.025037551298737526,
0.026835031807422638,
0.0657610297203064,
0.01808570884168148,
0.0026328733656555414,
0.009243346750736237,
-0.0533493310213089,
-0.0004968882421962917,
-0.021816756576299667,
0.0447203703224659,
-0.004211728926748037,
0.006628542207181454,
0.0315801203250885,
-0.0034007872454822063,
0.004789788741618395,
-0.004167655017226934,
0.04859349876642227,
-0.0025657734367996454,
-0.028471535071730614,
-0.025487951934337616,
0.010581022128462791,
-0.03164109215140343,
-0.0021407618187367916,
-0.011012415401637554,
0.009059478528797626,
-0.022948255762457848,
0.006941292900592089,
0.00670674629509449,
0.04380008578300476,
-0.02750571444630623,
-0.011979673057794571,
-0.0241226963698864,
0.010571064427495003,
0.026143506169319153,
0.0028007952496409416,
-0.016867415979504585,
0.04671331122517586,
0.03337722271680832,
-0.015886832028627396,
-0.005584232974797487,
-0.031106790527701378,
-0.026683371514081955,
0.016650892794132233,
0.02224022150039673,
0.01840863563120365,
0.011650455184280872,
-0.07474493980407715,
-0.0038020119536668062,
0.03608956187963486,
-0.0223233662545681,
-0.009193544276058674,
-0.01636926829814911,
-0.026945574209094048,
0.009627347812056541,
-0.029879078269004822,
-0.026182038709521294,
0.024271680042147636,
-0.029748983681201935,
-0.012704278342425823,
-0.0649895891547203,
0.03158511966466904,
-0.029886944219470024,
0.006385278422385454,
0.006610048934817314,
0.04957388713955879,
0.004759858828037977,
0.036022085696458817,
-0.005928313359618187,
0.029297806322574615,
-0.02944807894527912,
-0.09214873611927032,
-0.025975527241826057,
0.04736809432506561,
0.010249809361994267,
0.045570872724056244,
-0.0679493099451065,
-0.05204915255308151,
-0.016242045909166336,
-0.034747518599033356,
-0.025886759161949158,
0.021451609209179878,
-0.08704401552677155,
0.033248379826545715,
0.022918427363038063,
-0.032950833439826965,
0.034584712237119675,
0.022668467834591866,
-0.031347714364528656,
-0.013549666851758957,
-0.02639680914580822,
-0.00009859464626060799,
-0.02154151163995266,
-0.00933148805052042,
-0.04134764522314072,
0.036578189581632614,
-0.014707489870488644,
0.0353262685239315,
0.02034267596900463,
0.022654114291071892,
0.019591426476836205,
-0.022578349336981773,
-0.011098970659077168,
0.013587200082838535,
-0.04935640096664429,
-0.017498910427093506,
-0.05577661469578743,
0.021969828754663467,
0.031000226736068726,
-0.0383225716650486,
0.024695439264178276,
0.010466082952916622,
-0.020572230219841003,
0.04280645027756691,
0.000651936570648104,
0.008145865052938461,
-0.045341119170188904,
-0.017620213329792023,
0.017387500032782555,
-0.02547108568251133,
0.02737221121788025,
0.003157298546284437,
-0.000911282142624259,
0.0012713918695226312,
-0.03710149601101875,
-0.0525018684566021,
0.008764185942709446,
-0.005106374155730009,
0.019356274977326393,
-0.01844736561179161,
-0.018721655011177063,
0.022649168968200684,
-0.02353190816938877,
-0.10749449580907822,
-0.028806257992982864,
0.019124601036310196,
-0.042836979031562805,
-0.010859805159270763,
-0.012380301021039486,
-0.00008553049701731652,
-0.012098713777959347,
-0.031765781342983246,
0.05110301822423935,
0.03423619642853737,
-0.020042061805725098,
-0.018491536378860474,
0.0065639144740998745,
0.0425863154232502,
0.03976104035973549,
-0.04198504611849785,
-0.015082393772900105,
-0.012005931697785854,
-0.02226547710597515,
0.021043147891759872,
0.04580234736204147,
0.022645512595772743,
-0.02093125507235527,
-0.04245329275727272,
-0.025731578469276428,
-0.0025651634205132723,
0.01581253483891487,
-0.026882756501436234,
-0.014234203845262527,
0.031962718814611435,
0.017549244686961174,
-0.014166360720992088,
-0.06306622922420502,
-0.0001935144973685965,
-0.016514524817466736,
0.02799004316329956,
0.010483253747224808,
0.029890771955251694,
-0.07258986681699753,
-0.023416532203555107,
0.027625689283013344,
-0.020045198500156403,
-0.019015353173017502,
0.020102020353078842,
0.016696074977517128,
0.02906089648604393,
-0.004912601318210363,
0.04967449977993965,
-0.02755637839436531,
0.00923678744584322,
0.01027399580925703,
0.034043073654174805,
0.032728224992752075,
-0.004336321726441383,
-0.027425015345215797,
-0.012122226879000664,
-0.013194599188864231,
0.021195022389292717,
0.011771855875849724,
-0.0007234970689751208,
0.028348151594400406,
0.0024625388905406,
-0.009552741423249245,
-0.03846820816397667,
0.005329853855073452,
0.003294152906164527,
0.029485071077942848,
-0.00011661875032586977,
0.0583697073161602,
-0.03733482584357262,
0.004496121313422918,
0.06442385911941528,
0.06061384826898575,
-0.0035124800633639097,
0.011934845708310604,
0.04345962777733803,
0.005189854186028242,
-0.007375035434961319,
-0.01546025462448597,
-0.04843418672680855,
0.05881213769316673,
0.004292786121368408,
0.02557046338915825,
0.0015795137733221054,
0.006181641016155481,
0.056685708463191986,
0.046155113726854324,
0.019623124971985817,
-0.01531059481203556,
-0.03265677019953728,
-0.055768657475709915,
0.041662611067295074,
0.0342034175992012,
-0.009254195727407932,
0.020954925566911697,
0.006961159408092499,
0.025834327563643456,
-0.013594787567853928,
0.02388419210910797,
0.026242675259709358,
-0.044936470687389374,
0.01995404250919819,
-0.04733482375741005,
-0.07173870503902435,
0.030425917357206345,
-0.009622976183891296,
0.02641930989921093,
-0.012927436269819736,
-0.021763993427157402,
0.0017666531493887305,
0.03965674340724945,
0.024425247684121132,
-0.04254907742142677,
0.07340404391288757,
-0.032289501279592514,
-0.014228738844394684,
-0.0014250158565118909,
0.0014592664083465934,
0.11322282254695892,
0.03489647060632706,
0.057607896625995636,
-0.05614199861884117,
0.027991464361548424,
-0.0019365927437320352,
0.03106011636555195,
-0.040136996656656265,
0.04133884608745575,
-0.006735651753842831,
-0.002802782692015171,
0.0013808348448947072,
0.04897307604551315,
0.013873973861336708,
0.003514885203912854,
0.035444475710392,
-0.03958043456077576,
-0.03099188581109047,
0.007970347069203854,
0.02711881510913372,
0.03784425929188728,
0.026066938415169716,
-0.02419457584619522,
0.0000378001386707183,
-0.023561473935842514,
0.019740164279937744,
-0.02763986401259899,
-0.023675942793488503,
0.007562266197055578,
-0.004679438192397356,
-0.059657562524080276,
0.002598945749923587,
0.011818029917776585,
-0.0314064659178257,
-0.03077556937932968,
-0.00850475300103426,
0.009807822294533253,
-0.027568046003580093,
0.0404851958155632,
0.003913668915629387,
0.001118910382501781,
0.016090821474790573,
0.036272864788770676,
0.013764658942818642,
-0.0639277920126915,
0.012360095977783203,
-0.0033616346772760153,
0.024263765662908554,
-0.01429076585918665,
-0.027823850512504578,
0.031940240412950516,
-0.021409090608358383,
0.015012731775641441,
-0.07487830519676208,
-0.013595555908977985,
-0.021125074476003647,
0.030667521059513092,
0.010498059913516045,
-0.018742363899946213,
-0.028024621307849884,
0.03026312030851841,
-0.023825753480196,
0.026851842179894447,
-0.025529416278004646,
-0.025034215301275253,
-0.0161320548504591,
0.005859907250851393,
0.05602921172976494,
0.012683704495429993,
-0.018143653869628906,
-0.025534937158226967,
-0.03181016445159912,
-0.027977637946605682,
-0.04014047980308533,
-0.00042488652979955077,
0.012899650260806084,
0.02232740819454193,
0.006240086164325476,
0.02459893561899662,
-0.018173955380916595,
-0.08291132003068924,
-0.0006764786085113883,
-0.03380680829286575,
0.025265535339713097,
0.007625492289662361,
0.008394245989620686,
0.0004971522139385343,
0.06624069064855576,
-0.09451740980148315,
-0.007130919490009546,
0.004829877987504005,
-0.0017219436122104526,
0.024334963411092758,
-0.02499348856508732,
-0.002690558321774006,
0.00850602611899376,
-0.019978661090135574,
0.02560899592936039,
-0.04390654340386391,
-0.005363128148019314,
0.03150222823023796,
-0.01501568965613842,
0.012592473067343235,
0.03534922003746033,
-0.025422757491469383,
0.006475005764514208,
-0.027361316606402397,
-0.017253072932362556,
0.016160037368535995,
0.03762805089354515,
0.033454254269599915,
-0.010307795368134975,
-0.006059311330318451,
-0.008754368871450424,
-0.002968038199469447,
0.01903732679784298,
0.021363720297813416,
-0.049768853932619095,
-0.011246670968830585,
-0.033807870000600815,
0.014492743648588657,
-0.010674961842596531,
0.0161246620118618,
-0.03581712022423744,
0.022513825446367264,
-0.036830075085163116,
-0.015616877004504204,
-0.020397774875164032,
0.0693528801202774,
0.001335828797891736,
-0.030233221128582954,
0.0172722190618515,
0.031623922288417816,
-0.05329073965549469,
0.014445856213569641,
0.018656471744179726,
-0.0002557281986810267,
0.03169110044836998,
0.00022287714818958193,
-0.03652975708246231,
0.039744783192873,
-0.017938192933797836,
-0.025907883420586586,
0.05147115886211395,
-0.023073116317391396,
0.018334288150072098,
0.003883269615471363,
0.000762176001444459,
-0.020348476245999336,
0.05811431631445885,
-0.041424188762903214,
0.008858921937644482,
-0.003408065065741539,
-0.045349057763814926,
-0.00009790900367079303,
-0.019340500235557556,
0.02062336727976799,
0.012796739116311073,
-0.0382329598069191,
0.030539626255631447,
0.022492671385407448,
-0.03275293856859207,
0.015383245423436165,
0.016606811434030533,
-0.02340175211429596,
0.016779087483882904,
0.037317726761102676,
0.013601647689938545,
-0.014129149727523327,
0.04890087619423866,
-0.047618236392736435,
-0.00497691472992301,
0.01568683050572872,
-0.001702462905086577,
-0.1001080870628357,
0.02766827866435051,
0.019942721351981163,
0.0329413041472435,
0.08192259818315506,
-0.012147406116127968,
0.014496313408017159,
0.0016212762566283345,
-0.05103741213679314,
0.04363114386796951,
-0.0032961375545710325,
-0.04218623787164688,
-0.010494943708181381,
-0.03139997646212578,
-0.072354257106781,
0.058423962444067,
0.005708186887204647,
0.07187971472740173,
0.0385284498333931,
0.02589993365108967,
-0.006558605935424566,
-0.040687765926122665,
0.00041611335473135114,
-0.008819782175123692,
0.017163384705781937,
-0.00884711928665638,
0.06697876751422882,
-0.022798484191298485,
-0.04336179792881012,
0.024830609560012817,
0.031180592253804207,
0.016491210088133812,
-0.027690788730978966,
0.01640385016798973,
-0.001760362065397203,
0.025520386174321175,
0.042649995535612106,
0.004732698202133179,
0.0015801585977897048,
-0.0003095132706221193,
0.01617213524878025,
-0.001793422270566225,
0.035566624253988266,
0.013216862455010414,
-0.02884414792060852,
-0.04273241385817528,
-0.03337932378053665,
0.04023392125964165,
-0.01324266754090786,
-0.010862069204449654,
-0.005866347346454859,
0.012641302309930325,
0.014106296002864838,
0.009153823368251324,
-0.006812563631683588,
-0.05733732134103775,
-0.007141763344407082,
0.026765894144773483,
-0.027300257235765457,
0.03530171886086464,
0.02975478209555149,
-0.03141874819993973,
0.0037298775278031826,
0.056749410927295685,
0.014291057363152504,
-0.008868049830198288,
-0.05274423211812973,
-0.008995400741696358,
0.025849875062704086,
0.05344552546739578,
0.029021622613072395,
-0.043133486062288284,
-0.03245752677321434,
0.0021786759607493877,
-0.0053914012387394905,
0.0032068451400846243,
-0.041047848761081696,
-0.02602042816579342,
0.020309828221797943,
-0.060095276683568954,
0.032437000423669815,
0.03359021618962288,
0.011534110642969608,
0.017579611390829086,
-0.006953347474336624,
0.012015887536108494,
0.006223374046385288,
0.08197525888681412,
0.03767155483365059,
-0.03816217556595802,
0.024518346413969994,
-0.003992373123764992,
0.021321197971701622,
-0.018796604126691818,
-0.016194863244891167,
-0.008856353349983692,
-0.006502047181129456,
0.009277554228901863,
0.00961446575820446,
-0.03186695650219917,
0.045436859130859375,
0.022764340043067932,
0.02251676470041275,
0.02568458393216133,
0.014130731113255024,
-0.0689491331577301,
0.030342664569616318,
-0.007694310043007135,
-0.04492737725377083,
0.0670129656791687,
-0.029365014284849167,
0.010692799463868141,
-0.0015964546473696828,
-0.019898364320397377,
-0.03760260343551636,
0.005411813035607338,
-0.029715266078710556,
0.004189586732536554,
-0.0376325324177742,
0.0029774773865938187,
0.03288932889699936,
-0.013230604119598866,
0.00857984833419323,
0.05850348249077797,
-0.010737930424511433,
-0.029667282477021217,
0.03963446617126465,
0.04007401689887047,
0.08272481709718704,
0.011620284989476204,
-0.010534336790442467,
0.012435738928616047,
-0.008823650889098644,
0.02325812354683876,
0.027357934042811394,
0.010234244167804718,
-0.011768434196710587,
-0.013668033294379711,
0.039993591606616974,
0.007478951010853052,
-0.008242969401180744,
0.055872593075037,
0.025784218683838844,
-0.04679102450609207,
0.03121159039437771,
0.03329635411500931,
-0.051485322415828705,
0.011282240971922874,
0.014884118922054768,
-0.04231498762965202,
0.10625242441892624,
-0.0117438780143857,
0.03075360134243965,
-0.030486829578876495,
0.015392623841762543,
-0.03982812911272049,
0.014546526595950127,
0.00948105938732624,
0.0912877544760704,
-0.00448428001254797,
-0.018649399280548096,
-0.017896238714456558,
0.01744861528277397,
0.00960233248770237,
-0.05259547755122185,
-0.03583391010761261,
0.006884904578328133,
-0.006202887278050184,
0.012996277771890163,
-0.017036745324730873,
-0.01494121365249157,
0.004943151492625475,
0.0423264354467392,
0.017959168180823326,
0.053124312311410904,
-0.02408513054251671,
-0.002322256099432707,
-0.02576170675456524,
0.042175475507974625,
-0.046545982360839844,
-0.028591707348823547,
-0.026457421481609344,
0.016054792329669,
-0.05628086254000664,
-0.016065606847405434
] |
<blockquote>
<p>Before answering, please see <a href="http://meta.physics.stackexchange.com/a/4698"><strong>our policy</strong></a> on
resource recommendation questions. Please try to give substantial answers that detail the
<strong>style, content, and prerequisites</strong> of the book or paper (or other resource). Explain what the
resource is like as much as you can; that way the reader can decide which one is most suited
for them rather than blindly relying on the suggestions of others. Answers which just suggest a book
or paper may be deleted. </p>
<p>And please, note that any answers to this are <strong>community-owned</strong>, which means that they are subject to heavy editing, especially to make them comply with the book policy, to avoid deletion. </p>
<p>This question specifically asks for the level to be that of <strong>Hobson</strong>. </p>
</blockquote>
<p>Are there any good video lectures for learning general relativity at the level of Hobson?
The internet has by L. Susskind, but it is a simple level. I found good one here <a href="http://www.youtube.com/watch?v=hcTNxJF_AjU&list=SPB11E80403FB98CFF" rel="nofollow">http://www.youtube.com/watch?v=hcTNxJF_AjU&list=SPB11E80403FB98CFF</a>
however, the acoustics is a little bit not so good.</p> | 1,444 | [
0.0019787491764873266,
-0.04881522059440613,
0.02437981404364109,
-0.01656554453074932,
0.01788005605340004,
0.012446586042642593,
-0.03226805478334427,
-0.03334668278694153,
-0.006124904844909906,
-0.040577758103609085,
0.02803829312324524,
0.03885386139154434,
0.05603969097137451,
0.036521073430776596,
0.004113828297704458,
-0.020714938640594482,
0.033366281539201736,
-0.011378881521522999,
-0.019515274092555046,
-0.029787596315145493,
0.005563128273934126,
0.013913515023887157,
0.010597791522741318,
0.005916098598390818,
-0.0321812741458416,
0.028481299057602882,
0.037842780351638794,
0.013681349344551563,
-0.02796367183327675,
0.0727713480591774,
-0.03551069274544716,
0.020085450261831284,
-0.02213016152381897,
0.04167214408516884,
-0.015913905575871468,
-0.006103086285293102,
-0.017378903925418854,
0.022263603284955025,
0.02949008159339428,
-0.024606861174106598,
-0.056751783937215805,
-0.022635556757450104,
-0.004571768455207348,
0.06844227015972137,
-0.0035944320261478424,
0.0070567503571510315,
0.009625596925616264,
-0.017404302954673767,
0.037638138979673386,
-0.05629861727356911,
0.06354707479476929,
0.04567032679915428,
0.020799310877919197,
0.04710329324007034,
-0.011372677981853485,
-0.03585808724164963,
0.06902848929166794,
0.0800972431898117,
-0.024208318442106247,
-0.03652727231383324,
-0.027540642768144608,
-0.010582528077065945,
-0.007982668466866016,
-0.009460272267460823,
-0.039581894874572754,
0.06230539456009865,
0.0063131810165941715,
0.013226162642240524,
0.010151869617402554,
-0.028671517968177795,
-0.025868825614452362,
0.0069956001825630665,
0.02933518961071968,
0.00929254200309515,
0.0013753629755228758,
-0.0036158945877104998,
0.013773206621408463,
-0.018490206450223923,
0.002548885764554143,
0.04652697592973709,
-0.0002545048191677779,
-0.003677323693409562,
0.007523773703724146,
0.037626393139362335,
0.010796490125358105,
0.004879461135715246,
0.1286420077085495,
-0.03066655807197094,
-0.04752707853913307,
0.025302646681666374,
-0.003002588637173176,
-0.033386167138814926,
0.01636592298746109,
-0.02051316574215889,
-0.033908408135175705,
0.056164879351854324,
0.015693683177232742,
0.03785111755132675,
0.019689269363880157,
-0.033113230019807816,
-0.01058674231171608,
-0.035516709089279175,
-0.01309194602072239,
0.04989626631140709,
0.01912929117679596,
-0.06638582050800323,
-0.046541791409254074,
0.006071057636290789,
-0.04563504830002785,
-0.0397181399166584,
-0.009056665934622288,
0.0186892282217741,
-0.04285520687699318,
0.007379958406090736,
0.00814239401370287,
-0.022695457562804222,
0.006156764924526215,
-0.03880069777369499,
0.05464397743344307,
0.08329840749502182,
0.11418100446462631,
-0.019861023873090744,
0.020111283287405968,
-0.03464096784591675,
-0.07525281608104706,
0.001784500782378018,
0.040214844048023224,
-0.010005773045122623,
-0.06787071377038956,
0.02616589516401291,
0.012974116019904613,
-0.0003654985048342496,
-0.025987569242715836,
0.012219991534948349,
0.022506043314933777,
0.0021122093312442303,
-0.0927647054195404,
-0.04841471463441849,
0.034292664378881454,
-0.00811940710991621,
-0.0327705517411232,
-0.07248931378126144,
0.020876284688711166,
0.022719569504261017,
0.02890072949230671,
0.024979446083307266,
0.029634099453687668,
0.006627743598073721,
0.04658176377415657,
-0.027058718726038933,
-0.04854406788945198,
-0.00028696752269752324,
-0.04871136695146561,
-0.01043791975826025,
0.0338805690407753,
-0.08369813859462738,
-0.007698241155594587,
0.038972143083810806,
0.028292616829276085,
-0.03293447941541672,
0.07483406364917755,
-0.04761370271444321,
-0.03200056403875351,
0.01597161963582039,
0.0002138042327715084,
0.0031607034616172314,
0.06677992641925812,
0.025691978633403778,
0.022946812212467194,
0.02345612272620201,
0.0016148833092302084,
0.03358747437596321,
-0.02439942955970764,
0.014475254341959953,
0.0366109237074852,
-0.02263725735247135,
-0.0016161210369318724,
0.007272257469594479,
-0.018829673528671265,
-0.011165103875100613,
0.008893569931387901,
-0.06512348353862762,
-0.004895435180515051,
-0.011456219479441643,
-0.019150998443365097,
0.05097799003124237,
-0.0200263112783432,
0.03203204646706581,
-0.0019465863006189466,
-0.06372693926095963,
-0.006152244750410318,
-0.03162325173616409,
0.025384515523910522,
0.010163778439164162,
0.027033019810914993,
0.037204399704933167,
-0.027161497622728348,
0.003699103370308876,
-0.03437604382634163,
-0.02593092992901802,
0.018155859783291817,
0.029839713126420975,
0.024870669469237328,
0.00345554668456316,
0.015485726296901703,
0.018658636137843132,
0.027852261438965797,
-0.047914184629917145,
0.03057944029569626,
-0.012034711427986622,
-0.05595577135682106,
0.03255927562713623,
0.004608971532434225,
0.047825880348682404,
-0.023845786228775978,
-0.009625806473195553,
0.02668459340929985,
-0.004561388399451971,
-0.007127922959625721,
0.02751578949391842,
-0.057444196194410324,
0.05076667293906212,
0.04502470791339874,
0.018912652507424355,
-0.013218139298260212,
0.048291176557540894,
0.007199591491371393,
-0.011419503949582577,
0.002064891392365098,
0.019965672865509987,
-0.01981990970671177,
-0.012869426049292088,
0.04647381976246834,
0.019875627011060715,
-0.054713211953639984,
0.045498788356781006,
0.017836935818195343,
0.020695634186267853,
0.01608097553253174,
0.019385989755392075,
-0.0576866939663887,
-0.0605161227285862,
0.04552214965224266,
0.017190149053931236,
-0.004225050564855337,
0.014762168750166893,
0.014173673465847969,
0.016801457852125168,
-0.0021057387348264456,
0.0163089819252491,
-0.01955372840166092,
0.016230624169111252,
-0.005363158416002989,
-0.04513796791434288,
-0.0012118789600208402,
-0.02398000657558441,
0.03490789234638214,
-0.023821784183382988,
-0.009735439904034138,
0.048264507204294205,
0.015561249107122421,
-0.00735661294311285,
-0.0312933623790741,
-0.009871484711766243,
0.018288925290107727,
-0.00491385767236352,
-0.0031697202939540148,
-0.0017230442026630044,
0.03847618028521538,
-0.0633409395813942,
0.013202945701777935,
-0.016433265060186386,
-0.005706968251615763,
-0.012953324243426323,
-0.0070365555584430695,
0.010057833045721054,
-0.008007211610674858,
0.01494698878377676,
-0.029040755704045296,
-0.023492638021707535,
0.006733394227921963,
0.006519542541354895,
0.018742606043815613,
0.01967778615653515,
-0.02486959844827652,
0.009819223545491695,
-0.034897055476903915,
-0.005761955864727497,
0.030537841841578484,
-0.00828858744353056,
0.012269445694983006,
0.046170301735401154,
0.028085287660360336,
-0.037939827889204025,
-0.003974552266299725,
-0.0016867443919181824,
0.029047353193163872,
-0.011751757003366947,
0.02228667214512825,
0.028406791388988495,
-0.028070097789168358,
-0.04503598436713219,
-0.0015118734445422888,
-0.02768651768565178,
-0.03635909780859947,
-0.012194355018436909,
-0.001204375410452485,
-0.001162277185358107,
-0.04194188117980957,
-0.0134723000228405,
0.02969454787671566,
-0.010242964141070843,
-0.006386965978890657,
-0.0670628547668457,
-0.010311433114111423,
0.03568456321954727,
0.02278265915811062,
0.039688605815172195,
0.017061639577150345,
-0.036441996693611145,
0.05555129051208496,
0.022963562980294228,
-0.006951612886041403,
-0.026619570329785347,
0.0009047758067026734,
0.010861348360776901,
-0.031339555978775024,
0.013243907131254673,
0.030134908854961395,
-0.020939406007528305,
0.02095601335167885,
0.021681873127818108,
0.016962792724370956,
0.032770246267318726,
0.04420766234397888,
-0.008542793802917004,
-0.01334394607692957,
-0.04835269972681999,
0.026360975578427315,
0.054819636046886444,
0.02583909220993519,
-0.04228048771619797,
-0.006224626209586859,
0.01583731919527054,
0.033900730311870575,
0.017605768516659737,
-0.043279826641082764,
0.0518818199634552,
-0.007497657556086779,
-0.03741411492228508,
-0.011314483359456062,
0.026913709938526154,
0.0071114348247647285,
-0.023416440933942795,
0.01877673529088497,
0.0008407331770285964,
-0.0024166139774024487,
0.004178694449365139,
0.0065524219535291195,
-0.0010738641722127795,
0.04131694883108139,
-0.01404539868235588,
-0.025423595681786537,
-0.013744603842496872,
-0.02257913537323475,
0.015438545495271683,
-0.01083458960056305,
-0.013175961561501026,
0.012554501183331013,
0.04491521418094635,
-0.007506638299673796,
-0.004939813166856766,
-0.0264859851449728,
0.0053406087681651115,
-0.08361594378948212,
0.005025593098253012,
-0.03896979242563248,
0.03306174650788307,
0.011918885633349419,
0.02143544889986515,
0.015691446140408516,
0.01458626426756382,
-0.006780602037906647,
0.015375697985291481,
-0.10454324632883072,
0.025462238118052483,
-0.03400185704231262,
-0.01610885187983513,
0.007440533023327589,
0.021856945008039474,
-0.010851611383259296,
-0.00979661289602518,
-0.01795593649148941,
-0.009518384002149105,
0.015850497409701347,
-0.050558384507894516,
-0.013290815986692905,
-0.04387339577078819,
-0.049962133169174194,
-0.034746311604976654,
0.02610856294631958,
0.05084187537431717,
-0.03003622405230999,
0.01922992803156376,
0.020240418612957,
-0.0351775661110878,
0.02183099091053009,
0.028456632047891617,
0.037530794739723206,
-0.004186613019555807,
0.03513572737574577,
0.010243501514196396,
0.002956454176455736,
-0.0012208656407892704,
0.0038989910390228033,
0.03601844608783722,
0.03408847376704216,
-0.00009567551023792475,
-0.034895159304142,
-0.016021957620978355,
-0.037796441465616226,
-0.006906892638653517,
0.006270581390708685,
0.0668497309088707,
-0.014789373613893986,
-0.033176615834236145,
0.021571870893239975,
0.02602779120206833,
-0.0064325882121920586,
0.03266281262040138,
0.06562670320272446,
-0.047166984528303146,
-0.02342340350151062,
-0.0010723851155489683,
-0.04629897326231003,
-0.02628953941166401,
0.0003832976508419961,
0.031016232445836067,
0.0036554017569869757,
-0.00370361702516675,
0.010199158452451229,
0.0022645271383225918,
0.029892435297369957,
-0.05142998695373535,
0.002661666367202997,
0.0293591171503067,
0.04052075371146202,
-0.023294424638152122,
-0.005967649631202221,
-0.03683139383792877,
0.048855941742658615,
0.0719086304306984,
0.0095336539670825,
-0.033168524503707886,
-0.06541133671998978,
-0.008162900805473328,
0.02736079692840576,
0.030170395970344543,
-0.00930364616215229,
0.012412706390023232,
-0.0530242845416069,
-0.01731957122683525,
0.0635104849934578,
-0.037107549607753754,
-0.016989419236779213,
-0.0413653627038002,
-0.0068472642451524734,
-0.014751614071428776,
-0.018357403576374054,
-0.011946605518460274,
0.0115619832649827,
0.01186462864279747,
0.0033552483655512333,
0.0026072224136441946,
0.04157273471355438,
-0.01939624547958374,
0.040002018213272095,
0.016922714188694954,
0.03753191605210304,
0.03240494802594185,
-0.01581401750445366,
0.011660357005894184,
0.028467876836657524,
-0.05159130319952965,
-0.05687817931175232,
-0.01998545601963997,
-0.004265094641596079,
-0.06989698112010956,
0.0013131826417520642,
-0.012930710799992085,
-0.013880972750484943,
0.044157516211271286,
0.005201501771807671,
-0.007242583204060793,
0.010923821479082108,
-0.03455333784222603,
0.044691361486911774,
-0.017725715413689613,
0.009622366167604923,
0.023874694481492043,
0.035265106707811356,
-0.020146306604146957,
-0.0036742195952683687,
-0.006852744612842798,
0.0320613868534565,
-0.032870128750801086,
-0.0010445674415677786,
-0.009702865034341812,
-0.03913378715515137,
-0.07018070667982101,
0.04287926107645035,
-0.0011580337304621935,
-0.012025237083435059,
-0.03425410017371178,
-0.03183683007955551,
0.021635165438055992,
0.020934347063302994,
-0.00047565309796482325,
-0.011505835689604282,
0.024282531812787056,
0.037416886538267136,
-0.01870068907737732,
0.0004706634790636599,
-0.0006215998437255621,
-0.003862271085381508,
0.004890034906566143,
0.02919807657599449,
-0.013461186550557613,
0.021045086905360222,
-0.025328176096081734,
-0.009564436040818691,
-0.002542608417570591,
-0.03992043063044548,
0.0831749215722084,
-0.008486148901283741,
0.013891034759581089,
0.025520749390125275,
-0.01867217943072319,
0.00044246838660910726,
0.03684233874082565,
0.003389467019587755,
0.04739812761545181,
-0.0388345941901207,
0.02317016012966633,
-0.003068306017667055,
0.003434974467381835,
-0.03655271232128143,
-0.02495572157204151,
0.027850158512592316,
0.046323325484991074,
-0.017377687618136406,
-0.04007236659526825,
0.018375592306256294,
-0.08514455705881119,
0.004291958175599575,
-0.022987041622400284,
0.05041274055838585,
-0.020519835874438286,
-0.01967897266149521,
-0.02484617382287979,
0.030110424384474754,
0.02864198572933674,
0.006415556184947491,
-0.02266089804470539,
0.006743134465068579,
-0.010997523553669453,
-0.035485126078128815,
-0.02501748502254486,
0.04377426579594612,
-0.004750794731080532,
-0.04503757879137993,
-0.015213940292596817,
-0.010448022745549679,
-0.015050164423882961,
-0.027495063841342926,
0.021236278116703033,
0.05951733887195587,
-0.013370129279792309,
-0.05067789927124977,
-0.044987231492996216,
0.010974647477269173,
-0.014388574287295341,
0.02060825191438198,
-0.03016773611307144,
0.0036423334386199713,
0.03592384234070778,
-0.031200965866446495,
0.010624313727021217,
0.019183099269866943,
-0.017872406169772148,
-0.017375130206346512,
0.046319976449012756,
-0.015256417915225029,
-0.022427352145314217,
0.05137307941913605,
-0.025728873908519745,
0.03200249746441841,
-0.03197702392935753,
0.02220192179083824,
0.05132957920432091,
-0.04236957058310509,
-0.017370939254760742,
-0.06117401644587517,
-0.05728545039892197,
0.022333549335598946,
0.051592662930488586,
0.015413692221045494,
-0.00916321761906147,
0.047322697937488556,
-0.014237548224627972,
-0.0002040362305706367,
-0.013703670352697372,
-0.04366619884967804,
-0.028170151636004448,
0.017714906483888626,
0.006376603618264198,
-0.022989284247159958,
-0.008259269408881664,
0.005549797788262367,
0.04096587002277374,
-0.01887933537364006,
-0.01742289587855339,
0.014608597382903099,
0.055011190474033356,
0.028603386133909225,
-0.05525059625506401,
-0.06473314762115479,
0.05691830441355705,
-0.058153185993433,
0.039653193205595016,
-0.0013439904432743788,
-0.006497158668935299,
0.029106223955750465,
0.04345450550317764,
0.04212450981140137,
-0.021455639973282814,
-0.04300662502646446,
-0.06101183220744133,
0.019081149250268936,
0.020734373480081558,
0.025048164650797844,
-0.011221409775316715,
0.017685724422335625,
0.005581842735409737,
-0.014234217815101147,
0.035809557884931564,
-0.004645796492695808,
-0.0872802734375,
-0.018277086317539215,
0.0005676280707120895,
-0.04989122599363327,
0.07071975618600845,
0.026534661650657654,
-0.027319520711898804,
0.0517323836684227,
-0.06893529742956161,
0.028496181592345238,
0.04185643792152405,
0.04125368967652321,
0.0036095904652029276,
0.06211808696389198,
-0.03335482254624367,
0.005242179613560438,
-0.02356112189590931,
-0.00015588848327752203,
0.15054598450660706,
0.05422157421708107,
0.023755179718136787,
-0.06868751347064972,
0.023666078224778175,
-0.0029536159709095955,
-0.004525531083345413,
-0.07788252830505371,
-0.009935852140188217,
0.0009843561565503478,
0.03456161171197891,
0.019194142892956734,
0.048991214483976364,
0.006475994363427162,
-0.012298507615923882,
0.041964009404182434,
-0.041789159178733826,
-0.00839211419224739,
0.00634789140895009,
-0.00014430542069021612,
-0.017336899414658546,
0.023146487772464752,
-0.01251997984945774,
-0.014065803028643131,
0.009556496515870094,
0.008165474981069565,
-0.05996834486722946,
-0.04059964790940285,
0.030578896403312683,
-0.017519716173410416,
-0.037491362541913986,
0.04086439311504364,
-0.013197194784879684,
-0.034240663051605225,
-0.024470416828989983,
0.01517242006957531,
0.007836045697331429,
0.008734924718737602,
0.010254299268126488,
0.003770401468500495,
0.010691066272556782,
-0.002737208502367139,
0.021616335958242416,
0.013693398796021938,
-0.0194010678678751,
0.006855548359453678,
-0.016001610085368156,
0.09320703148841858,
-0.01544125098735094,
-0.014522240497171879,
0.015542424283921719,
-0.016057221218943596,
0.02588772028684616,
-0.049771927297115326,
-0.01744830422103405,
0.01573239639401436,
0.053314458578825,
-0.0028742628637701273,
-0.044831808656454086,
-0.04484661668539047,
0.04858498275279999,
-0.011759955435991287,
-0.00228965119458735,
0.010774467140436172,
-0.014186764135956764,
-0.004016298800706863,
-0.0016961249057203531,
0.022262509912252426,
-0.006545044481754303,
-0.028958847746253014,
-0.030626388266682625,
0.04328552260994911,
-0.011402485892176628,
-0.021573733538389206,
0.008106212131679058,
0.028849462047219276,
0.02758636325597763,
0.001054899301379919,
0.009494801983237267,
0.022649720311164856,
-0.04378065839409828,
0.020251857116818428,
-0.03671577200293541,
-0.024386387318372726,
-0.00043222709791734815,
-0.03705376759171486,
-0.025147831067442894,
0.006168522406369448,
0.010704395361244678,
0.004797135479748249,
-0.0176547784358263,
0.0048727551475167274,
0.01673591136932373,
0.011203351430594921,
-0.009259534068405628,
-0.013799956068396568,
-0.04948445037007332,
0.0026012740563601255,
0.01887349970638752,
0.04986811801791191,
-0.006761184427887201,
0.05181878060102463,
0.021864552050828934,
0.015295933932065964,
-0.011933920904994011,
0.007298267912119627,
0.031211361289024353,
-0.06037703529000282,
0.01782834902405739,
0.025481661781668663,
0.013168144971132278,
-0.023007309064269066,
-0.029590656980872154,
-0.013022702187299728,
0.007071120198816061,
0.009226925671100616,
0.03617130219936371,
-0.036303162574768066,
0.05636400356888771,
-0.014001118019223213,
0.017911991104483604,
-0.03939349204301834,
0.0074377707205712795,
-0.009603457525372505,
0.020093606784939766,
0.0098468828946352,
0.0008887500152923167,
0.0026571338530629873,
0.050145141780376434,
0.0192018561065197,
-0.023939473554491997,
0.016583170741796494,
0.010398400947451591,
-0.005082061979919672,
0.005124121904373169,
0.00159655069001019,
-0.010132558643817902,
0.019709574058651924,
-0.008497101254761219,
-0.06027060002088547,
0.014954126439988613,
-0.0307138804346323,
-0.04460541531443596,
0.04056380316615105,
-0.024458637461066246,
0.016353271901607513,
0.026581693440675735,
-0.0409475676715374,
-0.014338034205138683,
0.05795980617403984,
0.01009727455675602,
-0.012871759943664074,
0.021886290982365608,
-0.01162405963987112,
-0.004643694031983614,
-0.021688004955649376,
0.05189662426710129,
0.005748731549829245,
-0.0172157883644104,
0.03316003456711769,
0.055572908371686935,
0.008428177796304226,
0.015848329290747643,
-0.011174790561199188,
-0.006362162530422211,
0.010618318803608418,
-0.014051184989511967,
0.025815268978476524,
0.0072714644484221935,
0.05574185773730278,
-0.03821416199207306,
0.0054987031035125256,
0.020038951188325882,
0.02490229718387127,
-0.1231347844004631,
0.0014845151454210281,
0.0032522049732506275,
0.02241118624806404,
0.031610261648893356,
-0.055920254439115524,
0.029044872149825096,
0.015875987708568573,
-0.05704094469547272,
0.023838011547923088,
-0.015133240260183811,
-0.055364228785037994,
-0.01938091591000557,
-0.014914575032889843,
0.02142106369137764,
0.01384801510721445,
0.011121531948447227,
0.04652613028883934,
0.01633075438439846,
-0.0198778435587883,
-0.018156439065933228,
-0.01653999462723732,
0.029854517430067062,
0.013116938062012196,
-0.0529957115650177,
0.005183870438486338,
0.038444843143224716,
0.03134054318070412,
-0.03500061482191086,
0.0340019054710865,
0.01016900036484003,
-0.015391448512673378,
0.008932782337069511,
0.020337343215942383,
0.013040724210441113,
0.020290201529860497,
0.033722709864377975,
0.01068047434091568,
-0.036973144859075546,
0.02166997455060482,
0.00515564763918519,
0.028982747346162796,
-0.019385000690817833,
-0.014552491717040539,
-0.0027975861448794603,
-0.036212190985679626,
-0.019894389435648918,
0.03100414015352726,
-0.03210911899805069,
-0.021059675142169,
-0.013925069943070412,
-0.013859354890882969,
-0.020824173465371132,
-0.028832294046878815,
-0.007158773951232433,
-0.06110795587301254,
-0.0068173473700881,
0.014204026199877262,
-0.011524253524839878,
-0.00965128093957901,
0.02774890698492527,
-0.006207438185811043,
0.002620059298351407,
0.02020811103284359,
-0.004183450248092413,
0.03605078533291817,
-0.026195092126727104,
-0.02526995539665222,
-0.03659876063466072,
-0.019443156197667122,
-0.00097970652859658,
-0.029423721134662628,
-0.021978752687573433,
0.041181907057762146,
0.005837454926222563,
0.03641771525144577,
-0.01846366934478283,
0.0126089658588171,
0.0004441369092091918,
-0.07749725878238678,
-0.002308809896931052,
0.02140575833618641,
0.0006777251837775111,
-0.0161252673715353,
0.030762311071157455,
0.009278054349124432,
0.02370728738605976,
0.03634810820221901,
0.005077381618320942,
-0.017740482464432716,
0.011583834886550903,
-0.02969917096197605,
0.007415524683892727,
-0.004966852255165577,
0.01587400957942009,
-0.011199676431715488,
-0.01103474386036396,
-0.0155329005792737,
-0.0024017079267650843,
-0.014096561819314957,
0.01856227219104767,
0.0071588498540222645,
0.04275492951273918,
0.028029948472976685,
-0.006419108249247074,
-0.006024688016623259,
0.07266725599765778,
0.01806344836950302,
0.022000005468726158,
0.05534539371728897,
-0.010239559225738049,
0.003380213864147663,
0.04920687898993492,
-0.022572435438632965,
-0.01729482039809227,
0.02850966528058052,
-0.046794719994068146,
-0.05786457285284996,
-0.013219453394412994,
0.0015396449016407132,
-0.002146682469174266,
-0.023385804146528244,
0.01679571345448494,
0.04854241758584976,
-0.024416716769337654,
0.02662164904177189,
0.029891664162278175,
0.009483333677053452,
0.029478445649147034,
0.021382715553045273,
-0.030297083780169487,
0.036179326474666595,
-0.019385339692234993,
-0.04563433304429054,
0.011616324074566364,
0.042007070034742355,
0.0032566345762461424,
-0.0039053037762641907,
0.009578521363437176,
-0.0031745494343340397,
-0.012760233134031296,
-0.004516663961112499,
0.047493886202573776,
-0.015784665942192078,
-0.03160186856985092,
0.010723327286541462,
0.00031742971623316407,
-0.025601644068956375,
0.03280011937022209,
-0.025193268433213234,
0.07259687036275864,
-0.030008845031261444,
0.011113493703305721,
-0.0006745311548002064,
-0.005158138927072287,
-0.02842048741877079,
-0.0035455815959721804,
0.03140975534915924,
0.04948986694216728,
-0.017624443396925926,
-0.0006099586607888341,
-0.04228406772017479,
0.006085623987019062,
0.026187801733613014,
-0.03827959671616554,
-0.0009063052129931748,
-0.004090291913598776,
0.004732823930680752,
0.012300333008170128,
-0.01698361709713936,
-0.02193545363843441,
-0.03268809616565704,
0.00882462877780199,
0.03908025473356247,
0.015866108238697052,
-0.04444541037082672,
0.013031739741563797,
-0.02576647885143757,
0.057052161544561386,
-0.06625927239656448,
0.02673296257853508,
-0.005349074024707079,
0.003054527100175619,
-0.011654905043542385,
0.04945162311196327
] |
<p>The length contraction means that an object is the longest in the frame in which it is at rest. </p>
<p>Lets assume i have a meter stick with length $\Delta x$ in my rest frame which is $x,ct$ and i want to know how long my meter stick seems to an observer moving with a frame $x',ct'$.</p>
<p><strong>1st:</strong> I draw world lines of a meter stick in a rest frame and they are vertical (parallel to $ct$ axis) as meter stick is stationary in this frame. </p>
<p><strong>2nd:</strong> If an observer in a moving frame $x',ct'$ wants to measure my meter stick he measures its edges at the same moment in his time, so i draw a tilted line (parallel to $x'$ axis).</p>
<p><strong>3rd:</strong> If i mesure the length $\Delta x'$ which is a length of a meter stick as observer in frame $x',ct'$ sees it, it seems to me that <strong>he sees a longer distance than me.</strong> </p>
<p>This is not correct. Could anyone tell me what am i missing here?</p>
<p><img src="http://i.stack.imgur.com/r4QzA.png" alt="enter image description here"></p> | 1,445 | [
0.020193587988615036,
-0.04312986508011818,
0.04389283061027527,
-0.00435612304136157,
0.009917410090565681,
0.004868303891271353,
-0.04599364846944809,
-0.030624765902757645,
-0.014670584350824356,
-0.013383304700255394,
0.051424212753772736,
0.03751327469944954,
0.07820063084363937,
0.05437750741839409,
0.029039599001407623,
0.0031807925552129745,
-0.004051879979670048,
-0.012436795979738235,
-0.00943194143474102,
-0.03276030346751213,
0.03053886629641056,
0.021084729582071304,
0.045717038214206696,
-0.03259732946753502,
-0.030150264501571655,
0.04903731867671013,
0.021584652364253998,
-0.006451149936765432,
0.015605091117322445,
0.07016640901565552,
-0.04377898946404457,
-0.011687212623655796,
-0.01569177769124508,
-0.0037190623115748167,
-0.008044196292757988,
-0.009391067549586296,
-0.02325667254626751,
-0.02018560841679573,
0.013880975544452667,
0.029609765857458115,
-0.04719322919845581,
0.027110664173960686,
0.003067751182243228,
0.07163701951503754,
-0.016104217618703842,
0.012690704315900803,
-0.019816121086478233,
-0.015946557745337486,
0.052645012736320496,
-0.0020931793842464685,
0.07161623239517212,
0.006659712176769972,
0.04487473517656326,
0.01084210630506277,
0.0012883407762274146,
-0.011209002695977688,
0.06267146021127701,
0.04286595806479454,
-0.05291612073779106,
-0.015768760815262794,
-0.006757067982107401,
-0.028710095211863518,
-0.019676264375448227,
0.004315570928156376,
0.0007831119000911713,
0.01666799932718277,
-0.008520836010575294,
0.007099416106939316,
0.004753926303237677,
-0.04030870273709297,
-0.027581924572587013,
-0.004435468930751085,
0.020615100860595703,
0.0006755267968401313,
0.004761822521686554,
-0.026872074231505394,
0.0070722936652600765,
0.06629703938961029,
0.039991650730371475,
0.06708798557519913,
0.0020434712059795856,
-0.0018276021583005786,
0.043664295226335526,
0.02191338501870632,
0.0010697467951104045,
-0.013952095061540604,
0.06514150649309158,
0.015885887667536736,
0.014870410785079002,
0.02541070058941841,
0.02054842747747898,
0.019176237285137177,
0.03359093517065048,
-0.023689819499850273,
-0.011419192887842655,
0.011528360657393932,
0.00016143245738931,
0.04755328595638275,
0.018754182383418083,
-0.004127989057451487,
-0.025725144892930984,
-0.033911123871803284,
0.007805751636624336,
0.047333311289548874,
0.010640827938914299,
0.005412518512457609,
-0.005148392636328936,
0.0077185677364468575,
0.0007878466276451945,
0.0031044501811265945,
-0.028590044006705284,
0.0013259199913591146,
0.019754668697714806,
0.05215100944042206,
-0.0061098686419427395,
-0.034489911049604416,
0.016556143760681152,
-0.01658817008137703,
0.0727929174900055,
0.05541689321398735,
0.016637377440929413,
-0.022103510797023773,
0.016416292637586594,
-0.019050249829888344,
-0.06853935122489929,
0.024368852376937866,
-0.009411287494003773,
-0.007947320118546486,
-0.01634281314909458,
0.019138522446155548,
0.020486826077103615,
-0.013979889452457428,
0.025505131110548973,
0.03682363033294678,
0.03327048569917679,
0.029026180505752563,
-0.10282625257968903,
-0.06936359405517578,
0.07451853901147842,
0.014491980895400047,
-0.010906348004937172,
-0.08278743922710419,
0.018910178914666176,
0.0372493602335453,
0.10383452475070953,
0.016456326469779015,
0.007263622712343931,
-0.011640314944088459,
0.007693037856370211,
-0.013028651475906372,
-0.039917148649692535,
-0.022186487913131714,
0.0020131380297243595,
-0.04588375613093376,
-0.016925126314163208,
-0.047479934990406036,
-0.037788499146699905,
0.05135683715343475,
-0.0017247266368940473,
-0.013887524604797363,
0.05872947722673416,
0.019314726814627647,
0.0046845986507833,
0.0024885283783078194,
-0.01243180688470602,
-0.049355026334524155,
0.07820595055818558,
-0.00979786179959774,
-0.022314658388495445,
0.045028459280729294,
-0.000659721961710602,
0.04793839529156685,
-0.0005447202129289508,
-0.006181190721690655,
0.02701489068567753,
-0.02184470370411873,
-0.023858796805143356,
0.048576027154922485,
-0.05681730434298515,
0.06127253174781799,
-0.025770902633666992,
-0.03493592143058777,
-0.04286222532391548,
-0.017839137464761734,
0.04061973839998245,
0.05300801247358322,
-0.019231783226132393,
0.04440518096089363,
-0.020727427676320076,
-0.04617075249552727,
-0.011606666259467602,
-0.058712542057037354,
0.017392195761203766,
0.010262435302138329,
-0.015743162482976913,
0.01297625433653593,
0.005410342942923307,
0.010046550072729588,
-0.01762249879539013,
-0.027706002816557884,
-0.010593212209641933,
0.03177880495786667,
-0.01944088563323021,
-0.024924514815211296,
0.01092423778027296,
0.043009668588638306,
0.04954271391034126,
0.0350605808198452,
-0.026664355769753456,
-0.01544198114424944,
-0.004533287137746811,
0.022722287103533745,
-0.02395627275109291,
-0.00638100178912282,
-0.00807164516299963,
0.04226439446210861,
-0.00885846558958292,
-0.005628271959722042,
0.002927025081589818,
0.0367002859711647,
-0.005208953749388456,
0.053779035806655884,
0.04653899744153023,
-0.024966195225715637,
-0.006505168508738279,
0.02223030850291252,
-0.00506403436884284,
0.03804983198642731,
0.007834834046661854,
-0.02497621439397335,
-0.04605157673358917,
-0.012897303327918053,
0.003461656626313925,
0.029018428176641464,
-0.04237448051571846,
-0.007443506270647049,
0.015848690643906593,
0.011914712376892567,
-0.01144325640052557,
-0.017308438196778297,
0.01872766762971878,
-0.030367273837327957,
-0.01055074017494917,
0.008889851160347462,
0.0052591306157410145,
-0.019834529608488083,
0.018774323165416718,
-0.0015742474934086204,
0.03441121056675911,
-0.022386018186807632,
-0.006260789930820465,
0.007337244693189859,
-0.026091156527400017,
0.031566597521305084,
0.0043103937059640884,
0.021421881392598152,
0.03237117454409599,
-0.01442518550902605,
0.031030967831611633,
0.061634454876184464,
0.009272513911128044,
-0.010542536154389381,
-0.04662232846021652,
0.011363971047103405,
0.022877763956785202,
0.01184892002493143,
0.009683572687208652,
-0.053729571402072906,
0.010764125734567642,
-0.052471138536930084,
-0.004739764146506786,
-0.032649438828229904,
-0.037751320749521255,
0.005919948220252991,
-0.013577543199062347,
0.04390473663806915,
0.04333120957016945,
0.020737983286380768,
-0.0523318313062191,
-0.029004937037825584,
0.00017394225869793445,
-0.029793569818139076,
0.011788876727223396,
0.012197778560221195,
-0.03302132338285446,
0.013524895533919334,
-0.06465466320514679,
-0.04458745941519737,
0.029158469289541245,
0.024882355704903603,
0.026175443083047867,
0.03774869441986084,
-0.013164682313799858,
-0.03114563785493374,
-0.034490540623664856,
0.011206530965864658,
-0.014531324617564678,
-0.031040459871292114,
0.000301085296086967,
0.06476215273141861,
0.0038607667665928602,
-0.014932068064808846,
0.01827358454465866,
-0.06656947731971741,
-0.04506043344736099,
-0.025344107300043106,
0.01617281697690487,
0.008676223456859589,
-0.008992656134068966,
0.03136690333485603,
0.01724057085812092,
0.004527903161942959,
-0.006683198735117912,
-0.07727976888418198,
-0.04586149379611015,
0.049301449209451675,
0.021418239921331406,
0.023871149867773056,
0.015335715375840664,
-0.017222711816430092,
0.08046680688858032,
0.0044271014630794525,
-0.01852307841181755,
-0.08076780289411545,
0.036701664328575134,
0.00037405535113066435,
-0.03461476415395737,
-0.04835690185427666,
0.008844438008964062,
-0.01803758181631565,
0.04066650569438934,
0.041497714817523956,
0.0576133206486702,
0.023944146931171417,
0.03963645547628403,
0.002222005045041442,
0.013994002714753151,
-0.027684476226568222,
-0.02766793966293335,
0.062380533665418625,
0.023915503174066544,
0.003781198989599943,
-0.00789900403469801,
-0.0056778425350785255,
0.035859640687704086,
0.0033472843933850527,
-0.05770246312022209,
0.03616573289036751,
-0.00800600741058588,
-0.0006127955857664347,
0.015784036368131638,
0.04543592035770416,
-0.00008334674930665642,
-0.011115715838968754,
-0.03363393247127533,
0.013975282199680805,
0.0421065092086792,
-0.04280809685587883,
0.00013363055768422782,
0.04555616155266762,
0.02133909799158573,
-0.01072938833385706,
-0.03788746893405914,
-0.021312307566404343,
-0.02222432568669319,
0.03643625229597092,
-0.04465639963746071,
-0.032944802194833755,
0.0541415736079216,
0.04813472181558609,
-0.0029291461687535048,
0.03537160903215408,
-0.029894838109612465,
-0.01364487037062645,
-0.06688353419303894,
-0.003852514084428549,
0.032636310905218124,
0.022976897656917572,
-0.003027785336598754,
0.03798999264836311,
0.04166664183139801,
0.029592832550406456,
0.00033202991471625865,
0.0033122387249022722,
-0.04154129698872566,
0.028959665447473526,
-0.04349548742175102,
-0.03962298482656479,
-0.0070221140049397945,
0.01162138395011425,
-0.007028499618172646,
-0.0338418073952198,
0.017685728147625923,
-0.04221997410058975,
0.012526054866611958,
-0.06563315540552139,
0.004758055787533522,
-0.014587214216589928,
-0.04466262087225914,
-0.028707046061754227,
0.05760028958320618,
0.06545823067426682,
-0.054929494857788086,
0.03269254043698311,
0.06569820642471313,
-0.025069307535886765,
0.010141049511730671,
-0.0038162628188729286,
-0.02893218956887722,
0.0430142842233181,
-0.002419151831418276,
0.013195185922086239,
0.008629576303064823,
0.027001740410923958,
0.013553770259022713,
0.04263506084680557,
0.04700218886137009,
-0.000017463587937527336,
-0.02457229048013687,
-0.029526032507419586,
-0.018865076825022697,
0.006244302727282047,
-0.0177120603621006,
0.07199259847402573,
-0.0007157849613577127,
-0.027149522677063942,
0.015856387093663216,
0.014537247829139233,
-0.016172777861356735,
0.03814828023314476,
0.04380796477198601,
0.0035573765635490417,
-0.026982737705111504,
-0.07420390099287033,
-0.03851846605539322,
-0.01615738868713379,
0.0016939712222665548,
0.005437321029603481,
0.0063115935772657394,
-0.008297262713313103,
-0.018425151705741882,
0.05139152705669403,
-0.00609216932207346,
-0.03606697916984558,
0.011564414948225021,
-0.04972796142101288,
-0.00858622882515192,
0.013501618057489395,
0.011774836108088493,
-0.010117534548044205,
0.032328832894563675,
0.016008494421839714,
-0.024194177240133286,
0.013729323633015156,
-0.08089400082826614,
0.00026520699611864984,
0.004945042077451944,
0.027471082285046577,
0.014366752468049526,
0.007352761458605528,
-0.048831645399332047,
-0.01144717913120985,
0.04551736265420914,
-0.00807547103613615,
0.05470183491706848,
0.0004857797175645828,
-0.008766652084887028,
-0.051485296338796616,
-0.006342530250549316,
-0.06534906476736069,
0.007018518168479204,
-0.002904192777350545,
0.03586835414171219,
-0.04185647889971733,
0.024416331201791763,
0.027425294741988182,
-0.0018203073414042592,
0.007832941599190235,
0.04417208582162857,
0.021712975576519966,
-0.03642403706908226,
0.005717365071177483,
0.022853989154100418,
-0.02878882922232151,
-0.015363257378339767,
0.004222074057906866,
0.012903707101941109,
-0.010484613478183746,
0.00833877269178629,
-0.008691690862178802,
-0.028260517865419388,
0.018365265801548958,
-0.010361765511333942,
0.007748512085527182,
0.04661118611693382,
-0.0328461155295372,
0.012995273806154728,
0.025526845827698708,
-0.008097844198346138,
0.015692967921495438,
0.03703778609633446,
0.03125539422035217,
0.014440078288316727,
-0.002664379309862852,
0.038826022297143936,
-0.024238089099526405,
-0.03964966535568237,
-0.03528045490384102,
-0.03267834708094597,
-0.0839465782046318,
0.03791401535272598,
-0.03717701882123947,
0.03734332695603371,
-0.027022533118724823,
-0.0299217589199543,
0.010658902116119862,
0.033721573650836945,
0.03906329348683357,
0.030101493000984192,
0.008137539960443974,
-0.005995376966893673,
0.022053074091672897,
-0.03744286671280861,
0.002653471427038312,
0.009571305476129055,
-0.016054391860961914,
0.03669241443276405,
-0.02533010020852089,
0.002628609072417021,
-0.0003493520198389888,
0.014209894463419914,
0.014007076621055603,
-0.04045915603637695,
0.035378348082304,
-0.01633671671152115,
0.0185625609010458,
0.02534433826804161,
0.009396676905453205,
-0.012854598462581635,
0.029647814109921455,
-0.05566912516951561,
0.033826638013124466,
-0.052442796528339386,
0.005312731023877859,
0.04128345102071762,
0.054470110684633255,
-0.06657413393259048,
-0.03463307395577431,
-0.001247922657057643,
0.0059646181762218475,
-0.02413908950984478,
0.005376514513045549,
0.014655019156634808,
0.008891984820365906,
-0.025574922561645508,
-0.04159737005829811,
0.03768380731344223,
0.016685782000422478,
-0.028651375323534012,
-0.009257453493773937,
0.034904830157756805,
0.01218483503907919,
-0.026238372549414635,
0.018765468150377274,
-0.038475897163152695,
-0.009928840212523937,
-0.017339477315545082,
0.00991330947726965,
0.02157243900001049,
-0.03619711101055145,
-0.0532672218978405,
-0.006289971526712179,
0.0021859132684767246,
-0.03886500746011734,
-0.016848906874656677,
-0.04055073484778404,
0.00985295232385397,
-0.0008603241294622421,
-0.012827793136239052,
-0.027780506759881973,
0.015684647485613823,
-0.007694039959460497,
-0.008096366189420223,
-0.004042936488986015,
0.028569316491484642,
-0.014734776690602303,
-0.041187260299921036,
0.004717166535556316,
0.030700847506523132,
-0.02966751903295517,
-0.017332568764686584,
0.05325230211019516,
-0.05085316300392151,
0.012576651759445667,
0.027469471096992493,
0.017470424994826317,
0.01585402712225914,
-0.0014718561433255672,
-0.009805635549128056,
0.02553493343293667,
-0.007404948119074106,
-0.035262417048215866,
0.035140324383974075,
-0.015405216254293919,
0.025749467313289642,
0.07174143940210342,
0.004527059383690357,
0.023192567750811577,
0.03291149064898491,
-0.02912449836730957,
0.04379083216190338,
-0.029535867273807526,
-0.018089843913912773,
-0.03769746050238609,
-0.0057764360681176186,
0.02668035589158535,
-0.06665664911270142,
-0.01702140085399151,
0.03357674926519394,
0.052849460393190384,
-0.02803327701985836,
-0.05019522085785866,
-0.026821555569767952,
0.031220311298966408,
0.009719520807266235,
-0.0018562371842563152,
-0.06198554486036301,
0.0249219611287117,
0.011168621480464935,
0.03573232516646385,
0.02050396427512169,
-0.002559366635978222,
0.03407136723399162,
-0.016777969896793365,
0.044686220586299896,
-0.03908935561776161,
0.006712763104587793,
-0.04000066593289375,
-0.018368445336818695,
0.007778748869895935,
0.012826499529182911,
0.01944647915661335,
-0.012475122697651386,
0.06503715366125107,
-0.027197612449526787,
0.04129284247756004,
-0.07284795492887497,
-0.06373488903045654,
-0.02333744801580906,
-0.024574441835284233,
-0.02812095358967781,
0.06564851105213165,
-0.014665873721241951,
-0.0008804509998299181,
0.020595179870724678,
-0.024810856208205223,
0.014203174971044064,
-0.0018438202096149325,
0.02440614253282547,
-0.01949542947113514,
0.039492640644311905,
-0.021106760948896408,
0.04002721235156059,
-0.027918849140405655,
0.010483991354703903,
0.1133834645152092,
0.009511382319033146,
0.03146085515618324,
-0.03648737445473671,
0.02870008535683155,
0.016833649948239326,
0.01259960513561964,
-0.04303053393959999,
0.01408353727310896,
-0.011390559375286102,
0.017714062705636024,
-0.01873753033578396,
0.035782329738140106,
-0.019666237756609917,
-0.003985476680099964,
0.0485817976295948,
-0.05518701672554016,
-0.038358982652425766,
0.015144609846174717,
0.006375729106366634,
-0.016216332092881203,
-0.024336498230695724,
-0.02340357005596161,
0.052352871745824814,
0.00329375546425581,
-0.025282258167862892,
0.002869273303076625,
-0.02884809300303459,
0.000369571935152635,
-0.02645002119243145,
-0.03924926370382309,
0.008913645520806313,
0.0009182483772747219,
-0.058785948902368546,
-0.036009784787893295,
-0.007712398190051317,
-0.00503644859418273,
0.017244301736354828,
0.03621857240796089,
0.046956319361925125,
-0.008524849079549313,
0.007241371553391218,
0.022687086835503578,
0.038092270493507385,
-0.038142912089824677,
-0.022356273606419563,
-0.03965030610561371,
0.04291641339659691,
0.01613813266158104,
-0.0014157837722450495,
0.028033090755343437,
0.007750902324914932,
-0.006013431120663881,
-0.071018747985363,
0.009940247982740402,
-0.01300893072038889,
0.006215329747647047,
0.022461459040641785,
-0.021313568577170372,
-0.02909594587981701,
0.041985608637332916,
0.0033390969038009644,
-0.025715915486216545,
0.0005080949631519616,
0.02131611667573452,
-0.007658541668206453,
-0.013442483730614185,
0.0424191951751709,
0.0246912632137537,
-0.013118288479745388,
-0.019506657496094704,
0.01879836805164814,
0.007124714553356171,
0.0030568616930395365,
0.005032377317547798,
0.010406027548015118,
0.01723765954375267,
-0.01601126790046692,
-0.0016217617085203528,
-0.019019601866602898,
-0.05476571246981621,
0.02285904996097088,
-0.04713156074285507,
-0.02173905447125435,
-0.013085709884762764,
0.024360354989767075,
0.02586640976369381,
0.02550557814538479,
0.003459120402112603,
0.013666675426065922,
-0.0031511809211224318,
0.03957270830869675,
-0.003029691055417061,
-0.0026438646018505096,
-0.016000913456082344,
0.011830574832856655,
-0.018388820812106133,
-0.025787482038140297,
-0.033362746238708496,
0.007589941378682852,
0.05057781934738159,
0.02239329367876053,
0.017752278596162796,
-0.0050394111312925816,
-0.030641760677099228,
-0.01436265092343092,
0.028845706954598427,
-0.05738374590873718,
0.041947659105062485,
0.01167745515704155,
-0.00917212013155222,
-0.05965924263000488,
-0.01267556194216013,
-0.023703724145889282,
-0.0107312286272645,
-0.016817091032862663,
0.00321411550976336,
-0.03578196465969086,
0.018198611214756966,
0.012325922958552837,
0.01745334267616272,
-0.02053220197558403,
-0.0011313094291836023,
-0.02515912801027298,
0.009908712469041348,
-0.01640700176358223,
-0.03519650921225548,
-0.0071970196440815926,
0.029508795589208603,
-0.009905706159770489,
-0.033752117305994034,
0.003041320713236928,
0.02997177094221115,
0.011571732349693775,
-0.027598418295383453,
0.02618595026433468,
0.022318897768855095,
-0.004322287626564503,
-0.006316345650702715,
-0.03642033413052559,
0.011248130351305008,
-0.023408157750964165,
0.0024087203200906515,
0.05885586887598038,
-0.0302572138607502,
0.04496719688177109,
-0.008353483863174915,
-0.0071865590289235115,
0.02110464870929718,
0.026145264506340027,
-0.030468402430415154,
-0.020138997584581375,
0.0016352713573724031,
-0.058553632348775864,
0.023870369419455528,
-0.026620935648679733,
-0.008897833526134491,
0.010019086301326752,
0.011166664771735668,
0.026525655761361122,
0.042713530361652374,
-0.02047889493405819,
0.004197857342660427,
0.007494525518268347,
-0.024018950760364532,
-0.019419515505433083,
0.01902713254094124,
0.00005080250775790773,
0.06969629228115082,
0.043562356382608414,
-0.03428010642528534,
0.03377330303192139,
-0.009857735596597195,
0.004406294319778681,
-0.09831329435110092,
0.01709970459342003,
0.00502125546336174,
0.034784410148859024,
0.039784058928489685,
-0.05225692316889763,
0.005236901808530092,
0.05011897534132004,
-0.07525912672281265,
-0.011975633911788464,
-0.05319356918334961,
-0.0027079666033387184,
-0.007803327403962612,
-0.006069357972592115,
0.030722202733159065,
0.05461837351322174,
0.04399772360920906,
0.05132494121789932,
0.014832216314971447,
0.04669467359781265,
-0.013502375222742558,
-0.07670639455318451,
-0.03410908207297325,
0.046455107629299164,
0.002585220616310835,
-0.03991800174117088,
0.06370457261800766,
-0.006076039280742407,
0.017826583236455917,
0.02558290585875511,
-0.008841081522405148,
0.046453241258859634,
0.0014517755480483174,
-0.006544037722051144,
-0.002376679563894868,
-0.0064894165843725204,
0.043596718460321426,
-0.03433862701058388,
-0.015810610726475716,
-0.005252324976027012,
0.0016459517646580935,
0.014126524329185486,
-0.0009669912979006767,
-0.06788434088230133,
0.029303357005119324,
-0.062300603836774826,
-0.03834741935133934,
0.035768840461969376,
0.0011569182388484478,
-0.00807693600654602,
0.0035960942041128874,
0.01891377754509449,
-0.00017617219418752939,
-0.051970306783914566,
-0.00511770648881793,
0.0003077660803683102,
-0.004416564013808966,
0.05599866434931755,
0.010263673961162567,
-0.029516473412513733,
0.010825959965586662,
-0.022402925416827202,
-0.03295769542455673,
-0.03620905429124832,
-0.019381847232580185,
0.001929515739902854,
-0.05445534735918045,
-0.0023860440123826265,
-0.004034246318042278,
-0.006303862202912569,
-0.00035202971776016057,
0.017864977940917015,
-0.01595981977880001,
0.014085167087614536,
0.004128588363528252,
0.0015221467474475503,
-0.0216361191123724,
-0.025654025375843048,
-0.04767901822924614,
-0.08606220036745071,
0.026493100449442863,
0.01900321990251541,
-0.02556806243956089,
-0.033458273857831955,
-0.006601084489375353,
-0.0360906608402729,
-0.0000948821398196742,
0.04356759041547775,
0.012748089618980885,
-0.0055100019089877605,
0.04138101264834404,
-0.006738241296261549,
0.005035391543060541,
-0.05286882817745209,
-0.003940344788134098,
-0.0005912988563068211,
-0.0019564791582524776,
0.02703794278204441,
0.005330633372068405,
-0.0013596408534795046,
-0.001889448263682425,
0.028962861746549606,
-0.030919184908270836,
0.06579937040805817,
0.023669350892305374,
-0.026012543588876724,
-0.0015528083313256502,
0.014456813223659992,
-0.016547659412026405,
0.07930979877710342,
0.02831357717514038,
-0.00727198226377368,
0.05223146826028824,
-0.04585013538599014,
-0.0498955063521862,
0.010621713474392891,
-0.014076120220124722,
-0.019432956352829933,
-0.009409929625689983,
0.0073471334762871265,
0.01215432584285736,
-0.03325459361076355,
-0.02786293998360634,
0.04336501285433769,
-0.020080996677279472,
-0.03660184144973755,
0.03352615609765053,
0.01964002475142479,
0.002287305425852537,
0.016862429678440094,
0.029338140040636063,
0.009535238146781921,
0.008356579579412937,
0.04405849799513817,
0.03642242029309273,
0.0655580684542656,
-0.02089727856218815,
0.006305414251983166,
0.0043581570498645306,
0.0024447389878332615,
0.029390238225460052,
-0.02103131264448166,
0.0784987136721611,
0.03207996487617493,
-0.021702956408262253,
-0.011614891700446606,
-0.0007435684092342854,
0.0043288166634738445,
0.03731614351272583,
-0.019720522686839104,
0.05759544298052788,
-0.02947913482785225,
0.0015757785877212882,
-0.030191050842404366,
-0.03240479528903961,
-0.020458204671740532,
0.03311799466609955,
0.020195068791508675,
0.004652902949601412,
0.0011388350976631045,
0.01621360331773758,
-0.002667167456820607,
-0.0021382072009146214,
-0.02536698803305626,
-0.034558530896902084,
-0.008439294062554836,
0.003627002937719226,
-0.015316369011998177,
0.004325335845351219,
-0.03694281354546547,
-0.000815887120552361,
0.005273164715617895,
0.05683307349681854,
0.037750665098428726,
0.019158154726028442,
-0.034467004239559174,
-0.02173948846757412,
-0.031984057277441025,
0.0159719530493021,
-0.09024662524461746,
-0.05931822210550308,
0.00580480694770813,
0.010496518574655056,
0.03921761363744736,
-0.008350014686584473
] |
<p>This is a quantum mechanics question, I don't quite understand what it's getting at...</p>
<blockquote>
<p>Suppose the we have a state described by $|1\,\,\, m\rangle$. Let its matrix representation be $\vec u$. The angular momentum measured in $(0, \sin\theta, \cos\theta)$ direction is $+1$. What are the components of $\vec u$?</p>
</blockquote>
<p>I presume one starts by assuming a basis $|1\,\,\, 1\rangle, |1\,\,\, 0\rangle, |1\,\,\, -1\rangle$ or something? I have no idea of what's going on...</p> | 1,446 | [
-0.009370537474751472,
-0.03544339910149574,
-0.035768840461969376,
-0.022698160260915756,
0.037610214203596115,
0.025907602161169052,
-0.04141708463430405,
-0.000804333365522325,
0.017453594133257866,
-0.028054308146238327,
0.022534700110554695,
0.04003190994262695,
0.07214522361755371,
0.0096858786419034,
0.0063993968069553375,
0.01602623239159584,
-0.028244223445653915,
-0.0010808369843289256,
-0.031027184799313545,
0.009176982566714287,
0.027632854878902435,
0.01082428079098463,
0.023429932072758675,
0.02682075835764408,
0.011723197996616364,
0.05308908596634865,
0.04482584074139595,
-0.00338597409427166,
0.021944165229797363,
0.04179873690009117,
-0.005251890979707241,
-0.050402116030454636,
0.005141380243003368,
-0.010477696545422077,
0.011334513314068317,
-0.05331701040267944,
-0.02858959697186947,
-0.0011787693947553635,
-0.03799033537507057,
0.0385960191488266,
-0.04738462343811989,
-0.057248007506132126,
-0.03493689373135567,
0.026472359895706177,
-0.051491618156433105,
-0.025743065401911736,
-0.009792382828891277,
0.002286632312461734,
0.052352968603372574,
-0.02310274727642536,
0.08985480666160583,
-0.008875705301761627,
0.025730380788445473,
-0.007022926118224859,
-0.006503445096313953,
0.009325755760073662,
0.08243194967508316,
0.08029957115650177,
0.005315947346389294,
-0.029122397303581238,
-0.006039537955075502,
-0.04376114159822464,
-0.015671808272600174,
-0.006799033377319574,
0.006115486845374107,
0.0123217161744833,
-0.0040636686608195305,
-0.019176200032234192,
0.03285517916083336,
0.010973414406180382,
0.018681606277823448,
-0.0016848139930516481,
0.013315684162080288,
-0.04669146239757538,
-0.02123991958796978,
-0.032457124441862106,
0.026796182617545128,
0.030977271497249603,
0.011745786294341087,
0.0005227227811701596,
-0.022583715617656708,
0.019199296832084656,
0.045480404049158096,
-0.005413155071437359,
-0.00195632828399539,
-0.0017925248248502612,
0.04704369604587555,
0.02159774675965309,
0.014079447835683823,
0.035427287220954895,
-0.0033774063922464848,
0.017153700813651085,
0.008932394906878471,
-0.012415125966072083,
-0.056640781462192535,
0.016628317534923553,
-0.005822419188916683,
0.041253071278333664,
0.031485579907894135,
-0.014375056140124798,
0.008946203626692295,
-0.014756107702851295,
0.022778840735554695,
0.0573381707072258,
-0.025345206260681152,
0.039016302675008774,
-0.02651442401111126,
0.012982369400560856,
-0.015898071229457855,
-0.035195086151361465,
-0.019802698865532875,
0.03492866829037666,
0.0020263497717678547,
0.009272533468902111,
0.017809126526117325,
-0.022658640518784523,
-0.0008937631500884891,
0.0008969999034889042,
0.04113828018307686,
0.06297770887613297,
0.04060238227248192,
-0.005390575155615807,
0.023285167291760445,
-0.015284336172044277,
-0.07910648733377457,
-0.005976792424917221,
0.020518848672509193,
-0.015212294645607471,
-0.032888270914554596,
0.030372880399227142,
-0.003678993321955204,
-0.019268717616796494,
0.05448673292994499,
0.014838067814707756,
0.02455664612352848,
-0.02381589636206627,
-0.1285904496908188,
-0.07058645784854889,
0.019320527091622353,
-0.034384485334157944,
-0.013991725631058216,
-0.0582854263484478,
0.04198214411735535,
0.03358607366681099,
0.08590922504663467,
-0.0021717168856412172,
0.021858951076865196,
0.03235660120844841,
0.017439434304833412,
0.011627170257270336,
0.021646948531270027,
-0.011197925545275211,
-0.04192674160003662,
-0.044922687113285065,
0.01862744800746441,
-0.026934847235679626,
0.034268252551555634,
0.032664794474840164,
0.019080180674791336,
-0.01939316838979721,
0.048069726675748825,
-0.01566888578236103,
0.01559827197343111,
0.03048371709883213,
-0.032506898045539856,
-0.021810228005051613,
0.07961082458496094,
0.02252834662795067,
-0.015520138666033745,
0.06367107480764389,
0.0018297593342140317,
-0.027443766593933105,
0.0038702525198459625,
0.04549967497587204,
0.05784342437982559,
-0.047564662992954254,
-0.027463076636195183,
-0.024908021092414856,
0.020356247201561928,
-0.021868854761123657,
-0.033561401069164276,
-0.054063066840171814,
0.0036336604971438646,
0.002924347063526511,
0.009894013404846191,
0.05283185467123985,
0.025116711854934692,
-0.009521703235805035,
-0.023481331765651703,
-0.014556324109435081,
0.0035365212243050337,
-0.02204241044819355,
0.028536705300211906,
0.0013352768728509545,
-0.03776685521006584,
0.04839912801980972,
0.012646897695958614,
0.03086843155324459,
-0.04604382440447807,
-0.022951766848564148,
-0.03693396970629692,
-0.008577343076467514,
-0.014056051149964333,
-0.030615419149398804,
0.011630930006504059,
0.029345929622650146,
0.029725641012191772,
0.014389283023774624,
0.0347488708794117,
-0.003553092712536454,
0.004774951376020908,
0.010770865716040134,
-0.021385768428444862,
0.02169528789818287,
0.05920770391821861,
-0.005512336269021034,
0.00458894670009613,
-0.007665516342967749,
0.001453620265237987,
0.03747309744358063,
-0.030446063727140427,
0.04968392848968506,
0.03742049261927605,
-0.01253549288958311,
0.010993783362209797,
0.04218926653265953,
0.028603455051779747,
0.013716285116970539,
0.016203729435801506,
-0.01417549792677164,
-0.03172720596194267,
-0.004657429177314043,
0.054505735635757446,
0.021694771945476532,
-0.04050859808921814,
-0.009665824472904205,
0.018646828830242157,
0.047088511288166046,
0.025995155796408653,
0.016316141933202744,
-0.014036127366125584,
-0.02268262580037117,
0.02589392475783825,
0.01803106628358364,
-0.058950770646333694,
0.013337844051420689,
0.0023269106168299913,
0.027013903483748436,
-0.004544765222817659,
0.011689364910125732,
-0.04929338023066521,
0.06537076830863953,
-0.06290280073881149,
0.029758617281913757,
-0.012822185643017292,
-0.04999980702996254,
0.02031826786696911,
-0.03250674903392792,
0.03002908080816269,
0.008248683996498585,
0.00033151014940813184,
-0.025528276339173317,
-0.03282097354531288,
-0.0034145829267799854,
-0.006687338929623365,
0.023464392870664597,
-0.03947725147008896,
-0.04446135833859444,
0.05069149285554886,
-0.030152881518006325,
0.037307851016521454,
-0.005569601897150278,
-0.03467760607600212,
-0.013832714408636093,
-0.013354591093957424,
0.05785277858376503,
0.00445825420320034,
0.015022782608866692,
-0.014793219044804573,
-0.045123640447854996,
0.01354694552719593,
-0.02395082823932171,
-0.006656106561422348,
0.04507344961166382,
-0.0649997740983963,
0.01994391717016697,
-0.05616999790072441,
-0.017912210896611214,
0.05464527755975723,
0.026660766452550888,
-0.03436747565865517,
-0.003140144981443882,
-0.01852647215127945,
-0.044805966317653656,
-0.04165998846292496,
-0.03794680908322334,
0.005568747408688068,
-0.02828262187540531,
-0.026239760220050812,
0.010405967012047768,
-0.006057133432477713,
-0.010963586159050465,
-0.028134869411587715,
-0.06068146228790283,
-0.01791050285100937,
-0.016410743817687035,
-0.018306445330381393,
0.04833812266588211,
-0.026275113224983215,
0.0267503522336483,
0.021421968936920166,
-0.038147564977407455,
0.007179718930274248,
-0.047819048166275024,
-0.03302234411239624,
-0.00368690537288785,
0.032982610166072845,
0.031219590455293655,
0.03995081037282944,
-0.0014753228751942515,
0.08120003342628479,
0.012169590219855309,
-0.044715721160173416,
-0.015173032879829407,
0.02496146224439144,
-0.001326811732724309,
-0.0769902765750885,
0.019863802939653397,
0.03504544124007225,
0.007353656459599733,
0.03431454300880432,
-0.0066726249642670155,
0.014852570369839668,
0.020766731351614,
0.03535439074039459,
-0.023865127936005592,
0.02772965282201767,
-0.009166753850877285,
0.004419523756951094,
0.04653523117303848,
0.0062422975897789,
0.011850516311824322,
-0.010011481121182442,
0.019084259867668152,
0.036280397325754166,
0.029114918783307076,
-0.03147337958216667,
0.05269373580813408,
-0.0032568699680268764,
0.027754319831728935,
-0.025130370631814003,
0.06625329703092575,
-0.01658712513744831,
0.0011974943336099386,
0.024647120386362076,
0.027186349034309387,
0.0020618813578039408,
-0.034873079508543015,
-0.01216221135109663,
0.03246155381202698,
-0.00983915850520134,
-0.0424482561647892,
0.0007107092533260584,
0.004967008251696825,
0.000873331620823592,
0.038370199501514435,
-0.04169618710875511,
-0.039890699088573456,
0.013317837379872799,
0.0241234228014946,
0.009982864372432232,
-0.004240391775965691,
-0.05155923590064049,
-0.0002794548054225743,
-0.04161311313509941,
0.004757901653647423,
0.009666183963418007,
0.021944895386695862,
-0.0159966628998518,
0.05016710236668587,
0.008225603960454464,
0.02086111158132553,
-0.00046056436258368194,
0.001740075065754354,
-0.06361901015043259,
0.019499357789754868,
-0.025720367208123207,
0.01114343386143446,
-0.014511189423501492,
-0.025640159845352173,
0.011007444001734257,
-0.04420156031847,
-0.02222803421318531,
0.02173565700650215,
-0.04018993675708771,
-0.05461805313825607,
0.05173325166106224,
-0.007277222815901041,
0.0030561904422938824,
-0.019401639699935913,
0.027880968526005745,
0.05914290249347687,
-0.025287477299571037,
-0.006513052154332399,
0.04699720814824104,
-0.036262135952711105,
-0.0034038759768009186,
-0.04963850975036621,
0.011262616142630577,
0.0214734748005867,
0.03166297823190689,
0.052955564111471176,
0.02199983038008213,
0.01660284586250782,
0.015905961394309998,
-0.006719720549881458,
0.07178287208080292,
0.012408892624080181,
-0.007844677194952965,
-0.023564491420984268,
-0.03734227269887924,
-0.018627198413014412,
0.007066709455102682,
0.061277393251657486,
0.0030856917146593332,
0.005579452030360699,
0.05756084620952606,
0.027055680751800537,
-0.016521185636520386,
0.014489677734673023,
0.05070740357041359,
0.017708513885736465,
-0.0036050716880708933,
-0.04280415549874306,
-0.011688443832099438,
-0.010439956560730934,
0.01721535064280033,
0.0022229310125112534,
-0.03679361939430237,
-0.023593470454216003,
0.021696889773011208,
0.004622561391443014,
-0.03406678885221481,
0.004286464303731918,
0.040961917489767075,
-0.01623452827334404,
0.007715287152677774,
-0.005875772330909967,
-0.0084978137165308,
-0.013041188009083271,
0.03193531930446625,
0.02648204192519188,
0.020807752385735512,
0.01926863007247448,
-0.036306947469711304,
0.012290888465940952,
0.022060547024011612,
0.006125719752162695,
-0.021434057503938675,
-0.012412483803927898,
-0.034989748150110245,
-0.047976329922676086,
0.04427402839064598,
0.0008188743959181011,
0.07111987471580505,
-0.025162935256958008,
-0.03477943688631058,
-0.016306132078170776,
-0.04531802982091904,
-0.03967608883976936,
-0.007502518594264984,
-0.02114878036081791,
0.02772941254079342,
-0.02005280926823616,
-0.007192352320998907,
-0.030301928520202637,
-0.005142980720847845,
0.0215911827981472,
0.028591612353920937,
0.025976888835430145,
-0.007937416434288025,
-0.006752061657607555,
0.04633360356092453,
0.0014382945373654366,
-0.08267056196928024,
0.014101574197411537,
0.0371420718729496,
-0.009471629746258259,
0.017780626192688942,
-0.07383192330598831,
-0.07033908367156982,
0.019841929897665977,
0.0251170564442873,
0.038698647171258926,
0.01748044788837433,
-0.03137807920575142,
0.047925423830747604,
0.01392446644604206,
-0.03519168496131897,
0.012821391224861145,
-0.0033755111508071423,
0.01870913617312908,
0.006272108759731054,
-0.01741647720336914,
0.003370535559952259,
-0.04229738563299179,
-0.011004696600139141,
-0.02809474617242813,
0.028116002678871155,
-0.006522563751786947,
0.03380202129483223,
-0.00017114476941060275,
0.02780044637620449,
-0.00953738484531641,
-0.05558622628450394,
-0.02030293084681034,
0.02770453691482544,
-0.023640967905521393,
-0.009562927298247814,
0.009367486461997032,
0.012314379215240479,
-0.011279196478426456,
-0.014372428879141808,
0.011928007006645203,
-0.054782118648290634,
0.029441948980093002,
0.032580841332674026,
0.01230604574084282,
0.001233812770806253,
-0.019115900620818138,
-0.013417390175163746,
0.001898200367577374,
-0.07475161552429199,
0.026929525658488274,
-0.04601423069834709,
0.02378903701901436,
0.012822362594306469,
-0.06463320553302765,
-0.0377376489341259,
0.017745666205883026,
-0.013890126720070839,
0.04611777886748314,
-0.009247466921806335,
-0.001256550312973559,
0.016852807253599167,
0.021049173548817635,
-0.05062607675790787,
-0.06845354288816452,
-0.014864078722894192,
0.04079607129096985,
-0.021593907848000526,
-0.022672560065984726,
0.007672822568565607,
-0.012259937822818756,
-0.0072191935032606125,
0.0186106339097023,
0.009293572045862675,
-0.0325242355465889,
0.004412489477545023,
0.06490958482027054,
0.04371599480509758,
0.06323909014463425,
-0.007869073189795017,
0.005348891485482454,
0.027710571885108948,
-0.005913810804486275,
0.004493365529924631,
-0.006604021415114403,
0.02665622904896736,
-0.02623932436108589,
-0.022668296471238136,
-0.019891053438186646,
0.0134709682315588,
0.016782986000180244,
-0.017056429758667946,
-0.0006540087633766234,
0.024735789746046066,
-0.0028359119314700365,
0.03078402765095234,
-0.010468324646353722,
0.026812542229890823,
0.012981554493308067,
0.012864746153354645,
0.007036143448203802,
-0.043888211250305176,
-0.0620766282081604,
-0.039576347917318344,
0.028441600501537323,
-0.007707542274147272,
0.0475308932363987,
0.013581081293523312,
0.05573122948408127,
0.014685959555208683,
-0.014438090845942497,
0.050358131527900696,
0.026584183797240257,
-0.0024589654058218002,
-0.008600019849836826,
0.025108972564339638,
0.023671476170420647,
0.0154679911211133,
-0.008317715488374233,
-0.016320811584591866,
-0.021089693531394005,
0.009878919459879398,
0.0729796290397644,
0.03137574344873428,
0.027293527498841286,
0.037417296320199966,
-0.010321301408112049,
-0.03317276015877724,
-0.023721490055322647,
-0.041219908744096756,
0.039966560900211334,
-0.015483895316720009,
0.040172748267650604,
-0.03387853503227234,
0.031046876683831215,
-0.004191985819488764,
0.021478107199072838,
-0.02555743232369423,
0.009376250207424164,
0.015516952611505985,
0.0032539137173444033,
0.07422410696744919,
0.04872724413871765,
-0.04416002705693245,
0.030168326571583748,
-0.017466804012656212,
0.008970338851213455,
-0.00888905767351389,
-0.003065532073378563,
0.03217247873544693,
0.0309361033141613,
0.07223120331764221,
-0.03997911885380745,
-0.00936373881995678,
-0.026901952922344208,
-0.0049026054330170155,
0.021362297236919403,
0.028134390711784363,
-0.05038120597600937,
0.016912449151277542,
0.05158191919326782,
0.015662580728530884,
0.02220247872173786,
0.012570152059197426,
-0.05335388332605362,
-0.03538352623581886,
-0.03795657679438591,
-0.043811582028865814,
0.02415505051612854,
-0.025706904008984566,
0.04137423634529114,
0.002569773932918906,
-0.03343440219759941,
0.0011076988885179162,
0.005992307793349028,
0.03823509067296982,
-0.04857632517814636,
0.0783001035451889,
0.0026547035668045282,
0.019488779827952385,
0.008421279489994049,
0.010128344409167767,
0.09457853436470032,
0.049720216542482376,
0.017349431291222572,
-0.08445869386196136,
-0.02529040165245533,
0.0014262523036450148,
-0.004857504274696112,
-0.040305767208337784,
0.01615148037672043,
0.023795129731297493,
0.031960584223270416,
-0.01673797331750393,
0.050086610019207,
-0.018567392602562904,
0.025830082595348358,
0.04127521440386772,
-0.038073018193244934,
-0.050558846443891525,
-0.0016779348952695727,
-0.0034196260385215282,
-0.0017814990133047104,
0.033005572855472565,
-0.052755292505025864,
0.013655987568199635,
-0.012067809700965881,
-0.04683057218790054,
-0.020458092913031578,
0.010526241734623909,
0.011657691560685635,
0.001541924779303372,
-0.010147232562303543,
0.005351035390049219,
-0.01782744750380516,
0.014298385940492153,
-0.03384986147284508,
0.03405606746673584,
0.005444793030619621,
0.0018806084990501404,
0.052523765712976456,
0.02523908205330372,
-0.0019834348931908607,
-0.01311859767884016,
0.024806808680295944,
-0.030643120408058167,
-0.02910005860030651,
0.005050234030932188,
-0.03336465731263161,
0.0770278126001358,
-0.030620060861110687,
-0.01796390861272812,
-0.03585140407085419,
0.01259621325880289,
-0.0033746971748769283,
-0.07514241337776184,
0.002981940284371376,
0.0034692217595875263,
0.045905157923698425,
-0.02140164189040661,
-0.006030602380633354,
-0.01366114616394043,
-0.015245143324136734,
0.009966394864022732,
0.029866743832826614,
-0.016919855028390884,
-0.025711823254823685,
0.02410903200507164,
0.002395888790488243,
0.015622304752469063,
0.028675928711891174,
-0.026347264647483826,
-0.0012501804158091545,
-0.03042919747531414,
-0.04109952598810196,
-0.011723554693162441,
0.049581222236156464,
0.009494883008301258,
0.0361117422580719,
0.019048474729061127,
-0.007234123535454273,
0.012434137053787708,
-0.06455639749765396,
0.011069945991039276,
-0.01821240782737732,
-0.0436081737279892,
0.018398083746433258,
0.010950841009616852,
-0.014409714378416538,
0.026376280933618546,
-0.021314317360520363,
-0.009372272528707981,
0.018315106630325317,
0.015428464859724045,
0.01902444288134575,
-0.013723219744861126,
-0.0378524474799633,
0.02026531659066677,
-0.047939978539943695,
0.014634307473897934,
-0.027113961055874825,
0.016368443146348,
0.03623548522591591,
-0.004941900260746479,
-0.03603189438581467,
0.016937877982854843,
-0.033122360706329346,
-0.02584698051214218,
0.0048177894204854965,
-0.049379169940948486,
0.013728666119277477,
0.023253822699189186,
0.000678760523442179,
-0.026902206242084503,
-0.0142998481169343,
-0.015902766957879066,
-0.007350711151957512,
0.026931282132864,
0.014401146210730076,
-0.020655633881688118,
-0.010904618538916111,
-0.016249127686023712,
0.015413213521242142,
0.02727474644780159,
-0.00782774668186903,
-0.0345337949693203,
0.004929832648485899,
0.005628685466945171,
-0.0345073826611042,
-0.005822513252496719,
0.012769877910614014,
-0.008344210684299469,
-0.020474975928664207,
0.014138934202492237,
0.04223619028925896,
-0.02126593515276909,
-0.0033382961992174387,
0.010204500518739223,
-0.004608656745404005,
0.04436438903212547,
-0.012174905277788639,
-0.008878097869455814,
0.0296076200902462,
-0.03062964603304863,
0.014361049048602581,
0.060538459569215775,
-0.007072725333273411,
0.0640873908996582,
0.005416938103735447,
-0.00835780892521143,
0.009325907565653324,
0.04135257750749588,
-0.05381288006901741,
0.01370555255562067,
0.007793033495545387,
-0.007758640218526125,
-0.016386166214942932,
-0.03249157965183258,
-0.010661167092621326,
0.013313367031514645,
-0.006447802297770977,
0.026747532188892365,
0.005315843038260937,
0.008863278664648533,
0.009191252291202545,
-0.005023886915296316,
0.03537178412079811,
0.04708736762404442,
0.08420973271131516,
0.007269904483109713,
0.020914550870656967,
0.04551856592297554,
-0.04567262530326843,
0.0429854542016983,
0.017897669225931168,
0.014991529285907745,
-0.07033539563417435,
-0.047140367329120636,
0.03489403799176216,
-0.00988084077835083,
0.04028509557247162,
-0.06397657096385956,
-0.021665560081601143,
0.025967035442590714,
-0.08458367735147476,
0.009180101566016674,
-0.028277216479182243,
-0.016093146055936813,
-0.02994583733379841,
-0.02753557451069355,
-0.0069867088459432125,
0.03478045389056206,
-0.00366111914627254,
0.021913563832640648,
0.016783928498625755,
-0.0018143601482734084,
-0.052257146686315536,
-0.03603479638695717,
0.0034213922917842865,
0.01536397635936737,
-0.011941327713429928,
-0.024667611345648766,
0.072533518075943,
-0.046055953949689865,
-0.025405531749129295,
0.023689312860369682,
-0.033895134925842285,
-0.010677386075258255,
-0.0038377416785806417,
0.010863206349313259,
0.0034413421526551247,
0.009062285535037518,
-0.009628549218177795,
-0.039778124541044235,
0.0027805925346910954,
-0.019860079512000084,
0.019197039306163788,
0.021707670763134956,
0.004925227724015713,
-0.024168094620108604,
0.0045881690457463264,
-0.05756375938653946,
-0.043905507773160934,
-0.007084629964083433,
-0.002943159081041813,
0.023532278835773468,
0.00729832099750638,
-0.01322558056563139,
0.003585629630833864,
-0.04833259433507919,
0.0036959517747163773,
-0.04642510041594505,
-0.014617274515330791,
0.006761473137885332,
-0.008206861093640327,
0.0395425409078598,
-0.005797854159027338,
0.006052118260413408,
-0.020456381142139435,
0.00958314910531044,
-0.01369548961520195,
-0.040662940591573715,
-0.06825036555528641,
-0.00525366747751832,
0.031213130801916122,
-0.007537382189184427,
0.01912677474319935,
-0.022590581327676773,
-0.028866665437817574,
0.017944173887372017,
-0.003242626553401351,
0.007819090038537979,
-0.021320048719644547,
-0.041995685547590256,
-0.03694901242852211,
-0.039173632860183716,
0.009218301624059677,
0.057535551488399506,
-0.012671152129769325,
-0.004231282044202089,
-0.03697547689080238,
0.010680046863853931,
0.011522693559527397,
0.05072721838951111,
0.029625456780195236,
-0.011332850903272629,
0.01956777833402157,
-0.016047099605202675,
0.022789213806390762,
-0.023946352303028107,
0.025548698380589485,
-0.02404119074344635,
-0.044910263270139694,
-0.008937748149037361,
-0.021265404298901558,
0.0068274810910224915,
0.004096654709428549,
0.011532295495271683,
-0.018476732075214386,
-0.05736749246716499,
-0.03469952195882797,
-0.01047155074775219,
0.04581774026155472,
-0.021359525620937347,
0.03874044120311737,
0.05366900563240051,
0.03413231670856476,
0.02129332348704338,
0.03970262408256531,
-0.02690008468925953,
-0.06917468458414078,
0.027070919051766396,
-0.035528264939785004,
-0.005427394062280655,
-0.0034267473965883255,
0.010128917172551155,
0.08588924258947372,
-0.029363662004470825,
-0.05017104744911194,
0.03337140008807182,
-0.03283297270536423,
0.014565978199243546,
0.024123670533299446,
-0.0029629687778651714,
0.05021755397319794,
0.015469971112906933,
0.027749858796596527,
0.04265068471431732,
-0.00584199745208025,
0.051464445888996124,
0.08574473857879639,
0.05444562807679176,
-0.01864960417151451,
-0.03937063366174698,
0.022574327886104584,
-0.01978008635342121,
0.010060462169349194,
0.01021354179829359,
0.03662537410855293,
-0.035705067217350006,
0.04250369220972061,
0.006558800116181374,
-0.022316517308354378,
-0.026259778067469597,
-0.009575865231454372,
-0.03406714275479317,
0.07084760069847107,
-0.04266267642378807,
-0.0070502860471606255,
-0.054547928273677826,
0.013934016227722168,
-0.039529457688331604,
0.030535703524947166,
0.05658956244587898,
0.04153653234243393,
-0.021611886098980904,
-0.018308797851204872,
-0.01356688141822815,
-0.03218330070376396,
0.014381824992597103,
-0.04907859489321709,
-0.010843159630894661,
0.002535626757889986,
0.011842518113553524,
-0.004007324576377869,
-0.03498069941997528,
-0.01037263311445713,
-0.04633835330605507,
0.02436821535229683,
0.02915390208363533,
0.018894053995609283,
-0.02411668933928013,
0.014248973689973354,
-0.03594115376472473,
0.04415049031376839,
-0.03697231411933899,
-0.03393296152353287,
-0.02771403081715107,
0.053199924528598785,
-0.01263886783272028,
0.007293662987649441
] |
<p>I am having some trouble interpreting a Hamiltonian in terms of "hopping" operators. The <a href="http://www.google.com/search?q=huckel+model+graphene" rel="nofollow">Huckel model</a> for nearest neighbour interaction in graphene is given by </p>
<p>$$H=-t\sum_\vec{R}|\vec R\rangle\langle \vec R+\vec \tau|+|\vec R\rangle\langle \vec R+\vec a+\vec \tau|+|\vec R\rangle\langle \vec R+\vec b+\vec \tau|+\text{h.c.}$$
where $t>0$ is a constant, $\vec a$ and $\vec b$ are the unit cell vectors for a two-atom unit cell, and $\vec \tau$ is the position of the second atom in the basis, the first atom being at the origin of the unit cell. The position of $\vec\tau$ is $\frac13(a,b)$ generalized over all space.</p>
<p>How can I interpret the different terms in the Hamiltonian as hopping processes?</p> | 1,447 | [
-0.006015140097588301,
-0.019545992836356163,
0.03864675387740135,
-0.022547287866473198,
0.03268863633275032,
-0.0018261998193338513,
-0.013479171320796013,
-0.0014263056218624115,
0.017868302762508392,
-0.049994681030511856,
0.0510786809027195,
0.013309566304087639,
0.031856194138526917,
0.00782058760523796,
0.02819301374256611,
0.032653260976076126,
-0.014284218661487103,
-0.055737171322107315,
-0.017941569909453392,
0.01542305201292038,
0.029362427070736885,
0.021057652309536934,
0.008583566173911095,
-0.01319526880979538,
0.02679583616554737,
0.0025213484186679125,
0.027278337627649307,
-0.008781041949987411,
0.01987917348742485,
0.04145772010087967,
-0.020767295733094215,
-0.03238706663250923,
0.028134208172559738,
-0.01001191046088934,
0.016368452459573746,
0.028074001893401146,
-0.06483332067728043,
-0.03265644609928131,
0.01631283387541771,
-0.007753819227218628,
-0.038165632635354996,
-0.03480973839759827,
-0.045158565044403076,
0.0670664831995964,
-0.008187194354832172,
-0.009866313077509403,
-0.008872108533978462,
-0.015869593247771263,
0.0165486391633749,
-0.03651435300707817,
0.08434102684259415,
0.01464963797479868,
0.002241934649646282,
0.014422867447137833,
0.02213369496166706,
0.02559860609471798,
0.06662619113922119,
0.07818098366260529,
-0.014375156722962856,
-0.02409483678638935,
-0.007955105043947697,
-0.0872940868139267,
-0.027127541601657867,
-0.004140917677432299,
-0.021213222295045853,
0.017101764678955078,
-0.011220674030482769,
-0.054617252200841904,
0.04567130282521248,
0.0014645745977759361,
0.013880770653486252,
-0.019470561295747757,
0.025300083681941032,
-0.05145874246954918,
0.0640273466706276,
-0.004795479122549295,
0.003926046192646027,
0.03332071751356125,
0.04114345461130142,
0.03135155513882637,
-0.025340043008327484,
0.025355719029903412,
0.011618542484939098,
0.03099680319428444,
0.005310522858053446,
-0.02159659005701542,
0.0446893684566021,
-0.015860654413700104,
0.010043968446552753,
0.011852633208036423,
-0.02658839337527752,
-0.004831178579479456,
0.061472997069358826,
0.00463906629011035,
-0.028618114069104195,
0.004805820994079113,
0.02622375451028347,
0.03424016758799553,
-0.007320547476410866,
-0.02577711082994938,
-0.004156270995736122,
-0.0432407520711422,
0.035254400223493576,
0.049011897295713425,
-0.04893261939287186,
0.0025768550112843513,
-0.02567204087972641,
0.010389719158411026,
-0.014766081236302853,
-0.010389191098511219,
-0.06232960894703865,
0.020654331892728806,
-0.018806735053658485,
0.037670426070690155,
-0.012962321750819683,
-0.017117468640208244,
-0.029672745615243912,
0.023296240717172623,
0.030510062351822853,
0.03952677547931671,
-0.0018262560479342937,
-0.014384051784873009,
0.04285295307636261,
-0.047452546656131744,
-0.05233687162399292,
0.016237160190939903,
0.01223722379654646,
-0.0037745689041912556,
-0.015711598098278046,
-0.013453621417284012,
0.02406940422952175,
-0.002705914434045553,
0.014313356019556522,
-0.01368361059576273,
0.04316192865371704,
-0.012351132929325104,
-0.11940144002437592,
-0.04540427029132843,
0.05584784969687462,
-0.031860899180173874,
0.003514623735100031,
-0.08093854784965515,
0.0022009548265486956,
0.04110138118267059,
0.09595092386007309,
0.0019484016811475158,
-0.017811428755521774,
0.004433259833604097,
0.0038677072152495384,
0.02061336860060692,
0.004993510898202658,
-0.025971032679080963,
0.007993562147021294,
-0.03319817781448364,
-0.006157573312520981,
-0.044521547853946686,
0.03429485857486725,
0.022746725007891655,
0.037351224571466446,
-0.009416076354682446,
0.07620292901992798,
-0.007223580498248339,
-0.0013893733266741037,
0.01843569427728653,
0.029667453840374947,
0.02661779709160328,
0.07757514715194702,
0.030756523832678795,
0.021314553916454315,
0.04041862487792969,
0.023474128916859627,
0.014279690571129322,
-0.010252892039716244,
0.03668258339166641,
0.0404997244477272,
-0.028881147503852844,
0.01020333543419838,
-0.022043749690055847,
-0.0027531851083040237,
-0.019403256475925446,
-0.03597236052155495,
-0.043597262352705,
0.006374344229698181,
-0.006823941599577665,
0.007325778249651194,
-0.023046690970659256,
0.007893302477896214,
0.020159635692834854,
0.01720777526497841,
-0.03430604562163353,
0.013027246110141277,
-0.0855555385351181,
0.02378564514219761,
-0.004883298184722662,
-0.00939868576824665,
0.07947224378585815,
0.02956559881567955,
-0.02321249060332775,
0.003629830665886402,
-0.04158695042133331,
0.00015166751109063625,
0.030740033835172653,
-0.0019756583496928215,
-0.012708539143204689,
0.0368732251226902,
0.06842146068811417,
0.038361817598342896,
0.030270256102085114,
0.053841590881347656,
-0.0012957759900018573,
-0.013816588558256626,
0.02561274915933609,
-0.010035301558673382,
0.024925649166107178,
-0.003434627316892147,
0.01535322330892086,
-0.039759378880262375,
-0.03063817322254181,
-0.016161005944013596,
0.03232226148247719,
-0.05701644718647003,
0.0717097669839859,
0.05296938866376877,
0.0349879153072834,
-0.02986755594611168,
0.04947778955101967,
0.002110104076564312,
0.005506347399204969,
-0.002633011667057872,
-0.029060810804367065,
-0.04272938147187233,
-0.016195125877857208,
0.06605423986911774,
0.03147919476032257,
-0.03121860884130001,
-0.030659150332212448,
0.03787783533334732,
0.026309292763471603,
0.04014349728822708,
0.027019081637263298,
-0.06560918688774109,
0.0076040285639464855,
0.07355206459760666,
-0.0063959751278162,
0.008503015153110027,
-0.018397537991404533,
0.008435796946287155,
0.001196955214254558,
0.02522232010960579,
-0.03429953008890152,
-0.02326195500791073,
0.03413444757461548,
-0.023197999224066734,
-0.003542310791090131,
0.00397101417183876,
-0.019184347242116928,
0.024822762235999107,
-0.023379217833280563,
0.023170530796051025,
0.07115068286657333,
0.0033624903298914433,
0.012329131364822388,
-0.056851547211408615,
-0.03152674809098244,
0.007889093831181526,
-0.017261553555727005,
-0.039532314985990524,
-0.05674407631158829,
0.01716398075222969,
-0.005203900393098593,
0.01961885206401348,
-0.04222148656845093,
0.011468861252069473,
0.0027100038714706898,
-0.0019708960317075253,
0.024760514497756958,
0.037499912083148956,
0.06124693900346756,
-0.027867266908288002,
-0.007570217829197645,
-0.001824275474064052,
-0.05716673657298088,
0.055994052439928055,
0.0131375128403306,
-0.0510597750544548,
0.02391625940799713,
-0.0585782565176487,
-0.013527405448257923,
0.0489836260676384,
0.009023443795740604,
-0.02553325518965721,
-0.02115458995103836,
-0.006621094886213541,
-0.045068077743053436,
-0.010954519733786583,
-0.006308317184448242,
0.012505685910582542,
-0.04508403688669205,
0.0167612936347723,
0.03532365337014198,
-0.010944024659693241,
-0.010444828309118748,
0.021463999524712563,
-0.020538736134767532,
-0.045148223638534546,
0.025631878525018692,
-0.004779093433171511,
0.013572609052062035,
-0.005021305754780769,
0.05103691294789314,
0.01430110540241003,
-0.025114845484495163,
-0.014939301647245884,
-0.03964459151029587,
-0.03489341214299202,
0.015913166105747223,
-0.02661954052746296,
0.02010776661336422,
-0.012096939608454704,
-0.029010390862822533,
0.09293822944164276,
0.009689079597592354,
-0.023275146260857582,
-0.001714829821139574,
-0.005897891242057085,
-0.01653863489627838,
0.007471354678273201,
0.024940097704529762,
0.05660420283675194,
-0.012721450999379158,
0.004883061163127422,
0.015898583456873894,
0.06099933758378029,
0.0664609745144844,
-0.010138403624296188,
-0.011121410876512527,
0.022574657574295998,
0.01615249738097191,
-0.01854667440056801,
0.059249479323625565,
-0.029179591685533524,
-0.00433355150744319,
0.011758092790842056,
-0.01825517602264881,
0.0012641607318073511,
0.03803281858563423,
-0.06863850355148315,
0.03535306081175804,
0.004668793641030788,
-0.010980053804814816,
-0.0064484779722988605,
0.010230214335024357,
-0.006700769532471895,
-0.04918103665113449,
0.021263839676976204,
0.024204237386584282,
0.0448991060256958,
-0.007886823266744614,
0.022465208545327187,
0.02723008580505848,
-0.0008368106791749597,
-0.00977992732077837,
-0.015343429520726204,
0.030597174540162086,
-0.005052345804870129,
0.029425369575619698,
-0.014079471118748188,
-0.039652545005083084,
0.03435124084353447,
0.01664566621184349,
0.010624198243021965,
-0.013581999577581882,
-0.06972727924585342,
-0.003079612972214818,
-0.01427634060382843,
-0.004195634741336107,
-0.024414869025349617,
0.03814293071627617,
0.0013562403619289398,
0.021239636465907097,
0.016768386587500572,
-0.007918909192085266,
0.04034612700343132,
0.00806050281971693,
-0.06175567954778671,
-0.014102083630859852,
-0.0005176386912353337,
-0.023221498355269432,
-0.003349067410454154,
-0.04997117817401886,
0.01737923175096512,
-0.010217026807367802,
-0.05015992745757103,
-0.005321390461176634,
-0.006829071324318647,
-0.06316761672496796,
0.003529575187712908,
-0.012225696817040443,
-0.030127929523587227,
-0.04475542530417442,
-0.011728769168257713,
0.03777744621038437,
-0.03721125051379204,
0.03845660760998726,
0.04512803629040718,
-0.02185538224875927,
0.02519625425338745,
0.0021189304534345865,
0.00940448697656393,
0.05662808194756508,
-0.002720750169828534,
0.021495403721928596,
0.018435809761285782,
0.025027507916092873,
-0.02463814616203308,
0.014836219139397144,
0.07845894992351532,
0.0132258590310812,
-0.02867518737912178,
0.01958540640771389,
-0.06454373151063919,
-0.01700841821730137,
-0.0060691311955451965,
0.05921391397714615,
-0.004138593561947346,
0.03539958968758583,
0.02335388772189617,
0.04639921337366104,
-0.015912678092718124,
0.029634585604071617,
0.05302475020289421,
0.016018692404031754,
-0.013936006464064121,
-0.0640801191329956,
-0.011957020498812199,
-0.028754593804478645,
-0.018196839839220047,
0.03510677069425583,
-0.06871466338634491,
-0.021405164152383804,
0.008312668651342392,
0.03558693826198578,
-0.007022482343018055,
-0.050974052399396896,
-0.03135544806718826,
-0.018018407747149467,
0.0010629914468154311,
-0.006268123164772987,
-0.03324253484606743,
-0.0028583339881151915,
0.011673609726130962,
-0.0022579145152121782,
0.01405014656484127,
0.022075410932302475,
-0.06902579218149185,
-0.031778816133737564,
0.02676079422235489,
-0.0039030606858432293,
-0.020418887957930565,
0.0022635275963693857,
-0.0375252403318882,
-0.010841695591807365,
0.034505896270275116,
-0.010093589313328266,
0.020196503028273582,
0.001851254957728088,
-0.010892286896705627,
-0.02344376966357231,
-0.02429257147014141,
-0.002071171998977661,
-0.007529578171670437,
0.006814474239945412,
0.02491077408194542,
-0.05028706416487694,
0.01046876423060894,
-0.018284708261489868,
-0.0029773754067718983,
0.008680945262312889,
0.07155588269233704,
-0.004015210550278425,
0.01267008576542139,
0.03245730698108673,
0.006917222402989864,
-0.0007519412320107222,
-0.0711420476436615,
0.0246743056923151,
0.030546240508556366,
0.046884793788194656,
0.06025676056742668,
-0.061399295926094055,
-0.043173205107450485,
0.03621560335159302,
-0.010567858815193176,
0.026631003245711327,
0.021086419001221657,
-0.009629457257688046,
0.059264812618494034,
0.034640125930309296,
-0.047153815627098083,
0.06675805151462555,
0.030108226463198662,
-0.012373900040984154,
0.010061238892376423,
-0.017923088744282722,
0.024112775921821594,
-0.0260771457105875,
0.02392425574362278,
-0.06395170837640762,
0.0016799335135146976,
-0.011701980605721474,
0.03925198316574097,
-0.01619214378297329,
0.007871418260037899,
-0.018170854076743126,
-0.06367738544940948,
-0.02866435796022415,
0.027768610045313835,
-0.02975849248468876,
-0.03108632192015648,
-0.01023188978433609,
0.031983617693185806,
0.025664422661066055,
-0.012021711096167564,
-0.022905493155121803,
-0.01443573646247387,
-0.021221792325377464,
0.00444978941231966,
0.011635870672762394,
0.028928132727742195,
-0.026603177189826965,
0.0061373040080070496,
0.02153235673904419,
-0.068494513630867,
0.022021785378456116,
0.009648336097598076,
-0.028697075322270393,
-0.03117004781961441,
-0.03491956740617752,
-0.059261225163936615,
0.0003094982821494341,
0.016333552077412605,
0.008846511133015156,
-0.025466730818152428,
0.02165478654205799,
-0.002362642204388976,
0.0029560995753854513,
-0.08005281537771225,
-0.053361907601356506,
0.010239413008093834,
0.002194394823163748,
-0.02800389565527439,
-0.028300758451223373,
0.03322947397828102,
-0.02968469075858593,
-0.021703755483031273,
0.07189573347568512,
0.03186993673443794,
-0.024157576262950897,
0.003064895048737526,
0.046645987778902054,
-0.006908821407705545,
0.052434951066970825,
0.018830744549632072,
-0.009706353768706322,
0.0004585321876220405,
-0.037426918745040894,
-0.00012550815881695598,
-0.011126658879220486,
0.0528959222137928,
-0.035146117210388184,
0.00016499146295245737,
-0.03197901323437691,
-0.014425890520215034,
0.04522305727005005,
-0.025735128670930862,
-0.03851897269487381,
0.01920950971543789,
0.04906873777508736,
-0.0057372841984033585,
-0.016000641509890556,
-0.017729733139276505,
0.0053469957783818245,
0.011429707519710064,
0.018711920827627182,
0.012570519000291824,
-0.02148040570318699,
0.0000317411104333587,
0.023191185668110847,
-0.01853414997458458,
0.009420741349458694,
-0.004405354615300894,
0.06743093580007553,
-0.010151010937988758,
0.01835247129201889,
0.05067620798945427,
-0.019006749615073204,
0.029120955616235733,
-0.0332522876560688,
-0.0020268692169338465,
0.04825756698846817,
-0.01427492219954729,
-0.01685464009642601,
-0.016239918768405914,
-0.08412296324968338,
0.02751443162560463,
0.03305710107088089,
-0.05137208104133606,
0.019352605566382408,
0.021062353625893593,
-0.02103528007864952,
-0.0028853300027549267,
-0.004685055464506149,
-0.02998034656047821,
0.019814809784293175,
0.0036457141395658255,
0.008355745114386082,
-0.04315949231386185,
0.006690861191600561,
0.0458940751850605,
0.058775853365659714,
-0.00971315149217844,
0.012210245244204998,
0.07293860614299774,
0.04432710260152817,
0.01604372076690197,
0.01579485461115837,
-0.031093060970306396,
0.022011857479810715,
0.00033624214120209217,
0.050872284919023514,
-0.0062285903841257095,
-0.022625619545578957,
0.0633372887969017,
0.017996540293097496,
0.02723935805261135,
-0.031501397490501404,
-0.014100906439125538,
-0.06786513328552246,
0.04350503906607628,
-0.008933058939874172,
-0.017186176031827927,
0.013144092634320259,
0.014322117902338505,
0.006092526018619537,
0.025596432387828827,
0.029769407585263252,
-0.0106676509603858,
-0.0588160865008831,
0.015342047438025475,
-0.02433064579963684,
-0.04704507440328598,
-0.004052910953760147,
0.0211116261780262,
-0.029195914044976234,
0.048289041966199875,
-0.016541820019483566,
0.020119383931159973,
0.025337889790534973,
0.050769221037626266,
-0.015561001375317574,
0.0903090089559555,
-0.018281303346157074,
0.01118442602455616,
0.009079028852283955,
-0.012140315026044846,
0.08709248900413513,
0.053708504885435104,
-0.013529877178370953,
-0.06897491961717606,
0.008312728255987167,
0.010693633928894997,
-0.0061650932766497135,
-0.029600100591778755,
0.007808158174157143,
0.044622112065553665,
0.008554530330002308,
-0.024487672373652458,
0.042789507657289505,
-0.006938048638403416,
0.009180942550301552,
0.036786239594221115,
-0.018497517332434654,
-0.03965378925204277,
0.006584491115063429,
0.002460324205458164,
-0.0070488047786056995,
-0.024930734187364578,
-0.04477991908788681,
-0.019292255863547325,
-0.03805449604988098,
0.013139181770384312,
-0.07062391936779022,
-0.029721412807703018,
0.01345881074666977,
0.02621004730463028,
-0.023543231189250946,
0.029233716428279877,
-0.025400247424840927,
0.005193681921809912,
-0.0023172006476670504,
0.020334796980023384,
-0.020326249301433563,
-0.02090936154127121,
0.03340484946966171,
0.021667364984750748,
0.027028009295463562,
-0.022172871977090836,
0.033019308000802994,
-0.011706575751304626,
-0.04324320703744888,
0.012847069650888443,
-0.008048909716308117,
0.053134649991989136,
-0.02652411349117756,
-0.01927529089152813,
0.009574622847139835,
0.008343934081494808,
0.010567858815193176,
-0.06782499700784683,
-0.006709640845656395,
-0.030754627659916878,
0.019104834645986557,
-0.016028359532356262,
-0.00536067271605134,
-0.07656658440828323,
0.002849845914170146,
-0.015590989962220192,
-0.0078014833852648735,
0.005870318505913019,
0.012743648141622543,
0.005762791261076927,
-0.02157513052225113,
0.025857875123620033,
-0.011389738880097866,
-0.027683790773153305,
-0.02463601715862751,
-0.011606019921600819,
-0.03572649881243706,
-0.015515738166868687,
-0.008919037878513336,
0.008797645568847656,
0.05522417277097702,
-0.02155761606991291,
-0.023354019969701767,
-0.0036546539049595594,
-0.058145228773355484,
0.004037713631987572,
-0.013626368716359138,
-0.003946410026401281,
0.013346816413104534,
0.008922363631427288,
0.051318734884262085,
0.02470688335597515,
-0.019796302542090416,
0.043674468994140625,
-0.028833726420998573,
-0.005216578487306833,
0.039277333766222,
-0.016310961917042732,
-0.014677931554615498,
0.006257426925003529,
-0.048470016568899155,
0.003001469885930419,
0.0013098625931888819,
0.007735438644886017,
0.024023551493883133,
-0.03689752519130707,
-0.03958965092897415,
0.01946795918047428,
-0.008478039875626564,
-0.04511912912130356,
0.00824654195457697,
-0.025279080495238304,
0.005138590466231108,
0.030119791626930237,
0.001969369128346443,
-0.02901282161474228,
-0.020722150802612305,
-0.010307103395462036,
0.008488034829497337,
-0.01154419407248497,
0.012929202988743782,
-0.03831913694739342,
-0.05121973156929016,
-0.008293664082884789,
0.01728629879653454,
0.01457156054675579,
0.030675649642944336,
-0.03570029139518738,
0.044788505882024765,
0.01389791164547205,
0.008206814527511597,
-0.027076616883277893,
0.04570475593209267,
0.04534775763750076,
-0.016626005992293358,
0.04610757902264595,
0.04243392124772072,
0.00897915568202734,
0.0040598176419734955,
0.013373659923672676,
-0.0515124537050724,
0.05293869972229004,
-0.012872212566435337,
-0.04085642099380493,
0.046532388776540756,
-0.02354430966079235,
-0.007811758667230606,
0.0193182323127985,
0.023937778547406197,
0.03575699403882027,
0.019087251275777817,
-0.019319741055369377,
0.009226658381521702,
0.047908294945955276,
-0.022522909566760063,
0.02540639042854309,
0.042539793998003006,
-0.026372496038675308,
-0.015418654307723045,
-0.024977153167128563,
0.0018286582781001925,
0.009686332195997238,
0.02045694924890995,
0.00937589630484581,
0.0476241260766983,
-0.02396341972053051,
-0.007100597955286503,
-0.006762352306395769,
-0.02321522869169712,
0.03015320934355259,
-0.00909794308245182,
-0.004710495471954346,
-0.00012183756189187989,
0.0784505307674408,
-0.021968817338347435,
0.042358577251434326,
0.010159656405448914,
0.04539841413497925,
-0.05993572622537613,
-0.014535865746438503,
-0.006053138989955187,
-0.02584136836230755,
0.027890218421816826,
-0.04898807778954506,
-0.015600929036736488,
0.024601144716143608,
-0.03673641011118889,
0.022055162116885185,
-0.010487564839422703,
0.009276271797716618,
-0.005257765296846628,
-0.029304848983883858,
-0.05044909939169884,
0.04267285019159317,
0.006670780945569277,
0.0630212277173996,
0.014761672355234623,
0.025090394541621208,
-0.043375782668590546,
-0.05144444480538368,
-0.0008365879766643047,
0.013603108935058117,
0.03158118575811386,
-0.028418555855751038,
0.04475162923336029,
-0.024109385907649994,
-0.040016353130340576,
0.03081144019961357,
-0.03588003292679787,
-0.04178191348910332,
-0.01608605682849884,
-0.006899756845086813,
0.021899651736021042,
0.04109333083033562,
0.010027051903307438,
-0.055516116321086884,
-0.0240426454693079,
-0.0027607178781181574,
0.021417707204818726,
0.03411945328116417,
0.009447145275771618,
-0.00479577761143446,
0.0028171774465590715,
-0.03300638869404793,
-0.04038423299789429,
0.041878536343574524,
-0.018999852240085602,
0.007033657282590866,
0.005538339260965586,
0.007672861684113741,
0.04379436746239662,
-0.02796713076531887,
-0.007435040548443794,
-0.002032146556302905,
-0.011706378310918808,
0.015109570696949959,
0.015794426202774048,
-0.00997370108962059,
-0.01269709412008524,
-0.059868358075618744,
-0.023710252717137337,
0.03661184012889862,
0.014777511358261108,
-0.05151247978210449,
-0.07897896319627762,
-0.02086251974105835,
-0.0005441167741082609,
-0.025750476866960526,
-0.008009682409465313,
-0.04859461635351181,
-0.003682234790176153,
0.014678703621029854,
-0.007335663307458162,
0.03094753995537758,
-0.03583260625600815,
-0.03544454276561737,
-0.00040519327740184963,
-0.05844543129205704,
0.02560046873986721,
0.0310335885733366,
-0.014063224196434021,
-0.04009979963302612,
-0.009509360417723656,
-0.002980115357786417,
0.005517316982150078,
0.053452104330062866,
0.015801692381501198,
-0.016881585121154785,
-0.018781127408146858,
0.002322340616956353,
0.03640442341566086,
-0.018625667318701744,
-0.008672854863107204,
-0.035234369337558746,
0.025179963558912277,
-0.010928592644631863,
-0.020168641582131386,
-0.03285231441259384,
0.03660362586379051,
-0.009169272147119045,
-0.02848157286643982,
-0.006946269888430834,
-0.011548969894647598,
-0.03125530853867531,
0.050669025629758835,
0.03874598443508148,
0.0011746120871976018,
0.081326924264431,
-0.0035983528941869736,
0.019854635000228882,
0.06253506243228912,
0.002103246981278062,
-0.0397617444396019,
-0.0002274630533065647,
-0.03367413952946663,
-0.01577797904610634,
0.0071684010326862335,
-0.003264680504798889,
0.01878935471177101,
-0.03066076710820198,
-0.02287842333316803,
0.0007868306711316109,
-0.01675431802868843,
-0.013454454950988293,
0.03422804921865463,
0.029372218996286392,
0.019585391506552696,
0.027502894401550293,
0.017894884571433067,
0.026109637692570686,
0.016637403517961502,
0.011784859001636505,
0.03908122703433037,
0.020566426217556,
0.012536617927253246,
0.030511975288391113,
-0.0011340139899402857,
-0.0249075498431921,
0.018394699320197105,
0.021656908094882965,
0.00704228738322854,
-0.02695525251328945,
0.026746749877929688,
0.0325603149831295,
-0.015212303958833218,
0.00162901496514678,
0.032627884298563004,
-0.015101571567356586,
0.07386215031147003,
-0.008900608867406845,
0.008678005076944828,
0.010141170583665371,
0.007511420175433159,
-0.0056913201697170734,
0.005071208346635103,
0.022578714415431023,
0.010248017497360706,
-0.0341971255838871,
-0.018957998603582382,
-0.03491867333650589,
0.025340311229228973,
0.02186155691742897,
-0.057861678302288055,
0.00823238305747509,
0.022812267765402794,
-0.030571386218070984,
0.012915171682834625,
-0.017494654282927513,
-0.015814026817679405,
0.015619182027876377,
0.03121093288064003,
0.03955305740237236,
-0.014484983868896961,
-0.008375902660191059,
-0.0013932351721450686,
-0.037616197019815445,
0.038125522434711456,
-0.04848789423704147,
-0.03595983237028122,
-0.04083723947405815,
0.015154124237596989,
-0.02376645617187023,
-0.0017650057561695576
] |
<p>Suppose we place a Hertzian dipole (short, ends loaded with capacitance) in a time varying electric field $\vec{E}\left(t\right)$, with magniture $E\left(t\right)$ and direction as shown in this figure. What will be the (steady state) current $I\left(t\right)$ flowing through the resistance $R$?</p>
<p><img src="http://i.stack.imgur.com/EM03d.png" alt="Dipole in time-varying electric field"></p>
<p>I expect that if $E\left(t\right)$ is time invariant, there should be <em>no</em> current? So I was wondering if $\displaystyle \frac {d E\left(t\right)}{d t}$ appears in the expression somewhere?</p>
<p>I understand that the condition of a loop inside a time varying magnetic field is handled by Faraday's law, with the EMF given by $\displaystyle\mathscr{E}\left(t\right) = -\iint_A \frac{d\vec{B}\left(t\right)}{dt} \cdot d\vec{a}$. So is there something similar for the electric case?</p> | 1,448 | [
-0.014024760574102402,
0.015790047124028206,
0.016238367184996605,
-0.0344291590154171,
0.053665097802877426,
-0.0015352193731814623,
-0.03586356341838837,
0.0005192425451241434,
0.007512414827942848,
0.009404393844306469,
0.027870934456586838,
0.03816558048129082,
0.016247449442744255,
0.018709426745772362,
0.00954397488385439,
0.010536257177591324,
-0.0059350780211389065,
-0.02236747369170189,
0.00277186487801373,
-0.040707726031541824,
0.010219662450253963,
0.023889372125267982,
0.03105195052921772,
0.0011102554854005575,
0.011271273717284203,
0.034665755927562714,
0.030524052679538727,
0.01652059331536293,
-0.026600049808621407,
0.07723133265972137,
-0.007347585167735815,
-0.035489846020936966,
-0.0163845494389534,
0.044042762368917465,
0.01194844488054514,
0.030283626168966293,
-0.06235393509268761,
-0.07215417176485062,
-0.007562645711004734,
0.011173618026077747,
-0.008337771520018578,
0.0010880075860768557,
-0.01085746195167303,
0.07539817690849304,
-0.010847754776477814,
0.006307130679488182,
0.0012863018782809377,
0.03189273178577423,
0.06014876067638397,
-0.06518638879060745,
0.07463295012712479,
-0.017949333414435387,
0.06999976187944412,
-0.0027618922758847475,
-0.01559123769402504,
-0.0077530452981591225,
0.04971535876393318,
0.06683861464262009,
-0.023421747609972954,
-0.03171177953481674,
-0.009314771741628647,
-0.027004826813936234,
0.014563419856131077,
-0.050280120223760605,
-0.0035307733342051506,
0.041180044412612915,
-0.004161335062235594,
-0.00393235357478261,
0.008095309138298035,
-0.009704290889203548,
0.02250690571963787,
-0.00334735494107008,
0.0026601601857692003,
-0.040514759719371796,
0.03322211280465126,
-0.02118833363056183,
0.022381506860256195,
0.017516590654850006,
0.04883671924471855,
0.04329962283372879,
-0.05250058323144913,
-0.02270554006099701,
0.024585900828242302,
0.03962601348757744,
0.029175439849495888,
-0.017836106941103935,
0.016250763088464737,
-0.013185597024857998,
0.0026010547298938036,
0.0169766154140234,
0.013848579488694668,
0.02377469651401043,
0.014916892163455486,
-0.02199125662446022,
-0.019385401159524918,
0.030418993905186653,
0.010644037276506424,
0.053788505494594574,
0.0022648819722235203,
-0.026483874768018723,
0.012301190756261349,
-0.010522297583520412,
0.015639569610357285,
0.07527418434619904,
0.03266238421201706,
-0.011517958715558052,
-0.03133387491106987,
-0.016598032787442207,
-0.024166734889149666,
-0.018735552206635475,
-0.07723043113946915,
0.021030990406870842,
0.015456692315638065,
0.01687437668442726,
0.0300190020352602,
-0.05013217404484749,
0.0036588276270776987,
0.006496668327599764,
0.017187539488077164,
0.04315245896577835,
-0.002182573080062866,
-0.05279916897416115,
0.020453298464417458,
-0.03152639791369438,
-0.07828381657600403,
-0.02152538299560547,
0.019562268629670143,
0.01152673177421093,
-0.028747934848070145,
0.01863146387040615,
-0.01676252670586109,
-0.038368333131074905,
0.011921810917556286,
0.02150656282901764,
0.04253345727920532,
-0.03855980560183525,
-0.07528091967105865,
-0.06304127722978592,
-0.01437277253717184,
-0.01689808815717697,
-0.0068383049219846725,
-0.07755491137504578,
0.0034732180647552013,
0.02899840660393238,
0.09675172716379166,
0.012400707229971886,
-0.041580140590667725,
-0.00854285154491663,
0.057800307869911194,
-0.002318449318408966,
-0.0091108288615942,
-0.01849929615855217,
0.00865713320672512,
0.00046792865032330155,
-0.0034348585177212954,
-0.07461090385913849,
0.07111960649490356,
0.052553486078977585,
0.04091620072722435,
-0.012045404873788357,
0.05723671615123749,
0.001551385736092925,
0.016890455037355423,
0.005141142290085554,
-0.053929924964904785,
0.002765072276815772,
0.07538403570652008,
-0.020041635259985924,
0.029988162219524384,
0.012934968806803226,
0.031395766884088516,
0.0329694002866745,
0.002862124005332589,
0.005682394839823246,
0.052434928715229034,
-0.06163078546524048,
-0.010714099742472172,
0.02170025184750557,
0.017617324367165565,
0.01194691751152277,
-0.01109731663018465,
-0.03693621605634689,
-0.005453037563711405,
-0.012906916439533234,
-0.01776396669447422,
0.051877424120903015,
-0.002957296557724476,
-0.003957546781748533,
0.005864301230758429,
-0.01906067132949829,
-0.020634809508919716,
-0.05662408098578453,
0.03330853208899498,
0.009944071993231773,
-0.04332501068711281,
0.015196828171610832,
0.007674847729504108,
0.01718941330909729,
-0.0222966056317091,
-0.04556560888886452,
0.020439619198441505,
-0.0049458215944468975,
-0.0206721480935812,
-0.03721732646226883,
0.03202011063694954,
-0.018354173749685287,
0.020809130743145943,
0.04470313712954521,
0.017468225210905075,
-0.04813665896654129,
-0.0329783596098423,
-0.004912251140922308,
-0.027358045801520348,
0.04656413570046425,
0.03736325725913048,
-0.004929762799292803,
-0.015801358968019485,
-0.009186670184135437,
-0.027392694726586342,
0.030779851600527763,
0.0074687618762254715,
0.02116992510855198,
0.06628617644309998,
0.017316743731498718,
0.034056734293699265,
0.058768197894096375,
0.013443615287542343,
0.03241067752242088,
-0.05934148281812668,
-0.045988887548446655,
-0.06674716621637344,
0.030945414677262306,
0.0388994961977005,
0.02643744833767414,
-0.05704905465245247,
0.024897627532482147,
0.03177228197455406,
0.04287707805633545,
0.02082756906747818,
0.0577346533536911,
-0.03579121083021164,
-0.04577239975333214,
-0.0032786871306598186,
0.040960170328617096,
-0.0030112352687865496,
0.0107151223346591,
0.00717995036393404,
-0.001414575963281095,
0.013963931240141392,
0.016498062759637833,
0.015491168946027756,
0.005158096086233854,
0.013730783946812153,
0.004196150694042444,
0.04771804064512253,
-0.052270546555519104,
0.05331020429730415,
-0.010154791176319122,
0.018909454345703125,
0.0003738410596270114,
-0.021157659590244293,
0.020005647093057632,
-0.010513385757803917,
-0.014302302151918411,
0.017680292949080467,
-0.032921209931373596,
-0.007405319716781378,
-0.05070485919713974,
0.010419624857604504,
-0.0035314082633703947,
0.01825338415801525,
-0.019071152433753014,
0.00032461094087921083,
-0.04317536950111389,
-0.040235504508018494,
0.01819372922182083,
0.013234931044280529,
0.02992960251867771,
-0.03205543011426926,
0.004752202425152063,
-0.017347143962979317,
-0.015758231282234192,
0.00993457529693842,
0.0243807602673769,
-0.03264126554131508,
0.016974201425909996,
-0.0061080846935510635,
-0.023847054690122604,
0.0753306895494461,
0.03407074138522148,
-0.01936470717191696,
0.016521457582712173,
0.001403828035108745,
-0.041861411184072495,
-0.027666717767715454,
0.01535310223698616,
0.023769833147525787,
-0.027081439271569252,
-0.0005709502147510648,
0.06363500654697418,
0.010789347812533379,
-0.016025584191083908,
-0.015169667080044746,
-0.05345236882567406,
-0.03234162926673889,
-0.01144347619265318,
-0.034472815692424774,
-0.0028186931740492582,
-0.03171209990978241,
0.029638534411787987,
0.04711363464593887,
-0.06774194538593292,
-0.04568224027752876,
-0.0454617403447628,
-0.0557565800845623,
0.015201801434159279,
0.003847684944048524,
0.04832296818494797,
-0.02367974817752838,
-0.05566278100013733,
0.056829504668712616,
0.04998569190502167,
-0.007038955111056566,
0.0009363961289636791,
-0.039909183979034424,
0.0069009894505143166,
-0.06743157655000687,
-0.02475651726126671,
0.021729128435254097,
-0.005247749388217926,
-0.037192560732364655,
0.035099223256111145,
0.02293158322572708,
0.012149576097726822,
0.03559805825352669,
0.012392964214086533,
0.02889850176870823,
0.02674436941742897,
0.02437981404364109,
0.03311444818973541,
0.038776785135269165,
-0.004874557256698608,
-0.0018389096949249506,
0.020949725061655045,
0.07985477149486542,
0.05448266118764877,
-0.0440235361456871,
0.04218849167227745,
-0.03479763865470886,
0.014833335764706135,
-0.04916340112686157,
0.019301000982522964,
-0.01839861273765564,
0.02980617806315422,
-0.03929124400019646,
0.0327574722468853,
0.04019111767411232,
-0.025502022355794907,
0.0015105213969945908,
0.03133879229426384,
-0.0018188095418736339,
0.0027200253680348396,
-0.006344659719616175,
-0.015746144577860832,
-0.035063840448856354,
0.04193032160401344,
-0.03627302125096321,
-0.014043071307241917,
0.03924572467803955,
0.03514331206679344,
0.010744556784629822,
0.002180099254474044,
-0.013646692968904972,
-0.007950568571686745,
-0.05236992985010147,
-0.006857037544250488,
0.0047172661870718,
0.04868699610233307,
0.041175130754709244,
0.017814138904213905,
-0.0046453471295535564,
0.028729626908898354,
0.01916731707751751,
0.000160300696734339,
-0.0587727315723896,
0.034802086651325226,
-0.04889332503080368,
-0.014608058147132397,
0.00407554442062974,
0.015756109729409218,
0.014416932128369808,
-0.02805459313094616,
-0.04016602784395218,
-0.00027789879823103547,
0.012598059140145779,
-0.05349835380911827,
0.013494054786860943,
-0.013894320465624332,
-0.06950991600751877,
-0.07816547900438309,
0.013919822871685028,
0.02724713832139969,
-0.05748248100280762,
0.036034245043992996,
0.018770774826407433,
-0.0005407643620856106,
0.005293147172778845,
0.009702335111796856,
-0.020125946030020714,
0.016255084425210953,
-0.010200705379247665,
0.041972238570451736,
-0.002736736787483096,
-0.011988712474703789,
0.014967011287808418,
0.014581585302948952,
0.04690653458237648,
0.000485105236293748,
-0.018584728240966797,
-0.030149221420288086,
-0.07046053558588028,
-0.019346216693520546,
-0.00882832333445549,
0.05949092283844948,
0.010725497268140316,
0.020687440410256386,
0.009980832226574421,
0.011607762426137924,
-0.011824574321508408,
0.007831420749425888,
0.019919605925679207,
0.01870383881032467,
0.004260459449142218,
-0.03870478644967079,
0.006311142351478338,
-0.025068296119570732,
0.005781683139503002,
0.005518620368093252,
0.008419879712164402,
0.001328498707152903,
-0.02785627171397209,
0.016191108152270317,
0.027144966647028923,
0.04295417666435242,
0.0029838255140930414,
0.02052254043519497,
-0.0038550642784684896,
0.025201117619872093,
0.008286344818770885,
0.01395498402416706,
0.03650612011551857,
0.05235244706273079,
0.015084018930792809,
-0.0088587561622262,
-0.0829690620303154,
-0.04549476131796837,
0.04397279769182205,
0.038767699152231216,
-0.02378811314702034,
-0.020202262327075005,
-0.061339929699897766,
-0.007768126204609871,
0.049542687833309174,
-0.028132230043411255,
0.051669225096702576,
-0.018631821498274803,
-0.03381700441241264,
-0.03966725245118141,
-0.05439992994070053,
-0.030193191021680832,
0.011297160759568214,
0.001028670696541667,
0.0244987141340971,
-0.028987234458327293,
-0.027182191610336304,
0.017671260982751846,
-0.03089272603392601,
0.03170254826545715,
0.04249812662601471,
0.011533978395164013,
0.019914524629712105,
0.015849672257900238,
0.02942747436463833,
-0.025001490488648415,
-0.0744730606675148,
0.019102491438388824,
-0.0006690575391985476,
0.019857708364725113,
0.014325259253382683,
-0.020107589662075043,
-0.04922151938080788,
0.02274942584335804,
0.009623441845178604,
0.02865639328956604,
0.011600316502153873,
-0.024262811988592148,
0.06305766850709915,
0.00848188903182745,
-0.015420429408550262,
0.02904200740158558,
0.03127923980355263,
0.021557915955781937,
-0.014544591307640076,
-0.01323913224041462,
0.013645521365106106,
0.0006639919010922313,
0.010387076064944267,
-0.024870850145816803,
0.03445223718881607,
-0.021479221060872078,
0.08888847380876541,
-0.034747760742902756,
-0.010875536128878593,
0.009995399974286556,
-0.03730195388197899,
0.02919047884643078,
0.01898094266653061,
-0.027239520102739334,
-0.03775491565465927,
-0.02628239616751671,
0.00911274366080761,
-0.02961134910583496,
-0.046586863696575165,
0.0037112957797944546,
-0.0124987056478858,
-0.01336569432169199,
0.04579766467213631,
0.007833748124539852,
-0.004466070793569088,
-0.016219506040215492,
-0.02443743497133255,
0.005701462272554636,
-0.03883097320795059,
0.044369082897901535,
-0.004660162143409252,
-0.011940507218241692,
0.00692715821787715,
-0.011387829668819904,
-0.003206599038094282,
0.015384134836494923,
-0.018290990963578224,
-0.022236516699194908,
-0.06258224695920944,
0.02511606737971306,
0.023232195526361465,
0.0010730201611295342,
-0.07181515544652939,
-0.07708130031824112,
0.03610242158174515,
-0.0035865360405296087,
-0.0013141895178705454,
-0.024520214647054672,
-0.02964363805949688,
-0.013797745108604431,
-0.03518417477607727,
-0.006904357112944126,
0.06282942742109299,
-0.03913262113928795,
0.0020536831580102444,
-0.014392471872270107,
0.031501419842243195,
0.03605036437511444,
0.0008317242609336972,
0.029806211590766907,
0.032091423869132996,
-0.06768544763326645,
-0.020080864429473877,
-0.013102992437779903,
0.030625414103269577,
-0.011951813474297523,
-0.001429455354809761,
-0.00619135657325387,
-0.0026314337737858295,
0.05015895143151283,
-0.020111342892050743,
-0.03219553455710411,
0.02924780547618866,
-0.015225875191390514,
-0.006321773398667574,
-0.008197001181542873,
-0.0035406704992055893,
0.017694931477308273,
0.037556733936071396,
-0.0008435817435383797,
-0.028144804760813713,
-0.05852736160159111,
-0.0112580806016922,
0.0294982697814703,
0.0178056713193655,
0.018061330541968346,
-0.0363248772919178,
0.04939199239015579,
-0.04282130300998688,
-0.013183209113776684,
0.030916815623641014,
-0.02393011748790741,
0.01521286554634571,
0.005891024135053158,
0.0092111025005579,
0.012521331198513508,
-0.009958989918231964,
-0.03230775147676468,
-0.046290021389722824,
-0.050933826714754105,
0.025496354326605797,
0.053418636322021484,
0.033662181347608566,
0.03284227475523949,
0.026333793997764587,
-0.02104763500392437,
-0.006468751467764378,
-0.02832815609872341,
-0.02736295387148857,
0.017484741285443306,
-0.009429494850337505,
0.002090367255732417,
-0.006376330740749836,
0.0035802714992314577,
0.02303966134786606,
0.009846974164247513,
-0.021017521619796753,
0.01677802950143814,
0.020680690184235573,
-0.0024403659626841545,
0.008574453182518482,
0.028341973200440407,
-0.04322222247719765,
0.015534293837845325,
-0.016342556104063988,
0.023293692618608475,
0.01956012472510338,
-0.0242842435836792,
0.02487797848880291,
0.062350060790777206,
0.03105550818145275,
-0.015681704506278038,
-0.0226716510951519,
-0.03247033432126045,
0.03658629208803177,
0.01284591481089592,
-0.004655327647924423,
-0.0019378855358809233,
0.039685577154159546,
0.020293058827519417,
-0.01947811432182789,
-0.003544878913089633,
-0.007648719009011984,
-0.014985411427915096,
0.011417829431593418,
-0.02129211463034153,
-0.025369441136717796,
0.08122008293867111,
0.0351870022714138,
0.01746184192597866,
-0.007002965547144413,
-0.011317692697048187,
0.03695652633905411,
0.05306487902998924,
0.045886483043432236,
-0.008122324012219906,
0.07600850611925125,
-0.015574044547975063,
0.031208869069814682,
-0.038192082196474075,
-0.00874515064060688,
0.09995552152395248,
0.03654903545975685,
0.021033136174082756,
-0.04168073832988739,
-0.007829112000763416,
-0.04793014004826546,
0.028506111353635788,
-0.024296466261148453,
-0.0013393897097557783,
-0.008429450914263725,
-0.01879320666193962,
0.01618252880871296,
0.023130029439926147,
-0.013786152005195618,
0.0008698569727130234,
0.051454611122608185,
-0.011911541223526001,
0.006214358378201723,
-0.0014921189285814762,
0.03341207653284073,
-0.01562831923365593,
0.022912120446562767,
-0.05894597992300987,
0.027493298053741455,
-0.009697506204247475,
0.013226984068751335,
-0.018556544557213783,
-0.02133360505104065,
0.014209548942744732,
-0.018015827983617783,
-0.055559370666742325,
-0.0060575297102332115,
-0.009911496192216873,
-0.021714195609092712,
-0.05972762033343315,
0.013370419852435589,
0.03188148885965347,
0.021160708740353584,
0.020535336807370186,
0.01442799437791109,
0.03005961701273918,
-0.022240709513425827,
0.04359392821788788,
0.017092566937208176,
-0.022302614524960518,
0.020173199474811554,
-0.04647793248295784,
0.04240605980157852,
-0.03926844894886017,
0.013097377493977547,
0.01772119849920273,
-0.011427844874560833,
0.04047564044594765,
-0.08112917095422745,
-0.02452428825199604,
-0.009309661574661732,
0.0004874127625953406,
0.004918969236314297,
0.022951524704694748,
-0.02704588696360588,
0.015375018119812012,
0.012504778802394867,
-0.02749486267566681,
0.002715436741709709,
0.004066574852913618,
0.01133703999221325,
-0.02815379947423935,
0.06791287660598755,
-0.007870495319366455,
-0.04196569696068764,
-0.03030332922935486,
-0.03552313521504402,
0.000643704435788095,
0.009335007518529892,
0.03324253484606743,
0.027204222977161407,
0.022080259397625923,
-0.013019380159676075,
-0.0262907687574625,
0.012511574663221836,
-0.06382305175065994,
0.014839517883956432,
0.036291226744651794,
-0.029405752196907997,
-0.026316693052649498,
-0.0032195281237363815,
-0.0037088932003825903,
0.053307101130485535,
-0.03194224834442139,
0.022161463275551796,
-0.006528893485665321,
0.03909536078572273,
0.027372591197490692,
-0.022669674828648567,
-0.02418096363544464,
0.028084052726626396,
-0.01551514957100153,
0.011375509202480316,
0.016036609187722206,
0.005831889342516661,
0.010305007919669151,
0.02852918766438961,
-0.07586747407913208,
0.03116672858595848,
-0.010652047581970692,
0.0017191370716318488,
-0.002795228036120534,
0.002402672776952386,
0.0019469691906124353,
0.0002810636069625616,
0.010042283684015274,
-0.01773834228515625,
0.012978658080101013,
-0.0284146498888731,
0.027849962934851646,
-0.009912874549627304,
-0.014260785654187202,
-0.02432558871805668,
-0.005720163229852915,
-0.02999775856733322,
0.0036705578677356243,
-0.040464919060468674,
0.005989889148622751,
-0.08995823562145233,
-0.050363939255476,
-0.010635451413691044,
0.03355174511671066,
0.03033187985420227,
0.04245918616652489,
-0.007822754792869091,
0.012495859526097775,
-0.001309789251536131,
0.030918823555111885,
-0.008885837160050869,
0.01646466553211212,
0.014114418998360634,
0.01876995339989662,
0.02488466165959835,
-0.035906169563531876,
-0.05292569100856781,
0.04974013939499855,
0.007940259762108326,
0.010227478109300137,
0.01594439335167408,
0.03604097664356232,
0.018915478140115738,
-0.023237448185682297,
-0.015099416486918926,
0.007732365746051073,
0.01421742420643568,
0.020363353192806244,
0.0018384805880486965,
0.008452457375824451,
-0.05435929447412491,
0.01238942239433527,
-0.023287279531359673,
0.02451252192258835,
0.007962350733578205,
-0.0102358628064394,
-0.007206429727375507,
0.040269095450639725,
-0.026819292455911636,
-0.05068613588809967,
0.004602556116878986,
0.01270356960594654,
-0.022648939862847328,
0.05293823778629303,
0.013368834741413593,
0.017859701067209244,
0.05119001865386963,
-0.003503301413729787,
-0.007358997594565153,
0.009050027467310429,
-0.022452982142567635,
-0.06698868423700333,
-0.0049421717412769794,
0.006930530071258545,
0.031385667622089386,
0.020543204620480537,
-0.03433086723089218,
-0.04052407294511795,
0.03842802718281746,
-0.10071133077144623,
-0.003164128167554736,
-0.020894458517432213,
0.01641007885336876,
-0.010275919921696186,
-0.02158561907708645,
-0.01521090418100357,
0.022936930879950523,
0.006615076679736376,
0.06073160842061043,
0.0068655917420983315,
-0.017981089651584625,
-0.016827311366796494,
-0.05316220968961716,
-0.04150611162185669,
0.04325835034251213,
0.030435457825660706,
-0.02316879667341709,
0.040357861667871475,
-0.016687050461769104,
0.018701182678341866,
0.023242220282554626,
0.004899758379906416,
0.010618156753480434,
-0.02504194900393486,
0.016941849142313004,
0.007601144257932901,
0.03961743414402008,
0.009398282505571842,
-0.019915154203772545,
-0.01926834136247635,
-0.01886911503970623,
-0.0010849145473912358,
0.00034269047318957746,
-0.014153064228594303,
0.001912270556204021,
-0.01490699127316475,
-0.0352788046002388,
-0.022908000275492668,
0.01478883158415556,
-0.04540259391069412,
-0.04061048477888107,
0.008588054217398167,
0.026146452873945236,
0.01482494454830885,
-0.035724006593227386,
0.00008427981083514169,
-0.0330185703933239,
-0.01710738055408001,
0.04416671022772789,
-0.016547763720154762,
0.022618195042014122,
0.014834336005151272,
0.0037046533543616533,
-0.04175815358757973,
0.041548434644937515,
0.027473192662000656,
-0.03879455849528313,
-0.0889865830540657,
-0.013419265858829021,
-0.023295560851693153,
-0.021541599184274673,
0.0065988763235509396,
-0.028446931391954422,
-0.02475164458155632,
0.026338674128055573,
0.02761770784854889,
-0.00729132117703557,
0.0015255860053002834,
-0.05970064178109169,
-0.013246456161141396,
-0.02083362266421318,
0.06155969575047493,
-0.014935208484530449,
-0.0504772923886776,
-0.025903712958097458,
-0.03651135787367821,
-0.020535124465823174,
0.006355985999107361,
0.09388689696788788,
-0.0013251890195533633,
-0.009049540385603905,
0.07109514623880386,
-0.005851629190146923,
0.004656495992094278,
-0.0820515900850296,
0.0357075035572052,
0.02796538546681404,
0.0462762825191021,
0.027121588587760925,
0.012430833652615547,
-0.010596901178359985,
0.007094850763678551,
-0.011747158132493496,
0.015007248148322105,
0.006446448154747486,
-0.009102260693907738,
-0.05144773796200752,
0.045636557042598724,
0.04438083991408348,
-0.02736102044582367,
0.027621394023299217,
-0.013813566416501999,
0.021122435107827187,
-0.013471640646457672,
-0.019637852907180786,
-0.03794867545366287,
0.019593801349401474,
-0.024291519075632095,
0.012981805950403214,
-0.03769078850746155,
0.013400251977145672,
0.03777167946100235,
-0.03945979103446007,
-0.026798084378242493,
0.031206559389829636,
-0.013319582678377628,
-0.01090829074382782,
0.061676543205976486,
-0.04993439465761185,
0.022585198283195496,
-0.009721938520669937,
0.020226581022143364,
0.0225237850099802,
0.00208128965459764,
-0.00989449955523014,
0.022112609818577766,
0.008133305236697197,
-0.037330254912376404,
-0.01295995619148016,
0.036743659526109695,
-0.008810030296444893,
0.004869773518294096,
0.019165830686688423,
-0.0003860659780912101,
-0.027117617428302765,
0.0010704263113439083,
0.03864142671227455,
-0.015159073285758495,
-0.050227146595716476,
0.03365575149655342,
-0.007631551008671522,
0.05715976655483246,
-0.014116041362285614,
0.018723197281360626,
0.017930656671524048,
0.009334303438663483,
0.014211142435669899,
0.054585423320531845,
0.003635354805737734,
0.017504369840025902,
-0.009080409072339535,
-0.03550131991505623,
-0.004692780319601297,
-0.02632649801671505,
0.05753154680132866,
-0.012706526555120945,
0.03897787630558014,
0.033137302845716476,
-0.01849324442446232,
-0.0045826854184269905,
-0.03224140778183937,
-0.038963433355093,
-0.05008091405034065,
0.009055277332663536,
0.01963689737021923,
0.024698888882994652,
-0.031221408396959305,
0.01548770722001791,
0.011314671486616135,
0.060514066368341446,
-0.0547194629907608,
-0.005878884810954332,
-0.00005928858809056692,
0.02350231446325779,
0.023750003427267075,
0.007860899902880192
] |
<p>Classical thermodynamics leads one to believe that if energy is transferred, and the universe is heading for maximum entropy, then back extrapolating to moments before the big bang, one could find a definitive answer of the total amount of energy of the system(universe) contains.</p>
<p>However I can't find this question explored without running into dark matter threads.</p> | 1,449 | [
-0.01794508844614029,
-0.0263235941529274,
-0.00534478947520256,
-0.01609676517546177,
0.03580965846776962,
0.03351392224431038,
-0.0417407751083374,
-0.024218933656811714,
-0.011690948158502579,
-0.03518645465373993,
-0.01148228533565998,
0.015816593542695045,
0.0048610493540763855,
0.03482608124613762,
0.009360016323626041,
-0.002356067067012191,
-0.009282042272388935,
-0.006505999248474836,
0.014262276701629162,
-0.03558777645230293,
0.011613433249294758,
0.03607794642448425,
-0.002119932323694229,
-0.01861398108303547,
-0.038474734872579575,
0.034560225903987885,
0.01573694869875908,
-0.0006529995007440448,
0.015922557562589645,
0.06635487824678421,
0.0013468032702803612,
-0.04314381256699562,
0.022440429776906967,
0.055269014090299606,
0.034808650612831116,
-0.0005991815705783665,
-0.016945378854870796,
-0.041775040328502655,
-0.01090320385992527,
0.012225398793816566,
-0.09440383315086365,
-0.03821956366300583,
0.0032727024517953396,
0.030748333781957626,
-0.05460100993514061,
0.02420353703200817,
0.004892037250101566,
0.006318954285234213,
0.044312670826911926,
-0.04720905050635338,
0.05542620271444321,
0.010335796512663364,
0.05459967628121376,
0.013797877356410027,
-0.03363686427474022,
-0.004964547231793404,
0.08022478222846985,
0.04851395636796951,
0.023194026201963425,
-0.04434569180011749,
-0.04392059147357941,
0.04030575230717659,
-0.007215780671685934,
-0.0046373954974114895,
-0.010697940364480019,
0.043405383825302124,
-0.003089956706389785,
-0.014834031462669373,
0.040985383093357086,
0.029330305755138397,
-0.0012825437588617206,
0.03100132942199707,
0.08104526996612549,
0.019227540120482445,
0.010757464915513992,
0.008612576872110367,
0.02781250700354576,
-0.010628138668835163,
0.028321996331214905,
0.043130047619342804,
-0.009229789488017559,
-0.012047357857227325,
0.06569275259971619,
0.08367642760276794,
0.01571652851998806,
0.010632569901645184,
0.029054764658212662,
-0.02959519438445568,
0.009600283578038216,
0.05196315795183182,
-0.003447610652074218,
0.014149033464491367,
0.03346053883433342,
-0.01832079328596592,
-0.04099027067422867,
0.033060088753700256,
-0.02668876200914383,
0.03994566947221756,
0.012932179495692253,
-0.03847883269190788,
0.0506993792951107,
0.010397090576589108,
0.009177201427519321,
0.06297042965888977,
0.019761281087994576,
0.002016570419073105,
-0.08218502253293991,
0.003992734011262655,
-0.014130407012999058,
0.00915402453392744,
-0.034073472023010254,
-0.007317390758544207,
0.00873444601893425,
0.0033532441593706608,
-0.002483105519786477,
-0.01994326151907444,
0.0008372709853574634,
-0.042561888694763184,
0.06807366013526917,
0.05050485581159592,
0.015482415445148945,
0.0035947796422988176,
-0.002943439409136772,
-0.03953390568494797,
-0.04383956268429756,
0.019435973837971687,
0.04729921370744705,
-0.005549603141844273,
-0.05378897860646248,
0.042169827967882156,
-0.024952322244644165,
-0.006390796042978764,
0.0017169199418276548,
-0.01684206910431385,
0.026672901585698128,
-0.032267678529024124,
-0.050599027425050735,
-0.07410117238759995,
0.026477716863155365,
-0.001458271057344973,
-0.035707488656044006,
-0.04892164096236229,
-0.005600804463028908,
0.02963547222316265,
0.05042804777622223,
-0.013591866008937359,
-0.0028756274841725826,
-0.04803084954619408,
0.03914054483175278,
0.007730003912001848,
-0.028208822011947632,
-0.03230058401823044,
0.022662101313471794,
-0.03977343067526817,
0.011519265361130238,
-0.07470687478780746,
0.020362289622426033,
0.04492814838886261,
-0.015089035034179688,
-0.009192436002194881,
0.01986234448850155,
-0.02118891105055809,
0.007204667665064335,
-0.011672343127429485,
-0.01070477720350027,
-0.04604817554354668,
0.10301852971315384,
0.041679490357637405,
0.008669672533869743,
0.007918187417089939,
0.019205333665013313,
0.009343812242150307,
0.033583320677280426,
0.002309744479134679,
0.030656641349196434,
-0.05503914877772331,
-0.03005736507475376,
-0.032664988189935684,
0.01562778651714325,
-0.006201957818120718,
-0.006399067118763924,
-0.008833031170070171,
0.01237844955176115,
-0.009932087734341621,
0.04288691282272339,
0.020843060687184334,
-0.015282961539924145,
-0.03742080554366112,
-0.0020026376005262136,
-0.03670254349708557,
-0.010371390730142593,
-0.04381981119513512,
0.005211822222918272,
0.00561934569850564,
-0.0019558558706194162,
-0.005551035515964031,
0.01552247442305088,
0.05759372189640999,
-0.047968462109565735,
-0.022181140258908272,
0.021317537873983383,
0.019431615248322487,
-0.0022253363858908415,
0.011653981171548367,
0.03169485181570053,
0.03685310482978821,
0.06180475279688835,
0.005364513024687767,
-0.0240615401417017,
0.013133984059095383,
-0.0803917720913887,
0.01915081776678562,
-0.01806330867111683,
0.026196585968136787,
-0.004825970157980919,
-0.0026482834946364164,
0.017927061766386032,
0.012041445821523666,
0.05154773220419884,
0.008601458743214607,
-0.008085483685135841,
0.08556909114122391,
0.016648638993501663,
0.026931164786219597,
-0.03257492557168007,
0.04384880140423775,
-0.013651284389197826,
0.008857334032654762,
-0.021939530968666077,
-0.025691842660307884,
-0.05736204609274864,
-0.012353564612567425,
0.021533219143748283,
0.0773506611585617,
-0.021945947781205177,
0.004672708921134472,
0.04718172922730446,
0.007829691283404827,
0.006383506581187248,
-0.01286628283560276,
-0.02314915508031845,
-0.02401644177734852,
-0.028876252472400665,
0.018359698355197906,
0.010345741175115108,
0.02919289469718933,
0.038576390594244,
0.013715081848204136,
-0.012551351450383663,
-0.01035146601498127,
-0.00017070534522645175,
0.03426709398627281,
0.04075746610760689,
0.006625458598136902,
-0.019483542069792747,
-0.05904999375343323,
0.019688386470079422,
-0.03262714669108391,
0.030758436769247055,
0.024022093042731285,
0.020803989842534065,
0.010540026240050793,
-0.041025903075933456,
-0.023929787799715996,
-0.027655990794301033,
0.012376411817967892,
-0.006392709910869598,
-0.005446288734674454,
0.04267226159572601,
-0.03521575406193733,
0.05545354261994362,
0.012692934833467007,
0.006816514767706394,
-0.020837387070059776,
-0.0216264296323061,
0.014464559964835644,
-0.0033673604484647512,
0.008559366688132286,
-0.058156806975603104,
-0.031148351728916168,
-0.005437827203422785,
-0.012639297172427177,
-0.013380259275436401,
0.030020475387573242,
-0.051185548305511475,
0.009721244685351849,
-0.026783501729369164,
-0.031026262789964676,
0.021211713552474976,
-0.030932284891605377,
0.03704822063446045,
0.048662301152944565,
-0.009641219861805439,
-0.027404887601733208,
0.010858738794922829,
-0.0006289268494583666,
-0.035374291241168976,
-0.04495427757501602,
0.027827704325318336,
0.07445648312568665,
-0.010397309437394142,
-0.07959666103124619,
-0.014620291069149971,
-0.057990364730358124,
-0.061057087033987045,
-0.014988545328378677,
0.0074247936718165874,
0.020786847919225693,
-0.017042461782693863,
0.07256212830543518,
0.014039221219718456,
-0.05540359765291214,
-0.014746027067303658,
-0.06993047893047333,
-0.07525563985109329,
0.045119188725948334,
-0.022356202825903893,
0.02090509980916977,
-0.012266794219613075,
-0.03578009456396103,
0.039363887161016464,
0.021319270133972168,
-0.023929186165332794,
-0.0022876604925841093,
-0.018933268263936043,
0.035018790513277054,
-0.005196077283471823,
-0.013310406357049942,
-0.006738389376550913,
0.031085917726159096,
0.04986071586608887,
0.018626635894179344,
0.05688688904047012,
-0.025526586920022964,
-0.019234420731663704,
-0.017827460542321205,
0.03130815923213959,
-0.020164204761385918,
0.010490610264241695,
0.03964458405971527,
-0.00911262258887291,
-0.034197043627500534,
0.0330793634057045,
-0.01180923730134964,
0.04110544174909592,
-0.002463458338752389,
-0.038822468370199203,
0.06410906463861465,
0.03117523342370987,
0.013562214560806751,
-0.030256660655140877,
0.0066538783721625805,
-0.027071863412857056,
0.0035773608833551407,
0.03605391085147858,
0.044202324002981186,
0.04829765856266022,
0.012575226835906506,
0.004937011282891035,
0.020571500062942505,
0.029469961300492287,
0.006007355637848377,
-0.0021648905239999294,
-0.023447899147868156,
0.0028435008134692907,
0.008751620538532734,
0.01513001974672079,
-0.02197207696735859,
0.024874882772564888,
0.01818772964179516,
0.028128117322921753,
-0.00376537861302495,
-0.010995692573487759,
-0.0050988332368433475,
-0.0630125030875206,
-0.024579335004091263,
-0.02425478771328926,
0.03647090494632721,
0.01947503350675106,
0.05805616453289986,
0.016969267278909683,
0.018508445471525192,
0.00819331780076027,
-0.00794608797878027,
-0.09756112098693848,
0.010251705534756184,
-0.04566064476966858,
0.007585297338664532,
0.00992927048355341,
0.0032603400759398937,
0.018010413274168968,
-0.03687360882759094,
0.015034683048725128,
-0.004046826623380184,
-0.01007467694580555,
-0.0645376518368721,
-0.00512551236897707,
-0.045386455953121185,
-0.032436203211545944,
0.017810620367527008,
0.02285081148147583,
0.06068751588463783,
-0.027975868433713913,
0.002282520988956094,
0.02572553977370262,
-0.029754066839814186,
-0.006822609808295965,
0.007422615308314562,
0.03000541776418686,
-0.011709069833159447,
0.03116319142282009,
0.01982339285314083,
0.016572441905736923,
-0.03784869238734245,
0.02051188237965107,
0.0126848379150033,
0.022139135748147964,
0.013325606472790241,
-0.04120587930083275,
-0.030422883108258247,
-0.002921469509601593,
-0.005725410766899586,
0.03552765026688576,
-0.0006711701862514019,
0.006728452164679766,
0.06111326813697815,
0.011746750213205814,
0.017769431695342064,
-0.024932701140642166,
0.031302135437726974,
0.06697645038366318,
-0.03207430988550186,
-0.05107484757900238,
-0.026427648961544037,
-0.0038534370250999928,
-0.011999526061117649,
0.007985761389136314,
0.00012199129560030997,
-0.010069296695291996,
-0.02247520163655281,
0.020043158903717995,
-0.019671831279993057,
0.02899944595992565,
-0.03347235172986984,
-0.03826478123664856,
0.013953473418951035,
0.046847227960824966,
-0.0128795700147748,
-0.0034616654738783836,
0.040711432695388794,
0.013587660156190395,
0.042213864624500275,
-0.02198987826704979,
0.005038590170443058,
-0.047953054308891296,
-0.012865844182670116,
0.03137790784239769,
0.048387642949819565,
0.0053999279625713825,
-0.014631731435656548,
-0.049669671803712845,
-0.019825585186481476,
0.04082063212990761,
-0.02958693914115429,
0.03882433846592903,
0.005353742744773626,
0.017446955665946007,
0.01555269118398428,
-0.04308973625302315,
-0.009424119256436825,
0.02612004242837429,
-0.006499289534986019,
0.002421123906970024,
0.003949621692299843,
0.029880331829190254,
-0.034726858139038086,
0.03223714604973793,
0.01867746189236641,
0.024228535592556,
-0.007829461246728897,
-0.00773370498791337,
-0.002165172016248107,
0.030633430927991867,
-0.02106703631579876,
-0.06281033903360367,
0.008448479697108269,
-0.02064608223736286,
-0.06127983704209328,
0.025943294167518616,
-0.048931337893009186,
-0.05129808932542801,
0.02439950220286846,
-0.006752622779458761,
-0.016376841813325882,
0.0049323649145662785,
-0.039768435060977936,
0.06344002485275269,
0.029356248676776886,
0.017062805593013763,
0.062058161944150925,
0.05055651068687439,
-0.0010251825442537665,
0.0269534420222044,
-0.02572840265929699,
0.04014190286397934,
-0.04891756922006607,
-0.003081729169934988,
-0.023224515840411186,
0.015038243494927883,
-0.018344223499298096,
0.016523610800504684,
-0.0035054199397563934,
0.029395554214715958,
0.026712564751505852,
-0.04326768219470978,
-0.01278647966682911,
0.00499032624065876,
0.03879806771874428,
0.020141854882240295,
-0.019176391884684563,
0.014413777738809586,
0.015251158736646175,
-0.010640604421496391,
0.03529968857765198,
0.035704758018255234,
0.0018694926984608173,
0.02283746749162674,
-0.0047575607895851135,
0.025691289454698563,
-0.006921738851815462,
-0.010713377967476845,
0.04388616234064102,
0.013810132630169392,
0.015498332679271698,
-0.005401741713285446,
0.03750893846154213,
0.02649914287030697,
-0.07635676115751266,
-0.03654821217060089,
0.006711768452078104,
-0.033853329718112946,
-0.005422128364443779,
-0.018332714214920998,
0.00536341080442071,
-0.00868131686002016,
0.022737499326467514,
-0.06201773136854172,
-0.018385116010904312,
0.027476007118821144,
0.02518175169825554,
0.002906372770667076,
-0.03601136803627014,
0.01243459340184927,
-0.04945823550224304,
0.019853191450238228,
-0.011282037943601608,
0.01332402229309082,
-0.006001426838338375,
0.017724577337503433,
-0.011518782004714012,
-0.012697448953986168,
0.0016530752182006836,
-0.008175795897841454,
-0.027759162709116936,
0.02777353674173355,
0.033439043909311295,
-0.015595171600580215,
0.018495498225092888,
0.03059384971857071,
-0.02123580127954483,
-0.014314128085970879,
0.033703140914440155,
0.006274717394262552,
0.046611666679382324,
-0.01504930667579174,
-0.019813045859336853,
0.0432422049343586,
-0.01453473325818777,
-0.016846980899572372,
-0.006998895201832056,
0.0361744649708271,
-0.02293340489268303,
0.004822123795747757,
-0.007724034134298563,
-0.023759661242365837,
0.011719245463609695,
-0.03808663412928581,
0.049165431410074234,
-0.0024280999787151814,
-0.005296606104820967,
0.0008665439090691507,
0.03696935251355171,
0.05642542615532875,
-0.07320248335599899,
0.008373964577913284,
-0.0027942380402237177,
0.005569112952798605,
-0.0029392519500106573,
0.0427456833422184,
0.0028075643349438906,
0.004541924223303795,
-0.03042263351380825,
-0.05263523384928703,
-0.04962971806526184,
-0.015950525179505348,
0.042298026382923126,
-0.005507275462150574,
0.04478290677070618,
-0.01678331010043621,
-0.0019946538377553225,
0.011655434966087341,
-0.03065057098865509,
0.00425892136991024,
0.039886847138404846,
0.0024400907568633556,
0.023939669132232666,
-0.03432423621416092,
-0.05033290013670921,
0.027747904881834984,
0.0044192601926624775,
-0.06378748267889023,
0.019404573366045952,
0.004678031429648399,
0.010847819037735462,
0.0525716096162796,
-0.06717336922883987,
-0.034222446382045746,
0.007985545322299004,
-0.04982580244541168,
0.04741279035806656,
0.008217026479542255,
-0.018394947052001953,
0.020473051816225052,
-0.0010814963607117534,
0.0024219651240855455,
-0.052289653569459915,
-0.013478465378284454,
-0.04231440648436546,
-0.01344760786741972,
0.010163720697164536,
0.04938540980219841,
0.008033380843698978,
0.00979494210332632,
0.002618455560877919,
-0.023431766778230667,
-0.010589244775474072,
0.016452552750706673,
-0.0657108724117279,
-0.022185470908880234,
-0.01589847542345524,
-0.060541655868291855,
0.039829071611166,
0.0069120596162974834,
0.0007401654147543013,
0.01052934117615223,
-0.027554810047149658,
-0.011076681315898895,
-0.033838167786598206,
0.026581713929772377,
0.02218443714082241,
0.092128224670887,
-0.021794667467474937,
0.033279526978731155,
-0.03813928738236427,
0.046044617891311646,
0.11866327375173569,
0.0541006363928318,
0.010041654109954834,
-0.040134504437446594,
0.012903552502393723,
-0.04109302908182144,
-0.008710496127605438,
-0.007147439289838076,
0.008613633923232555,
-0.01423475332558155,
0.003987279254943132,
0.030196363106369972,
0.027896439656615257,
-0.005001172423362732,
-0.026342488825321198,
0.027022438123822212,
-0.047417376190423965,
-0.0027778332587331533,
0.042024388909339905,
0.04308156669139862,
-0.009421441704034805,
-0.012030689045786858,
-0.04279642179608345,
-0.007141229696571827,
0.016185220330953598,
0.0262170247733593,
0.0018480061553418636,
-0.03498890995979309,
-0.014043868519365788,
-0.032624829560518265,
-0.030208859592676163,
0.0009309775778092444,
0.01685955934226513,
-0.027104588225483894,
-0.012004159390926361,
-0.0068285660818219185,
0.04157625511288643,
0.019009722396731377,
-0.007355400826781988,
0.028670819476246834,
0.018670260906219482,
0.04599960893392563,
-0.006925801280885935,
-0.012303744442760944,
-0.010786169208586216,
-0.024091649800539017,
-0.0072824773378670216,
0.034187719225883484,
-0.03243935853242874,
0.0058219823986291885,
0.0029210331849753857,
0.011423707008361816,
-0.0005977835971862078,
-0.012997480109333992,
0.009996914304792881,
0.021315868943929672,
0.033067770302295685,
-0.02430560812354088,
-0.03565624728798866,
-0.010700015351176262,
0.010863231495022774,
-0.00963975116610527,
0.04348067566752434,
-0.048203278332948685,
0.008738831616938114,
0.02065722830593586,
-0.012801367789506912,
0.04526952654123306,
-0.014802406542003155,
-0.02171511948108673,
0.0023250216618180275,
-0.0121866250410676,
-0.07231762260198593,
-0.011238940060138702,
0.009411447681486607,
-0.0005717662861570716,
0.01679890789091587,
0.021273409947752953,
0.004735174123197794,
-0.04317860305309296,
-0.022654782980680466,
0.015737004578113556,
-0.01905687339603901,
-0.00961216539144516,
-0.013810203410685062,
0.007071132771670818,
0.006704321596771479,
0.06975657492876053,
0.014805097132921219,
0.0008766406681388617,
0.024505481123924255,
0.021086018532514572,
0.03688466548919678,
-0.01824416220188141,
0.010098502039909363,
-0.020124787464737892,
-0.039923425763845444,
0.0010174989001825452,
-0.019225412979722023,
0.03212139382958412,
0.00097300746710971,
0.00550351245328784,
-0.00011214676487725228,
0.015663813799619675,
-0.006134714465588331,
0.03704822063446045,
0.022702191025018692,
-0.03192560747265816,
-0.0475764162838459,
-0.015045414678752422,
-0.016851214691996574,
-0.0011595464311540127,
-0.019071316346526146,
-0.03757293522357941,
0.0020951770711690187,
-0.002729740459471941,
0.01682473160326481,
-0.032471057027578354,
0.0261475071310997,
-0.023036163300275803,
0.019718067720532417,
-0.054534655064344406,
-0.017261741682887077,
-0.03483491390943527,
-0.005401736591011286,
0.019170939922332764,
-0.005407983902841806,
-0.010859612375497818,
0.06134340539574623,
0.0032711722888052464,
-0.06014922633767128,
0.023164071142673492,
0.010874510742723942,
-0.022247932851314545,
-0.04748902469873428,
0.0045325011014938354,
0.011070650070905685,
0.058321863412857056,
-0.012917506508529186,
0.008636620827019215,
0.05395662412047386,
-0.026239819824695587,
-0.027204999700188637,
0.022864490747451782,
-0.017740443348884583,
0.020394792780280113,
0.03777390345931053,
-0.01226852834224701,
-0.07875698804855347,
0.057449448853731155,
-0.029351573437452316,
-0.011797262355685234,
0.04980329051613808,
-0.0018784614512696862,
-0.0008817859925329685,
0.0022127325646579266,
0.03019418753683567,
-0.01605127938091755,
-0.01015070453286171,
0.03967053070664406,
-0.019628001376986504,
-0.007932009175419807,
-0.01922721043229103,
0.011521408334374428,
-0.054977741092443466,
-0.007418692111968994,
0.021455252543091774,
-0.0011451677419245243,
0.01870267279446125,
0.0563524104654789,
-0.039711013436317444,
0.04373233765363693,
0.04633864015340805,
-0.018174609169363976,
-0.08529601991176605,
0.003488855669274926,
-0.006327521521598101,
-0.02777528576552868,
0.034799229353666306,
-0.032432738691568375,
0.04719238355755806,
0.0009698232752270997,
-0.0692514181137085,
0.026432760059833527,
-0.03796340897679329,
-0.0012779150856658816,
-0.02524537406861782,
0.02403111197054386,
-0.0241987444460392,
0.047374315559864044,
0.07124681770801544,
0.06046255677938461,
0.007147651165723801,
0.020903008058667183,
-0.018625758588314056,
-0.011423974297940731,
-0.006516734603792429,
0.01941887103021145,
-0.005804513115435839,
0.02170148864388466,
0.05517304688692093,
-0.02951565384864807,
-0.03519118204712868,
0.013135678134858608,
0.0055973827838897705,
0.0024960224982351065,
-0.025923065841197968,
-0.001779066282324493,
0.023112211376428604,
0.05583968758583069,
0.035594839602708817,
-0.02631954476237297,
0.016717616468667984,
0.02470458298921585,
0.00865421537309885,
0.02085970714688301,
-0.022442298009991646,
-0.010403807274997234,
-0.00956614688038826,
-0.016788499429821968,
-0.04946624115109444,
0.04547273740172386,
0.006688603200018406,
-0.0019318261183798313,
0.027274200692772865,
0.013134010136127472,
0.00048408235306851566,
-0.029561709612607956,
-0.010066593065857887,
-0.03208179399371147,
-0.02807297743856907,
0.02702970802783966,
0.011220712214708328,
-0.02232741005718708,
-0.02147120237350464,
0.019605346024036407,
0.008237921632826328,
0.003492451971396804,
-0.002754055894911289,
-0.004623073153197765,
-0.055404387414455414,
-0.0023603143636137247,
-0.008119002915918827,
0.010468881577253342,
-0.012896807864308357,
-0.09453155100345612,
-0.07610233128070831,
0.06389891356229782,
0.02917288802564144,
0.03129899874329567,
0.011378278955817223,
-0.0687117725610733,
-0.0015729214064776897,
-0.06546985357999802,
0.011391797102987766,
-0.010206001810729504,
0.044307880103588104,
-0.03314069285988808,
-0.031648989766836166,
0.02579789236187935,
-0.04925316199660301,
0.058145828545093536,
-0.016627933830022812,
-0.04416051506996155,
0.00260340329259634,
-0.01012419257313013,
0.05331806838512421,
-0.03283063322305679,
0.0071675037033855915,
-0.04602112993597984,
-0.02816382795572281,
-0.003970143385231495,
-0.025782713666558266,
0.005268682260066271,
-0.008306225761771202,
0.043343693017959595,
-0.033220306038856506,
0.0006988761015236378,
-0.03277583420276642,
-0.009482104331254959,
0.06527422368526459,
-0.019612479954957962,
-0.0036419075913727283,
0.03649099916219711,
-0.02880306914448738,
0.03129139915108681,
0.060265202075242996,
-0.0024770854506641626,
-0.03622004762291908,
0.006960676051676273,
-0.003904095385223627,
-0.011642903089523315,
-0.02445339597761631,
0.008271612226963043,
0.019676901400089264,
-0.0029605107847601175,
-0.023341573774814606,
0.07042426615953445,
-0.030594853684306145,
-0.012853804044425488,
0.026893211528658867,
-0.018504953011870384,
0.045018136501312256,
-0.00020377525652293116,
0.01685984991490841,
-0.0003763310960493982,
0.018792936578392982,
-0.03862769901752472,
0.04704836755990982,
0.054503437131643295,
-0.005577344447374344,
-0.0026742802001535892,
-0.013035447336733341,
-0.010157457552850246,
0.005428370088338852,
0.0022921685595065355,
0.01944955252110958,
-0.07444843649864197,
-0.03009106032550335,
-0.005253470037132502,
-0.012694564647972584,
0.053543075919151306,
0.012670861557126045,
-0.007362339645624161,
0.06364446133375168,
-0.010762919671833515,
0.01273096352815628,
-0.03711812198162079,
-0.01919606886804104,
-0.028965996578335762,
-0.0008676672587171197,
-0.006901090033352375,
0.034352224320173264,
-0.003715496975928545,
-0.005857860203832388,
-0.021704144775867462,
0.03880913555622101,
0.012078134343028069,
-0.05845305696129799,
-0.004187204875051975,
0.006571380887180567,
0.00860734935849905,
-0.006444151047617197,
0.01884714886546135,
-0.026984626427292824,
-0.05335817113518715,
0.04769149050116539,
0.06075984612107277,
0.021323876455426216,
0.01024656556546688,
-0.02817700244486332,
0.00485789030790329,
0.0318414606153965,
-0.010507914237678051,
0.019731296226382256,
-0.04249157756567001,
0.041655585169792175,
-0.017903804779052734,
-0.0342203825712204
] |
<p>I recently found out about the discovery of 13 beautiful periodic solutions to the three-body problem, described in the paper</p>
<blockquote>
<p>Three Classes of Newtonian Three-Body Planar Periodic Orbits. Milovan Šuvakov and V. Dmitrašinović. <a href="http://dx.doi.org/10.1103/PhysRevLett.110.114301"><em>Phys. Rev. Lett.</em> <strong>110</strong> no. 11, 114301 (2013)</a>. <a href="http://arxiv.org/abs/1303.0181">arXiv:1303.0181</a>.</p>
</blockquote>
<p>I am particularly impressed by how elaborate the solutions are, and the tantalizing hint of an infinity of other distinct orbits given by the analogy with a <a href="http://en.wikipedia.org/wiki/Free_group">free group</a>. The solutions can be viewed in the <a href="http://suki.ipb.ac.rs/3body/">Three-Body Galery</a>, which has animations of the new orbits in real space and in something called the 'shape sphere', which is described in the paper.</p>
<p><img src="http://i.stack.imgur.com/2DPJi.jpg" alt="enter image description here"></p>
<hr>
<p>I was aware aware already of the figure-of-eight solution, which is described nicely in</p>
<blockquote>
<p><a href="http://www.ams.org/samplings/feature-column/fcarc-orbits1">A new solution to the three body problem - and more</a>. Bill Casselman. AMS Feature Column.</p>
</blockquote>
<p>and which was discovered numerically by Christopher Moore (<a href="http://dx.doi.org/10.1103/PhysRevLett.70.3675"><em>Phys. Rev. Lett.</em> <strong>70</strong>, 3675 (1993)</a>). I understand that the figure-of-eight solution has been proven to actually exist as a solution of the ODE problem, in</p>
<blockquote>
<p>A Remarkable Periodic Solution of the Three-Body Problem in the Case of Equal Masses. Alain Chenciner and Richard Montgomery. <a href="http://www.jstor.org/stable/2661357"><em>Ann. Math</em> <strong>152</strong> no. 3 (2000), pp. 881-901</a>.</p>
</blockquote>
<p>There is also a large class of solutions called <a href="http://www.scholarpedia.org/article/N-body_choreographies">$N$-body choreographies</a> by Carlés Simó, in which a number of bodies - possibly more than three - all follow the same curve. Simó found a large class of them in 2000 (<a href="http://dx.doi.org/10.1007/978-3-0348-8268-2_6">DOI</a>/<a href="http://www.mathematik.uni-bielefeld.de/~rehmann/ECM/cdrom/3ecm/pdfs/pant3/simo.pdf">pdf</a>), though <a href="http://www.imcce.fr/Equipes/ASD/preprints/prep.2001/CGMS.pdf">this nice review</a> (<a href="http://dx.doi.org/10.1007/0-387-21791-6_9">DOI</a>) seems to imply that formal theorematic proof that they exist as periodic solutions of the ODE problem is still lacking.</p>
<hr>
<p>So, this brings me to my actual question. For the numerical simulations, however well you do them, in the end you will only have a finite-precision approximation to a solution of a differential equation that is propagated for a finite time. Additionally, you might do a numerical stability analysis that strongly suggests (or rigorously proves?) that you are (or are not) in a stable orbit. However, this is quite a ways away from a rigorous existence theorem for a periodic orbit with that symmetry.</p>
<p>With this in mind, then, <strong>in what spirit are these simulations done?</strong> Is it purely a numerical approach, in the hope that good numerics do indicate existence, but with a rigorous proof left to the mathematicians through whatever other means they can manage? Or is there some overarching theorem that indicates the existence of a truly periodic solution after a given threshold? What tools are there for proving existence theorems of periodic solutions?</p> | 1,450 | [
-0.020165903493762016,
-0.00294658076018095,
0.030390048399567604,
-0.05005134642124176,
0.03626345470547676,
-0.01015250664204359,
-0.008564826101064682,
-0.034223973751068115,
0.0003219874924980104,
-0.08025002479553223,
0.0118345245718956,
0.006844724994152784,
-0.0027633158024400473,
0.04324699565768242,
-0.005617266986519098,
-0.014548742212355137,
-0.01575217768549919,
-0.003266166429966688,
-0.02918795496225357,
-0.03719604015350342,
0.06087879836559296,
0.003589833853766322,
0.017513858154416084,
-0.04055539518594742,
0.003464830806478858,
-0.006248013116419315,
0.02693653106689453,
-0.024887094274163246,
-0.00735607510432601,
0.08163859695196152,
-0.05371735244989395,
0.001963680610060692,
-0.002657642588019371,
0.0024875772651284933,
-0.0017348183318972588,
0.02432706579566002,
-0.01640692912042141,
0.003908089827746153,
0.06543521583080292,
0.029637547209858894,
-0.043584756553173065,
-0.022476844489574432,
-0.034963659942150116,
0.04666287824511528,
-0.02733246050775051,
0.009948588907718658,
-0.00526104960590601,
-0.04362732172012329,
0.08190209418535233,
-0.05356541648507118,
0.09715604037046432,
0.019078049808740616,
-0.025361692532896996,
-0.010553277097642422,
-0.026806263253092766,
-0.011418444104492664,
0.04267025366425514,
0.0862751454114914,
0.01657908782362938,
0.016938213258981705,
-0.034682661294937134,
-0.01505668181926012,
-0.0029330954421311617,
0.010077343322336674,
-0.0003160900960210711,
0.03500037267804146,
-0.009455496445298195,
-0.018172750249505043,
0.0012371842749416828,
0.008724378421902657,
0.013681484386324883,
0.016396539285779,
0.03301111236214638,
-0.034084342420101166,
0.024029308930039406,
0.00002216114262409974,
0.0020939060486853123,
-0.03130405396223068,
0.04329650476574898,
-0.002938897581771016,
-0.03458918631076813,
0.01802096515893936,
-0.007938995957374573,
0.0019606153946369886,
0.010857520624995232,
0.023917673155665398,
0.06367762386798859,
-0.025234365835785866,
-0.0071179550141096115,
0.011913417838513851,
0.015871254727244377,
-0.006826531141996384,
0.05389966443181038,
-0.015289687551558018,
-0.031073840335011482,
0.03685758635401726,
0.00324786314740777,
-0.0034221424721181393,
-0.03636160120368004,
-0.0037595094181597233,
-0.01798030361533165,
-0.034421492367982864,
-0.008261493407189846,
0.10707611590623856,
0.008771900087594986,
0.024996856227517128,
-0.043147776275873184,
-0.009305992163717747,
-0.016455484554171562,
0.011065245606005192,
-0.027826815843582153,
-0.003174252575263381,
-0.00019474636064842343,
-0.022300193086266518,
0.01272420585155487,
0.025910362601280212,
-0.0000287843904516194,
0.0007261881837621331,
0.04627299681305885,
0.06808917969465256,
0.009190516546368599,
0.006408512592315674,
0.009768693707883358,
-0.03508857637643814,
-0.05966868996620178,
0.03899838402867317,
0.05106619372963905,
-0.02062417007982731,
-0.03597228229045868,
0.022281212732195854,
0.015442749485373497,
-0.01575380004942417,
0.0392184779047966,
0.019323138520121574,
-0.02144061028957367,
0.0006897069979459047,
-0.0783744603395462,
-0.029848933219909668,
0.046212922781705856,
-0.0004420428886078298,
-0.003134064842015505,
-0.039884861558675766,
0.025370275601744652,
0.07162921875715256,
0.06942828744649887,
-0.026096252724528313,
-0.03950318694114685,
0.02612876705825329,
0.09475813806056976,
0.013068752363324165,
-0.011136068031191826,
0.055077195167541504,
-0.023545831441879272,
-0.04861973971128464,
-0.02016034908592701,
-0.0697571411728859,
0.03440278396010399,
-0.007111321669071913,
0.02629828080534935,
-0.014471588656306267,
0.07800842821598053,
0.0034586370456963778,
-0.010308913886547089,
-0.018317444249987602,
0.0002519426343496889,
0.0032403382938355207,
0.02714666537940502,
-0.010119793005287647,
-0.008538052439689636,
0.04169962927699089,
-0.00520282331854105,
0.05458254739642143,
0.005616708658635616,
0.02628476358950138,
0.0030093223322182894,
-0.01874639093875885,
-0.008247126825153828,
-0.0032760468311607838,
-0.012262899428606033,
-0.01622549258172512,
0.0006286042043939233,
-0.030788350850343704,
0.012754608877003193,
-0.015799880027770996,
0.029829472303390503,
0.05987973511219025,
0.0212357547134161,
0.002329065464437008,
0.036025725305080414,
-0.08736038953065872,
-0.003563418285921216,
-0.04201512783765793,
-0.022011371329426765,
-0.02040962688624859,
-0.0364079587161541,
0.051809053868055344,
0.006358958315104246,
-0.016587626188993454,
0.017249511554837227,
-0.04027188569307327,
-0.017815211787819862,
0.06200416758656502,
0.0018310099840164185,
-0.03463388979434967,
0.015529184602200985,
0.048783496022224426,
0.01766163296997547,
-0.029946081340312958,
0.002554618753492832,
-0.011067097075283527,
-0.0005243044579401612,
-0.022818518802523613,
0.0015713315224274993,
0.04578349366784096,
-0.011231557466089725,
0.015129223465919495,
0.0018496729899197817,
0.04633767902851105,
-0.026406077668070793,
0.02129252254962921,
-0.04974754527211189,
0.042858418077230453,
0.018213696777820587,
0.04141290485858917,
0.01570642925798893,
0.053717415779829025,
0.03161854296922684,
-0.002614862285554409,
0.004441938828676939,
-0.003939971327781677,
-0.03631047159433365,
-0.039609767496585846,
0.022733010351657867,
0.058941178023815155,
-0.010651675052940845,
-0.0035715762060135603,
0.07652059197425842,
0.03839201480150223,
0.023241352289915085,
0.005858124233782291,
0.0353306382894516,
-0.0163241159170866,
0.026905694976449013,
0.018991738557815552,
0.018147092312574387,
-0.031891170889139175,
0.02861776575446129,
0.011211715638637543,
-0.011021495796740055,
-0.013383838348090649,
-0.06432567536830902,
0.0016281011048704386,
-0.016761431470513344,
-0.03443177416920662,
-0.005577382165938616,
-0.009488225914537907,
0.014171107672154903,
-0.023717017844319344,
-0.002422882243990898,
0.017947742715477943,
0.000620030565187335,
-0.00597677705809474,
-0.04343709722161293,
0.0035696267150342464,
-0.02039521373808384,
0.02962850034236908,
-0.006770264822989702,
0.0123560456559062,
0.024468570947647095,
-0.04894255846738815,
0.03584564849734306,
-0.04262938350439072,
-0.015949396416544914,
-0.011723103001713753,
0.03766637295484543,
-0.03725747764110565,
0.029397204518318176,
-0.035657063126564026,
0.003415616462007165,
0.001453092321753502,
0.008767163380980492,
0.04052361845970154,
0.00967591255903244,
0.06407230347394943,
-0.072232685983181,
0.03640209138393402,
-0.03329392895102501,
-0.008522119373083115,
0.015823328867554665,
0.02490500546991825,
0.012062090449035168,
0.014841507188975811,
-0.011985964141786098,
-0.0360892154276371,
-0.013728457503020763,
-0.019277222454547882,
0.0065209632739424706,
-0.04500793293118477,
0.049779605120420456,
0.03874054178595543,
0.006822756491601467,
-0.061931438744068146,
-0.024281539022922516,
-0.010707446373999119,
-0.0164398904889822,
-0.000639421574305743,
0.019887059926986694,
0.02804459258913994,
-0.02003168873488903,
0.016097787767648697,
0.047105345875024796,
0.0019236116204410791,
0.04240301623940468,
-0.07125365734100342,
-0.056113582104444504,
-0.02384013682603836,
-0.017939183861017227,
0.049849383533000946,
-0.041674017906188965,
-0.011631948873400688,
0.08054763078689575,
0.02064342238008976,
-0.024745231494307518,
-0.007323138415813446,
0.03168420121073723,
-0.02469758689403534,
-0.03514697402715683,
0.04997790977358818,
0.012456605210900307,
-0.004545241594314575,
0.004205330740660429,
-0.024130569770932198,
0.01263290923088789,
0.05087536945939064,
-0.01153397373855114,
0.012200441211462021,
0.013274377211928368,
-0.012409091927111149,
-0.03485698252916336,
0.02935931645333767,
0.005120428744703531,
-0.008296665735542774,
0.032013654708862305,
0.004750151187181473,
0.03179537504911423,
0.023147033527493477,
-0.05992643162608147,
0.006070082075893879,
0.0033800157252699137,
0.02303505688905716,
0.03535887226462364,
-0.0009848115732893348,
0.0005849719746038318,
-0.037446171045303345,
-0.039874691516160965,
0.030391814187169075,
0.06182431802153587,
0.004036639351397753,
-0.013683314435184002,
0.01673830673098564,
0.03448657691478729,
0.010718832723796368,
-0.021051255986094475,
-0.03069460764527321,
-0.018145378679037094,
0.03388902172446251,
-0.0400964580476284,
-0.026896744966506958,
0.002911696210503578,
0.0010377297876402736,
0.019461898133158684,
0.034276824444532394,
0.0006725958664901555,
0.024971134960651398,
-0.029198767617344856,
-0.04579772427678108,
-0.05346710979938507,
0.03401364013552666,
-0.010257696732878685,
0.06610817462205887,
-0.06448785215616226,
0.019625136628746986,
0.012620124965906143,
-0.011011825874447823,
-0.053107425570487976,
0.010855046100914478,
0.000570990436244756,
0.012746555730700493,
0.011926543898880482,
0.0013311607763171196,
-0.015700381249189377,
0.030774731189012527,
-0.04899020865559578,
-0.027716856449842453,
0.015002619475126266,
-0.03762209042906761,
-0.006313462741672993,
-0.03748507425189018,
-0.021735914051532745,
0.025037754327058792,
0.04290461912751198,
0.06363355368375778,
-0.028229163959622383,
0.024823646992444992,
0.018181005492806435,
-0.04885365813970566,
-0.019191039726138115,
0.0067001632414758205,
0.030426183715462685,
-0.003089003963395953,
0.012441239319741726,
-0.03323793783783913,
0.03374688699841499,
-0.030007103458046913,
-0.008663657121360302,
-0.02731744572520256,
0.03291608393192291,
0.008847481571137905,
-0.003904645796865225,
0.015358194708824158,
-0.05494846776127815,
-0.01281260047107935,
0.027062024921178818,
0.029418161138892174,
-0.03156772628426552,
0.03124600276350975,
0.04100389778614044,
0.0009533740230835974,
0.016605855897068977,
0.023814715445041656,
-0.014025909826159477,
0.0027234910521656275,
-0.02732030674815178,
-0.03123413771390915,
-0.027674980461597443,
-0.018764706328511238,
-0.002633588155731559,
0.013471057638525963,
0.007750806398689747,
-0.03606916964054108,
0.04486144334077835,
0.027059953659772873,
0.017625145614147186,
-0.05071547254920006,
-0.021801700815558434,
-0.06662313640117645,
-0.0069199129939079285,
-0.07459361106157303,
0.022183196619153023,
0.03501515090465546,
0.004542367532849312,
0.03061933070421219,
0.01950846053659916,
-0.008176286704838276,
-0.05564446002244949,
-0.004905687179416418,
0.07400795817375183,
0.021908976137638092,
0.03702060133218765,
0.02055852860212326,
-0.08354540169239044,
-0.010275647044181824,
0.040528230369091034,
-0.04679468274116516,
0.04733290523290634,
-0.016653962433338165,
-0.029227277263998985,
-0.027450351044535637,
-0.0296113733202219,
-0.009140962734818459,
0.022096019238233566,
-0.016546372324228287,
0.0017185014439746737,
-0.029376564547419548,
0.011137528344988823,
0.003971992991864681,
0.0932750329375267,
-0.016569705680012703,
0.023928377777338028,
0.032686084508895874,
-0.001347315963357687,
0.004352351650595665,
-0.0073425909504294395,
-0.04230646789073944,
-0.029164887964725494,
0.01214339304715395,
0.010373403318226337,
-0.016919229179620743,
0.031176650896668434,
-0.08195479959249496,
-0.034107618033885956,
0.006548095028847456,
-0.027124470099806786,
0.035376083105802536,
-0.013210310600697994,
-0.06303354352712631,
0.007177866064012051,
0.017704561352729797,
0.006635637953877449,
0.020489385351538658,
0.012882034294307232,
-0.019947340711951256,
-0.02936205081641674,
-0.040861956775188446,
0.021486366167664528,
-0.02764899842441082,
-0.01859850063920021,
-0.025245675817131996,
-0.001291781198233366,
-0.025528088212013245,
0.017187492921948433,
0.012804031372070312,
0.020377378910779953,
0.007447229698300362,
-0.0196172297000885,
-0.01096784695982933,
0.028534188866615295,
0.020978469401597977,
0.05642132833600044,
0.02561226114630699,
0.00320377666503191,
0.017723796889185905,
-0.0050771189853549,
0.03246332332491875,
-0.038234829902648926,
-0.013602618128061295,
0.05397379398345947,
-0.02495143562555313,
0.004631130490452051,
-0.05495724454522133,
0.012550948187708855,
-0.017795544117689133,
-0.04584750905632973,
0.07211722433567047,
-0.022873420268297195,
0.022459136322140694,
0.03828069195151329,
-0.05403538793325424,
0.00834265723824501,
-0.00704078609123826,
-0.04718274623155594,
0.00596288125962019,
-0.006851766258478165,
-0.02918645180761814,
0.04050830379128456,
0.003836790332570672,
-0.07641127705574036,
-0.010407386347651482,
0.03786226361989975,
0.020808586850762367,
-0.06432430446147919,
-0.013218548148870468,
-0.002488587284460664,
-0.014229553751647472,
-0.018902014940977097,
0.0005862349062226713,
0.05995281785726547,
-0.07334516942501068,
-0.02861776575446129,
0.019657321274280548,
0.028649266809225082,
0.031878646463155746,
0.01985345594584942,
-0.021837711334228516,
0.021066460758447647,
0.004067185800522566,
0.03046310693025589,
0.014384269714355469,
0.024551041424274445,
-0.016386641189455986,
-0.009299307130277157,
-0.03762667253613472,
-0.03745206445455551,
-0.006001801695674658,
-0.04467848688364029,
-0.004968200344592333,
0.035972677171230316,
0.006782126147300005,
0.009951193816959858,
-0.02440003491938114,
-0.0074854823760688305,
-0.0019460134208202362,
0.021724995225667953,
-0.04344988986849785,
0.041068993508815765,
0.004167694132775068,
-0.02085232175886631,
0.052593160420656204,
-0.047596875578165054,
-0.03084789775311947,
-0.015987416729331017,
0.028960172086954117,
0.027705881744623184,
-0.011009212583303452,
0.020379887893795967,
0.0010268270270898938,
0.004210892133414745,
-0.041446637362241745,
0.03619380667805672,
-0.0076061212457716465,
0.04198196530342102,
-0.030768511816859245,
-0.041519321501255035,
-0.02156880311667919,
0.04014301300048828,
0.03135533258318901,
-0.012933710590004921,
0.044562116265296936,
0.02239494025707245,
0.006348270457237959,
-0.02242112159729004,
-0.007076864596456289,
-0.009663325734436512,
-0.0006542742485180497,
-0.002491617575287819,
0.0567924939095974,
-0.02235380746424198,
-0.0011347056133672595,
0.0048141879960894585,
0.007697128225117922,
-0.023525364696979523,
0.04387110844254494,
0.001105295610614121,
-0.007160544395446777,
0.013305384665727615,
-0.004777235444635153,
-0.02911095693707466,
0.05387233570218086,
-0.0377320796251297,
0.06288069486618042,
0.05072743073105812,
-0.007197909988462925,
0.03964746370911598,
0.03929302841424942,
0.013076062314212322,
-0.05893544852733612,
-0.025797802954912186,
-0.022159995511174202,
0.04054618626832962,
0.053572073578834534,
-0.006146453786641359,
-0.0025572413578629494,
-0.053987495601177216,
0.013015322387218475,
0.012665577232837677,
0.0190960131585598,
-0.02795739471912384,
-0.048035379499197006,
-0.01083969883620739,
-0.033861998468637466,
-0.036924123764038086,
0.017498983070254326,
0.008510852232575417,
0.005213335622102022,
0.002884764689952135,
0.013718546368181705,
0.026610231027007103,
0.016320981085300446,
0.028677845373749733,
-0.017607316374778748,
0.058782175183296204,
-0.021295232698321342,
0.022967901080846786,
-0.03338131681084633,
-0.011116357520222664,
0.15818074345588684,
0.022707508876919746,
0.006218601018190384,
-0.05673941597342491,
0.040240656584501266,
0.01080844271928072,
0.018623679876327515,
-0.035841360688209534,
-0.00037296570371836424,
0.011538905091583729,
0.002540131099522114,
-0.025686489418148994,
0.021000925451517105,
-0.021075241267681122,
0.010791731998324394,
0.03736928105354309,
0.0038722893223166466,
-0.03617578372359276,
-0.007290033157914877,
0.006859919521957636,
0.003561398247256875,
-0.0018098497530445457,
-0.02712058834731579,
0.023372448980808258,
-0.036529041826725006,
-0.010296260006725788,
-0.03429481014609337,
-0.027496417984366417,
0.027246231213212013,
0.024840733036398888,
-0.024329302832484245,
0.0016329949721693993,
0.013766027055680752,
-0.03419750556349754,
0.025347812101244926,
0.04202289506793022,
-0.015837619081139565,
-0.008018871769309044,
0.03427848964929581,
0.07352174818515778,
-0.0012520579621195793,
-0.006222858559340239,
-0.019251640886068344,
-0.004145743791013956,
-0.020294437184929848,
0.01693207584321499,
-0.06894316524267197,
0.0213286355137825,
-0.04605310782790184,
-0.014300929382443428,
-0.040563277900218964,
-0.001130680087953806,
-0.006316144950687885,
-0.038266781717538834,
0.017187651246786118,
-0.019728325307369232,
-0.026773540303111076,
-0.049275487661361694,
-0.05109981447458267,
0.025783950462937355,
-0.03035794198513031,
0.0016215144423767924,
0.0044148024171590805,
-0.030295593664050102,
0.023147713392972946,
0.0014962193090468645,
0.0008199537405744195,
0.019718725234270096,
0.03346932306885719,
-0.011309136636555195,
-0.06441816687583923,
0.005379523616284132,
-0.03460453823208809,
0.01122370082885027,
-0.030101902782917023,
0.019505633041262627,
0.02451426535844803,
0.023581841960549355,
-0.04017787054181099,
-0.0177450068295002,
-0.03510168939828873,
-0.006586943753063679,
0.02479378879070282,
-0.005009196233004332,
-0.021923573687672615,
-0.005164912901818752,
-0.0016666172305122018,
-0.007408673409372568,
-0.020031103864312172,
0.012088431976735592,
-0.011276415549218655,
0.05627515912055969,
-0.004983164370059967,
-0.004376085940748453,
0.011912573128938675,
-0.016853773966431618,
-0.022830087691545486,
0.023382795974612236,
-0.03613043576478958,
0.04336242005228996,
0.002499949187040329,
0.008271405473351479,
0.018233569338917732,
0.025209182873368263,
-0.011955146677792072,
0.003941361326724291,
0.06078162416815758,
-0.01164277270436287,
-0.0005067868041805923,
0.014523203484714031,
-0.016171230003237724,
-0.0347001776099205,
-0.020743422210216522,
-0.018727799877524376,
-0.00307463645003736,
-0.012734880670905113,
0.011664698831737041,
-0.06798196583986282,
0.035171836614608765,
-0.021920857951045036,
0.02190963178873062,
-0.034514445811510086,
0.03583386912941933,
-0.018455225974321365,
0.02349933423101902,
-0.029602056369185448,
0.02281619794666767,
-0.008088763803243637,
0.038706451654434204,
-0.02560582384467125,
-0.010177944786846638,
0.030150240287184715,
0.01040799729526043,
-0.001913835178129375,
-0.03817125782370567,
0.03282535448670387,
0.013608601875603199,
0.012791202403604984,
0.02805803157389164,
-0.005866016261279583,
-0.009376173838973045,
-0.026683814823627472,
-0.03071427531540394,
-0.015425428748130798,
-0.05902143940329552,
0.029021337628364563,
0.021140914410352707,
-0.0495225191116333,
-0.01796266995370388,
0.02634969726204872,
-0.021603384986519814,
0.008926315233111382,
0.02998177520930767,
0.0471336729824543,
-0.0034918261226266623,
0.01223780121654272,
0.019825614988803864,
-0.038166750222444534,
-0.009982628747820854,
0.02131243795156479,
0.019642574712634087,
-0.01733832061290741,
-0.03298914432525635,
-0.030028019100427628,
-0.0291131641715765,
-0.020171264186501503,
-0.02437979355454445,
0.05385526269674301,
0.07608191668987274,
-0.003230642294511199,
0.001788959838449955,
0.03857751190662384,
0.03416316583752632,
0.004638410173356533,
-0.06540945917367935,
-0.009153321385383606,
0.02240295521914959,
-0.0048231091350317,
0.05950474739074707,
-0.06028980761766434,
0.005059512332081795,
0.045438747853040695,
-0.08372492343187332,
0.04322343319654465,
-0.05513720214366913,
0.023010633885860443,
-0.015988139435648918,
-0.005539135076105595,
-0.02798137441277504,
0.04420428350567818,
0.012436470948159695,
-0.001266571693122387,
0.008267692290246487,
0.04039103165268898,
-0.0572785809636116,
-0.047477319836616516,
0.04759271815419197,
0.027470765635371208,
-0.006108214613050222,
-0.023354152217507362,
0.033857233822345734,
0.0019707251340150833,
-0.030463073402643204,
0.020590072497725487,
0.001954899402335286,
-0.010533689521253109,
-0.03795292228460312,
0.012957261875271797,
-0.03177480772137642,
0.03457639366388321,
0.01061441469937563,
0.011819490231573582,
0.003508753841742873,
-0.0385856032371521,
0.014814678579568863,
0.012197066098451614,
-0.00671251118183136,
-0.014519404619932175,
0.007846755906939507,
-0.00992224644869566,
-0.01726030744612217,
0.022090544924139977,
-0.006065170280635357,
0.04147050529718399,
-0.010522500611841679,
-0.007369826082140207,
-0.005477279890328646,
-0.024436162784695625,
-0.005869000218808651,
-0.006025012116879225,
0.030629223212599754,
-0.036813005805015564,
0.022273018956184387,
0.02434590272605419,
0.0019313087686896324,
-0.042485613375902176,
-0.03393636271357536,
-0.008632070384919643,
-0.007939380593597889,
0.004302923567593098,
-0.04711494594812393,
0.025795795023441315,
0.03467328101396561,
0.025000644847750664,
-0.01349099725484848,
0.007702257949858904,
-0.03931240364909172,
0.027846435084939003,
-0.0057209935039281845,
-0.01617111824452877,
-0.04305657744407654,
-0.016013938933610916,
-0.02579174004495144,
-0.080701544880867,
0.035834092646837234,
0.024831430986523628,
-0.0033819021191447973,
-0.03449951484799385,
-0.04663380980491638,
0.005107480566948652,
0.018890585750341415,
0.02445107512176037,
-0.01752081699669361,
0.036617789417505264,
0.009917405433952808,
0.011072960682213306,
0.023413484916090965,
-0.012051576748490334,
0.003505534725263715,
0.025290627032518387,
0.01702774129807949,
0.03248325362801552,
0.004942861385643482,
0.00531676085665822,
-0.020824840292334557,
0.02114908955991268,
-0.02223287709057331,
0.007339939009398222,
0.03768591210246086,
-0.039040643721818924,
0.032509952783584595,
0.02735864743590355,
-0.012021590024232864,
0.06634432822465897,
-0.026567062363028526,
-0.010576632805168629,
-0.011191480793058872,
-0.011325899511575699,
0.018363947048783302,
-0.010095205157995224,
-0.0664229467511177,
-0.013121189549565315,
-0.0495627261698246,
-0.047588881105184555,
0.023724254220724106,
-0.038722991943359375,
-0.01367320865392685,
0.026879362761974335,
-0.013666427694261074,
-0.0041653807274997234,
0.057968515902757645,
-0.013075509108603,
0.03902524337172508,
0.0012686137342825532,
0.052780963480472565,
-0.011760851368308067,
-0.027636468410491943,
-0.00419822009280324,
0.020631931722164154,
0.019904492422938347,
0.002119636395946145,
-0.01792885921895504,
0.01449093222618103,
-0.0006260497611947358,
0.023681240156292915,
0.04438648000359535,
0.057225145399570465,
0.004380248486995697,
-0.015197399072349072,
0.05868588015437126,
-0.0076436190865933895,
0.0034416343551129103,
0.013153606094419956,
-0.010388188064098358,
0.09614796191453934,
0.0034571753349155188,
-0.029577167704701424,
-0.034531161189079285,
0.013937169685959816,
-0.008584734052419662,
0.00815083459019661,
-0.015169559046626091,
0.035691630095243454,
-0.010395965538918972,
0.011214491911232471,
-0.008132610470056534,
0.028491124510765076,
0.027112336829304695,
-0.04363363981246948,
0.0227114949375391,
-0.0041356333531439304,
0.05120714753866196,
0.03160983324050903,
0.006446113809943199,
-0.007599904667586088,
-0.013616847805678844,
0.050740115344524384,
0.03340422734618187,
0.020016049966216087,
0.005170279182493687,
-0.0021074479445815086,
-0.025156768038868904,
0.06609036028385162,
-0.02068626694381237,
-0.05574299767613411,
-0.026753373444080353,
0.04452718049287796,
0.006753928959369659,
0.025808561593294144
] |
<p>This video ( <a href="http://www.youtube.com/watch?v=Vs3afgStVy4" rel="nofollow">http://www.youtube.com/watch?v=Vs3afgStVy4</a> ) demonstrates lenz's law, if the current produced by the magnet fall induces an opposing magnetic field , after many tries , can this field demagnetize the magnet? or decrease its magnetization ?</p> | 1,451 | [
-0.06403297930955887,
-0.014951265417039394,
-0.0013618689263239503,
-0.04884231463074684,
0.05655014142394066,
-0.0062138596549630165,
-0.07528649270534515,
0.0004733655077870935,
0.02697530947625637,
-0.030995849519968033,
0.032826878130435944,
0.03635893762111664,
0.04314073547720909,
0.023038631305098534,
0.04288768395781517,
0.02796647883951664,
0.009684658609330654,
-0.0060895392671227455,
-0.009590226225554943,
-0.0370890311896801,
-0.02326684631407261,
-0.003434909973293543,
0.017722701653838158,
0.010908232070505619,
-0.06349976360797882,
-0.024191487580537796,
0.051144201308488846,
-0.0004243706353008747,
0.0022881412878632545,
0.05082802101969719,
0.004203092772513628,
-0.0037457523867487907,
0.004808939527720213,
0.006142874248325825,
0.035014376044273376,
-0.016413774341344833,
-0.03742700070142746,
-0.05270214006304741,
-0.025340741500258446,
0.051992595195770264,
-0.015780294314026833,
-0.023743873462080956,
0.0022573317401111126,
0.04712322726845741,
-0.020190875977277756,
0.00009804473666008562,
0.01837078481912613,
-0.012710154987871647,
0.0477781780064106,
-0.03345348313450813,
0.05424799025058746,
-0.0226614810526371,
0.053059425204992294,
-0.029268285259604454,
0.004353970289230347,
-0.05715875327587128,
0.06592588126659393,
0.04063514247536659,
-0.001068632584065199,
-0.03441302850842476,
-0.010511324740946293,
-0.03745933622121811,
-0.011555895209312439,
-0.010592910461127758,
-0.03515520691871643,
0.037698157131671906,
0.007076480891555548,
0.02258126251399517,
0.03701566159725189,
0.009071487002074718,
-0.01707988604903221,
0.01557251252233982,
0.01847687177360058,
0.0036155248526483774,
0.040029071271419525,
-0.03879707306623459,
0.03029307909309864,
-0.004204609431326389,
-0.014109857380390167,
0.030683225020766258,
0.0010769135551527143,
0.00919291377067566,
0.026950405910611153,
0.03840922936797142,
0.008345214650034904,
-0.026660777628421783,
0.07103224098682404,
-0.0006888702628202736,
0.02636280097067356,
0.031213100999593735,
-0.00018234021263197064,
0.00785090308636427,
0.022241586819291115,
-0.022902172058820724,
-0.034268610179424286,
0.010018058121204376,
-0.005965670570731163,
0.049577753990888596,
0.007737955078482628,
-0.02489735558629036,
0.002984504448249936,
0.02852950617671013,
0.005280590150505304,
0.024540405720472336,
0.03644656762480736,
-0.022585498169064522,
-0.027181025594472885,
0.02909098193049431,
-0.0764685794711113,
-0.023727012798190117,
-0.022763431072235107,
0.0437035895884037,
-0.006765417288988829,
-0.06443991512060165,
0.013585987500846386,
-0.012556451372802258,
-0.0027611474506556988,
-0.00959774013608694,
0.020912058651447296,
0.057995736598968506,
0.036348335444927216,
-0.03525969386100769,
0.02511945366859436,
-0.024965057149529457,
-0.05822331830859184,
-0.011154445819556713,
0.0021361657418310642,
-0.017264695838093758,
-0.006566968746483326,
0.016259921714663506,
-0.04410528764128685,
-0.009342493489384651,
-0.010321334935724735,
-0.000789887213613838,
0.017437521368265152,
0.014188126660883427,
-0.11032131314277649,
-0.01830206997692585,
0.04682323336601257,
0.008709046058356762,
-0.0046236650086939335,
-0.06788907200098038,
0.0014418817590922117,
0.03139690309762955,
0.05835912749171257,
0.0064991433173418045,
-0.0018002111464738846,
-0.0035527122672647238,
0.016054145991802216,
-0.01949714496731758,
0.00456722266972065,
0.013452427461743355,
-0.017145736142992973,
-0.04603060707449913,
0.0013959127245470881,
-0.052653372287750244,
0.06771660596132278,
0.06493858247995377,
0.0010387328220531344,
-0.057728879153728485,
0.036757465451955795,
-0.036970023065805435,
0.004921483341604471,
-0.02489510364830494,
-0.03660063073039055,
-0.017606807872653008,
0.07696755230426788,
0.004401538986712694,
0.02287260815501213,
0.04343371093273163,
0.0075960783287882805,
0.0345919169485569,
-0.010623518377542496,
0.023334741592407227,
0.04510776698589325,
-0.02047327719628811,
-0.03988465666770935,
-0.0181602630764246,
0.0649387538433075,
0.000403465295676142,
-0.03670795261859894,
-0.03602389246225357,
-0.0092807961627841,
0.03377068042755127,
-0.03514520451426506,
0.03180349990725517,
0.0017910678870975971,
0.025779390707612038,
0.015151062980294228,
-0.02539817988872528,
0.000988240004517138,
-0.06551411002874374,
0.04021171107888222,
-0.03708561509847641,
-0.021342933177947998,
0.04942476749420166,
0.018272176384925842,
0.022417331114411354,
-0.02489260770380497,
-0.03188978135585785,
-0.0009697593050077558,
0.0012128293747082353,
0.008981887251138687,
-0.004147544037550688,
-0.03082650899887085,
0.03342191129922867,
0.04137636348605156,
0.00876314751803875,
0.06289833784103394,
-0.03506309166550636,
-0.01273400243371725,
-0.02067106030881405,
-0.01153552532196045,
-0.0045913332141935825,
0.028122881427407265,
0.03346622362732887,
0.061892420053482056,
0.027131373062729836,
-0.02795746922492981,
0.023691684007644653,
-0.015416533686220646,
0.08534970134496689,
0.04658963903784752,
0.00969483982771635,
0.030521588400006294,
-0.002600093139335513,
-0.0148394126445055,
-0.018193639814853668,
-0.03368072956800461,
-0.01927478052675724,
-0.028914108872413635,
0.003805632935836911,
0.025988811627030373,
0.03692701458930969,
-0.03452105447649956,
0.043730590492486954,
-0.010657249018549919,
0.0010340638691559434,
-0.001554991933517158,
0.04184451699256897,
-0.010441930033266544,
-0.03934897109866142,
0.022183464840054512,
0.03166995570063591,
-0.02717318944633007,
0.013386446051299572,
0.024884680286049843,
0.02742464281618595,
-0.006983608938753605,
-0.006565083283931017,
-0.024553537368774414,
0.03593550622463226,
-0.013154181651771069,
-0.025259701535105705,
0.0362275056540966,
-0.08973382413387299,
0.02045891433954239,
0.0012618639739230275,
0.02786189690232277,
0.0064581166952848434,
-0.026118697598576546,
0.03661157190799713,
-0.030276060104370117,
-0.005649874452501535,
0.020454084500670433,
-0.030208591371774673,
-0.004869948141276836,
-0.008748623542487621,
0.041793011128902435,
-0.053882844746112823,
-0.024287372827529907,
-0.017842283472418785,
0.0015864139422774315,
-0.03871092200279236,
0.020575322210788727,
0.01584441587328911,
0.010362966917455196,
0.02339721843600273,
-0.03792524337768555,
-0.04330775514245033,
-0.016990909352898598,
-0.0070352572947740555,
0.02147326059639454,
0.05304659157991409,
-0.0291421040892601,
0.06951478123664856,
-0.011659784242510796,
-0.012154330499470234,
0.02637621760368347,
0.028763500973582268,
0.01284707710146904,
0.008513416163623333,
-0.003526248736307025,
-0.05503879860043526,
-0.016735758632421494,
-0.00152989209163934,
0.021252909675240517,
0.0022742985747754574,
0.002147644991055131,
0.030806075781583786,
0.03458497300744057,
-0.026345092803239822,
0.009488395415246487,
-0.032733287662267685,
-0.038798268884420395,
-0.004253291059285402,
-0.007407818455249071,
0.021441126242280006,
-0.03332434967160225,
0.010965637862682343,
0.004845684859901667,
-0.062372539192438126,
-0.028644530102610588,
-0.054435938596725464,
-0.012260155752301216,
0.015801284462213516,
-0.03420963138341904,
0.01604718342423439,
-0.010893508791923523,
0.001937731634825468,
0.07126255333423615,
0.05965327098965645,
-0.020256195217370987,
-0.031147392466664314,
-0.05306283384561539,
-0.01595413312315941,
-0.0333726592361927,
-0.019009148702025414,
0.07174044847488403,
-0.04381515458226204,
-0.00283779832534492,
-0.017832953482866287,
0.019414041191339493,
0.0016975115286186337,
0.00772986002266407,
0.0017562975408509374,
0.01704608090221882,
0.046810053288936615,
-0.0010414656717330217,
0.05862736329436302,
0.012670088559389114,
0.00835531484335661,
0.01997840218245983,
0.048857126384973526,
0.07298621535301208,
-0.0027375423815101385,
-0.015913458541035652,
0.06369511783123016,
-0.010822063311934471,
0.00015980476746335626,
-0.031096577644348145,
0.029780546203255653,
0.0018673771992325783,
-0.0019841014873236418,
0.011312724091112614,
0.041300758719444275,
0.011366278864443302,
-0.04006737098097801,
-0.01113481167703867,
0.025929264724254608,
0.02299734205007553,
-0.0208534374833107,
-0.03602946922183037,
-0.019281668588519096,
-0.010025176219642162,
0.03161071613430977,
-0.01873207837343216,
0.01599505916237831,
0.005237964913249016,
0.027701903134584427,
0.05115934833884239,
0.011869228444993496,
-0.016527265310287476,
-0.006104691419750452,
-0.07423856854438782,
0.010650883428752422,
0.01645304448902607,
-0.00018171755073126405,
0.037259940057992935,
0.01579112559556961,
0.014590886421501637,
0.032672930508852005,
0.03159342333674431,
-0.01642284356057644,
-0.1163792759180069,
0.03720342740416527,
-0.01321977749466896,
0.0066335806623101234,
0.005877570249140263,
-0.00855141133069992,
0.011507444083690643,
-0.014488743618130684,
0.003646395169198513,
-0.040141355246305466,
0.002813274273648858,
-0.03669684752821922,
-0.014968427829444408,
-0.016215912997722626,
-0.03122544288635254,
-0.016971657052636147,
-0.006542086601257324,
0.056196246296167374,
-0.03047150932252407,
0.009368919767439365,
-0.0288461372256279,
0.019025808200240135,
0.02207983285188675,
-0.03206528723239899,
-0.004989170469343662,
0.013251117430627346,
0.0258974339812994,
0.010010532103478909,
-0.003948906436562538,
0.0045867664739489555,
0.025184882804751396,
0.04869689419865608,
0.019635427743196487,
0.024663614109158516,
-0.001935377949848771,
-0.03357236459851265,
-0.058241285383701324,
-0.03361593931913376,
-0.0285735335201025,
0.01900675892829895,
-0.012965049594640732,
0.025341365486383438,
0.002602913184091449,
0.015531263314187527,
-0.010506811551749706,
0.01537884958088398,
0.019748669117689133,
0.029118482023477554,
0.016583891585469246,
-0.03446570783853531,
-0.03122538886964321,
-0.03430255129933357,
-0.004602920729666948,
0.020192764699459076,
0.001818374963477254,
-0.03361014276742935,
0.017328768968582153,
0.031135648488998413,
0.0346623994410038,
0.014356749132275581,
0.0023323637433350086,
-0.01229235902428627,
0.02144288271665573,
-0.0028079315088689327,
0.015102465637028217,
-0.008947224356234074,
0.03668299689888954,
0.05722469091415405,
-0.01151655800640583,
-0.06582196056842804,
-0.11064907908439636,
-0.021730802953243256,
0.044126659631729126,
0.044497668743133545,
-0.008976740762591362,
0.026263581588864326,
-0.0684942826628685,
-0.041314586997032166,
-0.00861594919115305,
-0.04542945325374603,
0.039952412247657776,
0.011655808426439762,
0.023020420223474503,
-0.04823721945285797,
-0.05360056832432747,
-0.02104257047176361,
0.0419636107981205,
-0.0011934542562812567,
0.050371203571558,
-0.02242947928607464,
-0.016981560736894608,
0.02585931494832039,
0.009265813045203686,
0.053582336753606796,
0.05026981607079506,
-0.0073031093925237656,
0.043862663209438324,
-0.023829640820622444,
0.017992720007896423,
-0.06580282002687454,
-0.0842200517654419,
-0.010626208037137985,
0.012463623657822609,
-0.03952338546514511,
0.026426425203680992,
-0.004991396330296993,
-0.032526299357414246,
0.014321834780275822,
0.010306525975465775,
-0.03802904859185219,
-0.01441974751651287,
-0.018132582306861877,
0.03540263697504997,
0.0325155183672905,
-0.004323418252170086,
0.05035797134041786,
0.027417447417974472,
0.036734893918037415,
-0.01424588542431593,
0.010597341693937778,
0.05419974401593208,
-0.0019154882756993175,
0.017455460503697395,
0.0001760303130140528,
0.006337265949696302,
-0.03222498297691345,
0.07266906648874283,
-0.0057838307693600655,
0.015369043685495853,
-0.012169678695499897,
0.014532609842717648,
0.017472680658102036,
-0.007690998259931803,
0.00020231543749105185,
-0.02771172858774662,
-0.015308992937207222,
0.006409854628145695,
-0.005320989992469549,
-0.016096489503979683,
0.007602045312523842,
-0.021457558497786522,
0.016774877905845642,
0.01074181031435728,
-0.04467831552028656,
0.013898736797273159,
-0.030333630740642548,
-0.019618956372141838,
-0.007195762824267149,
-0.026632731780409813,
0.06168711557984352,
0.01129724457859993,
-0.009507380425930023,
0.001071062870323658,
0.018358983099460602,
-0.0228965375572443,
0.004812378901988268,
-0.034937791526317596,
0.013625960797071457,
-0.05351455882191658,
0.03766768425703049,
0.018984060734510422,
0.01911223493516445,
-0.05792892724275589,
-0.06545504182577133,
-0.0003408931370358914,
-0.010699787177145481,
0.018943870440125465,
0.0029757788870483637,
-0.036913059651851654,
-0.010397025384008884,
-0.06103849038481712,
0.0070527601055800915,
0.03762134909629822,
-0.04034886881709099,
0.007872989401221275,
0.006026359740644693,
-0.02129935286939144,
0.08483479917049408,
-0.0004954210598953068,
-0.02752074971795082,
-0.006835390813648701,
-0.03329959511756897,
-0.017908163368701935,
-0.003228291869163513,
0.004228213336318731,
-0.024912763386964798,
-0.02017113007605076,
0.027250533923506737,
-0.010571702383458614,
0.03875735029578209,
-0.020719608291983604,
-0.009980741888284683,
0.04117647930979729,
0.005254644900560379,
0.012531602755188942,
-0.012857881374657154,
-0.008279270492494106,
0.05780060216784477,
0.04138786345720291,
0.01976301148533821,
-0.02126212790608406,
-0.0019303270382806659,
-0.02290436066687107,
0.030875999480485916,
0.033508121967315674,
0.03408142924308777,
0.005373696330934763,
0.0808916687965393,
-0.024748176336288452,
-0.024523703381419182,
0.0037826809566468,
-0.018444696441292763,
0.01919236034154892,
-0.04530172795057297,
0.03297093138098717,
0.006798684597015381,
0.020050978288054466,
-0.030271457508206367,
-0.01650400087237358,
-0.03374325856566429,
0.021376200020313263,
0.0334877073764801,
-0.013911177404224873,
0.02029106579720974,
-0.009837152436375618,
-0.003935575485229492,
-0.01574370451271534,
-0.020778611302375793,
-0.004671170841902494,
-0.009281438775360584,
-0.029592635110020638,
0.022747062146663666,
0.008500808849930763,
0.02104109711945057,
0.03253075107932091,
0.013568631373345852,
-0.010336305014789104,
-0.0067301844246685505,
0.043058354407548904,
0.004625874105840921,
0.03415578976273537,
-0.00417714286595583,
-0.06125245243310928,
0.03207111731171608,
-0.04948830232024193,
0.03434787318110466,
-0.04490850120782852,
0.0005462477565743029,
0.06275675445795059,
-0.012927678413689137,
0.008693823590874672,
-0.04581455886363983,
-0.03264060989022255,
-0.03867721185088158,
0.017863137647509575,
0.017648763954639435,
0.012370003387331963,
0.04636574164032936,
0.028179848566651344,
0.010369387455284595,
0.031067701056599617,
0.008425994776189327,
0.022442007437348366,
-0.06406965106725693,
0.002158563118427992,
0.004592658951878548,
-0.024495642632246017,
0.04577138274908066,
0.013802213594317436,
-0.010271755047142506,
0.013997748494148254,
-0.03188733384013176,
0.044455744326114655,
0.03092065639793873,
0.020613063126802444,
-0.021628770977258682,
0.04919534549117088,
-0.029249543324112892,
0.047965157777071,
-0.004077664110809565,
-0.007629172410815954,
0.12846556305885315,
0.03505818173289299,
0.038348112255334854,
-0.04402615875005722,
-0.004732982721179724,
-0.028030401095747948,
0.013545227237045765,
-0.008999456651508808,
0.008905602619051933,
-0.0250400397926569,
0.02191944792866707,
0.0002343586675124243,
0.02158033289015293,
-0.01791384071111679,
-0.0022550374269485474,
0.02247140370309353,
-0.005503565073013306,
-0.00681793037801981,
-0.010395404882729053,
0.01773720793426037,
-0.01814126968383789,
0.010380462743341923,
-0.04346848279237747,
0.028311852365732193,
-0.024582242593169212,
-0.025387661531567574,
0.03833465278148651,
-0.037415944039821625,
0.018116269260644913,
0.013949447311460972,
-0.017181800678372383,
0.05853480100631714,
0.006955411750823259,
-0.011748440563678741,
-0.048801958560943604,
0.008644192479550838,
-0.008341275155544281,
0.02115250751376152,
-0.002537284279242158,
-0.012404772453010082,
0.029910681769251823,
0.021906424313783646,
-0.005707786418497562,
0.03618667647242546,
-0.03132597729563713,
0.05986182019114494,
-0.0400693379342556,
0.015473193489015102,
-0.013502330519258976,
0.033949147909879684,
0.021717408671975136,
0.004705296829342842,
0.03010270558297634,
-0.019654346629977226,
-0.04544087499380112,
0.015720048919320107,
-0.0001565592101542279,
-0.00023312777921091765,
-0.004507489036768675,
-0.007282671984285116,
0.04215108975768089,
0.0011429961305111647,
-0.0052483524195849895,
-0.0017984535079449415,
0.0072951000183820724,
0.02565058507025242,
0.05486904829740524,
0.07327134162187576,
0.009242760017514229,
-0.026406198740005493,
-0.07028720527887344,
0.002593086566776037,
-0.0038116583600640297,
0.021488336846232414,
0.02173786424100399,
-0.004141727462410927,
0.01139588188380003,
-0.014032762497663498,
-0.031160756945610046,
-0.011897354386746883,
-0.05220913887023926,
0.07723169028759003,
-0.01637178473174572,
0.015791868790984154,
-0.06171518564224243,
0.011034145019948483,
0.039061300456523895,
0.027195997536182404,
-0.06476808339357376,
-0.00821311678737402,
0.025721320882439613,
0.03797880932688713,
-0.008997431956231594,
-0.022959353402256966,
0.016349447891116142,
0.01936744712293148,
-0.03090045042335987,
0.011200588196516037,
-0.006272413767874241,
0.08822402358055115,
0.045365698635578156,
-0.015547147952020168,
0.008682901971042156,
0.014181504026055336,
-0.024091701954603195,
0.008706370368599892,
-0.0061063929460942745,
-0.007828635163605213,
0.0020044022239744663,
-0.02243940159678459,
-0.011229344643652439,
-0.04589306190609932,
-0.022147128358483315,
0.002289378782734275,
0.0021325103007256985,
0.02669549733400345,
0.023659080266952515,
-0.02344871126115322,
0.020423276349902153,
0.0036450366023927927,
0.03500441834330559,
-0.027730213478207588,
0.008853941224515438,
-0.011978003196418285,
0.0020060106180608273,
-0.022394830361008644,
-0.005345428828150034,
-0.01580694131553173,
-0.00230157352052629,
-0.016515450552105904,
0.026897408068180084,
-0.017312755808234215,
0.032330214977264404,
0.006718785502016544,
-0.011160963214933872,
0.03578648716211319,
-0.004485386423766613,
0.03395207226276398,
0.004730422981083393,
-0.02035205438733101,
0.07391229271888733,
-0.036751653999090195,
-0.048041969537734985,
0.00498774740844965,
-0.021339043974876404,
0.016527391970157623,
-0.01741539128124714,
0.005628098268061876,
-0.0032318332232534885,
0.017474813386797905,
0.020350761711597443,
-0.0046584028750658035,
0.001973204081878066,
-0.010538854636251926,
-0.011939936317503452,
0.011193783022463322,
0.006057008169591427,
-0.008620704524219036,
-0.005664145573973656,
0.018646670505404472,
0.056334320455789566,
0.002711281646043062,
-0.0017783389193937182,
-0.027329791337251663,
-0.0021435001399368048,
-0.034497153013944626,
0.03426772356033325,
-0.0035955491475760937,
0.016269417479634285,
0.01162002980709076,
0.016489798203110695,
-0.016514040529727936,
-0.04833706468343735,
-0.007789972238242626,
-0.10247950255870819,
0.012933874502778053,
0.004602461587637663,
-0.04668834060430527,
0.0348394475877285,
-0.04063927382230759,
-0.008683353662490845,
0.012588292360305786,
-0.05880964919924736,
0.014487452805042267,
-0.027604712173342705,
-0.026070546358823776,
-0.013026582077145576,
0.008197963237762451,
0.034368786960840225,
0.04395478591322899,
-0.024591384455561638,
0.039716143161058426,
0.018079832196235657,
-0.02068171091377735,
-0.018814947456121445,
0.012736051343381405,
-0.023475049063563347,
0.03370337933301926,
0.0027863476425409317,
-0.015489175915718079,
0.07995922863483429,
-0.008505609817802906,
-0.032851818948984146,
0.027686098590493202,
-0.030809704214334488,
-0.0006965682259760797,
0.024893883615732193,
0.03970419988036156,
0.00026972388150170445,
-0.008437572978436947,
-0.043813835829496384,
-0.020063329488039017,
0.014085711911320686,
-0.012921328656375408,
0.0066402074880898,
0.05290666222572327,
-0.01904641091823578,
-0.019282367080450058,
0.008724700659513474,
-0.03093801625072956,
0.00008864831033861265,
0.03563582897186279,
-0.03929857164621353,
-0.030989302322268486,
-0.02776804007589817,
-0.00639876164495945,
-0.02164630778133869,
-0.00343992467969656,
-0.009296991862356663,
-0.011347360908985138,
-0.04089230298995972,
0.03449758514761925,
-0.031009867787361145,
0.013016216456890106,
0.05166824534535408,
0.004294407553970814,
-0.02613857388496399,
0.004695528652518988,
0.01692352630198002,
-0.01992673985660076,
-0.005882264114916325,
0.03368249163031578,
0.002244337694719434,
-0.003951763268560171,
0.02402360364794731,
-0.051659438759088516,
-0.049191415309906006,
0.04346081241965294,
0.009561510756611824,
0.009932824410498142,
-0.005120649002492428,
-0.05040672421455383,
0.007688380777835846,
-0.08592389523983002,
0.0604146346449852,
-0.05181487649679184,
-0.026178067550063133,
-0.04405403882265091,
-0.006783655378967524,
0.008501438423991203,
-0.013042038306593895,
0.06036008521914482,
-0.031895626336336136,
0.00571412593126297,
0.008770772255957127,
-0.04013564810156822,
0.025482330471277237,
-0.014042805880308151,
0.022272488102316856,
-0.0130947669968009,
0.014275812543928623,
0.028261302039027214,
-0.002935678232461214,
-0.007364646065980196,
0.005301934666931629,
-0.03157862275838852,
0.030042825266718864,
0.0042536575347185135,
-0.016947239637374878,
-0.02812056429684162,
0.0392424538731575,
-0.01604582741856575,
-0.0007775263511575758,
0.027554556727409363,
-0.011665374040603638,
0.030096834525465965,
-0.04657630994915962,
-0.013390196487307549,
-0.0593089759349823,
0.016934577375650406,
-0.04430269077420235,
-0.0034464658237993717,
-0.03439977020025253,
-0.02141663245856762,
0.040586505085229874,
-0.05371459946036339,
-0.01010819897055626,
0.025892803445458412,
-0.014048788696527481,
-0.01103622280061245,
0.03204568102955818,
-0.01986449584364891,
0.05758996307849884,
-0.06925731897354126,
0.013173716142773628,
0.013415363617241383,
0.007138419430702925,
-0.020792953670024872,
0.042981017380952835,
-0.03820855915546417,
-0.03132888302206993,
-0.005152866244316101,
0.06722117960453033,
0.020654970780014992,
0.006910742726176977,
0.06872833520174026,
0.04554952308535576,
-0.01167288701981306,
-0.04789729788899422,
0.03018009103834629,
-0.022932039573788643,
-0.005002089776098728,
-0.007533418945968151,
-0.007894889451563358,
0.0620473213493824,
-0.045656803995370865,
0.02118998020887375,
-0.0022089420817792416,
-0.012074267491698265,
-0.012957829982042313,
-0.0061361053958535194,
0.007807863876223564,
0.07072608917951584,
-0.013483254238963127,
-0.045317843556404114,
-0.02727111428976059,
0.0009115449502132833,
0.05362703651189804,
0.010545659810304642,
0.05323344096541405,
-0.04006579890847206,
0.0128597691655159,
-0.006212035659700632,
-0.024512555450201035,
-0.04317495599389076,
-0.07158398628234863,
0.026476170867681503,
0.005015173461288214,
0.04122654348611832,
0.01936337538063526,
-0.00873814057558775,
-0.026150617748498917,
0.05799708887934685,
-0.06234223023056984,
-0.008641887456178665,
-0.05715176463127136,
0.040400560945272446,
-0.009329661726951599,
0.01488152053207159
] |
<p><img src="http://i.stack.imgur.com/ORjPY.png" alt="enter image description here"></p>
<p>Let me explain the picture just to make sure. Object with mass 2 kg is being pulled with a force of F = 14.4 N. The whole system has an acceleration of a = 2.8 m/s^2. The friction coefficient between the objects and the ground is k = 0.2 What is the tension in the rope?
So the question is simple I believe but I can't understand the concept of tension in the rope (red line). Also if it helps I have a solution for the problem, it says that the tension is 4.8 N. Can someone please elaborate this? Thank you!</p> | 1,452 | [
0.006726852618157864,
-0.0013428643578663468,
-0.01646200381219387,
0.017291001975536346,
0.014785346575081348,
-0.026374321430921555,
-0.015784977003932,
-0.02999716065824032,
0.003656892804428935,
-0.020756440237164497,
0.015274171717464924,
0.04084952175617218,
0.030521448701620102,
0.04786226898431778,
0.01744680479168892,
-0.009355270303785801,
-0.017331182956695557,
-0.040366653352975845,
0.018567483872175217,
-0.013597602024674416,
-0.014282756485044956,
-0.0010294230887666345,
-0.00347719294950366,
0.0007049810374155641,
0.015535133890807629,
0.016818763688206673,
0.042150307446718216,
-0.025238722562789917,
0.08533057570457458,
0.031881220638751984,
0.011728191748261452,
-0.040263693779706955,
-0.006734118796885014,
0.008309249766170979,
0.020377181470394135,
0.07240153849124908,
-0.023893844336271286,
-0.03314083069562912,
0.006187161896377802,
0.020733140408992767,
0.013376948423683643,
-0.04877553880214691,
-0.0014874233165755868,
0.05332547426223755,
-0.06488923728466034,
0.012736758217215538,
0.016718212515115738,
-0.026386504992842674,
0.0676741972565651,
-0.04869403317570686,
0.09622487425804138,
0.0007648317259736359,
0.04676768556237221,
0.053684305399656296,
-0.0016038293251767755,
0.000838679086882621,
0.032104868441820145,
0.0615493580698967,
-0.03648655489087105,
-0.06539203971624374,
-0.024090945720672607,
-0.0294580589979887,
-0.06151719018816948,
-0.04386593773961067,
-0.0017116902163252234,
-0.0008871580939739943,
-0.05220654979348183,
-0.04400448873639107,
0.04813819378614426,
0.026151595637202263,
-0.006081443279981613,
0.01778765581548214,
0.0617070309817791,
-0.0603439100086689,
-0.010136924684047699,
-0.013951894827187061,
0.02811780385673046,
0.005119245033711195,
0.031051328405737877,
0.03941582143306732,
0.0000785730589996092,
0.010884679853916168,
0.04130341112613678,
0.0656106024980545,
0.02551889233291149,
-0.038279373198747635,
0.045542582869529724,
0.02199372462928295,
0.04202732816338539,
-0.01577701047062874,
0.00456369761377573,
-0.01477472297847271,
0.0004332773678470403,
0.023040475323796272,
0.006802019197493792,
-0.002824162133038044,
-0.008430101908743382,
0.022045565769076347,
0.028248919174075127,
-0.023159824311733246,
-0.004834819119423628,
-0.001981170615181327,
0.02884633280336857,
0.0751391276717186,
0.007971272803843021,
-0.007139898836612701,
-0.024349458515644073,
-0.006270073354244232,
-0.0025836536660790443,
0.021121114492416382,
-0.02611483819782734,
-0.0005622575990855694,
0.003509976202622056,
-0.029895521700382233,
-0.025698382407426834,
-0.041643742471933365,
-0.03142601624131203,
0.017543695867061615,
0.04414421319961548,
0.04108544439077377,
0.0489596389234066,
-0.036254532635211945,
0.038050174713134766,
-0.01476634293794632,
-0.042969781905412674,
0.014070423319935799,
0.031066736206412315,
-0.03846193104982376,
-0.008256878703832626,
0.04255647212266922,
-0.03028295934200287,
-0.029884275048971176,
-0.02266751229763031,
0.027906611561775208,
0.04393739625811577,
-0.02687993273139,
-0.08808648586273193,
-0.10581119358539581,
0.03801465034484863,
-0.018823698163032532,
0.0018041657749563456,
-0.07706505060195923,
0.0025306674651801586,
0.03570656478404999,
0.04698435962200165,
0.007685719057917595,
0.01478656567633152,
0.0006053143879398704,
0.00902634859085083,
0.02531312219798565,
0.010548576712608337,
-0.03754010424017906,
0.024525227025151253,
-0.05172792822122574,
-0.010131290182471275,
-0.059883493930101395,
-0.002103271894156933,
0.027693936601281166,
0.0030721614602953196,
-0.05730431154370308,
0.061854247003793716,
0.004065155051648617,
-0.009394507855176926,
0.033701151609420776,
-0.017597194761037827,
-0.016610242426395416,
0.06982477754354477,
0.011324089951813221,
0.0027801725082099438,
0.046922508627176285,
0.030821722000837326,
0.017101848497986794,
-0.02451745979487896,
0.03165540471673012,
-0.0038272636011242867,
-0.02234816364943981,
-0.003220767481252551,
-0.0064888522028923035,
-0.005302298814058304,
-0.003763048443943262,
-0.059275925159454346,
-0.060349784791469574,
0.013429622165858746,
0.03338946774601936,
0.006344481371343136,
0.055758945643901825,
0.017213258892297745,
-0.023781297728419304,
-0.011143922805786133,
-0.0171562097966671,
-0.0053181773982942104,
-0.08691000938415527,
0.039269089698791504,
-0.03273504599928856,
-0.009350509382784367,
-0.033610954880714417,
0.012434601783752441,
0.011150493286550045,
-0.03425051271915436,
-0.014344748109579086,
-0.002932070754468441,
0.03721719607710838,
-0.019826823845505714,
0.00271049328148365,
0.0005131469224579632,
0.05266345292329788,
0.045353569090366364,
-0.0065367501229047775,
0.02273075468838215,
-0.045686982572078705,
-0.022969191893935204,
0.008740506134927273,
-0.045251861214637756,
-0.0010495726019144058,
0.022625381126999855,
0.019256964325904846,
0.011780181899666786,
-0.005628267768770456,
0.002799793379381299,
0.051470935344696045,
-0.0007593747577629983,
0.08813533186912537,
0.02808532491326332,
0.010986934415996075,
0.007458707317709923,
0.03126520290970802,
0.028075506910681725,
0.02289568819105625,
-0.02779557928442955,
-0.022474030032753944,
-0.020822135731577873,
0.013930391520261765,
0.04297574609518051,
0.025134814903140068,
-0.04223672300577164,
-0.03282824903726578,
0.04876537248492241,
0.0182181503623724,
0.049636319279670715,
0.04374606907367706,
-0.022265344858169556,
-0.0255636814981699,
0.009121939539909363,
0.02985144779086113,
-0.01611495204269886,
0.022566113620996475,
0.023905139416456223,
0.06761385500431061,
0.04916376248002052,
-0.019505271688103676,
-0.0026807235553860664,
0.07919371873140335,
-0.019939826801419258,
0.008955787867307663,
0.010990827344357967,
-0.04116066172719002,
0.05557682365179062,
-0.02270287275314331,
0.03077378123998642,
0.0579318106174469,
0.02450260892510414,
0.01908751018345356,
-0.019172756001353264,
-0.010989351198077202,
0.039760708808898926,
-0.05732329189777374,
-0.03177604824304581,
-0.044898513704538345,
0.016521790996193886,
0.013725051656365395,
0.005496640224009752,
0.0035760768223553896,
0.002471154322847724,
-0.007717902306467295,
0.0035896077752113342,
0.04581921175122261,
-0.028102045878767967,
0.06047607213258743,
0.01827792078256607,
-0.022526796907186508,
0.006872099358588457,
-0.04287734627723694,
0.013449706137180328,
-0.036337632685899734,
-0.044976092875003815,
-0.013494248501956463,
-0.010593458078801632,
-0.028697852045297623,
0.05966390669345856,
0.005454611498862505,
0.018070954829454422,
0.02684592828154564,
-0.04161505028605461,
0.02678600512444973,
-0.015466930344700813,
0.00014779930643271655,
0.028272433206439018,
-0.01747371256351471,
-0.008615481667220592,
0.05560455843806267,
-0.003573559457436204,
0.03851575776934624,
0.04766907915472984,
-0.07452723383903503,
-0.037147220224142075,
-0.03559323027729988,
-0.006896479986608028,
0.03991226479411125,
-0.025914965197443962,
0.018040476366877556,
0.006357408128678799,
-0.024181904271245003,
-0.009409388527274132,
-0.04547857865691185,
-0.04388054460287094,
-0.014795377850532532,
-0.0025245603173971176,
0.03405747935175896,
-0.007640381809324026,
-0.05648664012551308,
0.08368325978517532,
0.009823143482208252,
-0.013179278001189232,
-0.05126993730664253,
-0.027021707966923714,
-0.025237882509827614,
-0.07159942388534546,
0.007328552193939686,
0.00350208836607635,
-0.024216311052441597,
0.0036925815511494875,
0.00005848281944054179,
0.00496372114866972,
0.07594642043113708,
-0.009555552154779434,
-0.0001814441056922078,
0.001331982552073896,
0.017877880483865738,
-0.018718015402555466,
0.05358625948429108,
0.008965378627181053,
-0.030336687341332436,
-0.0008097013924270868,
0.00005299849362927489,
0.030833706259727478,
-0.013928818516433239,
-0.038043539971113205,
0.015503204427659512,
-0.0104760080575943,
0.012605196796357632,
-0.011945703066885471,
0.03891115263104439,
0.005396983120590448,
-0.004937455058097839,
0.02639298513531685,
-0.01654728874564171,
0.05255964770913124,
-0.025307632982730865,
0.003996741957962513,
0.0410773903131485,
0.032105281949043274,
-0.00588030694052577,
-0.03835562244057655,
0.013167325407266617,
0.016220727935433388,
0.04410647973418236,
-0.024697264656424522,
-0.026852469891309738,
-0.0024464959278702736,
0.011605341918766499,
0.04400774836540222,
-0.013594125397503376,
-0.06002397462725639,
0.018486380577087402,
-0.053653597831726074,
-0.012352462857961655,
0.043180737644433975,
0.016119541600346565,
-0.014939064159989357,
0.06210535392165184,
0.012945376336574554,
0.05168057233095169,
0.042875032871961594,
0.03253096714615822,
-0.08675745874643326,
0.02414264902472496,
-0.039703767746686935,
-0.024142181500792503,
0.027588684111833572,
-0.009417450986802578,
-0.04079073294997215,
-0.017535127699375153,
-0.027607420459389687,
0.027744757011532784,
0.011771585792303085,
-0.047951359301805496,
0.005517500452697277,
-0.026395263150334358,
0.012582710012793541,
-0.0015356636140495539,
0.006349877454340458,
0.03604630008339882,
-0.014951609075069427,
0.025917980819940567,
0.045875582844018936,
-0.012026563286781311,
-0.003659513546153903,
0.014612318947911263,
-0.026796746999025345,
0.029269754886627197,
0.02235657535493374,
-0.0037730769254267216,
0.021202273666858673,
0.00755395507439971,
0.01805839315056801,
-0.0029513731133192778,
0.049718886613845825,
-0.005107480566948652,
0.027441149577498436,
-0.01957625336945057,
-0.05751607567071915,
-0.04591546207666397,
-0.05978879705071449,
0.06556102633476257,
-0.01974445767700672,
0.00822935625910759,
0.0016837813891470432,
-0.022129880264401436,
-0.04230618104338646,
0.022748097777366638,
0.04878536984324455,
0.013654106296598911,
-0.0330217219889164,
-0.04433426260948181,
-0.008965063840150833,
-0.04725755378603935,
-0.001339436275884509,
0.009567096829414368,
-0.00655029434710741,
-0.04085754603147507,
0.01381365954875946,
0.07215100526809692,
0.00627533532679081,
-0.002185117918998003,
0.022732969373464584,
-0.011639976873993874,
0.01619008742272854,
0.003784331725910306,
-0.019056405872106552,
-0.010942802764475346,
0.016076454892754555,
0.0213602464646101,
-0.017680376768112183,
-0.019781721755862236,
-0.08739589154720306,
-0.039489977061748505,
0.015077770687639713,
0.011842249892652035,
-0.014269303530454636,
-0.0012193822767585516,
-0.03997233882546425,
-0.03465144336223602,
0.04904486611485481,
-0.040268220007419586,
0.06674692779779434,
-0.01320898998528719,
0.041574496775865555,
0.013173495419323444,
0.004420444369316101,
-0.0073285470716655254,
0.0211105365306139,
-0.004291615914553404,
0.016412146389484406,
-0.004811903461813927,
-0.008331802673637867,
0.030174365267157555,
0.010622152127325535,
0.03578583896160126,
0.03354369476437569,
0.011843647807836533,
-0.03633267804980278,
0.013155167922377586,
0.0012515503913164139,
-0.05009899660944939,
-0.03748544678092003,
0.007258178200572729,
-0.03875819593667984,
-0.03804224357008934,
0.00811992958188057,
-0.01516952645033598,
-0.03245784342288971,
-0.01347595639526844,
-0.004665633663535118,
0.013833628036081791,
0.010289615020155907,
-0.010726680979132652,
-0.008209377527236938,
0.0793924555182457,
-0.019710827618837357,
0.056107133626937866,
0.042863696813583374,
-0.024798482656478882,
0.03276219591498375,
-0.051807139068841934,
0.019802993163466454,
0.019775277003645897,
-0.021093081682920456,
-0.018648410215973854,
0.013268117792904377,
-0.05191963165998459,
0.051774654537439346,
0.020449645817279816,
0.017110830172896385,
0.006629848852753639,
-0.05385603383183479,
0.0008613374084234238,
0.018456801772117615,
0.0295920018106699,
-0.0030738338828086853,
0.018731672316789627,
0.0054338122718036175,
0.009705839678645134,
-0.02368336357176304,
-0.02010698989033699,
0.02066514454782009,
-0.012911760248243809,
0.015317671932280064,
0.001487006084062159,
0.013903065584599972,
-0.011224460788071156,
-0.05655701085925102,
0.0044481027871370316,
-0.08299273252487183,
0.019120363518595695,
-0.009760857559740543,
-0.007006960455328226,
-0.014157310128211975,
-0.05736732482910156,
-0.025313058868050575,
-0.029804890975356102,
-0.015962941572070122,
0.048689816147089005,
-0.027752051129937172,
0.045512083917856216,
0.03400127589702606,
0.005154414568096399,
-0.023828009143471718,
-0.04520311951637268,
0.029956424608826637,
-0.01468634232878685,
-0.024690542370080948,
0.002972470363602042,
-0.005274789407849312,
0.017044544219970703,
-0.013814515434205532,
0.0201110877096653,
0.09427547454833984,
-0.04771200940012932,
-0.008183296769857407,
0.0380033403635025,
0.0014127170434221625,
0.022944705560803413,
0.03088443912565708,
-0.00599507475271821,
-0.010985979810357094,
-0.04556157812476158,
-0.04355580359697342,
-0.012687874026596546,
0.04981886222958565,
-0.034565914422273636,
-0.035549700260162354,
-0.006725169252604246,
-0.0027960138395428658,
0.03981708362698555,
0.00045215553836897016,
0.03193075209856033,
0.012065490707755089,
0.0698036402463913,
0.03784114494919777,
0.0010749173816293478,
0.032241176813840866,
0.016652176156640053,
0.05600574240088463,
-0.009442823939025402,
0.011201350949704647,
-0.011683524586260319,
-0.028368309140205383,
0.012288515456020832,
0.01110650785267353,
0.028445297852158546,
0.018957292661070824,
0.061780139803886414,
-0.04364616051316261,
-0.030767496675252914,
0.0010815118439495564,
0.01358967274427414,
0.04497594013810158,
0.02447577752172947,
-0.007197339087724686,
0.029151147231459618,
0.007445824332535267,
-0.038545120507478714,
-0.002221375470981002,
0.00003622296571847983,
-0.006841304246336222,
0.07289717346429825,
-0.046493496745824814,
0.05981528013944626,
0.028580209240317345,
0.020549284294247627,
0.04327262192964554,
0.03342905268073082,
-0.010923891328275204,
-0.007048015482723713,
0.03302773833274841,
0.007427441421896219,
-0.035883449018001556,
0.0057122609578073025,
0.013700117357075214,
0.017204929143190384,
0.00789321307092905,
0.005472150631248951,
0.01753372885286808,
0.031206993386149406,
0.0088692307472229,
-0.0171823650598526,
-0.03052893653512001,
0.004784522112458944,
0.023406313732266426,
0.0645495355129242,
0.005530606023967266,
-0.033866677433252335,
0.04595252498984337,
-0.008290224708616734,
0.013731892220675945,
-0.02899176999926567,
-0.018962526693940163,
-0.013105987571179867,
0.0008598897256888449,
0.004006036091595888,
-0.026107320562005043,
-0.0005303280777297914,
0.02144429460167885,
0.03547677770256996,
0.01131676696240902,
0.03852809965610504,
-0.03600617125630379,
-0.057932138442993164,
-0.021482042968273163,
-0.03518547862768173,
-0.047468338161706924,
0.04471280798316002,
0.0234846044331789,
-0.06686034053564072,
0.04164908081293106,
-0.011884214356541634,
0.006044212728738785,
0.035365160554647446,
0.02429846301674843,
-0.022219518199563026,
0.08339772373437881,
-0.04244600981473923,
0.016193313524127007,
-0.02374142035841942,
0.012855065055191517,
0.08911895751953125,
0.05739358440041542,
-0.005942134186625481,
-0.0294794999063015,
-0.015989691019058228,
-0.03282780572772026,
-0.02588685229420662,
-0.03042268566787243,
0.01692860946059227,
0.012637673877179623,
-0.008764723315834999,
0.023353245109319687,
0.02777823433279991,
-0.03856766223907471,
-0.002814461477100849,
0.02927122823894024,
-0.0063417451456189156,
-0.02732231095433235,
-0.016728153452277184,
-0.017388390377163887,
-0.0017392884474247694,
0.027387460693717003,
-0.04251614212989807,
0.022220991551876068,
-0.0008853376493789256,
0.008180737495422363,
-0.010950541123747826,
-0.030109204351902008,
0.010212628170847893,
-0.03987118601799011,
-0.04172845184803009,
0.016025420278310776,
-0.0001975486084120348,
-0.047476012259721756,
-0.02643480710685253,
0.04491730034351349,
0.0028059622272849083,
-0.018013620749115944,
-0.011563699692487717,
-0.016979435458779335,
-0.016718335449695587,
-0.0061330110765993595,
0.021523838862776756,
-0.0008610592922195792,
-0.05288306996226311,
0.014123898930847645,
-0.011495516635477543,
0.0182957760989666,
-0.002316197147592902,
0.015449963510036469,
0.01610478200018406,
-0.00344521994702518,
-0.006164242047816515,
-0.02925235964357853,
-0.004233677405864,
0.009102522395551205,
0.02539907768368721,
-0.025649994611740112,
-0.040613751858472824,
-0.050272684544324875,
-0.003061073599383235,
0.01671024225652218,
0.009917016141116619,
0.024681273847818375,
0.004217084031552076,
0.023136811330914497,
-0.014690251089632511,
0.041636623442173004,
-0.013036119751632214,
-0.0064615109004080296,
-0.011946707032620907,
-0.011095905676484108,
-0.008580404333770275,
-0.019640855491161346,
0.006096400320529938,
0.03883971646428108,
0.015763679519295692,
-0.01021351758390665,
-0.03293997421860695,
-0.0011661425232887268,
-0.02314845100045204,
0.027955498546361923,
-0.01828470267355442,
-0.005704502109438181,
-0.04358192905783653,
-0.03511137515306473,
0.012257964350283146,
0.01204733457416296,
-0.015636198222637177,
0.013287143781781197,
0.0035491243470460176,
-0.014579775743186474,
0.04472668841481209,
-0.05709889903664589,
-0.020305393263697624,
-0.005814655683934689,
-0.010325281880795956,
0.010286576114594936,
-0.0019768273923546076,
0.043679747730493546,
0.007994071580469608,
-0.002464370569214225,
-0.017934158444404602,
0.03495984524488449,
-0.0329422727227211,
0.02527039684355259,
0.005000108387321234,
-0.02404538355767727,
-0.002153652021661401,
0.022362375631928444,
-0.011618096381425858,
-0.07169550657272339,
-0.012299982830882072,
-0.020341303199529648,
-0.04142773523926735,
0.007698915898799896,
0.010635055601596832,
-0.02823384292423725,
0.0002524249139241874,
-0.021683020517230034,
0.034676071256399155,
-0.031576041132211685,
0.012215851806104183,
-0.04170272499322891,
-0.019060319289565086,
0.00013847730588167906,
0.037162426859140396,
-0.02263547293841839,
0.03962637856602669,
-0.035282038152217865,
0.03275078162550926,
-0.001514246454462409,
0.0008902470581233501,
0.0033875955268740654,
-0.0004175276553723961,
0.0030237147584557533,
-0.022071141749620438,
0.041226938366889954,
-0.012951581738889217,
-0.04757405072450638,
0.03126668184995651,
-0.033332135528326035,
-0.017699846997857094,
0.017852112650871277,
0.011091319844126701,
0.04792054370045662,
0.02088911086320877,
-0.03937653452157974,
-0.034861620515584946,
0.05341620370745659,
-0.036457762122154236,
0.007299779448658228,
0.009429536759853363,
-0.03344763070344925,
-0.0309430044144392,
-0.020835569128394127,
-0.022365478798747063,
-0.00949061382561922,
0.0026873559691011906,
0.0031898922752588987,
0.021818503737449646,
-0.014355868101119995,
-0.028806596994400024,
0.059636302292346954,
0.007787181530147791,
-0.008357125334441662,
0.05131932348012924,
0.010352945886552334,
0.046270206570625305,
0.027927404269576073,
-0.022928470745682716,
0.014642227441072464,
-0.02447829581797123,
0.015337545424699783,
-0.07319186627864838,
-0.006263916380703449,
0.00444113090634346,
0.02268727496266365,
0.042866118252277374,
-0.04796834662556648,
-0.02121991477906704,
0.049394942820072174,
-0.018786156550049782,
-0.0016658398089930415,
-0.029194284230470657,
-0.04353131353855133,
-0.01690879836678505,
-0.025431431829929352,
0.003716663457453251,
0.05406893417239189,
-0.0172592606395483,
0.03761177137494087,
0.007813181728124619,
-0.016377201303839684,
-0.03303438052535057,
-0.027059298008680344,
0.018757063895463943,
0.05093421787023544,
-0.007756604813039303,
-0.02708725817501545,
0.05046342313289642,
0.03331629931926727,
0.012917041778564453,
0.017471283674240112,
-0.03872246295213699,
-0.010705732740461826,
0.0452185682952404,
0.0000915945420274511,
-0.02044222131371498,
0.010528952814638615,
-0.06344334036111832,
-0.012300465255975723,
-0.005463884677737951,
0.01769890822470188,
-0.0024665200617164373,
0.004823812749236822,
-0.006492585875093937,
-0.009823901578783989,
0.028693076223134995,
-0.03660915046930313,
-0.02307627536356449,
0.04802537336945534,
-0.05251085385680199,
0.025903305038809776,
0.02956630103290081,
-0.012623106129467487,
-0.006868704687803984,
-0.07762867957353592,
-0.006438698153942823,
0.02138514816761017,
0.0321454294025898,
0.026590440422296524,
-0.027052048593759537,
-0.0008306821691803634,
0.03231913223862648,
0.0013618513476103544,
0.00940151046961546,
0.01100315060466528,
-0.0050179860554635525,
-0.05340156331658363,
-0.05478880554437637,
-0.009097302332520485,
0.014188847504556179,
-0.02221646159887314,
0.02162599004805088,
-0.02438202127814293,
-0.007415184285491705,
0.03814361244440079,
0.0340178981423378,
0.025372561067342758,
-0.0037881142925471067,
-0.03699599206447601,
-0.02367756888270378,
-0.10524487495422363,
0.02827158011496067,
0.01773751527070999,
-0.02842923067510128,
-0.013864705339074135,
0.018660394474864006,
-0.01815270073711872,
0.01501275785267353,
0.04184878244996071,
-0.018646448850631714,
-0.0008508423925377429,
-0.007931717671453953,
-0.019317759200930595,
0.0005726275267079473,
-0.016359692439436913,
0.019208092242479324,
-0.004181137774139643,
-0.027619892731308937,
0.0005112325889058411,
0.026438681408762932,
0.006362521089613438,
-0.0022689199540764093,
0.006949559319764376,
-0.0006403530132956803,
0.00976639986038208,
-0.020915308967232704,
-0.02248477004468441,
-0.0009358447859995067,
0.00648809690028429,
-0.027244925498962402,
0.0697282999753952,
-0.05713498219847679,
0.009582660160958767,
0.029466187581419945,
-0.013362010009586811,
-0.011815340258181095,
0.05677888169884682,
-0.003419748740270734,
0.03177748620510101,
-0.030563291162252426,
-0.03754182159900665,
0.04516415297985077,
-0.09378702938556671,
-0.008431695401668549,
0.004068152979016304,
-0.06011373549699783,
-0.029831670224666595,
0.041317518800497055,
0.05803826451301575,
0.016303712502121925,
-0.009969733655452728,
0.036001209169626236,
0.032030850648880005,
0.0017535232473164797,
0.026695245876908302,
0.022244315594434738,
0.031604040414094925,
-0.00948831345885992,
0.006273828912526369,
0.03567070513963699,
-0.019343161955475807,
0.05642307549715042,
-0.007472997065633535,
-0.013095305301249027,
-0.023464692756533623,
-0.005974939092993736,
-0.006355066318064928,
0.005519650876522064,
0.010126400738954544,
0.03209419921040535,
-0.036451004445552826,
0.06159641221165657,
-0.028593849390745163,
-0.014669546857476234,
0.03072201833128929,
0.011541377753019333,
-0.016321992501616478,
-0.025669721886515617,
0.028939763084053993,
-0.008011353202164173,
-0.0032400102354586124,
0.001319661969318986,
0.021756334230303764,
0.007180115673691034,
0.030639758333563805,
0.002394408220425248,
0.035379085689783096,
-0.019947845488786697,
-0.03205930069088936,
-0.018706226721405983,
-0.027983659878373146,
-0.026493247598409653,
-0.036942463368177414,
0.0317622609436512,
0.0279073566198349,
-0.02541901357471943,
-0.026216378435492516,
0.008332294411957264,
-0.008917196653783321,
0.05977598950266838,
-0.0559372641146183,
-0.034015264362096786,
-0.006750647909939289,
0.032593823969364166,
-0.0026055641938000917,
-0.004767997656017542
] |
<p>For the wave function of a scattered particle when finding the scattering aptitude we have:</p>
<p>$$\psi(r)=Ae^{ik_0∙r}+\frac{2\mu}{\hbar^2} ∫G(r-r')V(r')\psi(r')d^3r'$$</p>
<p>I was wondering what the variables $r$ and $r'$ represent. I think r just represents the position of the particle and $r'$ the size of the detector, but this seems wrong. I say this as when we do the Born approximation on it we substitute the $r'$ for e.g. $r_1$
. So what do they actually represent? thanks </p> | 1,453 | [
0.032366570085287094,
-0.03534385934472084,
0.011773441918194294,
-0.03847678378224373,
0.03700168803334236,
0.006142613478004932,
-0.032978206872940063,
-0.027889441698789597,
0.00530245853587985,
-0.007540425751358271,
0.04422973841428757,
0.013988596387207508,
0.08347276598215103,
-0.020635059103369713,
0.03213828429579735,
0.04814836382865906,
-0.004139854572713375,
0.005186000838875771,
-0.0033190064132213593,
-0.026313357055187225,
0.03829214349389076,
0.006441858131438494,
0.03597898408770561,
-0.0005296182353049517,
-0.005623241886496544,
0.06105653941631317,
0.006204095669090748,
0.007924942299723625,
0.023532962426543236,
0.03805850073695183,
0.011138040572404861,
-0.012020413763821125,
0.02800520695745945,
0.03155260160565376,
-0.0011357716284692287,
-0.029791170731186867,
-0.0327230766415596,
-0.010131048038601875,
-0.031856004148721695,
0.019927287474274635,
-0.03460664674639702,
-0.03031419776380062,
0.02149011939764023,
0.04455145075917244,
0.00700910110026598,
-0.003929861355572939,
0.004773010965436697,
-0.026568356901407242,
0.05500984936952591,
-0.05682849511504173,
0.07532112300395966,
0.02116679586470127,
0.026995623484253883,
0.01722763478755951,
0.012318389490246773,
0.012684596702456474,
0.07531081140041351,
0.04369260370731354,
-0.007660772185772657,
-0.01272883266210556,
-0.0025881528854370117,
-0.022788623347878456,
-0.002998613752424717,
0.005546447355300188,
0.0027353926561772823,
-0.0030883322469890118,
0.005364726297557354,
-0.012946804985404015,
0.0029262227471917868,
0.013622086495161057,
0.05037371441721916,
0.03185402229428291,
0.006757302209734917,
-0.012485547922551632,
0.015536646358668804,
-0.010070106945931911,
-0.00020128407049924135,
0.0158359594643116,
0.035310048609972,
-0.011351965367794037,
0.0019352593226358294,
-0.015847941860556602,
0.022372577339410782,
0.028172096237540245,
-0.005947636440396309,
-0.0008734577568247914,
0.04359547793865204,
-0.010202662087976933,
-0.01544254645705223,
0.006745345890522003,
-0.02582399919629097,
0.026548773050308228,
0.062487225979566574,
0.0008557631517760456,
-0.030418945476412773,
-0.00338248023763299,
0.010952319949865341,
0.07604659348726273,
-0.0046010068617761135,
-0.0033916879910975695,
0.0016645886935293674,
-0.03682705760002136,
0.03658280521631241,
0.07505729794502258,
-0.01826387457549572,
-0.036367591470479965,
-0.038551367819309235,
0.0174570269882679,
0.0013779033906757832,
-0.028657907620072365,
-0.021770868450403214,
0.030218571424484253,
-0.006902606226503849,
0.05016857758164406,
0.04327024891972542,
-0.03359396383166313,
-0.028296995908021927,
0.024304615333676338,
0.06296541541814804,
0.05332939326763153,
0.03720419481396675,
-0.03177833929657936,
0.020794708281755447,
-0.018734993413090706,
-0.0575178861618042,
0.049152813851833344,
0.005076726898550987,
-0.00291463197208941,
-0.03801620379090309,
0.033119674772024155,
0.0330396443605423,
-0.011108188889920712,
0.016955018043518066,
-0.008076178841292858,
-0.0035150053445249796,
-0.0169408917427063,
-0.08070097118616104,
-0.03679447993636131,
0.0084918774664402,
-0.007587023079395294,
-0.001632969593629241,
-0.0926341712474823,
-0.007142656482756138,
0.04166993871331215,
0.06205620989203453,
-0.012158682569861412,
0.018865015357732773,
-0.005345758516341448,
0.01274374220520258,
0.020025432109832764,
-0.00888806115835905,
-0.03166460618376732,
-0.03991354629397392,
-0.0020444190595299006,
-0.018447311595082283,
-0.055237479507923126,
0.017596369609236717,
0.04236450791358948,
-0.01046164333820343,
-0.002653823932632804,
0.0898750051856041,
-0.004963588900864124,
-0.004753817804157734,
0.02245103381574154,
-0.02943900227546692,
-0.010343054309487343,
0.11509355157613754,
0.033643338829278946,
-0.0021617934107780457,
0.03321373835206032,
-0.005017728079110384,
0.00017736908921506256,
0.004456410184502602,
0.019647561013698578,
0.049344927072525024,
-0.0020016806665807962,
-0.022678332403302193,
-0.03022846393287182,
0.00514731090515852,
0.006927747279405594,
-0.050848815590143204,
-0.037871867418289185,
-0.015331355854868889,
0.00297373509965837,
-0.022892961278557777,
0.028337035328149796,
-0.006022041663527489,
-0.031049858778715134,
-0.0315399169921875,
-0.04617776721715927,
-0.017928119748830795,
-0.06051155552268028,
-0.011957768350839615,
-0.024002840742468834,
-0.04964800924062729,
0.04712555184960365,
0.03245821222662926,
-0.014525377191603184,
0.007930896244943142,
-0.0756729394197464,
-0.03868739679455757,
0.019985049962997437,
-0.007229331415146589,
0.012258832342922688,
0.00516884820535779,
0.05242326483130455,
0.0288395918905735,
-0.0030836625955998898,
0.027618486434221268,
-0.004106604959815741,
-0.003655912121757865,
-0.0034657292999327183,
-0.009137213230133057,
0.0011162328300997615,
-0.004748775623738766,
-0.016121327877044678,
-0.013573815114796162,
-0.005581364035606384,
0.020744893699884415,
-0.012832666747272015,
-0.040963321924209595,
0.0540626123547554,
0.00729448301717639,
0.02954486571252346,
-0.005234587471932173,
0.04714878648519516,
-0.02854270674288273,
0.04817252233624458,
0.0007336864364333451,
-0.02551714889705181,
-0.011293886229395866,
-0.019374022260308266,
0.011261122301220894,
-0.005029748659580946,
-0.041973743587732315,
0.00006757592927897349,
0.005658652167767286,
0.029587406665086746,
0.033722661435604095,
0.002058971207588911,
-0.01797662489116192,
-0.021431203931570053,
0.007591322064399719,
0.0010820028837770224,
-0.05499181151390076,
-0.014755494892597198,
0.009594850242137909,
0.009347322396934032,
0.025592327117919922,
-0.011826860718429089,
-0.03839258849620819,
0.013084602542221546,
-0.054606739431619644,
0.02858300693333149,
-0.05384029820561409,
-0.03534960746765137,
-0.0053719463758170605,
-0.054284773766994476,
0.03210306912660599,
0.052573900669813156,
-0.02887861244380474,
-0.017595484852790833,
-0.03071214258670807,
-0.011225622147321701,
0.04442316293716431,
-0.0063743288628757,
0.008451128378510475,
-0.007465486880391836,
0.026617519557476044,
-0.03690814971923828,
-0.00981572363525629,
-0.009784845635294914,
-0.022456463426351547,
-0.020952682942152023,
0.02833748795092106,
0.043000031262636185,
0.0189785435795784,
0.001929271500557661,
0.010727042332291603,
-0.04126359149813652,
-0.0063744159415364265,
-0.015029698610305786,
0.03203319385647774,
0.04208363592624664,
-0.0538499541580677,
0.0385909266769886,
-0.07247842103242874,
-0.02253425493836403,
0.021365387365221977,
-0.006220452021807432,
-0.03464064002037048,
0.027443205937743187,
-0.017165478318929672,
-0.04050971195101738,
-0.02726830542087555,
0.02478349208831787,
0.01387337688356638,
-0.020225031301379204,
0.0290147103369236,
0.014984140172600746,
-0.0031964860390871763,
0.03460513427853584,
0.014797361567616463,
-0.047544751316308975,
-0.03510027006268501,
0.00844569131731987,
-0.0280064195394516,
0.001931095845066011,
-0.012556072324514389,
0.04643423855304718,
0.070647232234478,
-0.0437985323369503,
-0.011967652477324009,
-0.02747083641588688,
-0.033365972340106964,
0.017827045172452927,
0.02576959878206253,
0.012014000676572323,
0.005242357030510902,
-0.007554437965154648,
0.10633115470409393,
-0.017603684216737747,
-0.05448925122618675,
-0.013775937259197235,
0.0220880676060915,
-0.012734415009617805,
-0.026441087946295738,
-0.011445246636867523,
0.04660624638199806,
0.011746089905500412,
0.0409800186753273,
-0.019575487822294235,
0.039537183940410614,
0.024157850071787834,
0.00471733883023262,
-0.011434833519160748,
0.027183229103684425,
-0.012481855228543282,
-0.016682034358382225,
0.07204132527112961,
-0.041400596499443054,
-0.028846081346273422,
0.00856546126306057,
-0.008374080993235111,
0.05151116102933884,
0.029399709776043892,
-0.021908875554800034,
0.03246476128697395,
-0.0017908512381836772,
0.008721132762730122,
0.02958529442548752,
0.023021694272756577,
0.007772980723530054,
-0.022793719545006752,
-0.0317596010863781,
0.02666618488729,
0.03920597955584526,
-0.04248356819152832,
0.03015756979584694,
0.02093852497637272,
0.027443666011095047,
-0.03437891975045204,
-0.029412632808089256,
-0.03613344207406044,
-0.016079604625701904,
0.054773081094026566,
0.010821920819580555,
-0.0584547258913517,
0.06048077717423439,
-0.0018483329331502318,
0.013031761161983013,
-0.004227994009852409,
-0.0565631166100502,
-0.01446010172367096,
-0.038773491978645325,
-0.04093199223279953,
-0.012406586669385433,
0.04309900104999542,
0.009504958055913448,
0.029069624841213226,
0.043265700340270996,
-0.017125722020864487,
0.016635796055197716,
-0.008124818094074726,
-0.025787901133298874,
-0.0014819023199379444,
-0.028161097317934036,
-0.03741990029811859,
-0.018207799643278122,
-0.02800019457936287,
-0.014336647465825081,
-0.06884783506393433,
-0.018427088856697083,
0.029736964032053947,
-0.009973173961043358,
-0.012719668447971344,
0.0019387219799682498,
-0.0014790669083595276,
-0.007364192511886358,
-0.053533006459474564,
0.05430132523179054,
0.010831515304744244,
-0.01130575593560934,
0.019772132858633995,
0.04649953916668892,
-0.048866089433431625,
-0.03147416561841965,
-0.022670408710837364,
0.0018203362124040723,
0.039037447422742844,
0.020587453618645668,
0.0753493383526802,
0.0032364276703447104,
-0.00866624154150486,
0.018840845674276352,
0.03342301771044731,
0.06597142666578293,
0.03278783708810806,
-0.021997464820742607,
-0.002639172598719597,
-0.03361834958195686,
0.004162859637290239,
-0.025283310562372208,
0.049202851951122284,
0.0017305542714893818,
0.0040762294083833694,
0.03646128997206688,
-0.00043416148400865495,
-0.012007524259388447,
-0.009425199590623379,
0.04820874333381653,
0.026666568592190742,
-0.013551551848649979,
-0.06617933511734009,
0.02913859486579895,
-0.013565742410719395,
-0.00035919836955145,
0.01945253647863865,
-0.001174616627395153,
0.0008310510311275721,
0.015416596084833145,
0.04295025393366814,
-0.00826534628868103,
-0.012547245249152184,
-0.022420190274715424,
-0.023452170193195343,
-0.03109949268400669,
-0.016650313511490822,
-0.02287951111793518,
-0.0018103431211784482,
0.0783606618642807,
0.01384678389877081,
-0.003945502918213606,
0.018680188804864883,
-0.038950901478528976,
0.005447494797408581,
0.03234656900167465,
0.035077087581157684,
-0.030317729339003563,
-0.012277817353606224,
-0.04563052952289581,
-0.03151562437415123,
0.05362242832779884,
-0.016547534614801407,
0.012720228172838688,
-0.02959725446999073,
-0.003564721206203103,
-0.013258843682706356,
-0.0039102560840547085,
-0.029382625594735146,
-0.0007554979529231787,
0.0027677188627421856,
0.01550084725022316,
-0.04977428913116455,
0.028576653450727463,
0.009610684588551521,
0.02256680466234684,
-0.005178377963602543,
0.04529433697462082,
0.005801770836114883,
0.016223063692450523,
-0.0005150785436853766,
0.036222439259290695,
0.0122489919885993,
-0.06113056093454361,
0.010985791683197021,
0.00409826822578907,
0.023352254182100296,
0.04330113157629967,
-0.03226587548851967,
-0.03616919741034508,
0.03289873152971268,
0.02043551579117775,
-0.0037113784346729517,
0.018911343067884445,
-0.04010511189699173,
0.06646976619958878,
0.04417400807142258,
-0.011710294522345066,
0.0621163435280323,
-0.0014668861404061317,
0.02789289504289627,
-0.018931344151496887,
-0.00803160760551691,
0.02644241787493229,
-0.021130379289388657,
-0.010418824851512909,
-0.05731924623250961,
-0.012682147324085236,
-0.014284058474004269,
0.04117423668503761,
-0.009335125796496868,
0.03739815205335617,
-0.05046508461236954,
-0.04250756651163101,
-0.03250107169151306,
0.02723238430917263,
-0.02420775592327118,
-0.027358749881386757,
0.024898001924157143,
0.02401590533554554,
-0.006894578691571951,
-0.02228730544447899,
0.02707705833017826,
-0.016112931072711945,
0.024118026718497276,
0.039387382566928864,
0.018650244921445847,
0.06168849766254425,
-0.004880251828581095,
-0.028948867693543434,
0.08859538286924362,
-0.052142418920993805,
0.012008045800030231,
-0.027839409187436104,
-0.010451112873852253,
0.005707042757421732,
-0.052120160311460495,
-0.03463387489318848,
-0.0044687422923743725,
-0.03380860388278961,
0.04496470466256142,
-0.05176074802875519,
0.03941136598587036,
0.024532439187169075,
0.038398973643779755,
-0.056144341826438904,
0.0001668576296651736,
0.004445360507816076,
0.0013604082632809877,
-0.028090806677937508,
0.01765790395438671,
0.000256936444202438,
-0.0005397393251769245,
0.005133023485541344,
0.01016772910952568,
0.03210776671767235,
0.00810145866125822,
-0.01660030148923397,
-0.00494237057864666,
0.007999212481081486,
0.020992429926991463,
-0.0041926405392587185,
0.02247694507241249,
0.02942921407520771,
-0.0068869017995893955,
0.006424414459615946,
0.025921694934368134,
0.06906481087207794,
-0.021751007065176964,
0.002156607573851943,
-0.03832712024450302,
0.0010200467659160495,
0.020091861486434937,
-0.025289343670010567,
-0.012436776421964169,
-0.005486190784722567,
-0.003811497939750552,
0.008555715903639793,
-0.03106800653040409,
-0.008064198307693005,
0.014209305867552757,
-0.008229157887399197,
0.009044050239026546,
-0.007274037692695856,
-0.025912335142493248,
0.00560509879142046,
0.0027432232163846493,
-0.01610175333917141,
0.0165422223508358,
0.012154191732406616,
0.04863031208515167,
-0.00399744464084506,
0.0230238176882267,
0.012663179077208042,
0.015267811715602875,
0.0011588518973439932,
-0.03882281482219696,
0.002543077804148197,
0.03498794138431549,
0.04743937775492668,
-0.04297240078449249,
-0.031215624883770943,
-0.08749641478061676,
0.0007559389341622591,
0.07813630998134613,
-0.03721760958433151,
0.04791555181145668,
-0.009168114513158798,
-0.05061733350157738,
-0.012687868438661098,
-0.012253514491021633,
-0.04358511045575142,
-0.017086483538150787,
-0.019776515662670135,
0.05322021245956421,
-0.03430742025375366,
0.0036417669616639614,
-0.029518434777855873,
0.03574907034635544,
-0.027592327445745468,
0.006804205011576414,
0.0013234911020845175,
0.04413110390305519,
-0.00042574736289680004,
0.005451329983770847,
-0.0021884895395487547,
0.030772287398576736,
0.020746758207678795,
0.010960803367197514,
0.032413870096206665,
-0.009049984626471996,
0.0248800590634346,
0.029519157484173775,
0.019751165062189102,
-0.02984323538839817,
0.0007274841191247106,
-0.05691076070070267,
-0.0007353242835961282,
0.013915454968810081,
-0.021964211016893387,
-0.024342305958271027,
0.0006323317647911608,
0.02663830853998661,
0.030058663338422775,
0.029717298224568367,
-0.003960920963436365,
-0.05872638151049614,
-0.020115850493311882,
-0.07077918201684952,
-0.008799555711448193,
0.008143363520503044,
-0.058143939822912216,
-0.003924430813640356,
0.03151283040642738,
-0.03633362427353859,
0.04803265631198883,
0.0149311488494277,
0.01409907080233097,
-0.02218151092529297,
0.06421145796775818,
-0.0018336353823542595,
0.030770564451813698,
-0.016410520300269127,
-0.0009196106111630797,
0.11161162704229355,
0.08220473676919937,
0.0015024504391476512,
-0.05718023329973221,
0.0069345226511359215,
-0.003339015878736973,
0.03211180120706558,
-0.01499979104846716,
-0.00297975423745811,
0.008717137388885021,
-0.014057641848921776,
-0.015409931540489197,
0.023404721170663834,
-0.0007779130828566849,
0.019002269953489304,
-0.023411652073264122,
-0.015387436375021935,
-0.0808185487985611,
0.0050678979605436325,
0.012515532784163952,
0.0029793467838317156,
-0.020382041111588478,
-0.03685451298952103,
0.033617082983255386,
0.00015446961333509535,
-0.011622793972492218,
-0.005203591659665108,
-0.016692737117409706,
0.03079010546207428,
-0.012259476818144321,
-0.029581984505057335,
0.013443538919091225,
-0.0379638709127903,
0.0063292356207966805,
-0.009693956933915615,
0.04832656681537628,
0.026956822723150253,
-0.0690026506781578,
0.018533332273364067,
0.024460935965180397,
0.020808007568120956,
-0.01827574148774147,
-0.01350848376750946,
0.024406414479017258,
-0.03373394533991814,
-0.04156435281038284,
-0.004382215440273285,
0.054702237248420715,
-0.01782134361565113,
-0.030309239402413368,
-0.04340484365820885,
0.01995266228914261,
0.02568923495709896,
-0.07631383836269379,
0.011670026928186417,
0.014784217812120914,
-0.0016315828543156385,
-0.01902896910905838,
0.004498885944485664,
-0.020724130794405937,
0.006699640769511461,
-0.0010093327146023512,
0.00036993937101215124,
-0.002439475618302822,
-0.01101623009890318,
0.026463299989700317,
-0.04028686508536339,
0.047204580157995224,
0.014630795456469059,
-0.028548412024974823,
-0.04628391191363335,
-0.0025773721281439066,
-0.04385972023010254,
-0.0052483403123915195,
0.04554939270019531,
0.023764988407492638,
0.05414159223437309,
-0.04422478750348091,
0.004102877341210842,
-0.014085253700613976,
-0.05671189725399017,
0.03144175559282303,
-0.052662648260593414,
-0.03063582442700863,
-0.024765996262431145,
-0.010252687148749828,
0.023607585579156876,
0.027671851217746735,
0.027781996876001358,
-0.0167600829154253,
0.00013140434748493135,
0.024817483499646187,
0.007887403480708599,
-0.04796639084815979,
-0.004056213889271021,
0.058120232075452805,
-0.04777531698346138,
-0.00978875532746315,
-0.005420640576630831,
0.008236978203058243,
0.01792200841009617,
0.015870898962020874,
-0.017050115391612053,
0.02758999727666378,
-0.02805277891457081,
-0.0044561754912137985,
-0.009330191649496555,
-0.04139086231589317,
-0.018128054216504097,
-0.03494129702448845,
-0.02620149590075016,
-0.07391468435525894,
-0.0038872554432600737,
-0.049758609384298325,
-0.0009449102799408138,
-0.0008569621131755412,
0.001968023367226124,
-0.011738463304936886,
0.02134517766535282,
-0.047319892793893814,
-0.006586560048162937,
0.011257919482886791,
0.026486998423933983,
-0.024680450558662415,
0.03506580367684364,
-0.02568548545241356,
-0.011226873844861984,
-0.02188110537827015,
0.011539225466549397,
0.022832093760371208,
-0.029273206368088722,
0.007720166351646185,
0.045550353825092316,
0.00827369000762701,
-0.019198184832930565,
-0.014680047519505024,
-0.00606093555688858,
0.03440539166331291,
-0.019774658605456352,
0.013591103255748749,
0.007918785326182842,
-0.07062780857086182,
-0.0652339905500412,
0.03063104674220085,
0.01568995788693428,
0.009476573206484318,
0.04367435351014137,
-0.0037622549571096897,
-0.02075297012925148,
0.053324710577726364,
-0.013849077746272087,
-0.023683514446020126,
0.0074052512645721436,
-0.03821234032511711,
-0.0017514199716970325,
-0.038333866745233536,
0.008202400989830494,
-0.011205131188035011,
0.020585281774401665,
0.06080196052789688,
-0.004932263866066933,
-0.02740185149013996,
0.052571773529052734,
-0.002266837749630213,
0.003685262519866228,
0.007426061667501926,
0.009631281718611717,
-0.034523993730545044,
0.017008112743496895,
0.035176534205675125,
-0.001524677500128746,
0.06529634445905685,
0.05035991221666336,
0.008054355159401894,
-0.06874408572912216,
-0.00002376950578764081,
0.012083722278475761,
-0.03072178363800049,
0.021577313542366028,
-0.09691452980041504,
0.021292129531502724,
0.025519927963614464,
-0.09273849427700043,
0.01221497729420662,
-0.05694977939128876,
0.0010584776755422354,
-0.022664472460746765,
0.026473894715309143,
-0.004194211680442095,
0.048296649008989334,
-0.004451891407370567,
0.037260979413986206,
0.003919844049960375,
0.0003422910813242197,
0.01620386727154255,
-0.04673352465033531,
-0.04572233930230141,
0.061660751700401306,
-0.0295725017786026,
-0.041101034730672836,
0.09027741849422455,
-0.01805988699197769,
-0.005829826463013887,
0.030444422736763954,
-0.011013790965080261,
0.023514464497566223,
-0.006239017937332392,
0.02152533270418644,
0.019364921376109123,
0.025114452466368675,
0.009456326253712177,
-0.04001214727759361,
0.001774500240571797,
-0.012762056663632393,
0.00781355518847704,
0.009485195390880108,
0.006272060330957174,
-0.004628357011824846,
-0.014191624708473682,
-0.05145827680826187,
-0.01835000142455101,
0.04487346485257149,
-0.01040585059672594,
-0.02927100472152233,
-0.002872631186619401,
-0.00201777764596045,
0.029308658093214035,
-0.054367341101169586,
0.019533146172761917,
-0.04655766487121582,
0.018261516466736794,
0.019602036103606224,
-0.01657695882022381,
-0.020173436030745506,
0.03779638558626175,
-0.04006544128060341,
-0.035870667546987534,
-0.0005827918648719788,
0.03415340557694435,
-0.022185737267136574,
-0.02835925854742527,
-0.012253516353666782,
0.024965010583400726,
0.02819722145795822,
0.007133011240512133,
-0.023303546011447906,
-0.03823985904455185,
0.006469934247434139,
0.001322777708992362,
0.0073890420608222485,
0.0022658954840153456,
-0.021019719541072845,
-0.020527802407741547,
-0.06879305839538574,
0.04964108392596245,
0.038381606340408325,
-0.02604835107922554,
-0.024225080385804176,
-0.0019081153441220522,
0.010140743106603622,
0.0061461953446269035,
0.0505714975297451,
0.010645533911883831,
-0.03174110874533653,
-0.019054509699344635,
0.007494156248867512,
0.013969925232231617,
-0.06218668445944786,
-0.009768525138497353,
0.024064339697360992,
0.015295782126486301,
-0.05396674573421478,
0.015848945826292038,
0.0027974583208560944,
0.049926236271858215,
0.0025704107247292995,
0.004544998984783888,
0.03110473044216633,
-0.026785902678966522,
-0.03378190100193024,
0.047529637813568115,
0.012069785967469215,
0.02728952281177044,
0.05138805881142616,
0.01394262071698904,
0.01625719480216503,
0.04223599284887314,
-0.03740708902478218,
-0.006581893190741539,
0.013677717186510563,
-0.0032147159799933434,
-0.019675681367516518,
0.019415592774748802,
0.012137251906096935,
0.060058094561100006,
-0.021473100408911705,
-0.012973364442586899,
0.025808895006775856,
-0.04276652634143829,
-0.037315841764211655,
0.06821898370981216,
0.04640845209360123,
0.0448853075504303,
0.05106364190578461,
0.020361142233014107,
0.008280551061034203,
-0.04035929962992668,
0.024996671825647354,
0.0453602634370327,
-0.002739383140578866,
0.012786687351763248,
0.026728428900241852,
0.022394385188817978,
-0.03671671450138092,
0.013044800609350204,
0.007067753002047539,
0.05040878430008888,
-0.01647242158651352,
0.027151357382535934,
-0.01373582985252142,
-0.036916229873895645,
0.010969281196594238,
0.02904491499066353,
-0.01577930338680744,
0.09294229000806808,
-0.04356679320335388,
-0.012792187742888927,
-0.0004707258485723287,
-0.0001277475239476189,
0.005195675417780876,
0.020363837480545044,
0.022213567048311234,
0.0042123375460505486,
-0.02520855702459812,
-0.031217148527503014,
-0.04082142934203148,
0.023039236664772034,
0.025265837088227272,
-0.06642331928014755,
-0.0003047747886739671,
-0.0029948765877634287,
-0.017321502789855003,
-0.024374578148126602,
-0.01605740189552307,
0.006046382710337639,
0.008991881273686886,
0.023780986666679382,
0.0402398481965065,
0.05065826326608658,
-0.015136602334678173,
-0.00570718152448535,
-0.00771356699988246,
0.04304695874452591,
-0.055358532816171646,
-0.00015981086471583694,
-0.03402698040008545,
0.0439455509185791,
0.020596574991941452,
0.014565929770469666
] |
<p>I have heard that when a sailboat is sailing against the wind, it operates on the principle of 'lift'. I am unable to understand the explanation, based on Bernoulli principle, completely. My question is, when it says 'lift', it literally means that the boat is being 'lifted' out of the water? Like when we throw a stone across the lake and it skims and hops on the water?</p> | 1,454 | [
-0.00607152096927166,
0.005040861666202545,
-0.025837652385234833,
0.006304014008492231,
0.035090602934360504,
0.02615930140018463,
0.008300990797579288,
0.01748482882976532,
0.007471480406820774,
-0.04740885645151138,
-0.001284073106944561,
0.08554349094629288,
0.03059784322977066,
0.007179331034421921,
0.035359758883714676,
0.024921607226133347,
-0.02097433991730213,
-0.015477431006729603,
0.03291994705796242,
0.012778365053236485,
-0.026487823575735092,
0.031185410916805267,
0.004202523734420538,
0.014630517922341824,
-0.0115196006372571,
-0.021339189261198044,
0.048158325254917145,
0.007998590357601643,
0.037537768483161926,
0.033519893884658813,
-0.005903928074985743,
-0.04567933455109596,
0.006744320038706064,
0.0350976400077343,
0.033835530281066895,
0.006359429098665714,
-0.014984182082116604,
-0.017989499494433403,
0.005047214683145285,
0.012115529738366604,
-0.011292783543467522,
-0.024315660819411278,
-0.006840940564870834,
0.033659350126981735,
-0.055553995072841644,
0.015479749999940395,
0.028875647112727165,
-0.03121270425617695,
0.050901032984256744,
-0.07302073389291763,
0.056062012910842896,
0.0074576265178620815,
0.04725022241473198,
0.019778376445174217,
0.02015412412583828,
0.02613837644457817,
0.07300731539726257,
0.028321320191025734,
-0.03550480306148529,
-0.024928247556090355,
0.004033094272017479,
-0.03659180924296379,
-0.021665671840310097,
-0.045610833913087845,
-0.024844156578183174,
-0.000936203810852021,
-0.010185914114117622,
-0.028237592428922653,
0.03594481945037842,
0.03930886834859848,
-0.011513041332364082,
-0.005862221121788025,
0.03329641744494438,
-0.061196111142635345,
0.024247396737337112,
-0.03596526011824608,
0.0020616278052330017,
0.03137693554162979,
0.009994261898100376,
0.02965119667351246,
-0.012161961756646633,
0.027543775737285614,
0.04837328568100929,
0.060031674802303314,
0.02093484438955784,
-0.03539569675922394,
0.06461112946271896,
-0.021973149850964546,
0.04274020716547966,
-0.005329418927431107,
0.003432983998209238,
-0.0176882091909647,
-0.004961618687957525,
-0.021871551871299744,
-0.015554926358163357,
0.01306569017469883,
-0.0076665389351546764,
0.028470074757933617,
0.05547115206718445,
-0.0381433442234993,
0.01739761419594288,
-0.04123447835445404,
0.022533511742949486,
0.05668509379029274,
-0.016215281561017036,
-0.0072836619801819324,
-0.05188850685954094,
0.03151663392782211,
-0.03478643298149109,
-0.012277179397642612,
-0.04346933588385582,
0.01871199905872345,
0.00585001427680254,
-0.028202082961797714,
-0.01727687381207943,
-0.018897954374551773,
-0.0011568117188289762,
0.017947468906641006,
0.05812579020857811,
0.039801448583602905,
0.03966822475194931,
-0.05927935615181923,
0.01215378101915121,
0.00008269557292805985,
-0.06396662443876266,
0.03751029074192047,
-0.022958731278777122,
-0.04107451066374779,
-0.018663421273231506,
0.007752460893243551,
-0.009597971104085445,
-0.024982932955026627,
0.010973023250699043,
0.027850419282913208,
0.03589056059718132,
0.010293466970324516,
-0.08613181859254837,
-0.019468754529953003,
0.05423346906900406,
-0.018557315692305565,
-0.00830905418843031,
-0.07091472297906876,
0.045478031039237976,
0.050696566700935364,
0.0998537614941597,
-0.0008210818050429225,
0.028754539787769318,
-0.014949138276278973,
0.005253581330180168,
-0.010817487724125385,
-0.011989904567599297,
-0.03249982371926308,
-0.0067881029099226,
-0.017856605350971222,
-0.024822227656841278,
-0.07881395518779755,
0.0076938956044614315,
0.015283431857824326,
-0.017338499426841736,
-0.05267181247472763,
0.027158861979842186,
-0.003234642092138529,
-0.006158775649964809,
0.0057650404050946236,
0.0301358662545681,
-0.015088329091668129,
0.07467438280582428,
0.023126378655433655,
0.0164854247123003,
0.07670677453279495,
0.013733219355344772,
0.00586901418864727,
-0.013549917377531528,
0.02158084698021412,
0.050912968814373016,
-0.035290371626615524,
-0.028701405972242355,
-0.00840094406157732,
0.052030231803655624,
-0.002998954150825739,
-0.06665834784507751,
-0.03731996938586235,
-0.001686320872977376,
0.0042876871302723885,
-0.009274499490857124,
0.03086164779961109,
-0.004839030094444752,
-0.012779759243130684,
0.01711166463792324,
-0.05920528620481491,
-0.006406182888895273,
-0.08338277786970139,
0.025657255202531815,
-0.05725119635462761,
0.009198245592415333,
0.007061994634568691,
0.03258467838168144,
0.03726448863744736,
-0.0630936399102211,
0.006195663474500179,
-0.02403218485414982,
0.014355668798089027,
0.0019236046355217695,
0.000027761871024267748,
0.026992814615368843,
0.01675436832010746,
0.017126012593507767,
0.05324503779411316,
0.04422957822680473,
-0.017945578321814537,
-0.034560587257146835,
6.346708119053801e-7,
-0.05346253514289856,
0.006300534121692181,
0.017002951353788376,
-0.012486630119383335,
0.00310411280952394,
-0.0026688366197049618,
0.010028551332652569,
0.018210701644420624,
-0.00813972670584917,
0.0770760178565979,
0.04236733913421631,
0.005955671891570091,
0.02888260968029499,
0.03456658869981766,
-0.01175550278276205,
-0.009780613705515862,
0.02431219443678856,
-0.024002762511372566,
-0.01683235540986061,
0.02033834531903267,
0.013490039855241776,
0.034401390701532364,
0.004600126296281815,
-0.009988844394683838,
0.04001786559820175,
0.028965186327695847,
0.01577967405319214,
0.04664232209324837,
-0.02830040268599987,
-0.005783443804830313,
-0.0022367786150425673,
0.039864733815193176,
0.014393324963748455,
0.009730536490678787,
0.04219379276037216,
0.034623563289642334,
0.00956112053245306,
-0.007397073786705732,
-0.05022961273789406,
0.04070350527763367,
0.039036110043525696,
0.03292753919959068,
-0.04247741401195526,
-0.01210358738899231,
0.024827949702739716,
-0.03572743386030197,
0.01617290824651718,
-0.00690122926607728,
0.005066874902695417,
-0.0027226789388805628,
-0.02101946249604225,
0.0004519163921941072,
0.021937059238553047,
0.00732202734798193,
-0.020077649503946304,
-0.020552722737193108,
0.03898949548602104,
-0.043963104486465454,
0.023334085941314697,
-0.04243216663599014,
-0.017910851165652275,
-0.01671348512172699,
-0.0064971111714839935,
0.012450717389583588,
0.03687738627195358,
0.062448881566524506,
-0.0029417250771075487,
-0.03834620863199234,
-0.02775045484304428,
-0.02507351152598858,
-0.023868892341852188,
0.01025835145264864,
-0.046821095049381256,
0.020417004823684692,
-0.049348048865795135,
-0.014846811071038246,
0.07889705151319504,
-0.001393127953633666,
-0.011925995349884033,
-0.0025141017977148294,
-0.018447672948241234,
-0.018687637522816658,
-0.00879453681409359,
-0.06352225691080093,
0.010280565358698368,
-0.0017562415450811386,
-0.026194270700216293,
0.0551479198038578,
-0.0022278325632214546,
-0.004916175734251738,
0.03470737487077713,
-0.07167607545852661,
-0.044878628104925156,
-0.029302354902029037,
0.006810396909713745,
0.010313308797776699,
-0.011428659781813622,
0.009488821029663086,
-0.02609492465853691,
-0.048000041395425797,
0.019479434937238693,
-0.029950061812996864,
-0.02765863575041294,
-0.01102907583117485,
0.0001202120038215071,
0.003774457611143589,
0.003147053997963667,
-0.04790998622775078,
0.08064113557338715,
0.004675249103456736,
-0.03143445402383804,
0.013874003663659096,
-0.0066193584352731705,
-0.02596994675695896,
-0.00040193539462052286,
0.007719964720308781,
0.03148899972438812,
-0.012523572891950607,
0.06427067518234253,
0.008915828540921211,
0.013998543843626976,
0.021535124629735947,
0.0036380505189299583,
0.0032968753948807716,
-0.01195690967142582,
0.009862241335213184,
0.02540276013314724,
0.03482051193714142,
0.005093053914606571,
-0.02415481023490429,
0.027961473912000656,
-0.0004985014093108475,
0.052064310759305954,
0.028833838179707527,
-0.008143918588757515,
0.054844047874212265,
0.003475183853879571,
0.008280782960355282,
-0.009056517854332924,
0.04999026283621788,
-0.019726388156414032,
-0.008606888353824615,
0.03185534477233887,
0.02049989439547062,
0.042971398681402206,
-0.0067054047249257565,
0.010543795302510262,
0.010712401941418648,
0.06028842553496361,
-0.02998335100710392,
-0.038975149393081665,
-0.0075790900737047195,
-0.006628822535276413,
0.026567060500383377,
-0.028828280046582222,
-0.01665494777262211,
0.0385519303381443,
0.015784256160259247,
0.0007936827605590224,
-0.0025659233797341585,
-0.040415674448013306,
0.030007408931851387,
-0.04906398802995682,
-0.007697212044149637,
0.025743214413523674,
0.012337876483798027,
-0.03638089448213577,
0.04795586317777634,
-0.010872120968997478,
0.07142028957605362,
0.06132306903600693,
0.006113693583756685,
-0.10008194297552109,
0.03342771530151367,
-0.05266960710287094,
-0.013085717335343361,
-0.025855103507637978,
-0.010667596012353897,
0.00678376667201519,
-0.026483867317438126,
-0.047635532915592194,
-0.036814991384744644,
-0.022585848346352577,
-0.06436620652675629,
0.026107655838131905,
-0.0004025216039735824,
-0.046036865562200546,
0.014511615969240665,
-0.0007046099635772407,
0.010567590594291687,
-0.04437209293246269,
0.01615506410598755,
0.03595089167356491,
-0.001572582870721817,
0.0028124384116381407,
-0.006624377332627773,
0.01769724301993847,
0.01566128619015217,
-0.020695801824331284,
0.04247867316007614,
0.045491017401218414,
-0.04700907692313194,
0.01827724650502205,
0.029096882790327072,
0.033195335417985916,
-0.0026973376516252756,
0.018033871427178383,
-0.032202161848545074,
-0.04437178373336792,
0.00848857220262289,
0.01371346227824688,
-0.0019052756251767278,
0.032523006200790405,
-0.005448589567095041,
0.029895693063735962,
0.013178708963096142,
-0.03935951739549637,
0.06661152839660645,
0.03944109007716179,
0.03302406892180443,
-0.0024564783088862896,
-0.03382400795817375,
0.01077569741755724,
0.01300046592950821,
-0.012193016707897186,
0.021241527050733566,
0.011394093744456768,
-0.027281736955046654,
-0.005105812102556229,
0.040987204760313034,
-0.023126235231757164,
-0.009918774478137493,
0.03811291977763176,
0.000004338181042840006,
0.015488575212657452,
0.0008016229839995503,
-0.02080254629254341,
0.01314530335366726,
0.05524173751473427,
0.026161344721913338,
0.012739721685647964,
-0.0032379082404077053,
-0.04969395324587822,
-0.012921330519020557,
0.05808069929480553,
0.015798093751072884,
-0.049801796674728394,
0.006987733766436577,
-0.039325397461652756,
-0.017570102587342262,
0.02732919529080391,
-0.012130764313042164,
0.003023887285962701,
-0.053073592483997345,
-0.008608026430010796,
0.005818473175168037,
0.01010862272232771,
-0.002256253734230995,
0.027264058589935303,
-0.03060157224535942,
0.01969028078019619,
-0.018160736188292503,
0.003140610409900546,
-0.006371976342052221,
0.022063853219151497,
0.035057201981544495,
0.04713727533817291,
0.009887027554214,
0.021928811445832253,
-0.04265987128019333,
0.025505058467388153,
-0.03602645546197891,
-0.0683816447854042,
0.009399152360856533,
0.023483650758862495,
-0.030247386544942856,
-0.0019688992761075497,
-0.03061729483306408,
-0.05204300954937935,
-0.00812475010752678,
0.00267644040286541,
0.0021061350125819445,
-0.007539648562669754,
-0.04717507213354111,
-0.025593513622879982,
0.04217744246125221,
0.01308336853981018,
0.06767544895410538,
0.03971600905060768,
-0.06161937862634659,
-0.025529753416776657,
0.008207329548895359,
0.019721008837223053,
-0.018088703975081444,
-0.08247224241495132,
-0.04378798231482506,
0.00704826507717371,
-0.03853132575750351,
0.04953368008136749,
-0.01376535464078188,
0.014266569167375565,
-0.026185696944594383,
-0.04771268367767334,
-0.03969850018620491,
0.03840005770325661,
0.018019285053014755,
-0.019444135949015617,
0.017680255696177483,
0.03373415395617485,
0.01187359169125557,
-0.03916102275252342,
0.009520587511360645,
0.018205853179097176,
-0.01064007543027401,
0.02067188359797001,
0.005599668249487877,
0.010783348232507706,
-0.01621050015091896,
-0.007980252616107464,
0.005795844830572605,
-0.0344243086874485,
0.0477970652282238,
-0.04432077705860138,
-0.0030111283995211124,
0.000611222698353231,
-0.08937758207321167,
-0.061209786683321,
-0.013441691175103188,
0.02857585996389389,
0.012555246241390705,
-0.03527386486530304,
0.011657766997814178,
0.04438409581780434,
0.004851954057812691,
-0.05919339135289192,
-0.06987351924180984,
0.030253397300839424,
-0.0036969950888305902,
0.0035435431636869907,
-0.017587484791874886,
-0.0015485016629099846,
-0.03681314364075661,
-0.059149470180273056,
0.007504954002797604,
0.008059167303144932,
-0.04089829698204994,
-0.0006491897511295974,
0.03319990634918213,
-0.035347532480955124,
0.06419608741998672,
0.001536769326776266,
-0.026498978957533836,
0.004184568766504526,
-0.014184893108904362,
0.024164939299225807,
-0.041696012020111084,
0.058457184582948685,
-0.01543116569519043,
0.00831728894263506,
0.023157380521297455,
-0.027406638488173485,
0.02798730693757534,
-0.024331847205758095,
0.012577170506119728,
0.014725029468536377,
0.0408334918320179,
0.004128750413656235,
-0.03098067082464695,
0.0005588725907728076,
-0.00041355821304023266,
0.03781302273273468,
0.03816154599189758,
-0.006440723780542612,
-0.023467760533094406,
-0.05752911791205406,
0.027123253792524338,
0.00032365985680371523,
0.0024859048426151276,
0.0001819692406570539,
0.040275007486343384,
-0.006788215134292841,
-0.01329717691987753,
0.034738969057798386,
0.00931625533849001,
0.016772234812378883,
0.043287493288517,
0.02356085553765297,
0.007697745691984892,
0.03432086482644081,
-0.0027775827329605818,
-0.0037556367460638285,
-0.02072357013821602,
0.0231007132679224,
0.08960254490375519,
-0.024633532389998436,
0.0288668405264616,
0.027728168293833733,
0.0030839305836707354,
0.020617075264453888,
-0.018417656421661377,
-0.004906325601041317,
-0.014284011907875538,
-0.013225041329860687,
0.02885529212653637,
-0.03033488430082798,
-0.0018932040547952056,
0.027030743658542633,
0.04238754138350487,
0.014962087385356426,
0.005195175763219595,
0.030573518946766853,
0.03423693776130676,
-0.00422883965075016,
0.016809405758976936,
-0.051137179136276245,
0.02082371897995472,
-0.02726275473833084,
0.05231776461005211,
0.0006579246837645769,
-0.007083235774189234,
0.03522370010614395,
0.011344239115715027,
0.01701505482196808,
-0.059739403426647186,
0.00949837639927864,
-0.033791881054639816,
0.004083182197064161,
-0.021725710481405258,
-0.00950341671705246,
-0.004515173379331827,
0.01339678093791008,
0.007800851482897997,
0.005624466575682163,
0.030616644769906998,
-0.03321477025747299,
-0.024454103782773018,
-0.037845660001039505,
-0.036419741809368134,
-0.02005445584654808,
0.011294410564005375,
0.00305234850384295,
-0.026866279542446136,
-0.000034098076866939664,
0.005899016745388508,
0.018720457330346107,
0.014285153709352016,
0.03260386735200882,
-0.018297724425792694,
0.07739987224340439,
-0.022029820829629898,
0.029005372896790504,
-0.005320971831679344,
-0.003442412009462714,
0.10855602473020554,
0.011457100510597229,
0.012376734055578709,
-0.054107945412397385,
-0.02389456331729889,
-0.016282949596643448,
-0.008360465057194233,
-0.005301022436469793,
0.0058485399931669235,
0.03370087966322899,
0.022212667390704155,
0.016762230545282364,
0.05430999770760536,
0.012856771238148212,
-0.007528956048190594,
0.020295966416597366,
-0.04176989942789078,
-0.025503549724817276,
-0.02393963746726513,
0.02853276953101158,
-0.04612291231751442,
0.026638297364115715,
-0.061260707676410675,
-0.004869441967457533,
-0.009792236611247063,
-0.02150004543364048,
0.008439670316874981,
-0.02790154702961445,
-0.0001747804635670036,
0.020319342613220215,
-0.0568515881896019,
-0.01778506115078926,
-0.024265727028250694,
-0.028865274041891098,
-0.04345443472266197,
0.03370582312345505,
-0.0202854722738266,
-0.024861786514520645,
0.008261606097221375,
0.005815607029944658,
0.022254502400755882,
0.013214556500315666,
0.011097295209765434,
0.008096497505903244,
-0.04811669886112213,
-0.0017980339471250772,
-0.015930358320474625,
0.01645580120384693,
0.015845220535993576,
0.005510225426405668,
-0.022049322724342346,
0.014362343586981297,
0.027290575206279755,
-0.06916382163763046,
-0.023094743490219116,
-0.009298069402575493,
0.02128930203616619,
-0.022628765553236008,
-0.0571160763502121,
-0.009647713974118233,
0.019346121698617935,
-0.010684412904083729,
0.008229845203459263,
0.006651698146015406,
-0.002560944762080908,
-0.011226500384509563,
0.004862381611019373,
0.011644204147160053,
-0.011665058322250843,
-0.029640957713127136,
-0.00184899743180722,
0.0031685270369052887,
-0.05325189605355263,
0.0024792030453681946,
0.019213534891605377,
0.015117950737476349,
-0.010303596034646034,
0.01404417585581541,
-0.010720932856202126,
-0.0012732211034744978,
-0.04086872190237045,
0.042161136865615845,
-0.01159996073693037,
-0.011187032796442509,
-0.006047950591892004,
-0.03214622661471367,
0.05073763057589531,
0.04397384822368622,
0.0074442001059651375,
-0.002043354557827115,
-0.02478696033358574,
-0.00484071159735322,
0.0013742077862843871,
-0.038678430020809174,
-0.019090762361884117,
0.02989661693572998,
-0.023198161274194717,
-0.023666666820645332,
-0.010630794800817966,
0.012178387492895126,
0.06118030846118927,
-0.013974438421428204,
-0.045984186232089996,
0.006156696006655693,
-0.038910381495952606,
-0.00839914195239544,
0.021721119061112404,
-0.01845429092645645,
-0.0013181206304579973,
0.03718123957514763,
-0.02675262652337551,
-0.0344647616147995,
0.008723798207938671,
-0.00705970311537385,
0.004138492979109287,
-0.03876855969429016,
0.013467785902321339,
-0.02121833898127079,
-0.0010246721794828773,
-0.016073208302259445,
0.0424981415271759,
-0.05338451638817787,
-0.030152959749102592,
-0.09959603101015091,
0.030257239937782288,
0.020753683522343636,
0.01175672560930252,
-0.04685244336724281,
0.005102794151753187,
-0.028895169496536255,
-0.0331784151494503,
-0.011277960613369942,
-0.01902036927640438,
0.002886146539822221,
-0.016016703099012375,
0.06112776696681976,
-0.053942207247018814,
0.02809314616024494,
-0.03696071356534958,
-0.009529856033623219,
0.05327468737959862,
-0.03048100695014,
-0.03920210897922516,
0.007368342950940132,
-0.0199079941958189,
0.018365254625678062,
0.005828253924846649,
-0.0070755695924162865,
-0.030406655743718147,
0.06341449171304703,
0.0007713799714110792,
0.0016129538416862488,
-0.035037342458963394,
-0.005580737255513668,
-0.013075418770313263,
-0.024517260491847992,
0.01266059186309576,
-0.03799954429268837,
-0.0017428427236154675,
0.02510441280901432,
0.052320078015327454,
0.0036477704998105764,
0.0102199986577034,
0.021309413015842438,
0.009544012136757374,
-0.042068421840667725,
0.018625754863023758,
0.0006809525075368583,
0.005777022801339626,
0.04694310575723648,
-0.02003074437379837,
0.0387478843331337,
-0.009342486038804054,
0.023691890761256218,
-0.11376488953828812,
0.024309182539582253,
0.021437808871269226,
-0.02870750240981579,
0.06721176952123642,
-0.05213396996259689,
0.02783713862299919,
0.0045832362957298756,
-0.03551352769136429,
-0.006234790664166212,
-0.06269713491201401,
0.014256313443183899,
-0.009767947718501091,
0.013212286867201328,
0.028280632570385933,
0.0881766825914383,
0.007672842592000961,
0.005925377830862999,
0.005421244073659182,
0.020824391394853592,
-0.012522776611149311,
0.02999325841665268,
-0.02114727534353733,
0.06532660871744156,
0.009501021355390549,
-0.0010986350243911147,
0.06285189092159271,
-0.0202943067997694,
-0.02977753058075905,
0.04177222028374672,
0.000744825869332999,
0.03242231905460358,
0.003431495977565646,
0.021333709359169006,
-0.02209383063018322,
-0.001459903665818274,
0.006877834443002939,
-0.012130305171012878,
-0.013400974683463573,
0.05316181853413582,
0.04766660928726196,
0.025967435911297798,
-0.00457971915602684,
-0.006736145820468664,
-0.0020312906708568335,
-0.05681726709008217,
-0.04104671999812126,
0.02403922751545906,
-0.010574192740023136,
0.01719219610095024,
-0.0007274726522155106,
0.007213633041828871,
0.018023759126663208,
-0.03320016711950302,
0.018288422375917435,
-0.03537183254957199,
0.0111622903496027,
0.024522986263036728,
-0.031432852149009705,
-0.032892365008592606,
0.027648968622088432,
0.03255528211593628,
-0.03706381842494011,
-0.023487849161028862,
-0.02540823258459568,
0.010736456140875816,
-0.04225677624344826,
-0.028838496655225754,
0.024492649361491203,
-0.016733644530177116,
0.007750495802611113,
-0.01040809415280819,
-0.020260000601410866,
0.00923240277916193,
0.06792544573545456,
0.02855406515300274,
0.011892887763679028,
-0.048089399933815,
-0.02716737799346447,
-0.045018915086984634,
0.08126818388700485,
0.04727144539356232,
-0.005165425129234791,
-0.056334126740694046,
-0.0005757423932664096,
0.02495909295976162,
-0.01804252155125141,
0.0370042510330677,
-0.016087358817458153,
-0.00494524696841836,
0.007539344951510429,
0.00945978332310915,
-0.011766058392822742,
-0.008873087354004383,
0.01795830950140953,
0.01765420287847519,
-0.07479022443294525,
-0.0253433994948864,
-0.029264623299241066,
-0.017515841871500015,
-0.008867285214364529,
0.020870266482234,
-0.00508873350918293,
0.04538603127002716,
0.028093332424759865,
-0.02349083498120308,
0.030934059992432594,
0.061358802020549774,
-0.0042181783355772495,
0.057625677436590195,
-0.03854949027299881,
0.029473287984728813,
0.005093039944767952,
-0.0235226359218359,
-0.044831886887550354,
0.05591537058353424,
-0.026266546919941902,
0.03444992005825043,
-0.011475668288767338,
-0.029990140348672867,
0.0025242329575121403,
-0.05213220790028572,
-0.0033928523771464825,
0.0009434831445105374,
-0.03624444454908371,
0.012197552248835564,
0.041561055928468704,
0.02497476525604725,
0.0662878006696701,
-0.04051163047552109,
-0.02539597451686859,
0.022919125854969025,
0.02634207345545292,
0.030947256833314896,
0.05886473134160042,
0.02548598311841488,
0.003746375907212496,
-0.007192819844931364,
0.030330974608659744,
0.010069569572806358,
0.058377768844366074,
0.040988970547914505,
0.00989037100225687,
-0.040177274495363235,
-0.024240881204605103,
-0.02790401689708233,
-0.0286391731351614,
-0.00359409861266613,
0.025755958631634712,
-0.019793914631009102,
0.08385509252548218,
-0.021713826805353165,
0.02470257319509983,
0.0038365020882338285,
0.003363188123330474,
0.008001158945262432,
-0.0354299359023571,
0.008143704384565353,
0.045578647404909134,
0.011253807693719864,
-0.03620534390211105,
0.010738813318312168,
0.006009024567902088,
-0.007288532331585884,
0.0015734900953248143,
0.03354952484369278,
-0.0006242824019864202,
0.027490021660923958,
-0.040521085262298584,
-0.020184380933642387,
-0.007186767645180225,
-0.015534287318587303,
0.006305388640612364,
0.012431002222001553,
0.005254375282675028,
0.03930645436048508,
-0.018546484410762787,
-0.026082843542099,
0.045828837901353836,
-0.06706688553094864,
0.006037222687155008,
-0.0179035235196352,
0.0388193279504776,
-0.034518759697675705,
-0.02786010503768921
] |
<p>Suppose you have a state described by the wave function $\psi(x) = \phi_1(x)+2\phi_2(x)+3\phi_3(x)$ , where the $\phi$s are normalised eigenfunctions of a Hermitian operator $\hat{O}$ with eigenvalues $\lambda_1 = 1, \lambda_2 = 5, \lambda_3 = 9$.</p>
<p><strong>What happens to the wave function if you measure $\hat{O}$ and you obtain the result $\lambda_2=5$?</strong></p>
<p>My answer is that the wave function immediately collapses to $\psi(x) = 5\phi_2$</p>
<p><em><strong>EDIT</strong>: My answer should be $\psi(x) = 10\phi_2$, I think</em></p>
<p>Is that correct? Or should I state the probability with which the wave function will collapse to that state:</p>
<p>$<\hat{O}> = \sum|c_n|^2\lambda_n$ where $|c_n|^2$ is the probability of the $n^{th}$ state.</p> | 1,455 | [
-0.010988817550241947,
-0.03370186313986778,
0.006133426912128925,
-0.05114362761378288,
0.02929523028433323,
0.0016673008212819695,
-0.04899342358112335,
-0.053243979811668396,
0.06833789497613907,
-0.035653963685035706,
0.06214010342955589,
0.056632041931152344,
0.05212116241455078,
0.0035606292076408863,
-0.0029396642930805683,
0.050120770931243896,
-0.020051289349794388,
0.0014267477672547102,
-0.01432359404861927,
-0.03167368471622467,
0.01024721097201109,
0.04085976630449295,
-0.008498157374560833,
-0.02261047624051571,
-0.04970139265060425,
0.03514283895492554,
0.03332978114485741,
-0.02095216140151024,
0.01599770225584507,
0.06569737941026688,
-0.029178738594055176,
-0.0428970567882061,
0.02513822726905346,
0.071722112596035,
0.015294663608074188,
-0.023057343438267708,
-0.030778273940086365,
-0.05702333152294159,
0.004693941678851843,
0.00015826788148842752,
-0.047441836446523666,
-0.041692931205034256,
-0.007874366827309132,
0.007218930404633284,
-0.030507581308484077,
-0.007066024467349052,
0.0003403098089620471,
-0.017646441236138344,
0.0012063583126291633,
-0.04407728090882301,
0.06038793921470642,
0.004115914925932884,
0.04181491956114769,
0.009727639146149158,
-0.0037798192352056503,
-0.03065326251089573,
0.06611768156290054,
0.057625140994787216,
0.010913357138633728,
-0.04101298749446869,
-0.009795949794352055,
-0.04147401452064514,
-0.030308358371257782,
-0.005189457908272743,
-0.038245681673288345,
0.04405970871448517,
0.01069581974297762,
-0.030761729925870895,
0.024758122861385345,
-0.026886790990829468,
0.0035918508656322956,
0.027441667392849922,
0.036037545651197433,
-0.05466742813587189,
0.020227015018463135,
0.004799629561603069,
0.04456685110926628,
0.020801624283194542,
0.04164625704288483,
0.022395530715584755,
0.012028264813125134,
0.01840939000248909,
0.03006601333618164,
0.02137288637459278,
0.012937761843204498,
-0.017938634380698204,
0.07273360341787338,
-0.0023455244954675436,
0.0013755555264651775,
0.04533587768673897,
0.024488473311066628,
0.014287238009274006,
0.04744810611009598,
-0.05212362855672836,
-0.021557774394750595,
0.02027343399822712,
-0.009297754615545273,
0.04377899318933487,
0.016347866505384445,
0.011895670555531979,
-0.036555685102939606,
-0.044841740280389786,
0.02761227637529373,
0.042242810130119324,
-0.02511846274137497,
0.011434460990130901,
-0.06452745944261551,
-0.008087586611509323,
0.013489196076989174,
-0.028114739805459976,
-0.027051791548728943,
0.03698728606104851,
-0.00693019712343812,
0.01798056624829769,
0.014806041494011879,
-0.027797769755125046,
-0.0016532083973288536,
-0.01846550777554512,
0.05183735489845276,
0.05808588117361069,
0.01541432086378336,
-0.011070935055613518,
0.021333938464522362,
-0.03523942455649376,
-0.049172673374414444,
0.020311612635850906,
0.019079426303505898,
-0.011683095246553421,
-0.050959955900907516,
0.01809067465364933,
0.024876847863197327,
-0.012553735636174679,
0.02736073173582554,
-0.023857995867729187,
0.0006887862109579146,
-0.023596646264195442,
-0.130568265914917,
-0.04884182661771774,
0.026117056608200073,
-0.008304361253976822,
-0.015379819087684155,
-0.03271844983100891,
0.021971212700009346,
0.05271754041314125,
0.06486436724662781,
-0.018120555207133293,
0.03948923945426941,
-0.0048662819899618626,
0.02987966127693653,
0.010606431402266026,
-0.007502725347876549,
-0.026414329186081886,
-0.02126220613718033,
-0.03147038444876671,
-0.02023787796497345,
-0.03470081463456154,
0.02666311524808407,
0.04570923000574112,
0.041294362396001816,
-0.038537342101335526,
0.022295266389846802,
-0.027510343119502068,
0.02192385122179985,
0.005474111530929804,
0.01787431538105011,
-0.03513174504041672,
0.07343412190675735,
0.026072010397911072,
0.0035613703075796366,
0.015058686025440693,
-0.02480313368141651,
0.008675195276737213,
-0.016863277181982994,
0.03062756173312664,
0.03196417912840843,
-0.03770192340016365,
-0.02139011211693287,
-0.049543291330337524,
0.025557702407240868,
-0.004575351253151894,
0.002305306727066636,
-0.021365894004702568,
-0.023067869246006012,
0.018087781965732574,
0.02906622178852558,
0.019414644688367844,
0.014233184978365898,
-0.028520507737994194,
-0.029770150780677795,
-0.03832833468914032,
-0.04877699911594391,
-0.07636280357837677,
0.029139647260308266,
0.032469358295202255,
-0.006714233197271824,
0.04577471688389778,
0.006794273853302002,
0.03554568439722061,
-0.004109247121959925,
-0.02903260849416256,
-0.010427692905068398,
-0.0027754362672567368,
-0.001206152024678886,
-0.054675813764333725,
-0.0010736169060692191,
0.06920590251684189,
0.03651142492890358,
0.012629939243197441,
0.0553034208714962,
-0.03922590985894203,
-0.015849033370614052,
-0.03154434636235237,
0.004794117994606495,
0.011980531737208366,
-0.01989315263926983,
-0.01803305745124817,
0.02213565818965435,
-0.026049796491861343,
-0.0014257641742005944,
0.020034829154610634,
-0.07165342569351196,
0.072810098528862,
0.04051218926906586,
0.005134562961757183,
-0.002800599206238985,
0.011547201313078403,
-0.002375413663685322,
-0.0154750170186162,
0.01736137829720974,
-0.028848839923739433,
-0.038496360182762146,
0.009888015687465668,
-0.008659636601805687,
0.0438716746866703,
-0.024527639150619507,
0.026653368026018143,
0.06881402432918549,
0.01868676021695137,
0.02821040153503418,
0.012426476925611496,
-0.027913708239793777,
0.004994062706828117,
-0.008005091920495033,
0.007968906313180923,
0.020562447607517242,
0.011160100810229778,
0.02032436430454254,
0.0206319447606802,
0.04427843540906906,
0.04290814697742462,
-0.03528805449604988,
0.040280960500240326,
-0.02960171550512314,
0.029128748923540115,
-0.03025572933256626,
-0.012776583433151245,
-0.001395363244228065,
-0.012576139532029629,
-0.016202839091420174,
-0.018971167504787445,
-0.021173972636461258,
0.005561105441302061,
-0.040157441049814224,
-0.0341365784406662,
0.028350040316581726,
0.007273379247635603,
-0.029640618711709976,
-0.017908308655023575,
0.009200047701597214,
-0.007133727893233299,
-0.038457706570625305,
-0.029538283124566078,
0.02197982743382454,
0.0028618385549634695,
0.012003195472061634,
0.03522390127182007,
-0.03369389846920967,
0.02124526910483837,
-0.05555504932999611,
-0.07678860425949097,
-0.008919156156480312,
-0.021716633811593056,
0.036873750388622284,
0.030954575166106224,
-0.06682323664426804,
-0.008387897163629532,
-0.06815171986818314,
-0.05635949969291687,
0.027970416471362114,
-0.02911265380680561,
-0.00597129762172699,
-0.002102047670632601,
-0.004617799073457718,
-0.06541071832180023,
-0.013770281337201595,
0.015082649886608124,
-0.006907235831022263,
-0.05955033376812935,
-0.013531544245779514,
0.06818214058876038,
-0.015251312404870987,
0.003947301767766476,
-0.0028368982020765543,
-0.022997159510850906,
-0.07029110193252563,
-0.024089841172099113,
0.006241609808057547,
0.026940854266285896,
-0.055405281484127045,
0.0036142582539469004,
0.012486813589930534,
0.0021563407499343157,
0.008494646288454533,
-0.05329279601573944,
-0.03864491730928421,
0.015573100186884403,
-0.007745135109871626,
0.02660328894853592,
0.007925063371658325,
0.004843932576477528,
0.08465658873319626,
0.020104479044675827,
-0.009600833989679813,
0.01158073265105486,
0.03995035961270332,
0.011104527860879898,
-0.032828930765390396,
-0.020357826724648476,
0.027237819507718086,
-0.026007743552327156,
0.05237475037574768,
0.006534118205308914,
0.030860668048262596,
0.027263218536973,
-0.008981268852949142,
-0.013326979242265224,
0.056669678539037704,
0.02785981073975563,
-0.0022513349540531635,
0.047637928277254105,
0.01239633746445179,
-0.01182369701564312,
-0.011466643773019314,
-0.00678128469735384,
-0.013279866427183151,
-0.019335471093654633,
-0.059597428888082504,
0.06561078131198883,
-0.01287886593490839,
0.026692159473896027,
-0.001965089701116085,
0.07754140347242355,
0.009539156220853329,
-0.03145284950733185,
-0.01747848466038704,
0.02855486050248146,
0.060453493148088455,
-0.020039746537804604,
-0.001796900061890483,
0.0056975302286446095,
0.015523441135883331,
-0.03964247182011604,
-0.028202828019857407,
-0.013974870555102825,
-0.011419452726840973,
0.02783818356692791,
-0.01917499303817749,
-0.04866451770067215,
0.020920250564813614,
0.07138330489397049,
0.017989667132496834,
-0.03044394589960575,
-0.046694181859493256,
0.014033493585884571,
-0.034619539976119995,
-0.021551532670855522,
0.009284055791795254,
0.04189573600888252,
0.027178194373846054,
0.050212983042001724,
0.0452929325401783,
-0.012254445813596249,
0.01382585521787405,
-0.02019038237631321,
-0.07504594326019287,
0.004551884718239307,
0.014185843989253044,
-0.0022571799345314503,
0.019221745431423187,
-0.009493027813732624,
0.008402618579566479,
0.012651970610022545,
-0.018480615690350533,
-0.012439061887562275,
-0.0015450346982106566,
-0.04193703457713127,
-0.007826010696589947,
-0.014462814666330814,
-0.003661659313365817,
-0.0339738167822361,
0.018418703228235245,
0.01718916930258274,
-0.008626960217952728,
0.03151202201843262,
0.023725656792521477,
-0.036365851759910583,
0.013929971493780613,
-0.013964859768748283,
0.010735142044723034,
0.017035778611898422,
0.021433591842651367,
0.04275956004858017,
0.03264372795820236,
-0.016463587060570717,
0.029001520946621895,
-0.00917067751288414,
0.05637513846158981,
0.017955832183361053,
-0.008491412736475468,
0.04547605291008949,
-0.015840046107769012,
0.005078669171780348,
0.01935899816453457,
0.020581450313329697,
0.024257386103272438,
0.00990484468638897,
0.014050798490643501,
0.014069353230297565,
-0.0016398488078266382,
0.020641541108489037,
0.020823830738663673,
0.0012656530598178506,
0.0034177559427917004,
-0.037412624806165695,
0.022139685228466988,
-0.03843115270137787,
-0.006293417885899544,
-0.028045078739523888,
0.005315529648214579,
-0.011810928583145142,
0.0029319818131625652,
0.019671956077218056,
-0.003425468923524022,
-0.015209447592496872,
-0.0010363844921812415,
-0.006176650989800692,
-0.002264085691422224,
-0.0029511889442801476,
-0.034777041524648666,
0.020954709500074387,
0.038169924169778824,
0.006346735637634993,
0.006813408341258764,
-0.009388364851474762,
-0.007510134018957615,
0.005926425103098154,
0.042137254029512405,
0.023917846381664276,
-0.011482667177915573,
0.009330418892204762,
-0.029556013643741608,
-0.02930007502436638,
0.04894847422838211,
-0.045542292296886444,
0.040336258709430695,
-0.0011017272481694818,
-0.027438929304480553,
-0.01920396275818348,
-0.04337257146835327,
-0.04944153502583504,
0.006123751401901245,
-0.0020416576880961657,
0.046949733048677444,
-0.029634302482008934,
-0.0057347421534359455,
-0.02152358368039131,
0.0028822871390730143,
-0.0030520299915224314,
0.04462628439068794,
-0.014680437743663788,
-0.01419858355075121,
-0.017248481512069702,
0.02479325607419014,
0.00048737000906839967,
-0.08252716809511185,
0.01274771150201559,
-0.009112284518778324,
-0.0008432724862359464,
0.033908434212207794,
-0.028512340039014816,
-0.049383629113435745,
0.004409961402416229,
-0.0043017868883907795,
-0.026649335399270058,
0.051649946719408035,
-0.028965430334210396,
0.08383364230394363,
0.033220235258340836,
0.004178094211965799,
0.04780489206314087,
0.028243809938430786,
0.018129387870430946,
0.034066665917634964,
-0.029679525643587112,
0.017432082444429398,
-0.045169930905103683,
0.045159731060266495,
-0.040055837482213974,
0.00601899903267622,
-0.011112982407212257,
0.06243054196238518,
-0.0021600627806037664,
0.01922135055065155,
0.004917247220873833,
-0.01612352766096592,
0.0014655841514468193,
-0.01904306747019291,
0.005325441248714924,
0.022365715354681015,
-0.007551522459834814,
0.002183857373893261,
0.02165238745510578,
-0.040412161499261856,
-0.02456028386950493,
-0.0242142453789711,
0.031156348064541817,
0.022274291142821312,
-0.011046885512769222,
0.02449420467019081,
-0.05668244883418083,
0.004088904708623886,
0.021702487021684647,
-0.07278650254011154,
0.023442570120096207,
-0.012340225279331207,
0.03768320009112358,
-0.0022534995805472136,
-0.002224966185167432,
-0.04845103248953819,
0.009103440679609776,
-0.0009408043115399778,
-0.0009732951293699443,
-0.03613314405083656,
-0.005521656945347786,
0.004445425234735012,
0.017775924876332283,
-0.05769766867160797,
0.013094653375446796,
-0.0026035266928374767,
0.021845083683729172,
0.001271287677809596,
-0.007109337951987982,
0.017327548936009407,
-0.02847619168460369,
-0.030598383396863937,
-0.010860816575586796,
0.029086684808135033,
-0.02723260223865509,
0.0033671266864985228,
0.023405080661177635,
-0.0006135794101282954,
0.06883824616670609,
-0.02453356236219406,
-0.01593930274248123,
0.011021876707673073,
-0.003583126701414585,
-0.025497006252408028,
-0.014405857771635056,
0.023081336170434952,
-0.05086526274681091,
-0.04327418655157089,
-0.018506275489926338,
-0.029579807072877884,
0.030795078724622726,
-0.013844301924109459,
-0.03244253993034363,
-0.019340459257364273,
-0.0033939373679459095,
0.02386321686208248,
0.00305730476975441,
-0.0161326564848423,
-0.012029712088406086,
0.016894929111003876,
0.0295142512768507,
-0.018576357513666153,
0.0014220370212569833,
-0.04479819908738136,
0.019308365881443024,
0.022277003154158592,
0.010011541657149792,
0.01973618008196354,
0.04031587019562721,
0.012500595301389694,
0.007805195637047291,
0.004641812294721603,
-0.03136173635721207,
-0.011936994269490242,
0.006860793102532625,
-0.004714264068752527,
0.02762770839035511,
-0.003906186204403639,
-0.02426939457654953,
-0.03102634847164154,
-0.06933096796274185,
0.020268604159355164,
0.03188944607973099,
0.01430355105549097,
0.013547847047448158,
0.013416437432169914,
0.0156317837536335,
-0.022480737417936325,
-0.02224883809685707,
-0.01275788526982069,
-0.022836703807115555,
0.030632128939032555,
0.02640700526535511,
-0.01291822362691164,
0.02592111937701702,
0.01608181558549404,
0.03768415004014969,
0.010806801728904247,
0.027704715728759766,
0.041552502661943436,
0.004113337490707636,
0.032258614897727966,
-0.03453468903899193,
-0.021432865411043167,
0.03707493469119072,
-0.05647299066185951,
-0.00645339535549283,
-0.022198840975761414,
-0.0037724331486970186,
0.003436254570260644,
-0.007937910966575146,
0.01579846441745758,
-0.02780745178461075,
-0.03259770944714546,
-0.03782845288515091,
0.0061741978861391544,
0.019605331122875214,
-0.011729913763701916,
-0.01952504925429821,
0.04059255123138428,
0.02735234797000885,
0.017540397122502327,
0.005197965074330568,
-0.011948558501899242,
-0.06279624998569489,
-0.024751590564846992,
-0.008768687024712563,
-0.04513830319046974,
0.012471039779484272,
-0.016247067600488663,
0.008268441073596478,
0.028740305453538895,
-0.017472118139266968,
0.033309295773506165,
0.01721492037177086,
0.05184129998087883,
-0.039318956434726715,
0.05775155872106552,
0.0688357800245285,
0.013485425151884556,
0.0036375164054334164,
0.022616302594542503,
0.11817260086536407,
0.08377426862716675,
0.047826677560806274,
-0.01664441078901291,
0.0009670470026321709,
0.017512746155261993,
0.019882438704371452,
-0.011195870116353035,
-0.011095800437033176,
0.010849012061953545,
0.004220389295369387,
-0.019509995356202126,
0.08414973318576813,
-0.0026395830791443586,
0.010070745833218098,
0.02402782440185547,
-0.04041631519794464,
-0.04760934039950371,
0.001244118670001626,
0.018251262605190277,
-0.020682230591773987,
0.0014154498931020498,
-0.05023709312081337,
0.01299851294606924,
-0.02687411569058895,
-0.0030182304326444864,
-0.01851014606654644,
-0.010478257201611996,
0.01810494437813759,
-0.01695471629500389,
-0.021824529394507408,
0.006174640264362097,
-0.007309395354241133,
-0.020479653030633926,
-0.023242555558681488,
0.04858118295669556,
0.03389686346054077,
-0.015888381749391556,
0.051793213933706284,
0.04573624208569527,
0.014558998867869377,
0.04049932584166527,
-0.004078615456819534,
0.033060453832149506,
-0.045729730278253555,
-0.015171109698712826,
-0.002853445941582322,
0.06593473255634308,
-0.03424835205078125,
0.006536336615681648,
-0.035062745213508606,
0.0046739233657717705,
-0.004297676030546427,
-0.04098411649465561,
-0.011792071163654327,
-0.012380874715745449,
0.019581379368901253,
-0.03111066110432148,
-0.0064716944471001625,
-0.017928997054696083,
-0.019614117220044136,
0.0033828166779130697,
0.0137083251029253,
0.009610893204808235,
-0.01236551720649004,
0.01565350405871868,
0.003344363532960415,
0.005957606714218855,
0.010076410137116909,
-0.001084328512661159,
-0.015534148551523685,
0.002525875810533762,
-0.05260074883699417,
-0.06113051250576973,
0.02205505780875683,
-0.007071715779602528,
0.07016448676586151,
0.007702921982854605,
0.004666691645979881,
-0.01569044031202793,
-0.08287215232849121,
0.005409508012235165,
-0.015589747577905655,
-0.02138439193367958,
-0.010060016065835953,
0.0018036419060081244,
-0.029680311679840088,
0.04181312769651413,
-0.01364849042147398,
-0.028653329238295555,
0.0038092127069830894,
0.04199136048555374,
0.04548599570989609,
-0.014820405282080173,
-0.007539644837379456,
0.008366692811250687,
-0.033392589539289474,
-0.011940169148147106,
-0.02243931218981743,
0.023346824571490288,
0.008734563365578651,
-0.0023646673653274775,
0.0026449908036738634,
0.029245182871818542,
-0.013329526409506798,
-0.04376564174890518,
-0.020875388756394386,
-0.04863322153687477,
0.017428629100322723,
0.05776478350162506,
0.03683096915483475,
-0.01240225974470377,
-0.03433588147163391,
-0.015573575161397457,
0.0026841615326702595,
0.027423342689871788,
-0.0020669898949563503,
-0.06330327689647675,
0.018358830362558365,
-0.009284553118050098,
0.05805864930152893,
0.020686127245426178,
-0.02676616609096527,
-0.05391674488782883,
0.01708431914448738,
0.03272116556763649,
-0.020654406398534775,
-0.012285968288779259,
0.007100140210241079,
0.03735727816820145,
-0.014085781760513783,
0.018908631056547165,
0.04125358909368515,
-0.005828442983329296,
-0.013623119331896305,
0.007414865307509899,
0.028748996555805206,
0.049978263676166534,
0.026377497240900993,
-0.013945254497230053,
0.05073641240596771,
-0.0426124706864357,
-0.009972437284886837,
0.057174015790224075,
-0.013988315127789974,
0.049699217081069946,
0.04613056033849716,
0.004046515561640263,
-0.0045979442074894905,
-0.01414300873875618,
-0.04895851016044617,
-0.020816827192902565,
0.01163389254361391,
-0.014828207902610302,
0.024011563509702682,
0.017507115378975868,
0.00841630157083273,
0.00494343088939786,
0.01236639078706503,
0.016819318756461143,
0.036103714257478714,
0.00605354830622673,
0.03169761598110199,
0.005602281074970961,
0.0032307018991559744,
0.023749643936753273,
0.008565624244511127,
-0.020886752754449844,
-0.027752380818128586,
0.03639835864305496,
-0.04358448460698128,
0.04572826996445656,
0.014832676388323307,
-0.0011279729660600424,
-0.1230957880616188,
-0.03238755464553833,
0.018677039071917534,
-0.00038841235800646245,
0.025309892371296883,
-0.018437258899211884,
0.042895570397377014,
0.04183291643857956,
-0.08408770710229874,
0.05970339849591255,
-0.02002568542957306,
-0.013047903776168823,
-0.042524632066488266,
0.029151666909456253,
-0.05075329542160034,
0.052734002470970154,
0.02305975928902626,
0.022592226043343544,
0.0034872654359787703,
0.012929266318678856,
-0.008671504445374012,
-0.045675914734601974,
-0.014344175346195698,
0.04428945854306221,
-0.03064345195889473,
-0.0411333292722702,
0.08078030496835709,
-0.029785659164190292,
-0.022258061915636063,
0.04625542834401131,
-0.02205764688551426,
-0.006577789783477783,
-0.04316689074039459,
-0.028490401804447174,
0.017293084412813187,
0.010974396951496601,
0.022107617929577827,
0.007064513862133026,
0.0047021592035889626,
0.013656717725098133,
0.03034498170018196,
0.004382191225886345,
-0.02404005452990532,
-0.005057946313172579,
0.027580108493566513,
-0.03567454218864441,
-0.07425785809755325,
0.0039876047521829605,
0.04156925529241562,
0.02861279994249344,
0.021359950304031372,
-0.021900201216340065,
0.027287762612104416,
-0.031635671854019165,
0.015686893835663795,
-0.033988285809755325,
-0.01814986765384674,
-0.0028510817792266607,
0.023001136258244514,
-0.015012076124548912,
-0.021428562700748444,
-0.008158884011209011,
-0.04364539310336113,
0.021864863112568855,
0.0069623286835849285,
-0.009429482743144035,
-0.06069590151309967,
-0.03159917891025543,
0.024872921407222748,
0.010461636818945408,
0.05055343359708786,
-0.011183449998497963,
-0.02922220341861248,
0.03172807767987251,
-0.02445853129029274,
-0.0131358178332448,
-0.006521622184664011,
-0.034797538071870804,
-0.03698107600212097,
-0.09103677421808243,
0.030808495357632637,
0.027716433629393578,
0.018345236778259277,
-0.03297581151127815,
0.023714976385235786,
-0.0064913611859083176,
0.00034307496389374137,
0.06286963820457458,
0.014251893386244774,
-0.032449256628751755,
-0.012233658693730831,
0.010509885847568512,
0.041902054101228714,
-0.03956088796257973,
-0.020361460745334625,
-0.01498410850763321,
0.013970364816486835,
-0.03919015824794769,
-0.010659376159310341,
0.026498306542634964,
0.017860494554042816,
0.04131661728024483,
0.015413734130561352,
-0.015532084740698338,
-0.04076209291815758,
-0.022479653358459473,
0.07354950159788132,
0.02507844939827919,
-0.0004496512410696596,
0.07178649306297302,
-0.020337805151939392,
0.014862369745969772,
0.039399515837430954,
-0.03350123390555382,
-0.056493643671274185,
0.012867826968431473,
-0.035131409764289856,
-0.03473546728491783,
-0.005752039607614279,
0.014713642187416553,
0.012844019569456577,
-0.01821920834481716,
-0.03709675744175911,
0.016718683764338493,
-0.03736370801925659,
-0.02606404572725296,
0.05999569594860077,
0.008938555605709553,
0.07204177230596542,
0.038036614656448364,
0.007014055270701647,
0.01814490556716919,
-0.029744938015937805,
-0.02894488535821438,
0.02542044408619404,
0.033150166273117065,
0.015887225046753883,
0.045840490609407425,
0.014237666502594948,
-0.032723549753427505,
0.01948351413011551,
0.013132252730429173,
0.05448395758867264,
-0.035294681787490845,
-0.010936710052192211,
0.016620658338069916,
0.012338251806795597,
-0.011155362240970135,
-0.014309876598417759,
-0.014094924554228783,
0.07408901304006577,
-0.008318566717207432,
0.017810547724366188,
-0.04310540109872818,
0.0223581250756979,
-0.06395550817251205,
0.005009038373827934,
0.03519808128476143,
0.06377515941858292,
-0.006420563440769911,
0.01868998259305954,
-0.040571630001068115,
0.044496748596429825,
0.04917207732796669,
-0.06057437136769295,
0.01829354465007782,
-0.010017367079854012,
-0.017659850418567657,
-0.0025423241313546896,
-0.00456622987985611,
-0.0002595445257611573,
-0.00848307367414236,
-0.01754208467900753,
0.03320673108100891,
0.013887595385313034,
0.001713230274617672,
-0.0009495455306023359,
-0.011891404166817665,
0.04135220870375633,
-0.02459966391324997,
-0.024616820737719536,
-0.024410836398601532,
0.030333423987030983,
0.010488230735063553,
-0.02889975905418396
] |
<p>I know people will say it violates many laws of motion and conservation but could anyone explain why it is so?
It's NOT a question about free energy.</p>
<p>Imagine a motor in space. It has an arm (rod) attached to it. At the end of the arm there's a ball (weight) attached to it. The motor produces a circular motion. So the motor is the center and the rod is the radius. To the ball there is a rope attached which connects to the rod aswell, but the rod keeps the ball in place. The rope is longer than the radius. The rod has a realease mechanism to let the ball go. When the ball is released, it disconnects from the rod and flies away in a tangent. Then the ball flies for some distance until it is stopped by the rope.</p>
<p>Does the sudden stopping of the ball by the rope make the motor move off its place and head in a single direction?</p>
<p>Is there any opposite reaction force to the direction of the moving ball on the moment that it is released?</p>
<p>Is there an opposite reaction force somewhere that makes this impossible and cancels out any potential movement causing forces all together?</p>
<p>Is it possible that this can make the system as a whole (motor, ball, rope and rod) move in a single direction without reaction mass being expelled and without external forces acting upon it? And if so, will this system stop moving when it catches up with its ball?</p>
<p>I appreciate help a lot.</p> | 1,456 | [
-0.07172320038080215,
-0.009817312471568584,
-0.029312558472156525,
-0.014485469087958336,
-0.01913403533399105,
-0.03567441552877426,
-0.0319303423166275,
0.010059253312647343,
0.007539344485849142,
-0.04704863578081131,
-0.008182737044990063,
0.05679740011692047,
0.050921835005283356,
0.008262843824923038,
0.03712375462055206,
-0.010738059878349304,
0.005375084932893515,
-0.03941991925239563,
0.012079001404345036,
-0.045766688883304596,
-0.02140098251402378,
-0.020565707236528397,
0.017703795805573463,
0.007540715858340263,
-0.00937925186008215,
0.009483981877565384,
0.023081058636307716,
-0.02732084132730961,
0.0086553655564785,
0.07140133529901505,
0.0054830750450491905,
0.01261139940470457,
-0.023626262322068214,
0.02336239255964756,
0.03821883723139763,
0.026049382984638214,
-0.02340417541563511,
-0.016228847205638885,
-0.01599040813744068,
0.01576126553118229,
-0.013128498569130898,
-0.0012484912294894457,
-0.029422540217638016,
0.05276554077863693,
-0.044404756277799606,
0.01466389000415802,
-0.010573240928351879,
0.023070814087986946,
0.07921573519706726,
-0.06459131836891174,
0.06245578080415726,
0.009640287607908249,
0.03232327476143837,
0.001272928318940103,
0.00517545361071825,
0.0038480348885059357,
0.07169046252965927,
0.07239009439945221,
-0.010747196152806282,
-0.0555262453854084,
-0.03907562047243118,
-0.007502948399633169,
-0.04848477244377136,
-0.048876941204071045,
-0.031462136656045914,
0.04601913318037987,
0.0034456122666597366,
-0.0042154621332883835,
0.02873747982084751,
0.02044091187417507,
0.010903664864599705,
-0.004564392846077681,
0.049318887293338776,
-0.0064047034829854965,
0.00769673241302371,
-0.01978670246899128,
0.034225668758153915,
-0.004735897295176983,
0.0025268748868256807,
0.07144451886415482,
-0.02473650872707367,
-0.023560672998428345,
0.028628364205360413,
0.07198566198348999,
0.01882619597017765,
0.0046746740117669106,
0.03215249255299568,
0.01731863245368004,
0.02632255293428898,
0.027498729526996613,
0.014039301313459873,
0.014528331346809864,
0.03642481192946434,
0.027004461735486984,
-0.020278440788388252,
0.042700327932834625,
0.022052880376577377,
0.06306800991296768,
0.029971932992339134,
-0.02885879948735237,
-0.010704384185373783,
-0.0026067171711474657,
0.0310937762260437,
0.056865762919187546,
0.028102628886699677,
-0.010909060016274452,
-0.038618069142103195,
0.003656302811577916,
-0.0317702554166317,
0.002284713787958026,
-0.04385167732834816,
-0.0007582695689052343,
0.024577975273132324,
-0.012778736650943756,
0.03246740996837616,
0.005966334603726864,
-0.017547141760587692,
-0.007718162145465612,
0.08052323758602142,
0.06072709709405899,
0.036498408764600754,
-0.04347610846161842,
0.012707551009953022,
-0.035365648567676544,
-0.008059466257691383,
-0.02021058276295662,
0.042411189526319504,
-0.007918035611510277,
-0.010702379047870636,
0.005633675958961248,
0.012671957723796368,
-0.029007581993937492,
0.005938774906098843,
-0.01574518531560898,
0.07006445527076721,
-0.016432814300060272,
-0.09137280285358429,
-0.030701439827680588,
0.04547616094350815,
-0.006051565054804087,
-0.009675759822130203,
-0.06834407150745392,
-0.006371321622282267,
0.04297732561826706,
0.08551450073719025,
-0.02269350178539753,
-0.01823277398943901,
-0.0012530134990811348,
0.05945507809519768,
-0.013651867397129536,
-0.014660540036857128,
-0.049046799540519714,
0.021137671545147896,
-0.046919748187065125,
-0.03324194252490997,
-0.07326386868953705,
0.005376444663852453,
0.02569972723722458,
0.03027021326124668,
-0.01870078407227993,
-0.0021905263420194387,
-0.022650452330708504,
0.01977331005036831,
0.015726130455732346,
0.021107930690050125,
0.0034380932338535786,
0.09087758511304855,
0.009957714937627316,
-0.03504319489002228,
0.03069484606385231,
0.05349712446331978,
0.05077434331178665,
-0.010832489468157291,
0.023938577622175217,
0.02522745169699192,
-0.029109656810760498,
-0.026256399229168892,
-0.015493837185204029,
-0.0030719367787241936,
-0.022084977477788925,
-0.06137523800134659,
-0.08131775259971619,
0.005844234488904476,
0.011513338424265385,
-0.0030945201870054007,
0.04820166900753975,
0.0003639679925981909,
-0.006401666905730963,
0.00927630066871643,
0.0027881746646016836,
-0.00947193056344986,
-0.037993915379047394,
0.03721092641353607,
-0.030146127566695213,
-0.003953020088374615,
0.017225008457899094,
0.046086180955171585,
0.03493295609951019,
-0.05594680458307266,
-0.01790948584675789,
-0.015786612406373024,
0.015655824914574623,
-0.040345463901758194,
0.033303096890449524,
-0.004303635563701391,
0.03591383621096611,
0.037539176642894745,
-0.0019464249489828944,
-0.019117651507258415,
0.002049061469733715,
-0.052626509219408035,
-0.013296828605234623,
-0.019505541771650314,
-0.010882498696446419,
0.013792358338832855,
0.020935965701937675,
0.03478297218680382,
0.004977173171937466,
0.004799589980393648,
0.010700040496885777,
-0.011098756454885006,
0.09547214955091476,
0.02140110544860363,
-0.0032751578837633133,
0.03735930472612381,
0.055374015122652054,
0.00895185861736536,
-0.02246811054646969,
-0.023792611435055733,
-0.044272229075431824,
-0.03728191554546356,
-0.0013166714925318956,
0.023983722552657127,
0.0377994030714035,
-0.020780621096491814,
0.027197960764169693,
0.026613621041178703,
0.035861045122146606,
0.046686988323926926,
0.0213360283523798,
-0.021323921158909798,
-0.010713785886764526,
0.047054748982191086,
0.018065454438328743,
-0.0170179083943367,
-0.01663947105407715,
0.024776900187134743,
0.015557370148599148,
0.012853357940912247,
0.014600414782762527,
-0.019603490829467773,
0.026085328310728073,
0.049443699419498444,
0.011926640756428242,
0.008230163715779781,
-0.047398608177900314,
0.04260100796818733,
-0.009190468117594719,
0.03693877160549164,
0.04013386368751526,
0.026465771719813347,
0.019212475046515465,
-0.050111204385757446,
-0.021609244868159294,
-0.03305479884147644,
0.034478042274713516,
-0.024328093975782394,
-0.06113232672214508,
0.015145216137170792,
-0.06272187829017639,
-0.013514285907149315,
-0.002065494656562805,
0.017974484711885452,
-0.04898164048790932,
0.006602380890399218,
-0.012785806320607662,
0.011222927831113338,
0.0366537943482399,
-0.032045867294073105,
-0.017976684495806694,
-0.03227849304676056,
-0.0575685128569603,
-0.004343936685472727,
0.012455884367227554,
-0.02650880441069603,
0.0232686884701252,
-0.03393666818737984,
-0.04204731434583664,
0.06984423100948334,
-0.016021640971302986,
0.018961993977427483,
0.03635607659816742,
-0.003209859598428011,
-0.0728585422039032,
-0.010401826351881027,
-0.009832780808210373,
0.002406537067145109,
-0.027250023558735847,
0.013468329794704914,
0.046327587217092514,
-0.010783680714666843,
-0.025070996955037117,
0.011212330311536789,
-0.10361848771572113,
-0.04709155857563019,
0.006320900283753872,
0.0265059657394886,
0.06092045083642006,
-0.01531512476503849,
0.0034123591613024473,
0.020998327061533928,
-0.025398042052984238,
0.014411411248147488,
-0.06770811975002289,
-0.024743186309933662,
-0.01334233395755291,
0.00997665710747242,
0.03705700486898422,
-0.007474197540432215,
-0.030551785603165627,
0.07489387691020966,
0.037300627678632736,
-0.01627316139638424,
-0.029625575989484787,
0.01002143882215023,
-0.018760332837700844,
-0.04196043312549591,
0.012111210264265537,
0.0014444099506363273,
-0.002334711840376258,
0.02220924198627472,
0.031738754361867905,
0.024633409455418587,
-0.0017129635671153665,
0.003995511215180159,
0.008667346090078354,
-0.0113737927749753,
0.0334373414516449,
-0.020340854302048683,
0.02587834931910038,
0.02762218937277794,
-0.015996159985661507,
0.024303480982780457,
-0.017374474555253983,
0.06027600169181824,
-0.022379672154784203,
-0.03884934261441231,
0.0435030534863472,
-0.014251552522182465,
0.017907429486513138,
0.004161445423960686,
0.03573201596736908,
0.004584411159157753,
-0.020949477329850197,
0.014741905964910984,
0.01884445548057556,
0.06220029667019844,
-0.011053803376853466,
0.0012867817422375083,
0.0357079841196537,
0.008836875669658184,
-0.030746521428227425,
-0.040078647434711456,
-0.022132067009806633,
0.01808209717273712,
0.001381417503580451,
-0.009740099310874939,
-0.039778005331754684,
0.022384587675333023,
0.0034098285250365734,
0.04578743875026703,
0.015132149681448936,
-0.02173132263123989,
-0.008550490252673626,
-0.0587262324988842,
0.0057326494716107845,
-0.016784027218818665,
0.0267869271337986,
0.01616024412214756,
0.04714062437415123,
0.041098255664110184,
0.03998832404613495,
0.006616758648306131,
0.010482904501259327,
-0.09511955827474594,
0.03169257566332817,
-0.051473408937454224,
-0.020543070510029793,
0.0019842509645968676,
0.011404113844037056,
-0.03669355437159538,
-0.0023462821263819933,
-0.011996077373623848,
0.004747207276523113,
-0.01817401684820652,
-0.08148054033517838,
0.0076323323883116245,
-0.02854350209236145,
-0.03916912525892258,
0.003948727156966925,
0.01077206525951624,
0.0187741219997406,
-0.029134728014469147,
0.046181850135326385,
0.025878768414258957,
-0.05205952003598213,
-0.015811609104275703,
-0.017184048891067505,
0.0023868989665061235,
0.011590113863348961,
0.0005432586185634136,
0.030660521239042282,
0.02452402375638485,
0.018714502453804016,
0.020930137485265732,
0.01975664496421814,
0.053464218974113464,
0.005791072733700275,
0.021220795810222626,
-0.016194457188248634,
-0.052727580070495605,
-0.028870174661278725,
0.00824833195656538,
0.013978631235659122,
0.01663563773036003,
0.0201780516654253,
0.03776909038424492,
0.019151851534843445,
0.004008157644420862,
0.01947285607457161,
0.0333087220788002,
0.016205884516239166,
-0.018149884417653084,
-0.04295063763856888,
-0.025512412190437317,
0.006076382473111153,
-0.015525641851127148,
0.004040081985294819,
-0.03603300079703331,
-0.02147701010107994,
-0.012381475418806076,
0.019762642681598663,
0.044831421226263046,
-0.034105852246284485,
-0.015970760956406593,
-0.03728509321808815,
0.022281048819422722,
-0.03435148671269417,
0.020491745322942734,
0.030115671455860138,
0.01190952304750681,
0.028329728171229362,
-0.019538501277565956,
0.00566251901909709,
-0.05624505504965782,
-0.002411785302683711,
0.044780977070331573,
0.028014132753014565,
-0.00938445795327425,
-0.0027682313229888678,
-0.02421863190829754,
-0.04444299265742302,
0.03168013319373131,
-0.0389338918030262,
0.06357882916927338,
-0.036457359790802,
-0.002284800400957465,
0.010196232236921787,
-0.04337161034345627,
-0.024932410567998886,
0.0035998804960399866,
-0.031845495104789734,
0.00581815792247653,
-0.012340985238552094,
0.003672118065878749,
-0.01626545377075672,
-0.013035510666668415,
0.01731162890791893,
0.025649502873420715,
0.0019965555984526873,
-0.00944008119404316,
-0.01110116671770811,
0.013641786761581898,
-0.025571484118700027,
-0.10304393619298935,
0.011747964657843113,
-0.00934593565762043,
-0.035877276211977005,
0.03953935578465462,
-0.05405019223690033,
-0.035827796906232834,
0.014872743748128414,
0.0008335465681739151,
0.028333237394690514,
0.0074934824369847775,
-0.03365989029407501,
0.002429298125207424,
0.037600550800561905,
-0.024673981592059135,
0.03579046577215195,
0.003311136504635215,
-0.004711567889899015,
-0.0005302687059156597,
-0.012312229722738266,
0.023886391893029213,
-0.0009184422087855637,
0.009365013800561428,
-0.05325986072421074,
0.0382271409034729,
-0.025582946836948395,
0.044036395847797394,
0.00802006945014,
-0.016081327572464943,
-0.02428637258708477,
-0.0062692114152014256,
0.009151067584753036,
0.027508696541190147,
0.013946069404482841,
-0.009354647248983383,
-0.009092611260712147,
0.03537023440003395,
-0.0403888076543808,
-0.018638666719198227,
0.003185356268659234,
0.0030844577122479677,
-0.001978654647246003,
0.03555506095290184,
0.01432326901704073,
0.0030675188172608614,
-0.005982117261737585,
-0.0367572046816349,
0.0051453132182359695,
-0.06966568529605865,
0.05090005695819855,
-0.025329284369945526,
0.008174700662493706,
0.03885172680020332,
-0.029587160795927048,
-0.04817667230963707,
-0.025646163150668144,
-0.025568248704075813,
0.005132751073688269,
-0.03693675994873047,
0.01525020319968462,
-0.03248901292681694,
-0.0016474141739308834,
-0.04940119758248329,
-0.0685107409954071,
0.04266031086444855,
0.0008475254871882498,
-0.004652379546314478,
-0.02310977317392826,
0.005108395591378212,
-0.0446847602725029,
-0.031481243669986725,
-0.0009003794984892011,
0.013039142824709415,
-0.042502500116825104,
0.028086872771382332,
0.07969710230827332,
-0.019023999571800232,
0.05011608079075813,
0.02981424704194069,
-0.03403675928711891,
0.01839890144765377,
0.0002843204711098224,
-0.019093254581093788,
-0.027919994667172432,
0.08670459687709808,
-0.029731057584285736,
-0.05310938507318497,
0.00337688229046762,
-0.0028228946030139923,
0.024482361972332,
-0.02865482121706009,
0.013239756226539612,
0.022677848115563393,
0.0030251687858253717,
0.008732090704143047,
0.0031626299023628235,
0.023307079449295998,
0.013650117442011833,
0.01757710985839367,
0.038572538644075394,
0.019984442740678787,
-0.048810482025146484,
-0.07486406713724136,
0.054882802069187164,
-0.006174428388476372,
0.0018337102374061942,
-0.004000518471002579,
0.044481270015239716,
0.013770797289907932,
-0.002116564894095063,
0.013111583888530731,
0.019553083926439285,
0.032362647354602814,
-0.03655611723661423,
-0.018659815192222595,
-0.01154851634055376,
-0.0013515821192413568,
-0.05170164629817009,
-0.018902065232396126,
0.008811011910438538,
0.014967530034482479,
0.04764116182923317,
-0.04252916947007179,
0.06819920986890793,
0.008375098928809166,
0.0286476518958807,
-0.022805646061897278,
-0.011396855115890503,
0.020109588280320168,
-0.01977291703224182,
0.028846366330981255,
0.011794046498835087,
-0.04918553680181503,
0.016795281320810318,
0.029574275016784668,
0.0390290804207325,
0.0008461346151307225,
-0.0007678980473428965,
0.041716817766427994,
0.011256332509219646,
0.053049445152282715,
0.00708699319511652,
-0.027015233412384987,
-0.002840344561263919,
-0.02221851237118244,
0.06802894175052643,
0.010427502915263176,
-0.030167335644364357,
0.05203166976571083,
0.027780966833233833,
0.01930602453649044,
-0.053367700427770615,
-0.014181410893797874,
-0.018199577927589417,
0.03355187550187111,
0.008898485451936722,
-0.0012664744863286614,
-0.0039445627480745316,
0.0033675318118184805,
0.039537470787763596,
0.016194887459278107,
0.029556773602962494,
-0.02509235590696335,
-0.035565365105867386,
-0.035279780626297,
-0.06859544664621353,
-0.035261575132608414,
0.04916367679834366,
0.005048121325671673,
-0.011435972526669502,
-0.004361074883490801,
-0.0071614766493439674,
0.017685523256659508,
-0.016038300469517708,
0.055967483669519424,
-0.02310144156217575,
0.06318587809801102,
-0.0070524634793400764,
0.03341015428304672,
-0.04738641157746315,
0.027986742556095123,
0.11607063561677933,
0.016113441437482834,
-0.009146380238234997,
-0.015450112521648407,
-0.03080781362950802,
-0.015145240351557732,
0.010074407793581486,
-0.04565297067165375,
0.012589978985488415,
0.009127268567681313,
0.002720755524933338,
0.04582042992115021,
0.0396793857216835,
-0.018695931881666183,
-0.03041723743081093,
0.047613147646188736,
-0.03578606992959976,
-0.019982188940048218,
-0.025270435959100723,
-0.014065094292163849,
-0.005804639309644699,
-0.0015494432300329208,
-0.015455993823707104,
0.03753006085753441,
-0.02669519931077957,
-0.024121077731251717,
-0.017288846895098686,
-0.03346959128975868,
0.024327192455530167,
0.03526468947529793,
-0.04553155601024628,
0.0005877779913134873,
-0.011225012131035328,
-0.05098646134138107,
-0.0185907743871212,
0.019637422636151314,
0.024463839828968048,
-0.028738701716065407,
-0.011056913994252682,
0.05010906234383583,
0.020128171890974045,
0.04396829754114151,
0.03517472743988037,
-0.005888712126761675,
-0.03206096217036247,
0.013029120862483978,
-0.011811682023108006,
0.047033846378326416,
-0.0005505388253368437,
0.05424223467707634,
0.020100107416510582,
0.026197198778390884,
0.028646482154726982,
-0.06554239988327026,
0.002248067408800125,
-0.03529978543519974,
0.022578071802854538,
-0.0019939688500016928,
0.0039773741737008095,
-0.027769247069954872,
0.007597988937050104,
0.028797853738069534,
-0.013092750683426857,
-0.005625167395919561,
-0.00031697508529759943,
0.0037636018823832273,
-0.005717051215469837,
0.025443296879529953,
-0.007346488535404205,
-0.02523733302950859,
-0.03101527877151966,
-0.007543601561337709,
-0.033352356404066086,
0.04509846493601799,
0.028717592358589172,
0.03046879917383194,
0.0025978642515838146,
-0.018893001601099968,
0.01841495744884014,
-0.02060062251985073,
-0.03237603232264519,
0.03475078567862511,
-0.0032927736174315214,
-0.017509784549474716,
-0.016195492818951607,
-0.03786851465702057,
0.05158926174044609,
0.04502900317311287,
-0.02887500263750553,
-0.027038363739848137,
-0.0396844707429409,
0.048455070704221725,
0.0056283134035766125,
0.0061998264864087105,
-0.038279686123132706,
0.0014461020473390818,
-0.029881173744797707,
0.02649250440299511,
-0.01312642078846693,
0.05792877450585365,
0.03623291850090027,
0.003347218967974186,
0.002067089080810547,
0.020277295261621475,
-0.0232496727257967,
-0.015420107170939445,
0.022346071898937225,
-0.01765097863972187,
-0.008628596551716328,
-0.00978622492402792,
-0.009870645590126514,
-0.02863364666700363,
-0.005385396536439657,
-0.027779346331954002,
-0.03287401422858238,
-0.007879839278757572,
0.038399264216423035,
-0.0434146486222744,
-0.004841570742428303,
-0.028840631246566772,
0.020683858543634415,
-0.055245134979486465,
0.0236196368932724,
-0.05146940425038338,
-0.025345375761389732,
0.03815619647502899,
0.008594783022999763,
-0.023396139964461327,
0.03540145978331566,
-0.025214195251464844,
-0.01701248437166214,
0.003951127640902996,
0.01688109152019024,
-0.014864105731248856,
0.013777418062090874,
-0.013583467341959476,
-0.003433226840570569,
0.051735807210206985,
-0.003819477977231145,
-0.012939631938934326,
0.04427720978856087,
-0.028088783845305443,
-0.0297287255525589,
0.01866290159523487,
-0.04225436970591545,
0.039970170706510544,
0.03698206692934036,
-0.041009627282619476,
-0.02933695912361145,
0.051474105566740036,
0.01121259294450283,
-0.016077378764748573,
0.02435465343296528,
-0.037375617772340775,
-0.031181352213025093,
0.003484590444713831,
0.03648489713668823,
-0.03616306185722351,
-0.04432358965277672,
0.01279962994158268,
0.04352939501404762,
0.014633074402809143,
0.0036061962600797415,
-0.0035619575064629316,
-0.007854762487113476,
-0.04522884637117386,
0.027048954740166664,
0.005046317353844643,
0.03351305425167084,
0.04783238098025322,
-0.01532515324652195,
0.04107845947146416,
0.015681680291891098,
-0.016825668513774872,
-0.09334724396467209,
0.007402127608656883,
-0.030825989320874214,
0.013269464485347271,
-0.0004435048613231629,
-0.046147655695676804,
-0.01344133447855711,
0.029460616409778595,
-0.09221743047237396,
0.019955076277256012,
-0.047646936029195786,
-0.024071702733635902,
-0.028723977506160736,
-0.021118158474564552,
-0.008281178772449493,
0.04748854413628578,
0.011025795713067055,
0.029563745483756065,
0.013436700217425823,
-0.015189530327916145,
-0.021574627608060837,
-0.0028071270789951086,
0.0005676069995388389,
0.02094881981611252,
-0.023598110303282738,
0.04581363871693611,
0.06380227953195572,
-0.04197773337364197,
-0.028471564874053,
0.012629068456590176,
-0.03963196277618408,
0.020926279947161674,
0.002316201338544488,
-0.0004972066381014884,
0.013487128540873528,
0.0336599200963974,
-0.008257376030087471,
-0.01423194631934166,
-0.02793906256556511,
0.04280245304107666,
0.02269742265343666,
0.018672529608011246,
-0.05176757276058197,
-0.004654739052057266,
0.03940815478563309,
-0.058623574674129486,
-0.016878550872206688,
0.006076023448258638,
-0.041388630867004395,
0.026658853515982628,
-0.009056434035301208,
0.03131270036101341,
-0.017344295978546143,
-0.00334294606000185,
-0.012750094756484032,
-0.02160431072115898,
-0.00840648915618658,
0.035138558596372604,
0.002459482057020068,
-0.010733643546700478,
0.024236436933279037,
0.0016263822326436639,
0.01399306021630764,
-0.009481771849095821,
-0.016602544113993645,
0.0013884445652365685,
-0.02748679742217064,
-0.0019512150902301073,
-0.008286235854029655,
-0.04683457314968109,
-0.02868226356804371,
-0.045346517115831375,
0.012920094653964043,
0.037463393062353134,
0.04569230228662491,
0.03668801113963127,
0.039400614798069,
-0.0580885075032711,
-0.022338218986988068,
-0.08739225566387177,
0.015927620232105255,
0.008166166953742504,
-0.01853046752512455,
-0.04682838171720505,
-0.05417235195636749,
0.026893123984336853,
0.025263942778110504,
0.03023778647184372,
-0.041202109307050705,
0.027178557589650154,
0.04722732678055763,
-0.004253636114299297,
0.011436885222792625,
-0.03541399538516998,
0.023301001638174057,
-0.021699363365769386,
-0.027960408478975296,
0.006648107897490263,
-0.003053251188248396,
-0.02149052917957306,
-0.002629026537761092,
0.04240545257925987,
-0.014138723723590374,
-0.009079365991055965,
-0.008416246622800827,
-0.06789350509643555,
0.03446277976036072,
0.0372014082968235,
0.02434275485575199,
0.046434689313173294,
-0.0024696439504623413,
0.015322844497859478,
0.00836502481251955,
-0.017314327880740166,
-0.03703997656702995,
0.04625796154141426,
-0.04573775455355644,
-0.0008918987005017698,
-0.043407149612903595,
-0.012586996890604496,
0.014653822407126427,
-0.00802692025899887,
0.040769051760435104,
0.0006996825686655939,
-0.020941361784934998,
-0.00587047915905714,
0.028086557984352112,
0.005854374263435602,
0.019958660006523132,
-0.02882491983473301,
0.0273270420730114,
0.04216098412871361,
0.024617426097393036,
-0.0032190235797315836,
0.055280301719903946,
-0.0002143881720257923,
0.0011675790883600712,
-0.01860954612493515,
0.031371913850307465,
0.002508383709937334,
0.027282405644655228,
0.0077639492228627205,
0.04907987639307976,
-0.0005590587970800698,
-0.00004706441905000247,
0.008399921469390392,
-0.009715097956359386,
0.026359211653470993,
0.020774733275175095,
-0.029864655807614326,
0.07870358973741531,
-0.01797843538224697,
0.005634571425616741,
0.02218030020594597,
0.01862006075680256,
0.008210401982069016,
0.01095824595540762,
0.0014251505490392447,
0.0028549630660563707,
0.002410145476460457,
-0.02818494848906994,
-0.018492089584469795,
0.014482809230685234,
0.03867082670331001,
0.017371533438563347,
0.027086853981018066,
-0.00009017167758429423,
0.0018105817725881934,
-0.011171511374413967,
-0.0020575791131705046,
-0.02639414370059967,
-0.03281427547335625,
0.033028025180101395,
0.029710115864872932,
0.014465630985796452,
-0.013923786580562592,
0.030406014993786812,
-0.04084400087594986,
0.045366328209638596,
-0.03429064899682999,
-0.03462960198521614,
0.008314418606460094,
0.045026056468486786,
0.0015541068278253078,
0.008430545218288898
] |
<p>I know that one of the dangers of a nuclear attack is the shockwave which compresses the air and can cause a pulmonary embolism in creatures in the area of effect. Is the shockwave directional in effect?</p>
<p>In other words, lets say your building is on the outskirts of a city and is built so that all the windows face AWAY from the city and only thick, concrete walls face the city side.</p>
<p>Will this protect the occupants from the shockwave of an explosion over the city or will the shockwave wash over the building and then go "backwards" through the windows?</p> | 1,457 | [
-0.02790175937116146,
-0.05873514711856842,
-0.02465984784066677,
-0.01268743071705103,
0.02693474106490612,
0.013687281869351864,
0.0008714411524124444,
0.004713185131549835,
0.017921680584549904,
-0.03638328239321709,
0.02852039597928524,
0.03706991299986839,
0.06490781158208847,
0.00787684228271246,
-0.024266771972179413,
-0.02845064178109169,
-0.04734806716442108,
-0.01917991228401661,
-0.009047094732522964,
-0.04631361737847328,
-0.012453514151275158,
-0.012640873901546001,
-0.012971709482371807,
0.01094843354076147,
-0.02605912834405899,
0.051714953035116196,
0.01580899953842163,
-0.034600138664245605,
0.04473961144685745,
-0.026115762069821358,
-0.004714976064860821,
-0.022404655814170837,
0.003746393136680126,
0.0227219108492136,
0.02884184755384922,
-0.04216042906045914,
-0.05742066353559494,
-0.033612269908189774,
-0.03453885763883591,
0.001629377482458949,
0.03156452625989914,
-0.006998746190220118,
0.013256270438432693,
0.03432423248887062,
-0.04683306813240051,
0.011949384585022926,
-0.025797437876462936,
-0.007698685862123966,
0.037155356258153915,
-0.06380265206098557,
0.05640003830194473,
-0.044405821710824966,
0.020533299073576927,
0.03763403743505478,
0.016727261245250702,
-0.015447174198925495,
0.05977537855505943,
0.03782273083925247,
-0.0034583588130772114,
-0.04830998554825783,
0.003036889946088195,
0.02945557050406933,
-0.03292960673570633,
0.006638815626502037,
-0.0279705673456192,
0.03310500457882881,
-0.0069079408422112465,
-0.057141728699207306,
0.016108842566609383,
-0.008040842600166798,
0.0031463634222745895,
0.0015098501462489367,
0.027550438418984413,
0.005700035020709038,
0.04733482003211975,
-0.024493958801031113,
0.034038759768009186,
0.03617969900369644,
0.01874764822423458,
0.0033587366342544556,
-0.00506128603592515,
-0.00891273282468319,
0.011343973688781261,
0.013304907828569412,
0.03462305665016174,
-0.0055265892297029495,
0.09722216427326202,
-0.012346833012998104,
-0.006131344009190798,
0.002121914643794298,
0.012652982026338577,
0.0057876682840287685,
0.030363453552126884,
-0.01913016475737095,
-0.005805312190204859,
0.06163965165615082,
0.0016872611595317721,
0.08086897432804108,
-0.012295125983655453,
0.004982056096196175,
-0.019673919305205345,
0.009851031936705112,
0.007384149357676506,
0.056150950491428375,
0.0009619038319215178,
-0.01730988174676895,
-0.0412345752120018,
0.03597818687558174,
-0.018023274838924408,
-0.014467033557593822,
-0.07638254016637802,
0.01666819304227829,
-0.022426845505833626,
-0.015305145643651485,
0.04721161723136902,
-0.024415230378508568,
0.018834026530385017,
-0.0026533231139183044,
-0.0008107587927952409,
0.05057402327656746,
0.06257180869579315,
0.0006784582510590553,
0.00027511391090229154,
-0.02991238422691822,
-0.08765986561775208,
-0.020198674872517586,
0.06263359636068344,
-0.018379198387265205,
-0.05869114771485329,
0.041947171092033386,
0.024091389030218124,
-0.01353147067129612,
0.022010397166013718,
-0.040676966309547424,
0.05440559983253479,
-0.02139202505350113,
-0.12412568181753159,
-0.045371174812316895,
0.031784698367118835,
0.042207423597574234,
-0.007870235480368137,
-0.06693346053361893,
-0.044693153351545334,
0.009425107389688492,
0.059182748198509216,
-0.01512298732995987,
-0.004916400648653507,
0.022846659645438194,
0.03218543156981468,
-0.0033596439752727747,
-0.004263424314558506,
0.04541383311152458,
0.00026013093884103,
-0.03550157696008682,
-0.005606751888990402,
-0.043617840856313705,
0.03552006557583809,
0.014848724007606506,
0.006350230425596237,
-0.039254676550626755,
0.042680155485868454,
-0.0023442150559276342,
0.0028454679995775223,
-0.012171846814453602,
-0.04563010856509209,
-0.045316629111766815,
0.0503101721405983,
0.024736538529396057,
-0.038368526846170425,
0.011102171614766121,
0.02266448736190796,
-0.0007539632497355342,
0.003699732944369316,
-0.0018719201907515526,
0.023474901914596558,
-0.043134886771440506,
0.013298255391418934,
-0.01106218621134758,
-0.001266753883101046,
-0.03614819049835205,
-0.05359717085957527,
-0.018221141770482063,
-0.01533823274075985,
0.005029205232858658,
0.029278570786118507,
0.02769949659705162,
0.01290112268179655,
-0.02018960751593113,
0.001954614417627454,
0.0007167977746576071,
-0.0337810143828392,
-0.05107865482568741,
0.053568821400403976,
-0.019772790372371674,
-0.004875684157013893,
0.018578749150037766,
0.0007263160077854991,
0.033392082899808884,
-0.025455469265580177,
-0.012102075852453709,
0.012071574106812477,
0.006205565296113491,
0.05563220754265785,
-0.0028896848671138287,
0.007924779318273067,
0.059515513479709625,
0.024613963440060616,
-0.03591591864824295,
0.044571202248334885,
-0.013561435975134373,
0.0032002651132643223,
-0.018908964470028877,
-0.029055336490273476,
0.00844073761254549,
0.002536546438932419,
-0.03297652676701546,
0.011418106034398079,
-0.008933384902775288,
0.02679791860282421,
-0.022967172786593437,
-0.04746398702263832,
0.0647190511226654,
0.06537249684333801,
0.00786861777305603,
0.026562685146927834,
0.011049561202526093,
0.014139832928776741,
0.036061059683561325,
0.034791793674230576,
-0.04193565249443054,
-0.05737793445587158,
0.0018971222452819347,
0.021696029230952263,
-0.05394606664776802,
-0.030633699148893356,
0.017636321485042572,
-0.018187180161476135,
0.041884347796440125,
0.019805777817964554,
0.035217683762311935,
-0.015662232413887978,
-0.03299366310238838,
0.0025264944415539503,
-0.00591250928118825,
0.022856254130601883,
-0.030418241396546364,
0.037360481917858124,
-0.0014836505288258195,
-0.02053782157599926,
-0.023521175608038902,
0.010800191201269627,
0.0012822236167266965,
-0.01761220581829548,
0.009066666476428509,
-0.00010755454422906041,
-0.05749961733818054,
0.028239160776138306,
-0.009053829126060009,
0.015335320495069027,
-0.010809481143951416,
-0.030441567301750183,
-0.007273213937878609,
-0.016900697723031044,
0.0026848744601011276,
0.015307792462408543,
0.057153522968292236,
-0.0023966655135154724,
-0.0071730841882526875,
0.04835107550024986,
-0.04932470992207527,
-0.009172352962195873,
0.0251946821808815,
0.005664831027388573,
0.02090860903263092,
-0.038364749401807785,
0.10269838571548462,
0.02793022058904171,
0.028796760365366936,
-0.017912384122610092,
-0.022293396294116974,
-0.015270919539034367,
-0.03154841810464859,
-0.010838037356734276,
0.00447577191516757,
-0.0381213016808033,
0.03711991384625435,
-0.0034061544574797153,
-0.002001293236389756,
0.010611425153911114,
-0.024415891617536545,
0.026562029495835304,
0.059920623898506165,
-0.029583508148789406,
-0.046758636832237244,
-0.03209718316793442,
-0.038675457239151,
0.021713944151997566,
-0.019334226846694946,
-0.010939247906208038,
0.04163896664977074,
0.0018820883706212044,
0.0032211681827902794,
-0.013249088078737259,
-0.04360736533999443,
-0.013490910641849041,
-0.018445579335093498,
-0.02964666672050953,
0.0015395452501252294,
-0.029132233932614326,
-0.016481656581163406,
0.018554216250777245,
-0.07406724989414215,
-0.01651192642748356,
-0.022910838946700096,
-0.05628412961959839,
0.02054733969271183,
0.024520959705114365,
0.02047954685986042,
0.0002773960877675563,
-0.024441974237561226,
0.041758570820093155,
0.009489662013947964,
-0.048244599252939224,
0.022970274090766907,
-0.02565578743815422,
0.008159397169947624,
-0.009521910920739174,
0.007861990481615067,
0.03485424816608429,
0.018923401832580566,
0.03278661519289017,
0.026010513305664062,
0.03121933341026306,
0.0007699875277467072,
0.018622085452079773,
-0.03811442479491234,
0.024999964982271194,
-0.006925353314727545,
0.01825620047748089,
0.0027985391207039356,
0.02207142859697342,
-0.029627492651343346,
-0.010171366855502129,
-0.027136437594890594,
-0.019497497007250786,
0.062491342425346375,
-0.05604171380400658,
0.031300827860832214,
-0.00287256040610373,
0.019660385325551033,
-0.060457728803157806,
0.03330403193831444,
-0.04280713200569153,
0.044996436685323715,
-0.02865760400891304,
0.002485580276697874,
0.04809128865599632,
-0.024589095264673233,
0.003197337267920375,
-0.03970806300640106,
0.06465527415275574,
-0.024097559973597527,
-0.03067093901336193,
-0.01192673109471798,
0.011937817558646202,
0.03687041997909546,
0.044669680297374725,
0.026598505675792694,
0.03303799033164978,
0.03281150758266449,
0.03597155213356018,
0.024456080049276352,
-0.007559840567409992,
-0.019824182614684105,
-0.07379356771707535,
0.017755713313817978,
-0.006665973924100399,
0.02174297720193863,
0.021729836240410805,
0.048718225210905075,
0.010792700573801994,
0.03524182364344597,
0.03824719041585922,
0.013290805742144585,
-0.03948976844549179,
0.009986946359276772,
-0.002538680098950863,
-0.020649030804634094,
-0.031944211572408676,
-0.022873278707265854,
-0.02437732368707657,
0.0016224919818341732,
-0.06964308023452759,
0.0008077331585809588,
-0.020050745457410812,
-0.05167155712842941,
0.027656707912683487,
-0.029461681842803955,
-0.06654349714517593,
0.0012069680960848927,
0.08217375725507736,
0.019007816910743713,
-0.019433490931987762,
0.04105443134903908,
0.04420878738164902,
-0.018215999007225037,
-0.009922346100211143,
0.0030626896768808365,
0.03262864798307419,
-0.004899909254163504,
0.061719365417957306,
0.011181418783962727,
-0.013327376917004585,
-0.029825160279870033,
0.02696090377867222,
0.01645856350660324,
-0.000671196379698813,
-0.01370776817202568,
0.0020927265286445618,
-0.03644568473100662,
-0.01694018580019474,
-0.03213166818022728,
0.02214367687702179,
0.0021409597247838974,
0.017999179661273956,
0.037019457668066025,
0.0456230491399765,
0.006737042684108019,
-0.019501252099871635,
0.019608013331890106,
0.05594237521290779,
-0.01021658070385456,
0.016265302896499634,
-0.018575748428702354,
0.007517436984926462,
-0.018549436703324318,
-0.02987927384674549,
-0.029666170477867126,
-0.0052189151756465435,
-0.025056207552552223,
0.02567458152770996,
0.009678957052528858,
-0.006703672930598259,
-0.010002010501921177,
0.0511331781744957,
-0.0017823940142989159,
-0.023871105164289474,
0.012582546100020409,
0.011206034570932388,
0.04019053652882576,
-0.01378637831658125,
0.019793372601270676,
0.04505259916186333,
-0.045890092849731445,
-0.04144197702407837,
-0.002508428879082203,
0.032279226928949356,
0.016531581059098244,
-0.01782429777085781,
-0.001439226558431983,
-0.07316844165325165,
-0.03377450630068779,
0.040312815457582474,
0.01053693424910307,
0.02561858482658863,
-0.008876840583980083,
0.0010821870528161526,
-0.008485309779644012,
-0.03684956952929497,
-0.04152306914329529,
-0.025427548214793205,
-0.024569837376475334,
-0.0007960248040035367,
0.004143101628869772,
-0.0051235780119895935,
-0.031447961926460266,
-0.030562596395611763,
0.04117175564169884,
0.01302915345877409,
0.020868953317403793,
-0.020998608320951462,
-0.044774822890758514,
0.011588675901293755,
-0.007641952484846115,
-0.019215792417526245,
0.008809485472738743,
0.02816864661872387,
-0.0023118925746530294,
0.04305629804730415,
-0.0058292062021791935,
0.015544001944363117,
0.07638894766569138,
0.003888785606250167,
-0.00028049718821421266,
0.018615886569023132,
-0.015390018932521343,
0.04354824125766754,
0.021453270688652992,
0.011142341420054436,
0.03966855630278587,
0.07560344785451889,
-0.02579490654170513,
0.012206515297293663,
0.00041538276127539575,
0.018072549253702164,
-0.050320565700531006,
0.017058664932847023,
0.019931713119149208,
0.012569722719490528,
-0.01795821450650692,
0.012112895026803017,
-0.016225755214691162,
0.021580370143055916,
0.02478867769241333,
-0.019370224326848984,
0.00417141430079937,
0.00016471486014779657,
-0.02658114582300186,
-0.015727931633591652,
-0.037319984287023544,
0.0345313623547554,
-0.024969279766082764,
-0.040899600833654404,
-0.032699648290872574,
-0.03605654463171959,
0.01058973465114832,
0.03846282511949539,
-0.046862248331308365,
-0.0027337379287928343,
-0.035786133259534836,
-0.020290685817599297,
0.011626498773694038,
-0.04578497260808945,
0.03152421861886978,
0.004523519892245531,
-0.01533923763781786,
0.021535737439990044,
-0.027577396482229233,
0.034364160150289536,
0.04768837243318558,
0.001936954795382917,
0.016228623688220978,
-0.025353392586112022,
0.04922860115766525,
-0.024989664554595947,
0.04556417837738991,
-0.0477038137614727,
-0.03431705757975578,
0.022471357136964798,
0.01574629358947277,
-0.03400331735610962,
-0.08620427548885345,
0.0009175994782708585,
-0.023620715364813805,
-0.06390843540430069,
-0.03377516195178032,
0.016004756093025208,
-0.036339931190013885,
0.01416308619081974,
0.048620808869600296,
-0.02818061038851738,
0.0740293562412262,
0.015181044116616249,
-0.04388332739472389,
0.02780378796160221,
-0.02404576912522316,
-0.010683906264603138,
-0.038787439465522766,
0.03203561529517174,
-0.013011588715016842,
-0.00918623711913824,
0.008390983566641808,
0.015731405466794968,
0.023712821304798126,
-0.024762555956840515,
-0.0048543293960392475,
0.05704377964138985,
0.016911907121539116,
-0.05168479308485985,
-0.017828261479735374,
0.023033123463392258,
-0.04270787164568901,
0.02825620025396347,
-0.017816221341490746,
0.01522768009454012,
-0.027679793536663055,
-0.052478257566690445,
-0.0004656297678593546,
0.0219650287181139,
0.01841043494641781,
0.04439971596002579,
0.03318726271390915,
-0.023984014987945557,
0.0016186235006898642,
0.018826426938176155,
-0.033825356513261795,
0.057028260082006454,
-0.06028912588953972,
0.006260258611291647,
-0.0005790358991362154,
0.031919293105602264,
-0.0038026554975658655,
-0.02824200503528118,
-0.04779298976063728,
0.00808512233197689,
0.02524200640618801,
-0.048214998096227646,
0.02296137996017933,
0.00006874127575429156,
0.0696030855178833,
-0.01364724338054657,
-0.03976336121559143,
-0.007226643618196249,
0.042395833879709244,
0.013504674658179283,
0.03802373632788658,
0.00321596791036427,
0.021106930449604988,
0.010108030401170254,
0.07314663380384445,
-0.008442016318440437,
0.021542515605688095,
0.011119747534394264,
0.0031505892984569073,
0.02761205844581127,
-0.00015526034985668957,
-0.01695980317890644,
0.03168580308556557,
-0.07074024528265,
-0.002623877255246043,
-0.009303825907409191,
-0.0043755206279456615,
0.013579864986240864,
0.010484655387699604,
-0.011485862545669079,
-0.06163281947374344,
0.017783863469958305,
-0.016756542026996613,
0.019850516691803932,
-0.02771705947816372,
0.048059962689876556,
-0.04503472149372101,
0.00911472924053669,
0.09388695657253265,
-0.01565653458237648,
0.01658708043396473,
0.00796426273882389,
-0.0854380652308464,
-0.011870068497955799,
-0.02850053831934929,
-0.02088697999715805,
0.019630949944257736,
0.006119817961007357,
-0.006851913873106241,
0.01619548909366131,
-0.045824356377124786,
0.06023281440138817,
0.008257309906184673,
0.044173259288072586,
0.05669073015451431,
0.06620582193136215,
0.014639895409345627,
-0.04067709669470787,
-0.0077268024906516075,
-0.016870934516191483,
0.11897464096546173,
0.034677695482969284,
0.021013371646404266,
-0.01643514819443226,
-0.03600035607814789,
-0.036003533750772476,
0.026633989065885544,
0.003431066870689392,
-0.009253962896764278,
0.006397010292857885,
0.008125250227749348,
0.02116204984486103,
0.05119623243808746,
0.03334501385688782,
-0.023524075746536255,
0.031385570764541626,
-0.037141330540180206,
-0.06775446236133575,
-0.0014192824019119143,
-0.016499502584338188,
-0.015109661035239697,
-0.003706211457028985,
-0.014606504701077938,
0.041406262665987015,
0.00811182614415884,
0.0261108186095953,
-0.02321779541671276,
-0.04202279821038246,
0.04555885121226311,
0.035190120339393616,
-0.043025627732276917,
-0.014940396882593632,
-0.0018778532976284623,
-0.0009087598300538957,
-0.056316494941711426,
0.001652789767831564,
0.02149192988872528,
-0.015701578930020332,
-0.0039064763113856316,
0.019758393988013268,
0.02043238654732704,
0.01846768520772457,
0.01993490941822529,
0.02867049165070057,
-0.07617088407278061,
0.009519575163722038,
-0.015519627369940281,
-0.0069143325090408325,
-0.016787709668278694,
-0.010100207291543484,
-0.01609191484749317,
-0.002678751712664962,
0.033662889152765274,
-0.03566707670688629,
-0.016238342970609665,
-0.01516622956842184,
0.04321373999118805,
-0.019434476271271706,
0.00981032196432352,
0.02090276964008808,
0.02904842048883438,
-0.005566389299929142,
0.024761566892266273,
0.006528180092573166,
-0.0010834797285497189,
0.0012613522121682763,
-0.02275213785469532,
0.057691317051649094,
-0.012503133155405521,
-0.01993509940803051,
-0.03850824013352394,
0.005729599855840206,
-0.05673660710453987,
0.01294770184904337,
0.046100370585918427,
0.044810451567173004,
-0.0006470761727541685,
0.03784177824854851,
0.004165253601968288,
-0.015186935663223267,
-0.02520175836980343,
0.07312203198671341,
-0.045860543847084045,
-0.03833899646997452,
-0.011490521021187305,
-0.00569344125688076,
0.036719828844070435,
0.03461677208542824,
-0.0454825796186924,
-0.00785759650170803,
-0.039321042597293854,
0.0179451871663332,
0.000035589386243373156,
-0.003910692408680916,
-0.028599780052900314,
0.01972034201025963,
-0.01275345403701067,
0.03028932772576809,
-0.0007759424042887986,
0.025055667385458946,
0.024843823164701462,
-0.01432875171303749,
0.02944747358560562,
0.014087708666920662,
-0.03213415667414665,
-0.012044774368405342,
0.016166403889656067,
-0.066192127764225,
-0.0027511685620993376,
0.0024263542145490646,
-0.016611475497484207,
-0.03210693225264549,
0.004439951851963997,
-0.028280505910515785,
-0.00489960378035903,
-0.015706725418567657,
0.03790828213095665,
0.00009685009717941284,
0.009237386286258698,
-0.000358047429472208,
0.02667640708386898,
0.011251203715801239,
-0.021281013265252113,
-0.04327593743801117,
0.008193393237888813,
-0.008275720290839672,
-0.03900253027677536,
-0.017299652099609375,
0.006293938960880041,
-0.042882733047008514,
0.0038235082756727934,
-0.010150899179279804,
0.008923809044063091,
-0.001986331306397915,
0.030079759657382965,
0.002028638729825616,
0.002786896424368024,
0.07546766102313995,
0.0022745474707335234,
0.03337781876325607,
-0.012004044838249683,
-0.018624374642968178,
-0.080088309943676,
0.055118244141340256,
-0.000013941328688815702,
0.02419421076774597,
-0.008426106534898281,
0.030225152149796486,
0.006000010762363672,
0.10071352869272232,
-0.014738094992935658,
0.006401405669748783,
0.004733153153210878,
0.011070122942328453,
0.01421281136572361,
-0.011234365403652191,
-0.010063892230391502,
-0.050004858523607254,
-0.004456597380340099,
0.04738350585103035,
0.018131602555513382,
-0.01914823427796364,
0.026785477995872498,
-0.019413447007536888,
-0.0528421513736248,
0.015666481107473373,
-0.022372925654053688,
-0.0009471790981478989,
0.014573258347809315,
0.04923579841852188,
-0.01951686106622219,
0.010565231554210186,
0.023887714371085167,
-0.030098246410489082,
-0.09337378293275833,
-0.018235856667160988,
0.0134727256372571,
-0.01296558789908886,
-0.002746648620814085,
-0.039970893412828445,
0.04626966640353203,
0.052356962114572525,
-0.06967468559741974,
0.0018314705230295658,
-0.017985740676522255,
-0.02850422076880932,
-0.03922365605831146,
0.03242524340748787,
0.017364023253321648,
0.034061502665281296,
-0.001116118859499693,
0.03505052253603935,
0.06383701413869858,
0.03455483913421631,
-0.03345980495214462,
-0.006561748217791319,
0.021540675312280655,
0.0023345989175140858,
0.03394348546862602,
0.010041657835245132,
0.05474686622619629,
-0.024747205898165703,
-0.03183482587337494,
0.03478645905852318,
-0.024649575352668762,
0.04645171016454697,
0.005276527255773544,
0.03906077891588211,
0.019853439182043076,
0.05042877793312073,
0.019321907311677933,
0.011322727426886559,
0.008035898208618164,
0.0035837742034345865,
0.015981469303369522,
-0.007624619174748659,
-0.015958430245518684,
0.009609004482626915,
0.0062028104439377785,
-0.015452212654054165,
0.008550322614610195,
0.02565603144466877,
-0.003896852256730199,
-0.03246103227138519,
-0.05480228736996651,
-0.022198962047696114,
0.04777774214744568,
0.02234467677772045,
0.027022341266274452,
-0.05462738126516342,
-0.003318839706480503,
0.0048064799048006535,
0.0019306143512949347,
-0.005891773384064436,
0.023355916142463684,
-0.02142907679080963,
-0.035527799278497696,
-0.011921101249754429,
0.02457020804286003,
-0.04108806326985359,
-0.0022337220143526793,
0.0077424379996955395,
-0.021770136430859566,
0.010186402127146721,
-0.02099243737757206,
-0.032029490917921066,
-0.026075465604662895,
-0.0062647974118590355,
0.04520120844244957,
0.04958207905292511,
0.052385538816452026,
-0.004374077543616295,
-0.04409904032945633,
-0.03495187684893608,
0.0370994471013546,
0.01691553369164467,
-0.0059782834723591805,
-0.03375418484210968,
-0.04266434535384178,
0.018472714349627495,
0.033739980310201645,
0.0438796691596508,
0.005795206408947706,
0.012125497683882713,
0.0010557560017332435,
0.008283882401883602,
0.02373252809047699,
-0.058213893324136734,
-0.02907102182507515,
0.01083146408200264,
-0.0473814532160759,
-0.011900133453309536,
0.007252510637044907,
-0.012295912019908428,
0.026957280933856964,
0.015521419234573841,
-0.014565803110599518,
0.008798991329967976,
-0.037111517041921616,
-0.05550302192568779,
-0.0035050089936703444,
0.04529257118701935,
-0.004445216618478298,
0.06081242859363556,
0.0034033351112157106,
0.01599748432636261,
0.03503328189253807,
-0.05207518860697746,
-0.038984354585409164,
0.005000869743525982,
-0.004979378543794155,
-0.03383796289563179,
0.009751347824931145,
-0.012949058786034584,
0.05469051003456116,
-0.028976328670978546,
0.011660401709377766,
0.007432142738252878,
-0.05304161459207535,
0.03328094258904457,
0.014193754643201828,
0.015618653036653996,
0.006422174628823996,
-0.011750695295631886,
0.0045672813430428505,
0.04466535896062851,
0.014807689934968948,
-0.01590454950928688,
0.028601059690117836,
0.02381889522075653,
0.009174489416182041,
-0.02326999418437481,
0.02477158047258854,
-0.0013568109134212136,
0.02654053457081318,
-0.010475714690983295,
-0.013578208163380623,
-0.008198435418307781,
-0.0019440794130787253,
0.06427642703056335,
0.0029927953146398067,
-0.03222906216979027,
0.03465999290347099,
-0.039445456117391586,
0.05436968058347702,
0.00036658524186350405,
0.01447766087949276,
-0.022914644330739975,
-0.02151396870613098,
-0.0013694394147023559,
0.012951801531016827,
0.0232427679002285,
0.00939492229372263,
-0.009875383228063583,
0.011529683135449886,
0.04327381029725075,
-0.009788698516786098,
0.007616829127073288,
-0.059500474482774734,
0.01715947687625885,
-0.015015789307653904,
-0.014649500139057636,
-0.019187966361641884,
0.0025398635771125555,
-0.024242091923952103,
-0.007482292130589485,
0.02577390894293785,
0.055900268256664276,
0.011970478110015392,
0.016261044889688492,
-0.030840963125228882,
0.007834658958017826,
0.055984728038311005,
-0.0414629764854908,
-0.014199181459844112,
-0.00897889118641615,
0.012374048121273518,
-0.002766577759757638,
0.030264630913734436
] |
<p>I was unable to answer this question from my daughter. Is it just a coincidence or is there a connection between the following two observations: (1) the core of the earth is made of an iron (-nickel alloy) as well as the existence of iron meteorites with the fact that (2) the heaviest element that can be produced by a star (prior to supernova) is iron? </p>
<p>Related: <a href="http://physics.stackexchange.com/questions/35143/elements-of-a-planet-reveals-nearby-supernova-remnant">Elements of a Planet reveals nearby supernova remnant?</a></p> | 1,458 | [
-0.05659446120262146,
-0.03184499964118004,
-0.008619719184935093,
0.015849553048610687,
0.05701828375458717,
0.03188028931617737,
-0.03247935697436333,
-0.05521317943930626,
0.02499513514339924,
-0.0512385331094265,
0.030548878014087677,
0.025600112974643707,
0.04968275502324104,
0.028340274468064308,
0.016643371433019638,
0.013249391689896584,
0.0034069321118295193,
-0.02312072180211544,
-0.0018474686658009887,
-0.03131973743438721,
0.015103626064956188,
-0.02944563515484333,
-0.010366067290306091,
0.0014253670815378428,
-0.04329613223671913,
0.014393726363778114,
-0.017559990286827087,
-0.002404338913038373,
0.04730535298585892,
0.0390908308327198,
0.033199455589056015,
0.0057077729143202305,
0.05276014655828476,
0.039106737822294235,
0.04551213979721069,
0.011251275427639484,
0.004947102162986994,
-0.004945894703269005,
0.015789633616805077,
0.07085006684064865,
-0.03397245332598686,
-0.047414686530828476,
-0.008486003614962101,
0.03409714251756668,
-0.02234775945544243,
-0.01478642225265503,
-0.01815192401409149,
-0.048778604716062546,
0.07157972455024719,
-0.026723302900791168,
0.024482624605298042,
-0.00984019786119461,
0.012360929511487484,
0.008016522973775864,
0.0018081226153299212,
-0.015058085322380066,
0.07615716755390167,
0.0743374153971672,
0.05390677601099014,
-0.03383843973278999,
-0.014431552030146122,
-0.004967960994690657,
-0.02199813351035118,
0.024527398869395256,
-0.0219641774892807,
0.07224275916814804,
-0.0287329014390707,
-0.05911844223737717,
0.026989422738552094,
0.032805025577545166,
0.03864886984229088,
-0.004394253715872765,
-0.0030578472651541233,
-0.009362463839352131,
-0.006043463479727507,
-0.04278817027807236,
0.037624090909957886,
-0.014393769204616547,
0.02839280664920807,
0.025290193036198616,
-0.024633251130580902,
0.010494493879377842,
0.05387192964553833,
0.03031926229596138,
0.002063644817098975,
0.037982381880283356,
0.05197048932313919,
0.02601473033428192,
0.0312776155769825,
0.0535224974155426,
-0.00467701768502593,
0.00540608586743474,
0.03361670672893524,
-0.025553572922945023,
-0.020698433741927147,
0.005678020883351564,
-0.0011332867434248328,
0.042210761457681656,
-0.0012382077984511852,
0.022072777152061462,
0.01848181150853634,
-0.016064684838056564,
0.048806075006723404,
0.07687697559595108,
0.045924536883831024,
-0.03944927826523781,
-0.07249346375465393,
0.018742280080914497,
-0.059500716626644135,
0.006451823282986879,
0.00023905228590592742,
0.017221326008439064,
0.0026111064944416285,
-0.023097530007362366,
0.013927893713116646,
-0.004166229162365198,
-0.0003879694559145719,
-0.010418121702969074,
0.04527214169502258,
0.06376095116138458,
0.008533566258847713,
0.007017937023192644,
-0.011724555864930153,
-0.04039766639471054,
-0.049070991575717926,
0.03577328100800514,
0.016363797709345818,
-0.04678388312458992,
0.01657075434923172,
0.04335486516356468,
-0.02228449285030365,
-0.0007075938628986478,
-0.012399684637784958,
-0.01662852056324482,
0.01623278483748436,
0.016522599384188652,
-0.09322468191385269,
-0.04375699907541275,
0.030405087396502495,
-0.010666986927390099,
-0.0492117777466774,
-0.0725468173623085,
0.005345770623534918,
0.030301248654723167,
0.0523463636636734,
0.008220895193517208,
-0.0012844633311033249,
-0.006545428652316332,
0.04303477331995964,
0.03588331118226051,
-0.018859542906284332,
-0.02233869582414627,
0.01660221442580223,
-0.0477895513176918,
-0.01574784144759178,
-0.06757425516843796,
0.017637375742197037,
-0.030554648488759995,
0.005316403228789568,
-0.011742383241653442,
0.027542656287550926,
-0.04976580664515495,
0.012672293931245804,
0.010378536768257618,
0.028496725484728813,
-0.041820842772722244,
0.09378781914710999,
0.05055547133088112,
0.0006835180683992803,
0.02972053736448288,
0.001940630259923637,
0.05601365119218826,
0.06756564974784851,
0.06832918524742126,
0.021192917600274086,
-0.021556271240115166,
-0.056451085954904556,
-0.04492774233222008,
0.035209447145462036,
-0.008757351897656918,
-0.04311814904212952,
0.0032407022081315517,
-0.006407553795725107,
0.03189866617321968,
0.0421857051551342,
0.09119918197393417,
-0.0031349053606390953,
-0.0703001320362091,
0.023023685440421104,
-0.028324434533715248,
0.0007940030191093683,
-0.01571320742368698,
-0.02021242491900921,
-0.030667545273900032,
-0.048451587557792664,
0.015866508707404137,
-0.01977219618856907,
0.010374360717833042,
0.006477635353803635,
-0.0013132522581145167,
0.0059562805108726025,
0.022765828296542168,
0.0023624813184142113,
-0.019034188240766525,
0.006870917044579983,
0.0468364842236042,
0.0254596546292305,
-0.007057494483888149,
0.013358883559703827,
0.005448934156447649,
-0.053034622222185135,
-0.029905002564191818,
0.010841173119843006,
0.00012257388152647763,
0.008792161010205746,
-0.011879483237862587,
0.040776848793029785,
0.03745146468281746,
-0.0179841797798872,
0.02962724305689335,
-0.025971122086048126,
0.10261516273021698,
0.01423836499452591,
0.0028313493821769953,
0.01515163667500019,
0.002768157050013542,
0.03155269846320152,
0.057229962199926376,
-0.002435950795188546,
-0.0162366833537817,
-0.05705242604017258,
-0.030499575659632683,
0.017351187765598297,
0.0128626748919487,
-0.04134110361337662,
0.003225061809644103,
0.020687395706772804,
0.011464104987680912,
-0.0037626957055181265,
-0.004118097946047783,
-0.017300982028245926,
-0.038027118891477585,
-0.013005994260311127,
-0.008460058830678463,
-0.012759584933519363,
0.03960739076137543,
0.013818216510117054,
0.013744273222982883,
0.016438614577054977,
-0.01401058305054903,
-0.011695626191794872,
0.01882331632077694,
0.011178879998624325,
0.013714988715946674,
-0.015589125454425812,
-0.01791536808013916,
0.06066064536571503,
-0.05429545417428017,
0.017138415947556496,
0.03687651827931404,
-0.004444211721420288,
0.0037621473893523216,
-0.03837744891643524,
0.004488647449761629,
0.020895475521683693,
-0.03429668769240379,
-0.027546895667910576,
0.031142398715019226,
0.020557446405291557,
-0.04272416979074478,
-0.003429373726248741,
-0.02304244600236416,
-0.01869731768965721,
-0.018742207437753677,
0.032112978398799896,
0.042999785393476486,
-0.007601235061883926,
0.018279535695910454,
-0.010790437459945679,
-0.036140844225883484,
-0.03475531190633774,
-0.04069759324193001,
-0.02516856975853443,
0.021682556718587875,
-0.06009164825081825,
0.03569211810827255,
0.0029317117296159267,
0.03273110091686249,
0.03389885649085045,
0.024548020213842392,
-0.001145237940363586,
0.008455812931060791,
0.0023255271371454,
-0.024268338456749916,
0.0232948437333107,
0.0093381367623806,
0.018033429980278015,
-0.01768643781542778,
-0.0006107407389208674,
0.03053193911910057,
-0.016524042934179306,
-0.010617444291710854,
-0.007351359818130732,
-0.04509485512971878,
-0.05536888912320137,
-0.04115825146436691,
-0.025686029344797134,
-0.027544526383280754,
-0.005754199810326099,
-0.005399639718234539,
0.05709630250930786,
-0.00686606764793396,
-0.0016512129222974181,
-0.023009061813354492,
-0.03276233747601509,
0.019728731364011765,
-0.0507236123085022,
0.022462058812379837,
-0.03839953988790512,
-0.04797067120671272,
0.04973924905061722,
0.03371358662843704,
-0.01313877198845148,
-0.04452819004654884,
0.03335946425795555,
0.0018578263698145747,
-0.02595069631934166,
0.0012699684593826532,
0.02160537801682949,
0.016732152551412582,
0.036492425948381424,
0.013110002502799034,
0.02997119165956974,
0.013853664509952068,
0.010384248569607735,
-0.00520430039614439,
0.0040100873447954655,
-0.0022122710943222046,
-0.006742609664797783,
0.032636549323797226,
-0.007849336601793766,
-0.00029985353467054665,
0.0201377272605896,
-0.03260321542620659,
0.08672500401735306,
0.02445060946047306,
-0.044318124651908875,
0.014778310433030128,
-0.0005295669543556869,
0.003178205108270049,
-0.042669568210840225,
0.03786773234605789,
0.010377687402069569,
-0.004466626793146133,
-0.00042788771679624915,
0.02385353483259678,
0.07341718673706055,
-0.03673214092850685,
-0.012562684714794159,
0.035109225660562515,
0.0061332425102591515,
-0.025352364405989647,
0.0004952372401021421,
-0.007087266072630882,
0.011810336261987686,
-0.011865297332406044,
-0.009206208400428295,
0.026746852323412895,
0.006689008325338364,
0.020937016233801842,
0.009465470910072327,
-0.019470548257231712,
-0.05087505653500557,
0.014390535652637482,
-0.07431662827730179,
-0.034316956996917725,
-0.008080235682427883,
0.01145524438470602,
-0.0050505767576396465,
0.04270126670598984,
0.009875592775642872,
-0.0007720392313785851,
-0.004136175382882357,
-0.03275122493505478,
-0.06833089143037796,
0.019788870587944984,
-0.058134716004133224,
-0.007319934666156769,
-0.014018134213984013,
-0.015249831601977348,
-0.03663865476846695,
-0.029338490217924118,
0.016837041825056076,
-0.010676761157810688,
-0.011318274773657322,
-0.046484604477882385,
0.005621983669698238,
-0.00874983612447977,
-0.019906049594283104,
-0.013987032696604729,
0.06641648709774017,
0.027103370055556297,
0.0013480613706633449,
0.013189823366701603,
-0.029845571145415306,
-0.050016745924949646,
0.010839221999049187,
-0.03825824707746506,
0.001852281391620636,
-0.003653697669506073,
-0.0011757536558434367,
0.029438441619277,
-0.007380761206150055,
-0.01970154233276844,
-0.007341765332967043,
0.0308860894292593,
0.017476677894592285,
0.025490762665867805,
-0.0010394740384072065,
-0.03929049149155617,
-0.025107670575380325,
-0.03233545273542404,
0.021698009222745895,
0.0410933718085289,
-0.04353254660964012,
0.04566716402769089,
0.015374651178717613,
0.009935694746673107,
-0.022290535271167755,
0.04577072709798813,
0.04893729090690613,
0.01189497858285904,
-0.03429451212286949,
-0.025219615548849106,
-0.023353535681962967,
-0.03939281404018402,
-0.016098182648420334,
0.0225775558501482,
0.039069440215826035,
0.0029066542629152536,
-0.034922391176223755,
-0.001159256906248629,
0.009388343431055546,
-0.018571119755506516,
0.0172568392008543,
-0.027641043066978455,
0.03828190267086029,
-0.02237061969935894,
0.0021527458447963,
-0.03497236222028732,
0.011893030256032944,
0.07483962178230286,
-0.00293268752284348,
-0.03168977424502373,
-0.030544519424438477,
-0.024716440588235855,
0.0009992221603170037,
0.061715420335531235,
-0.04392009600996971,
0.015355157665908337,
-0.06178399547934532,
-0.009446367621421814,
0.014860467985272408,
-0.009363057091832161,
0.040349479764699936,
-0.01872948184609413,
-0.010630996897816658,
0.027275582775473595,
-0.050691939890384674,
0.028889125213027,
0.01543687004595995,
0.013976715505123138,
0.056946489959955215,
-0.03613284230232239,
-0.016599463298916817,
-0.025238150730729103,
0.008009502664208412,
0.0031076306477189064,
0.04100729525089264,
0.022093266248703003,
-0.004244291689246893,
-0.023150023072957993,
0.020600896328687668,
-0.043685369193553925,
-0.08410758525133133,
-0.028166813775897026,
-0.020274018868803978,
-0.0348363034427166,
0.018708407878875732,
-0.04613092169165611,
-0.09368874132633209,
0.020490696653723717,
0.017226766794919968,
-0.019611094146966934,
-0.04573267698287964,
-0.015539360232651234,
0.02642000839114189,
0.046648167073726654,
-0.03920005261898041,
0.01075685117393732,
0.024705559015274048,
-0.010130904614925385,
-0.008822104893624783,
-0.006162210833281279,
0.035611268132925034,
-0.038990169763565063,
0.013724187389016151,
-0.001565756043419242,
0.030322007834911346,
-0.0114431818947196,
0.00596661539748311,
0.031543415039777756,
0.016536369919776917,
0.014376669190824032,
-0.0038453342858701944,
0.006775589194148779,
0.0012555727735161781,
0.016004284843802452,
-0.02742237038910389,
-0.03367313742637634,
0.021281074732542038,
-0.003969038836658001,
-0.014010963030159473,
0.03880878537893295,
-0.02318253368139267,
-0.012394892983138561,
0.004218594636768103,
-0.0050090341828763485,
0.037812571972608566,
-0.05661166459321976,
-0.011916931718587875,
0.0335521325469017,
-0.0659245178103447,
0.01761055178940296,
-0.024595322087407112,
0.005413787439465523,
0.02119877003133297,
-0.0560479573905468,
-0.019818658009171486,
0.0018263879464939237,
-0.02188165672123432,
0.020198775455355644,
-0.023433523252606392,
0.059837955981492996,
0.007123247254639864,
0.00653737410902977,
-0.027622923254966736,
-0.026952125132083893,
0.0044092158786952496,
0.014400416053831577,
-0.050864238291978836,
-0.03060428611934185,
-0.015792671591043472,
-0.028499554842710495,
-0.007178648374974728,
0.02948617748916149,
0.04885159432888031,
-0.04895373806357384,
-0.04429057613015175,
0.02579977735877037,
-0.0011233801487833261,
0.07674626260995865,
-0.012375256977975368,
-0.01821037568151951,
0.017143769189715385,
0.01609162427484989,
0.031534042209386826,
-0.024843880906701088,
0.03247176483273506,
-0.013450301252305508,
-0.03242340683937073,
-0.0017319004982709885,
0.02183910459280014,
-0.005317965522408485,
0.0034714573994278908,
-0.012678644619882107,
0.04377630725502968,
0.010708584450185299,
0.019289083778858185,
0.0017889817245304585,
0.04274267330765724,
-0.02387164905667305,
0.004321335814893246,
-0.03604741021990776,
0.028565039858222008,
-0.012763720005750656,
-0.030006708577275276,
0.012437604367733002,
-0.03640098497271538,
0.025976575911045074,
-0.003956448286771774,
0.06656898558139801,
0.022670073434710503,
-0.030178437009453773,
0.024105271324515343,
0.0005769777344539762,
-0.000977309187874198,
0.008678664453327656,
0.039796020835638046,
0.039439037442207336,
0.005895830690860748,
0.005231091286987066,
-0.006692908238619566,
-0.01580769196152687,
0.03525422513484955,
0.05791598930954933,
-0.06637075543403625,
0.03268134593963623,
-0.0025721185375005007,
0.005383217707276344,
0.024812763556838036,
-0.06490417569875717,
0.02451418712735176,
-0.024696659296751022,
-0.021902676671743393,
0.04412897303700447,
-0.021265093237161636,
-0.005141028668731451,
0.07135012000799179,
0.0225895494222641,
-0.05015039071440697,
0.013283220119774342,
-0.0071596247144043446,
-0.020265761762857437,
0.012934790924191475,
0.021990958601236343,
-0.05843878909945488,
0.02418326400220394,
0.00033795114723034203,
0.03740258514881134,
0.02784503810107708,
-0.02258608303964138,
0.0429631806910038,
-0.004371581599116325,
0.014996848069131374,
-0.07437239587306976,
-0.045174118131399155,
-0.034566279500722885,
-0.004049067385494709,
0.046146050095558167,
0.025954414159059525,
-0.009633205831050873,
0.004361208528280258,
0.019181471318006516,
0.03088010661303997,
-0.018262522295117378,
-0.022615384310483932,
-0.07401895523071289,
-0.028561053797602654,
-0.0037969190161675215,
-0.027828609570860863,
0.02316274307668209,
-0.037996966391801834,
-0.03716268762946129,
0.024628808721899986,
-0.03741050511598587,
0.011952554807066917,
0.015460720285773277,
0.02797933854162693,
-0.00046274959458969533,
0.06665366142988205,
-0.019619597122073174,
0.01828870177268982,
0.04951717332005501,
0.031594619154930115,
0.10776045173406601,
0.0625421479344368,
0.01547363493591547,
-0.0427933894097805,
-0.0028456044383347034,
0.010437064804136753,
-0.010821206495165825,
0.03151264786720276,
-0.005704488139599562,
0.005111973732709885,
-0.0005919360555708408,
0.013245264999568462,
0.04464724287390709,
0.004564074799418449,
-0.008910303004086018,
0.031882911920547485,
-0.011274722404778004,
0.02587617002427578,
-0.016772087663412094,
-0.004480441566556692,
0.012837737798690796,
-0.023590562865138054,
-0.05918385088443756,
0.013512156903743744,
-0.03377646580338478,
-0.019848546013236046,
0.0030776523053646088,
0.0099008958786726,
-0.022458376362919807,
0.014870117418467999,
-0.022035816684365273,
0.0016970043070614338,
0.027839142829179764,
0.014634239487349987,
-0.003991373814642429,
-0.006086960434913635,
-0.010404512286186218,
0.009110797196626663,
0.01687212474644184,
-0.011198369786143303,
0.02094942517578602,
0.020275816321372986,
-0.008655229583382607,
0.05780092254281044,
-0.06680756062269211,
-0.001771428156644106,
-0.05418127775192261,
0.026097116991877556,
0.029968619346618652,
0.000014578221453120932,
-0.0336008220911026,
0.007250121328979731,
0.04095927253365517,
-0.008522137999534607,
-0.010103761218488216,
0.008775349706411362,
0.0006717964424751699,
-0.030761539936065674,
-0.04436906799674034,
-0.021545879542827606,
0.008204040117561817,
-0.008636157028377056,
0.014871894381940365,
-0.025867484509944916,
0.0021488750353455544,
0.0369843915104866,
-0.004967093002051115,
0.023453444242477417,
0.022399086505174637,
-0.030641086399555206,
-0.02211771346628666,
-0.0034687381703406572,
-0.015019669197499752,
0.04421268403530121,
0.0005763511871919036,
0.02750958874821663,
0.04778091982007027,
0.022201931104063988,
-0.02357318624854088,
-0.019912758842110634,
-0.011586809530854225,
0.054541829973459244,
-0.030812332406640053,
-0.028167234733700752,
-0.020691441372036934,
-0.030509894713759422,
0.020140355452895164,
0.007721270900219679,
-0.039440132677555084,
0.046243418008089066,
0.026317507028579712,
0.027133656665682793,
-0.013100321404635906,
-0.06252699345350266,
0.016441121697425842,
-0.0021694276947528124,
-0.051217783242464066,
0.02532084845006466,
-0.03563658893108368,
0.016743049025535583,
0.03421216830611229,
-0.01134614646434784,
0.06007181107997894,
0.0168345645070076,
-0.03524382412433624,
0.014631824567914009,
0.026029428467154503,
0.012705178931355476,
0.022504597902297974,
-0.028787579387426376,
-0.03698405995965004,
-0.029583636671304703,
-0.0005587743362411857,
-0.024630244821310043,
-0.03338118642568588,
0.009732730686664581,
0.005361916963011026,
-0.024120934307575226,
0.04520070180296898,
-0.0502006821334362,
0.0039945668540894985,
-0.03722972422838211,
0.0072369566187262535,
-0.057747792452573776,
0.022129153832793236,
0.014034762978553772,
-0.04353870078921318,
-0.002003931440412998,
0.02533314749598503,
0.015526391565799713,
-0.02943423204123974,
0.02282840944826603,
0.007003366947174072,
0.007052148226648569,
-0.023561755195260048,
0.021611105650663376,
-0.0037351406645029783,
0.030800769105553627,
-0.03105880320072174,
-0.014724346809089184,
0.04755381494760513,
-0.05515560507774353,
-0.06014908105134964,
0.05594807490706444,
-0.02453584596514702,
-0.007083007600158453,
0.0057169548235833645,
0.017180155962705612,
0.0024297800846397877,
0.0695350393652916,
-0.022156592458486557,
-0.0132569819688797,
0.02211792953312397,
0.044763922691345215,
-0.002185784513130784,
0.012731241062283516,
-0.006606237962841988,
0.0211135596036911,
-0.0189447533339262,
0.0021862643770873547,
-0.007573331706225872,
-0.021851010620594025,
0.0013646900188177824,
-0.03940216451883316,
-0.044991783797740936,
-0.02183433808386326,
0.03644396364688873,
0.014010794460773468,
0.05590543523430824,
0.03282555565237999,
-0.02000386454164982,
0.08350235968828201,
0.010948523879051208,
-0.029165787622332573,
-0.061188627034425735,
0.024346936494112015,
-0.015960797667503357,
-0.032272450625896454,
0.01301510352641344,
-0.04425913840532303,
0.035635944455862045,
0.012054667808115482,
-0.092282235622406,
0.003726413706317544,
-0.012334255501627922,
-0.027261056005954742,
-0.04286736249923706,
-0.026724588125944138,
0.010380366817116737,
0.014182576909661293,
0.005239573307335377,
0.036979805678129196,
0.07598412036895752,
0.055997736752033234,
-0.03591996431350708,
0.0008555414970032871,
-0.04148634150624275,
0.031152941286563873,
-0.016966549679636955,
0.01108323223888874,
0.02600155770778656,
-0.01102631539106369,
-0.046147625893354416,
0.002628103829920292,
-0.003052621381357312,
-0.003820850048214197,
0.024125706404447556,
0.015174112282693386,
-0.0236835777759552,
-0.03138604387640953,
0.004096347838640213,
-0.0229457076638937,
0.02993168495595455,
0.03321992605924606,
-0.001520911930128932,
0.0455746091902256,
-0.0020889947190880775,
0.0013012971030548215,
0.03897713124752045,
-0.013761932030320168,
0.02257702685892582,
0.008761418983340263,
0.02115008421242237,
0.0007634102366864681,
0.01043760310858488,
0.03432304784655571,
0.009159629233181477,
-0.03331010788679123,
-0.026285158470273018,
-0.05459541454911232,
-0.047532737255096436,
-0.005156106315553188,
0.009948769584298134,
0.008303368464112282,
0.04133886098861694,
-0.023710202425718307,
-0.009752613492310047,
-0.029534243047237396,
0.022267719730734825,
-0.04134349152445793,
-0.0038073405157774687,
0.02327832579612732,
0.044108033180236816,
0.013207949697971344,
-0.054409462958574295,
-0.05479783937335014,
-0.029060818254947662,
0.05176897719502449,
0.009623108431696892,
0.04786176234483719,
-0.014531522057950497,
-0.050810087472200394,
0.02176973968744278,
-0.05350016430020332,
0.02881222404539585,
-0.026634616777300835,
0.026463711634278297,
-0.017239846289157867,
-0.009198031388223171,
0.013223854824900627,
0.01005268469452858,
0.0221087783575058,
-0.015008355490863323,
0.009850922971963882,
0.017243526875972748,
-0.02235509641468525,
0.002261487999930978,
-0.05284509062767029,
0.04915912076830864,
0.00673208711668849,
-0.012076868675649166,
0.02169840969145298,
-0.039128437638282776,
0.028299909085035324,
0.001927737845107913,
0.025869477540254593,
-0.01504222210496664,
0.030738465487957,
0.011672933585941792,
0.0174039788544178,
0.048200998455286026,
-0.019925277680158615,
-0.014707928523421288,
0.08996632695198059,
-0.0056908149272203445,
-0.026820939034223557,
0.022231200709939003,
0.01251305267214775,
-0.024103540927171707,
0.05359550938010216,
0.017324553802609444,
0.004267841577529907,
0.024490419775247574,
-0.015268610790371895,
0.02825092151761055,
-0.07349016517400742,
0.006999781355261803,
0.03055005520582199,
-0.003735160455107689,
-0.03291042894124985,
0.032190363854169846,
0.029092086479067802,
0.018035100772976875,
0.00426828907802701,
0.028711654245853424,
0.0013190486934036016,
-0.017399242147803307,
-0.015880843624472618,
0.058558911085128784,
0.014860357157886028,
0.0213504396378994,
0.011418205685913563,
0.0190634373575449,
0.011041034013032913,
0.023957891389727592,
-0.0016454120632261038,
0.02829677425324917,
-0.06449054181575775,
-0.013555290177464485,
-0.010910962708294392,
-0.0049661011435091496,
0.0335509218275547,
0.034877028316259384,
-0.013400135561823845,
0.07286841422319412,
-0.020048335194587708,
-0.021204624325037003,
-0.020237404853105545,
-0.01335193682461977,
0.0009735861676745117,
0.023924851790070534,
-0.0002367509005125612,
-0.006377647165209055,
0.00413316348567605,
-0.029510734602808952,
0.0021083964966237545,
0.010357257910072803,
0.024681854993104935,
-0.026408426463603973,
0.013198466040194035,
-0.02939504198729992,
0.026284867897629738,
-0.01853260025382042,
0.0037241773679852486,
-0.03519705310463905,
-0.047765571624040604,
0.021809197962284088,
0.011764907278120518,
0.004963876213878393,
0.004492146894335747,
-0.038528818637132645,
0.0074934521690011024,
0.0638790875673294,
-0.057030174881219864,
0.0076097166165709496,
-0.06716549396514893,
0.027736250311136246,
-0.039398159831762314,
-0.029593341052532196
] |
<p>A particle of mass $m$ is at a very large distance $p$ from origin $O$ and is moving with velocity $\vec{V}$ which is perpendicular to $\vec{OP}$. I have to calculate angular momentum $L$ of the particle. </p>
<p>I know that $\vec{L}=\vec{r}\times m\vec{\dot r}$.<br>
Since $|\vec{r}|=p$ and $|\dot r|=V$ and $\alpha=90^{\circ}$ is angle between $\vec{r}$ and $\vec{\dot r}$, I got that $L=|\vec{r}||m\vec{\dot r}|sin\alpha=pmV\cdot 1=pmV$. </p>
<p>In the book, it's written that $L=pV$. What happened with mass?</p> | 1,459 | [
-0.014575457200407982,
0.003235108917579055,
-0.024470502510666847,
-0.0210272166877985,
0.051216378808021545,
0.03803576901555061,
-0.041917622089385986,
0.004517421592026949,
-0.012599972076714039,
-0.03202106058597565,
0.0254588071256876,
0.044578127562999725,
0.06286835670471191,
0.023679735139012337,
0.015681101009249687,
-0.01180489081889391,
-0.02892499789595604,
0.007782347034662962,
0.012649639509618282,
-0.014454955235123634,
-0.018627990037202835,
0.005666831508278847,
0.03359756991267204,
-0.011486287228763103,
0.005544926505535841,
0.038213714957237244,
0.043409015983343124,
-0.012112515978515148,
-0.010049933567643166,
0.04344802722334862,
-0.003925159573554993,
0.006050429306924343,
0.020951734855771065,
-0.022456999868154526,
0.007246876135468483,
0.0035385359078645706,
0.002646364737302065,
-0.00804213434457779,
-0.012129195034503937,
0.04515227675437927,
-0.03331001475453377,
-0.015238680876791477,
-0.03154267743229866,
0.04590374603867531,
-0.03187540918588638,
0.04993859678506851,
-0.018676046282052994,
-0.007985019125044346,
0.05918516591191292,
-0.03917890042066574,
0.051033928990364075,
0.018348453566432,
0.010873871855437756,
0.008765635080635548,
0.00701530696824193,
-0.004239374306052923,
0.07013066112995148,
0.037711165845394135,
-0.005066335201263428,
-0.05177491158246994,
-0.003826384199783206,
-0.040394581854343414,
-0.022847723215818405,
-0.025298070162534714,
-0.006049150135368109,
0.0008978309924714267,
0.005064670462161303,
0.0025080249179154634,
0.028105584904551506,
0.016585951671004295,
0.009125384502112865,
0.017044847831130028,
-0.003202456049621105,
-0.017782889306545258,
-0.013041854836046696,
-0.03725682944059372,
0.01952151022851467,
0.018165143206715584,
0.03945719078183174,
0.027915433049201965,
0.0006014510290697217,
0.020278727635741234,
0.04645732045173645,
0.018752440810203552,
-0.01577184908092022,
-0.021679706871509552,
0.062254149466753006,
0.04687058925628662,
-0.009634113870561123,
0.0515342578291893,
0.009542432613670826,
0.03219395875930786,
0.01897595264017582,
0.0023210870567709208,
0.002578980289399624,
0.06427523493766785,
0.0004281896981410682,
0.044617507606744766,
0.0016787861241027713,
0.0018741392996162176,
0.0007090292638167739,
-0.017001014202833176,
0.03154405578970909,
0.0546288900077343,
0.03242042288184166,
-0.03727927431464195,
-0.015534676611423492,
0.017177054658532143,
-0.026500703766942024,
-0.032564446330070496,
-0.04578724130988121,
0.025782888755202293,
-0.010136325843632221,
-0.013072691857814789,
-0.00505118677392602,
-0.02440686896443367,
0.004724618513137102,
-0.006124759558588266,
0.04015497490763664,
0.0578637458384037,
0.013226195238530636,
-0.03477558121085167,
0.02184084802865982,
-0.04453571140766144,
-0.08303018659353256,
0.0057794032618403435,
0.02762896753847599,
-0.001793967094272375,
-0.030986107885837555,
0.06288516521453857,
0.03577578067779541,
0.004214197397232056,
0.01675419881939888,
-0.007566938176751137,
0.0033210301771759987,
-0.020801125094294548,
-0.10317470878362656,
-0.04318898171186447,
0.024623023346066475,
0.006986506283283234,
-0.012307079508900642,
-0.06013649329543114,
0.011084050871431828,
0.02785191312432289,
0.08538495004177094,
0.01756918616592884,
0.006107458379119635,
0.03202860802412033,
0.025945885106921196,
-0.030284656211733818,
0.0049730222672224045,
-0.004458381794393063,
0.011638282798230648,
-0.02166878432035446,
0.012499291449785233,
-0.0544588603079319,
0.0283421128988266,
0.03265572339296341,
0.026741132140159607,
-0.03173796087503433,
0.044630032032728195,
-0.0396115705370903,
0.025017092004418373,
0.015291239134967327,
-0.01779221184551716,
-0.053416039794683456,
0.08436659723520279,
0.018759710714221,
0.007200533989816904,
0.038331396877765656,
0.014562752097845078,
0.011667892336845398,
-0.007615304086357355,
0.007881013676524162,
0.05389430373907089,
-0.008748392574489117,
-0.04001833498477936,
-0.036615367978811264,
0.021398348733782768,
0.03799504414200783,
-0.021189136430621147,
-0.06324578821659088,
0.02530699037015438,
0.028011590242385864,
-0.012288461439311504,
0.06339455395936966,
0.0061885579489171505,
0.018715593963861465,
-0.020363852381706238,
-0.014282903634011745,
-0.00751762930303812,
-0.040109291672706604,
0.04103473946452141,
0.01366700790822506,
-0.023556819185614586,
0.03016151674091816,
0.002466123318299651,
0.03230895474553108,
-0.007550794165581465,
-0.020036205649375916,
0.005203342065215111,
0.03915717825293541,
-0.013748004101216793,
-0.0037277061492204666,
0.019056683406233788,
0.06213320419192314,
0.03369464725255966,
0.023388206958770752,
-0.002015206031501293,
0.0028832918033003807,
0.007614591158926487,
-0.017475269734859467,
0.019992707297205925,
-0.008960502222180367,
0.03003377467393875,
-0.005597588140517473,
0.011440527625381947,
-0.0008517677197232842,
0.005683857016265392,
0.042911458760499954,
-0.0021518575958907604,
0.0747625008225441,
0.031882669776678085,
-0.014648212119936943,
0.030497416853904724,
0.024582957848906517,
0.02518211491405964,
0.023805802688002586,
0.010095919482409954,
-0.015675412490963936,
-0.0175654124468565,
-0.018494507297873497,
0.032606277614831924,
-0.005281554535031319,
-0.04161820933222771,
0.05013452097773552,
0.01349931862205267,
0.055930253118276596,
0.013767031952738762,
0.010537954978644848,
-0.027231698855757713,
-0.06354106217622757,
0.006534249521791935,
0.021091079339385033,
-0.04231875017285347,
0.014552131295204163,
0.00713373301550746,
0.011274769902229309,
0.009712214581668377,
0.0031527625396847725,
-0.03552791848778725,
0.018710054457187653,
0.007004811894148588,
0.010653635486960411,
0.028764046728610992,
-0.02652359940111637,
0.05853947624564171,
-0.028972264379262924,
0.02887319214642048,
0.031863804906606674,
-0.011445227079093456,
-0.025272132828831673,
-0.05449001491069794,
0.011805323883891106,
-0.017451902851462364,
0.007053143344819546,
-0.029118448495864868,
-0.021515989676117897,
0.014159449376165867,
-0.052437618374824524,
0.00042849176679737866,
0.012788857333362103,
-0.031876400113105774,
-0.014180157333612442,
0.021735770627856255,
-0.0010524298995733261,
0.02408115193247795,
0.010052061639726162,
0.008805612102150917,
-0.031383030116558075,
0.0031961698550730944,
-0.022160779684782028,
-0.0021379648242145777,
0.053104467689991,
-0.04976530745625496,
0.015273574739694595,
-0.04170737415552139,
-0.026430869475007057,
0.04383651912212372,
0.027338387444615364,
0.012582766823470592,
0.00900464691221714,
-0.01606925204396248,
-0.05853120610117912,
-0.04075852409005165,
-0.019765617325901985,
-0.023111671209335327,
-0.033088523894548416,
0.011646641418337822,
0.03287806734442711,
0.0021384155843406916,
-0.004511630162596703,
-0.00876654777675867,
-0.06199667602777481,
-0.030483407899737358,
-0.017921805381774902,
0.003091372549533844,
0.022077906876802444,
-0.022282879799604416,
0.006181098986417055,
0.011297250166535378,
-0.00802590511739254,
0.004758424125611782,
-0.05810660496354103,
-0.03190375864505768,
-0.010336608625948429,
-0.010767731815576553,
0.026779932901263237,
0.014095782302320004,
-0.03513357415795326,
0.09843683987855911,
0.033689092844724655,
-0.041722238063812256,
-0.02203143574297428,
0.030068032443523407,
0.006902249529957771,
-0.04514731094241142,
-0.008961379528045654,
0.04508253559470177,
-0.026863329112529755,
-0.013305245898663998,
0.001189915114082396,
0.0002818917855620384,
0.020296940580010414,
0.05729163438081741,
-0.0042548757046461105,
0.00005323245204635896,
0.0016737694386392832,
0.00432959571480751,
0.033468443900346756,
0.0006259596557356417,
-0.010264626704156399,
0.021891959011554718,
0.013434126041829586,
0.049186669290065765,
0.013517746701836586,
-0.06567448377609253,
0.04123878479003906,
0.016071364283561707,
0.0017227351199835539,
-0.022634541615843773,
0.05572448670864105,
0.0029019941575825214,
0.013407167047262192,
0.02006112039089203,
0.027405744418501854,
0.03241134062409401,
-0.027104083448648453,
-0.02242698147892952,
0.039353612810373306,
0.004214723594486713,
-0.018278446048498154,
-0.0010187142761424184,
-0.02776353433728218,
0.00035874024615623057,
0.021649951115250587,
-0.043790869414806366,
-0.009312056936323643,
0.01696927286684513,
0.05217616632580757,
0.044213104993104935,
-0.026523789390921593,
-0.07222543656826019,
0.029560847207903862,
-0.043406520038843155,
0.017651796340942383,
-0.017558399587869644,
0.02427440509200096,
-0.0014438688522204757,
0.06953135877847672,
0.04583289101719856,
0.007094178348779678,
0.0295221246778965,
0.010665987618267536,
-0.07080385833978653,
0.03547517582774162,
-0.02507496252655983,
-0.05714591220021248,
0.0027715819887816906,
-0.004134179092943668,
-0.027406733483076096,
-0.010188207030296326,
0.005483176559209824,
-0.024434179067611694,
-0.0704704076051712,
-0.044494736939668655,
0.02387373521924019,
-0.043338414281606674,
-0.012717513367533684,
-0.024090101942420006,
0.0377807542681694,
0.03131004795432091,
-0.02362682670354843,
0.047228362411260605,
0.055715207010507584,
-0.08585530519485474,
0.004526822362095118,
-0.04745706170797348,
-0.008682389743626118,
-0.008353573270142078,
0.001526430482044816,
0.00542957941070199,
0.021029187366366386,
-0.00400040578097105,
0.014461587183177471,
0.010109824128448963,
0.05430951714515686,
0.03510146588087082,
-0.015158124268054962,
-0.016147736459970474,
-0.05652998387813568,
-0.012967734597623348,
-0.0032474277541041374,
0.018863819539546967,
-0.027072206139564514,
-0.025414053350687027,
0.03014063835144043,
-0.013668450526893139,
-0.018735239282250404,
0.03749404102563858,
0.01323739904910326,
0.033649247139692307,
-0.005656654480844736,
-0.023587577044963837,
0.02290908806025982,
-0.004011212382465601,
-0.027226276695728302,
0.01043014507740736,
-0.052248455584049225,
-0.029574081301689148,
-0.05268131569027901,
-0.025844592601060867,
0.018995443359017372,
-0.009968124330043793,
-0.00529759144410491,
-0.027339765802025795,
0.011524509638547897,
-0.028014183044433594,
-0.004674340598285198,
-0.0049324338324368,
0.02077840268611908,
0.048441674560308456,
0.00484401173889637,
0.034117426723241806,
-0.05462391674518585,
0.0007063267985358834,
-0.007338992320001125,
0.03162549436092377,
-0.02201334945857525,
0.030178328976035118,
-0.04590965807437897,
-0.028608767315745354,
0.0382939949631691,
-0.014018413610756397,
0.045065756887197495,
-0.04816426709294319,
0.022866791114211082,
-0.020115656778216362,
-0.0519290566444397,
-0.061505530029535294,
-0.0011539661791175604,
-0.03710290789604187,
0.01233774796128273,
-0.04609644412994385,
-0.029884302988648415,
-0.024630161002278328,
0.005452431738376617,
0.04594062268733978,
0.042861513793468475,
0.032434575259685516,
-0.015263278968632221,
-0.021135808899998665,
0.030047008767724037,
-0.04325176775455475,
-0.09842368960380554,
0.011339742690324783,
-0.019944678992033005,
-0.004525240510702133,
0.018371552228927612,
-0.044366925954818726,
-0.08555163443088531,
0.0563369020819664,
0.017256097868084908,
0.009766291826963425,
-0.023044440895318985,
-0.04546363651752472,
0.01157661247998476,
0.026934050023555756,
-0.012863261625170708,
0.03340303152799606,
-0.01625813916325569,
0.008118775673210621,
-0.017045332118868828,
-0.025133032351732254,
0.032902441918849945,
-0.014562603086233139,
-0.018695924431085587,
-0.03984547406435013,
0.01715284213423729,
-0.013573698699474335,
0.07073737680912018,
0.0042765322141349316,
0.03104928508400917,
-0.01668591797351837,
-0.030904261395335197,
-0.012449980713427067,
0.02252538502216339,
-0.0028985736425966024,
-0.00028919553733430803,
0.016384968534111977,
-0.00302010215818882,
0.0020515562500804663,
0.00038216356188058853,
0.02416684478521347,
-0.01690520904958248,
0.012948203831911087,
0.020594468340277672,
0.007518904283642769,
0.033818259835243225,
-0.03850174322724342,
-0.0021831851918250322,
0.01615658774971962,
-0.02747800201177597,
0.0426640659570694,
-0.026975346729159355,
-0.013000656850636005,
0.028594275936484337,
-0.06862238049507141,
-0.07785440981388092,
0.011848240159451962,
-0.030121680349111557,
0.03634684532880783,
-0.0581568218767643,
-0.03628131374716759,
0.026027970016002655,
0.025200366973876953,
0.005871632136404514,
-0.06899192184209824,
0.016679862514138222,
0.00844529177993536,
-0.02182198315858841,
0.04976259917020798,
-0.0012147007510066032,
-0.014721143059432507,
-0.06364680826663971,
-0.024435611441731453,
0.013334917835891247,
-0.05554642155766487,
-0.0032607121393084526,
0.009310480207204819,
0.014187044464051723,
0.07930561155080795,
-0.014470929279923439,
-0.03267575055360794,
0.01472848653793335,
-0.006071587558835745,
0.010482776910066605,
-0.0012734284391626716,
0.08343452960252762,
-0.019979214295744896,
-0.058257024735212326,
-0.00043702806578949094,
0.0024954359978437424,
0.0414288155734539,
0.006635304540395737,
-0.002556625986471772,
0.012939897365868092,
0.01404646411538124,
0.02639600820839405,
0.031249534338712692,
0.030318770557641983,
0.04126099869608879,
0.029452040791511536,
-0.02257378399372101,
-0.028127189725637436,
-0.025215458124876022,
-0.0531805045902729,
0.014592433348298073,
-0.0016984748654067516,
0.06370886415243149,
-0.018463440239429474,
0.06368862837553024,
-0.050244614481925964,
0.004793812055140734,
0.02327875606715679,
0.011733959428966045,
0.011823366396129131,
0.009632770903408527,
-0.005738380830734968,
0.018714729696512222,
0.00506969029083848,
-0.024837257340550423,
-0.023693684488534927,
-0.02815384790301323,
0.019280986860394478,
0.07270288467407227,
0.018415849655866623,
0.03427945077419281,
0.03128593787550926,
0.014858687296509743,
-0.01147389691323042,
-0.018267856910824776,
-0.04477715492248535,
0.010602466762065887,
0.03099360689520836,
0.015812702476978302,
-0.03872188925743103,
0.020671296864748,
0.02720733731985092,
0.039932381361722946,
-0.02840505726635456,
-0.010255138389766216,
0.01697755604982376,
0.014684513211250305,
0.003029503393918276,
0.010395864956080914,
-0.030824363231658936,
0.030087893828749657,
0.0004611884360201657,
0.03422487899661064,
-0.037637680768966675,
-0.030695410445332527,
0.04510484263300896,
0.027941256761550903,
0.033347953110933304,
-0.017918072640895844,
-0.017180679365992546,
-0.018479011952877045,
-0.011114433407783508,
0.028752055019140244,
-0.017882689833641052,
-0.025322189554572105,
0.03137180581688881,
0.030309714376926422,
0.024450255557894707,
0.02105032652616501,
-0.02525719441473484,
-0.05328163132071495,
-0.028235549107193947,
-0.011040990240871906,
-0.05758747085928917,
0.04406258836388588,
-0.030112434178590775,
0.002255445346236229,
0.03197600692510605,
-0.06757722049951553,
0.020242558792233467,
0.05371979624032974,
0.00790861714631319,
-0.04497416317462921,
0.08733447641134262,
-0.011400410905480385,
0.011208999902009964,
-0.03232758492231369,
-0.002737238770350814,
0.10704517364501953,
0.02103150077164173,
0.017851226031780243,
-0.04163666442036629,
0.020630691200494766,
-0.05000007525086403,
0.008024023845791817,
-0.0634506568312645,
0.02507006749510765,
-0.04456818103790283,
-0.013440024107694626,
-0.006332961842417717,
0.04826578125357628,
-0.027958068996667862,
0.0046258787624537945,
0.05017581582069397,
-0.041494060307741165,
-0.07657203823328018,
-0.021068722009658813,
0.0006838074186816812,
-0.02507120929658413,
-0.0016431318363174796,
-0.04035922884941101,
0.03636579588055611,
-0.04020475968718529,
-0.02066822536289692,
-0.022604165598750114,
-0.03194546326994896,
0.024760454893112183,
-0.023143284022808075,
-0.04202640801668167,
0.026379317045211792,
0.020395739004015923,
-0.02491995505988598,
-0.013860796578228474,
0.05768630653619766,
0.047312572598457336,
-0.015621265396475792,
0.0291061382740736,
0.04630855843424797,
0.010728971101343632,
0.017180727794766426,
0.00668245367705822,
0.006015286315232515,
-0.05837095156311989,
-0.003843157086521387,
-0.029157614335417747,
0.07447012513875961,
-0.017864247784018517,
0.03162016347050667,
-0.016649719327688217,
0.019842008128762245,
-0.0036591235548257828,
-0.06905423849821091,
0.040378887206315994,
0.021484671160578728,
0.03547370806336403,
0.00011597920092754066,
-0.00350591610185802,
0.000725269434042275,
0.026122748851776123,
0.030852116644382477,
-0.005723194219172001,
-0.03202851861715317,
0.0012001527938991785,
0.0023103526327759027,
0.010920857079327106,
0.004868129268288612,
-0.021087607368826866,
-0.0010839742608368397,
-0.012746504507958889,
-0.0008291388512589037,
-0.025521228089928627,
-0.0037076270673424006,
0.034278273582458496,
0.029100866988301277,
0.005932230036705732,
0.0010872338898479939,
-0.021655935794115067,
-0.03626834601163864,
-0.06865858286619186,
-0.0019509833073243499,
-0.010455481708049774,
-0.02844250574707985,
-0.011979117058217525,
-0.02304631657898426,
0.0053610121831297874,
0.04684312641620636,
-0.0070333522744476795,
0.008082347922027111,
0.01099073514342308,
0.02592451497912407,
0.016820432618260384,
-0.032638855278491974,
-0.04336882382631302,
0.015702689066529274,
-0.0058745285496115685,
-0.0027880731504410505,
-0.024660760536789894,
0.011349070817232132,
0.05441572889685631,
-0.012489056214690208,
0.009346899576485157,
0.05147393420338631,
0.029191285371780396,
-0.026547405868768692,
-0.001546073704957962,
0.004003526177257299,
0.02703053131699562,
0.03479655459523201,
0.027697773650288582,
-0.03203819692134857,
0.027238434180617332,
-0.008609378710389137,
-0.01980683021247387,
0.000005020296612201491,
0.007848817855119705,
0.002430027350783348,
0.015990035608410835,
-0.057907480746507645,
0.010267079807817936,
-0.006687587592750788,
0.013835201971232891,
-0.026198850944638252,
0.02268032915890217,
-0.009559567086398602,
-0.007502368185669184,
-0.053533464670181274,
0.037653885781764984,
0.001433319877833128,
0.001562379184179008,
-0.033681720495224,
0.03043457493185997,
-0.000590584590099752,
-0.013751921243965626,
0.011198430322110653,
-0.01563245616853237,
0.046687398105859756,
-0.046180710196495056,
-0.017175912857055664,
0.051323991268873215,
-0.009388775564730167,
-0.04008935019373894,
0.020586654543876648,
0.0003426215553190559,
0.04017436131834984,
0.016857460141181946,
-0.020210372284054756,
-0.03024407848715782,
0.05896759405732155,
-0.013954131864011288,
-0.031364697962999344,
-0.014592020772397518,
-0.05688744783401489,
-0.01329872291535139,
-0.004638287238776684,
-0.010780961252748966,
-0.00937372725456953,
0.018438976258039474,
0.026788393035531044,
0.005029913038015366,
-0.057720668613910675,
0.03020741231739521,
0.012041984125971794,
0.04349101334810257,
0.03547075390815735,
0.03216811642050743,
-0.0016913829604163766,
0.0025296739768236876,
0.027058901265263557,
-0.020402034744620323,
0.015562945045530796,
0.02219500206410885,
0.008600086905062199,
-0.09625592082738876,
-0.015220403671264648,
-0.003360365517437458,
0.0025256171356886625,
0.051303040236234665,
-0.04723906144499779,
-0.017625560984015465,
0.04764574021100998,
-0.11156885325908661,
-0.015228052623569965,
-0.04483960568904877,
0.006314047612249851,
-0.009902700781822205,
-0.02065184712409973,
-0.001435689628124237,
0.09073563665151596,
0.008953964337706566,
0.04478020220994949,
0.028509629890322685,
0.010684216395020485,
0.010854230262339115,
-0.04424448683857918,
-0.028216790407896042,
0.03387130796909332,
-0.029593508690595627,
0.007781671360135078,
0.03493879362940788,
-0.04608413204550743,
-0.02987826243042946,
0.024886537343263626,
-0.02918742597103119,
0.028599804267287254,
-0.004950560163706541,
0.02900620549917221,
-0.0007144889677874744,
0.029026653617620468,
-0.015031644143164158,
-0.0017530611949041486,
-0.031249914318323135,
-0.001421670662239194,
-0.01249307207763195,
0.0154059873893857,
-0.01369126420468092,
-0.007143936585634947,
0.004327866714447737,
-0.06427105516195297,
-0.03784188628196716,
0.00024197364109568298,
-0.03394925221800804,
-0.0011376033071428537,
0.016438769176602364,
0.00885683111846447,
-0.0327751561999321,
-0.049873095005750656,
0.014218522235751152,
-0.05237841233611107,
0.022252947092056274,
0.02469944767653942,
-0.02862701378762722,
0.0051134261302649975,
-0.0023579082917422056,
0.0008932326454669237,
-0.035573314875364304,
0.015075750648975372,
0.0034417579881846905,
-0.015064011327922344,
-0.04362286627292633,
0.001469477778300643,
0.01412091962993145,
0.014246664009988308,
0.02359956130385399,
-0.028488749638199806,
-0.036570820957422256,
-0.00031490856781601906,
0.02224588207900524,
-0.00036358332727104425,
-0.007463912479579449,
0.002472130348905921,
-0.008699127472937107,
-0.05902433395385742,
0.008079258725047112,
0.018870016559958458,
-0.023381320759654045,
-0.025588110089302063,
-0.04567500948905945,
0.025512849912047386,
0.04532637447118759,
0.024706825613975525,
0.03318050131201744,
-0.02668529935181141,
0.022784972563385963,
-0.01617121696472168,
-0.012577719986438751,
-0.028915148228406906,
0.026573341339826584,
-0.00310304737649858,
0.0037468571681529284,
0.013405002653598785,
0.010616287589073181,
-0.015291300602257252,
0.006345959845930338,
0.009766444563865662,
0.00854661874473095,
-0.007180730812251568,
-0.010543123818933964,
-0.02226654253900051,
0.03561647981405258,
0.0043470892123878,
0.026687409728765488,
0.05527251586318016,
0.03851772099733353,
0.007603672798722982,
0.03393521159887314,
-0.04249773919582367,
-0.04858918488025665,
0.016227349638938904,
-0.07933085411787033,
-0.0182789396494627,
-0.020157447084784508,
0.021315645426511765,
0.042176250368356705,
0.0069848280400037766,
0.005611006170511246,
0.03402097523212433,
-0.003832448972389102,
-0.018005767837166786,
0.05161415785551071,
0.003290151245892048,
0.028838740661740303,
0.02397208847105503,
0.029128270223736763,
0.03976765647530556,
-0.04213801026344299,
0.013490411452949047,
0.025376494973897934,
0.07707460969686508,
0.007383174262940884,
-0.01871475577354431,
0.06551694124937057,
0.022963816300034523,
-0.00015838295803405344,
0.014800025150179863,
0.05148564651608467,
-0.013382612727582455,
0.026128707453608513,
-0.022653691470623016,
-0.04789423942565918,
-0.009387386962771416,
0.026846397668123245,
-0.02422834187746048,
0.07862091809511185,
-0.01132527831941843,
0.03074292093515396,
0.014343710616230965,
0.008199283853173256,
-0.03158603608608246,
-0.012484892271459103,
-0.01955246552824974,
0.041787512600421906,
-0.006741552148014307,
-0.04485831409692764,
-0.05262094363570213,
-0.023272812366485596,
0.04546022042632103,
-0.0047933501191437244,
-0.03720959275960922,
0.019081832841038704,
-0.013672920875251293,
-0.02101319283246994,
-0.04358302801847458,
-0.009005225263535976,
-0.032768793404102325,
0.03596336394548416,
0.006589718163013458,
0.027568737044930458,
-0.017768720164895058,
-0.0020897977519780397,
-0.03444627299904823,
0.028106022626161575,
-0.0592292957007885,
-0.014544075354933739,
-0.014055470936000347,
0.05433180555701256,
0.0045064715668559074,
0.005227640271186829
] |
<p>Let's have the system of point-like non-interacting particles and it's own angular momentum
$$
\mathbf L_{1} = \mathbf L - [\mathbf R_{E} \times \mathbf P],
$$
where $\mathbf R_{E}$ - center of energy of the system, $\mathbf P $ - impulse of center of energy,</p>
<p>and it's operator,</p>
<p>$$
\hat {\mathbf L}_{1} = \hat {\mathbf L} - [\hat {\mathbf R}_{E} \times \hat {\mathbf P}] .
$$</p>
<p>What physical value is described by following operator? Does it connect with spin of the system? </p>
<p>In my opinion, it consist only orbital component of full spin of the system (i.e., summ of orbital angular momentum of the particles in the center of energy system), but does not contain spin as quantum value. </p>
<p>Can you help me?</p> | 1,460 | [
-0.030627045780420303,
-0.00505128363147378,
-0.025002673268318176,
-0.04703425243496895,
0.0624275803565979,
0.017320796847343445,
-0.023256562650203705,
-0.028419354930520058,
0.018080661073327065,
-0.0807267278432846,
0.025710107758641243,
0.05399612337350845,
0.05913810804486275,
0.03782793506979942,
-0.028869375586509705,
0.002955493051558733,
-0.0024538752622902393,
0.006715433206409216,
-0.006699938792735338,
-0.031776588410139084,
0.008884907700121403,
0.04161001741886139,
0.020411968231201172,
-0.00838672835379839,
-0.007167385891079903,
0.06622938066720963,
0.009010330773890018,
-0.01930154114961624,
0.028966698795557022,
0.03278133273124695,
-0.03705691173672676,
-0.0377819761633873,
-0.0005343634402379394,
-0.0254841186106205,
-0.0012282312382012606,
0.017384804785251617,
-0.04508892446756363,
-0.01686245948076248,
-0.0017249537631869316,
0.010006822645664215,
-0.037583861500024796,
-0.029291294515132904,
-0.014519267715513706,
0.0299677811563015,
0.0023621043656021357,
-0.017707252874970436,
-0.02438966929912567,
-0.008696157485246658,
0.056317780166864395,
-0.04120596498250961,
0.07162272930145264,
-0.005431287921965122,
-0.0009357368107885122,
-0.01801028661429882,
-0.023895110934972763,
0.018996141850948334,
0.07384809851646423,
0.10674716532230377,
-0.021881861612200737,
-0.05034160986542702,
-0.00805168692022562,
-0.02577066980302334,
0.02652057074010372,
-0.01727434992790222,
-0.02535879984498024,
0.005091887898743153,
0.034610651433467865,
-0.013395942747592926,
0.047174565494060516,
0.038713812828063965,
0.009214651770889759,
0.0031355072278529406,
0.030387457460165024,
-0.01581679657101631,
0.022607427090406418,
-0.020530184730887413,
0.038420479744672775,
-0.0023997912649065256,
0.034869901835918427,
-0.005274769850075245,
0.0016511611174792051,
0.0023270598612725735,
0.014374803751707077,
0.023050060495734215,
0.017155908048152924,
0.004396981559693813,
0.03172634541988373,
0.008854782208800316,
0.03507503494620323,
0.005875234957784414,
-0.026331953704357147,
0.017031023278832436,
0.03264309838414192,
-0.016177520155906677,
-0.045297157019376755,
0.036285996437072754,
0.011514900252223015,
0.05085616931319237,
-0.0018616041634231806,
-0.039440833032131195,
0.008894767612218857,
-0.03043196350336075,
-0.018881969153881073,
0.07015256583690643,
0.009462199173867702,
-0.025234710425138474,
-0.03499831259250641,
0.00503019941970706,
-0.017455849796533585,
-0.043152257800102234,
-0.033599574118852615,
0.02930942364037037,
-0.02298038639128208,
0.022539738565683365,
0.021484743803739548,
-0.048948027193546295,
-0.014807924628257751,
0.023231185972690582,
0.06811678409576416,
0.056434374302625656,
0.01797191984951496,
-0.009173459373414516,
-0.020672496408224106,
-0.05006890371441841,
-0.0501834936439991,
0.024103613570332527,
0.04529073089361191,
-0.020932894200086594,
-0.04521454870700836,
0.028244752436876297,
0.009932952001690865,
-0.021929126232862473,
0.021039672195911407,
-0.00672139972448349,
0.01775772124528885,
-0.043376315385103226,
-0.11644492298364639,
-0.024594565853476524,
0.010884585790336132,
-0.02663939632475376,
-0.021403750404715538,
-0.07026050984859467,
-0.005271422676742077,
0.025055723264813423,
0.09828308969736099,
0.02022787556052208,
0.0003518401354085654,
0.015654150396585464,
0.04906942695379257,
0.026538141071796417,
-0.0058167558163404465,
-0.04163774847984314,
0.01752747781574726,
-0.07220153510570526,
0.00974456686526537,
-0.04961109906435013,
0.0035011288709938526,
0.03595617040991783,
0.004729929845780134,
0.03638992831110954,
0.01883700303733349,
-0.02008078061044216,
0.023098157718777657,
0.06257854402065277,
-0.005899100098758936,
-0.044778820127248764,
0.08490975946187973,
0.031981028616428375,
0.021756533533334732,
0.07764025032520294,
0.008741284720599651,
0.02870362624526024,
0.011136738583445549,
0.05160699412226677,
0.05024044215679169,
-0.02832314744591713,
-0.025762571021914482,
-0.019202163442969322,
-0.0003527758817654103,
-0.03715516999363899,
-0.056411318480968475,
-0.019925495609641075,
-0.017021019011735916,
0.0025504473596811295,
0.02907034568488598,
0.05281379073858261,
-0.005351778585463762,
-0.0204642191529274,
0.01133781485259533,
-0.030551278963685036,
0.017003079876303673,
-0.04448404535651207,
-0.014533084817230701,
-0.000501504517160356,
-0.034590065479278564,
0.08259525895118713,
0.0149771673604846,
0.0019920479971915483,
-0.022289685904979706,
-0.015556471422314644,
-0.004184097982943058,
0.02709355391561985,
0.04472505673766136,
-0.006842855829745531,
0.014312408864498138,
0.06336916238069534,
0.022055109962821007,
0.013427287340164185,
-0.021533772349357605,
-0.01132608950138092,
-0.034728311002254486,
0.005665218457579613,
0.0010683713480830193,
0.0026496811769902706,
0.04171035811305046,
0.024171747267246246,
0.007516775280237198,
0.020946016535162926,
-0.0017253271071240306,
0.01587863638997078,
-0.03360951319336891,
0.06879433989524841,
0.05668536573648453,
0.009811523370444775,
0.03142813220620155,
0.030842559412121773,
0.023313326761126518,
0.052052970975637436,
0.00868360884487629,
-0.010680478066205978,
-0.004772852174937725,
0.005406200420111418,
0.04029555991292,
0.018147319555282593,
-0.04953431338071823,
-0.005088293459266424,
0.04186178743839264,
0.05957386642694473,
0.03715524449944496,
-0.002788142068311572,
-0.015115300193428993,
-0.017979580909013748,
0.010145788080990314,
-0.015767617151141167,
-0.019856614992022514,
-0.008640352636575699,
-0.013268883340060711,
-0.010428412817418575,
0.06451298296451569,
0.020946329459547997,
-0.007860918529331684,
0.03209730237722397,
-0.032949041575193405,
-0.003933674655854702,
-0.011237374506890774,
-0.017047520726919174,
0.03464813157916069,
-0.019440827891230583,
0.015420962125062943,
0.03675801679491997,
-0.03975217789411545,
-0.007109671365469694,
-0.03371094539761543,
-0.06488325446844101,
-0.02442421019077301,
0.00231451028957963,
-0.022008799016475677,
-0.044027913361787796,
0.020319078117609024,
0.0027274824678897858,
-0.006977114826440811,
0.010092317126691341,
-0.009820425882935524,
-0.023332158103585243,
0.017659446224570274,
0.04012975096702576,
0.020639246329665184,
-0.020554013550281525,
0.004590990021824837,
-0.030407043173909187,
-0.006736392620950937,
-0.02948427014052868,
-0.00022956248722039163,
0.023051880300045013,
-0.0932355672121048,
0.006524086929857731,
-0.05566001683473587,
0.010005722753703594,
0.016151709482073784,
-0.003962647635489702,
-0.003007846185937524,
0.002178714144974947,
-0.004246314521878958,
-0.07357550412416458,
-0.0032183127477765083,
-0.026646703481674194,
0.02993755042552948,
-0.04394042119383812,
-0.023430272936820984,
0.050993964076042175,
-0.025733012706041336,
-0.025651052594184875,
-0.004678274970501661,
-0.019018299877643585,
-0.04730768874287605,
0.013946369290351868,
-0.020921699702739716,
0.026239782571792603,
-0.02098652347922325,
0.03649032115936279,
0.010187635198235512,
0.019330047070980072,
-0.020175646990537643,
-0.09031499177217484,
-0.05726346746087074,
0.0025699594989418983,
0.02279968559741974,
0.008724155835807323,
-0.00030626810621470213,
-0.05452869459986687,
0.06353474408388138,
0.012742940336465836,
-0.049372393637895584,
-0.05065477639436722,
0.012146835215389729,
-0.012046035379171371,
-0.010407713241875172,
-0.0007108210120350122,
0.009287321008741856,
0.013357375748455524,
0.030466783791780472,
0.02494124509394169,
0.02595258131623268,
0.014215366914868355,
0.030981067568063736,
0.007802798878401518,
0.001496184733696282,
-0.021223198622465134,
-0.014277388341724873,
0.07187491655349731,
0.011080136522650719,
-0.020962167531251907,
0.048709701746702194,
0.012819124385714531,
0.02518446184694767,
0.03075355850160122,
-0.045176777988672256,
0.03562447056174278,
-0.0023097340017557144,
0.0103892982006073,
0.01362250279635191,
0.062272198498249054,
0.02276112698018551,
-0.007962367497384548,
-0.008405004628002644,
0.030094478279352188,
0.03488265722990036,
-0.012552313506603241,
-0.0030844202265143394,
0.06659595668315887,
-0.0006692638853564858,
-0.017390549182891846,
-0.002541207242757082,
0.021740194410085678,
0.00006883344030939043,
0.030868014320731163,
-0.028078902512788773,
-0.012387732975184917,
0.015096944756805897,
0.05030406638979912,
0.014719351194798946,
-0.022524913772940636,
-0.06830079108476639,
0.02324477955698967,
-0.055557265877723694,
0.033178992569446564,
-0.0071709295734763145,
0.06481921672821045,
0.008150617592036724,
0.05999692901968956,
0.027044054120779037,
-0.009720946662127972,
0.003855001414194703,
0.027767835184931755,
-0.03370894491672516,
0.009918466210365295,
-0.0045889802277088165,
-0.004713654983788729,
-0.030692171305418015,
0.02359399013221264,
-0.007983523420989513,
-0.015127889811992645,
-0.0019279217813163996,
-0.016177115961909294,
-0.05567791312932968,
-0.023644698783755302,
0.021585555747151375,
-0.03978021442890167,
-0.007984594441950321,
-0.029233520850539207,
0.04450876638293266,
-0.0018803247949108481,
-0.036304183304309845,
0.01405536849051714,
0.05762944743037224,
-0.030188940465450287,
0.041600245982408524,
-0.0051512825302779675,
0.0027328385040163994,
0.037926990538835526,
0.01949997805058956,
0.04378915950655937,
-0.009884530678391457,
-0.042144276201725006,
0.03065263107419014,
0.004727085120975971,
0.06338794529438019,
0.007543726358562708,
-0.03054826334118843,
-0.024895265698432922,
-0.04885312169790268,
0.004629780072718859,
-0.007449361030012369,
0.046184517443180084,
0.01044885627925396,
-0.00309919030405581,
0.06178708001971245,
-0.006531477440148592,
0.014949027448892593,
0.023114744573831558,
0.053845543414354324,
0.02008485235273838,
-0.04478362947702408,
-0.03552775830030441,
0.011578578501939774,
-0.0012923668837174773,
-0.030502906069159508,
0.03599710389971733,
0.006547874305397272,
-0.010971805080771446,
-0.005583606660366058,
-0.006800028495490551,
0.04888519272208214,
-0.02245647832751274,
0.006057030521333218,
0.0064153061248362064,
-0.0068680159747600555,
-0.026992132887244225,
-0.00973823294043541,
-0.015225337818264961,
0.04709944128990173,
0.03561164066195488,
-0.010948628187179565,
0.019122200086712837,
-0.0355105847120285,
-0.0032663345336914062,
0.02363838069140911,
0.025839539244771004,
-0.022877853363752365,
-0.015511216595768929,
-0.013456612825393677,
-0.00667943898588419,
0.029038863256573677,
-0.05478595942258835,
0.037835560739040375,
-0.026932328939437866,
-0.016629040241241455,
-0.0012170665431767702,
-0.027421046048402786,
-0.013821110129356384,
0.014014293439686298,
-0.030179589986801147,
0.04021424427628517,
-0.06103123724460602,
0.0025043454952538013,
-0.006534971762448549,
0.0011404437245801091,
-0.010617788881063461,
0.012254785746335983,
0.021266203373670578,
-0.03755854442715645,
0.004054213874042034,
0.05857916176319122,
0.009428134188055992,
-0.08008230477571487,
-0.011929846368730068,
0.002529977122321725,
-0.01958741806447506,
0.053057651966810226,
-0.061207208782434464,
-0.04803994670510292,
0.004125643987208605,
0.02039724960923195,
0.03612041473388672,
0.0025421902537345886,
-0.06444001942873001,
0.0676400363445282,
0.04004170000553131,
-0.032914724200963974,
0.05212162435054779,
0.03705621510744095,
-0.05110234022140503,
-0.015995368361473083,
-0.03593003749847412,
0.028526488691568375,
-0.022816961631178856,
0.040823593735694885,
-0.04294188693165779,
0.029758792370557785,
-0.0027339106891304255,
0.05242456495761871,
-0.027892697602510452,
0.01027905847877264,
-0.006924082525074482,
-0.016100332140922546,
-0.04571099951863289,
0.015253948047757149,
-0.01573934033513069,
-0.007332004606723785,
-0.023750662803649902,
0.030540460720658302,
0.033120233565568924,
0.013355208560824394,
-0.018979588523507118,
0.0004641372652258724,
0.03234434500336647,
0.04453485086560249,
0.00007470545824617147,
0.04203609377145767,
-0.04582858085632324,
-0.010974214412271976,
-0.005633494351059198,
-0.04292168468236923,
0.03105814754962921,
-0.010282919742166996,
-0.03275937959551811,
0.020081108435988426,
-0.03173721954226494,
-0.05204998329281807,
0.021152161061763763,
-0.01541707944124937,
0.02795037440955639,
-0.061398398131132126,
-0.01555713452398777,
-0.019285039976239204,
-0.0002664195781107992,
-0.040173254907131195,
-0.04331237077713013,
0.02369328774511814,
0.0016546896658837795,
0.0015243177767843008,
-0.03666947782039642,
-0.025423750281333923,
-0.0056799934245646,
0.0024340981617569923,
0.036539286375045776,
0.02201594039797783,
-0.04366512969136238,
-0.03633046895265579,
0.029927439987659454,
0.013642152771353722,
0.04797222465276718,
0.011957918293774128,
-0.011448315344750881,
0.007904578000307083,
0.009444726631045341,
0.015057720243930817,
0.005370901897549629,
0.03731921315193176,
-0.02455824799835682,
-0.053690072149038315,
-0.028931932523846626,
0.009012248367071152,
0.014436259865760803,
-0.008580845780670643,
-0.010835418477654457,
0.015888042747974396,
0.04644786939024925,
-0.013947519473731518,
-0.0009409204358235002,
0.0018022707663476467,
-0.012882848270237446,
-0.001303850207477808,
0.01857130229473114,
0.021802930161356926,
-0.022900743409991264,
-0.03396788612008095,
0.028108658269047737,
-0.018222423270344734,
-0.0008889205637387931,
0.007556323427706957,
0.025146612897515297,
0.02736860141158104,
0.03669631481170654,
0.03498506173491478,
-0.015261578373610973,
0.03589556738734245,
0.02112715132534504,
-0.02177102491259575,
0.0049020699225366116,
0.03710867837071419,
-0.023208513855934143,
0.009187269024550915,
-0.015281826257705688,
-0.0030272281728684902,
0.049704939126968384,
0.002210599835962057,
0.03325185552239418,
0.0267926137894392,
0.0011601066216826439,
-0.05726887658238411,
0.0019041196210309863,
0.013222393579781055,
0.020451022312045097,
-0.010045300237834454,
0.04972219467163086,
0.009950637817382812,
-0.015819279477000237,
0.06097954884171486,
0.05879179760813713,
-0.04650121182203293,
0.02844696305692196,
0.0443442240357399,
0.01200801320374012,
0.025951851159334183,
-0.00412092637270689,
-0.030429398640990257,
0.04913897067308426,
-0.018649457022547722,
0.02512451447546482,
0.0021819116082042456,
-0.02138255164027214,
0.015391749329864979,
0.010366768576204777,
0.058752067387104034,
-0.025541536509990692,
-0.009973754175007343,
-0.0413486622273922,
0.009154667146503925,
0.016003452241420746,
-0.045210253447294235,
-0.028916766867041588,
0.021599775180220604,
0.044485725462436676,
-0.0063077714294195175,
0.004876757971942425,
-0.02023150585591793,
-0.060968734323978424,
0.005809687077999115,
-0.012900814414024353,
-0.06154274195432663,
0.0040984200313687325,
-0.028205089271068573,
0.024748696014285088,
0.02442297525703907,
-0.006177674513310194,
-0.0005597415147349238,
-0.010271625593304634,
-0.009572205133736134,
-0.015017221681773663,
0.06778068840503693,
0.009762556292116642,
0.00965148862451315,
0.018217148259282112,
-0.01103117223829031,
0.10401260107755661,
0.006179723888635635,
0.006930280476808548,
-0.06871266663074493,
-0.013266723603010178,
-0.011293028481304646,
0.0266171395778656,
-0.027412761002779007,
0.017367910593748093,
0.007346685975790024,
-0.030929312109947205,
0.016374759376049042,
0.010746263898909092,
-0.0033193365670740604,
-0.03802492097020149,
0.029563212767243385,
-0.050608061254024506,
-0.056521039456129074,
-0.005540536250919104,
-0.02070813998579979,
0.02281668223440647,
-0.011405465193092823,
-0.04098720848560333,
-0.013698083348572254,
-0.015483511611819267,
0.06130953133106232,
-0.04239775612950325,
-0.06061309948563576,
0.03813019022345543,
-0.0009090962121263146,
-0.011452608741819859,
0.0033375718630850315,
-0.039054423570632935,
0.012654585763812065,
-0.008499179035425186,
0.04529409855604172,
0.04373076185584068,
-0.011044556275010109,
0.04174786061048508,
0.03472568094730377,
0.027150431647896767,
0.014724238775670528,
0.03698063641786575,
0.0021670253481715918,
-0.06557732820510864,
0.01780635677278042,
-0.023892788216471672,
0.040402088314294815,
-0.01398440357297659,
0.029316533356904984,
-0.017885006964206696,
0.0005096555687487125,
-0.0005425825947895646,
-0.049994830042123795,
-0.02607598900794983,
-0.005784943699836731,
0.04134566709399223,
0.0025769860949367285,
-0.011736782267689705,
-0.025078382343053818,
-0.014800717122852802,
-0.0040527512319386005,
0.03416392579674721,
-0.047278281301259995,
-0.020549124106764793,
0.056532904505729675,
0.01621614769101143,
0.03817753866314888,
-0.0045736487954854965,
0.005777538754045963,
-0.03840632364153862,
-0.025139518082141876,
-0.018487686291337013,
0.007784175220876932,
0.03155152127146721,
0.01946200430393219,
-0.002544647315517068,
-0.012255129404366016,
-0.008332439698278904,
-0.014839268289506435,
-0.06005816161632538,
0.028380749747157097,
-0.0382939949631691,
-0.05756979435682297,
0.004716602154076099,
0.0024158982560038567,
0.022351812571287155,
0.06147225201129913,
-0.05012907460331917,
-0.03193936124444008,
0.002455145353451371,
0.03205201402306557,
0.024303706362843513,
-0.0384492389857769,
-0.02127976343035698,
0.0063935332000255585,
-0.01826457306742668,
0.024843310937285423,
-0.02464444935321808,
-0.0011107116006314754,
0.028692791238427162,
-0.02057289518415928,
-0.007589798420667648,
0.00986938551068306,
-0.009742414578795433,
-0.05556032434105873,
0.048310358077287674,
0.008607261814177036,
0.008283001370728016,
0.010100114159286022,
0.021072551608085632,
-0.06478339433670044,
-0.014591644518077374,
-0.014643576927483082,
-0.026247141882777214,
-0.01120864599943161,
0.012696570716798306,
-0.04054692015051842,
-0.04104207456111908,
-0.02134123258292675,
-0.0006670187576673925,
-0.017558958381414413,
0.03430965915322304,
-0.06338389217853546,
0.043078817427158356,
0.009935107082128525,
-0.02036431059241295,
0.006613318808376789,
0.042446382343769073,
0.022819362580776215,
-0.029905913397669792,
0.024414395913481712,
0.039287399500608444,
-0.016288165003061295,
0.025288589298725128,
-0.0002624098560772836,
-0.020186470821499825,
0.05506258085370064,
-0.02409757487475872,
0.0008760694181546569,
0.03313731774687767,
-0.039415549486875534,
-0.05741719529032707,
0.04272889345884323,
-0.0008069915929809213,
0.03193814679980278,
0.022395821288228035,
0.011674986220896244,
-0.03400921821594238,
0.05303427204489708,
-0.011433126404881477,
-0.018152786418795586,
0.004386200103908777,
-0.026562441140413284,
-0.02140692062675953,
-0.022723358124494553,
0.010211652144789696,
0.001781123224645853,
-0.033036425709724426,
0.0029953422490507364,
0.019024459645152092,
-0.06105708330869675,
0.014587588608264923,
0.020642807707190514,
-0.010182739235460758,
0.009740099310874939,
0.01524046715348959,
-0.021634507924318314,
0.01709439605474472,
0.017108019441366196,
-0.026801863685250282,
0.036995455622673035,
0.018880901858210564,
0.014232880435883999,
-0.08640137314796448,
-0.016631105914711952,
0.005862170364707708,
-0.004070380236953497,
0.021869372576475143,
-0.006667655427008867,
0.03457977995276451,
0.0285887960344553,
-0.08277032524347305,
0.04635372385382652,
-0.015171760693192482,
-0.0005747427931055427,
-0.040817856788635254,
0.0035333207342773676,
-0.038770586252212524,
0.0287138931453228,
-0.0033935762476176023,
0.009174717590212822,
0.016005536541342735,
0.0072206477634608746,
-0.010900248773396015,
-0.016126379370689392,
-0.026883278042078018,
0.025174636393785477,
-0.0038403337821364403,
-0.02942718006670475,
0.0877583771944046,
-0.04733628034591675,
-0.033258918672800064,
0.019865648820996284,
-0.0009269688744097948,
-0.019138123840093613,
-0.013682692311704159,
0.0017818717751652002,
-0.02270158752799034,
0.07801426947116852,
-0.0010685182642191648,
-0.017019569873809814,
-0.004932025913149118,
-0.003421355038881302,
0.0352184996008873,
0.04103296995162964,
-0.02669513039290905,
0.0005240305908955634,
-0.011973259039223194,
-0.04417570307850838,
-0.007942111231386662,
0.009503456763923168,
0.004868184216320515,
-0.02169959433376789,
0.005030356347560883,
0.005915627349168062,
-0.0032022944651544094,
-0.0309173371642828,
0.023562416434288025,
-0.043400153517723083,
0.0029932716861367226,
0.00537600414827466,
-0.033651940524578094,
-0.009024866856634617,
0.023004623129963875,
-0.02197636291384697,
-0.044653624296188354,
0.008472214452922344,
0.035649389028549194,
-0.03857360780239105,
-0.06751435250043869,
0.019222652539610863,
0.035979267209768295,
-0.0001043624070007354,
-0.027720371261239052,
-0.04989702254533768,
-0.02451963722705841,
0.00664905970916152,
-0.013939044438302517,
0.036348987370729446,
0.01502632349729538,
0.0015778354136273265,
-0.02156616933643818,
-0.08753138780593872,
0.027392758056521416,
0.014206326566636562,
-0.019884569570422173,
-0.012033598497509956,
-0.012496773153543472,
-0.023676058277487755,
0.012395617552101612,
0.048200465738773346,
0.02376401610672474,
-0.042002059519290924,
0.013406306505203247,
-0.003744320012629032,
0.01414947584271431,
-0.030349308624863625,
0.014476419426500797,
-0.018574437126517296,
0.008550229482352734,
0.01507817767560482,
-0.015249972231686115,
-0.04269151762127876,
0.028753824532032013,
0.04540177434682846,
0.03039626032114029,
-0.006583148613572121,
-0.04682299867272377,
-0.06451740860939026,
0.05490195006132126,
-0.01283255498856306,
0.007805774454027414,
0.053243573755025864,
-0.0019156488124281168,
0.016441814601421356,
0.03004644066095352,
-0.04907110333442688,
-0.03580209240317345,
0.021952860057353973,
-0.015716319903731346,
-0.04107442498207092,
-0.009558692574501038,
0.007594128604978323,
0.042337607592344284,
-0.038881827145814896,
-0.004070547875016928,
0.044341832399368286,
-0.020538348704576492,
-0.028287995606660843,
0.035885173827409744,
0.0023635942488908768,
0.01195807196199894,
0.009782939217984676,
0.03736215829849243,
-0.0013086354592815042,
-0.03252878040075302,
-0.01142446044832468,
0.05312605947256088,
0.04657718911767006,
0.04172670468688011,
-0.004415823146700859,
0.016669703647494316,
0.002406564075499773,
0.03422676399350166,
0.02035674825310707,
0.01168705802410841,
-0.010243309661746025,
0.016317272558808327,
0.04959630221128464,
-0.015253948047757149,
0.03963500261306763,
0.017487840726971626,
-0.009504230692982674,
0.06842277944087982,
-0.003460627980530262,
0.019183170050382614,
-0.033755213022232056,
0.029371393844485283,
-0.023364126682281494,
0.0009887557243928313,
0.020424438640475273,
0.019129961729049683,
-0.03581495210528374,
-0.018769150599837303,
-0.026827652007341385,
-0.017837580293416977,
0.011975647881627083,
-0.0638454481959343,
0.01106880884617567,
0.012523607350885868,
-0.006706849671900272,
0.014913002029061317,
-0.04082901030778885,
-0.02806321531534195,
-0.019266212359070778,
0.0020956238731741905,
0.029193518683314323,
0.024017980322241783,
0.004110449925065041,
-0.011514993384480476,
-0.012055979110300541,
0.055173952132463455,
-0.04219099506735802,
-0.0008182585588656366,
0.012611623853445053,
0.04633153975009918,
-0.019226737320423126,
-0.0018654635641723871
] |
<p>I was watching a video on Youtube which deduce Einstein's relation $E=mc^2$ and the process of deduction used the relation between <a href="http://en.wikipedia.org/wiki/Mass_in_special_relativity" rel="nofollow">relativistic mass and rest mass</a>, which is</p>
<p>$$m= \frac{m_0}{\sqrt{1-\frac{v^2}{c^2}}}.$$ </p>
<p>So I look for a nice deduction of this relation. </p> | 20 | [
0.00475903507322073,
-0.05037228390574455,
-0.01154287438839674,
-0.010548187419772148,
0.0259309783577919,
0.016244277358055115,
-0.003083436517044902,
-0.03273738920688629,
-0.011308577843010426,
-0.02189052477478981,
0.021222110837697983,
0.040794674307107925,
0.06897088140249252,
-0.006953647825866938,
0.024455951526761055,
-0.0189204104244709,
0.020711813122034073,
-0.040778353810310364,
-0.008024584501981735,
-0.0751129537820816,
0.017562923952937126,
-0.006782008334994316,
0.03086627461016178,
0.006089680828154087,
-0.032431285828351974,
0.04837678372859955,
0.04032367840409279,
0.01260506734251976,
-0.0013119206996634603,
0.07214318960905075,
-0.024362966418266296,
-0.004575119353830814,
0.016305342316627502,
0.03196543827652931,
0.010614519938826561,
-0.00038949615554884076,
0.005721581634134054,
-0.010130725800991058,
0.023875270038843155,
0.04355812072753906,
-0.023711994290351868,
-0.015385582111775875,
0.0008475235081277788,
0.05153777077794075,
-0.0028728062752634287,
0.009387023746967316,
0.026132171973586082,
-0.0395648367702961,
0.06144629418849945,
-0.06648419797420502,
0.07980303466320038,
0.035961758345365524,
0.052658356726169586,
0.013016985729336739,
-0.008698548190295696,
0.00571791036054492,
0.06236029416322708,
0.06839251518249512,
-0.01523144356906414,
-0.03374795988202095,
-0.04002305865287781,
-0.02516959421336651,
-0.005159588530659676,
-0.01347354520112276,
0.00756561616435647,
0.048206787556409836,
-0.03805733844637871,
0.013004631735384464,
0.04277266934514046,
-0.01758095808327198,
0.01812429539859295,
0.011954168789088726,
0.03416145592927933,
-0.00801370944827795,
-0.007530421484261751,
-0.032375507056713104,
0.03718671202659607,
0.022237149998545647,
0.025063181295990944,
0.03799665719270706,
-0.026853952556848526,
0.004787303041666746,
0.029269758611917496,
0.059122033417224884,
-0.01734270714223385,
0.000536169100087136,
0.04929300397634506,
0.009676630608737469,
-0.0022035331930965185,
0.04526440426707268,
-0.034749533981084824,
-0.00004442562931217253,
0.020976843312382698,
-0.023246459662914276,
-0.048070866614580154,
0.04021144285798073,
0.0012718902435153723,
0.04069041460752487,
0.009914498776197433,
-0.015736855566501617,
-0.02784058451652527,
0.008108082227408886,
0.01777462288737297,
0.05779755860567093,
0.006430685520172119,
-0.02196146547794342,
-0.04356526583433151,
0.042468734085559845,
-0.01865248568356037,
-0.022088637575507164,
-0.009039811789989471,
0.008746463805437088,
0.008980289101600647,
-0.00468870485201478,
0.029425423592329025,
-0.027387864887714386,
0.010042956098914146,
-0.045431189239025116,
0.05354195460677147,
0.03207891806960106,
0.03843030706048012,
-0.009052172303199768,
0.03995838016271591,
-0.004317587707191706,
-0.07524514198303223,
0.017555326223373413,
0.01891053281724453,
-0.021285830065608025,
-0.012997321784496307,
0.04134966805577278,
-0.007604081649333239,
0.003412861144170165,
-0.012700214982032776,
-0.00688374787569046,
0.01592276804149151,
-0.008358757011592388,
-0.0951443761587143,
-0.07894077152013779,
0.04346085712313652,
-0.01090491097420454,
-0.0184467863291502,
-0.08411579579114914,
0.030030110850930214,
0.03248770162463188,
0.07733757048845291,
0.03729958087205887,
-0.019588463008403778,
-0.024729974567890167,
0.05119708180427551,
-0.001040671137161553,
0.008540719747543335,
-0.052521079778671265,
0.0031140903010964394,
-0.03314104303717613,
0.029819246381521225,
-0.07625965029001236,
-0.019722571596503258,
0.016934528946876526,
-0.009475397877395153,
-0.006717095151543617,
0.09529949724674225,
-0.028370684012770653,
-0.01378046628087759,
0.02966720052063465,
0.04057013988494873,
-0.02530689351260662,
0.06644950807094574,
0.026730023324489594,
-0.020244264975190163,
0.058103736490011215,
0.018802110105752945,
0.05582200735807419,
0.0327027253806591,
0.029009688645601273,
0.036688804626464844,
-0.03714669495820999,
-0.02258702740073204,
0.02203359641134739,
0.005491792690008879,
0.006731856148689985,
-0.02680329792201519,
-0.05650642141699791,
-0.012646540999412537,
0.015818247571587563,
0.0006251398008316755,
0.058862581849098206,
-0.036093998700380325,
0.046222489327192307,
0.02212539315223694,
-0.035965628921985626,
-0.017291611060500145,
-0.06694326549768448,
0.013209969736635685,
0.011622783727943897,
0.0010040851775556803,
0.006504493299871683,
-0.02257292903959751,
0.017996909096837044,
-0.02481953054666519,
-0.015367845073342323,
0.0003475999110378325,
0.03895959630608559,
0.013645382598042488,
-0.0007196508231572807,
0.03660359978675842,
0.017307065427303314,
0.033787596970796585,
-0.0117065804079175,
-0.0010236126836389303,
0.006465982645750046,
-0.017955821007490158,
0.003518653567880392,
-0.021156465634703636,
0.0017710457323119044,
-0.02462143264710903,
0.018236760050058365,
0.008203334175050259,
-0.02242971770465374,
0.0076823108829557896,
0.05046697333455086,
-0.00862414762377739,
0.06858854740858078,
0.02033396251499653,
0.014090672135353088,
-0.015312637202441692,
0.0462978258728981,
0.023150114342570305,
0.01432677824050188,
-0.001133082085289061,
-0.031140046194195747,
-0.020791437476873398,
-0.0158261489123106,
0.04329390078783035,
0.03625993803143501,
-0.058057643473148346,
0.028033895418047905,
0.041684478521347046,
0.028479265049099922,
0.01966106705367565,
0.005472015123814344,
-0.02534826099872589,
-0.039220910519361496,
0.002663176041096449,
0.018027745187282562,
0.002841200213879347,
0.01796501688659191,
-0.0006202963413670659,
0.027473747730255127,
0.002569114090874791,
0.0018358170054852962,
-0.004713498521596193,
0.005839725956320763,
-0.011326462961733341,
0.021403666585683823,
0.036165751516819,
-0.01868191547691822,
0.04185192659497261,
-0.038788050413131714,
0.027986813336610794,
0.03639863058924675,
-0.024328213185071945,
-0.0069459243677556515,
-0.0448128804564476,
-0.0200793594121933,
0.035095151513814926,
0.0020851853769272566,
-0.01786639355123043,
-0.007275898940861225,
0.010162931866943836,
-0.05643659830093384,
-0.01067894883453846,
-0.0024703084491193295,
-0.03386219963431358,
-0.05154187232255936,
0.0040149325504899025,
-0.0020123058930039406,
0.011438126675784588,
0.019965197890996933,
-0.018647249788045883,
-0.05165273696184158,
0.0002548512420617044,
-0.047962162643671036,
0.0052213529124855995,
0.0004351292736828327,
-0.025048304349184036,
0.04656682908535004,
-0.026355862617492676,
-0.03604202717542648,
0.03094463050365448,
0.018704358488321304,
0.017740700393915176,
0.030415290966629982,
0.0037389148492366076,
-0.0437772236764431,
-0.01461298018693924,
-0.01693609729409218,
0.0037553643342107534,
-0.025118255987763405,
0.006403946317732334,
0.04375535994768143,
-0.021219488233327866,
-0.060479141771793365,
-0.006100030150264502,
-0.02762414515018463,
-0.05967262014746666,
-0.04985834285616875,
-0.007026012986898422,
0.022999489679932594,
-0.06301957368850708,
0.04087434709072113,
0.01770874299108982,
-0.000012128857633797452,
0.006311229430139065,
-0.04209534823894501,
-0.04687534645199776,
0.050703298300504684,
0.02973678708076477,
0.045157454907894135,
0.02542971447110176,
-0.04842647910118103,
0.07457315921783447,
0.002699307631701231,
-0.036368031054735184,
-0.04344705864787102,
0.021950287744402885,
0.04222777858376503,
-0.007254460360854864,
-0.009718548506498337,
0.041692718863487244,
-0.03449748829007149,
0.02181803621351719,
0.039759013801813126,
0.024852747097611427,
-0.0007913218578323722,
0.006428959313780069,
-0.022160189226269722,
-0.0066565838642418385,
-0.03427621349692345,
-0.017946453765034676,
0.05051117390394211,
0.017494969069957733,
-0.002210393315181136,
0.0346207395195961,
0.03601356968283653,
0.06019306555390358,
0.008360689505934715,
-0.04419302940368652,
0.032478298991918564,
-0.008700481615960598,
-0.005874271038919687,
-0.015520834363996983,
0.014979090541601181,
-0.009070835076272488,
-0.0015863795997574925,
0.04582633450627327,
-0.005005305632948875,
0.0030987912323325872,
-0.04018908366560936,
-0.019439170137047768,
0.05680040642619133,
0.04529912769794464,
-0.01809043623507023,
-0.05029524490237236,
-0.0387386791408062,
-0.013961216434836388,
-0.005551210604608059,
-0.008096574805676937,
-0.023523835465312004,
0.06923895329236984,
0.014573135413229465,
0.03157885745167732,
-0.01430479995906353,
-0.02252218872308731,
0.00339580699801445,
-0.05770283192396164,
-0.019963881000876427,
0.019212160259485245,
0.027062149718403816,
-0.023476602509617805,
0.05634903535246849,
0.008926911279559135,
-0.01773095689713955,
0.001825676765292883,
0.012541303411126137,
-0.07577700167894363,
0.02048482373356819,
-0.06454045325517654,
-0.015488583594560623,
-0.02355765365064144,
0.015483977273106575,
-0.006128620821982622,
-0.03580400347709656,
-0.014007771387696266,
-0.025351008400321007,
-0.00331089086830616,
-0.04639425873756409,
0.008768592029809952,
-0.03829209879040718,
-0.0633954107761383,
-0.03250288590788841,
-0.015149425715208054,
0.04307902604341507,
-0.010609282180666924,
-0.013930696062743664,
0.04978793486952782,
-0.04179295524954796,
0.00041915816836990416,
-0.031192418187856674,
-0.015694234520196915,
0.02998233214020729,
0.008054141886532307,
0.03807568550109863,
-0.015787968412041664,
-0.012313349172472954,
0.014080435037612915,
-0.018277905881404877,
0.03976371884346008,
0.015656594187021255,
-0.008577161468565464,
-0.045219700783491135,
-0.00613899203017354,
-0.01939322240650654,
-0.010848644189536572,
0.045548081398010254,
-0.022978095337748528,
0.009699168615043163,
0.020445389673113823,
-0.005779182072728872,
-0.00047677915426902473,
0.059043947607278824,
0.07164283096790314,
0.0016782610910013318,
-0.022530447691679,
-0.05714654549956322,
-0.007091009058058262,
-0.019589096307754517,
-0.02071860246360302,
0.03452256694436073,
0.028181085363030434,
-0.01242339238524437,
-0.024618307128548622,
0.007321273908019066,
0.011254768818616867,
-0.03000626154243946,
-0.02512064389884472,
-0.007529245223850012,
0.032190948724746704,
0.0042663258500397205,
-0.012185607105493546,
-0.025761764496564865,
-0.002320419065654278,
0.030933015048503876,
-0.013968088664114475,
0.004296547267585993,
-0.09579375386238098,
-0.027588406577706337,
0.048218321055173874,
0.04249941185116768,
-0.028850091621279716,
0.012861907482147217,
-0.05146113410592079,
-0.005654747597873211,
0.05008861422538757,
-0.04355902597308159,
0.004146598279476166,
-0.0020854708272963762,
0.0033086875919252634,
0.00004997069845558144,
-0.023816272616386414,
-0.014486487954854965,
0.045629605650901794,
-0.00006525893695652485,
0.005795844364911318,
-0.01629890874028206,
0.019801439717411995,
-0.029498783871531487,
0.012347951531410217,
0.0698070377111435,
0.04236052185297012,
0.027906542643904686,
-0.026820866391062737,
-0.021548490971326828,
0.050155848264694214,
-0.03761936351656914,
-0.0875415951013565,
-0.04635067656636238,
-0.008680274710059166,
-0.031131060793995857,
0.006770326755940914,
-0.02106199972331524,
-0.025943608954548836,
0.015923429280519485,
0.004860221408307552,
-0.026627954095602036,
-0.015723999589681625,
-0.038745518773794174,
0.020311489701271057,
0.006350615993142128,
0.0033271790016442537,
0.018211010843515396,
0.02244630455970764,
0.00033969435025937855,
-0.027641864493489265,
0.0024042492732405663,
0.0377112440764904,
-0.024146245792508125,
-0.04867381229996681,
-0.0090029276907444,
-0.009882780723273754,
-0.06522752344608307,
0.013555956073105335,
-0.015757877379655838,
0.04038190469145775,
-0.015821529552340508,
-0.027797266840934753,
-0.011716220527887344,
0.02723289094865322,
0.015313936397433281,
0.023906340822577477,
0.0016522655496373773,
-0.011050613597035408,
0.013376560062170029,
-0.02914910390973091,
0.033247824758291245,
0.02348504215478897,
0.0007210816256701946,
0.01961580291390419,
-0.023098213598132133,
0.03333846852183342,
-0.003220943035557866,
-0.0248580239713192,
0.0062239705584943295,
-0.07268684357404709,
0.03577239811420441,
-0.03585387393832207,
-0.027233079075813293,
0.010388136841356754,
-0.0337953045964241,
-0.034905798733234406,
0.012496259063482285,
0.0027747852727770805,
0.021921804174780846,
-0.03811516985297203,
-0.021340977400541306,
-0.0055540320463478565,
0.015245982445776463,
-0.07970278710126877,
-0.055975038558244705,
0.004041449632495642,
0.00869180541485548,
-0.0058206962421536446,
-0.02399187721312046,
-0.005296045448631048,
-0.04465506598353386,
-0.018156172707676888,
0.004276305437088013,
0.09546215832233429,
-0.0192802045494318,
-0.009045186452567577,
-0.028265802189707756,
0.016272390261292458,
0.04733305796980858,
-0.028176438063383102,
-0.02212691865861416,
0.010852620005607605,
-0.004286390263587236,
-0.00792184378951788,
0.03786027431488037,
0.07967168092727661,
-0.023461109027266502,
-0.03337891399860382,
-0.021657103672623634,
0.003796834498643875,
0.009473960846662521,
-0.028768956661224365,
0.0027371880132704973,
0.04508724808692932,
0.027431027963757515,
0.009774931706488132,
-0.006770565174520016,
0.016384752467274666,
-0.0013815927086398005,
0.036666981875896454,
0.017260698601603508,
0.01105024665594101,
-0.004900627303868532,
-0.05238219350576401,
0.038264498114585876,
0.01759033091366291,
0.022520342841744423,
-0.026350751519203186,
0.047423847019672394,
-0.008059798739850521,
0.009868892841041088,
0.014665710739791393,
-0.00885564461350441,
0.007395863067358732,
0.013056297786533833,
0.001359481131657958,
0.011100835166871548,
0.011394423432648182,
-0.026401473209261894,
-0.012610125355422497,
-0.02503885328769684,
-0.009440942667424679,
0.08695179224014282,
0.0009240508661605418,
0.050769854336977005,
-0.005555927287787199,
0.0034266943112015724,
0.023199770599603653,
0.00011314135190332308,
-0.03481519594788551,
-0.01846144162118435,
-0.009669605642557144,
0.04546741768717766,
-0.027896974235773087,
-0.01735302060842514,
0.050784993916749954,
0.055316559970378876,
-0.01789032854139805,
-0.004170738160610199,
0.04236304759979248,
0.050594259053468704,
0.007215756922960281,
0.003975414205342531,
-0.034452687948942184,
0.049883365631103516,
-0.004234544467180967,
0.02350809797644615,
-0.01733984984457493,
0.02860832028090954,
0.038108061999082565,
-0.0011616386473178864,
0.03594104200601578,
-0.018277879804372787,
-0.03906458616256714,
-0.0604085773229599,
0.02703445963561535,
0.04520220682024956,
-0.012098945677280426,
-0.009470648132264614,
0.014964012429118156,
0.022302625700831413,
0.0060607027262449265,
0.03762442246079445,
-0.012411011382937431,
-0.07530263811349869,
-0.015511929988861084,
-0.03931017965078354,
-0.04595448821783066,
0.04149644449353218,
-0.025213319808244705,
-0.011074955575168133,
-0.004264237824827433,
-0.049246594309806824,
-0.004956546239554882,
0.04556458815932274,
0.022361917421221733,
-0.017010031268000603,
0.06934135407209396,
0.013067837804555893,
-0.009587470442056656,
0.02048102766275406,
0.007182947359979153,
0.10800963640213013,
0.030447058379650116,
0.010773773305118084,
-0.050136055797338486,
0.03621019423007965,
0.009219381026923656,
0.014747175388038158,
-0.060447633266448975,
0.03887716308236122,
-0.03399655595421791,
0.028773007914423943,
0.030924707651138306,
0.04405197501182556,
0.0016148333670571446,
0.016638170927762985,
0.06504055112600327,
0.005560894496738911,
-0.03936721384525299,
-0.002577338134869933,
0.035759370774030685,
-0.023117385804653168,
0.01496000587940216,
-0.0057832589372992516,
0.05258461460471153,
-0.05421122536063194,
0.001883725170046091,
-0.0481555201113224,
-0.02094409056007862,
0.02089731954038143,
0.017769699916243553,
-0.043713103979825974,
0.028365379199385643,
0.021518204361200333,
-0.009935186244547367,
-0.04431403800845146,
-0.008748479187488556,
0.02003566175699234,
0.03128191456198692,
0.005200025625526905,
0.010907236486673355,
-0.01410855446010828,
0.020985685288906097,
0.000293691671686247,
0.004932851996272802,
-0.06390461325645447,
-0.0021198694594204426,
-0.05574946850538254,
0.05629562959074974,
-0.00001357307792204665,
-0.0030243645887821913,
0.032304611057043076,
-0.023220695555210114,
-0.015685629099607468,
-0.03273676335811615,
0.007492172997444868,
0.0016818295698612928,
0.000669554341584444,
0.00010533404565649107,
0.0030560193117707968,
-0.024740753695368767,
0.06726564466953278,
-0.0198119655251503,
-0.003719365457072854,
-0.01911235600709915,
0.008480294607579708,
-0.02465297281742096,
-0.01225395780056715,
0.002913707634434104,
-0.029996076598763466,
-0.04767705872654915,
0.017427749931812286,
-0.023002898320555687,
-0.03272806480526924,
-0.01017268467694521,
0.003952086437493563,
0.026969484984874725,
0.03398639336228371,
-0.0017682705074548721,
0.0039415620267391205,
-0.023420577868819237,
-0.06361695379018784,
0.03577824681997299,
-0.022531893104314804,
-0.024277323856949806,
-0.02820795401930809,
-0.00364503962919116,
0.01850038953125477,
0.03487328812479973,
-0.05010635405778885,
0.007660223171114922,
0.018460607156157494,
0.0224261786788702,
-0.013045147992670536,
-0.04638310894370079,
0.006901101674884558,
0.024601884186267853,
-0.019199484959244728,
0.005943074356764555,
-0.028950732201337814,
0.01459154486656189,
0.026938896626234055,
0.0545746274292469,
0.0021292937453836203,
0.017973855137825012,
-0.014637460932135582,
0.027707966044545174,
-0.01223262120038271,
-0.03599138185381889,
0.021782876923680305,
0.0034988427069038153,
0.010007857345044613,
-0.011911251582205296,
-0.022102972492575645,
0.00763182295486331,
-0.008829002268612385,
-0.03866441175341606,
0.037888020277023315,
-0.016343513503670692,
0.038964804261922836,
-0.04430783540010452,
0.018470583483576775,
-0.051361631602048874,
0.018873827531933784,
-0.03803294152021408,
0.0441136471927166,
0.0009486410999670625,
-0.024892669171094894,
-0.01281062327325344,
0.009943190962076187,
0.004330738913267851,
-0.0034037232398986816,
0.0008780653006397188,
0.034034840762615204,
-0.027786271646618843,
-0.02917638048529625,
0.018578272312879562,
-0.010994724929332733,
0.03778963163495064,
-0.03453559800982475,
-0.02668452076613903,
0.015505009330809116,
-0.050002411007881165,
-0.03755616769194603,
0.006025133654475212,
-0.01625743880867958,
0.024694059044122696,
0.01275686826556921,
-0.029903847724199295,
0.011328339576721191,
0.08404938876628876,
-0.010602117516100407,
-0.00745744165033102,
-0.021612608805298805,
-0.04613373428583145,
0.006565554067492485,
0.012230856344103813,
0.019442735239863396,
-0.040649108588695526,
-0.014026463963091373,
0.049158815294504166,
0.05186190456151962,
-0.057640764862298965,
0.016322148963809013,
-0.006886085495352745,
-0.005199474282562733,
0.022976936772465706,
0.030521802604198456,
0.011930571869015694,
0.028676366433501244,
0.03716777265071869,
-0.0328994058072567,
0.02264750562608242,
-0.00011427847493905574,
0.010463496670126915,
-0.09093467891216278,
-0.009167454205453396,
-0.03146292269229889,
0.01080545037984848,
0.0572916604578495,
-0.018054891377687454,
0.03366544097661972,
0.025186169892549515,
-0.035455379635095596,
0.011120455339550972,
-0.049956779927015305,
-0.04047558084130287,
0.012697720900177956,
-0.037495192140340805,
-0.0018935110419988632,
0.05439443141222,
0.025410864502191544,
0.028980514034628868,
0.038557108491659164,
0.0058060591109097,
-0.01126435399055481,
-0.04504106193780899,
0.0038478064816445112,
0.0319477841258049,
0.003256339579820633,
-0.03885922208428383,
0.060171179473400116,
-0.007942164316773415,
-0.012969018891453743,
0.06650260090827942,
0.004297582898288965,
0.04190804064273834,
-0.0012407675385475159,
0.035855766385793686,
-0.01348144467920065,
0.02172914147377014,
-0.0004717647098004818,
0.011524406261742115,
-0.029172252863645554,
0.013769722543656826,
0.04114583134651184,
0.03356563299894333,
-0.02652738429605961,
-0.007581692188978195,
0.006356877740472555,
-0.04528753086924553,
-0.035261474549770355,
0.060149744153022766,
-0.03614610433578491,
-0.06189350038766861,
-0.005305700469762087,
0.0018053537933155894,
0.008294222876429558,
-0.026850905269384384,
0.031124861910939217,
-0.08344408869743347,
-0.008472278714179993,
0.03721396625041962,
-0.020901881158351898,
-0.01309280376881361,
0.029197098687291145,
0.024827681481838226,
-0.015022515319287777,
0.00015470849757548422,
0.028403446078300476,
-0.01390922348946333,
-0.0464455783367157,
-0.012079802341759205,
0.01600544899702072,
0.016833636909723282,
-0.018167966976761818,
-0.0722147524356842,
-0.018597319722175598,
0.06417608261108398,
0.04247515648603439,
0.010012605227530003,
-0.005019241478294134,
-0.005875848699361086,
-0.00872369296848774,
-0.06769583374261856,
0.011953962966799736,
0.01087093260139227,
0.009765824303030968,
-0.024329476058483124,
-0.011605528183281422,
0.02125076949596405,
-0.007476629689335823,
0.05661237612366676,
0.01808624155819416,
-0.005166651215404272,
-0.0009528386872261763,
-0.0032086267601698637,
-0.010677914135158062,
-0.04971464350819588,
0.0007675875094719231,
0.010651259683072567,
-0.019346997141838074,
0.002064908156171441,
0.0008695920114405453,
-0.00836283341050148,
-0.010026494041085243,
0.017223631963133812,
0.01973053067922592,
0.028218301013112068,
0.00596769480034709,
-0.0031523308716714382,
0.04727634787559509,
0.0011224847985431552,
-0.02075285278260708,
0.07506276667118073,
0.0039712805300951,
0.04423726722598076,
0.04583638906478882,
-0.020701294764876366,
-0.01567166857421398,
0.02841416373848915,
-0.03173789754509926,
-0.02085072360932827,
-0.025395164266228676,
-0.004363522864878178,
0.016533613204956055,
-0.04595010727643967,
0.024472588673233986,
0.04461230710148811,
-0.034839238971471786,
-0.01599843241274357,
0.043652113527059555,
0.017312269657850266,
0.028691450133919716,
0.009014097973704338,
-0.012352929450571537,
0.008603538386523724,
-0.016722705215215683,
0.019472917541861534,
0.02698623016476631,
0.03545115143060684,
-0.007391112856566906,
-0.016511326655745506,
0.0578632727265358,
-0.002642131643369794,
0.012011481449007988,
-0.03161051496863365,
0.010692461393773556,
-0.03025076910853386,
-0.02534804865717888,
-0.0133764473721385,
-0.04672171548008919,
0.014293613843619823,
-0.009525110013782978,
-0.009584428742527962,
0.07289573550224304,
-0.018655912950634956,
0.045638564974069595,
-0.02196989394724369,
-0.007638696581125259,
-0.0020888755097985268,
0.008702774532139301,
0.02815392054617405,
0.027728566899895668,
0.003214782802388072,
-0.006699978373944759,
-0.005064807366579771,
-0.04142582789063454,
0.018454022705554962,
-0.023153511807322502,
0.022409386932849884,
-0.006635046564042568,
-0.020008711144328117,
-0.01615070551633835,
-0.024384034797549248,
-0.0057563092559576035,
-0.010603360831737518,
0.0199495367705822,
0.04358658194541931,
0.03054119274020195,
-0.018820377066731453,
-0.016015879809856415,
-0.030938580632209778,
0.05622842162847519,
-0.06815575808286667,
-0.014471897855401039,
-0.020977238193154335,
-0.00637441361322999,
-0.026058919727802277,
-0.024687519297003746
] |
<p>Given a stream of random binary numbers(*)</p>
<p>Is there any way to differentiate if they came from a Truly Random or from a formula/algorithm ? how?</p>
<p>if there is no way to decide this, then, I can't find any basis, to keep denying that behind the "truly random" of quantum mechanics can be a hidden algorithm.</p>
<p>I know I am talking about the posibility of a "hidden variables" theory, but I can't find any other explanation.</p>
<p>(*) Is known that is possible to create <a href="http://www-2.dc.uba.ar/profesores/becher/turing.pdf" rel="nofollow">computable normal numbers</a> from which first is possible to extract an infinite random binary stream, second, it tell us that a finite logic expression (again a binary stream) can contain a rational, and even an irrational number, so there is no big difference within a bit stream and the measurement of a random outcome, (and even less if we consider the accuracy) I say this, because the argument that obtaining bits is not the same as answer the complex question that can be made to quantum experiments, I think that "random" results can be perfectly read from a random stream of bits</p> | 1,461 | [
0.002959944074973464,
-0.033441558480262756,
-0.022443929687142372,
-0.06845991313457489,
0.005065941717475653,
0.018999887630343437,
-0.02818523533642292,
-0.012249172665178776,
0.007027069106698036,
0.0010494141606613994,
0.05045576021075249,
0.03283325210213661,
0.014417333528399467,
0.06830688565969467,
0.010734318755567074,
0.006643469911068678,
-0.008746208623051643,
0.026005635038018227,
-0.037116896361112595,
0.002651826711371541,
0.028414780274033546,
0.06041991338133812,
0.021942388266324997,
-0.007193461526185274,
-0.019730478525161743,
0.006977004464715719,
0.01561197079718113,
-0.000638142169918865,
0.027103401720523834,
0.06774085015058517,
0.003875735914334655,
-0.0312567800283432,
0.0005942627904005349,
0.0423566997051239,
0.028429832309484482,
0.017776621505618095,
-0.0168580561876297,
0.011605394072830677,
0.025541136041283607,
-0.029730292037129402,
-0.02510443888604641,
-0.00696948217228055,
0.009845388121902943,
0.05765990912914276,
-0.013910794630646706,
-0.004244075156748295,
-0.0005187341012060642,
-0.01662941835820675,
0.021950477734208107,
-0.06212247908115387,
0.05149416625499725,
-0.017102191224694252,
0.03796776756644249,
0.025083787739276886,
0.0033423693384975195,
-0.002302399603649974,
0.055925726890563965,
0.07122638821601868,
-0.024192290380597115,
-0.04704643413424492,
0.01355016976594925,
0.008123374544084072,
0.006122338119894266,
0.004582306370139122,
-0.053140901029109955,
0.006200525444000959,
0.017235804349184036,
-0.015261896885931492,
0.027613859623670578,
-0.020229101181030273,
0.0036659438628703356,
0.02275499328970909,
0.04071274772286415,
0.00033765085390768945,
0.03739157319068909,
0.0004968451103195548,
0.02721734717488289,
0.006951508577913046,
-0.0034962338395416737,
0.049964629113674164,
-0.013564095832407475,
-0.012971294112503529,
0.017779536545276642,
0.0389079712331295,
0.02713031880557537,
-0.028916334733366966,
0.03093893826007843,
-0.04999450594186783,
0.020831966772675514,
0.07181262224912643,
0.0033958437852561474,
-0.012008200399577618,
0.015431195497512817,
-0.022533999755978584,
-0.05239104479551315,
0.032165318727493286,
0.000016981803128146566,
0.04037662595510483,
0.017016077414155006,
-0.033084359019994736,
0.026167217642068863,
-0.035485174506902695,
0.03075089119374752,
0.06926944851875305,
-0.03643880411982536,
-0.008249360136687756,
0.006715447176247835,
0.044430483132600784,
-0.009236017242074013,
-0.009042813442647457,
0.009999772533774376,
0.03994417563080788,
0.017831873148679733,
0.04632765054702759,
0.001167205162346363,
-0.03493960201740265,
0.004652852192521095,
-0.030491288751363754,
0.06791313737630844,
0.05737513303756714,
0.018857749179005623,
-0.04769148305058479,
-0.00820421427488327,
-0.041750188916921616,
0.006072556134313345,
0.03135485574603081,
0.02647174708545208,
0.010666877962648869,
-0.05044626072049141,
0.028341243043541908,
-0.020850664004683495,
-0.004989590961486101,
0.029495634138584137,
0.020484982058405876,
0.03194818273186684,
-0.014256542548537254,
-0.11722127348184586,
-0.052056748420000076,
0.03753424808382988,
0.01702420972287655,
-0.04860841482877731,
-0.07646200060844421,
0.031635113060474396,
0.05337491258978844,
0.03464943543076515,
-0.018700312823057175,
0.053269244730472565,
-0.023046765476465225,
-0.016973579302430153,
0.023219261318445206,
-0.010643579065799713,
-0.007913697510957718,
0.022718243300914764,
-0.025248616933822632,
-0.013992480002343655,
-0.020342161878943443,
0.021545210853219032,
0.024085810407996178,
-0.02283693104982376,
-0.03274796903133392,
0.003942095208913088,
-0.013448517769575119,
-0.03602219745516777,
-0.00714261457324028,
0.018743183463811874,
-0.05011602118611336,
0.08679121732711792,
0.01583450846374035,
0.013842909596860409,
0.05998426303267479,
-0.023103423416614532,
0.011868544854223728,
0.020367775112390518,
0.007686145603656769,
0.030200408771634102,
-0.049240607768297195,
-0.04707540199160576,
-0.012538116425275803,
0.026557542383670807,
-0.005807732231914997,
-0.017863914370536804,
0.01566987670958042,
-0.024167681112885475,
0.025503402575850487,
0.013886867091059685,
0.0073926132172346115,
0.00021427296451292932,
-0.0032108621671795845,
0.028193345293402672,
-0.041270628571510315,
-0.007848124019801617,
-0.05899001657962799,
0.016238613054156303,
0.006742527242749929,
0.00141045730561018,
0.024439936503767967,
0.01826881803572178,
0.029583385214209557,
-0.008367183618247509,
-0.011091060936450958,
-0.026126664131879807,
0.0275660902261734,
0.018565312027931213,
-0.02128714881837368,
-0.006722270045429468,
0.057340286672115326,
0.02880372852087021,
-0.022571539506316185,
0.024338340386748314,
0.01159620750695467,
-0.07115799188613892,
0.014789951965212822,
-0.05094534158706665,
0.02371499314904213,
0.005772106349468231,
-0.015110788866877556,
0.033181093633174896,
-0.015086891129612923,
-0.004208817146718502,
-0.0005666926153935492,
-0.04131149500608444,
0.0647256076335907,
0.020178591832518578,
0.02890101447701454,
-0.04724996164441109,
0.029285704717040062,
0.02886289916932583,
-0.041007936000823975,
0.005482768174260855,
-0.027879279106855392,
-0.03656953573226929,
0.006016732193529606,
0.011368963867425919,
0.05641564354300499,
-0.022358866408467293,
0.023183153942227364,
0.04109371080994606,
0.03608975559473038,
0.0314067117869854,
0.04333921894431114,
-0.04577223211526871,
-0.0067853303626179695,
0.0007148557924665511,
0.013581025414168835,
0.015208341181278229,
0.04653794690966606,
0.008874115534126759,
-0.01474529318511486,
-0.018636057153344154,
-0.013990486040711403,
-0.025833288207650185,
0.02126310020685196,
-0.021274380385875702,
0.013017022982239723,
-0.04113715514540672,
-0.0654204711318016,
0.006065569818019867,
-0.021133042871952057,
-0.008204222656786442,
-0.006090614013373852,
-0.005258382763713598,
-0.03293025866150856,
-0.023662103340029716,
-0.022625058889389038,
0.030953671783208847,
0.013120819814503193,
-0.048020754009485245,
-0.01196675281971693,
0.03675428032875061,
0.0009148764656856656,
0.018196532502770424,
-0.028816111385822296,
0.004329481162130833,
-0.06011374294757843,
0.02082192711532116,
-0.0021743278484791517,
-0.03461937606334686,
0.0005113730439916253,
-0.06081545352935791,
-0.03452296927571297,
0.015741398558020592,
-0.014853563159704208,
-0.0030855960212647915,
-0.023988621309399605,
-0.06857919692993164,
0.014203079044818878,
-0.023346899077296257,
-0.03102829121053219,
0.020852403715252876,
-0.04457603022456169,
0.04213877394795418,
-0.002000747248530388,
-0.027070673182606697,
-0.045503392815589905,
-0.0006582581554539502,
-0.060902953147888184,
0.014497460797429085,
-0.026993820443749428,
-0.010335116647183895,
0.03505996987223625,
0.012433347292244434,
-0.04620629921555519,
0.015386386774480343,
-0.019838565960526466,
-0.060609735548496246,
0.0041494471952319145,
-0.014121736399829388,
0.011910734698176384,
-0.03621906787157059,
0.04783431068062782,
0.004214574117213488,
-0.056547172367572784,
-0.025276580825448036,
-0.047756947576999664,
-0.0863802507519722,
0.028216831386089325,
-0.009675568901002407,
0.031423501670360565,
-0.00005384659016272053,
-0.018005050718784332,
0.06498028337955475,
0.024396568536758423,
-0.056527383625507355,
-0.00903751514852047,
0.012380439788103104,
0.038870006799697876,
-0.00606404198333621,
0.004013737663626671,
0.03058837354183197,
-0.0257074274122715,
0.04438437893986702,
0.0026636228431016207,
0.039967238903045654,
0.029767032712697983,
0.016267450526356697,
-0.028831355273723602,
0.030852099880576134,
0.006926847156137228,
-0.010699300095438957,
0.045000143349170685,
-0.014266814105212688,
-0.07638020813465118,
0.0006327339797280729,
0.0425177700817585,
0.013043591752648354,
0.016562260687351227,
-0.02127089351415634,
0.06206442415714264,
0.03414691239595413,
0.03828848898410797,
-0.040764644742012024,
0.022588973864912987,
-0.05164540559053421,
-0.033633455634117126,
0.007492344826459885,
0.020612165331840515,
0.013856492936611176,
0.00762871652841568,
0.042452119290828705,
0.03930190950632095,
0.05824771150946617,
-0.025369927287101746,
-0.026960087940096855,
-0.01161979977041483,
-0.03251263126730919,
0.039601605385541916,
-0.034859709441661835,
-0.0051273200660943985,
0.028800740838050842,
0.03742799907922745,
0.038566991686820984,
0.005974034313112497,
0.007245721761137247,
-0.04724531248211861,
-0.022209057584404945,
-0.011180892586708069,
-0.04174824059009552,
0.0689210519194603,
0.02997605688869953,
0.05516795068979263,
0.004372292663902044,
-0.001167104346677661,
-0.00600977148860693,
0.0009567361557856202,
-0.08739170432090759,
-0.016535362228751183,
-0.022901859134435654,
-0.025843197479844093,
-0.03975765034556389,
-0.05004477873444557,
-0.017088493332266808,
-0.02891554869711399,
-0.05635373294353485,
-0.027086788788437843,
0.013228918425738811,
-0.07690886408090591,
0.005071674007922411,
-0.007593315560370684,
-0.055550578981637955,
-0.009122288785874844,
0.02144862897694111,
0.023176606744527817,
-0.017755087465047836,
-0.007282820995897055,
-0.014250732958316803,
-0.04184548184275627,
-0.01202426664531231,
-0.016783390194177628,
0.019740309566259384,
-0.009883598424494267,
0.06346439570188522,
0.03783321753144264,
0.03310289606451988,
-0.000007906684913905337,
0.012241344898939133,
0.0063141342252492905,
0.06073800101876259,
0.00743073457852006,
0.003242203500121832,
-0.007573464885354042,
-0.037269141525030136,
0.03812047094106674,
0.018557850271463394,
0.016485420987010002,
-0.004842408467084169,
0.001151695498265326,
0.04741377755999565,
0.0019279859261587262,
-0.04291735962033272,
0.006064150482416153,
0.04690411686897278,
-0.028839409351348877,
0.008823536336421967,
0.0032133522909134626,
-0.006218771915882826,
-0.020820388570427895,
-0.02424515038728714,
0.017077356576919556,
0.02464950643479824,
0.03528885915875435,
0.0067138103768229485,
0.024455025792121887,
0.0061111762188375,
-0.029355807229876518,
-0.015453498810529709,
-0.023376842960715294,
0.008097357116639614,
0.010364068672060966,
0.013891592621803284,
0.03059600666165352,
0.037173401564359665,
0.0017153267981484532,
0.0341225303709507,
-0.013783136382699013,
-0.046237751841545105,
0.0054885526187717915,
0.052407845854759216,
0.03277727961540222,
-0.025676295161247253,
-0.008520245552062988,
-0.04692060127854347,
0.002165656303986907,
0.031940679997205734,
0.0199055727571249,
0.04749792069196701,
0.0008166495244950056,
0.012178580276668072,
-0.02211127243936062,
0.010769959539175034,
-0.018564460799098015,
-0.0059014782309532166,
0.03713619336485863,
0.038507577031850815,
-0.01952568255364895,
-0.014904269948601723,
-0.04748515412211418,
0.013406877405941486,
0.02062620222568512,
0.06406557559967041,
-0.011648058891296387,
0.005935259163379669,
-0.016333458945155144,
0.0037476737052202225,
-0.03661678731441498,
-0.06945512443780899,
0.03678165748715401,
0.00820750929415226,
-0.0010226505110040307,
0.03202599287033081,
-0.013039479963481426,
-0.08353292942047119,
0.013215488754212856,
-0.012039335444569588,
-0.01602901704609394,
0.045759476721286774,
-0.0437995009124279,
0.045968279242515564,
0.004020571243017912,
0.039892055094242096,
0.041708555072546005,
0.036041006445884705,
-0.0008758181938901544,
-0.033604614436626434,
-0.00589411286637187,
0.03131944686174393,
-0.038772571831941605,
-0.005335009191185236,
-0.04557056352496147,
0.007978199981153011,
-0.027770373970270157,
0.018354224041104317,
0.05806459113955498,
-0.00018871262727770954,
0.0036592637188732624,
-0.036007072776556015,
-0.05861841142177582,
0.024163728579878807,
-0.00041109920130111277,
0.026413310319185257,
-0.04961016774177551,
0.014429373666644096,
-0.027053017169237137,
-0.023398421704769135,
0.02035183645784855,
-0.0009231818257831037,
0.015925295650959015,
0.04307897016406059,
-0.0233093723654747,
0.049917686730623245,
-0.03326043486595154,
0.008588536642491817,
0.03125768154859543,
-0.014428466558456421,
0.03689673915505409,
0.018428290262818336,
0.011984911747276783,
0.024085411801934242,
-0.05064470320940018,
-0.01325094886124134,
0.009659393690526485,
-0.011013826355338097,
-0.011889505200088024,
-0.033095914870500565,
0.012801529839634895,
-0.006588717456907034,
-0.002756776288151741,
-0.08216431736946106,
-0.0478011853992939,
0.009219305589795113,
0.01948266662657261,
0.0006653663003817201,
-0.01863965578377247,
0.01506941206753254,
0.010371595621109009,
0.017038147896528244,
-0.006096528843045235,
0.03668125718832016,
-0.015644226223230362,
-0.012514942325651646,
0.013915476389229298,
0.006280696485191584,
0.06450442224740982,
-0.007417531684041023,
-0.017867490649223328,
-0.00023172967485152185,
-0.025978587567806244,
-0.010991448536515236,
0.037561241537332535,
0.013055677525699139,
-0.024052098393440247,
-0.03414544835686684,
-0.016607914119958878,
-0.0025869791861623526,
0.038759149610996246,
-0.02546641230583191,
-0.00016057959874160588,
-0.00020469274022616446,
0.00029179465491324663,
0.004461409989744425,
-0.0046104006469249725,
-0.01844266802072525,
0.020217984914779663,
0.0180682186037302,
0.0053303781896829605,
-0.03468836471438408,
-0.010329402051866055,
-0.009575693868100643,
0.023945821449160576,
-0.020639503374695778,
-0.039243731647729874,
0.014968021772801876,
0.0018884544260799885,
0.01297337468713522,
-0.026231836527585983,
-0.003976046573370695,
-0.0344926118850708,
0.022225720807909966,
-0.024355819448828697,
0.020637117326259613,
0.006390411406755447,
-0.006444294936954975,
-0.020260730758309364,
-0.0655306875705719,
-0.04441874474287033,
-0.008958622813224792,
0.03856080770492554,
0.01864885911345482,
0.04470841959118843,
0.03035598248243332,
-0.0009087256039492786,
-0.013363058678805828,
0.012383188121020794,
-0.0022219358943402767,
-0.0019976452458649874,
-0.002672856207937002,
0.01215988676995039,
-0.033658724278211594,
-0.0068119545467197895,
-0.02114139124751091,
0.011035390198230743,
-0.006598975043743849,
-0.00011544992594281211,
0.021109677851200104,
0.007446316536515951,
0.03126213327050209,
-0.016704518347978592,
-0.032448798418045044,
0.007628550287336111,
-0.055222999304533005,
0.014302029274404049,
0.03099227137863636,
-0.002539915032684803,
0.03281761333346367,
0.0043504498898983,
-0.022784417495131493,
-0.019298838451504707,
0.010259767062962055,
-0.05315370112657547,
0.015404569916427135,
0.0003022747114300728,
0.02325402945280075,
0.020213088020682335,
-0.016119398176670074,
-0.015429948456585407,
0.0009938779985532165,
0.013801736757159233,
-0.011145989410579205,
-0.06740599125623703,
-0.01050935871899128,
-0.059745606034994125,
-0.05823030695319176,
0.06505869328975677,
0.011266998015344143,
-0.037664495408535004,
0.0317717008292675,
-0.046025265008211136,
0.052590832114219666,
0.032532595098018646,
0.03918320685625076,
-0.05095214024186134,
0.03862786665558815,
-0.013097553513944149,
0.026384228840470314,
-0.013581154868006706,
-0.005230874288827181,
0.09429924935102463,
0.06422463804483414,
0.02007233537733555,
-0.08143767714500427,
0.014618964865803719,
-0.012928844429552555,
0.034982915967702866,
0.023850703611969948,
0.01821545884013176,
0.018583595752716064,
0.020938076078891754,
0.02119937352836132,
-0.012273112311959267,
-0.011652659624814987,
0.007610269356518984,
0.049141883850097656,
-0.06913800537586212,
-0.033888861536979675,
0.01530689001083374,
0.033718645572662354,
0.022715989500284195,
-0.0024001658894121647,
-0.05173049867153168,
0.006397556979209185,
-0.0026368056423962116,
-0.03676893562078476,
0.014281042851507664,
0.008063719607889652,
0.009069872088730335,
0.0015422236174345016,
-0.03671775013208389,
-0.010467772372066975,
0.06569714844226837,
-0.006944564636796713,
0.001326015335507691,
0.005673101171851158,
0.023456083610653877,
-0.016920166090130806,
0.011792737059295177,
0.03871363773941994,
0.0428592748939991,
-0.029504116624593735,
0.010976862162351608,
0.03281985595822334,
-0.05092756822705269,
-0.036299798637628555,
-0.021072300150990486,
0.03270436450839043,
-0.043866854161024094,
-0.0305843073874712,
-0.00010890526755247265,
-0.03346695378422737,
-0.007135861087590456,
-0.040047500282526016,
-0.007996141910552979,
0.019668448716402054,
0.006103580817580223,
-0.003830335568636656,
-0.043209146708250046,
0.007545031141489744,
0.046162355691194534,
-0.04713991656899452,
0.03577331081032753,
-0.0017220275476574898,
-0.013517634943127632,
-0.006148579064756632,
0.012671241536736488,
0.03879091888666153,
0.009222480468451977,
-0.02704334445297718,
-0.03144245222210884,
-0.03439848870038986,
-0.02545514702796936,
-0.04712282121181488,
0.001935720443725586,
-0.012181265279650688,
0.03121078386902809,
0.016661277040839195,
-0.0009060826851055026,
0.024755874648690224,
-0.0316958874464035,
0.044077832251787186,
-0.028128601610660553,
0.006324660032987595,
-0.01735500432550907,
0.009055598638951778,
0.018085354939103127,
0.035246942192316055,
0.02557905949652195,
-0.0012556536821648479,
0.03754657879471779,
0.009136215783655643,
0.0314163938164711,
-0.05257632955908775,
-0.0035948208533227444,
0.022183101624250412,
-0.025779247283935547,
0.004117359407246113,
0.0009246706031262875,
0.02880227565765381,
0.018084894865751266,
0.033949222415685654,
-0.025456316769123077,
0.04959478601813316,
-0.018338285386562347,
0.015251058153808117,
-0.03052881732583046,
-0.01748252846300602,
-0.021338965743780136,
0.005559111014008522,
0.03674789518117905,
-0.027326205745339394,
-0.03982434794306755,
-0.027650585398077965,
0.018885664641857147,
0.010211247950792313,
-0.028235891833901405,
-0.026747528463602066,
-0.0063740042969584465,
0.016863403841853142,
0.012211442925035954,
-0.011186621151864529,
-0.021168027073144913,
0.0028096993919461966,
-0.001994275487959385,
-0.01233153510838747,
0.012292977422475815,
-0.02291073463857174,
0.04020315781235695,
0.02371419034898281,
-0.04103851318359375,
0.06395313143730164,
0.019912611693143845,
-0.015618432313203812,
-0.026369472965598106,
0.02857317589223385,
-0.000994245638139546,
0.03787878155708313,
-0.04347220063209534,
-0.024446159601211548,
0.027618829160928726,
-0.04324347898364067,
-0.01630719192326069,
0.0344926193356514,
-0.025326449424028397,
-0.0035438924096524715,
0.025315120816230774,
-0.015705334022641182,
-0.0138630922883749,
0.056294962763786316,
-0.015864674001932144,
-0.00938781164586544,
0.009089385159313679,
0.018507709726691246,
-0.006929040886461735,
0.025875519961118698,
0.018348969519138336,
0.010182274505496025,
-0.02653595805168152,
0.027808507904410362,
0.024329185485839844,
0.035425931215286255,
0.0287175290286541,
0.031866490840911865,
0.006778587121516466,
0.013992820866405964,
0.028403541073203087,
-0.022684279829263687,
-0.01719989813864231,
0.025148043408989906,
-0.01839054748415947,
0.06009087339043617,
0.009498730301856995,
0.00009541962208459154,
-0.10073508322238922,
-0.016302581876516342,
-0.007490102667361498,
0.0050903065130114555,
0.029269656166434288,
-0.029764488339424133,
0.011386014521121979,
0.02050180360674858,
-0.06670858711004257,
-0.026127150282263756,
-0.022092781960964203,
0.007581300102174282,
-0.014112883247435093,
0.047282248735427856,
-0.0695454329252243,
0.036447905004024506,
0.03177456185221672,
0.04224305599927902,
0.07392469793558121,
0.010103590786457062,
-0.01276315376162529,
-0.0061180139891803265,
-0.028647994622588158,
0.00356732914224267,
0.0009675506735220551,
0.0072477576322853565,
0.03958282619714737,
-0.04479985684156418,
-0.025371026247739792,
0.0034306696616113186,
0.013604584150016308,
0.05488178879022598,
-0.03033689223229885,
0.021385684609413147,
0.047132525593042374,
0.019817939028143883,
0.00399826979264617,
-0.004359465092420578,
-0.010894992388784885,
-0.025741377845406532,
0.029099496081471443,
0.042671263217926025,
-0.002327599097043276,
-0.03418087959289551,
0.011821876280009747,
-0.026545733213424683,
-0.05413792282342911,
0.024189386516809464,
-0.004278755281120539,
-0.01115388423204422,
-0.02136976830661297,
0.011646455153822899,
-0.0009334036149084568,
-0.016196532174944878,
0.035700373351573944,
-0.06338441371917725,
-0.004297974519431591,
0.020770056173205376,
0.04313094913959503,
-0.022719940170645714,
-0.004488218575716019,
-0.007049914449453354,
-0.04145371541380882,
0.034096308052539825,
0.03240111842751503,
-0.00254276511259377,
-0.05116662010550499,
-0.04404177889227867,
0.0263643991202116,
0.018025007098913193,
0.0361286886036396,
-0.045246951282024384,
-0.021702732890844345,
0.02271728590130806,
-0.01572365313768387,
0.031012635678052902,
-0.03219974786043167,
-0.010005724616348743,
-0.03699703887104988,
-0.07908947765827179,
0.06544066965579987,
0.005723954178392887,
0.034630291163921356,
-0.08006295561790466,
-0.009541581384837627,
-0.018364274874329567,
0.04045862704515457,
0.03997744247317314,
-0.014041091315448284,
-0.026320913806557655,
0.012769751250743866,
0.008048094809055328,
0.04667763411998749,
-0.002469612518325448,
-0.0097800362855196,
-0.05090786889195442,
-0.013730575330555439,
-0.019489990547299385,
-0.05812912434339523,
-0.008083303458988667,
0.04293615370988846,
0.029331091791391373,
-0.011380360461771488,
-0.03189733624458313,
0.002019168110564351,
-0.0522746779024601,
0.07068824023008347,
0.0015872882213443518,
0.011682024225592613,
0.027869267389178276,
-0.038904059678316116,
0.040544092655181885,
0.013613885268568993,
0.010686870664358139,
-0.050156787037849426,
0.05341571196913719,
0.00516214594244957,
-0.027293603867292404,
-0.0017919682431966066,
0.022607946768403053,
0.005256363190710545,
-0.024471662938594818,
-0.026039788499474525,
0.03925866261124611,
-0.03123348206281662,
0.005867652129381895,
0.08354553580284119,
-0.03265484422445297,
0.01618625968694687,
0.00821184366941452,
0.04750226065516472,
0.012591835111379623,
-0.014817645773291588,
0.008880393579602242,
0.035681236535310745,
0.04257625341415405,
-0.03136548399925232,
0.029552092775702477,
0.0646272823214531,
-0.010658340528607368,
0.07000124454498291,
0.01448757667094469,
0.05511055141687393,
-0.05109402537345886,
-0.004598359111696482,
0.012096799910068512,
-0.01023937575519085,
-0.007775064557790756,
0.02865939773619175,
-0.01139447744935751,
0.09521998465061188,
0.005970867350697517,
0.005099704023450613,
-0.057528212666511536,
-0.0013780159642919898,
0.0007539212238043547,
-0.01263117603957653,
0.003327603917568922,
0.021186361089348793,
-0.012667075730860233,
0.003970204386860132,
-0.03243393823504448,
0.03422459587454796,
0.04252627119421959,
-0.03673337399959564,
-0.02914637327194214,
-0.003912292420864105,
-0.014752194285392761,
-0.009096702560782433,
-0.03704353794455528,
-0.027428798377513885,
-0.00933490227907896,
0.0444231815636158,
0.032889168709516525,
0.032428089529275894,
0.0017819938948377967,
-0.022695451974868774,
-0.03352382406592369,
0.06253502517938614,
-0.05655767023563385,
0.02618049457669258,
-0.02267685905098915,
0.05635347217321396,
0.007482722867280245,
-0.04129409417510033
] |
<p>I recently bought some <a href="http://www.getbuckyballs.com/" rel="nofollow">buckyballs</a>, considered to be the world's best selling desk toy. Essentially, they are little, spherical magnets that can form interesting shapes when a bunch of them are used together.</p>
<p>After playing around with these buckyballs for a while, I wondered: "Can these guys ever lose their magnetism?" Then I went a step further and thought, "How are magnets affected by the 2nd law of thermodynamics?"</p>
<p>So, how are magnets affected by the 2nd law of thermodynamics? Do they break down and lose their magnetism over time (like iron rusts over time)?</p> | 1,462 | [
-0.057083215564489365,
-0.019944041967391968,
0.022230660542845726,
-0.037459660321474075,
0.027397368103265762,
0.024964574724435806,
-0.06778077781200409,
0.004791289567947388,
-0.008535481058061123,
-0.017818231135606766,
0.0020924247801303864,
0.0475873239338398,
0.020779384300112724,
0.02416778728365898,
0.010296599939465523,
-0.015040536411106586,
0.00786737259477377,
-0.03274033963680267,
0.007949281483888626,
-0.013312432914972305,
0.0244972575455904,
-0.024295689538121223,
0.012226512655615807,
0.02680184878408909,
-0.033647265285253525,
0.0053081875666975975,
0.03596733883023262,
-0.008595221675932407,
0.02120133675634861,
0.04438279569149017,
0.009680118411779404,
-0.02211802266538143,
0.014011798426508904,
0.017095811665058136,
0.03875529393553734,
-0.03476826101541519,
-0.030139708891510963,
-0.0691961795091629,
-0.010240103118121624,
0.035213809460401535,
-0.04725579172372818,
-0.03460574522614479,
-0.023871280252933502,
0.06669868528842926,
-0.041084785014390945,
-0.016110502183437347,
-0.03471871465444565,
-0.022539805620908737,
0.06581810116767883,
-0.038369070738554,
0.08643189817667007,
-0.008433951064944267,
0.03584068641066551,
-0.0035176065284758806,
-0.02134285680949688,
-0.03502558916807175,
0.05595788732171059,
0.05121169984340668,
0.003571843495592475,
-0.04926319047808647,
-0.03162859007716179,
0.0030464371666312218,
-0.021243836730718613,
-0.040069613605737686,
-0.005977682303637266,
0.09131346642971039,
-0.02782134711742401,
-0.04576009139418602,
0.05287877470254898,
0.0014647712232545018,
0.023454057052731514,
-0.0003714285558089614,
0.06106821075081825,
-0.014920554123818874,
-0.007916602306067944,
-0.018642133101820946,
0.03373970091342926,
-0.0008089873590506613,
0.04538637027144432,
0.08070384711027145,
-0.06252501904964447,
0.00881939847022295,
0.04045668989419937,
0.026150628924369812,
0.001590211526490748,
-0.02543669566512108,
0.07677467912435532,
-0.020822620019316673,
0.06989829242229462,
0.02589951828122139,
0.03853487968444824,
0.007610363885760307,
0.044260673224925995,
-0.004923112224787474,
-0.05076279118657112,
0.015287909656763077,
-0.014905114658176899,
0.04445888102054596,
-0.00498978840187192,
-0.038455892354249954,
0.03127975016832352,
0.012002512812614441,
0.02316368743777275,
0.06108635663986206,
0.0017211305676028132,
-0.051812395453453064,
-0.018762266263365746,
0.0017564299050718546,
-0.024601636454463005,
-0.024894826114177704,
-0.019611718133091927,
0.009191127493977547,
-0.0028174077160656452,
-0.05859307944774628,
0.043994661420583725,
-0.014694261364638805,
-0.030079402029514313,
-0.03521682694554329,
0.013167952187359333,
0.0535910502076149,
0.023476075381040573,
-0.01239749789237976,
0.0013186358846724033,
-0.027610408142209053,
-0.05352094769477844,
-0.0032339070457965136,
0.03343772888183594,
-0.0194132998585701,
-0.026138747110962868,
0.01295413263142109,
-0.008021191693842411,
-0.007907704450190067,
0.000397339987102896,
-0.019567856565117836,
0.011334485374391079,
0.008281980641186237,
-0.08555807173252106,
-0.025156797841191292,
0.05545474961400032,
-0.00950543861836195,
0.004429199732840061,
-0.05989500880241394,
-0.0046072001568973064,
0.03376369550824165,
0.05956239253282547,
0.0071263788267970085,
-0.029990006238222122,
-0.03195808082818985,
0.06840554624795914,
0.02827407605946064,
-0.02160703018307686,
-0.009157082065939903,
0.0023468611761927605,
-0.031710781157016754,
-0.0029217852279543877,
-0.0759836807847023,
0.04053409397602081,
0.048139773309230804,
0.0043270946480333805,
-0.05426197871565819,
0.042520567774772644,
-0.03127375617623329,
-0.004115513991564512,
-0.017944185063242912,
-0.020853472873568535,
-0.05662981793284416,
0.07852768898010254,
-0.005421006120741367,
0.04041630029678345,
0.008825365453958511,
0.008761382661759853,
0.00892021507024765,
0.03454601392149925,
0.059370871633291245,
0.05901195853948593,
-0.008287234231829643,
-0.018946003168821335,
-0.016034476459026337,
0.0016474266303703189,
0.030380502343177795,
-0.09262596815824509,
-0.03338264673948288,
-0.01871507614850998,
0.02007528580725193,
-0.020430272445082664,
0.04568237066268921,
0.0032913479954004288,
-0.024197693914175034,
-0.009360729716718197,
-0.04224376007914543,
-0.024727238342165947,
-0.12275958061218262,
0.04836970195174217,
-0.02676202915608883,
-0.010556641966104507,
0.036125604063272476,
0.0347653329372406,
0.010419857688248158,
-0.05273380130529404,
-0.0683421865105629,
-0.0006705209380015731,
0.024334430694580078,
0.01517643965780735,
-0.03220907226204872,
0.0000859982828842476,
0.03604656457901001,
0.031112903729081154,
0.02480320818722248,
0.05279826745390892,
-0.06370532512664795,
-0.05332280322909355,
0.005671171937137842,
-0.0008904322166927159,
-0.006590060889720917,
0.02247808314859867,
-0.013499369844794273,
0.042208801954984665,
-0.01981968991458416,
-0.027518337592482567,
-0.011142892763018608,
0.011431618593633175,
0.04781803488731384,
0.01880413480103016,
-0.012942874804139137,
0.004685429390519857,
0.035569608211517334,
-0.007649123668670654,
0.0021002423018217087,
-0.024917960166931152,
-0.012701403349637985,
-0.0328129418194294,
0.029897088184952736,
0.019355062395334244,
0.06540735810995102,
-0.013033833354711533,
0.030058257281780243,
-0.015372409485280514,
0.04676418751478195,
-0.012123112566769123,
-0.024565596133470535,
-0.011802871711552143,
-0.010142777115106583,
0.0027670548297464848,
-0.010829325765371323,
0.04518662765622139,
0.02897382527589798,
0.03625275939702988,
0.02764645777642727,
-0.008902362547814846,
0.04301459714770317,
-0.020345579832792282,
0.04277419671416283,
0.03370685130357742,
0.006551727186888456,
0.012384301982820034,
-0.05566016212105751,
0.04495371878147125,
0.0030910340137779713,
-0.011968194507062435,
-0.003134375438094139,
0.013991634361445904,
-0.011078989133238792,
-0.029305094853043556,
-0.015804564580321312,
-0.024463411420583725,
0.0033099083229899406,
-0.011180784553289413,
-0.017419343814253807,
0.023773502558469772,
0.008554281666874886,
-0.040349654853343964,
0.02062881924211979,
-0.005633259657770395,
0.011945904232561588,
0.035016994923353195,
-0.007213122211396694,
0.007109494414180517,
0.01318671926856041,
-0.019229574128985405,
-0.028689449653029442,
-0.0145812863484025,
-0.04621944949030876,
0.02324805036187172,
0.019417768344283104,
-0.04349428787827492,
0.033671315759420395,
-0.0017765936208888888,
-0.016448741778731346,
0.008352559059858322,
0.013769210316240788,
0.018146859481930733,
-0.0008526348974555731,
-0.011302166618406773,
-0.07482099533081055,
0.0017985894810408354,
0.010130727663636208,
-0.004546417389065027,
-0.022187378257513046,
0.020555229857563972,
0.049707069993019104,
-0.01811058633029461,
-0.005288218148052692,
0.002131430897861719,
-0.0451454296708107,
-0.05102043226361275,
-0.017852062359452248,
-0.013018066063523293,
0.02180846408009529,
0.009910940192639828,
-0.014528273604810238,
0.054670412093400955,
-0.05147897079586983,
-0.013126643374562263,
-0.06924160569906235,
-0.04117906466126442,
-0.00478034233674407,
-0.02510174922645092,
-0.009156682528555393,
-0.020470671355724335,
-0.014001483097672462,
0.050168849527835846,
0.033503927290439606,
-0.022669654339551926,
0.010288411751389503,
-0.02423086389899254,
0.015949834138154984,
-0.06404424458742142,
-0.004112502560019493,
0.014836528338491917,
-0.01277211681008339,
-0.015404336154460907,
0.023351483047008514,
0.03286707028746605,
-0.009315603412687778,
-0.005786741152405739,
-0.02713581919670105,
0.01658644713461399,
0.021600918844342232,
-0.011011219583451748,
0.0002745405654422939,
0.004133161623030901,
0.0023853988386690617,
0.04449421539902687,
0.010270202532410622,
0.10133711248636246,
0.028616072610020638,
-0.041445326060056686,
0.0439763143658638,
-0.03160552680492401,
0.01298990286886692,
-0.028218034654855728,
0.0756661668419838,
-0.04538924619555473,
-0.014401369728147984,
0.008485422469675541,
0.0004862036439590156,
0.07051841169595718,
0.01912757195532322,
0.026096003130078316,
0.017631134018301964,
0.03250966593623161,
0.0022976109758019447,
0.0075270081870257854,
-0.032141972333192825,
0.002840269124135375,
-0.0055662645027041435,
0.004715698771178722,
0.018303846940398216,
-0.00687495619058609,
0.018207067623734474,
0.029332218691706657,
0.009005417115986347,
-0.003934483043849468,
-0.0006438085110858083,
-0.0733209028840065,
-0.01493689976632595,
0.012019619345664978,
0.02587859146296978,
-0.0003070583625230938,
0.023928094655275345,
-0.009995087049901485,
0.008331005461513996,
0.0019526333780959249,
-0.04304749518632889,
-0.09056992083787918,
0.05556190386414528,
-0.024518361315131187,
0.0005690166144631803,
0.029810788109898567,
0.017105231061577797,
0.04068129137158394,
-0.015256877057254314,
0.015978435054421425,
-0.02865593507885933,
-0.006466040853410959,
-0.03938528150320053,
-0.013299012556672096,
-0.031173771247267723,
-0.052815183997154236,
-0.014712049625813961,
0.02291441150009632,
0.03783585503697395,
-0.04315014183521271,
0.006969326641410589,
-0.015999311581254005,
-0.029497087001800537,
0.026753373444080353,
-0.03619637340307236,
0.022595277056097984,
0.020625092089176178,
0.019306078553199768,
0.017469750717282295,
0.00706920400261879,
0.005997972562909126,
-0.008486941456794739,
0.007436839397996664,
0.020854242146015167,
0.00994165986776352,
0.011951756663620472,
-0.024436425417661667,
-0.09332474321126938,
-0.01407949160784483,
-0.01771792396903038,
0.05984411761164665,
-0.01536432933062315,
0.04575604945421219,
0.004283031914383173,
-0.0040485369972884655,
-0.026881173253059387,
0.0029058638028800488,
0.036253273487091064,
0.011271537281572819,
-0.0379878468811512,
-0.0037527314852923155,
-0.031402043998241425,
-0.037031352519989014,
0.012780754826962948,
0.006929665803909302,
-0.04362151026725769,
-0.059693243354558945,
0.015457660891115665,
0.006486806087195873,
0.04326041787862778,
-0.032547056674957275,
-0.013655129820108414,
-0.006128284614533186,
0.03347362205386162,
-0.0067488569766283035,
0.026261601597070694,
0.04411059617996216,
0.02068259008228779,
0.029330674558877945,
0.000497766537591815,
-0.015734758228063583,
-0.06556291878223419,
0.03820737078785896,
0.016284672543406487,
0.025737039744853973,
0.015085983090102673,
0.01040622778236866,
-0.03190658241510391,
-0.019387120380997658,
0.07932605594396591,
-0.042705122381448746,
0.028234878554940224,
0.020111529156565666,
-0.010615956038236618,
-0.03525126725435257,
-0.032200220972299576,
-0.001517519704066217,
0.02253759652376175,
-0.010585998184978962,
0.027952268719673157,
-0.008752542547881603,
-0.005567136686295271,
-0.0013385085621848702,
0.030663231387734413,
0.05105319991707802,
0.025327377021312714,
-0.014704898931086063,
0.04677779972553253,
0.0027242444921284914,
0.008908012881875038,
-0.024380406364798546,
-0.07211919128894806,
0.01840793341398239,
-0.00048804725520312786,
-0.012701806612312794,
0.05849936604499817,
-0.003921594936400652,
-0.0481981560587883,
0.015591631643474102,
-0.009752744808793068,
0.015603836625814438,
-0.022269802168011665,
-0.020102232694625854,
0.02984422817826271,
0.01586228609085083,
0.0030865995213389397,
0.02288052625954151,
0.031050674617290497,
-0.001178635866381228,
-0.0041219377890229225,
-0.002466774545609951,
0.04973756894469261,
0.0217269379645586,
0.034124597907066345,
-0.04538867250084877,
-0.007815072312951088,
-0.021117452532052994,
0.06765014678239822,
-0.017287779599428177,
-0.0045466641895473,
-0.005188147537410259,
-0.003995461855083704,
0.011431246064603329,
0.00444364408031106,
0.03818168863654137,
-0.03721703961491585,
-0.0011250977404415607,
0.041583351790905,
-0.032594744116067886,
-0.00398047361522913,
0.006285622715950012,
-0.03308871015906334,
-0.0013033102732151747,
0.011765131726861,
-0.031868599355220795,
0.025161735713481903,
-0.04800078272819519,
-0.008500021882355213,
-0.027168748900294304,
-0.02429358661174774,
0.024968907237052917,
-0.027918243780732155,
-0.02946588397026062,
0.03649646043777466,
-0.02612258866429329,
-0.016300855204463005,
0.0018451728392392397,
-0.017527977004647255,
0.0015040572034195065,
-0.0190278310328722,
0.034479398280382156,
0.03160131350159645,
0.013250630348920822,
-0.03667588531970978,
-0.05480232834815979,
0.006054112687706947,
0.009655210189521313,
-0.020209239795804024,
0.005009545013308525,
0.039164550602436066,
-0.024601148441433907,
-0.03313617408275604,
0.013314612209796906,
0.04958586394786835,
-0.017437638714909554,
0.008336570113897324,
0.04828079789876938,
-0.014838124625384808,
0.07625329494476318,
0.016616150736808777,
-0.057982318103313446,
0.024058884009718895,
-0.01325914729386568,
-0.03383777663111687,
-0.023288501426577568,
0.025312596932053566,
-0.02935580164194107,
-0.014131237752735615,
0.024893498048186302,
0.010689983144402504,
0.05846686661243439,
-0.027149738743901253,
-0.01496212836354971,
0.032176341861486435,
0.012905227020382881,
0.014600257389247417,
0.001503173029050231,
0.015186279080808163,
0.019317656755447388,
0.0241643525660038,
0.004868980031460524,
-0.016458457335829735,
0.03879551216959953,
-0.0357668474316597,
0.02090521901845932,
0.018170451745390892,
0.012351813726127148,
0.03104623220860958,
0.04011673480272293,
-0.026785559952259064,
-0.02490932308137417,
0.03896061331033707,
-0.05332377925515175,
0.022481588646769524,
0.02874142862856388,
0.002013706834986806,
-0.017114324495196342,
-0.0025629594456404448,
-0.04345638304948807,
-0.026112275198101997,
-0.01753360964357853,
0.007271826732903719,
0.05582993105053902,
-0.03422475978732109,
0.02792365476489067,
-0.00644727936014533,
0.004659084603190422,
0.0029865207616239786,
-0.06341320276260376,
-0.005908631253987551,
0.0013172776671126485,
-0.03916578367352486,
0.011185538955032825,
-0.0003279454249422997,
-0.008739326149225235,
0.04676813259720802,
0.009151811711490154,
-0.02886766940355301,
0.0014886832796037197,
0.0015872757649049163,
-0.007841316983103752,
0.028713122010231018,
-0.029185596853494644,
-0.03264676406979561,
0.03657460957765579,
-0.037473976612091064,
0.031327664852142334,
0.0023554740473628044,
0.01600256748497486,
0.03016158752143383,
0.0006405187305063009,
-0.004851252771914005,
-0.05072857066988945,
-0.029811354354023933,
-0.05393923819065094,
0.017152709886431694,
0.018560724332928658,
0.006269774399697781,
0.022244557738304138,
0.030237309634685516,
0.027370011433959007,
0.02772596850991249,
-0.016729379072785378,
0.0034584503155201674,
-0.05171002447605133,
-0.01468666922301054,
-0.014732825569808483,
-0.020791519433259964,
0.0428791381418705,
0.007010952569544315,
0.007966413162648678,
0.0023244498297572136,
-0.024671193212270737,
0.015353195369243622,
0.015203427523374557,
0.0520460344851017,
-0.018259869888424873,
0.05458603799343109,
-0.0020530663896352053,
0.021140361204743385,
-0.026269780471920967,
0.008423002436757088,
0.1262865662574768,
0.0025262064300477505,
0.0056458101607859135,
-0.060534823685884476,
0.024185577407479286,
-0.029817868024110794,
-0.00913416501134634,
-0.015724211931228638,
-0.036241330206394196,
-0.026829620823264122,
0.008577118627727032,
0.015144637785851955,
0.06456851959228516,
-0.022882992401719093,
-0.012322290800511837,
0.07004346698522568,
-0.034360360354185104,
0.022140908986330032,
-0.004525416065007448,
0.03850870579481125,
-0.025727946311235428,
0.024688130244612694,
-0.047810982912778854,
0.03682532161474228,
-0.017493899911642075,
0.012570776976644993,
0.017727447673678398,
-0.04814355820417404,
-0.023428767919540405,
-0.006597242783755064,
-0.0026691691018640995,
0.030665038153529167,
-0.007970653474330902,
0.002029443858191371,
-0.021051745861768723,
0.012328129261732101,
0.062110379338264465,
0.009046556428074837,
0.003342690411955118,
0.021514717489480972,
0.049812350422143936,
0.04954620823264122,
-0.019462106749415398,
0.03169907256960869,
-0.023386595770716667,
-0.0169315617531538,
-0.05047830194234848,
0.01855390891432762,
-0.022092869505286217,
0.0202502328902483,
-0.009069357067346573,
-0.02466615103185177,
0.011338618583977222,
-0.007076901383697987,
-0.006134149618446827,
0.011829032562673092,
0.010781518183648586,
-0.005353562533855438,
0.02304609678685665,
-0.045059312134981155,
0.003388727782294154,
0.0027327202260494232,
0.015035191550850868,
0.004431669134646654,
0.006383050233125687,
0.038791391998529434,
0.030612101778388023,
0.028709132224321365,
-0.004589983727782965,
-0.0050421711057424545,
-0.06505067646503448,
-0.024126026779413223,
-0.03687300533056259,
0.028064459562301636,
-0.01386968418955803,
0.020413801074028015,
0.013250837102532387,
-0.0206013023853302,
-0.018308551982045174,
-0.013750634156167507,
-0.04359236732125282,
0.029860012233257294,
0.008235473185777664,
-0.008545862510800362,
-0.02409602515399456,
-0.028532644733786583,
0.025257647037506104,
0.035694584250450134,
-0.03101736679673195,
0.002629064954817295,
-0.003297058865427971,
0.013441858813166618,
0.008541442453861237,
-0.009676767513155937,
0.014250773005187511,
0.0363144613802433,
-0.06331269443035126,
-0.030021797865629196,
-0.032341647893190384,
0.07136721909046173,
0.03319752961397171,
-0.01194708701223135,
0.0322306863963604,
0.01751338131725788,
-0.01999361626803875,
0.0036735590547323227,
0.05187665671110153,
-0.04888537526130676,
-0.006759889889508486,
0.001983704511076212,
-0.0673227459192276,
-0.013157355599105358,
-0.012013958767056465,
-0.02306760661303997,
-0.0008203750476241112,
0.008334903046488762,
0.027714982628822327,
-0.0010165827115997672,
0.009312169626355171,
-0.033625729382038116,
0.05212271213531494,
-0.035911571234464645,
0.01161840371787548,
-0.0647011324763298,
-0.014644249342381954,
0.02063480019569397,
-0.025531671941280365,
0.017520025372505188,
0.049280859529972076,
-0.006698962766677141,
-0.012615269050002098,
0.016729576513171196,
0.025082116946578026,
0.013890957459807396,
-0.024626795202493668,
0.01375754363834858,
0.021819936111569405,
0.06184251233935356,
-0.010541963391005993,
-0.06190728023648262,
0.05111529678106308,
0.005164770875126123,
-0.023897510021924973,
0.020984243601560593,
-0.03131910786032677,
0.002365084132179618,
0.026490390300750732,
-0.02111426740884781,
-0.019518058747053146,
0.049910806119441986,
-0.05340385437011719,
0.009125476703047752,
-0.009854337200522423,
-0.020779721438884735,
0.009250424802303314,
0.02961069718003273,
0.02819187007844448,
-0.002891708165407181,
-0.039194878190755844,
0.030407292768359184,
0.021535513922572136,
-0.015142091549932957,
-0.015844887122511864,
-0.03173583000898361,
0.014519782736897469,
-0.02219432219862938,
-0.009422913193702698,
0.04914484918117523,
0.04021792858839035,
0.04247133806347847,
-0.01864943839609623,
0.011843397282063961,
-0.004311828408390284,
-0.026826992630958557,
-0.08611675351858139,
0.023692041635513306,
-0.008628466166555882,
-0.019506676122546196,
0.01227173488587141,
-0.064073346555233,
-0.00820655282586813,
0.014410424046218395,
-0.08093962073326111,
0.04297848790884018,
-0.06435554474592209,
-0.042420368641614914,
-0.03307068720459938,
-0.00902971625328064,
0.00316339242272079,
0.04113607481122017,
0.01229650154709816,
0.06386969238519669,
0.021836400032043457,
0.018951911479234695,
-0.046602290123701096,
-0.01868506707251072,
-0.006904019042849541,
0.019598454236984253,
-0.030705250799655914,
-0.0009550623362883925,
0.05143864080309868,
-0.013298755511641502,
-0.007977234199643135,
0.025617172941565514,
-0.05107754096388817,
0.02320076711475849,
0.006957364734262228,
0.0134976701810956,
0.005273408256471157,
0.010057060979306698,
0.004295335151255131,
-0.003314635483548045,
0.024016117677092552,
0.03285245597362518,
0.012713111005723476,
0.013922068290412426,
0.005000756587833166,
0.025228796526789665,
0.009665160439908504,
-0.034363504499197006,
0.024243749678134918,
0.03041977621614933,
-0.002335459226742387,
0.03782103210687637,
0.03287282958626747,
0.01791941002011299,
0.027079295367002487,
-0.001665023504756391,
0.01678059808909893,
-0.004009775817394257,
-0.026349475607275963,
0.03912153095006943,
-0.003671266371384263,
0.01989964209496975,
0.03426288813352585,
-0.025744907557964325,
-0.010001284070312977,
0.011860071681439877,
0.010435408912599087,
-0.01833912543952465,
-0.012729942798614502,
0.03003605082631111,
0.01156973373144865,
0.02818586491048336,
-0.028189636766910553,
-0.050750549882650375,
-0.030899161472916603,
0.03695908188819885,
0.04968186840415001,
0.038267724215984344,
-0.030215637758374214,
-0.044914815574884415,
-0.042996689677238464,
-0.034926436841487885,
0.026256123557686806,
-0.02866024523973465,
-0.009676042944192886,
-0.048522669821977615,
-0.035513002425432205,
0.022351277992129326,
0.022504117339849472,
0.06173895299434662,
-0.022006647661328316,
0.0054923165589571,
0.01058273110538721,
-0.02625276707112789,
0.0322624035179615,
-0.042622242122888565,
0.026380455121397972,
0.009298701770603657,
0.02575739659368992,
0.025597743690013885,
0.005662314128130674,
-0.0012747276341542602,
-0.018755603581666946,
0.051939982920885086,
0.010410902090370655,
0.014178406447172165,
0.00981970876455307,
-0.041316162794828415,
0.02258511632680893,
-0.003037303453311324,
-0.034778814762830734,
0.05058220401406288,
-0.05048607289791107,
0.0306671354919672,
-0.00708353566005826,
-0.002648024121299386,
-0.028161318972706795,
0.03605324774980545,
0.00504350708797574,
0.014684722758829594,
-0.033909596502780914,
-0.025015302002429962,
0.019937770441174507,
-0.028970496729016304,
0.006427705753594637,
0.02422739379107952,
-0.006958472076803446,
-0.004075340926647186,
0.029069602489471436,
-0.000826863688416779,
0.024811506271362305,
-0.03203357756137848,
0.0045597064308822155,
0.0012826732126995921,
0.02869684435427189,
0.008981848135590553,
0.06787571310997009,
-0.008858602494001389,
0.010450117290019989,
-0.016868729144334793,
0.026906302198767662,
-0.03249496594071388,
0.002343764528632164,
0.016501566395163536,
0.03331618010997772,
-0.06196152791380882,
-0.04549384117126465,
-0.0034276433289051056,
-0.03850015625357628,
-0.0011166584445163608,
0.03169720247387886,
-0.017972653731703758,
0.06273353844881058,
-0.014240402728319168,
0.006156387738883495,
-0.029666336253285408,
0.015117085538804531,
0.020820576697587967,
-0.006679436191916466,
0.013058760203421116,
0.03474923223257065,
0.022916000336408615,
-0.0023095784708857536,
-0.012307924218475819,
0.005274870432913303,
0.03993681073188782,
0.0057725789956748486,
0.07286177575588226,
0.006740208249539137,
0.027601812034845352,
-0.026657551527023315,
0.007085912860929966,
-0.05134786665439606,
-0.06874547153711319,
-0.010565861128270626,
0.040961988270282745,
0.016975395381450653,
-0.010848495177924633,
0.013922780752182007,
-0.04133250191807747,
0.01969432458281517,
-0.04564367234706879,
0.0051839775405824184,
-0.06497030705213547,
0.03591330349445343,
-0.03646069020032883,
-0.008843746036291122
] |
<p><em>I've read the following question:</em> <a href="http://physics.stackexchange.com/q/27303/">Negative probabilities in quantum physics</a>
<em>and I'm not sure I understand all the details about my actual question. I think mine is more direct.</em></p>
<p>It is known that the <a href="https://en.wikipedia.org/wiki/Wigner_quasiprobability_distribution" rel="nofollow">Wigner function</a> can become negative in certain region of phase-space. Some people claim that the negativity of this quasi-probability distribution signifies that the system behaves quantum mechanically (as opposed to classical physics, when probabilities are always positive). Apparently, there are still some controversies about this point. Please read the answers from the previously cited post: <a href="http://physics.stackexchange.com/q/27303/">Negative probabilities in quantum physics</a></p>
<p><strong>I would like to know whether there is an equivalence between the negativity of the Wigner distribution and some quantum behaviours or not.</strong> Is it still a question under debate / actual research or not ? </p>
<p>My main concern is that there are more and more experimental studies of the Wigner function (or other tomography captures) reporting negativity of the Wigner function. I would like to understand what did these studies actually probe.</p>
<p>As an extra question (that I could eventually switch to an other question): What is the <em>quantum behaviour</em> the negativity of the Wigner function may probe ? </p>
<p><em>Having not a lot of time at the moment, I would prefer an explicit answer rather than a bunch of (perhaps contradictory) papers regarding this subject. But I would satisfy myself with what you want to share of course :-)</em></p> | 1,463 | [
-0.026215240359306335,
-0.05487482622265816,
-0.0068264310248196125,
-0.07308869808912277,
0.05267121270298958,
0.002451864769682288,
-0.04336605966091156,
-0.005928352940827608,
0.012801991775631905,
-0.03691469132900238,
0.01803942769765854,
0.041781455278396606,
0.03522615134716034,
0.03006378933787346,
-0.005106550175696611,
0.011866997927427292,
-0.014708279632031918,
-0.029692819342017174,
-0.03774431720376015,
0.002408575266599655,
-0.014104149304330349,
0.02626355178654194,
0.00734333973377943,
0.01714685559272766,
-0.030504662543535233,
0.012926006689667702,
0.036358099430799484,
-0.01982218399643898,
0.031776320189237595,
0.061790984123945236,
-0.010089640505611897,
0.01631440594792366,
0.015417994931340218,
0.02001931704580784,
0.0242555420845747,
-0.009122445248067379,
-0.025950077921152115,
-0.03921309486031532,
0.0038686846382915974,
0.03670250624418259,
-0.046467483043670654,
-0.00025665550492703915,
-0.03388458862900734,
0.053584352135658264,
-0.03508027642965317,
0.011603809893131256,
0.00978901144117117,
-0.016656097024679184,
0.033229317516088486,
-0.05767594277858734,
0.05330647900700569,
-0.011130514554679394,
0.026363495737314224,
0.02129887416958809,
-0.002758121583610773,
-0.0031540347263216972,
0.07625256478786469,
0.0859299898147583,
-0.013404199853539467,
-0.07026883959770203,
-0.013495282270014286,
-0.030874578282237053,
-0.0024263353552669287,
0.011470410972833633,
-0.019945058971643448,
0.03433333337306976,
0.03977375850081444,
-0.05088549107313156,
0.021411504596471786,
-0.0005402238457463682,
-0.019895073026418686,
0.021062584593892097,
0.04616682976484299,
0.0007327130879275501,
0.02911829762160778,
-0.012988586910068989,
0.027890319004654884,
0.026446009054780006,
0.009999624453485012,
0.07059817016124725,
-0.015302798710763454,
-0.009789325296878815,
-0.013663366436958313,
0.027479693293571472,
-0.0002827112330123782,
-0.02562778815627098,
0.09336524456739426,
-0.02309276908636093,
-0.014133857563138008,
0.05581140145659447,
-0.01155428122729063,
0.00529773673042655,
0.015071457251906395,
-0.0037111788988113403,
-0.04974563792347908,
0.029467644169926643,
0.015007518231868744,
0.035394687205553055,
-0.0005715410807169974,
-0.03497477248311043,
-0.0023106555454432964,
-0.03115374781191349,
0.04320085421204567,
0.03643876686692238,
-0.022351594641804695,
0.01087648794054985,
-0.024906661361455917,
0.031139224767684937,
-0.03166132792830467,
-0.028036411851644516,
-0.03281937912106514,
0.026451382786035538,
0.018565749749541283,
-0.016124730929732323,
-0.00920232106000185,
-0.04783235490322113,
-0.0029758657328784466,
-0.026531143113970757,
0.052416786551475525,
0.08708912134170532,
0.0022544709499925375,
0.004820114467293024,
0.016551511362195015,
-0.03989031910896301,
-0.04351048171520233,
-0.013713164255023003,
0.06008529290556908,
0.005986629985272884,
-0.016803694888949394,
0.05348055064678192,
0.03501705080270767,
0.005127698183059692,
0.06063905730843544,
-0.01608223281800747,
0.034182608127593994,
0.00878063216805458,
-0.11786521226167679,
-0.0786566212773323,
0.09536128491163254,
-0.010927852243185043,
-0.007261323742568493,
-0.09249990433454514,
-0.0020779245533049107,
0.02881217747926712,
0.07167509198188782,
-0.004049184266477823,
0.010423334315419197,
-0.04567938670516014,
0.02500787563621998,
0.015841856598854065,
-0.002721228403970599,
0.0014622177695855498,
-0.00998395774513483,
-0.038051310926675797,
-0.02680213376879692,
-0.04858793318271637,
0.02530541643500328,
0.044514477252960205,
0.00750523479655385,
-0.014103427529335022,
0.03988846763968468,
-0.011208344250917435,
-0.011087506078183651,
-0.00026635779067873955,
-0.006609485950320959,
-0.02910931408405304,
0.1047993078827858,
0.04138602688908577,
-0.03351940959692001,
0.014279047958552837,
0.0012061814777553082,
0.00818117056041956,
-0.014094495214521885,
0.001341157709248364,
0.02988414652645588,
-0.06415978074073792,
0.0004048087866976857,
-0.018045416101813316,
0.03822704404592514,
-0.028537387028336525,
-0.008228621445596218,
0.026965772733092308,
-0.03960014507174492,
-0.005767542868852615,
0.044764500111341476,
0.025677917525172234,
-0.005857654847204685,
-0.008558491244912148,
0.03987152501940727,
-0.02465658448636532,
-0.02668498270213604,
-0.045156434178352356,
-0.0009510894306004047,
-0.01703248731791973,
-0.004457763396203518,
0.053069472312927246,
-0.0013668684987351298,
0.0024830095935612917,
-0.02601282112300396,
0.0168385598808527,
0.030269324779510498,
0.020826177671551704,
-0.016148479655385017,
-0.0004088300047442317,
0.01897786185145378,
0.02695237286388874,
0.023846404626965523,
-0.04810551926493645,
0.012959854677319527,
-0.05047032982110977,
-0.06030215322971344,
-0.02576587349176407,
-0.010494686663150787,
0.043500326573848724,
0.03197838366031647,
-0.024038681760430336,
0.005900563672184944,
-0.00273093837313354,
-0.0044727325439453125,
-0.02909618243575096,
-0.03834697976708412,
0.046821244060993195,
0.04905605688691139,
-0.007936974987387657,
0.0013983126264065504,
0.03189641609787941,
0.031459223479032516,
0.0113781513646245,
0.035720281302928925,
-0.005941204726696014,
-0.053363136947155,
0.020360521972179413,
0.055955011397600174,
0.03161507472395897,
-0.029223740100860596,
0.02774764597415924,
0.03242283686995506,
-0.001378582208417356,
0.006034775171428919,
0.005620910320430994,
-0.05710237845778465,
-0.06960318237543106,
-0.0012461579171940684,
-0.008448975160717964,
0.024387924000620842,
0.019630320370197296,
0.009021871723234653,
-0.019946645945310593,
0.01903173327445984,
-0.005469403695315123,
-0.03244216740131378,
0.05905724689364433,
-0.017138559371232986,
-0.0052644615061581135,
0.003184956731274724,
-0.061085935682058334,
0.023364758118987083,
-0.007029206492006779,
-0.001991207944229245,
0.0008985020685940981,
-0.007320455741137266,
0.03378061205148697,
-0.011516023427248001,
-0.02979656495153904,
0.0014613927341997623,
0.013143901713192463,
-0.021260706707835197,
0.03480513393878937,
0.003116796724498272,
0.015074512921273708,
0.01392828207463026,
-0.015557271428406239,
0.024871204048395157,
-0.00916444230824709,
0.005247057881206274,
0.027844034135341644,
0.0322369784116745,
0.01633666642010212,
-0.046475447714328766,
-0.04670333489775658,
-0.008632787503302097,
-0.0243606586009264,
0.025049405172467232,
0.041417136788368225,
-0.014097646810114384,
0.0070514073595404625,
-0.05632881447672844,
-0.020932884886860847,
0.006800686474889517,
-0.03206774964928627,
0.01595689356327057,
0.002056736731901765,
0.001060466398485005,
-0.053079962730407715,
-0.0186475720256567,
-0.03539002686738968,
-0.02262013778090477,
-0.028738508000969887,
-0.02151443623006344,
0.07467291504144669,
-0.03522435203194618,
-0.017032086849212646,
0.0013518502237275243,
-0.015201003290712833,
-0.06066825985908508,
-0.020845577120780945,
-0.003957850392907858,
0.02088395319879055,
-0.03418707102537155,
0.01698974147439003,
0.03906029462814331,
-0.04020741954445839,
-0.015818916261196136,
-0.04303864762187004,
-0.07367487996816635,
0.004458355717360973,
-0.03395197540521622,
0.02721531130373478,
0.0034064138308167458,
-0.028310099616646767,
0.053332213312387466,
0.004741756711155176,
-0.011866461485624313,
0.0002877435181289911,
-0.009154154919087887,
-0.039398789405822754,
-0.020277831703424454,
-0.017937730997800827,
0.038592517375946045,
-0.004846206400543451,
0.07349593937397003,
0.015923375263810158,
0.01636231690645218,
0.02841254509985447,
0.01920994371175766,
-0.01883333921432495,
0.0014676221180707216,
0.007602115627378225,
-0.026046674698591232,
0.025069713592529297,
0.019250838086009026,
-0.012470569461584091,
-0.00014569232007488608,
0.00666669150814414,
0.0005802115774713457,
0.009740525856614113,
-0.02783278562128544,
0.05124695599079132,
-0.007885442115366459,
0.028187913820147514,
-0.04423724487423897,
0.046247292309999466,
-0.0270545557141304,
0.008198907598853111,
-0.002665015170350671,
0.0030555673874914646,
0.003327232552692294,
0.015112986788153648,
0.009417502209544182,
0.029032588005065918,
0.004901623819023371,
-0.014306395314633846,
-0.012978918850421906,
-0.022547494620084763,
0.0023154730442911386,
0.02945784293115139,
-0.03979511559009552,
-0.006055445875972509,
0.03532098978757858,
0.03181048855185509,
0.024596111848950386,
-0.009335772134363651,
-0.007265358231961727,
-0.027683863416314125,
-0.019903406500816345,
0.025867270305752754,
-0.007064554840326309,
0.029948769137263298,
0.010288849472999573,
-0.004970670212060213,
0.016238003969192505,
0.007241254672408104,
-0.04899157956242561,
-0.024541517719626427,
-0.045467521995306015,
0.016509443521499634,
-0.03420534357428551,
-0.001810533693060279,
-0.008739129640161991,
0.02791057713329792,
0.017757456749677658,
-0.0015686297556385398,
-0.034037552773952484,
-0.008878630585968494,
0.012828202918171883,
-0.05498836562037468,
-0.030998123809695244,
-0.026736507192254066,
-0.0318414643406868,
-0.041146136820316315,
0.01465073972940445,
0.03477178141474724,
-0.010991734452545643,
0.03982491046190262,
0.01219185907393694,
-0.050186336040496826,
0.030970769003033638,
0.013735444284975529,
0.0235536377876997,
0.05975765734910965,
0.014842189848423004,
0.0002561600995250046,
0.026199089363217354,
-0.024501807987689972,
0.02975626289844513,
0.013557996600866318,
0.05479150265455246,
0.029070472344756126,
-0.032168325036764145,
0.021784234791994095,
-0.03292561694979668,
-0.012426957488059998,
-0.023423241451382637,
0.043470349162817,
0.03657856956124306,
0.009690217673778534,
0.015493322163820267,
0.001349840546026826,
-0.02222338132560253,
0.007745975628495216,
0.03769729286432266,
-0.005876451730728149,
0.05602192133665085,
-0.03051171451807022,
-0.015210742130875587,
-0.02884119749069214,
0.005821541417390108,
0.0148380221799016,
0.0004914877354167402,
0.007390784099698067,
0.023689262568950653,
0.007259550970047712,
0.036452099680900574,
-0.003165986854583025,
-0.01572253555059433,
-0.027656804770231247,
0.00723149674013257,
0.0004616623918991536,
0.031891897320747375,
0.016064494848251343,
-0.00010882078640861437,
0.0238126739859581,
0.0024457997642457485,
-0.024559248238801956,
-0.07313019037246704,
-0.036269716918468475,
0.06349609792232513,
0.058567214757204056,
-0.002459273673593998,
-0.027440091595053673,
-0.06551133096218109,
-0.012647459283471107,
0.033059049397706985,
-0.019717451184988022,
0.04136333242058754,
-0.0020844487007707357,
-0.00011844202526845038,
-0.04312911257147789,
-0.03780106455087662,
0.009058956988155842,
0.006094477605074644,
0.03556114435195923,
0.008725173771381378,
-0.022824076935648918,
-0.014792182482779026,
-0.05462212860584259,
-0.019469905644655228,
0.0114186592400074,
0.09727257490158081,
-0.02033560909330845,
0.008364681154489517,
-0.027621814981102943,
0.017811710014939308,
-0.026079274713993073,
-0.10309386998414993,
0.01170699205249548,
0.0014294942375272512,
-0.0016455774893984199,
0.059337686747312546,
-0.05689876154065132,
-0.041906971484422684,
-0.016245897859334946,
-0.03241030499339104,
-0.04993700608611107,
0.024024607613682747,
-0.03288234397768974,
0.056942496448755264,
0.01174293365329504,
-0.024902621284127235,
0.057682912796735764,
0.030144721269607544,
-0.007394327782094479,
0.007394383195787668,
-0.009339728392660618,
0.01798417419195175,
-0.06451287865638733,
0.021055562421679497,
-0.01682770811021328,
-0.014177823439240456,
-0.018260091543197632,
0.07260334491729736,
0.016183706000447273,
0.0031576519832015038,
-0.028689473867416382,
-0.011811207979917526,
-0.009341289289295673,
-0.015910129994153976,
0.007430681958794594,
0.0016848316881805658,
0.01763034053146839,
-0.0015512070385739207,
-0.0006061730091460049,
-0.02104826830327511,
0.00215587648563087,
0.0037877627182751894,
0.028448184952139854,
0.046869490295648575,
-0.012196667492389679,
-0.0038574268110096455,
-0.03746074065566063,
0.009868458844721317,
0.0006650786381214857,
-0.025340167805552483,
0.007471861783415079,
0.011887258850038052,
-0.020093820989131927,
0.029618963599205017,
-0.04346868395805359,
-0.008994280360639095,
0.020735973492264748,
-0.006706485524773598,
0.010523250326514244,
-0.0433005765080452,
0.028441812843084335,
0.0012336907675489783,
0.008857200853526592,
-0.09154049307107925,
-0.03358512371778488,
-0.0041660284623503685,
0.015786640346050262,
-0.01000231597572565,
-0.017078615725040436,
-0.010467368178069592,
-0.017228059470653534,
-0.020365793257951736,
-0.01166627462953329,
0.04374813288450241,
-0.028940631076693535,
0.005916468799114227,
0.04003587365150452,
-0.02154039405286312,
0.047355204820632935,
-0.04905116930603981,
-0.019830510020256042,
0.03191433846950531,
-0.024910584092140198,
-0.02505798079073429,
-0.0033088354393839836,
0.0325816385447979,
-0.024169960990548134,
-0.05761159956455231,
0.0009880013531073928,
0.0030589632224291563,
0.014457895420491695,
0.006598102860152721,
-0.034164100885391235,
0.0014871930470690131,
0.001737741637043655,
0.030270572751760483,
-0.01677960902452469,
0.006102683488279581,
-0.0038915337063372135,
0.034866709262132645,
0.011562096886336803,
0.0009387750178575516,
-0.0370074063539505,
-0.03775285929441452,
0.0334552526473999,
-0.0045511056669056416,
-0.047928810119628906,
0.016223695129156113,
0.023970603942871094,
0.00033044928568415344,
0.008465778082609177,
0.022232644259929657,
-0.054354868829250336,
-0.002745575737208128,
0.008711681701242924,
-0.006823352538049221,
-0.013487724587321281,
-0.022701110690832138,
-0.03490671142935753,
-0.07385746389627457,
-0.069686658680439,
-0.023676132783293724,
0.04763385280966759,
0.024177270010113716,
0.055024195462465286,
0.01595175638794899,
-0.008623463101685047,
-0.04408279433846474,
-0.03731263428926468,
0.039530981332063675,
0.00836524460464716,
0.002879707608371973,
0.0039899954572319984,
-0.016025610268115997,
0.052499111741781235,
0.05023748055100441,
0.040906790643930435,
-0.005484989378601313,
0.02980021759867668,
0.023222217336297035,
0.040046293288469315,
0.053869422525167465,
-0.017315512523055077,
-0.04504796862602234,
0.06722008436918259,
-0.06831369549036026,
0.03153179585933685,
0.004136374685913324,
-0.034122034907341,
0.028939012438058853,
0.014507628045976162,
-0.008947550319135189,
-0.032430365681648254,
0.005849090870469809,
-0.011603633873164654,
0.015822086483240128,
0.00022622940014116466,
0.004964900203049183,
0.008704207837581635,
-0.022080114111304283,
0.025530904531478882,
0.011208081617951393,
0.013795409351587296,
-0.018492765724658966,
-0.046882688999176025,
0.004327753558754921,
-0.030605295673012733,
-0.049577947705984116,
0.026844695210456848,
-0.011394239962100983,
-0.005116589833050966,
0.019019346684217453,
-0.05033187195658684,
0.01885337010025978,
-0.007910532876849174,
0.046222586184740067,
-0.030485117807984352,
0.05327240750193596,
-0.021142948418855667,
0.01971784047782421,
-0.011270534247159958,
-0.001653769752010703,
0.10046228021383286,
0.04207061231136322,
0.028331544250249863,
-0.029846934601664543,
-0.010916409082710743,
-0.0029214383102953434,
0.020894236862659454,
-0.02622320130467415,
-0.0005096903187222779,
0.016508139669895172,
0.001678262371569872,
0.027498586103320122,
0.07069658488035202,
0.04755965620279312,
-0.019220827147364616,
0.04924726113677025,
-0.047711171209812164,
-0.0363212414085865,
0.013568377122282982,
-0.017176402732729912,
0.027841877192258835,
-0.011100557632744312,
-0.037127815186977386,
0.04297041893005371,
-0.01750667206943035,
0.01879800856113434,
0.002633244963362813,
-0.02090836688876152,
0.014525942504405975,
0.008454542607069016,
-0.03930774703621864,
-0.008713362738490105,
0.01023721881210804,
-0.0013843656051903963,
-0.026239434257149696,
-0.0014602115843445063,
0.02402959205210209,
0.00815340131521225,
0.0401657409965992,
0.039691586047410965,
0.01377225574105978,
-0.03060777112841606,
-0.002047182060778141,
0.026938576251268387,
-0.06511971354484558,
-0.010294663719832897,
0.004831292200833559,
0.023837879300117493,
-0.006173888221383095,
0.006292272824794054,
0.012061630375683308,
-0.013915922492742538,
0.021425331011414528,
-0.054388437420129776,
-0.021654903888702393,
-0.00724070006981492,
0.039059218019247055,
-0.01629115268588066,
-0.03090943582355976,
-0.02741149440407753,
0.01322320569306612,
-0.008698035962879658,
0.02044013701379299,
-0.022030673921108246,
0.020093558356165886,
-0.025844503194093704,
0.020898399874567986,
-0.006394883617758751,
0.003007593099027872,
0.00034381166915409267,
-0.02368520386517048,
-0.003581495489925146,
-0.05775316059589386,
0.005410129204392433,
0.02549748681485653,
-0.026805708184838295,
0.07115355134010315,
0.003180281724780798,
-0.00506853312253952,
-0.01817491091787815,
-0.06856405735015869,
0.001275093061849475,
-0.016577433794736862,
-0.007402963005006313,
0.00563367735594511,
-0.023954110220074654,
0.03363954648375511,
0.02925964444875717,
-0.029711728915572166,
0.003560092533007264,
0.02667994238436222,
0.046874698251485825,
0.037536442279815674,
-0.006217968184500933,
-0.030467312783002853,
-0.0013592956820502877,
-0.0065424200147390366,
-0.02751259133219719,
-0.04948393255472183,
0.02250412479043007,
-0.015890667214989662,
0.021627474576234818,
0.02665235847234726,
0.01711174100637436,
-0.0019623618572950363,
-0.03174349665641785,
0.012312375009059906,
-0.02783210016787052,
-0.028959525749087334,
0.009068060666322708,
0.02732940949499607,
-0.0159673560410738,
-0.02049947902560234,
-0.01600474864244461,
0.0010500949574634433,
0.011024607345461845,
0.02816258743405342,
-0.01999710127711296,
-0.017511090263724327,
-0.02369813621044159,
0.010110326111316681,
-0.04609895870089531,
-0.03130205348134041,
-0.019048605114221573,
0.0009602648206055164,
-0.006336112041026354,
0.0013524664100259542,
0.004986942745745182,
0.023383090272545815,
-0.005553733557462692,
-0.010575610212981701,
0.00990962702780962,
0.0562896654009819,
-0.009224836714565754,
0.006545195821672678,
0.03140866756439209,
0.002795000560581684,
0.03223743662238121,
-0.004748767241835594,
-0.024466373026371002,
0.08236207067966461,
-0.025695353746414185,
-0.041034020483493805,
0.045563384890556335,
-0.010563844814896584,
0.006040663458406925,
0.05667835474014282,
-0.03396904841065407,
0.0059725381433963776,
0.026724081486463547,
-0.006496523041278124,
-0.03494330868124962,
0.025221452116966248,
-0.03257579356431961,
-0.03133928030729294,
0.0007632761262357235,
0.007991510443389416,
-0.011355630122125149,
-0.019969476386904716,
0.045792561024427414,
0.05991826206445694,
-0.007480625994503498,
-0.01316750142723322,
0.018115544691681862,
-0.030242951586842537,
0.041543543338775635,
0.03337233141064644,
0.025328295305371284,
0.02390449121594429,
0.047554027289152145,
-0.01782228797674179,
0.04736156389117241,
-0.048162031918764114,
0.0018826626474037766,
-0.09950026124715805,
-0.02417304925620556,
-0.000029343829737626947,
0.00038951088208705187,
0.04402032494544983,
-0.037031665444374084,
0.0030087761115282774,
0.0496596060693264,
-0.0558600053191185,
0.03740856796503067,
0.008237030357122421,
-0.03737521544098854,
-0.03405317664146423,
0.01885124295949936,
-0.027976250275969505,
0.04565645754337311,
-0.012930418364703655,
0.05432270094752312,
0.026455897837877274,
0.039158739149570465,
-0.03034473955631256,
-0.016080087050795555,
-0.010366415604948997,
0.03739919885993004,
-0.008115912787616253,
0.02148408070206642,
0.044911596924066544,
-0.028526127338409424,
-0.02491900511085987,
0.067068912088871,
-0.007740700617432594,
-0.001687422627583146,
0.00768048781901598,
0.002341634826734662,
-0.0214224960654974,
0.029311902821063995,
0.08141870051622391,
-0.03343934193253517,
0.0037548195105046034,
0.019012223929166794,
0.006097541190683842,
0.040307313203811646,
-0.011110203340649605,
-0.005974540952593088,
0.01805003732442856,
-0.053389959037303925,
-0.018059708178043365,
0.043764080852270126,
0.016447581350803375,
0.018551787361502647,
0.0027694806922227144,
0.007943881675601006,
0.030434587970376015,
-0.010160510428249836,
0.03325984627008438,
-0.04251662269234657,
0.021847780793905258,
-0.00009127506200456992,
0.022533008828759193,
-0.0035878189373761415,
0.009874764829874039,
-0.004093892406672239,
-0.05600989609956741,
0.038995277136564255,
-0.021997882053256035,
-0.013151351362466812,
-0.06021370366215706,
-0.02260715700685978,
-0.014913573861122131,
0.0367722287774086,
0.006604817230254412,
-0.049249112606048584,
-0.05828588828444481,
0.03871897980570793,
-0.02798384800553322,
0.03045244701206684,
0.00354589126072824,
-0.021840136498212814,
-0.01872188039124012,
-0.09519383311271667,
0.00956538412719965,
0.012996610254049301,
0.029832124710083008,
-0.04406901076436043,
0.004591440316289663,
0.009260580874979496,
-0.007917804643511772,
0.03853597491979599,
-0.013171244412660599,
-0.03551897406578064,
0.013085772283375263,
-0.007176849991083145,
0.020453277975320816,
-0.03120272606611252,
0.016568472608923912,
-0.0281540397554636,
0.00543976342305541,
-0.010462199337780476,
-0.0021720589138567448,
-0.027533873915672302,
0.025091085582971573,
0.032540272921323776,
0.01648874767124653,
0.0057264529168605804,
-0.0015301036182790995,
-0.039436765015125275,
0.12081136554479599,
0.02536841854453087,
-0.005076933186501265,
0.08038315176963806,
-0.008561143651604652,
0.020969394594430923,
-0.011714699678122997,
-0.0352659672498703,
-0.0033551454544067383,
0.015027455054223537,
-0.0047297305427491665,
-0.03502822667360306,
0.013723247684538364,
0.024623798206448555,
0.04351812228560448,
-0.02185833267867565,
-0.049827177077531815,
0.062248293310403824,
-0.04463135451078415,
-0.027644917368888855,
0.017769262194633484,
0.040852561593055725,
0.0329112745821476,
-0.008701547048985958,
0.004946034401655197,
-0.002430377993732691,
0.01913435198366642,
-0.007880567573010921,
0.05336330831050873,
0.02260834351181984,
-0.00007101515802787617,
0.03655415028333664,
0.007533767726272345,
-0.03575441986322403,
0.027483340352773666,
0.027931977063417435,
0.0490785650908947,
-0.024027185514569283,
0.006333895958960056,
0.03477267175912857,
0.017522145062685013,
-0.007986211217939854,
0.0217675119638443,
-0.016791900619864464,
0.07913469523191452,
0.025220192968845367,
-0.001762061845511198,
-0.01352465245872736,
0.0011099379044026136,
-0.030720476061105728,
-0.0011061732657253742,
0.015245158225297928,
0.06460656970739365,
0.01537219900637865,
-0.022703632712364197,
-0.011213011108338833,
-0.0015953939873725176,
0.015897633507847786,
-0.06364210695028305,
0.0070239463821053505,
-0.02074577286839485,
-0.003642649156972766,
-0.023116862401366234,
-0.0017436272464692593,
-0.01176675595343113,
-0.004845075309276581,
0.001619576709344983,
0.03461921215057373,
0.05759410560131073,
-0.007814559154212475,
0.003985648043453693,
-0.027456073090434074,
0.06681312620639801,
-0.022089125588536263,
0.02508966252207756,
-0.027793314307928085,
0.005953128915280104,
-0.00019644887652248144,
-0.011295736767351627
] |
<p>I am reading a <a href="http://www.cambridge.org/us/academic/subjects/physics/particle-physics-and-nuclear-physics/foundations-perturbative-qcd" rel="nofollow">book</a> on perturbative QCD by John Collins. In Chapter 5, the terms <strong><em>reduced graph</em></strong> and <strong><em>pinch-singular surface</em></strong> are used for the analysis of mass singularities. However, their meanings are not explainded very clearly. It says (Sect 5.1.4, page 91)</p>
<blockquote>
<p>The PSSs (for the physical region, which is all that concerns us) are where
the on-shell propagators and momenta correspond to classically allowed
scattering processes treated in coordinate space.</p>
</blockquote>
<p>I cannot get the key points from this <em>definition</em>. For reduced graphs, it provides some examples. But I still cannot understand why they are important and how they are related to the Feynman diagrams. Could someone help me to clarify these terminologies? Many thanks!</p> | 1,464 | [
0.05000145360827446,
-0.027906961739063263,
-0.008277932181954384,
-0.06041332334280014,
0.018236836418509483,
0.021131843328475952,
0.008226134814321995,
-0.025484800338745117,
0.020260388031601906,
-0.04766838625073433,
0.0016673252684995532,
-0.01035716850310564,
0.07360251247882843,
0.008547957986593246,
0.007552781607955694,
0.018803590908646584,
0.00414974195882678,
-0.013141513802111149,
0.0029808038379997015,
-0.008638757281005383,
0.011692024767398834,
-0.01903517358005047,
0.02563050389289856,
0.001167444628663361,
0.011152366176247597,
0.008319700136780739,
0.008553513325750828,
0.03372945263981819,
0.009159048087894917,
0.03420481085777283,
-0.009062706492841244,
-0.03183523565530777,
0.010909130796790123,
-0.0012302291579544544,
0.008946381509304047,
-0.008500419557094574,
-0.023112084716558456,
-0.024100961163640022,
-0.027424687519669533,
0.017989246174693108,
0.000491756945848465,
-0.023909850046038628,
-0.010592296719551086,
0.04346000775694847,
-0.04782959073781967,
-0.0032455280888825655,
-0.037136733531951904,
-0.0072424220852553844,
0.04835499823093414,
-0.09336347877979279,
0.04122091457247734,
0.02029884234070778,
0.05423750728368759,
0.05857216566801071,
-0.009795472025871277,
-0.0011211329838261008,
0.03459828719496727,
0.03549237176775932,
-0.025566810742020607,
-0.09784995764493942,
-0.02206772193312645,
-0.032584063708782196,
-0.0015368533786386251,
0.0035841399803757668,
-0.03870787099003792,
0.028648652136325836,
-0.025484154000878334,
-0.035333726555109024,
0.03001866117119789,
0.010852774605154991,
-0.0074296556413173676,
0.014978485181927681,
0.0032905801199376583,
-0.0045383344404399395,
0.020243939012289047,
-0.037938691675662994,
0.015775281935930252,
-0.0013228203170001507,
0.033505700528621674,
0.06129349023103714,
-0.020553262904286385,
0.04875988885760307,
-0.0014694734709337354,
0.03554680198431015,
-0.020462527871131897,
0.001452507684007287,
0.08757372200489044,
-0.022202439606189728,
0.0007101925439201295,
0.015048250555992126,
-0.001566958031617105,
0.001851669861935079,
0.029100336134433746,
-0.008678286336362362,
-0.01776871830224991,
-0.02158021554350853,
0.051250163465738297,
0.02994951233267784,
-0.020843375474214554,
0.0038944350089877844,
-0.03145597502589226,
-0.026203880086541176,
0.014297924004495144,
0.05782589688897133,
-0.0018520086305215955,
-0.0015085028717294335,
-0.05341695249080658,
-0.007373865693807602,
-0.023539189249277115,
-0.029267052188515663,
-0.048960037529468536,
-0.029060767963528633,
-0.006765192840248346,
0.028475776314735413,
-0.012484216131269932,
-0.02765542082488537,
-0.021680237725377083,
0.02654765360057354,
0.046683549880981445,
0.030742883682250977,
0.05145122855901718,
-0.024944176897406578,
0.030908020213246346,
-0.04272817075252533,
-0.10513782501220703,
0.03864479437470436,
0.04386793449521065,
0.012316976673901081,
-0.008153163827955723,
0.023290665820240974,
0.0331665575504303,
0.01209541130810976,
0.01611538790166378,
-0.002475663321092725,
0.04622439295053482,
-0.03618723526597023,
-0.07303766906261444,
-0.04674416035413742,
0.04314287379384041,
0.01905730739235878,
-0.009193372912704945,
-0.05580219626426697,
-0.002114024944603443,
0.009343760088086128,
0.050353702157735825,
-0.03994496166706085,
0.007575249765068293,
-0.003868535626679659,
0.04513097554445267,
0.006164916325360537,
-0.046362631022930145,
-0.0006575669976882637,
-0.04089818149805069,
-0.02796495333313942,
-0.034045446664094925,
-0.047883041203022,
0.03144846484065056,
0.019014963880181313,
0.013867109082639217,
-0.007244766689836979,
0.08158909529447556,
-0.07198034971952438,
0.004392540082335472,
0.045069944113492966,
-0.01586245745420456,
-0.0018796623917296529,
0.08180467784404755,
0.03581696376204491,
0.015307593159377575,
0.07784560322761536,
0.008581189438700676,
0.01696026511490345,
-0.008811632171273232,
0.05601096898317337,
0.025598308071494102,
-0.013772591017186642,
-0.01439008116722107,
-0.001988140633329749,
-0.037979576736688614,
0.013641071505844593,
-0.0366024374961853,
-0.03304026275873184,
-0.02980112098157406,
0.0002952562354039401,
-0.015320222824811935,
0.04702386260032654,
-0.012361641973257065,
-0.006730517838150263,
-0.0031691081821918488,
-0.03870991989970207,
-0.07247994095087051,
-0.05648672580718994,
0.02430563047528267,
-0.009561904706060886,
0.010629949159920216,
0.04201545566320419,
0.002533460734412074,
-0.013127847574651241,
-0.0038078471552580595,
-0.020947739481925964,
-0.0163224209100008,
0.039248090237379074,
0.0031089491676539183,
0.011670315638184547,
-0.009444025345146656,
0.007103974465280771,
-0.0016653152415528893,
-0.0051590618677437305,
0.04674140736460686,
-0.048443712294101715,
-0.015576545149087906,
0.015374364331364632,
-0.03177325800061226,
0.0014423590619117022,
0.00022993111633695662,
-0.010142482817173004,
-0.00145596859510988,
-0.0002881346154026687,
0.0041026100516319275,
0.035538509488105774,
-0.02416289784014225,
0.054508406668901443,
0.02973674237728119,
0.02915562316775322,
0.0118246553465724,
0.0026748895179480314,
-0.002419173950329423,
0.03531942516565323,
0.0018798112869262695,
-0.0027497278060764074,
-0.011488665826618671,
-0.020078694447875023,
0.015766290947794914,
0.04119562730193138,
-0.033584319055080414,
0.01883474737405777,
0.05107421427965164,
0.016328422352671623,
0.02326626144349575,
-0.00471703102812171,
-0.04019920900464058,
-0.020437685772776604,
0.013394352048635483,
0.016885070130228996,
-0.01466412004083395,
0.018735652789473534,
-0.044336672872304916,
0.024906480684876442,
0.006367941852658987,
-0.01717306673526764,
-0.013501749373972416,
0.054849132895469666,
-0.016866371035575867,
-0.02664114348590374,
0.002713605063036084,
-0.001391911064274609,
0.021847480908036232,
-0.015143909491598606,
0.05409986898303032,
0.018776793032884598,
0.002012021606788039,
0.0035718223080039024,
-0.025309784337878227,
-0.01392797939479351,
-0.0019443808123469353,
-0.008542735129594803,
0.01918857917189598,
-0.0042499518021941185,
0.016791827976703644,
-0.06045706197619438,
0.02819407731294632,
-0.007402745541185141,
0.007089139427989721,
-0.002147926250472665,
0.044649723917245865,
0.06001710146665573,
0.010013459250330925,
0.019012924283742905,
-0.006185205187648535,
-0.05261676758527756,
-0.015731798484921455,
-0.03778089955449104,
0.02711709588766098,
0.049661435186862946,
-0.06544183939695358,
0.0009702829993329942,
-0.09686103463172913,
0.014390678144991398,
0.018927300348877907,
-0.036861736327409744,
0.005158083513379097,
0.011654935777187347,
0.0038821601774543524,
-0.02210628241300583,
-0.024944335222244263,
-0.02051558904349804,
0.04269510507583618,
0.006622173823416233,
-0.002871812554076314,
0.05931203067302704,
0.031767718493938446,
-0.024465437978506088,
0.0008219301817007363,
-0.015792591497302055,
-0.008379610255360603,
-0.025990379974246025,
-0.01499219797551632,
0.02818431705236435,
-0.011260256171226501,
0.01696069724857807,
0.05182281881570816,
-0.02044779062271118,
-0.01684494875371456,
-0.04986149072647095,
-0.01049676164984703,
-0.01314855832606554,
0.007792592979967594,
0.01657373644411564,
0.022370165213942528,
-0.04801439493894577,
0.117921382188797,
0.0013807796640321612,
-0.03702253848314285,
-0.039828360080718994,
0.00824615266174078,
-0.0209710281342268,
-0.02023235149681568,
-0.01679249480366707,
-0.0052353739738464355,
0.004524752497673035,
0.009157424792647362,
0.015707021579146385,
0.03930272161960602,
0.037241071462631226,
-0.014501556754112244,
-0.019665643572807312,
0.03346464782953262,
-0.037983473390340805,
-0.02981415018439293,
0.012192240916192532,
0.008142130449414253,
-0.05763500928878784,
0.015115453861653805,
-0.03518166393041611,
0.018320001661777496,
-0.024644766002893448,
-0.055272553116083145,
0.0253547765314579,
0.0002905838191509247,
0.005883093923330307,
-0.0032249484211206436,
0.036777544766664505,
0.0041176327504217625,
-0.07105640321969986,
0.014011901803314686,
0.04375867173075676,
0.014326061122119427,
-0.06230434402823448,
-0.0006568299140781164,
0.009970762766897678,
0.05312197655439377,
-0.03209922835230827,
-0.038743551820516586,
-0.011504027992486954,
-0.027569113299250603,
0.0315185971558094,
-0.008907766081392765,
0.002144784200936556,
0.04781167581677437,
0.05839073285460472,
0.014851605519652367,
-0.014597272500395775,
-0.02782256528735161,
-0.01747043989598751,
-0.05165056884288788,
0.00939004123210907,
0.025523288175463676,
0.06940571218729019,
-0.00647700484842062,
0.041958317160606384,
0.010381084866821766,
-0.005942697636783123,
-0.01213614922016859,
-0.01715124398469925,
-0.05875866487622261,
-0.0008364325040020049,
0.00650515453889966,
-0.021931540220975876,
0.03292195126414299,
-0.024998435750603676,
0.0040281848050653934,
-0.027339566498994827,
-0.04584130644798279,
-0.028094101697206497,
0.0011351214488968253,
-0.049216050654649734,
0.03311728686094284,
-0.04007411375641823,
-0.0024396718945354223,
-0.01616920344531536,
0.03264784812927246,
0.07596295326948166,
-0.0641210526227951,
0.028458043932914734,
0.010667775757610798,
-0.06662765145301819,
-0.044717174023389816,
-0.0016024215146899223,
0.05033358931541443,
0.0054230778478085995,
0.025269903242588043,
0.04802875965833664,
0.05293623358011246,
-0.03142784908413887,
0.003958606161177158,
0.03245203197002411,
0.09008888900279999,
0.009585537016391754,
-0.015636203810572624,
0.000867249327711761,
-0.032991472631692886,
0.007374473847448826,
-0.00787571631371975,
0.05824558436870575,
0.020703885704278946,
-0.005712905898690224,
0.031270548701286316,
0.025639627128839493,
-0.016617558896541595,
0.06027175486087799,
0.028268761932849884,
0.010185188613831997,
-0.0013802822213619947,
-0.027761710807681084,
0.017336923629045486,
-0.026381688192486763,
-0.007894748821854591,
0.024059848859906197,
0.011422381736338139,
-0.028659338131546974,
0.02478695660829544,
0.025312334299087524,
-0.002051342511549592,
-0.08423418551683426,
0.026002002879977226,
-0.015780124813318253,
-0.026668526232242584,
0.008734695613384247,
-0.00624316930770874,
0.01790608838200569,
0.03989128768444061,
0.04193955659866333,
0.00820863712579012,
-0.0071248929016292095,
-0.04837607592344284,
-0.0066256774589419365,
0.040722791105508804,
0.05650750547647476,
0.02874120883643627,
-0.02843213453888893,
-0.0075074308551847935,
0.020682821050286293,
0.023253710940480232,
-0.04217354953289032,
0.012345953844487667,
-0.030134376138448715,
0.01914789155125618,
-0.04660400375723839,
-0.026671193540096283,
0.005181060638278723,
0.008946225978434086,
-0.01260721031576395,
0.01837252266705036,
-0.021410850808024406,
-0.012013619765639305,
-0.05093910172581673,
0.0004770446103066206,
-0.05435803160071373,
0.0282907634973526,
0.02312817983329296,
-0.0011162727605551481,
-0.004896471742540598,
0.029475165531039238,
-0.009703370742499828,
-0.1063104197382927,
0.014788702130317688,
0.0019869590178132057,
0.02542966790497303,
0.07708121836185455,
-0.026163939386606216,
-0.00027333502657711506,
0.00817189458757639,
0.005262718535959721,
0.00633773859590292,
-0.016455326229333878,
-0.02316521853208542,
0.04171554371714592,
0.04521952196955681,
-0.005657223518937826,
0.03057495318353176,
0.012722760438919067,
-0.052222587168216705,
-0.002591643249616027,
-0.047709718346595764,
-0.006339937448501587,
-0.01811150088906288,
-0.0006100264727137983,
-0.05803440511226654,
-0.03037288784980774,
-0.04306668043136597,
0.03707461804151535,
-0.03487614169716835,
0.02490735799074173,
-0.007545826956629753,
-0.027067502960562706,
-0.03279838338494301,
0.01201699674129486,
0.0017444792902097106,
0.00045897389645688236,
0.006818908266723156,
0.04803062230348587,
-0.005682592745870352,
-0.028003768995404243,
0.04155787080526352,
-0.03310885652899742,
0.012981484644114971,
0.010059770196676254,
0.007380778901278973,
0.012720874510705471,
-0.003630503313615918,
-0.022149773314595222,
0.027313143014907837,
-0.05198923498392105,
0.03232242166996002,
0.009588921442627907,
0.010374220088124275,
0.018502527847886086,
-0.02988918125629425,
-0.03223422169685364,
-0.012098655104637146,
-0.016013093292713165,
0.0007747734198346734,
-0.030217068269848824,
0.0352080799639225,
0.02422095276415348,
0.004282190464437008,
-0.04294709861278534,
-0.04827221855521202,
0.02749808505177498,
0.017773114144802094,
-0.06376520544290543,
0.013304696418344975,
-0.0333557054400444,
0.005753583274781704,
-0.024748168885707855,
-0.010889383964240551,
0.049587979912757874,
-0.06632083654403687,
-0.036446329206228256,
0.04003883898258209,
0.0264072734862566,
0.05125932767987251,
-0.018249334767460823,
-0.011426763609051704,
-0.0014691060641780496,
0.020230870693922043,
0.006122801918536425,
-0.02231491170823574,
0.051214322447776794,
-0.024153949692845345,
-0.030169177800416946,
-0.02371533215045929,
0.013179284520447254,
0.03597741946578026,
-0.01578610949218273,
0.010411294177174568,
0.011690727435052395,
0.0178303774446249,
0.013385644182562828,
-0.01426040381193161,
-0.025787081569433212,
-0.015911532565951347,
0.042875487357378006,
0.005503450520336628,
0.011344892904162407,
0.00817731861025095,
-0.0037279846146702766,
0.03645819053053856,
-0.02297147922217846,
-0.0005384021787904203,
0.0527488999068737,
0.02343483455479145,
-0.014379431493580341,
0.02861565165221691,
0.02011098526418209,
-0.03157084062695503,
0.04554382711648941,
0.0000368606997653842,
0.01742248237133026,
0.009315933100879192,
-0.005132933612912893,
-0.014369175769388676,
-0.003587699495255947,
-0.057833243161439896,
0.013406186364591122,
0.03354619815945625,
0.005818913225084543,
0.03156791254878044,
-0.025052161887288094,
-0.04395890235900879,
0.03333364799618721,
-0.01681545376777649,
-0.003349324921146035,
-0.016027458012104034,
-0.004167017061263323,
0.05099072307348251,
-0.07782769948244095,
-0.0246562622487545,
0.04607005789875984,
0.04367579147219658,
-0.03779538720846176,
0.00882120244204998,
0.02893636003136635,
-0.008644478395581245,
0.01588887721300125,
-0.006942623294889927,
-0.0026681364979594946,
0.04284216836094856,
-0.020660510286688805,
0.025317160412669182,
0.045557357370853424,
-0.0052696531638503075,
0.023732177913188934,
0.007321679964661598,
0.007822345942258835,
-0.025538908317685127,
-0.015565463341772556,
-0.048120640218257904,
0.025437131524086,
0.016841987147927284,
-0.039607804268598557,
-0.001924207666888833,
-0.023270847275853157,
0.053751882165670395,
-0.008056334219872952,
0.02642149105668068,
0.011197024025022984,
-0.04459525644779205,
-0.039272669702768326,
-0.019564080983400345,
-0.012073989026248455,
0.012743351049721241,
-0.06847066432237625,
-0.04779282957315445,
0.03500135987997055,
-0.037074003368616104,
0.04177502542734146,
-0.015254439786076546,
0.0527786910533905,
-0.032972682267427444,
0.04626733064651489,
-0.009145147167146206,
0.028642622753977776,
-0.022252801805734634,
-0.03746826574206352,
0.11675084382295609,
0.06630241870880127,
-0.019163228571414948,
-0.06754281371831894,
-0.009563186205923557,
0.0359162762761116,
0.046049971133470535,
-0.009710232727229595,
0.02604440599679947,
0.00233310810290277,
0.0017226483905687928,
0.0013352242531254888,
0.0866488590836525,
0.0037905098870396614,
0.04042815417051315,
0.01774676702916622,
-0.05331287533044815,
-0.07798173278570175,
0.01903371512889862,
0.04083539545536041,
-0.025077011436223984,
0.012772256508469582,
-0.07690812647342682,
0.016703004017472267,
0.012971235439181328,
0.017695117741823196,
-0.015987928956747055,
-0.012594571337103844,
0.03042391873896122,
0.012353879399597645,
-0.017735477536916733,
0.025904320180416107,
0.016826000064611435,
-0.0009912061505019665,
-0.00015752273611724377,
0.022979360073804855,
0.017955446615815163,
-0.019524212926626205,
0.023804789409041405,
0.07136087864637375,
-0.02209930494427681,
-0.02169385552406311,
0.021377546712756157,
0.02115175500512123,
-0.03242062032222748,
-0.01607678271830082,
-0.021797630935907364,
0.051021285355091095,
-0.0064012352377176285,
-0.0012273284373804927,
-0.00516401045024395,
0.008489717729389668,
0.01332141924649477,
-0.010853112675249577,
-0.008838040754199028,
-0.0004739072173833847,
0.03586646541953087,
-0.054935015738010406,
-0.015228909440338612,
-0.03815055266022682,
0.020717956125736237,
-0.023341748863458633,
0.022901015356183052,
0.004030914045870304,
0.007692631799727678,
0.033317890018224716,
-0.04306808486580849,
0.03942592442035675,
0.00045913137728348374,
-0.0065050190314650536,
-0.020998530089855194,
0.016093241050839424,
-0.015069588087499142,
-0.03529835864901543,
0.002483035670593381,
0.004223879426717758,
0.03990275412797928,
-0.006086661014705896,
0.0022758105769753456,
-0.039203595370054245,
-0.044866375625133514,
0.054567188024520874,
-0.05905408412218094,
-0.037023190408945084,
-0.01165885291993618,
-0.011934883892536163,
0.03561396151781082,
0.0732073187828064,
0.011136623099446297,
-0.01737877167761326,
-0.04241195693612099,
0.06423607468605042,
0.015407842583954334,
-0.025356069207191467,
-0.028056662529706955,
0.033039212226867676,
-0.03246279060840607,
0.003197643207386136,
-0.0044278292916715145,
0.03407596796751022,
0.038350291550159454,
-0.01281192246824503,
-0.003650262951850891,
0.030198851600289345,
0.035782333463430405,
-0.03323976323008537,
0.026463354006409645,
-0.03150394931435585,
0.026642467826604843,
0.03229643777012825,
-0.006621437147259712,
-0.010252479463815689,
-0.005814501084387302,
-0.01612204872071743,
0.0011087304446846247,
-0.005271664820611477,
0.031382229179143906,
-0.0330665148794651,
0.00739259785041213,
-0.013596762903034687,
0.04099974408745766,
-0.006840257439762354,
0.008343309164047241,
-0.04331770911812782,
0.018271153792738914,
0.025309396907687187,
-0.011280638165771961,
-0.01119473110884428,
0.023808563128113747,
-0.0005557360709644854,
-0.005973557475954294,
-0.03374125063419342,
-0.0018922671442851424,
-0.016853276640176773,
-0.018040550872683525,
-0.03195284307003021,
0.014260286465287209,
0.02937363088130951,
-0.00417990842834115,
0.02321241796016693,
0.014195508323609829,
-0.07528578490018845,
-0.062266431748867035,
0.026693090796470642,
0.004957932513207197,
0.03663356974720955,
0.028524911031126976,
-0.0046804193407297134,
-0.034649986773729324,
0.01976853609085083,
0.005674183368682861,
-0.021662911400198936,
-0.02009063959121704,
-0.0057816156186163425,
-0.010997581295669079,
-0.0012603375362232327,
0.01403363049030304,
0.009021979756653309,
0.00791977159678936,
0.005568956024944782,
0.015481388196349144,
-0.018273362889885902,
-0.0017377686453983188,
-0.03967229276895523,
0.015677016228437424,
0.04557007923722267,
-0.00238338322378695,
0.010628842748701572,
0.030960939824581146,
0.03491559252142906,
-0.045391686260700226,
-0.01219215802848339,
-0.013599767349660397,
0.005489526316523552,
-0.08091708272695541,
-0.016535431146621704,
-0.028878748416900635,
-0.025212682783603668,
0.022555485367774963,
-0.05809098109602928,
0.05600352957844734,
0.03310362622141838,
-0.03394632413983345,
0.013258621096611023,
0.003292044159024954,
-0.008386215195059776,
0.00481308763846755,
-0.012071261182427406,
-0.006198018789291382,
0.08113128691911697,
0.05122753605246544,
0.023704200983047485,
0.00035953655606135726,
-0.0022896057926118374,
0.014658643864095211,
0.02060113660991192,
-0.03895057737827301,
0.017438821494579315,
-0.02865837700664997,
-0.07836189866065979,
0.08569128811359406,
-0.025952016934752464,
-0.024256154894828796,
0.019046416506171227,
0.0007942965603433549,
-0.015855900943279266,
0.010644936934113503,
-0.004310084506869316,
0.01900920458137989,
-0.00042348334682174027,
0.042596232146024704,
-0.0019998964853584766,
0.00021897089027334005,
-0.0029652041848748922,
-0.012673841789364815,
0.014671184122562408,
0.01482989639043808,
0.03160247951745987,
0.016951020807027817,
-0.05475578084588051,
-0.012329677119851112,
0.013892898336052895,
-0.020049763843417168,
-0.06597234308719635,
-0.0099909333512187,
-0.017266005277633667,
0.06042732298374176,
-0.006724073551595211,
0.025500085204839706,
-0.04608917608857155,
0.010790507309138775,
0.05384625494480133,
-0.010230990126729012,
0.02167936973273754,
0.05454787239432335,
-0.007369607221335173,
-0.025702713057398796,
-0.005350417457520962,
0.016502859070897102,
-0.02396058477461338,
-0.04937442019581795,
-0.010959704406559467,
0.01208613533526659,
0.009103290736675262,
-0.029092276468873024,
-0.011109049431979656,
-0.006797729525715113,
0.020970596000552177,
0.03532346710562706,
0.010090485215187073,
-0.040872860699892044,
-0.027433140203356743,
-0.0006993149872869253,
-0.037788961082696915,
0.000008425238775089383,
0.03960062190890312,
-0.024454645812511444,
-0.021007178351283073,
-0.009333115071058273,
0.024516088888049126,
0.056802429258823395,
0.031081151217222214,
0.010540606454014778,
-0.02894991636276245,
0.015109444968402386,
-0.0044298600405454636,
0.04073648527264595,
-0.054023973643779755,
-0.010811829939484596,
0.002837975975126028,
0.00964516494423151,
0.019124189391732216,
-0.011611520312726498,
0.0012829446932300925,
0.048726316541433334,
0.020623434334993362,
-0.004375020042061806,
-0.010286130011081696,
0.0018978245789185166,
-0.058699946850538254,
0.045294519513845444,
0.01628372259438038,
-0.000905607535969466,
0.06735868006944656,
-0.001331694540567696,
-0.00033921076101250947,
0.023115644231438637,
-0.04118987172842026,
0.0021315407939255238,
0.02846253290772438,
-0.02321687899529934,
-0.02028539776802063,
0.016662079840898514,
-0.03801022842526436,
-0.00957200676202774,
-0.04655895754694939,
0.004757323767989874,
0.04074971750378609,
-0.0038270417135208845,
-0.04394463822245598,
0.05994098260998726,
0.027286631986498833,
0.01885310746729374,
0.036393601447343826,
-0.01312617864459753,
-0.005741526838392019,
-0.03974081203341484,
0.02283068560063839,
0.05049740895628929,
0.03283824399113655,
0.027693334966897964,
-0.015165894292294979,
-0.006187196355313063,
0.013014094904065132,
0.014744887128472328,
0.0060994732193648815,
0.03898891806602478,
-0.006068960297852755,
-0.007339643780142069,
0.017495058476924896,
0.00015301902021747082,
0.006921514868736267,
0.022219130769371986,
-0.009432553313672543,
0.07358036190271378,
-0.03772488981485367,
0.003918844275176525,
-0.014487504959106445,
0.01599848084151745,
-0.015645399689674377,
0.02136664092540741,
0.02543792687356472,
0.04254193231463432,
-0.05118788406252861,
-0.02162466011941433,
-0.006333052180707455,
-0.008868838660418987,
0.03580605611205101,
-0.03162740170955658,
0.010712660849094391,
0.035614319145679474,
0.0013030124828219414,
0.0010688361944630742,
-0.03191427141427994,
0.002153891371563077,
0.04338458552956581,
0.021066782996058464,
0.040029559284448624,
-0.008161785081028938,
-0.0007472711149603128,
-0.03621416166424751,
-0.016332417726516724,
-0.011285782791674137,
-0.08165416866540909,
0.006015081889927387,
-0.011926661245524883,
-0.006886450573801994,
-0.013294583186507225,
0.0095041673630476
] |
<p>Is there a manageable formula or set of formulas or simple algorithms that approximate stellar luminosity and effective temperature (or radius) as a function of stellar age?</p>
<p>I'm aware that accurate modeling of these attributes is complex and is determined by many factors; what I'm looking for is something that serves as a decent approximation of the sort used in numerous illustrations or applets that show example "paths" taken by representative stars as they trace their evolution across the H-R diagram.</p> | 604 | [
-0.01934962347149849,
-0.05019007623195648,
0.0005698702880181372,
-0.001273358124308288,
0.06224604696035385,
-0.028036784380674362,
-0.04924231767654419,
-0.017747677862644196,
0.003283815225586295,
-0.03960082307457924,
0.042330704629421234,
0.010807152837514877,
0.05672741308808327,
0.008907275274395943,
0.024494405835866928,
-0.014639063738286495,
0.024985775351524353,
-0.0234901774674654,
-0.011285223066806793,
-0.004536530468612909,
0.011792011559009552,
-0.007554185576736927,
0.011285326443612576,
-0.01796484738588333,
-0.044200729578733444,
0.05367357283830643,
0.026421761140227318,
-0.020563799887895584,
-0.004363494925200939,
0.061399415135383606,
-0.0019028688548132777,
-0.009646814316511154,
0.07225314527750015,
0.06472877413034439,
0.03267216682434082,
-0.0028601055964827538,
-0.015774188563227654,
-0.010847616009414196,
-0.0494864284992218,
0.024807972833514214,
-0.07615267485380173,
-0.018989993259310722,
0.017410146072506905,
0.005064213648438454,
0.04572531208395958,
-0.0069616371765732765,
-0.036587294191122055,
-0.0097705302760005,
0.0709134191274643,
-0.044841863214969635,
0.060962289571762085,
0.021405884996056557,
0.060708675533533096,
0.03933392092585564,
-0.04065335541963577,
0.0021126088686287403,
0.06300123780965805,
0.07373356074094772,
0.003864897647872567,
-0.03780869022011757,
-0.021794859319925308,
0.01723741739988327,
-0.0162090715020895,
-0.05008712038397789,
-0.024715129286050797,
0.015549332834780216,
-0.024055631831288338,
-0.027936600148677826,
0.03684120625257492,
0.007629863452166319,
0.028171047568321228,
0.009517114609479904,
0.02634468302130699,
0.005447373725473881,
0.024675097316503525,
-0.03804071247577667,
-0.003674362786114216,
0.00659091304987669,
0.03435270115733147,
0.03405734896659851,
-0.03147968649864197,
0.0294931773096323,
0.0377843864262104,
0.023309117183089256,
-0.01221424713730812,
0.00968837272375822,
0.07188120484352112,
-0.01871957816183567,
0.005056311842054129,
-0.008008802309632301,
-0.01869453303515911,
0.030633142217993736,
0.07739729434251785,
-0.0085065932944417,
-0.025547323748469353,
0.02077222615480423,
-0.014792045578360558,
0.023260341957211494,
-0.011345773935317993,
-0.0030802127439528704,
0.006831963546574116,
-0.025981884449720383,
0.02669096365571022,
0.052852753549814224,
-0.008453263901174068,
-0.050894346088171005,
-0.026741566136479378,
-0.04290061444044113,
0.00036678859032690525,
-0.012083766050636768,
-0.006431779824197292,
0.009735285304486752,
-0.0009001137805171311,
0.015789717435836792,
0.025817004963755608,
-0.040634676814079285,
-0.014761898666620255,
-0.024160264059901237,
0.04289529100060463,
0.04172983393073082,
0.01979226805269718,
-0.031814783811569214,
0.05856959894299507,
-0.018264267593622208,
-0.04524807631969452,
0.045197807252407074,
-0.0026003627572208643,
-0.01660664565861225,
-0.03540651872754097,
0.02879651077091694,
0.0007390532409772277,
-0.05687455087900162,
0.03908697888255119,
-0.019493799656629562,
0.019882403314113617,
-0.019182849675416946,
-0.05963463336229324,
-0.060845427215099335,
-0.0010787317296490073,
-0.01373137068003416,
0.0004994368064217269,
-0.031511228531599045,
0.03727399557828903,
0.04443313181400299,
0.07801344245672226,
0.010200838558375835,
-0.031719207763671875,
0.007072011474519968,
0.0729510635137558,
-0.0244956836104393,
-0.052712708711624146,
-0.02522631175816059,
-0.009693766944110394,
-0.021033355966210365,
-0.010119129903614521,
-0.09712124615907669,
0.022888312116265297,
0.023923924192786217,
-0.036412108689546585,
-0.013849545270204544,
0.08088457584381104,
-0.02387734316289425,
0.00492824986577034,
0.021378900855779648,
0.04929105192422867,
-0.031949132680892944,
0.08152074366807938,
0.011454777792096138,
-0.012500246986746788,
0.03011024370789528,
-0.01949716918170452,
-0.003917836584150791,
0.026824984699487686,
0.01875011809170246,
0.065719835460186,
0.011615213006734848,
-0.006432530470192432,
-0.023312434554100037,
-0.014437141828238964,
0.034567274153232574,
-0.025936279445886612,
-0.061446305364370346,
-0.020607538521289825,
-0.04945199936628342,
0.04957825317978859,
0.026569657027721405,
0.0009497266728430986,
0.002779235364869237,
0.04232881963253021,
-0.03054279088973999,
-0.009372258558869362,
-0.06202401593327522,
-0.00282677193172276,
0.010095122270286083,
-0.00032320807804353535,
0.0012846441240981221,
0.020764125511050224,
0.022752152755856514,
0.005554551258683205,
-0.05036323145031929,
-0.01386778149753809,
0.010098087601363659,
0.01950887218117714,
-0.026291102170944214,
0.027475016191601753,
0.07540667057037354,
0.05739094316959381,
-0.025108113884925842,
0.038367513567209244,
-0.05251412093639374,
-0.0616808719933033,
-0.011424830183386803,
-0.031699687242507935,
0.02437661960721016,
-0.035052765160799026,
-0.0000016189826510526473,
-0.013098075054585934,
-0.015165560878813267,
0.03744087740778923,
-0.01603425107896328,
-0.023928938433527946,
0.048714835196733475,
0.012525429017841816,
0.04026283696293831,
0.0016060795169323683,
0.0674758180975914,
-0.013229643926024437,
0.024944841861724854,
-0.01126885786652565,
-0.013956750743091106,
-0.03713303431868553,
-0.010219128802418709,
0.0598275326192379,
0.02563578262925148,
-0.03852473571896553,
0.017567478120326996,
0.04604440554976463,
0.023859912529587746,
0.05151059851050377,
0.012658113613724709,
-0.05456449091434479,
0.00031777206459082663,
-0.010301253758370876,
-0.021359529346227646,
0.011346378363668919,
0.01730111613869667,
0.0002947885950561613,
0.055976349860429764,
0.006042782217264175,
-0.015687638893723488,
-0.028713449835777283,
0.02614777348935604,
0.013376499526202679,
-0.008997741155326366,
-0.033810362219810486,
-0.04776020720601082,
0.05519745126366615,
-0.023581745103001595,
-0.007790875155478716,
0.030525419861078262,
-0.0027015332598239183,
0.025468280538916588,
-0.021724002435803413,
0.012729471549391747,
0.01047224085777998,
0.030692782253026962,
-0.0012964628404006362,
0.003428438678383827,
0.009359698742628098,
0.0011935963993892074,
0.05176497995853424,
-0.05329617112874985,
0.005424714181572199,
-0.033522170037031174,
-0.008834490552544594,
0.01540957298129797,
0.009385944344103336,
-0.0074190180748701096,
-0.021858414635062218,
-0.02130143530666828,
-0.006921038962900639,
-0.007272057700902224,
0.002435015980154276,
0.029353072866797447,
-0.032017096877098083,
-0.010853548534214497,
0.011509347707033157,
-0.04031725600361824,
0.01824331097304821,
0.0010139624355360866,
-0.027454286813735962,
-0.0016570029547438025,
0.019998205825686455,
-0.06816361844539642,
0.0002172785170841962,
-0.005200170446187258,
-0.02657591737806797,
-0.03154602274298668,
0.04851706326007843,
0.008312657475471497,
-0.0046485248021781445,
-0.05179942399263382,
0.023132363334298134,
-0.04975561052560806,
-0.04314053803682327,
-0.03449112921953201,
0.013357341289520264,
0.004542296286672354,
-0.025941813364624977,
0.023574961349368095,
0.07925151288509369,
-0.026386413723230362,
0.0037748699542135,
-0.04195522889494896,
-0.03864404931664467,
0.034476932138204575,
-0.002234889892861247,
0.032845597714185715,
0.014838955365121365,
0.015572766773402691,
0.04162892326712608,
0.01913238875567913,
-0.011944686993956566,
-0.04504178836941719,
0.011643133126199245,
-0.0007926946855150163,
0.005063745193183422,
0.026033727452158928,
0.002725403755903244,
-0.017090635374188423,
-0.019645681604743004,
-0.008289141580462456,
-0.009101558476686478,
0.05164846405386925,
0.022806279361248016,
0.03038538619875908,
0.036702319979667664,
-0.014893440529704094,
-0.00854585226625204,
0.039752233773469925,
0.0023182120639830828,
-0.001400762819685042,
0.03676346316933632,
-0.020445192232728004,
0.06375734508037567,
0.036893803626298904,
-0.04862784594297409,
0.025887349620461464,
-0.026216063648462296,
-0.017391178756952286,
-0.0017224099719896913,
-0.004538242239505053,
0.008760021068155766,
-0.00023755493748467416,
-0.00022142076340969652,
0.03324843943119049,
0.01174931786954403,
0.0024790908209979534,
-0.0202430821955204,
0.016717849299311638,
0.026007696986198425,
0.001937398104928434,
-0.001147282775491476,
0.01918034441769123,
-0.033258311450481415,
0.02408810332417488,
-0.029797565191984177,
0.013909108005464077,
0.06900010257959366,
0.03238973394036293,
0.005285558756440878,
0.0019827119540423155,
-0.0386478565633297,
0.021371817216277122,
-0.10164882987737656,
-0.03880143538117409,
-0.05846777185797691,
0.06401918828487396,
0.0012295290362089872,
0.009035555645823479,
0.001300800940953195,
0.01594243012368679,
0.04992701858282089,
0.00011200491280760616,
-0.09587981551885605,
0.04487302154302597,
-0.036496005952358246,
-0.02241908200085163,
-0.021108709275722504,
0.016686787828803062,
-0.004508777987211943,
-0.03112684190273285,
-0.02742936834692955,
-0.0012282893294468522,
0.015485362149775028,
0.006434308830648661,
0.0026537810917943716,
-0.009995058178901672,
-0.02213832177221775,
-0.012584256939589977,
0.016837310045957565,
0.041293829679489136,
-0.023707780987024307,
0.06330686807632446,
0.029071008786559105,
0.00003910197119694203,
-0.03714291751384735,
-0.05026286095380783,
0.03624138981103897,
-0.0018048303900286555,
0.029550496488809586,
0.046984508633613586,
0.02107410319149494,
-0.04044457897543907,
0.005211370997130871,
0.022364767268300056,
0.02749159000813961,
0.02483871951699257,
-0.005558812525123358,
0.0035859541967511177,
-0.03528662025928497,
-0.000041803923522820696,
0.05882297083735466,
0.03200798109173775,
-0.04907653108239174,
0.033449821174144745,
0.02875775657594204,
-0.007320419419556856,
-0.015487199649214745,
0.01814051903784275,
0.05673409253358841,
0.004892219789326191,
-0.02391764707863331,
-0.01860593818128109,
0.0039601074531674385,
0.0006105454522185028,
0.004508365876972675,
0.024699337780475616,
0.04866940155625343,
0.004877363331615925,
-0.02670416049659252,
-0.002403808059170842,
-0.0005708575481548905,
-0.04712837189435959,
-0.0065181320533156395,
0.0012059893924742937,
0.04171723872423172,
-0.03633970022201538,
-0.0068572452291846275,
0.02298358455300331,
0.050740499049425125,
0.03351328521966934,
-0.014588122256100178,
0.014255165122449398,
-0.08010794967412949,
-0.008355746045708656,
0.02458006702363491,
0.025822218507528305,
0.01506703719496727,
-0.03729959577322006,
-0.0688944086432457,
-0.021341057494282722,
0.06044319272041321,
-0.010427667759358883,
0.013785657472908497,
0.0017236736603081226,
-0.016600897535681725,
0.0048104845918715,
-0.03568959981203079,
0.000605426961556077,
0.012386860325932503,
-0.012948095798492432,
0.013136092573404312,
-0.03191651403903961,
0.031590383499860764,
-0.009133524261415005,
0.04249327629804611,
0.01637907885015011,
0.0255015529692173,
-0.0022984452079981565,
-0.032470718026161194,
-0.0025755474343895912,
-0.013086717575788498,
-0.012478381395339966,
-0.06593763083219528,
-0.02686488814651966,
0.0027242121286690235,
-0.0064715235494077206,
0.04778529331088066,
-0.020862426608800888,
-0.03059917502105236,
0.06157270073890686,
0.008637819439172745,
-0.03226093575358391,
-0.00689507694914937,
-0.01707778312265873,
0.03179892152547836,
0.009700561873614788,
0.017907140776515007,
0.07071932405233383,
0.06407257914543152,
-0.01104552112519741,
0.006261914502829313,
-0.028818124905228615,
0.008200128562748432,
-0.0011536858510226011,
-0.012015165761113167,
-0.04751259461045265,
-0.013186579570174217,
-0.022654173895716667,
0.029294723644852638,
-0.02256893552839756,
0.027667496353387833,
-0.017535153776407242,
-0.0021032970398664474,
0.011428462341427803,
0.021376218646764755,
-0.02000463753938675,
-0.008336205035448074,
0.029475262388586998,
0.03183729201555252,
0.016273055225610733,
-0.004013304598629475,
0.06275764107704163,
0.01395004615187645,
0.010788238607347012,
0.015467623248696327,
-0.030076000839471817,
0.029253603890538216,
-0.01887497678399086,
-0.014008876867592335,
0.009961206465959549,
-0.02976861037313938,
0.06483414769172668,
-0.04236685112118721,
0.07156948000192642,
0.0681435763835907,
-0.03848537802696228,
-0.004259683191776276,
-0.016129078343510628,
-0.020756199955940247,
0.038890838623046875,
-0.005832478404045105,
-0.008742447011172771,
-0.03223545104265213,
-0.03541571646928787,
-0.072785384953022,
0.01807994395494461,
0.009838257916271687,
0.0052304742857813835,
-0.05195885896682739,
-0.03570033237338066,
0.019142495468258858,
-0.014625550247728825,
-0.00021633316646330059,
0.009644582867622375,
0.04975064471364021,
-0.004400263074785471,
-0.00813639722764492,
-0.017253901809453964,
0.02908293344080448,
0.051073089241981506,
0.02234695851802826,
0.03174085170030594,
0.006919870153069496,
-0.006775914691388607,
-0.011307081207633018,
0.02170071005821228,
0.04061659798026085,
-0.02123219333589077,
-0.039691973477602005,
-0.030845744535326958,
0.02046876959502697,
0.01803317293524742,
-0.024728922173380852,
0.009617729112505913,
0.01961589977145195,
-0.01058055181056261,
-0.00254442123696208,
-0.006143415812402964,
0.031173555180430412,
-0.034461043775081635,
0.001966770738363266,
-0.03271200880408287,
-0.013936186209321022,
0.013999096117913723,
0.015339656732976437,
0.022036882117390633,
-0.029938954859972,
0.03444220498204231,
0.026180163025856018,
0.03790200129151344,
-0.008222422562539577,
-0.011956971138715744,
0.022301387041807175,
0.006152176298201084,
0.0057959710247814655,
0.013686684891581535,
-0.015105603262782097,
0.006290731951594353,
-0.03034132532775402,
-0.040483009070158005,
-0.03687579557299614,
-0.05349082499742508,
-0.004146192688494921,
0.07836348563432693,
-0.034715574234724045,
0.05656340345740318,
-0.00017444642435293645,
0.010965713299810886,
0.016199136152863503,
-0.04346015304327011,
-0.030326614156365395,
0.004571635741740465,
-0.02771657146513462,
0.07266473025083542,
-0.016954051330685616,
-0.009180793538689613,
0.02137162908911705,
-0.006982889492064714,
-0.009968380443751812,
0.03447280824184418,
0.00647734384983778,
0.03228491172194481,
0.01646803505718708,
-0.03209591656923294,
-0.006912015378475189,
0.02500920742750168,
-0.04158354178071022,
-0.007062186487019062,
-0.0017160383285954595,
0.034481991082429886,
0.04085299000144005,
0.0027645304799079895,
0.008442082442343235,
-0.02973022684454918,
-0.025785719975829124,
-0.02284138649702072,
-0.005929919891059399,
0.037961408495903015,
0.008013494312763214,
0.004340370185673237,
0.04285543039441109,
0.001078663277439773,
-0.01432123500853777,
0.024861318990588188,
-0.010208677500486374,
-0.04135427251458168,
-0.015655450522899628,
-0.020785661414265633,
-0.06256446987390518,
0.014865566045045853,
0.027226194739341736,
-0.04360995069146156,
0.014998356811702251,
0.01691965013742447,
-0.013614371418952942,
-0.001347843324765563,
0.021927768364548683,
-0.001589674036949873,
0.0686684399843216,
-0.033681660890579224,
-0.013158229179680347,
-0.026474108919501305,
0.021607330068945885,
0.11796875298023224,
0.06259375810623169,
0.02418832667171955,
-0.06428639590740204,
0.009933652356266975,
-0.01233656145632267,
-0.011920630931854248,
-0.03172347694635391,
0.026623966172337532,
-0.02347620576620102,
-0.008981021121144295,
0.01582159660756588,
0.019177036359906197,
0.007576668169349432,
-0.01918387971818447,
0.025415215641260147,
-0.027665821835398674,
0.0352698378264904,
0.01501799188554287,
0.017969554290175438,
-0.002080520149320364,
0.0529356487095356,
-0.05595889315009117,
0.009457161650061607,
-0.012983902357518673,
-0.0010573347099125385,
-0.017399046570062637,
-0.03745473921298981,
0.024713516235351562,
-0.004752814304083586,
-0.08321112394332886,
0.03444726765155792,
0.01751902885735035,
-0.020816626027226448,
0.019854750484228134,
-0.011550011113286018,
0.009041454643011093,
-0.012831115163862705,
0.0029709318187087774,
0.04962265491485596,
0.0390937440097332,
0.022144818678498268,
-0.011907788924872875,
0.02790839597582817,
-0.02323576807975769,
-0.023895030841231346,
-0.055517226457595825,
0.04136081039905548,
0.0034755016677081585,
-0.004992857109755278,
-0.01292460411787033,
0.006658304948359728,
-0.0012136605801060796,
-0.038513876497745514,
0.019481804221868515,
0.014212519861757755,
0.013515623286366463,
-0.007410428486764431,
-0.017689870670437813,
0.0029988400638103485,
0.020908601582050323,
-0.01561401505023241,
0.036718644201755524,
-0.026670075953006744,
-0.009558350779116154,
-0.016990939155220985,
-0.07432663440704346,
0.03825605288147926,
-0.00375120691023767,
-0.043663084506988525,
-0.018224483355879784,
-0.006057442165911198,
-0.035525333136320114,
-0.0009414255619049072,
-0.0009933762485161424,
0.015624315477907658,
0.032108500599861145,
0.018878266215324402,
0.00317463674582541,
-0.020112505182623863,
-0.08417448401451111,
0.008138136006891727,
-0.012872962281107903,
-0.02747843787074089,
-0.027708567678928375,
-0.019742541015148163,
0.03969116136431694,
0.02600213512778282,
-0.0008615606930106878,
0.002018118277192116,
-0.02123645693063736,
0.03278971090912819,
0.014721370302140713,
-0.05780963599681854,
-0.02304479293525219,
0.008720123209059238,
-0.055695973336696625,
-0.01643027551472187,
-0.025873854756355286,
0.06030140817165375,
0.015127395279705524,
-0.0017041151877492666,
-0.009661899879574776,
0.04029574617743492,
-0.00008668456575833261,
0.03150658681988716,
-0.03929520025849342,
-0.0342462882399559,
0.02624703198671341,
-0.06635358184576035,
0.01660742610692978,
-0.021120158955454826,
-0.02717512845993042,
-0.033809490501880646,
-0.033588409423828125,
-0.01298604253679514,
-0.01391152199357748,
-0.0418817512691021,
0.053789831697940826,
-0.032346196472644806,
-0.021462703123688698,
-0.020848851650953293,
0.019380124285817146,
-0.0006738413358107209,
0.014225324615836143,
-0.021450882777571678,
-0.016599532216787338,
0.004035918042063713,
0.028226647526025772,
0.002016104757785797,
-0.009220380336046219,
0.03596799075603485,
-0.011123355478048325,
0.027506237849593163,
0.004747008439153433,
-0.010142468847334385,
-0.024446964263916016,
0.03370314836502075,
-0.026847172528505325,
-0.03326980024576187,
-0.013383404351770878,
-0.014485110528767109,
-0.0832185223698616,
0.01808307133615017,
-0.030515078455209732,
0.02501319907605648,
0.011644680052995682,
-0.03642246127128601,
-0.024465354159474373,
0.07396209239959717,
0.011908049695193768,
-0.05143330618739128,
0.024341780692338943,
0.027356265112757683,
0.017196286469697952,
0.006875837221741676,
0.013227186165750027,
0.0024007337633520365,
-0.0068054720759391785,
0.024205589666962624,
0.01409018225967884,
-0.03369848430156708,
0.008174161426723003,
-0.007070243824273348,
0.005171249154955149,
0.011171058751642704,
-0.0017495237989351153,
-0.0003084965283051133,
0.06150561198592186,
0.0014502863632515073,
0.004600083455443382,
0.08513485640287399,
0.08110765367746353,
-0.0022440822795033455,
-0.09982957690954208,
0.005266435910016298,
-0.02308741584420204,
0.026066575199365616,
0.0316392257809639,
-0.0984729528427124,
0.03761548548936844,
0.015044555999338627,
-0.05117868632078171,
0.012849136255681515,
-0.0037943965289741755,
-0.00015625491505488753,
-0.03015127032995224,
-0.03785382956266403,
-0.02367217093706131,
0.021337274461984634,
0.0281863734126091,
0.01751314289867878,
0.0004175057401880622,
0.010080613195896149,
-0.022002890706062317,
-0.05272515118122101,
0.005055610090494156,
-0.011179993860423565,
-0.0016340218717232347,
-0.0307152196764946,
0.004564128816127777,
-0.010738913901150227,
-0.0034230216406285763,
0.020549796521663666,
0.00016219115059357136,
0.050238363444805145,
-0.015576924197375774,
-0.013707350008189678,
0.0022364177275449038,
0.023498134687542915,
0.043865449726581573,
-0.04406898468732834,
-0.019469473510980606,
0.005061826203018427,
-0.024353202432394028,
0.03802043944597244,
-0.02053322270512581,
0.021895723417401314,
0.02487294375896454,
-0.04216602072119713,
-0.011978664435446262,
0.045847658067941666,
0.006144441198557615,
0.007580463774502277,
-0.009079755283892155,
-0.03341368958353996,
-0.03528314828872681,
-0.007622694130986929,
-0.003344515571370721,
-0.043554116040468216,
0.012555123306810856,
0.03826439380645752,
0.022062325850129128,
0.019959991797804832,
-0.0024422353599220514,
-0.0037531794514507055,
-0.016834929585456848,
-0.012621895410120487,
0.0009294692426919937,
0.006160707678645849,
-0.0047845542430877686,
0.02642522193491459,
0.034508269280195236,
-0.01101305615156889,
-0.02894316241145134,
-0.017794422805309296,
-0.0651526227593422,
0.050382696092128754,
0.015425939112901688,
0.009135248139500618,
-0.0026764075737446547,
-0.032159965485334396,
-0.018560370430350304,
-0.028972934931516647,
0.03860136494040489,
-0.014486601576209068,
0.005438570864498615,
-0.01773826591670513,
-0.031038613989949226,
-0.010007764212787151,
-0.003324673743918538,
0.05426871404051781,
-0.002978747943416238,
-0.02586478367447853,
-0.01377316564321518,
0.01067732460796833,
0.0037167875561863184,
-0.05923834070563316,
0.007915493100881577,
0.015532005578279495,
-0.009606871753931046,
-0.00319838710129261,
-0.02650528959929943,
0.003778699319809675,
0.015017657540738583,
0.03368449583649635,
-0.004411774221807718,
0.009079345501959324,
0.05147603899240494,
-0.04196185991168022,
0.02486409991979599,
0.039303429424762726,
-0.012430006638169289,
0.05679246783256531,
0.001573099521920085,
-0.027609555050730705,
0.05786958336830139,
0.01242594514042139,
-0.026117214933037758,
0.0323575995862484,
-0.025560593232512474,
-0.061735738068819046,
0.020900603383779526,
-0.018160443753004074,
-0.027436302974820137,
-0.04641101881861687,
-0.0012681991793215275,
0.03650272265076637,
-0.04013577103614807,
-0.028233058750629425,
0.03723074123263359,
-0.004259489011019468,
0.056014273315668106,
-0.017057199031114578,
-0.005566707346588373,
0.05344519019126892,
-0.015621158294379711,
-0.02446676790714264,
0.0027852521743625402,
0.011492162011563778,
0.003699349006637931,
0.039121631532907486,
-0.006276375148445368,
0.030035292729735374,
0.00877318624407053,
-0.004869881551712751,
0.036669518798589706,
-0.021117260679602623,
-0.02044243924319744,
0.036605238914489746,
-0.011737868189811707,
0.042529527097940445,
0.019297774881124496,
-0.01919286884367466,
0.06811176240444183,
-0.023594869300723076,
-0.0066540976986289024,
-0.04135395586490631,
-0.006148817483335733,
-0.04012567549943924,
0.03235200047492981,
-0.0094114039093256,
0.026465019211173058,
-0.027950724586844444,
0.006499315612018108,
0.0025565887335687876,
0.03569302335381508,
0.040425390005111694,
-0.042418643832206726,
0.0012170289410278201,
0.007010957691818476,
0.017294498160481453,
-0.01639343425631523,
0.0074003287591040134,
-0.014508017338812351,
-0.013694286346435547,
-0.019612373784184456,
0.06579484790563583,
0.01498376950621605,
0.0025420114398002625,
-0.010508066974580288,
-0.011356965638697147,
0.025101127102971077,
-0.09164748340845108,
-0.008585774339735508,
-0.020513663068413734,
0.026418112218379974,
-0.014584213495254517,
-0.039280980825424194
] |
<p>String theory false vacua can be described by effective Lagrangians at low energy. Is there generally a correspondence between these effective Lagrangians and SU(N) gauge theories? Or do the effective Lagrangians often not respect local invariance with respect to some or any gauge groups? </p> | 1,465 | [
0.022685308009386063,
0.009599950164556503,
-0.007254226133227348,
-0.04800330102443695,
0.010951821692287922,
0.043788764625787735,
-0.03959858417510986,
-0.03362613916397095,
0.0015070970403030515,
-0.04944569617509842,
0.0025124275125563145,
-0.0334441214799881,
0.07308618724346161,
0.019361315295100212,
-0.00867424439638853,
0.011336117051541805,
-0.0019073267467319965,
-0.0016442456981167197,
-0.00624160235747695,
-0.030648965388536453,
-0.0030905655585229397,
0.02537345327436924,
-0.01206582598388195,
-0.002354430966079235,
0.006098172627389431,
-0.015605754218995571,
0.02240591123700142,
0.037352290004491806,
-0.004543310031294823,
0.06452517956495285,
-0.013955165632069111,
-0.019785577431321144,
0.0014992528595030308,
0.006491017993539572,
-0.039861008524894714,
0.0036438810639083385,
-0.005024007987231016,
-0.054139912128448486,
0.02044287882745266,
0.0017412872985005379,
-0.02793027088046074,
-0.031685106456279755,
-0.03833791986107826,
0.07251401245594025,
-0.027683401480317116,
0.01464733574539423,
-0.011162009090185165,
-0.011401339434087276,
0.06770039349794388,
-0.06254693120718002,
0.0681743398308754,
0.03484347090125084,
-0.014857504516839981,
0.03177983686327934,
-0.018885571509599686,
-0.00877121090888977,
0.06793027371168137,
0.05819718912243843,
-0.0005829380243085325,
-0.06425122916698456,
-0.06271643191576004,
-0.0398210734128952,
0.010828875005245209,
-0.04250749200582504,
-0.005802277009934187,
0.00485767237842083,
0.023904195055365562,
-0.0023549888283014297,
-0.015279240906238556,
0.0184470321983099,
-0.02175363153219223,
0.013675973750650883,
0.009019997902214527,
0.015392668545246124,
0.02833164855837822,
-0.004973325878381729,
0.0004190692852716893,
-0.023579498752951622,
0.02268592081964016,
0.025273075327277184,
-0.011212218552827835,
0.019706174731254578,
0.031100215390324593,
0.030410803854465485,
-0.01741686463356018,
-0.010141273029148579,
0.07551872730255127,
-0.022094914689660072,
-0.005308140534907579,
0.02199035882949829,
-0.03559073805809021,
-0.0071902102790772915,
0.04854549095034599,
-0.0226876400411129,
-0.036472246050834656,
0.021812357008457184,
0.03243947774171829,
0.05674624443054199,
0.011296621523797512,
0.004827430471777916,
-0.03866823390126228,
-0.008560913614928722,
0.004200330004096031,
0.08901885151863098,
0.030242111533880234,
-0.06021096557378769,
-0.032020095735788345,
0.005068048369139433,
-0.03400827944278717,
-0.0051374793983995914,
-0.03082224167883396,
-0.01176630798727274,
-0.025817852467298508,
-0.016966061666607857,
0.0076626078225672245,
-0.020150141790509224,
-0.007411296479403973,
-0.04182981327176094,
0.058426596224308014,
0.05855853483080864,
0.06520233303308487,
0.01074312999844551,
0.026233311742544174,
-0.00167365453671664,
-0.023325283080339432,
-0.016424544155597687,
0.05778574198484421,
0.0021875740494579077,
-0.045451339334249496,
-0.009775703772902489,
0.03768105432391167,
-0.054794792085886,
0.0016926428070291877,
-0.027130112051963806,
0.06906935572624207,
0.0038926100824028254,
-0.09640342742204666,
-0.03681868314743042,
0.035575926303863525,
0.014185905456542969,
-0.001196090946905315,
-0.03607305511832237,
-0.011459571309387684,
0.031582560390233994,
0.05942850559949875,
-0.029025563970208168,
0.002912017982453108,
0.029128005728125572,
0.012403649277985096,
-0.024214444682002068,
0.000744957709684968,
-0.007163878995925188,
0.006180466152727604,
-0.052900530397892,
-0.007752370089292526,
-0.020533272996544838,
0.038331206887960434,
0.021415511146187782,
-0.011044790968298912,
-0.019771084189414978,
0.102988101541996,
-0.03335585817694664,
0.03769990801811218,
0.01751599833369255,
0.021329624578356743,
0.015164305455982685,
0.061455558985471725,
-0.013493645936250687,
0.002225136384367943,
0.025223201140761375,
-0.03898744285106659,
0.0052042496390640736,
0.05254819989204407,
0.04599171504378319,
0.057277098298072815,
-0.0175800584256649,
-0.00582495192065835,
0.009056203998625278,
0.010639181360602379,
0.031239889562129974,
-0.03620346635580063,
-0.013462111353874207,
-0.014715814031660557,
-0.009722786955535412,
-0.04584693908691406,
0.00837294477969408,
-0.03753598406910896,
-0.05291186645627022,
-0.011801649816334248,
-0.02437998540699482,
0.005885368678718805,
-0.05858563259243965,
-0.004832420032471418,
0.007712263148277998,
0.021989798173308372,
0.03254733607172966,
0.05515021085739136,
-0.027271917089819908,
-0.03421714901924133,
-0.02799927443265915,
-0.03609495237469673,
0.03729069232940674,
-0.023312747478485107,
0.013966826722025871,
0.020182110369205475,
-0.004039067775011063,
0.021863587200641632,
-0.03996599093079567,
0.0558355338871479,
-0.04203067347407341,
-0.05304471403360367,
0.011504570953547955,
-0.012938352301716805,
0.038068585097789764,
0.00215738033875823,
0.013819401152431965,
0.003192764474079013,
-0.029422709718346596,
-0.03454923629760742,
0.054914578795433044,
-0.05936746299266815,
0.031710948795080185,
0.01376216858625412,
0.010577472858130932,
0.0008649490191601217,
0.018407801166176796,
-0.006487918086349964,
0.020184651017189026,
0.022508390247821808,
-0.04468073695898056,
-0.042074959725141525,
-0.02996682934463024,
0.027433887124061584,
0.06472819298505783,
-0.0104047991335392,
0.026775585487484932,
0.014015480875968933,
0.026285894215106964,
0.01034289039671421,
0.006246617529541254,
-0.03223998099565506,
-0.05004753917455673,
0.03791727498173714,
0.021467838436365128,
-0.009005275554955006,
0.006426207721233368,
0.001500084763392806,
0.02222813479602337,
0.011653933674097061,
-0.01669805310666561,
-0.028286119922995567,
0.029794825240969658,
-0.0003471800300758332,
0.013579124584794044,
0.01364080049097538,
-0.030615100637078285,
0.030837034806609154,
-0.001004106248728931,
0.04410520941019058,
-0.0008479386451654136,
0.0008798115304671228,
0.02210201509296894,
-0.01267671026289463,
-0.024875139817595482,
0.035600267350673676,
-0.006950762122869492,
-0.003307175822556019,
-0.007388673722743988,
0.026197237893939018,
-0.045532889664173126,
0.012934431433677673,
-0.04330870136618614,
0.014334926381707191,
0.020973358303308487,
0.054043304175138474,
0.02074451744556427,
-0.017557883635163307,
0.016060899943113327,
-0.03690357506275177,
-0.026149891316890717,
0.02995450235903263,
-0.02405441738665104,
0.02311547100543976,
0.0503341369330883,
-0.017263183370232582,
0.022511832416057587,
-0.07223771512508392,
-0.012784382328391075,
0.042829521000385284,
-0.01000192016363144,
0.021119767799973488,
0.026516789570450783,
-0.030352693051099777,
-0.0376763679087162,
0.000045131935621611774,
-0.01369248516857624,
0.005154979415237904,
0.03389623016119003,
-0.02210243232548237,
0.03246487304568291,
0.03373848274350166,
-0.00026532498304732144,
0.006935844197869301,
-0.025494104251265526,
-0.007371294312179089,
-0.011226162314414978,
0.018210645765066147,
0.009432317689061165,
-0.031004300341010094,
0.03454996645450592,
0.05841024965047836,
-0.049903661012649536,
0.03447757661342621,
-0.04952794685959816,
-0.03742910176515579,
0.010387777350842953,
0.005138716660439968,
0.02210981771349907,
0.010996313765645027,
-0.03919573500752449,
0.09648073464632034,
0.028897546231746674,
-0.029970688745379448,
0.03037584386765957,
-0.052077069878578186,
-0.04160597547888756,
-0.010909376665949821,
0.026821797713637352,
0.026759373024106026,
0.00794608797878027,
0.017468491569161415,
0.053044937551021576,
0.021894529461860657,
-0.013103869743645191,
0.003517843782901764,
-0.019627423956990242,
-0.011140736751258373,
0.04227777570486069,
0.0031587400007992983,
0.04659654572606087,
0.013024134561419487,
-0.01974276825785637,
-0.021858656778931618,
0.013286314904689789,
0.030512817203998566,
0.020610613748431206,
-0.03288303688168526,
0.06222157180309296,
0.0073661599308252335,
0.013662987388670444,
-0.0003051235980819911,
0.057121776044368744,
0.026254596188664436,
-0.03667468577623367,
-0.0152742313221097,
0.014729630202054977,
0.023621032014489174,
-0.007418354507535696,
0.0005997186526656151,
0.0026534758508205414,
0.04361121356487274,
-0.0457693450152874,
-0.03824494779109955,
0.008277189917862415,
-0.022493358701467514,
0.0280812606215477,
-0.028437690809369087,
-0.02218720316886902,
0.05229474976658821,
0.02123628929257393,
0.00967228040099144,
0.006119037978351116,
-0.04645033925771713,
0.015949813649058342,
-0.049052804708480835,
0.004365317989140749,
0.018305499106645584,
0.018033834174275398,
0.002463946118950844,
0.015200614929199219,
-0.00932944193482399,
0.029463717713952065,
-0.038486238569021225,
0.020411713048815727,
-0.04882579669356346,
-0.008118940517306328,
-0.05514875426888466,
-0.016923552379012108,
-0.022797010838985443,
-0.03145623952150345,
0.010890982113778591,
-0.0028053452260792255,
-0.04148614779114723,
-0.03513640537858009,
-0.015525191091001034,
-0.01723399944603443,
0.0036812075413763523,
-0.059565722942352295,
-0.0401446670293808,
0.005332591012120247,
0.034537069499492645,
0.03570689260959625,
-0.013614576309919357,
-0.012536353431642056,
0.014141208492219448,
-0.044660117477178574,
-0.025745248422026634,
-0.0023660582955926657,
0.05306776240468025,
-0.0014040912501513958,
0.024286868050694466,
0.020739933475852013,
0.025291353464126587,
-0.03395073860883713,
-0.011291936039924622,
0.038125596940517426,
0.036198243498802185,
-0.013789555057883263,
0.0017678738804534078,
0.009232197888195515,
-0.06490902602672577,
-0.035704001784324646,
0.026175424456596375,
0.08034981042146683,
0.005728097632527351,
-0.003127114614471793,
0.051286954432725906,
0.023298708721995354,
-0.034878555685281754,
0.04237206280231476,
0.02042720839381218,
0.034215569496154785,
-0.04942593351006508,
-0.052527014166116714,
0.013450807891786098,
0.013579698279500008,
0.018855057656764984,
0.00101733417250216,
-0.02277746982872486,
-0.04117358475923538,
0.020976129919290543,
0.018577132374048233,
0.016284547746181488,
-0.06797347962856293,
-0.008922882378101349,
0.02559887245297432,
0.003343797056004405,
-0.01990288682281971,
0.03382692113518715,
0.040633849799633026,
0.051151227205991745,
0.04101936146616936,
-0.008936407044529915,
-0.004060776438564062,
-0.0685526505112648,
0.005112634971737862,
0.020176425576210022,
0.02515527978539467,
0.01402425579726696,
-0.04691477492451668,
-0.0816534236073494,
-0.022555947303771973,
0.052423443645238876,
0.002011546865105629,
0.0069331033155322075,
0.019497312605381012,
0.004518015775829554,
-0.017356444150209427,
-0.0009293844341300428,
0.02250746637582779,
0.025035332888364792,
-0.01462397538125515,
0.01634995825588703,
-0.037184104323387146,
-0.010167603380978107,
-0.018263166770339012,
0.033125296235084534,
0.01994815096259117,
0.028612492606043816,
0.05480368807911873,
0.040383998304605484,
-0.01969182677567005,
0.01991806924343109,
-0.017364026978611946,
-0.06170425936579704,
0.01595696434378624,
0.027678851038217545,
-0.03872183337807655,
0.0743848979473114,
-0.03686424717307091,
-0.0015472712693735957,
0.002738151466473937,
-0.0368875190615654,
0.015611451119184494,
-0.03292138874530792,
-0.06065704673528671,
0.000822533736936748,
0.03174005076289177,
-0.016315557062625885,
0.02370234578847885,
0.042191337794065475,
-0.04680873826146126,
-0.01140441931784153,
-0.028988434001803398,
0.055075503885746,
-0.029943922534585,
0.015910519286990166,
-0.026216713711619377,
-0.03171555697917938,
-0.009792063385248184,
0.022938277572393417,
-0.03991261497139931,
0.024479342624545097,
-0.02348710224032402,
-0.015232043340802193,
-0.026253674179315567,
0.00409812293946743,
0.043685853481292725,
-0.02550061047077179,
0.01868678443133831,
0.03524989262223244,
0.006274270359426737,
-0.01911160722374916,
0.0280939731746912,
0.004446889739483595,
0.0030929504428058863,
0.037115104496479034,
0.017398590222001076,
0.010894637554883957,
-0.000012150339898653328,
-0.028454944491386414,
0.03517154976725578,
-0.05474264174699783,
0.02224571444094181,
0.015497916378080845,
-0.03571515530347824,
-0.014760774560272694,
-0.01813468337059021,
-0.003148535033687949,
0.0018488807836547494,
-0.024302532896399498,
0.04469911754131317,
-0.02413664385676384,
0.07554356008768082,
0.04734184220433235,
0.011264075525105,
-0.08256638050079346,
-0.04209854453802109,
-0.03047105483710766,
0.008199267089366913,
-0.013543647713959217,
-0.04226994886994362,
-0.017794735729694366,
-0.04345162957906723,
0.017782840877771378,
-0.008344982750713825,
0.05572282895445824,
-0.021687034517526627,
0.009861249476671219,
-0.021523484960198402,
0.04252838343381882,
0.046092912554740906,
-0.003843070473521948,
-0.023094458505511284,
-0.0022790913935750723,
-0.04121510311961174,
0.002091658068820834,
-0.0019108817214146256,
0.05244632065296173,
-0.011055795475840569,
0.016880042850971222,
-0.0022768958006054163,
-0.023012368008494377,
0.012248215265572071,
-0.0038037202320992947,
0.023095257580280304,
0.06609263271093369,
0.02868434228003025,
-0.0001349659578409046,
-0.0222803745418787,
-0.0022514841984957457,
-0.022861352190375328,
0.032719679176807404,
-0.03369965776801109,
0.0018929133657366037,
0.0006810402846895158,
-0.017246829345822334,
0.042041994631290436,
0.003344060154631734,
-0.001541227102279663,
0.03174338489770889,
0.05021240562200546,
-0.009925403632223606,
-0.030018020421266556,
0.026332005858421326,
-0.04182682931423187,
-0.011104683391749859,
-0.02182251214981079,
0.009629368782043457,
-0.009166956879198551,
-0.011779512278735638,
-0.00855768658220768,
-0.0752376988530159,
-0.023590510711073875,
0.028417257592082024,
0.04875342547893524,
0.0038026203401386738,
0.029119377955794334,
-0.014069546945393085,
-0.03492036461830139,
0.027750052511692047,
-0.04543250426650047,
-0.02104548178613186,
-0.024333229288458824,
-0.029535340145230293,
0.02415875345468521,
-0.03382720425724983,
-0.0060022673569619656,
0.01958993263542652,
0.03467202186584473,
-0.0376138910651207,
0.059171244502067566,
0.03431473672389984,
0.005659793503582478,
0.028937404975295067,
-0.0034742853604257107,
-0.05595444142818451,
0.054163362830877304,
-0.04042680189013481,
0.04008406028151512,
0.008614911697804928,
-0.0014443743275478482,
0.020213881507515907,
0.011879497207701206,
0.0011303507490083575,
0.008094404824078083,
-0.030967429280281067,
-0.041958533227443695,
0.048521123826503754,
0.004162499215453863,
0.05673778057098389,
-0.0054692053236067295,
-0.015077676624059677,
0.05500384792685509,
-0.0023110508918762207,
0.03691577538847923,
0.013980474323034286,
-0.07573751360177994,
-0.028348376974463463,
-0.016771525144577026,
-0.01579037494957447,
0.04663415998220444,
-0.009479707106947899,
-0.03232552483677864,
-0.0062605589628219604,
-0.024265864863991737,
0.02707522362470627,
-0.03482142463326454,
0.0406150221824646,
-0.006919977720826864,
0.061940163373947144,
-0.016487859189510345,
0.031006040051579475,
-0.031872980296611786,
-0.0038864577654749155,
0.1205807700753212,
0.05657593905925751,
-0.039989206939935684,
-0.08656036108732224,
0.006265864707529545,
-0.014853017404675484,
-0.0011670205276459455,
-0.028305459767580032,
0.005488452035933733,
0.017496664077043533,
-0.009549552574753761,
-0.018344039097428322,
0.054294653236866,
0.024627581238746643,
-0.051728442311286926,
0.06872379779815674,
-0.02797369472682476,
-0.04147324711084366,
0.011672127060592175,
0.0385848768055439,
-0.015694016590714455,
0.0025720729026943445,
-0.019455183297395706,
0.011704004369676113,
-0.013639119453728199,
0.0005685538053512573,
-0.00551972771063447,
-0.026198070496320724,
0.0320618711411953,
0.03082391805946827,
-0.016225852072238922,
0.019311875104904175,
-0.023199163377285004,
-0.011897656135261059,
-0.052887920290231705,
-0.005342365242540836,
0.009059296920895576,
-0.00898781605064869,
0.04385156184434891,
0.043388571590185165,
0.005061771254986525,
0.004259208217263222,
0.010710134170949459,
0.024235866963863373,
-0.07182034105062485,
-0.000561373948585242,
-0.0016142220702022314,
0.0012675481848418713,
0.037085991352796555,
0.033199429512023926,
-0.012099973857402802,
-0.0005080582923255861,
0.018533984199166298,
-0.012486555613577366,
-0.020269129425287247,
-0.024968698620796204,
0.00660442840307951,
-0.0443667508661747,
0.0013085684040561318,
-0.01442914828658104,
0.019676653668284416,
0.023841068148612976,
0.03533175215125084,
0.008824778720736504,
-0.01569627784192562,
0.003481140825897455,
-0.016442012041807175,
0.002841596258804202,
-0.017061805352568626,
-0.010592035949230194,
-0.018216237425804138,
0.0028342031873762608,
0.005138230975717306,
-0.0069938660599291325,
-0.0000357256067218259,
0.030999423936009407,
0.0574459470808506,
0.019539684057235718,
0.028965914621949196,
0.010542881675064564,
-0.09929079562425613,
0.03538317233324051,
-0.0195926446467638,
0.0032724456395953894,
-0.023546284064650536,
-0.01447239052504301,
0.0364983044564724,
0.014559599570930004,
-0.010700656101107597,
0.015331268310546875,
-0.017138300463557243,
0.035531193017959595,
0.03164663165807724,
-0.011826089583337307,
-0.014201750047504902,
-0.01160459965467453,
-0.053488243371248245,
-0.020146096125245094,
0.010020123794674873,
0.02501802146434784,
0.014229346998035908,
-0.01286705955862999,
0.00781232537701726,
0.040319159626960754,
-0.00350711471401155,
-0.029347358271479607,
-0.009503893554210663,
-0.04320358857512474,
0.030292311683297157,
0.04493420198559761,
0.011098578572273254,
-0.00901715736836195,
-0.028437552973628044,
0.0009677708731032908,
0.0025079092010855675,
0.000597839942201972,
0.024723494425415993,
-0.040812473744153976,
0.0035464614629745483,
-0.01672992669045925,
0.03252239152789116,
-0.046993695199489594,
-0.035326264798641205,
-0.038520339876413345,
0.04130270332098007,
-0.03329380974173546,
0.012100229039788246,
0.002411129418760538,
0.029072126373648643,
-0.06445875018835068,
-0.033110685646533966,
0.014835469424724579,
-0.007741161156445742,
-0.03302442282438278,
0.005036220885813236,
0.01994214951992035,
-0.0009618363110348582,
0.013706453144550323,
0.009141596965491772,
-0.09013987332582474,
0.014203076250851154,
-0.02500316873192787,
-0.06454461812973022,
0.05273215100169182,
-0.00273863784968853,
0.015837717801332474,
0.025636931881308556,
-0.03644756227731705,
-0.020067309960722923,
0.023938225582242012,
-0.026185913011431694,
-0.01174300629645586,
0.006355647463351488,
-0.03882049769163132,
-0.017426222562789917,
-0.05631882697343826,
0.01826239377260208,
0.025943217799067497,
0.007612893357872963,
0.006393857765942812,
-0.0008338094339706004,
0.013609285466372967,
-0.03420537710189819,
-0.012368506751954556,
-0.03025299310684204,
0.009800361469388008,
-0.022578569129109383,
0.015474994666874409,
-0.05423808470368385,
0.03367093950510025,
-0.02534475550055504,
-0.005870829802006483,
-0.022614682093262672,
0.018422741442918777,
-0.0858544409275055,
-0.03269057720899582,
0.031054722145199776,
0.03627783805131912,
0.04917416349053383,
-0.058569882065057755,
0.043516553938388824,
0.019326476380228996,
-0.034924961626529694,
0.04063529893755913,
-0.030093053355813026,
0.006009905599057674,
-0.03602246940135956,
-0.0008717636810615659,
0.0034051656257361174,
0.010803860612213612,
0.02775680460035801,
0.011073448695242405,
-0.01746685616672039,
0.0017499126261100173,
-0.005560717079788446,
0.004172030836343765,
-0.047683943063020706,
0.00019108808191958815,
0.05368999391794205,
-0.04046877473592758,
0.07287349551916122,
-0.008587797172367573,
-0.045588891953229904,
0.009994402527809143,
0.015678593888878822,
-0.02201203815639019,
-0.004998397082090378,
-0.011132151819765568,
0.01732071116566658,
0.0023690182715654373,
0.04668748378753662,
-0.015218362212181091,
-0.00003812868817476556,
0.017391487956047058,
-0.009832308627665043,
0.042358219623565674,
-0.02916373685002327,
-0.0061925980262458324,
-0.02059846743941307,
-0.023262763395905495,
-0.015559452585875988,
0.020380793139338493,
-0.0018940364243462682,
-0.03698835149407387,
-0.012527963146567345,
-0.017847899347543716,
0.023868530988693237,
0.012553049251437187,
0.0049135698936879635,
-0.059347983449697495,
-0.009121151641011238,
0.05332823097705841,
-0.02130790986120701,
0.015193379484117031,
0.045216914266347885,
0.027978789061307907,
-0.00922334659844637,
0.016310911625623703,
0.04020792245864868,
0.009812028147280216,
-0.028174839913845062,
0.0036646081134676933,
0.0008507305174134672,
0.012114793993532658,
-0.017460394650697708,
-0.06143017113208771,
0.01936522126197815,
0.03990182280540466,
0.008408140391111374,
0.01799028553068638,
-0.023502081632614136,
0.001180338324047625,
-0.0006984940846450627,
-0.021053040400147438,
0.011646191589534283,
-0.015339469537138939,
0.04472183436155319,
-0.009810226038098335,
0.023810792714357376,
0.026343125849962234,
0.018928349018096924,
-0.0032067811116576195,
0.009617721661925316,
-0.039738498628139496,
0.06886053085327148,
-0.00024095774278976023,
0.0028408837970346212,
0.002763151889666915,
0.0012642598012462258,
-0.012596662156283855,
-0.0162561796605587,
-0.03011135756969452,
0.007361488416790962,
-0.0489741787314415,
0.04451414570212364,
0.008633764460682869,
-0.000294022960588336,
-0.0045362492091953754,
0.007455845363438129,
-0.03305404633283615,
0.0720272809267044,
-0.0016742051811888814,
-0.01693013496696949,
0.061347488313913345,
-0.007682956289499998,
0.040234051644802094,
0.03415245562791824,
-0.02011934295296669,
-0.01782103069126606,
0.006052827928215265,
-0.015518763102591038,
-0.008877032436430454,
0.011467299424111843,
0.02405029721558094,
0.012848366983234882,
-0.031093601137399673,
-0.004095019306987524,
0.04409755393862724,
-0.00840693898499012,
-0.006706718821078539,
0.047424014657735825,
-0.004777317866683006,
0.03424409031867981,
0.03879503905773163,
0.027139445766806602,
0.0312633290886879,
0.015346091240644455,
0.03231673687696457,
0.0680602565407753,
0.03174580633640289,
-0.023953456431627274,
0.015268613584339619,
-0.007708115968853235,
-0.039907053112983704,
-0.010717133991420269,
0.013166152872145176,
0.04382680356502533,
-0.04866060987114906,
0.01831534504890442,
0.04344720020890236,
-0.02476830594241619,
0.0065115648321807384,
0.02914268895983696,
-0.03629438206553459,
0.06732051819562912,
-0.01598861813545227,
-0.013266350142657757,
-0.04355505853891373,
0.016276724636554718,
-0.003821480320766568,
0.03010617382824421,
0.010726404376327991,
0.08144056051969528,
-0.0061932457610964775,
0.005177749320864677,
-0.022319622337818146,
0.005726288538426161,
0.025050049647688866,
-0.04503351077437401,
-0.006641405168920755,
-0.027812454849481583,
0.015813978388905525,
-0.0003695082268677652,
-0.054013386368751526,
-0.03680894151329994,
-0.026496071368455887,
0.0004748505598399788,
0.03352779895067215,
0.02401554211974144,
-0.03489163890480995,
-0.030671121552586555,
-0.007658103015273809,
0.03375118225812912,
-0.05608762800693512,
0.02606814354658127,
-0.03358716890215874,
-0.009614969603717327,
-0.017018940299749374,
-0.027299189940094948
] |
<p>I took a bucket, drilled 2 different sized holes on the side near the bottom and filled it with water. The stream of water the proceeded from the larger hole traveled further than the stream from the smaller one. How does the size of the hole affect the distance that the water travels?</p>
<p>See also: <a href="http://en.wikipedia.org/wiki/Torricelli%27s_law" rel="nofollow">Torricelli's Law</a>.</p> | 1,466 | [
-0.0011341692879796028,
-0.028746264055371284,
-0.018503041937947273,
0.021730979904532433,
0.01327947061508894,
-0.025723714381456375,
0.0007771312375552952,
0.0059495470486581326,
-0.019070718437433243,
0.027535663917660713,
0.021171076223254204,
0.025046413764357567,
0.038706012070178986,
0.016573181375861168,
0.03348148241639137,
0.034570299088954926,
-0.028653576970100403,
-0.005040542688220739,
-0.012485705316066742,
-0.01808088645339012,
-0.03538820520043373,
0.02995654195547104,
0.029356371611356735,
0.0059261200949549675,
-0.04085211455821991,
0.01472971960902214,
0.02073199674487114,
-0.004123592749238014,
0.00854798499494791,
0.0014718840830028057,
0.03250528499484062,
-0.047208722680807114,
0.016750218346714973,
0.04018404707312584,
0.003738758387044072,
-0.02775060385465622,
-0.060351643711328506,
-0.013669176958501339,
-0.008714615367352962,
0.004889363422989845,
-0.017319846898317337,
-0.03131593018770218,
-0.008022132329642773,
0.041994497179985046,
-0.019870910793542862,
0.023027101531624794,
0.03571311756968498,
-0.07225941866636276,
0.062085818499326706,
-0.03227017819881439,
0.06542634963989258,
0.019739842042326927,
0.05567491799592972,
-0.00528089189901948,
0.02444082498550415,
0.027611734345555305,
0.06849582493305206,
0.05908096954226494,
-0.06009654700756073,
-0.035322509706020355,
-0.0013790142256766558,
0.01739167980849743,
-0.01632702350616455,
-0.03279876708984375,
-0.010943549685180187,
0.0009475075639784336,
-0.03973386809229851,
-0.009995079599320889,
0.01768769882619381,
-0.03693845123052597,
0.007038232870399952,
0.009599491022527218,
0.06042942404747009,
-0.03347007930278778,
0.00372968427836895,
-0.016157912090420723,
0.02507215179502964,
0.02844228222966194,
0.015919780358672142,
0.04447823017835617,
-0.01642621122300625,
0.00045353436144068837,
0.03578689694404602,
0.0336671881377697,
0.03854690119624138,
-0.03109983168542385,
0.021168198436498642,
0.019393671303987503,
0.01067835371941328,
0.050295863300561905,
-0.03732889145612717,
0.01109989546239376,
0.01039134617894888,
0.000004540387180895777,
0.0037369776982814074,
0.02447819709777832,
-0.010494177229702473,
0.042744822800159454,
0.0008669138769619167,
0.00881910603493452,
0.00967416726052761,
-0.0005373468156903982,
0.03344939276576042,
0.0822533592581749,
0.005853796377778053,
-0.006995897740125656,
-0.025116559118032455,
0.04087838530540466,
-0.04257649555802345,
0.007191278971731663,
-0.025426773354411125,
-0.026759730651974678,
-0.005086800549179316,
-0.02847166173160076,
0.005109261255711317,
-0.0474240817129612,
0.014692582190036774,
-0.021431846544146538,
0.04658704251050949,
0.04461846873164177,
0.06960105150938034,
-0.05844736844301224,
0.04764934629201889,
-0.028315767645835876,
-0.07751191407442093,
0.05947094410657883,
0.023345910012722015,
-0.051260318607091904,
-0.005578092765063047,
0.05760899931192398,
-0.01862940564751625,
0.022192493081092834,
-0.02139297127723694,
-0.006662910338491201,
0.059634968638420105,
0.009462517686188221,
-0.07533031702041626,
-0.056749116629362106,
0.07770444452762604,
0.023341966792941093,
-0.020617611706256866,
-0.05932421237230301,
0.01245210412889719,
0.021261293441057205,
0.0989086776971817,
-0.014765040017664433,
0.018986469134688377,
0.022975511848926544,
0.0018727987771853805,
0.0012698464561253786,
-0.02130146324634552,
0.019544070586562157,
0.03261991962790489,
-0.017333371564745903,
0.06387491524219513,
-0.013230232521891594,
0.009102268144488335,
0.00998667348176241,
0.005594092886894941,
-0.04759661853313446,
0.06528577953577042,
-0.015278410166501999,
-0.02090846560895443,
0.005248326808214188,
0.0038048692513257265,
-0.033110734075307846,
0.09392561763525009,
-0.01138527411967516,
-0.03085956908762455,
0.032658111304044724,
0.0025388975627720356,
-0.01694823056459427,
0.017033973708748817,
0.030634308233857155,
0.03773394972085953,
0.006195631809532642,
-0.011904140003025532,
-0.03231199458241463,
0.023584801703691483,
-0.006751639768481255,
-0.006600067485123873,
-0.05607256293296814,
-0.0242602676153183,
0.014939566142857075,
0.005807782988995314,
0.01080351509153843,
0.0044357553124427795,
-0.00043643356184475124,
-0.014512750320136547,
-0.015679707750678062,
0.00299929641187191,
-0.056085605174303055,
0.026693027466535568,
-0.012979796156287193,
0.01769530028104782,
0.0019578728824853897,
-0.03586892783641815,
0.013128266669809818,
-0.03535951301455498,
0.021923422813415527,
-0.020015055313706398,
-0.010082648135721684,
-0.02144090086221695,
0.0044015576131641865,
0.027659829705953598,
0.07073371112346649,
0.0474884994328022,
0.004147834610193968,
0.00920428242534399,
-0.004122295416891575,
0.005469505675137043,
0.023839300498366356,
-0.0248093344271183,
0.049824878573417664,
-0.034660570323467255,
-0.0024769138544797897,
-0.0010059879859909415,
0.021003970876336098,
0.013376088812947273,
0.03726895526051521,
-0.03902257978916168,
0.11153188347816467,
0.03070293925702572,
0.01152687519788742,
-0.01053997129201889,
0.0073723504319787025,
-0.010676834732294083,
-0.010543068870902061,
-0.006632633972913027,
-0.019931679591536522,
-0.05211000144481659,
-0.011400610208511353,
0.0011542956344783306,
0.014930713921785355,
-0.0032338020391762257,
0.00038681310252286494,
-0.010572205297648907,
0.013642217963933945,
-0.01306914072483778,
0.026691138744354248,
-0.016027064993977547,
-0.017050931230187416,
-0.01336424145847559,
0.059829920530319214,
-0.01196999754756689,
0.0134948855265975,
0.04774012044072151,
0.037319306284189224,
0.04187142103910446,
-0.037722278386354446,
-0.025602715089917183,
0.03633003309369087,
-0.0049743433482944965,
0.05359014868736267,
0.011766146868467331,
0.012108867056667805,
0.006849916651844978,
-0.03225114941596985,
-0.01903476193547249,
0.011951272375881672,
-0.020221276208758354,
0.006702396087348461,
-0.05526287481188774,
0.003101515118032694,
0.029768282547593117,
0.0026762450579553843,
-0.0016003180062398314,
-0.0017020079540088773,
0.0212071742862463,
-0.044518306851387024,
0.04016274958848953,
-0.028260154649615288,
-0.03909743204712868,
-0.06567548215389252,
-0.006425433326512575,
0.027975687757134438,
0.02294844016432762,
0.008642134256660938,
-0.02570412866771221,
-0.00874339509755373,
-0.024567794054746628,
-0.007137177512049675,
-0.022322634235024452,
-0.0031013241969048977,
-0.0342242494225502,
0.04173242673277855,
0.007015058770775795,
-0.0008270833059214056,
0.042379241436719894,
-0.01992199942469597,
0.007002871483564377,
-0.005574236623942852,
0.001967270625755191,
0.00315282610245049,
-0.013864419423043728,
-0.04711791127920151,
0.03379841521382332,
-0.008677694946527481,
0.0156733188778162,
0.07136427611112595,
-0.02265739068388939,
-0.03738429769873619,
0.019146597012877464,
-0.05477885901927948,
-0.03583326190710068,
-0.019221117720007896,
0.0004412703274283558,
0.01694311946630478,
-0.0023611364886164665,
-0.015627644956111908,
-0.018633488565683365,
-0.05574386566877365,
-0.004911266267299652,
-0.05147314444184303,
-0.04992577061057091,
0.04286569356918335,
-0.009352616034448147,
0.049512509256601334,
-0.033542450517416,
-0.04338991269469261,
0.028009478002786636,
0.012333640828728676,
-0.04324960708618164,
-0.014983111061155796,
-0.007949881255626678,
-0.0017146284226328135,
-0.03775913640856743,
0.04196315258741379,
0.07631640136241913,
-0.05404336750507355,
0.004439757205545902,
0.035404007881879807,
0.0816052109003067,
0.03463391214609146,
0.03812345862388611,
-0.004993236158043146,
-0.03673907369375229,
0.0207323357462883,
-0.022293642163276672,
0.03294464200735092,
0.016671743243932724,
-0.044238265603780746,
-0.01909816637635231,
-0.01983632892370224,
0.04782097041606903,
0.035019103437662125,
-0.02057061530649662,
0.0262798760086298,
0.0054456014186143875,
-0.019727498292922974,
-0.05174275115132332,
0.028623707592487335,
-0.02194826677441597,
-0.00021603588538710028,
0.040721166878938675,
0.0008854037150740623,
0.06307657808065414,
-0.015598294325172901,
0.004002407193183899,
0.008347059600055218,
0.04379509389400482,
-0.05958034470677376,
-0.01878298819065094,
-0.01993938535451889,
-0.0038445142563432455,
0.04076499491930008,
-0.023155085742473602,
-0.030420390889048576,
0.04437156394124031,
0.036928653717041016,
0.014905575662851334,
-0.0023016866762191057,
-0.020967744290828705,
-0.026422427967190742,
-0.06393259018659592,
-0.004176189191639423,
-0.005581886041909456,
0.05089704319834709,
0.012805858626961708,
0.049359411001205444,
0.0028522671200335026,
-0.023331530392169952,
0.029244454577565193,
-0.01399132702499628,
-0.07392248511314392,
0.028539493680000305,
-0.024260995909571648,
-0.03565678745508194,
0.006751929875463247,
-0.034059204161167145,
-0.008336425758898258,
-0.015691017732024193,
0.017598295584321022,
0.027316544204950333,
-0.006490499246865511,
-0.037943705916404724,
0.008963022381067276,
-0.01952497474849224,
-0.07152418047189713,
0.010866976343095303,
0.007501689717173576,
0.018727853894233704,
-0.04439022019505501,
0.06773217767477036,
0.03553425148129463,
-0.04071398451924324,
-0.012869706377387047,
-0.03293224796652794,
-0.015732644125819206,
0.020934714004397392,
0.01930467039346695,
0.01113421656191349,
0.006036975886672735,
-0.013076969422399998,
0.03246447816491127,
-0.01038426999002695,
0.02775976061820984,
0.0180992279201746,
0.018004238605499268,
-0.04629642516374588,
-0.036265790462493896,
0.029932893812656403,
-0.017735591158270836,
0.059887126088142395,
-0.023802196606993675,
0.0022168101277202368,
0.035525351762771606,
-0.0052897450514137745,
-0.029466288164258003,
0.024378972128033638,
0.012100879102945328,
0.017357228323817253,
-0.016307741403579712,
-0.04677315801382065,
-0.03883947432041168,
-0.011065212078392506,
-0.014348934404551983,
-0.01454746164381504,
0.019223568961024284,
-0.041181694716215134,
-0.03710215538740158,
0.041010331362485886,
-0.004253826569765806,
0.013566558249294758,
-0.01229862216860056,
0.005031723063439131,
0.008585653267800808,
-0.014593304134905338,
0.0020078890956938267,
0.029138147830963135,
0.00034414781839586794,
0.01748822256922722,
0.0002771914005279541,
-0.023957202211022377,
-0.08352108299732208,
-0.041957415640354156,
0.03972804546356201,
0.035115908831357956,
-0.019653772935271263,
0.03325235843658447,
-0.04509367421269417,
-0.04153171926736832,
0.07837569713592529,
-0.03730909898877144,
0.03334883227944374,
-0.03251126781105995,
0.019573384895920753,
-0.03986445814371109,
0.0010386189678683877,
-0.049356769770383835,
0.02307085692882538,
-0.0029288209043443203,
0.016495829448103905,
0.0006932204705663025,
-0.0200151689350605,
-0.017648715525865555,
0.0035471299197524786,
0.03736076131463051,
0.03754293546080589,
0.0026380661875009537,
0.007722590118646622,
-0.005286971107125282,
0.003288445994257927,
-0.006909057032316923,
-0.03945104777812958,
0.014790825545787811,
-0.003710417775437236,
0.0027770043816417456,
0.015382654964923859,
-0.030579326674342155,
-0.02361839823424816,
0.03637678176164627,
0.006685060448944569,
-0.03203793987631798,
-0.010938780382275581,
-0.02114945277571678,
0.023956894874572754,
0.023261331021785736,
0.009805753827095032,
0.034992508590221405,
0.02421971969306469,
0.0003276883508078754,
-0.03707176446914673,
-0.0189518965780735,
0.03903140127658844,
-0.0019222777336835861,
-0.030123909935355186,
-0.04344271495938301,
0.015355868265032768,
-0.033969536423683167,
0.03543940559029579,
0.04297874867916107,
0.02384422905743122,
-0.04037587344646454,
-0.059460289776325226,
-0.013871796429157257,
0.0229511559009552,
-0.011672789230942726,
0.01328090950846672,
0.01923493668437004,
0.028672408312559128,
0.049803607165813446,
-0.02509981207549572,
0.0026238812133669853,
0.0016710448544472456,
0.027754487469792366,
0.036431167274713516,
0.007707258686423302,
0.032684728503227234,
-0.01918039284646511,
0.02041025087237358,
0.020210150629281998,
-0.0482449010014534,
0.051147498190402985,
0.011791818775236607,
-0.03385766223073006,
0.010275288484990597,
-0.02703087404370308,
-0.022427942603826523,
0.028173714876174927,
-0.03945682570338249,
0.009838460944592953,
-0.03075990453362465,
0.019421910867094994,
0.04207340627908707,
0.030070658773183823,
-0.07773810625076294,
-0.04748772829771042,
0.0014551370404660702,
0.00664210831746459,
0.026451846584677696,
-0.008454819209873676,
-0.03339378163218498,
-0.02513636089861393,
-0.049680743366479874,
0.027707401663064957,
0.043620627373456955,
-0.032515257596969604,
-0.000483369774883613,
0.005674317944794893,
-0.00952061265707016,
0.05401281267404556,
0.027270419523119926,
0.011416886001825333,
-0.016266940161585808,
-0.03328389301896095,
-0.05275828763842583,
0.00247269868850708,
0.021888265386223793,
-0.048628780990839005,
-0.0070094335824251175,
-0.009121758863329887,
0.02013096958398819,
0.031211571767926216,
-0.03715050220489502,
0.012371299788355827,
-0.028076445683836937,
0.052506398409605026,
-0.003338376060128212,
0.007438019849359989,
-0.00086629280121997,
0.04355217143893242,
0.009320131503045559,
-0.030105942860245705,
-0.027708597481250763,
-0.032840974628925323,
-0.029650961980223656,
-0.020237576216459274,
0.030345965176820755,
-0.00415098387748003,
-0.014833216555416584,
0.029432887211441994,
-0.05160362273454666,
-0.0007296786061488092,
0.032304875552654266,
-0.023668035864830017,
0.028227176517248154,
0.012585495598614216,
-0.06041542440652847,
-0.02644645795226097,
-0.012633747421205044,
-0.03164471685886383,
-0.011166447773575783,
-0.014913045801222324,
-0.017085282132029533,
0.05339287593960762,
-0.014286914840340614,
0.025509562343358994,
0.0066132680512964725,
-0.0387989841401577,
0.020350858569145203,
-0.011994672939181328,
-0.004403071943670511,
0.006700889207422733,
-0.017155669629573822,
0.03963296487927437,
-0.02992267534136772,
0.028029100969433784,
0.03498942777514458,
0.04497499018907547,
-0.025095870718359947,
0.0067237429320812225,
0.04710890352725983,
0.017006544396281242,
0.02103484980762005,
-0.00144504988566041,
-0.047669682651758194,
0.033701419830322266,
-0.03502580150961876,
0.012317784130573273,
-0.03920046240091324,
0.012969901785254478,
0.10070113837718964,
-0.002808405552059412,
-0.04199471324682236,
-0.003625930519774556,
-0.012339399196207523,
-0.05953121930360794,
0.003262551501393318,
-0.007510493043810129,
0.03177843987941742,
0.008440351113677025,
0.037989769130945206,
0.01215540524572134,
0.03022807091474533,
-0.0035918978974223137,
-0.03718134015798569,
-0.039912957698106766,
-0.01363593339920044,
-0.044415708631277084,
-0.04563780128955841,
0.027809571474790573,
0.0073900120332837105,
-0.07916957885026932,
0.026509126648306847,
-0.017099570482969284,
-0.0025729830376803875,
0.014572426676750183,
-0.0020720032043755054,
-0.02746465988457203,
0.06145445629954338,
0.022589847445487976,
0.0031890543177723885,
-0.004807064309716225,
0.018011081963777542,
0.10357207804918289,
0.07258778810501099,
0.03322519361972809,
-0.05779241770505905,
0.010048884898424149,
0.002803747309371829,
0.008756079711019993,
-0.03934117779135704,
0.04744836315512657,
-0.029694925993680954,
-0.00011382960656192154,
0.06877178698778152,
0.02832215651869774,
-0.02414945513010025,
0.011231738142669201,
0.0721520185470581,
-0.01632792502641678,
-0.03575422242283821,
0.0005672011757269502,
0.007103150710463524,
-0.002904291730374098,
0.016345027834177017,
-0.036214787513017654,
0.03957346826791763,
-0.04701513424515724,
0.007601132616400719,
-0.013316097669303417,
-0.04272311180830002,
0.02688160166144371,
0.019019896164536476,
-0.05510025471448898,
0.0109612001106143,
0.03135932236909866,
-0.004804869182407856,
-0.03411238268017769,
0.016098517924547195,
0.04201432317495346,
-0.002963819308206439,
-0.009223572909832,
0.024941014125943184,
-0.00039463199209421873,
0.01881755143404007,
-0.023173287510871887,
0.028854230418801308,
-0.0599721223115921,
-0.01587156392633915,
-0.02285655587911606,
-0.019319765269756317,
0.009557165205478668,
0.005049986764788628,
0.0018007330363616347,
0.01811581663787365,
0.01557073462754488,
-0.039080213755369186,
-0.0244700126349926,
0.018559975549578667,
0.029188714921474457,
0.014121975749731064,
-0.016620099544525146,
0.004600785207003355,
0.014908714219927788,
-0.014936305582523346,
0.02225051075220108,
0.02251737378537655,
0.02300129272043705,
-0.032492976635694504,
0.0025749835185706615,
0.04228893667459488,
0.004776553716510534,
-0.039945490658283234,
-0.036721371114254,
0.018513767048716545,
-0.0017302273772656918,
0.03688835725188255,
-0.0055640037171542645,
0.04062439128756523,
-0.00007115194603102282,
0.031136292964220047,
-0.0034657949581742287,
0.010553525760769844,
-0.040122874081134796,
0.0031189071014523506,
-0.005519390571862459,
0.008156441152095795,
-0.05262025073170662,
-0.004996512550860643,
-0.010537251830101013,
0.03334224969148636,
-0.011219040490686893,
-0.013403033837676048,
0.0064013260416686535,
0.02185189351439476,
0.03079720214009285,
-0.038478683680295944,
-0.034873101860284805,
-0.01349063403904438,
-0.03368641436100006,
-0.037508800625801086,
0.007185632828623056,
0.046416353434324265,
0.021320901811122894,
0.03242120519280434,
0.036615777760744095,
-0.0034520712215453386,
-0.03366204351186752,
0.028183702379465103,
0.021338241174817085,
0.0005471124895848334,
-0.03004196472465992,
0.020014826208353043,
-0.01409508939832449,
-0.04130174219608307,
-0.000748390972148627,
0.01477032620459795,
0.009386919438838959,
0.028925450518727303,
0.002624509623274207,
-0.028837308287620544,
0.016805877909064293,
-0.07284436374902725,
0.01151517778635025,
-0.026168562471866608,
-0.0015269916038960218,
-0.0782415047287941,
-0.037421029061079025,
0.005443552974611521,
-0.001935051055625081,
-0.0241467896848917,
0.0442771278321743,
-0.043782301247119904,
-0.007053401321172714,
0.011109525337815285,
-0.00911939237266779,
-0.010026756674051285,
-0.005178533960133791,
0.053736500442028046,
0.007084114942699671,
0.05621694400906563,
-0.007500851061195135,
-0.037957873195409775,
0.038796231150627136,
-0.017370030283927917,
0.007888134568929672,
0.049603432416915894,
-0.00371094373986125,
0.0389171838760376,
0.01217696350067854,
-0.0033085953909903765,
-0.015876224264502525,
0.07158441841602325,
0.0035872056614607573,
-0.005078740883618593,
-0.019037701189517975,
-0.04098830744624138,
0.01118024904280901,
-0.009967098943889141,
0.006505265366286039,
-0.016289889812469482,
0.00011593080853344873,
0.0013711296487599611,
0.0327950082719326,
0.02085823193192482,
0.004366914741694927,
0.00557168060913682,
0.005765048786997795,
0.001686684088781476,
-0.0010902629001066089,
0.0012862596195191145,
0.02177828922867775,
0.06201125681400299,
0.0022421821486204863,
0.02639535814523697,
0.004536509979516268,
0.005220133811235428,
-0.1262565404176712,
0.04281070828437805,
-0.007796491961926222,
-0.0055371420457959175,
0.018957315012812614,
-0.06138996779918671,
-0.009090397506952286,
0.00020080844115000218,
-0.038340307772159576,
0.00938993040472269,
-0.030448293313384056,
0.022705325856804848,
-0.03196457400918007,
-0.03061862289905548,
-0.0058822063729166985,
0.0560598224401474,
0.041333213448524475,
0.022627973929047585,
0.00705626280978322,
0.004109447821974754,
-0.015118785202503204,
-0.01861378736793995,
0.007633112836629152,
0.01354182604700327,
-0.02181720919907093,
0.033633798360824585,
-0.0014292647829279304,
0.0018284163670614362,
0.007684069219976664,
0.027127308771014214,
-0.05632942542433739,
0.02883869782090187,
0.00751939183101058,
-0.003788713365793228,
0.009849566034972668,
0.027923520654439926,
-0.017953798174858093,
0.015239594504237175,
-0.0027674620505422354,
-0.015962984412908554,
-0.011371461674571037,
0.013549691997468472,
-0.01272965781390667,
0.0006544165080413222,
0.017631055787205696,
-0.023421000689268112,
-0.011076276190578938,
0.035286448895931244,
-0.02317875809967518,
0.007778892293572426,
0.0016726180911064148,
0.002954097231850028,
0.04230255261063576,
-0.0123910466209054,
0.0019992482848465443,
-0.008858460932970047,
-0.03401397168636322,
0.07108545303344727,
0.004309802316129208,
-0.040516793727874756,
-0.009954090230166912,
0.029508957639336586,
-0.019812174141407013,
-0.0395805649459362,
0.014591643586754799,
-0.005730339791625738,
-0.027843382209539413,
-0.002940055914223194,
-0.00008165124745573848,
0.006574670318514109,
0.0009681519586592913,
-0.057702865451574326,
-0.010580023750662804,
0.06697820872068405,
-0.0008403754327446222,
0.02558496966958046,
0.01642696186900139,
-0.014966873452067375,
-0.01236981712281704,
-0.06044803559780121,
0.026608336716890335,
-0.008319197222590446,
-0.031354133039712906,
-0.05974390730261803,
-0.015127118676900864,
0.028646422550082207,
0.03452335670590401,
0.05401356518268585,
0.018394896760582924,
-0.0018261391669511795,
0.011492881923913956,
-0.0027647584211081266,
0.04399808123707771,
-0.04244817793369293,
-0.03256579115986824,
-0.010550117120146751,
-0.024688396602869034,
0.009382561780512333,
-0.01101522333920002,
-0.015605310909450054,
-0.0012894816463813186,
0.0038231918588280678,
0.02129555493593216,
0.03096069023013115,
-0.02457515336573124,
-0.026334460824728012,
0.004068184643983841,
0.029528962448239326,
0.008902729488909245,
0.08343122899532318,
-0.001358688808977604,
0.00028186733834445477,
-0.0011559576960280538,
-0.04854700714349747,
-0.051387302577495575,
0.011211937293410301,
-0.04789659008383751,
0.024399450048804283,
0.010524069890379906,
-0.03764013573527336,
0.04163315147161484,
-0.05491729825735092,
-0.031006935983896255,
0.03399986773729324,
-0.03749403357505798,
-0.026808584108948708,
0.060580942779779434,
0.03226630389690399,
0.042945679277181625,
-0.06422410160303116,
0.013941486366093159,
0.015210870653390884,
-0.027005258947610855,
-0.011106932535767555,
0.038484130054712296,
0.024474188685417175,
-0.01868889480829239,
-0.04735277593135834,
0.023825157433748245,
0.004804297816008329,
0.005170262418687344,
0.011126453056931496,
0.0333763062953949,
-0.006777200382202864,
-0.05752654746174812,
-0.002398796146735549,
-0.017834411934018135,
0.017611464485526085,
0.014543057419359684,
-0.006416277959942818,
0.05572216585278511,
0.022648124024271965,
0.022409413009881973,
-0.026354702189564705,
-0.002232186496257782,
-0.01588561199605465,
-0.0004934156313538551,
-0.019449086859822273,
0.012326058931648731,
0.03614587336778641,
-0.01861865259706974,
0.008717655204236507,
-0.017050234600901604,
-0.004588080570101738,
-0.025095313787460327,
0.012556128203868866,
0.02505703642964363,
0.010919087566435337,
-0.029113156720995903,
0.018616782501339912,
-0.003044725162908435,
-0.032714277505874634,
0.08674407750368118,
0.057125888764858246,
0.015634076669812202,
0.01872260309755802,
-0.00433554919436574,
0.028233574703335762,
0.08498460799455643,
-0.10023099184036255,
-0.023029331117868423,
-0.055186741054058075,
0.01759309321641922,
-0.0025867761578410864,
-0.06803213059902191
] |
<p>My teacher mentioned that field line density = no. of lines / area and the total area of a sphere is $4\pi r^2$ and so an electric force is inversely proportional to $r^2$. Actually, why can the total area of the sphere be applied to this case and is this true? How does one come up with the Coulomb's law?</p> | 1,467 | [
-0.01799607463181019,
0.003062167204916477,
0.006617956329137087,
0.0007609770982526243,
0.012933030724525452,
-0.007242365274578333,
-0.010490656830370426,
-0.03475338965654373,
0.023956824094057083,
0.0015537271974608302,
0.03722228854894638,
0.0033875382505357265,
0.10901059210300446,
0.02525067888200283,
0.008634503930807114,
-0.02051757089793682,
-0.040435533970594406,
0.006236768327653408,
-0.019847294315695763,
-0.029250137507915497,
-0.014595523476600647,
0.028668785467743874,
0.022444993257522583,
0.004641604609787464,
0.007561628706753254,
0.05222802981734276,
0.03494110330939293,
-0.026718640699982643,
0.025466974824666977,
0.05055480822920799,
0.00255512073636055,
-0.037229686975479126,
0.04891914874315262,
0.02891233004629612,
0.04124846309423447,
-0.005112544633448124,
-0.01053598988801241,
-0.006759938318282366,
-0.008142503909766674,
0.019639810547232628,
-0.031453024595975876,
-0.04887494444847107,
0.010238896124064922,
0.03773778676986694,
-0.028110669925808907,
0.016786742955446243,
-0.0037912719417363405,
-0.036371126770973206,
0.052038002759218216,
-0.08801311999559402,
0.07443728297948837,
0.03831201791763306,
0.06487192213535309,
0.04364344850182533,
0.04309549927711487,
-0.017333371564745903,
0.0601329542696476,
0.044020552188158035,
0.009195051155984402,
-0.028457587584853172,
-0.018547791987657547,
-0.021599983796477318,
-0.053482428193092346,
-0.06617675721645355,
-0.012304158881306648,
0.041468728333711624,
-0.022681046277284622,
-0.008938025683164597,
0.025827709585428238,
-0.01893826760351658,
0.010322414338588715,
0.03188007324934006,
0.012893390841782093,
-0.03134820610284805,
-0.011213596910238266,
-0.001892000320367515,
0.037794146686792374,
-0.0030545543413609266,
-0.01778400130569935,
0.035731397569179535,
-0.011760294437408447,
0.016447342932224274,
0.04290017485618591,
0.060503553599119186,
0.015119249932467937,
-0.007406148593872786,
0.026531238108873367,
0.010297990404069424,
0.04060240462422371,
0.009215909987688065,
0.008216182701289654,
0.00039761699736118317,
0.01380288228392601,
-0.019885102286934853,
-0.021183451637625694,
0.01947353407740593,
-0.028789326548576355,
0.054230011999607086,
-0.00044078665086999536,
0.00350290909409523,
0.03452090546488762,
0.007245891727507114,
0.0007845459040254354,
0.08420303463935852,
0.0070963106118142605,
-0.05218742787837982,
-0.06477080285549164,
0.01070843730121851,
-0.0006496559362858534,
0.003990046214312315,
-0.0469217449426651,
0.053495392203330994,
-0.0025867235381156206,
-0.002635309938341379,
0.011013916693627834,
0.007229904178529978,
0.014558008871972561,
-0.0032297505531460047,
0.05631248280405998,
0.049760349094867706,
0.02535487525165081,
-0.012116164900362492,
0.024195263162255287,
-0.047414280474185944,
-0.022850457578897476,
0.02528291754424572,
0.02504502609372139,
-0.027569716796278954,
-0.025529565289616585,
0.026238521561026573,
-0.008685185573995113,
0.010443774051964283,
-0.03971490636467934,
0.041768450289964676,
0.044094786047935486,
-0.010729596018791199,
-0.08240250498056412,
-0.033471740782260895,
0.03973788395524025,
-0.009236008860170841,
0.002872348530218005,
-0.08301392197608948,
0.02771606482565403,
0.015483480878174305,
0.04392417520284653,
0.0067581553012132645,
0.006544416304677725,
-0.027673181146383286,
0.03792034089565277,
0.015055526047945023,
-0.014290674589574337,
-0.01839480549097061,
0.018224747851490974,
-0.0499250553548336,
0.020774878561496735,
-0.059085097163915634,
0.026692131534218788,
0.010590391233563423,
0.003749716794118285,
-0.03763658553361893,
0.0737108364701271,
-0.013020879589021206,
-0.009671050123870373,
0.013945484533905983,
-0.02394910342991352,
-0.03470629081130028,
0.04120917618274689,
-0.005911121144890785,
-0.020331157371401787,
0.05459370091557503,
0.017193976789712906,
0.029888637363910675,
0.01043383963406086,
0.03090791590511799,
0.041146375238895416,
-0.010971277952194214,
-0.03045862726867199,
-0.0441327765583992,
0.016937650740146637,
0.01437221560627222,
-0.03245051950216293,
-0.039268773049116135,
0.037735339254140854,
0.05952320620417595,
-0.004098380450159311,
0.052997294813394547,
0.005698332563042641,
-0.021788977086544037,
-0.00751515431329608,
-0.020408401265740395,
0.00728100910782814,
-0.061367738991975784,
0.06599484384059906,
0.011867235414683819,
-0.024280011653900146,
0.013048977591097355,
0.00875029992312193,
0.010985711589455605,
-0.022126000374555588,
-0.0328182578086853,
-0.0165322944521904,
0.03168320655822754,
0.0034495857544243336,
-0.026186928153038025,
0.051105402410030365,
0.03490794450044632,
-0.01270641852170229,
0.006735142320394516,
0.009320739656686783,
-0.0447237566113472,
-0.00798420887440443,
-0.04340501129627228,
-0.03209884464740753,
0.015544379130005836,
0.014231735840439796,
-0.017568392679095268,
0.016754038631916046,
0.011833355762064457,
-0.009048991836607456,
0.06654664874076843,
-0.02309226803481579,
0.06860940158367157,
0.041557248681783676,
0.011450214311480522,
0.013470331206917763,
0.033916812390089035,
0.007360792253166437,
-0.002535368548706174,
0.0032719147857278585,
-0.02683827094733715,
-0.039169494062662125,
0.036879438906908035,
0.03637932240962982,
0.019465213641524315,
-0.004143069963902235,
-0.010296252556145191,
0.025393661111593246,
0.028462715446949005,
0.02289866842329502,
0.009748770855367184,
-0.018054114654660225,
-0.04587574675679207,
0.007192449644207954,
0.033299367874860764,
-0.01214133482426405,
-0.007771192118525505,
-0.008365437388420105,
0.03886853903532028,
0.013216158375144005,
0.031625501811504364,
-0.024990465492010117,
0.0034836209379136562,
-0.04296356439590454,
0.03209071606397629,
0.023753944784402847,
0.015827050432562828,
0.021266095340251923,
-0.061455320566892624,
0.049588657915592194,
0.03535707667469978,
-0.007893006317317486,
-0.008157479576766491,
-0.050322696566581726,
-0.029502348974347115,
0.042260829359292984,
-0.022197237238287926,
-0.03200923278927803,
-0.017004601657390594,
0.019744575023651123,
-0.06352519243955612,
-0.010161209851503372,
0.04986787587404251,
-0.024975081905722618,
-0.04582758992910385,
0.01730428636074066,
0.0442512147128582,
0.00009782776760403067,
0.03722346946597099,
0.0018663143273442984,
-0.008358257822692394,
-0.0035468710120767355,
-0.014325198717415333,
0.008592664264142513,
-0.001913571497425437,
-0.011277670972049236,
0.013015097938477993,
-0.019229447469115257,
-0.00052521942416206,
0.027299603447318077,
0.00873147789388895,
0.020331233739852905,
0.03142707422375679,
0.00228664418682456,
-0.046478383243083954,
0.014812080189585686,
-0.022502269595861435,
0.01424185000360012,
-0.005860375706106424,
0.015670180320739746,
0.03777951002120972,
-0.02763599157333374,
-0.01787271909415722,
0.001345032243989408,
-0.05038021504878998,
-0.08223938196897507,
-0.033230338245630264,
-0.041491299867630005,
0.03596418723464012,
-0.02699527144432068,
0.027460357174277306,
-0.004631752148270607,
-0.05281386524438858,
-0.04144752398133278,
-0.02932712994515896,
-0.025682732462882996,
0.000888183421920985,
0.013492698781192303,
0.047572676092386246,
-0.03037104383111,
-0.06262146681547165,
0.052396319806575775,
0.01777336373925209,
-0.05454009026288986,
-0.01077585481107235,
-0.007031901273876429,
-0.02473086677491665,
-0.04832028970122337,
-0.005099511239677668,
0.04197987541556358,
-0.021513188257813454,
-0.006962312385439873,
0.021551746875047684,
0.03774828091263771,
0.013763640075922012,
0.013086306862533092,
0.006928471848368645,
0.016250379383563995,
0.00327610457316041,
-0.01189412735402584,
0.06384017318487167,
-0.020659569650888443,
-0.003237830474972725,
-0.01836821436882019,
0.02092820405960083,
0.05829685926437378,
0.0362393893301487,
-0.03499554470181465,
-0.0038592200726270676,
-0.04522540420293808,
0.043377410620450974,
-0.04257742688059807,
0.017525117844343185,
0.014135817997157574,
-0.0005140250432305038,
0.049685534089803696,
-0.01235672552138567,
0.028933605179190636,
-0.04746292904019356,
-0.01815192773938179,
0.02278299257159233,
0.022950412705540657,
-0.03910551965236664,
-0.029264211654663086,
0.019665177911520004,
0.03611002862453461,
0.029736768454313278,
-0.030961763113737106,
-0.026856804266572,
0.046021122485399246,
0.026295453310012817,
0.018845882266759872,
-0.020546888932585716,
-0.04646214470267296,
0.005433270242065191,
-0.0771675556898117,
-0.016170592978596687,
-0.022533059120178223,
0.0487169548869133,
0.003986350726336241,
0.06277526170015335,
0.006082822103053331,
0.01502484455704689,
0.010323580354452133,
0.00840927753597498,
-0.06473225355148315,
0.007088341284543276,
-0.05307627469301224,
-0.01674780808389187,
-0.04365036264061928,
-0.03445116803050041,
-0.013620828278362751,
-0.006948508787900209,
-0.015281397849321365,
-0.030877290293574333,
-0.017294304445385933,
-0.0581759512424469,
0.0005265658837743104,
-0.020912274718284607,
-0.01986655965447426,
-0.033296067267656326,
0.06180402263998985,
0.0013326478656381369,
-0.04606609791517258,
0.024155309423804283,
0.0624520406126976,
-0.03470529988408089,
-0.01605943962931633,
-0.02893853187561035,
-0.004174364730715752,
0.026738090440630913,
0.016048086807131767,
0.012820618227124214,
-0.001553512061946094,
-0.009603563696146011,
-0.008749502710998058,
0.002206637989729643,
0.03190504014492035,
0.01829700730741024,
0.0011192223755642772,
-0.044246528297662735,
-0.03939446061849594,
-0.024510780349373817,
-0.014283489435911179,
0.07322456687688828,
0.003295962465927005,
-0.013403047807514668,
0.01949533261358738,
-0.023218976333737373,
0.018157536163926125,
0.048007238656282425,
0.03305888548493385,
0.02813161164522171,
-0.00690522650256753,
-0.061578378081321716,
0.011441480368375778,
-0.043882761150598526,
0.008189952000975609,
0.04483534395694733,
-0.015652606263756752,
-0.026057332754135132,
-0.031107429414987564,
0.02285260707139969,
0.003065027529373765,
0.01294108759611845,
-0.004569150973111391,
-0.006589879747480154,
0.005001625511795282,
-0.02009514346718788,
-0.01672864332795143,
0.02347807213664055,
0.033284079283475876,
0.055996451526880264,
0.014036388136446476,
-0.031043874099850655,
-0.07385993748903275,
-0.012487963773310184,
0.008430552668869495,
0.010543827898800373,
0.006960763130337,
0.0015742252580821514,
-0.031677667051553726,
-0.005754387471824884,
0.052528660744428635,
-0.01899770274758339,
-0.0007133594481274486,
-0.023911386728286743,
0.018931439146399498,
-0.021898869425058365,
-0.040287356823682785,
-0.05063021183013916,
0.029730288311839104,
0.018860692158341408,
0.01529623195528984,
-0.010467485524713993,
0.014575059525668621,
0.0009439620189368725,
0.03555980697274208,
0.017684627324342728,
0.05343771353363991,
0.03189588338136673,
-0.005209177266806364,
-0.006650748196989298,
0.0137478681281209,
-0.028343440964818,
-0.057568132877349854,
-0.01758056879043579,
-0.00035659526474773884,
0.015606559813022614,
0.04353285953402519,
-0.03905085474252701,
-0.023196622729301453,
0.004835154395550489,
-0.0033862858545035124,
0.0005504275904968381,
-0.01136105228215456,
-0.040877509862184525,
0.039532750844955444,
0.0267612487077713,
-0.017392778769135475,
0.06475909799337387,
0.004360381513834,
-0.0018209248082712293,
-0.04376611113548279,
-0.02306436561048031,
0.03460748493671417,
-0.017726803198456764,
-0.03950759768486023,
0.00299535458907485,
0.015069765038788319,
-0.013869860209524632,
0.015019310638308525,
-0.021911637857556343,
0.021730082109570503,
-0.059032466262578964,
-0.027454474940896034,
0.00514096999540925,
0.017763933166861534,
-0.01350340060889721,
0.009378389455378056,
-0.015398751012980938,
0.022839097306132317,
0.030285578221082687,
-0.06864561885595322,
0.01756463386118412,
0.0326579287648201,
0.008396630175411701,
-0.0009370247717015445,
0.022137632593512535,
0.026713473722338676,
-0.014193952083587646,
-0.02026813104748726,
-0.008132980205118656,
-0.0630822405219078,
0.05682171881198883,
-0.014204778708517551,
-0.049069032073020935,
0.005369879771023989,
-0.06427542865276337,
-0.028175337240099907,
-0.007183789741247892,
-0.001744970679283142,
0.03932403773069382,
-0.04885881766676903,
0.010448738932609558,
-0.011624513193964958,
0.023145560175180435,
-0.07624687999486923,
-0.05541042238473892,
0.015345457941293716,
0.002131765941157937,
-0.01829025335609913,
-0.019061293452978134,
-0.01926233619451523,
-0.010605061426758766,
-0.04661707207560539,
0.0077181668020784855,
0.04611118510365486,
-0.04015382379293442,
0.006242580711841583,
0.012170867063105106,
-0.023209312930703163,
0.050955139100551605,
-0.02555084601044655,
-0.0076794009655714035,
0.014830338768661022,
-0.03551725670695305,
0.015012379735708237,
-0.014993895776569843,
0.05609932169318199,
-0.02228613570332527,
-0.017064882442355156,
-0.005735254846513271,
-0.033417269587516785,
0.020230064168572426,
-0.048841383308172226,
-0.01508188433945179,
0.0422828309237957,
0.022578056901693344,
-0.055918216705322266,
-0.012907189317047596,
-0.004298476502299309,
-0.008555545471608639,
0.037353672087192535,
-0.017303286120295525,
-0.012597055174410343,
-0.05508587881922722,
-0.015725547447800636,
0.0008094711811281741,
0.015092965215444565,
0.06932135671377182,
-0.010801040567457676,
0.05786221846938133,
-0.008635876700282097,
-0.006527504418045282,
0.02192072756588459,
-0.005253016483038664,
0.007844129577279091,
-0.0012206456158310175,
-0.022176582366228104,
0.015011440962553024,
0.012251668609678745,
-0.05649171024560928,
0.006296183448284864,
-0.013200371526181698,
0.007738049607723951,
0.06824180483818054,
-0.04598132520914078,
0.04997837543487549,
0.016306912526488304,
0.011340447701513767,
0.014238257892429829,
-0.022464849054813385,
-0.027559880167245865,
-0.017682265490293503,
-0.00792628526687622,
0.02637176774442196,
-0.03926054388284683,
0.012134974822402,
0.04738015681505203,
0.041496358811855316,
-0.024988140910863876,
0.007708138320595026,
0.01120283268392086,
0.03666703775525093,
-0.017166446894407272,
0.0223529189825058,
-0.048133231699466705,
0.02357359230518341,
-0.0035778945311903954,
0.01670083962380886,
0.010492056608200073,
-0.00199120189063251,
0.08744698762893677,
-0.027175763621926308,
0.009088821709156036,
-0.045708682388067245,
-0.015657195821404457,
-0.0012921149609610438,
0.032787781208753586,
0.010381585918366909,
0.0016297590918838978,
-0.04205191880464554,
0.019095884636044502,
0.00949089229106903,
-0.002297875704243779,
0.013292663730680943,
-0.021397706121206284,
-0.08056388795375824,
-0.0421399287879467,
-0.03750455379486084,
-0.04706490784883499,
0.012613902799785137,
-0.001540292869322002,
-0.03825594484806061,
0.02095925249159336,
-0.008489411324262619,
0.05601806566119194,
0.03248514235019684,
0.00901581346988678,
-0.002363001462072134,
0.06058797240257263,
0.006032336503267288,
0.03620128333568573,
-0.012070488184690475,
0.013474504463374615,
0.11442401260137558,
0.04101879149675369,
0.026341598480939865,
-0.03546552732586861,
0.023673884570598602,
-0.05730003863573074,
0.006230803672224283,
-0.059523820877075195,
-0.012520532123744488,
-0.06121008098125458,
0.002592915203422308,
0.04909321665763855,
0.05066404864192009,
-0.007854028604924679,
0.005128221586346626,
0.052242815494537354,
-0.030256042256951332,
-0.039881087839603424,
-0.030860163271427155,
0.048778045922517776,
-0.012338753789663315,
0.02457253448665142,
-0.06275846064090729,
0.0454854778945446,
-0.05427074059844017,
-0.008122800849378109,
-0.024594243615865707,
-0.006411084905266762,
0.018716774880886078,
-0.012479566968977451,
-0.07460874319076538,
0.012154328636825085,
0.014351867139339447,
-0.02747572585940361,
-0.0707181915640831,
-0.0018893295200541615,
0.024364547803997993,
-0.017979750409722328,
-0.03469029441475868,
0.014119797386229038,
-0.004038599785417318,
0.03728767856955528,
0.013088046573102474,
0.03374612703919411,
-0.029894497245550156,
0.020397527143359184,
-0.033129628747701645,
0.0697433352470398,
-0.039661768823862076,
0.05621279776096344,
0.005525423213839531,
0.023674583062529564,
0.0058080763556063175,
-0.03473782539367676,
-0.04308701306581497,
-0.032297100871801376,
0.03833603113889694,
0.009974055923521519,
-0.006182291079312563,
-0.025271356105804443,
0.019207026809453964,
-0.015122962184250355,
0.027691025286912918,
0.006681453436613083,
0.03234892338514328,
0.007109074853360653,
0.017304062843322754,
0.06618520617485046,
-0.012010381557047367,
-0.03384188935160637,
0.005505478475242853,
-0.010822460055351257,
-0.01661638170480728,
-0.004822114482522011,
0.007730196695774794,
0.035572782158851624,
0.02048502303659916,
-0.011041682213544846,
-0.036243680864572525,
0.006069617811590433,
-0.07500486820936203,
0.015264160931110382,
-0.010640108957886696,
0.005536176264286041,
-0.010325087234377861,
0.008169387467205524,
0.005135950166732073,
0.04234551265835762,
-0.01179344579577446,
-0.005476194433867931,
0.007094969041645527,
-0.004478948190808296,
0.00467465678229928,
-0.03258366882801056,
-0.022564873099327087,
-0.008585844188928604,
-0.025659793987870216,
-0.024878721684217453,
0.010472351685166359,
-0.011616282165050507,
0.030531665310263634,
0.042243268340826035,
0.008242822252213955,
0.04769189655780792,
-0.04076187312602997,
0.027579018846154213,
0.01147528551518917,
-0.008557385765016079,
0.013014781288802624,
0.012900382280349731,
-0.01078555267304182,
-0.051336370408535004,
-0.0066447630524635315,
-0.019079113379120827,
0.009791333228349686,
0.0020788591355085373,
0.018757712095975876,
0.0021470801439136267,
-0.014616112224757671,
-0.0007699948037043214,
0.003941642586141825,
-0.02043275348842144,
-0.004033645149320364,
-0.05715586617588997,
-0.0003913439577445388,
0.02661270648241043,
-0.002091816160827875,
-0.01838826946914196,
0.04713756591081619,
-0.02756156213581562,
0.011543537490069866,
0.024715077131986618,
0.013279684819281101,
0.0010403604246675968,
-0.004559180699288845,
0.0010847400408238173,
-0.01757686957716942,
0.0416053868830204,
-0.007447818759828806,
-0.03308422118425369,
0.041531164199113846,
-0.038074009120464325,
-0.060628972947597504,
0.0018257919000461698,
-0.001772361691109836,
0.029620768502354622,
0.02640715427696705,
0.018780287355184555,
-0.02581792324781418,
0.07744958996772766,
-0.016025707125663757,
0.008668015711009502,
-0.0013050695415586233,
-0.024603189900517464,
0.034373048692941666,
-0.02216535620391369,
0.01786232367157936,
-0.005744739901274443,
0.043860066682100296,
0.021078312769532204,
0.015280067920684814,
-0.018708486109972,
0.019546186551451683,
0.04954032227396965,
0.0005128822522237897,
-0.0037580335047096014,
0.031021203845739365,
0.02928292565047741,
0.03852397948503494,
0.06950639188289642,
-0.02329840324819088,
0.02788613550364971,
0.013267457485198975,
0.027964403852820396,
-0.06160757318139076,
-0.011731659062206745,
0.010690141469240189,
-0.005492717027664185,
0.006594906095415354,
-0.061215490102767944,
-0.016930682584643364,
0.01574994996190071,
-0.09218967705965042,
0.008159716613590717,
-0.05365745350718498,
-0.023284774273633957,
-0.0319371223449707,
-0.031138578429818153,
0.0010567328426986933,
0.037438664585351944,
0.0023130225017666817,
0.05508045852184296,
0.025348788127303123,
0.008696661330759525,
-0.016715608537197113,
-0.03192831203341484,
-0.015033031813800335,
0.05523722991347313,
0.005771419033408165,
-0.019737226888537407,
0.044604457914829254,
-0.0011886690044775605,
0.015179683454334736,
0.0031344813760370016,
-0.006380502600222826,
0.011860380880534649,
-0.022318042814731598,
0.017134644091129303,
-0.006170105654746294,
0.01433906052261591,
-0.0054093170911073685,
-0.005467440467327833,
-0.007838704623281956,
0.03597862273454666,
0.04549390450119972,
-0.017241543158888817,
-0.013832991011440754,
0.00166655657812953,
0.04145362600684166,
-0.04183662310242653,
-0.009914647787809372,
0.0405840128660202,
-0.009283358231186867,
-0.00524746673181653,
0.0011787652038037777,
0.027866072952747345,
0.0015486229676753283,
-0.03189218044281006,
0.020541289821267128,
-0.04805304482579231,
-0.03941154479980469,
0.030129121616482735,
-0.029971851035952568,
0.010309948585927486,
0.020441100001335144,
-0.005850071553140879,
-0.0335158035159111,
0.011416059918701649,
-0.003241780446842313,
0.005835871212184429,
-0.06482245028018951,
0.028367966413497925,
0.02480003796517849,
-0.012896028347313404,
0.017799660563468933,
-0.040067557245492935,
-0.044753044843673706,
0.02591453120112419,
0.05368172749876976,
0.004514487460255623,
-0.007935525849461555,
-0.03897765278816223,
0.004897225182503462,
-0.03812682256102562,
0.022168368101119995,
0.0032727576326578856,
-0.039261769503355026,
-0.007399467285722494,
-0.01959679089486599,
0.028896786272525787,
0.011217492632567883,
0.0524027980864048,
-0.0028010185342282057,
0.009725186973810196,
-0.00114365853369236,
0.020740017294883728,
0.013574381358921528,
-0.07854542881250381,
-0.006822692696005106,
0.03213699162006378,
-0.013590780086815357,
0.019066955894231796,
0.030728332698345184,
-0.007852171547710896,
-0.011491834186017513,
-0.009505128487944603,
0.015699228271842003,
0.0326949767768383,
-0.014117386192083359,
-0.049730539321899414,
0.018228216096758842,
0.02881968580186367,
-0.01271795853972435,
0.0705561563372612,
-0.01554587110877037,
0.02804194577038288,
0.0015463046729564667,
-0.013459023088216782,
-0.021432416513562202,
0.0334043987095356,
-0.03214577957987785,
0.0294280294328928,
-0.043387364596128464,
0.02686403878033161,
0.03716881200671196,
-0.040668878704309464,
-0.00927339494228363,
0.05673317238688469,
-0.041464075446128845,
-0.0020701561588793993,
0.0602782666683197,
-0.0012761278776451945,
0.035565655678510666,
-0.014860482886433601,
0.01605626381933689,
0.0033319019712507725,
0.0046317558735609055,
-0.030400671064853668,
0.02944525144994259,
0.0377860851585865,
-0.0011085739824920893,
-0.019858667626976967,
0.09096907824277878,
0.017258301377296448,
0.029633887112140656,
0.0011429553851485252,
0.017164073884487152,
-0.02665524184703827,
-0.022214578464627266,
-0.027272716164588928,
-0.04133789613842964,
0.037819866091012955,
0.02311565726995468,
-0.007852180860936642,
0.09502553939819336,
-0.04822339862585068,
0.00514874467626214,
-0.007060296833515167,
-0.02712060697376728,
-0.029621055349707603,
0.02425656095147133,
0.01612614095211029,
0.02715625800192356,
0.00035773604759015143,
-0.02995046228170395,
-0.033236972987651825,
-0.013855243101716042,
0.025320272892713547,
-0.006663666572421789,
0.02387193776667118,
0.011619174852967262,
0.008915606886148453,
-0.012875428423285484,
-0.00766898225992918,
-0.0026806103996932507,
-0.007607176899909973,
0.028996620327234268,
0.0020262175239622593,
0.026488544419407845,
0.03244960308074951,
0.00004438585165189579,
-0.014475386589765549,
0.07023151218891144,
-0.05853242427110672,
-0.043019142001867294,
-0.03460494056344032,
0.02575721964240074,
-0.0009766913717612624,
-0.009807934053242207
] |
<p>I apologize if this question is not up to par.
When I was doing exercises in basic mechanics I checked the answers and I can't seem to find what I'm doing wrong.
Suppose we have a ball with mass $m$ and radius $r$ on an inclined plane with height $h$. At the end of the inclined plane is a loop with a radius of $R$ and we can assume that $r<<R$. We are asked what the minimum height is the inclined plane should have so as to let the ball complete the loop. Here is my reasoning:</p>
<p>We have $U_1\geq K_{rot,2}+K_{trans,2}+U_2$.</p>
<p>For the ball rotating we have $I=\frac{1}{2}mr^2$ and $\omega=\frac{v}{r}$.</p>
<p>So $mgh\geq \frac{1}{2}I\omega^2+\frac{1}{2}mv^2+mg\cdot2R=\frac{3}{4} mv^2+mg\cdot 2R$.</p>
<p>The minimal speed to complete the loop implies $F_{centripetal}=\frac{mv^2}{R}= mg$</p>
<p>So $v^2= Rg$ and we have $gh\geq \frac{3}{4}Rg+g\cdot 2R$ which means $h\geq 2\frac{3}{4}R$, while the book says that the answer should be $h\geq 2.70R$. Can you explain what I am doing wrong?</p>
<p>Thank you</p>
<p><strong>EDIT:</strong>
Moment of inertia corrected.</p>
<p>For the ball rotating we have $I=\frac{2}{5}mr^2$ and $\omega=\frac{v}{r}$.</p>
<p>So $mgh\geq \frac{1}{2}I\omega^2+\frac{1}{2}mv^2+mg\cdot2R=\frac{7}{10} mv^2+mg\cdot 2R$.</p>
<p>After the edit with correction of the moment of inertia I am getting the right answer.
We get $gh\geq\frac{7}{10}Rg+g\cdot 2R$ so $h\geq2\frac{7}{10}R$ in accordance with the book.</p> | 1,468 | [
-0.045367930084466934,
-0.016312338411808014,
0.009343467652797699,
0.036436695605516434,
0.0274182315915823,
-0.007950235158205032,
-0.03689705953001976,
-0.04926975443959236,
-0.00029118021484464407,
0.024859895929694176,
0.014932932332158089,
0.032507315278053284,
0.03773372620344162,
0.0419185571372509,
0.013273777440190315,
0.005497243721038103,
-0.00484255887567997,
-0.019491061568260193,
0.0139046935364604,
-0.03344811126589775,
-0.05233855918049812,
0.0031144586391747,
0.044882453978061676,
-0.03088896907866001,
-0.017146797850728035,
0.009274822659790516,
0.04901318997144699,
-0.015088201500475407,
-0.036632828414440155,
0.021265773102641106,
-0.0411161445081234,
0.017258331179618835,
0.023964371532201767,
0.027385052293539047,
0.028344962745904922,
0.06489543616771698,
-0.04512260854244232,
0.017981622368097305,
-0.021989043802022934,
0.03979172557592392,
-0.003479345003142953,
0.023823466151952744,
-0.002621477236971259,
0.024283193051815033,
0.016480574384331703,
0.03504826873540878,
-0.0041734604164958,
0.011030024848878384,
0.061838336288928986,
-0.04579577222466469,
0.08910728245973587,
0.014924569986760616,
0.0054835486225783825,
-0.01631416566669941,
0.0027536586858332157,
-0.02575519308447838,
0.06103873997926712,
0.05570584535598755,
0.007680507376790047,
-0.04175611957907677,
-0.022248312830924988,
-0.060236454010009766,
-0.039364710450172424,
-0.025258852168917656,
0.02130933851003647,
0.013472369872033596,
-0.00956646353006363,
0.024039937183260918,
0.03176398575305939,
0.018942395225167274,
-0.01074575912207365,
0.008451910689473152,
0.02491695247590542,
-0.03982356935739517,
0.013921506702899933,
0.02060782164335251,
-0.004865844268351793,
-0.006454348564147949,
0.007654333952814341,
0.02230570651590824,
-0.025864984840154648,
-0.00825841911137104,
0.051105063408613205,
0.049398984760046005,
-0.007019380107522011,
-0.0015735937049612403,
0.048517581075429916,
0.0028133930172771215,
-0.008264019154012203,
0.02108532004058361,
-0.01002697553485632,
-0.0156689640134573,
0.007282122038304806,
-0.0029118654783815145,
-0.0018876934191212058,
0.040204308927059174,
0.007799585349857807,
0.04316667467355728,
-0.02052067220211029,
0.008397436700761318,
-0.044041868299245834,
-0.07720120251178741,
0.02819962613284588,
0.0908735916018486,
0.026758307591080666,
-0.021823043003678322,
-0.020144877955317497,
-0.038971345871686935,
0.007860551588237286,
0.0024406379088759422,
-0.040162842720746994,
0.007216667756438255,
-0.023050742223858833,
-0.026482123881578445,
-0.02366356924176216,
-0.010279839858412743,
-0.013196012005209923,
-0.006773195695132017,
0.027112595736980438,
-0.002053517382591963,
0.02231929451227188,
-0.020700862631201744,
-0.012233763933181763,
-0.05635112524032593,
-0.06653587520122528,
0.00001586895996297244,
0.023848455399274826,
-0.02727263979613781,
-0.004369197878986597,
0.023778289556503296,
0.005591325927525759,
0.027078736573457718,
-0.011868692934513092,
0.02341371960937977,
0.034104615449905396,
-0.05431574583053589,
-0.0802949070930481,
-0.050146326422691345,
0.07568381726741791,
0.007911867462098598,
0.011263690888881683,
-0.07338501513004303,
-0.02411237731575966,
0.03868955746293068,
0.09406421333551407,
0.007416144013404846,
0.024253059178590775,
0.015942394733428955,
0.0061973752453923225,
-0.009456316009163857,
-0.02060621790587902,
0.01171757560223341,
-0.010149857960641384,
-0.011192589066922665,
-0.010750523768365383,
-0.04143156856298447,
0.04065263643860817,
0.007017301861196756,
0.023500069975852966,
-0.01187355350703001,
0.031232213601469994,
-0.03173699229955673,
0.051097821444272995,
-0.014223901554942131,
-0.022934438660740852,
-0.0014758077450096607,
0.03234472870826721,
0.003360554575920105,
0.0001124157861340791,
0.028060395270586014,
-0.02144644595682621,
0.022441385313868523,
-0.005421622656285763,
0.007437307387590408,
0.07040804624557495,
-0.014572477899491787,
0.007998879998922348,
-0.0050628166645765305,
-0.01488520111888647,
0.0019522433867678046,
0.0016028338577598333,
-0.04553729668259621,
0.016731038689613342,
-0.0017781620845198631,
-0.008854562416672707,
0.03558605536818504,
0.003950810991227627,
0.0331558920443058,
0.019015081226825714,
-0.02242906391620636,
0.01411028765141964,
-0.03645637631416321,
0.011123217642307281,
0.04014795646071434,
-0.019392071291804314,
0.000131130131194368,
0.013011599890887737,
0.014804321341216564,
0.00943723227828741,
-0.03332960978150368,
0.012892422266304493,
0.04930605739355087,
0.020888492465019226,
0.005257750861346722,
0.040314529091119766,
0.05645681172609329,
0.004845681134611368,
0.046834856271743774,
0.010824711062014103,
-0.009636239148676395,
0.01856100745499134,
-0.017379790544509888,
0.013273908756673336,
0.010631773620843887,
0.011260776780545712,
0.02185264229774475,
0.02584220841526985,
0.006287953816354275,
-0.009906903840601444,
0.018385527655482292,
-0.027227113023400307,
0.06673929840326309,
0.04648713394999504,
0.010545246303081512,
0.009996346198022366,
0.02194860763847828,
-0.011019907891750336,
0.03823370113968849,
0.0003798851976171136,
-0.023124441504478455,
-0.03648770973086357,
-0.0006140240584500134,
-0.03059917315840721,
0.061148177832365036,
-0.05009156093001366,
-0.007285617291927338,
0.023629698902368546,
0.017618833109736443,
0.013610313646495342,
0.030985616147518158,
0.0014546425081789494,
-0.042925942689180374,
0.04129861667752266,
0.044761061668395996,
-0.023814750835299492,
0.027726560831069946,
0.010766989551484585,
0.05135089159011841,
0.0028225097339600325,
-0.021056558936834335,
0.004880258347839117,
0.027780750766396523,
0.05696849897503853,
0.0033299773931503296,
0.026747582480311394,
0.007195824757218361,
0.05172748491168022,
0.020718326792120934,
0.02180587500333786,
0.08156164735555649,
0.003365186508744955,
0.017562229186296463,
-0.02022097259759903,
-0.012136230245232582,
0.01062886044383049,
0.0006844170275144279,
0.00678207678720355,
-0.03308757022023201,
0.00990999210625887,
-0.05053464695811272,
-0.03909721225500107,
-0.03875007852911949,
-0.01200221385806799,
-0.004017420578747988,
-0.00635149423032999,
0.015028461813926697,
-0.02215718850493431,
0.016409097239375114,
0.015047958120703697,
0.026545023545622826,
-0.025268467143177986,
-0.01279779989272356,
0.015014514327049255,
-0.026879863813519478,
-0.04739638790488243,
-0.01572231389582157,
-0.04403899982571602,
-0.011283616535365582,
0.013528884388506413,
0.02367815561592579,
-0.013207542710006237,
0.02171621285378933,
0.039852190762758255,
-0.018107227981090546,
0.00125565764028579,
-0.026823261752724648,
0.04060647264122963,
-0.059948232024908066,
-0.008987209759652615,
0.054707251489162445,
0.013513411395251751,
-0.01823342964053154,
-0.008421456441283226,
-0.052024178206920624,
-0.05619672313332558,
-0.016782181337475777,
0.019085820764303207,
0.023484867066144943,
-0.022034920752048492,
0.007894044741988182,
-0.01009080745279789,
0.03637387603521347,
-0.01563497632741928,
-0.0682438537478447,
-0.025968559086322784,
-0.010463529266417027,
-0.015105253085494041,
0.05483657494187355,
0.002787175355479121,
-0.011248522438108921,
0.09173126518726349,
0.06104058399796486,
0.00481811398640275,
-0.00020728984964080155,
-0.004199158400297165,
0.0341736264526844,
-0.05291574448347092,
-0.027950596064329147,
0.056673288345336914,
0.024505043402314186,
-0.018500452861189842,
0.013483228161931038,
0.0008128741756081581,
0.0368172787129879,
0.003823637729510665,
0.011891760863363743,
0.005034925416111946,
0.00022073219588492066,
0.008786828257143497,
0.03265897184610367,
0.0019342143787071109,
0.00840905774384737,
-0.004181974101811647,
-0.003315827576443553,
0.05094025284051895,
-0.014633274637162685,
-0.07431183010339737,
0.026310725137591362,
-0.007041884586215019,
0.020119065418839455,
-0.00598126882687211,
0.05097278207540512,
0.007254856638610363,
-0.060855984687805176,
0.0021534713450819254,
0.004915989004075527,
0.08851009607315063,
0.0029878253117203712,
0.022239841520786285,
0.057405147701501846,
-0.007654404267668724,
-0.01281399093568325,
0.0162942074239254,
-0.01232041697949171,
-0.004955576732754707,
0.02889603190124035,
-0.038620077073574066,
-0.029103467240929604,
0.007801102939993143,
0.04519723355770111,
-0.0026176460087299347,
0.004343709908425808,
-0.047457724809646606,
-0.0044443802908062935,
-0.06664896011352539,
-0.003085407894104719,
-0.029555868357419968,
0.06153056025505066,
-0.011278104968369007,
0.03232935070991516,
0.003027860075235367,
-0.0030515072867274284,
-0.0108802430331707,
-0.011576044373214245,
-0.0769951343536377,
0.022315410897135735,
-0.04432080686092377,
-0.004607342649251223,
0.006692585069686174,
-0.024825528264045715,
0.019579147920012474,
-0.05239584669470787,
-0.01697493903338909,
-0.03276074305176735,
-0.026946239173412323,
-0.0426749624311924,
0.024388065561652184,
-0.009155381470918655,
-0.0314258337020874,
0.03801094740629196,
0.02725943922996521,
0.05685756728053093,
-0.026251815259456635,
0.058670129626989365,
0.025751620531082153,
-0.034030523151159286,
0.023035284131765366,
-0.03805498778820038,
-0.017864733934402466,
0.008538957685232162,
0.02884412743151188,
0.01276126503944397,
0.018383877351880074,
0.019977105781435966,
-0.0487530417740345,
-0.013501236215233803,
0.013209815137088299,
0.025174444541335106,
-0.02121506817638874,
-0.03969091176986694,
-0.056473568081855774,
0.005334760993719101,
-0.011515282094478607,
0.03758447244763374,
-0.041379429399967194,
0.010248947888612747,
0.039354100823402405,
-0.03620825707912445,
0.004606000613421202,
0.02788134291768074,
0.03410455957055092,
0.011669671162962914,
-0.04068310931324959,
-0.07136275619268417,
-0.05156058818101883,
-0.03448529541492462,
-0.00834327656775713,
0.03199366480112076,
-0.02403896674513817,
-0.04181962087750435,
-0.030751751735806465,
0.04183247312903404,
0.04145154729485512,
0.01844482682645321,
0.016023963689804077,
-0.016879603266716003,
0.0483064204454422,
-0.01441153697669506,
-0.019651703536510468,
-0.006539836525917053,
0.026373952627182007,
0.04597892612218857,
0.006882955320179462,
0.003912739455699921,
-0.026433810591697693,
-0.03566845878958702,
0.008110199123620987,
0.05450330302119255,
-0.01800992526113987,
0.025519931688904762,
-0.042479146271944046,
-0.006392326205968857,
0.0679081380367279,
-0.036694157868623734,
0.05985645949840546,
-0.037046656012535095,
0.0170215405523777,
-0.011034557595849037,
-0.05091852694749832,
-0.06878511607646942,
-0.004502368625253439,
-0.003088848665356636,
-0.03507180139422417,
-0.035570256412029266,
0.020521746948361397,
0.02815079689025879,
-0.039387695491313934,
0.019092794507741928,
0.03311214968562126,
0.014857505448162556,
0.007158040069043636,
0.03689586743712425,
0.02690809592604637,
-0.037317294627428055,
-0.08477669954299927,
0.006533992011100054,
-0.015738049522042274,
-0.01332964189350605,
-0.0008224311168305576,
-0.04789411276578903,
-0.06231436878442764,
0.0718933716416359,
0.04560215026140213,
0.023609986528754234,
0.021833883598446846,
-0.04351496323943138,
0.02175755612552166,
0.02273845300078392,
-0.035350456833839417,
-0.005704832263290882,
0.029229192063212395,
-0.029080769047141075,
-0.009401182644069195,
-0.02386285364627838,
-0.019711952656507492,
-0.034431684762239456,
-0.022692544385790825,
-0.029655897989869118,
0.004094704519957304,
-0.045261774212121964,
0.036127083003520966,
0.007486169692128897,
0.04167177155613899,
0.0017884914996102452,
-0.03659531846642494,
0.014315780252218246,
0.019337451085448265,
0.017686203122138977,
0.0035611141938716173,
-0.018855765461921692,
0.0017163120210170746,
0.009055230766534805,
-0.04680398106575012,
-0.023283887654542923,
-0.018180930987000465,
0.01277841441333294,
0.05380292236804962,
0.014596642926335335,
-0.0021086609922349453,
-0.042426954954862595,
-0.030774565413594246,
-0.05564402788877487,
-0.051332809031009674,
0.0478401742875576,
-0.022427674382925034,
-0.03508613258600235,
0.01496391836553812,
-0.014270491898059845,
-0.0374046228826046,
0.005130699370056391,
-0.009533674456179142,
-0.041662342846393585,
0.014982840046286583,
0.009680090472102165,
0.032037124037742615,
0.023109788075089455,
-0.0076593453995883465,
-0.03845306858420372,
0.024545488879084587,
-0.002748711034655571,
-0.03037450835108757,
-0.013643795624375343,
0.010758093558251858,
-0.029121853411197662,
-0.048769351094961166,
-0.02352009527385235,
0.03108273260295391,
-0.03474971652030945,
0.010748465545475483,
0.0026291024405509233,
0.0228717178106308,
0.05176019296050072,
-0.013736940920352936,
-0.026189107447862625,
0.027499599382281303,
-0.0044298614375293255,
-0.03432871773838997,
-0.0016783096361905336,
0.025083251297473907,
-0.016252167522907257,
-0.032517123967409134,
-0.0012951213866472244,
-0.02106284350156784,
0.04700075089931488,
0.01837518997490406,
0.01433764398097992,
0.029783548787236214,
-0.01819082349538803,
-0.003972320817410946,
-0.01036920491605997,
0.0020714777056127787,
-0.02802523784339428,
0.031127827242016792,
-0.005155215971171856,
0.007737533189356327,
0.0183583814650774,
-0.04031091928482056,
0.06347888708114624,
0.005089791491627693,
-0.004147035535424948,
-0.02117297239601612,
0.07477999478578568,
-0.05188743397593498,
-0.014032779261469841,
-0.015980714932084084,
-0.0061861686408519745,
-0.000945563311688602,
0.000960508652497083,
-0.014746063388884068,
0.03326309472322464,
0.048244353383779526,
-0.012711497023701668,
-0.02195821702480316,
-0.06859558075666428,
0.04243749752640724,
0.07287269830703735,
-0.017484571784734726,
0.026767797768115997,
0.027408281341195107,
-0.010253403335809708,
0.006809751968830824,
0.011933423578739166,
-0.03449656069278717,
0.012287423945963383,
0.03352319076657295,
0.0350407175719738,
-0.029210753738880157,
0.012529305182397366,
0.006933088414371014,
-0.00024256296455860138,
-0.027445686981081963,
-0.01600981503725052,
0.02526441588997841,
-0.013731551356613636,
-0.03820653632283211,
-0.010272489860653877,
-0.046124547719955444,
0.0007386291981674731,
0.035556860268116,
0.07745018601417542,
-0.023593459278345108,
-0.013792203739285469,
0.008267947472631931,
0.020021682605147362,
0.01566656492650509,
-0.030101580545306206,
0.01865595579147339,
-0.012085436843335629,
0.004402412101626396,
0.014317246153950691,
-0.03809047117829323,
-0.025348376482725143,
0.003606617683544755,
0.029531165957450867,
-0.0151642682030797,
0.04915008693933487,
-0.06200109049677849,
-0.027679936960339546,
0.008553219959139824,
-0.010414347052574158,
-0.0752941146492958,
0.07628102600574493,
0.04209049046039581,
-0.03751739114522934,
0.044010553508996964,
-0.01190937589854002,
-0.0005264897481538355,
0.030895989388227463,
0.018863528966903687,
0.009996403008699417,
0.08736185729503632,
0.0016843245830386877,
0.014491377398371696,
-0.028178760781884193,
0.006826244294643402,
0.1511780470609665,
0.049533624202013016,
-0.00009768523159436882,
-0.030527187511324883,
0.02717461809515953,
-0.03419005870819092,
-0.01007932797074318,
-0.026206932961940765,
0.005944543983787298,
-0.01728764735162258,
-0.01242586225271225,
0.03835700452327728,
0.03704838082194328,
-0.05230363830924034,
0.020543096587061882,
0.025438843294978142,
-0.051910653710365295,
-0.013120279647409916,
-0.014102349989116192,
-0.001974385231733322,
-0.012943971902132034,
0.010729513131082058,
0.003947547636926174,
0.05558483675122261,
-0.024168377742171288,
-0.023305190727114677,
-0.019353266805410385,
-0.03403180465102196,
0.03695235028862953,
-0.026184147223830223,
-0.056969910860061646,
0.004681252874433994,
-0.001968586351722479,
-0.06614595651626587,
-0.022074298933148384,
0.038600821048021317,
0.002121987286955118,
-0.043584104627370834,
0.01697957143187523,
0.04474058374762535,
-0.02137400023639202,
0.02894631400704384,
0.03794560953974724,
0.016666725277900696,
-0.03078491985797882,
0.02146865986287594,
-0.05383918806910515,
0.03260517120361328,
-0.03984308987855911,
0.026314429938793182,
0.0026990375481545925,
-0.005242231767624617,
-0.01871759258210659,
-0.03304431587457657,
-0.00633081141859293,
-0.012721863575279713,
0.04379844292998314,
-0.02128293178975582,
0.009591162204742432,
-0.024209080263972282,
-0.0052003865130245686,
0.0795082151889801,
-0.013366056606173515,
-0.029144708067178726,
-0.023959120735526085,
-0.012649725191295147,
0.0008493539062328637,
0.050038114190101624,
-0.022915206849575043,
-0.02101122960448265,
-0.006796935107558966,
-0.0037908575031906366,
0.0008179876604117453,
0.005618471652269363,
0.006627148482948542,
0.013522328808903694,
0.020050112158060074,
0.017444046214222908,
-0.02946934662759304,
0.0064968629740178585,
-0.04576139152050018,
0.019886402413249016,
0.004847195465117693,
-0.02284211479127407,
-0.011044836603105068,
-0.03375028446316719,
-0.03941263258457184,
0.03498457744717598,
0.03832457587122917,
0.026594150811433792,
0.0022591128945350647,
0.036303479224443436,
-0.025887727737426758,
-0.01636114902794361,
-0.02865590900182724,
0.019724847748875618,
-0.02554847113788128,
0.02598498947918415,
-0.032858703285455704,
0.033179257065057755,
0.04629175737500191,
-0.00021757878130301833,
-0.019825197756290436,
0.004070594906806946,
-0.013350903056561947,
0.006348123773932457,
0.005177196580916643,
-0.018892157822847366,
0.0030571073293685913,
0.037419579923152924,
0.001248350366950035,
-0.06445618718862534,
0.010749170556664467,
0.0031985288951545954,
-0.006735444068908691,
-0.020146969705820084,
-0.03702583536505699,
-0.012683904729783535,
0.03103664331138134,
-0.058880794793367386,
0.005178139545023441,
-0.02577180415391922,
-0.020164692774415016,
-0.029870757833123207,
0.03133691847324371,
0.011948302388191223,
0.011043469421565533,
-0.04779991880059242,
0.026974113658070564,
0.029156556352972984,
-0.0012208254775032401,
-0.020893016830086708,
0.004858780652284622,
0.02563440427184105,
-0.02799830213189125,
0.006497126538306475,
0.010706312954425812,
0.04169917479157448,
-0.02012311853468418,
-0.003208394628018141,
0.03715256229043007,
-0.011351821944117546,
-0.03592945635318756,
0.030190743505954742,
0.03591453656554222,
0.0005402437527664006,
-0.010339468717575073,
-0.046887073665857315,
0.010066409595310688,
0.03758964315056801,
-0.027669083327054977,
-0.003637120360508561,
-0.03407520055770874,
-0.024479473009705544,
0.010881074704229832,
-0.049939483404159546,
-0.0298407431691885,
-0.05049992725253105,
0.004630792886018753,
0.02098700776696205,
0.00751112774014473,
-0.06603563576936722,
0.014614525251090527,
0.0016646572621539235,
0.017325405031442642,
0.009687928482890129,
0.023276111111044884,
0.05798846110701561,
0.04181283712387085,
0.012512209825217724,
-0.00594745110720396,
-0.012372405268251896,
0.002448583487421274,
0.0029362349305301905,
-0.10877200216054916,
-0.03247624635696411,
-0.0058020963333547115,
0.03266952559351921,
0.058388665318489075,
-0.07021456211805344,
-0.0011411673622205853,
0.042799051851034164,
-0.05613735690712929,
0.005195186007767916,
-0.018681567162275314,
0.020882971584796906,
-0.036254771053791046,
-0.05300804227590561,
-0.010363510809838772,
-0.008379855193197727,
-0.0031139347702264786,
0.008275743573904037,
0.024542104452848434,
0.015325076878070831,
-0.07182665914297104,
-0.024495620280504227,
0.044322893023490906,
0.05118517205119133,
-0.024264207109808922,
-0.01612713746726513,
0.05236433073878288,
0.009766310453414917,
-0.02458333782851696,
0.0029058498330414295,
-0.008351314812898636,
0.01862681284546852,
-0.02500040829181671,
0.03151911124587059,
-0.012242100201547146,
0.051689594984054565,
0.006457422859966755,
0.010637856088578701,
-0.0045354547910392284,
-0.014365719631314278,
0.03209979832172394,
0.048846714198589325,
-0.04736686125397682,
-0.007646133657544851,
0.007800247520208359,
-0.023117372766137123,
-0.03413926437497139,
0.047694217413663864,
-0.062296390533447266,
0.008711387403309345,
0.026476183906197548,
0.02783368155360222,
-0.027058251202106476,
-0.07899797707796097,
-0.00016531371511518955,
-0.012874125503003597,
0.018608955666422844,
0.027360903099179268,
-0.04762226715683937,
0.02520865574479103,
0.0010460159974172711,
0.010340544395148754,
-0.002199931535869837,
-0.01810205914080143,
-0.002148235449567437,
-0.040452077984809875,
-0.032600875943899155,
0.016823427751660347,
0.0003934511623810977,
0.008114508353173733,
-0.013737195171415806,
-0.03247674182057381,
-0.006134445779025555,
0.01685171201825142,
0.054594527930021286,
0.0053301104344427586,
-0.0330393947660923,
-0.002992149442434311,
-0.02570495195686817,
-0.05029910057783127,
-0.0028534168377518654,
0.02090333215892315,
-0.04444446414709091,
0.016856221482157707,
-0.05352232605218887,
0.022925114259123802,
0.0032969932071864605,
0.07684928923845291,
0.011570213362574577,
-0.03425393998622894,
0.03583361953496933,
-0.0028061855118721724,
0.039516691118478775,
-0.015202786773443222,
0.029376378282904625,
-0.006309908349066973,
0.020046353340148926,
0.015807321295142174,
-0.007279577199369669,
-0.0005703734932467341,
-0.03093595616519451,
-0.004527835175395012,
0.007983166724443436,
0.02972489595413208,
0.013821495696902275,
-0.009181794710457325,
0.031801946461200714,
0.010662567801773548,
-0.010726390406489372,
0.053637053817510605,
-0.01091163419187069,
0.003927281592041254,
0.03174556791782379,
-0.02632438950240612,
-0.022535348311066628,
0.04628020524978638,
-0.02006014809012413,
-0.028934156522154808,
-0.0289923083037138,
-0.030824724584817886,
-0.030160028487443924,
-0.030577898025512695,
-0.009512025862932205,
0.04849386215209961,
-0.01603945903480053,
-0.029001398012042046,
-0.006062121130526066,
0.017711305990815163,
0.053063128143548965,
0.010778996162116528,
0.03017556667327881,
0.0064280335791409016,
-0.04114260897040367,
0.04103919863700867,
-0.0044022975489497185,
0.031048079952597618,
0.03552989289164543,
-0.02888042852282524,
0.056814227253198624,
-0.02087518200278282,
0.04642723873257637,
0.005633893888443708,
0.01722065359354019,
0.00029609532793983817,
-0.025904715061187744,
-0.015584925189614296,
-0.030559200793504715,
0.002537809545174241,
0.045468397438526154,
-0.006484484300017357,
0.04958189278841019,
-0.00746448477730155,
0.025587210431694984,
-0.011000704020261765,
0.008467013016343117,
-0.017960768193006516,
0.030493920668959618,
-0.003238334786146879,
0.018192067742347717,
0.028063951060175896,
-0.0065048872493207455,
-0.035442810505628586,
-0.009321478195488453,
0.02538292668759823,
0.02008897252380848,
0.04390828683972359,
0.05507475137710571,
0.012256868183612823,
0.002137639792636037,
-0.05247705802321434,
0.014798980206251144,
-0.01649072952568531,
0.012479016557335854,
0.043188437819480896,
0.02162872441112995,
-0.03988268971443176,
-0.0051660300232470036,
0.016271183267235756,
0.052798930555582047,
-0.045567065477371216,
-0.02626796066761017,
-0.01963213086128235,
-0.0011904187267646194,
0.008795280940830708,
0.008880621753633022
] |
<p>While tossing a coin, it is commonly experienced that you get a head, if you toss it up with the head side up, and a tails if you toss with the tails side up. Is there a mathematical proof of this using classical mechanics? I would like to see a simple model of the coin as a symmetric top, and consider the precision of the body axis of symmetry about the angular momentum. </p> | 1,469 | [
-0.05631829425692558,
-0.04947102069854736,
-0.004616574849933386,
-0.03438796475529671,
0.035561561584472656,
0.013691588304936886,
-0.007622845005244017,
0.01887228526175022,
0.0013744710013270378,
-0.04198791831731796,
0.038653936237096786,
0.048820193856954575,
0.03889968618750572,
0.05280712619423866,
0.025066090747714043,
-0.000516042928211391,
0.0038486230187118053,
-0.011172879487276077,
0.008450550027191639,
-0.025075137615203857,
0.004560568835586309,
0.003470544470474124,
0.0037373939994722605,
-0.012795988470315933,
0.003403850831091404,
-0.0007011768175289035,
0.06257395446300507,
-0.008590154349803925,
0.020850012078881264,
0.07830799371004105,
-0.04042672738432884,
0.0023980254773050547,
0.012312293983995914,
0.04263251647353172,
0.04502308368682861,
-0.017082933336496353,
0.02654971368610859,
-0.0004971384769305587,
-0.006990238092839718,
0.0147659657523036,
-0.04506083205342293,
0.0009725111885927618,
-0.022069629281759262,
0.05350081995129585,
-0.004060421604663134,
0.03185487166047096,
-0.03353043273091316,
-0.024625711143016815,
0.06386321038007736,
-0.07290346920490265,
0.08790681511163712,
0.013047410175204277,
0.05029412358999252,
0.017685193568468094,
0.04485040903091431,
-0.018529532477259636,
0.06409955024719238,
0.045986488461494446,
-0.010943667031824589,
-0.05192679166793823,
-0.02916555665433407,
-0.038086555898189545,
0.01186399906873703,
-0.014168553985655308,
-0.04438850283622742,
0.020969919860363007,
0.0006722789839841425,
-0.06460747122764587,
0.0076223332434892654,
-0.016714412719011307,
-0.020719697698950768,
0.014069427736103535,
0.0659581795334816,
0.009659120813012123,
0.00432593934237957,
-0.016808420419692993,
0.02435287833213806,
-0.008237848058342934,
0.043477438390254974,
-0.0006116117001511157,
0.007032356224954128,
-0.00527540547773242,
0.02239738032221794,
0.05611434578895569,
0.018412558361887932,
-0.027422891929745674,
0.03857232630252838,
-0.027796035632491112,
0.022701052948832512,
0.0535726435482502,
-0.03842120245099068,
-0.03548390418291092,
0.02301361784338951,
-0.042272742837667465,
-0.0548737607896328,
0.019236218184232712,
0.021215807646512985,
0.04831601306796074,
0.023651599884033203,
-0.033683184534311295,
0.02592385932803154,
-0.034799207001924515,
0.005072902888059616,
0.09012232720851898,
0.007463262882083654,
-0.0027734588366001844,
-0.009676502086222172,
0.024032671004533768,
-0.028936980292201042,
-0.014521696604788303,
-0.037518344819545746,
0.011531486175954342,
-0.021351231262087822,
0.02102990262210369,
0.0008962030406109989,
-0.008027039468288422,
-0.039571363478899,
-0.04500967636704445,
0.027644647285342216,
0.02840684913098812,
0.06171536073088646,
0.01588723435997963,
0.002856422448530793,
-0.04073256254196167,
-0.04584849253296852,
-0.012546973302960396,
0.03479192405939102,
-0.010005071759223938,
-0.030018791556358337,
0.04932760074734688,
0.022559193894267082,
-0.03317560628056526,
0.023732351139187813,
0.01796717941761017,
-0.002144433790817857,
-0.020472388714551926,
-0.09336832910776138,
-0.04624708741903305,
0.05582233890891075,
-0.008615722879767418,
-0.03569335862994194,
-0.08673672378063202,
0.044162821024656296,
0.04918310418725014,
0.04955832660198212,
0.01048359740525484,
0.03603334724903107,
-0.03165698051452637,
0.05058598518371582,
0.0324571318924427,
0.011996871791779995,
-0.006711834110319614,
0.03448938950896263,
-0.029864666983485222,
-0.019925009459257126,
-0.08184938132762909,
0.009090451523661613,
-0.00343338749371469,
-0.0008290989208035171,
-0.062310297042131424,
0.019765028730034828,
0.0017439712537452579,
0.017473915591835976,
0.0010653574718162417,
-0.002274418482556939,
-0.013150975108146667,
0.07266943156719208,
0.025567546486854553,
-0.013485915027558804,
0.0014091761549934745,
-0.019176123663783073,
0.025796936824917793,
0.0007564647821709514,
0.034512948244810104,
0.014454608783125877,
-0.05353356897830963,
-0.010293282568454742,
0.0029438016936182976,
0.011790385469794273,
0.0018072840757668018,
-0.005918483715504408,
-0.0002004448469961062,
0.0005113823572173715,
0.01876198500394821,
-0.04062305763363838,
-0.004300341475754976,
0.017794711515307426,
-0.011166795156896114,
0.0015778348315507174,
-0.03665805980563164,
0.022921262308955193,
-0.05202382430434227,
0.008736098185181618,
-0.0344509556889534,
-0.04085336625576019,
0.028915133327245712,
0.03615501895546913,
0.03471778705716133,
-0.04879606515169144,
-0.03562365844845772,
0.002463642042130232,
0.016257014125585556,
0.025105925276875496,
-0.03415375202894211,
0.009164437651634216,
0.0626848116517067,
0.03004336915910244,
-0.0134279178455472,
0.015183773823082447,
0.023914339020848274,
0.006150451023131609,
-0.017997726798057556,
-0.016863316297531128,
-0.03322618454694748,
0.03198191523551941,
0.028316739946603775,
0.02874683402478695,
-0.013390867039561272,
0.030433809384703636,
0.03200376778841019,
-0.04024473950266838,
0.07282283157110214,
0.03282558172941208,
0.01579170487821102,
0.017005184665322304,
0.06009627878665924,
0.023264963179826736,
0.0007358248112723231,
-0.0004197970265522599,
-0.024778012186288834,
-0.006359445862472057,
-0.005815440788865089,
0.01039395947009325,
0.05979800596833229,
-0.03272707015275955,
0.015054636634886265,
0.04887187480926514,
0.0381966307759285,
0.01867707446217537,
0.01971985027194023,
-0.010825584642589092,
-0.022287916392087936,
-0.019243508577346802,
0.004175850190222263,
0.012232265435159206,
0.03610849753022194,
0.04151809215545654,
-0.007046226877719164,
-0.021941613405942917,
0.03995014354586601,
-0.0828099325299263,
0.013236460275948048,
0.014197740703821182,
-0.005362364929169416,
-0.017399150878190994,
-0.05290965363383293,
0.017471058294177055,
-0.022234400734305382,
0.005867380183190107,
0.015147832222282887,
-0.026071343570947647,
-0.023414673283696175,
-0.043408364057540894,
0.009700140915811062,
0.009527917020022869,
0.043090611696243286,
0.01185648050159216,
-0.005443810950964689,
0.0428454652428627,
-0.004140099510550499,
-0.01875966414809227,
-0.017246374860405922,
-0.01622290350496769,
-0.006141690071672201,
0.005994402803480625,
0.009626741521060467,
-0.0022806187625974417,
0.009975333698093891,
-0.021714989095926285,
-0.05164455249905586,
-0.01515853963792324,
-0.015399404801428318,
-0.00497529748827219,
0.02769026719033718,
-0.1037859097123146,
0.035258084535598755,
-0.044755011796951294,
-0.00007704894960625097,
0.042501866817474365,
-0.007432623766362667,
0.037457749247550964,
0.0031387319322675467,
0.010176033712923527,
-0.04396907985210419,
-0.03229111060500145,
-0.03126344084739685,
-0.017248891294002533,
-0.05228832736611366,
0.03158324584364891,
0.015165410004556179,
0.009386688470840454,
-0.026521237567067146,
0.03197140991687775,
-0.03485491871833801,
-0.061831019818782806,
-0.03710852190852165,
-0.00588273536413908,
0.04079963266849518,
-0.01567039079964161,
-0.002505124779418111,
0.035615917295217514,
-0.021618099883198738,
0.001332637039013207,
-0.05884549021720886,
-0.0643499493598938,
0.015761811286211014,
-0.01618373394012451,
0.016011932864785194,
0.015877194702625275,
-0.024913698434829712,
0.07754417508840561,
0.036172445863485336,
-0.04003218561410904,
0.0009761423571035266,
0.031937774270772934,
0.0005167117342352867,
-0.007866724394261837,
0.03202752396464348,
0.02698516473174095,
-0.020242009311914444,
0.05700616165995598,
0.02793685719370842,
-0.030623167753219604,
0.010384180583059788,
0.0029744855128228664,
-0.037813324481248856,
0.031310074031353,
-0.014148435555398464,
0.0017968292813748121,
0.01602049358189106,
0.007065257523208857,
-0.06688106060028076,
0.019108546897768974,
0.02008781209588051,
0.06034696102142334,
0.01603076048195362,
-0.037822265177965164,
0.06822750717401505,
0.025438668206334114,
0.0028277207165956497,
-0.003601829055696726,
0.04419737309217453,
-0.019931742921471596,
0.01076474878937006,
0.00022274676302913576,
0.05138689652085304,
0.04999666288495064,
-0.023668041452765465,
0.02644474245607853,
0.0475330650806427,
0.001491423463448882,
-0.027804994955658913,
-0.048667583614587784,
-0.01666497439146042,
-0.0026376433670520782,
0.04289409518241882,
-0.019623376429080963,
-0.03170929476618767,
0.0317048504948616,
0.024807104840874672,
0.06696559488773346,
0.012840577401220798,
-0.03994785621762276,
0.020450720563530922,
-0.049540311098098755,
0.036474909633398056,
-0.02148672565817833,
0.005042631179094315,
0.006563495844602585,
0.06384294480085373,
0.009485992603003979,
0.019657587632536888,
-0.0071608140133321285,
-0.026901960372924805,
-0.05697750672698021,
0.03200794383883476,
-0.021461283788084984,
-0.0232256893068552,
-0.030043233186006546,
-0.00523490970954299,
0.005248925182968378,
-0.06304056197404861,
-0.02079346776008606,
0.0028389301151037216,
0.01162694301456213,
-0.04642142727971077,
0.01922374591231346,
-0.025871122255921364,
-0.0622524656355381,
0.021554255858063698,
0.054855361580848694,
0.04655447229743004,
-0.050517503172159195,
0.05639638751745224,
0.036073774099349976,
-0.04282572492957115,
0.015604376792907715,
-0.01951284520328045,
0.034025825560092926,
0.0008358359918929636,
0.011453776620328426,
0.03463670238852501,
0.01971140317618847,
-0.04484453424811363,
0.03434563800692558,
-0.021495988592505455,
0.08058124780654907,
0.011985587887465954,
-0.01376402098685503,
-0.03390344977378845,
-0.048644114285707474,
-0.008098110556602478,
-0.011332047171890736,
0.00898881908506155,
0.012535050511360168,
0.009019020013511181,
0.05707878619432449,
-0.002903396263718605,
-0.037348683923482895,
0.02379325032234192,
0.03723949193954468,
0.039274558424949646,
-0.0012579241301864386,
-0.03858596459031105,
-0.015842286869883537,
-0.03598785027861595,
0.0033436445519328117,
0.00775414751842618,
-0.016054613515734673,
-0.01764615811407566,
0.03746597096323967,
0.04789275303483009,
0.015109652653336525,
0.002702695783227682,
0.0073213111609220505,
-0.002330661518499255,
0.05893068388104439,
-0.011078326031565666,
0.010440541431307793,
0.02737361751496792,
0.027337240055203438,
0.008160645142197609,
0.012050911784172058,
-0.037701498717069626,
-0.029047703370451927,
0.0016445126384496689,
0.04314352571964264,
0.003930510953068733,
-0.028649089857935905,
0.03968193382024765,
-0.03783528879284859,
-0.011391324922442436,
0.07955536991357803,
-0.001541232573799789,
0.040801212191581726,
0.0016260603442788124,
-0.010040841065347195,
0.008026940748095512,
0.0035528712905943394,
-0.031433310359716415,
0.02806253358721733,
-0.012554790824651718,
-0.017673328518867493,
-0.03935787081718445,
-0.014509014785289764,
-0.042885471135377884,
-0.0054910010658204556,
0.05329092592000961,
0.029926134273409843,
0.0010528293205425143,
-0.002366099040955305,
-0.038282621651887894,
0.026716401800513268,
-0.03129136934876442,
-0.09033998101949692,
-0.023238064721226692,
-0.02376672253012657,
-0.012453345581889153,
0.027339637279510498,
-0.034140169620513916,
-0.03628595918416977,
-0.017544342204928398,
-0.002212374471127987,
0.004070880822837353,
0.037998732179403305,
-0.016741137951612473,
0.011761792935431004,
-0.017225995659828186,
0.014173954725265503,
0.015498540364205837,
0.013034932315349579,
0.010981203988194466,
-0.027284014970064163,
-0.01061744149774313,
0.03874753415584564,
0.004125865641981363,
-0.006499971263110638,
-0.0496855229139328,
0.026330597698688507,
-0.03244563937187195,
0.03815828636288643,
0.017366725951433182,
0.018804281949996948,
0.008370624855160713,
-0.014031661674380302,
-0.038950636982917786,
0.014820083975791931,
0.029697608202695847,
-0.01666388474404812,
-0.0005647282814607024,
0.029787110164761543,
0.02706017717719078,
-0.0063723917119205,
0.013585194014012814,
-0.010115046985447407,
-0.04810880869626999,
0.019637275487184525,
-0.02672659419476986,
0.017004871740937233,
-0.04019541293382645,
-0.03646765276789665,
-0.003258601762354374,
-0.01119347382336855,
0.04520615562796593,
-0.05433942377567291,
0.01865394413471222,
0.027851294726133347,
-0.06578826159238815,
-0.028460808098316193,
-0.002032502321526408,
0.007339724339544773,
0.006327850744128227,
-0.04625707492232323,
-0.0244184248149395,
0.019633762538433075,
-0.007237155921757221,
-0.06560997664928436,
-0.021729731932282448,
0.019215034320950508,
0.010093833319842815,
-0.028521329164505005,
-0.009794920682907104,
0.010078046470880508,
-0.026770565658807755,
-0.009462585672736168,
0.0023420227225869894,
0.014921430498361588,
-0.008842334151268005,
-0.002522516530007124,
0.011869879439473152,
-0.013379408977925777,
0.05900849401950836,
0.005531843286007643,
-0.012479446828365326,
-0.011217398568987846,
-0.02919679880142212,
0.0026777980383485556,
-0.008155958727002144,
0.07897543907165527,
-0.018122892826795578,
-0.007729298435151577,
0.007215685676783323,
0.0008994776289910078,
0.016324207186698914,
-0.003246013540774584,
-0.04388166964054108,
0.004509808495640755,
0.021130964159965515,
0.02525010146200657,
-0.01556197740137577,
-0.005470623262226582,
-0.007953750900924206,
0.03708165884017944,
-0.007727425079792738,
0.009249872528016567,
-0.0020201203878968954,
-0.05695701017975807,
0.040682367980480194,
-0.015553979203104973,
-0.0023301250766962767,
0.0010944828391075134,
0.049500394612550735,
0.017690708860754967,
-0.01137523353099823,
0.020105037838220596,
0.010147850960493088,
-0.011759436689317226,
-0.018595777451992035,
-0.02304171770811081,
0.006511101499199867,
0.02274913527071476,
-0.024116648361086845,
-0.05652876943349838,
-0.01715504750609398,
0.04481426626443863,
0.07634416222572327,
-0.0022367897909134626,
0.05814061313867569,
0.009544976986944675,
0.019670451059937477,
-0.005747667513787746,
0.03520728647708893,
-0.005383171606808901,
-0.0226860661059618,
0.01713457517325878,
0.06287572532892227,
-0.04728679731488228,
0.03251831978559494,
0.06022559478878975,
0.04274880141019821,
-0.03178790211677551,
0.038951367139816284,
0.03398904576897621,
-0.012149672955274582,
0.009827920235693455,
0.018264107406139374,
-0.0242229625582695,
0.04248277097940445,
-0.03796094283461571,
0.05514763295650482,
-0.02313143014907837,
-0.03049803338944912,
-0.002335707889869809,
0.01316974125802517,
-0.007589391898363829,
-0.011656174436211586,
-0.005116525571793318,
-0.04875897988677025,
0.004235449247062206,
-0.007230626884847879,
0.02386976219713688,
-0.029738713055849075,
0.012683680281043053,
0.03481486439704895,
-0.005280714016407728,
-0.027584774419665337,
-0.05940020829439163,
-0.06154495105147362,
-0.03734781593084335,
-0.017590682953596115,
-0.04274991899728775,
0.042998794466257095,
0.019956381991505623,
0.0015651279827579856,
0.03462504222989082,
-0.014748789370059967,
0.022632872685790062,
0.012478459626436234,
0.0056701041758060455,
-0.008019056171178818,
0.07181622087955475,
0.005923776887357235,
0.016338977962732315,
-0.029787173494696617,
0.00020382566435728222,
0.10933105647563934,
0.019242150709033012,
0.03087977133691311,
-0.03743094578385353,
0.026270532980561256,
-0.0006617991020902991,
0.030997468158602715,
-0.03352490812540054,
0.031169207766652107,
0.011292279697954655,
0.03247321769595146,
-0.007717609405517578,
0.05441664904356003,
0.013710324652493,
-0.037329647690057755,
0.033263154327869415,
-0.03467940539121628,
-0.031975969672203064,
-0.014338083565235138,
-0.004850159864872694,
-0.008851326070725918,
-0.004320630803704262,
-0.058107782155275345,
-0.0025557244662195444,
-0.04187559336423874,
-0.02551095187664032,
-0.006241166032850742,
-0.028233932331204414,
-0.01587945967912674,
0.03497777134180069,
-0.0256304033100605,
-0.010605689138174057,
0.04049914330244064,
-0.005452136974781752,
-0.0475531667470932,
0.01333525124937296,
0.010910578072071075,
-0.01905936747789383,
0.05742638185620308,
0.00576937198638916,
0.02300371415913105,
0.0322614349424839,
0.010933402925729752,
0.027346353977918625,
-0.04277289658784866,
-0.014452343806624413,
-0.014352728612720966,
0.03690844774246216,
-0.037654079496860504,
0.0389975979924202,
-0.016942285001277924,
-0.05147537961602211,
-0.008730076253414154,
-0.04481840506196022,
-0.01339357253164053,
-0.0049011907540261745,
0.006460434291511774,
-0.04204849526286125,
-0.04130266606807709,
-0.024889813736081123,
0.029655011370778084,
-0.048879604786634445,
0.009148386307060719,
0.002873962512239814,
-0.012637169100344181,
-0.021690333262085915,
0.007595481351017952,
0.03515436500310898,
-0.0021347200963646173,
-0.0537758395075798,
-0.04199039191007614,
-0.03475145623087883,
-0.039199043065309525,
0.013376027345657349,
0.006469189189374447,
-0.013532058335840702,
0.010702683590352535,
0.018070073798298836,
-0.042134739458560944,
0.030747519806027412,
-0.033850785344839096,
0.024610156193375587,
-0.022817417979240417,
-0.0016367450589314103,
-0.009504190646111965,
-0.03773215040564537,
0.04035406932234764,
0.023698152974247932,
-0.05820349603891373,
-0.009294861927628517,
-0.00984172336757183,
0.004524969961494207,
0.007765436079353094,
-0.06699197739362717,
0.0027495743706822395,
0.03133070096373558,
-0.04154234379529953,
0.004585833754390478,
-0.05067414790391922,
0.02752903290092945,
0.03839360550045967,
0.04315189644694328,
-0.01595744863152504,
0.0442068874835968,
0.0014337506145238876,
-0.0015343461418524384,
0.028521906584501266,
-0.011610799469053745,
-0.01265235710889101,
0.0111993458122015,
-0.0044684153981506824,
-0.03164219111204147,
-0.051076699048280716,
-0.011939797550439835,
0.02404729090631008,
-0.022645821794867516,
0.007593493442982435,
-0.038703445345163345,
0.004215146880596876,
-0.01973307691514492,
0.010688400827348232,
-0.025641579180955887,
0.018375148996710777,
-0.041261520236730576,
0.0000790264384704642,
0.018878476694226265,
-0.02104499377310276,
-0.000282935390714556,
0.059844065457582474,
0.02096741646528244,
-0.039422933012247086,
0.04520980268716812,
0.026208074763417244,
0.022268079221248627,
0.0041050780564546585,
0.03791917487978935,
0.014056362211704254,
0.049457792192697525,
0.008169697597622871,
-0.036685261875391006,
0.05372663587331772,
-0.0465705581009388,
-0.022856060415506363,
0.0021858986001461744,
-0.01416503731161356,
0.0043394616805016994,
0.025412242859601974,
-0.01947108656167984,
-0.008618950843811035,
0.04501919820904732,
-0.02384939417243004,
-0.026299262419342995,
0.028992995619773865,
-0.0004188246966805309,
0.0035623551812022924,
-0.022667862474918365,
0.03169514983892441,
-0.02461319975554943,
-0.0327947661280632,
0.05802668631076813,
0.04194353520870209,
0.018165474757552147,
-0.024559952318668365,
0.023855596780776978,
-0.0030267050024122,
0.01307826116681099,
0.012821421027183533,
-0.019897552207112312,
0.008278720080852509,
0.05219833552837372,
-0.030820410698652267,
0.04178611561655998,
-0.005176169332116842,
0.011928312480449677,
-0.07752113789319992,
-0.0034266686998307705,
0.01186327449977398,
-0.015041968785226345,
0.04340303689241409,
-0.0596315823495388,
-0.010592782869935036,
0.04122530668973923,
-0.05025191232562065,
0.01940988563001156,
-0.03778773918747902,
-0.00666032824665308,
-0.01793529838323593,
-0.022881515324115753,
0.000004389455625641858,
0.055844031274318695,
0.0038597772363573313,
0.01710500195622444,
0.049887802451848984,
0.010160856880247593,
-0.026799118146300316,
-0.022745702415704727,
-0.022942878305912018,
0.044446397572755814,
-0.005412563215941191,
-0.045403510332107544,
0.06213035807013512,
-0.010777052491903305,
-0.06514523178339005,
0.04461676999926567,
0.007714003324508667,
-0.003734403057023883,
-0.029916124418377876,
-0.004233370069414377,
-0.03183361142873764,
0.03397348150610924,
-0.0027814111672341824,
0.0011652774410322309,
-0.0030522921588271856,
0.018848443403840065,
0.025107035413384438,
0.009655616246163845,
-0.014380990527570248,
-0.003932067193090916,
0.025463908910751343,
-0.023983852937817574,
-0.04428465664386749,
0.03334280103445053,
-0.0019548453856259584,
0.018978752195835114,
-0.0216784980148077,
-0.0023688252549618483,
0.038185350596904755,
-0.019953399896621704,
0.032679468393325806,
-0.02470799908041954,
0.033047545701265335,
0.008555413223803043,
0.02035634219646454,
-0.01936006359755993,
0.03819964826107025,
0.008603137917816639,
-0.01312300469726324,
-0.0027352427132427692,
0.017397399991750717,
-0.0008530892082490027,
-0.048630472272634506,
-0.003592838067561388,
0.009213287383317947,
0.03006080538034439,
0.007130402605980635,
-0.06246322765946388,
-0.02146884612739086,
0.025340352207422256,
0.00645118672400713,
0.059056393802165985,
0.018572071567177773,
-0.025898069143295288,
-0.0070175654254853725,
-0.05294949188828468,
0.03773357346653938,
0.0022502634674310684,
0.01480837818235159,
-0.01831202395260334,
0.015172927640378475,
-0.006645822897553444,
-0.012607685290277004,
0.044200003147125244,
0.018565483391284943,
-0.022768031805753708,
0.03225259855389595,
0.0019954307936131954,
0.01654881425201893,
-0.04038454219698906,
-0.006863223388791084,
-0.05572003498673439,
-0.01773238740861416,
0.008223268203437328,
-0.01068733911961317,
-0.00204445980489254,
-0.012967041693627834,
0.026932090520858765,
-0.037244729697704315,
0.005093857180327177,
0.020535288378596306,
-0.04679321497678757,
0.04275013133883476,
0.013025576248764992,
0.0011151855578646064,
0.08298417925834656,
0.0011375369504094124,
-0.0015305537963286042,
0.00765925832092762,
-0.031405042856931686,
-0.01112151239067316,
0.045662928372621536,
-0.029933063313364983,
-0.04966171458363533,
-0.04950552061200142,
0.03078591637313366,
0.011660950258374214,
-0.026223620399832726,
-0.015712091699242592,
0.01724219135940075,
-0.03628101199865341,
-0.028946345672011375,
0.02135627157986164,
0.007108970079571009,
0.004940893966704607,
-0.03644547238945961,
-0.02257542498409748,
0.053169094026088715,
-0.0070413462817668915,
0.016579674556851387,
0.03455347940325737,
0.026119118556380272,
0.007067517843097448,
-0.015956012532114983,
0.011744651943445206,
-0.009140091948211193,
0.059579893946647644,
0.013305436819791794,
0.03871144354343414,
-0.014333830215036869,
-0.024928361177444458,
0.015943286940455437,
-0.030690686777234077,
0.02108955569565296,
-0.015318959951400757,
-0.02650083228945732,
0.05217185616493225,
0.000028098309485358186,
0.00925216730684042,
-0.01642422378063202,
0.01214676909148693,
-0.0005359253264032304,
-0.037843894213438034,
0.026557035744190216,
0.03277912363409996,
-0.0274311825633049,
-0.038408249616622925,
0.011157364584505558,
0.016408851370215416,
0.015237810090184212,
-0.007995199412107468,
0.016788208857178688,
0.010906757786870003,
-0.004444804973900318,
-0.006499108858406544,
-0.023516057059168816,
-0.04400211200118065,
-0.03783769533038139,
0.027282552793622017,
0.03175276145339012,
0.0507211908698082,
-0.00948855560272932,
-0.021554479375481606,
-0.04610982537269592,
0.06457959115505219,
-0.07282288372516632,
-0.04193008691072464,
-0.03712921217083931,
0.042787130922079086,
-0.030246712267398834,
0.017154008150100708
] |
<p>I want to simulate the path of an electron through the anode of an electron gun. I therefore need to calculate the force on the electron due to the electric field from the anode and apply that to its existing velocity. The electron can start at any arbitrary point $p$ with velocity $v$ (both vectors).</p>
<p>I guess that I need to integrate the force on the electron from the whole inside surface of the cylinder. I'll be doing a numerical integration.</p>
<p>I'm struggling to find the appropriate vector equations. I can see that $F = q\frac{V}{d}$ but all these terms are scalar not vector quantities.</p> | 1,470 | [
0.011482804082334042,
-0.016371415928006172,
-0.013590425252914429,
-0.007765995804220438,
0.04982702434062958,
-0.033072102814912796,
0.0023547594901174307,
0.00023129803594201803,
-0.002220787340775132,
-0.003624456934630871,
0.035279061645269394,
0.02706991881132126,
0.0959259495139122,
0.00796815287321806,
0.034230731427669525,
0.03794276341795921,
-0.008651639334857464,
-0.010830603539943695,
0.017658988013863564,
-0.04521579295396805,
-0.043672025203704834,
0.023219576105475426,
0.012658897787332535,
0.011188415810465813,
0.020027698948979378,
0.036028310656547546,
0.053139135241508484,
-0.018132628872990608,
0.0018135554855689406,
0.061554256826639175,
-0.0066718305461108685,
-0.04266170784831047,
0.0009703563991934061,
0.033187735825777054,
0.027468757703900337,
0.022078702226281166,
-0.04506606236100197,
-0.045970674604177475,
-0.00026346827507950366,
0.022589685395359993,
-0.04234376549720764,
-0.006070747040212154,
-0.004705286119133234,
0.058296795934438705,
0.03226889297366142,
0.03478449210524559,
0.007300934754312038,
0.00775699969381094,
0.05766352266073227,
-0.05092749372124672,
0.04109472781419754,
0.0009791906923055649,
0.06967642903327942,
0.018069103360176086,
0.02607724815607071,
-0.040136076509952545,
0.05191018432378769,
0.03955863043665886,
-0.005078338086605072,
-0.03002624213695526,
-0.017609525471925735,
-0.02523769438266754,
-0.04963521286845207,
-0.05523831397294998,
-0.04449750483036041,
0.013353605754673481,
-0.030593540519475937,
-0.05601770430803299,
-0.019887879490852356,
-0.018932053819298744,
0.008292588405311108,
0.029160276055336,
-0.003110721940174699,
-0.03125316649675369,
-0.006880203261971474,
-0.00006488290819106624,
0.016496045514941216,
0.001978676998987794,
0.01245825830847025,
0.014708466827869415,
-0.03263768553733826,
0.010344426147639751,
0.03979325667023659,
0.029854506254196167,
0.017133543267846107,
-0.030304035171866417,
0.05477612838149071,
0.010784788057208061,
0.0012100639287382364,
0.012243407778441906,
-0.05632723122835159,
0.018312228843569756,
0.04529457539319992,
-0.012378915213048458,
-0.04855165258049965,
0.001583351637236774,
0.003956179600208998,
0.048044245690107346,
0.02845684066414833,
-0.046505529433488846,
0.010922141373157501,
-0.022645769640803337,
-0.003733859397470951,
0.09157063812017441,
0.011341258883476257,
-0.01971074566245079,
0.015910860151052475,
-0.002572123659774661,
-0.026388632133603096,
-0.023398665711283684,
-0.012120497412979603,
0.0507039874792099,
0.011018898338079453,
-0.006573379039764404,
-0.04852023720741272,
-0.025526518002152443,
0.011275502853095531,
-0.0084745604544878,
0.03093867562711239,
0.02516998164355755,
0.018729139119386673,
-0.05565482750535011,
0.016544388607144356,
-0.015185515396296978,
-0.0452604778110981,
0.000024598684831289575,
0.019795136526226997,
-0.014522753655910492,
0.007681713439524174,
0.020429259166121483,
-0.0035390849225223064,
-0.032974425703287125,
0.0008272237027995288,
0.0059540290385484695,
0.02035277895629406,
-0.017775313928723335,
-0.07211675494909286,
-0.0762384757399559,
0.03628735616803169,
-0.01235725823789835,
0.020789187401533127,
-0.06641489267349243,
-0.014455266296863556,
0.036460522562265396,
0.06728721410036087,
-0.006981425918638706,
0.005286918953061104,
0.009062123484909534,
0.03845049440860748,
-0.008852260187268257,
-0.024074574932456017,
0.014851783402264118,
-0.019011056050658226,
-0.010950105264782906,
-0.006845519877970219,
-0.042050935328006744,
0.01376063097268343,
0.006872958038002253,
0.004284946713596582,
0.007563842460513115,
0.06676534563302994,
-0.01849541626870632,
-0.0032770622055977583,
0.018465641885995865,
-0.007376567460596561,
-0.02982311323285103,
0.03430238738656044,
0.008891413919627666,
0.00710761034861207,
0.04617574065923691,
0.006229978520423174,
-0.0013231943594291806,
0.008059694431722164,
-0.004166694823652506,
0.05842185392975807,
-0.03914637863636017,
-0.017914611846208572,
-0.02633330039680004,
0.019119370728731155,
0.02421979233622551,
-0.03021901659667492,
-0.08313217759132385,
-0.013797733001410961,
0.0044038305059075356,
0.02700977213680744,
0.08104179054498672,
-0.009663515724241734,
0.005052234511822462,
-0.037753019481897354,
-0.01659911870956421,
-0.00026157806860283017,
-0.048185236752033234,
0.07144562900066376,
-0.011610203422605991,
-0.037181492894887924,
0.018731554970145226,
0.0015013973461464047,
0.010126347653567791,
0.0004958434146828949,
-0.02666155807673931,
-0.023703573271632195,
0.049823638051748276,
-0.0012106806971132755,
-0.00861723255366087,
-0.0042492542415857315,
0.03998595476150513,
0.0546460896730423,
0.008642517030239105,
0.03589408099651337,
-0.03230815380811691,
0.0020620515570044518,
-0.037848230451345444,
-0.032825447618961334,
0.010928122326731682,
0.01390960905700922,
-0.01006779633462429,
0.007394309155642986,
-0.006952916271984577,
0.033060867339372635,
0.03016805835068226,
-0.02326737716794014,
0.07318092882633209,
0.060699768364429474,
0.033718571066856384,
-0.0317966602742672,
0.014818347990512848,
0.03107660822570324,
0.021069364622235298,
0.005860680248588324,
-0.01159339677542448,
-0.021275382488965988,
0.017996393144130707,
0.05346051976084709,
0.015234643593430519,
-0.047422926872968674,
0.004497474525123835,
0.024951579049229622,
0.0041879406198859215,
0.04607033357024193,
0.03306611627340317,
-0.05461769923567772,
-0.018092386424541473,
0.035918109118938446,
0.01950555481016636,
-0.030760902911424637,
-0.011584056541323662,
0.022104768082499504,
0.013243507593870163,
0.040139731019735336,
0.006442247424274683,
-0.029621660709381104,
0.051245417445898056,
-0.0023160125128924847,
0.02335290238261223,
0.008903054520487785,
-0.030397824943065643,
0.04071693494915962,
-0.02521187998354435,
0.00829529482871294,
0.014633070677518845,
-0.021541444584727287,
-0.0011674194829538465,
-0.002203320385888219,
-0.003938761074095964,
0.044337864965200424,
0.0022155651822686195,
-0.006072531454265118,
-0.03424011543393135,
0.032614871859550476,
-0.020273998379707336,
-0.0020916173234581947,
-0.049274951219558716,
-0.012624683789908886,
-0.012093025259673595,
-0.000937526929192245,
0.017100319266319275,
0.06470303982496262,
0.034389346837997437,
-0.037766002118587494,
-0.04627251252532005,
0.01446243841201067,
-0.061231281608343124,
0.005575082264840603,
0.04772377014160156,
-0.022569002583622932,
0.03072112426161766,
-0.061569686979055405,
-0.047729771584272385,
0.06489546597003937,
-0.0002923687861766666,
0.006997669115662575,
0.019893327727913857,
-0.02585541270673275,
-0.05624007061123848,
0.013442909345030785,
-0.018322328105568886,
0.025581147521734238,
-0.032497286796569824,
0.004857046529650688,
0.014425390399992466,
-0.008518901653587818,
-0.019034601747989655,
0.03794216737151146,
-0.05491701513528824,
-0.04440196976065636,
0.008946270681917667,
0.005167785100638866,
0.03955310210585594,
-0.02261289395391941,
0.0443391390144825,
0.018418440595269203,
-0.013068175874650478,
0.0101381940767169,
-0.03662644699215889,
-0.017419835552573204,
0.011000989936292171,
-0.009365529753267765,
-0.00009405045420862734,
-0.014876632019877434,
-0.024286268278956413,
0.06341715902090073,
0.032335881143808365,
-0.029794778674840927,
-0.0016371487872675061,
-0.015832480043172836,
-0.004472697153687477,
-0.03923960402607918,
0.004203455522656441,
0.019186101853847504,
-0.033971529453992844,
-0.005438928492367268,
-0.007701972499489784,
0.020734842866659164,
0.023979835212230682,
-0.0067995167337358,
0.0024329018779098988,
0.04441484808921814,
0.015363886952400208,
-0.0012445392785593867,
0.07725998759269714,
0.02713048830628395,
-0.03044544719159603,
0.03981288895010948,
0.0005830528098158538,
0.030593624338507652,
0.030898157507181168,
-0.04187602922320366,
0.04265982285141945,
0.004089829977601767,
-0.030403586104512215,
-0.018467804417014122,
0.025592539459466934,
-0.007245470769703388,
-0.01723906211555004,
0.008346627466380596,
0.010683189146220684,
0.0009308853768743575,
-0.020602384582161903,
-0.015790680423378944,
0.02797902747988701,
0.027067797258496284,
-0.016082076355814934,
-0.045393116772174835,
0.012665409594774246,
0.005398877896368504,
0.007201368920505047,
-0.008657335303723812,
-0.011880415491759777,
0.03843539208173752,
0.044716380536556244,
0.046290840953588486,
0.018527308478951454,
-0.012269899249076843,
0.013531790114939213,
-0.031983207911252975,
0.01807020604610443,
0.003966945223510265,
0.07309623062610626,
-0.026933271437883377,
0.05508347600698471,
0.027410857379436493,
0.025971511378884315,
0.03785189613699913,
0.04307696968317032,
-0.07640001177787781,
0.03548244386911392,
-0.019343294203281403,
-0.04937509074807167,
-0.0479111485183239,
-0.012648625299334526,
-0.009693996049463749,
-0.03202128782868385,
-0.0016889512771740556,
-0.002693229354918003,
-0.04038212075829506,
-0.03158671781420708,
0.024057207629084587,
-0.04631205275654793,
-0.008905724622309208,
-0.015721293166279793,
0.05057436600327492,
0.033332981169223785,
-0.049552083015441895,
0.02019566483795643,
0.06073182448744774,
-0.0425097830593586,
-0.012913007289171219,
0.01883385330438614,
-0.009975898079574108,
0.003941196016967297,
0.046252693980932236,
0.021348385140299797,
0.009952504187822342,
-0.03107609413564205,
0.025177499279379845,
-0.022817345336079597,
0.08557401597499847,
0.010828394442796707,
0.007097206544131041,
-0.030223460868000984,
-0.05482923611998558,
-0.007536981254816055,
-0.04100751131772995,
0.05571873113512993,
-0.01922011189162731,
-0.01753959432244301,
0.0627279207110405,
-0.00800661277025938,
-0.020480068400502205,
0.03540787473320961,
0.049761660397052765,
0.019391197711229324,
-0.039075713604688644,
-0.05006850138306618,
0.03929884359240532,
-0.034163471311330795,
-0.002139428863301873,
-0.01015657838433981,
-0.006225933786481619,
-0.016931600868701935,
-0.0070343525148928165,
0.03780679032206535,
0.01507611759006977,
-0.01871943660080433,
0.030652008950710297,
-0.012698113918304443,
0.04365834593772888,
0.01175770815461874,
-0.018248196691274643,
0.016908971592783928,
-0.00438682921230793,
0.012868979945778847,
0.004055032506585121,
-0.003032011678442359,
-0.09510260075330734,
-0.0227240901440382,
0.05584762617945671,
0.05514654144644737,
-0.019885443150997162,
-0.010610129684209824,
-0.08574939519166946,
-0.021546175703406334,
0.07655901461839676,
-0.018121611326932907,
0.020306183025240898,
-0.022859420627355576,
-0.022559842094779015,
-0.03548049554228783,
-0.06411590427160263,
-0.06029902398586273,
-0.0038828374817967415,
-0.02515297383069992,
0.007498506922274828,
-0.057869043201208115,
0.0025211437605321407,
0.029620282351970673,
0.03646821156144142,
0.035725582391023636,
0.051075275987386703,
0.015321669168770313,
-0.02400078810751438,
0.004446639213711023,
0.02465059980750084,
-0.0045622908510267735,
-0.0717104896903038,
0.004274705890566111,
-0.006535929162055254,
0.02314288355410099,
0.00919218547642231,
-0.0450340211391449,
-0.021611763164401054,
0.039969854056835175,
-0.02389228530228138,
0.035381074994802475,
0.005258139688521624,
-0.039618004113435745,
0.03295915946364403,
0.006264411844313145,
-0.01257250551134348,
0.046318404376506805,
0.021206293255090714,
-0.020558621734380722,
-0.01920698583126068,
-0.014187940396368504,
0.024287449195981026,
0.002792786806821823,
-0.026716042309999466,
-0.04514860734343529,
0.009519299492239952,
-0.0400986410677433,
0.057802606374025345,
0.01414938922971487,
0.01651495136320591,
-0.03539226949214935,
-0.020212728530168533,
-0.00013237600796855986,
0.0023491419851779938,
0.003718658583238721,
-0.019022436812520027,
-0.012646707706153393,
0.009069693274796009,
-0.025677423924207687,
-0.03001183643937111,
-0.02100761979818344,
-0.00642743892967701,
-0.004615166690200567,
0.016237368807196617,
-0.011529247276484966,
-0.014665436930954456,
-0.01621333882212639,
-0.030037740245461464,
0.0009200811618939042,
-0.0760623961687088,
0.04691540077328682,
-0.03446612134575844,
-0.001258915988728404,
-0.011161958798766136,
-0.07164667546749115,
-0.04856260120868683,
-0.014038290828466415,
0.019954796880483627,
0.04377705231308937,
-0.04651504009962082,
0.004257156513631344,
-0.014809133484959602,
0.028349516913294792,
-0.06097445636987686,
-0.038569048047065735,
-0.002465663244947791,
-0.017691390588879585,
-0.03314216807484627,
-0.033546216785907745,
-0.02558346465229988,
-0.029581759124994278,
-0.015477246604859829,
0.009863318875432014,
0.04409076273441315,
-0.037016402930021286,
0.0010753587121143937,
0.021943693980574608,
0.008292170241475105,
-0.0031252549961209297,
-0.00940107274800539,
0.04782741144299507,
0.0023548156023025513,
-0.019933540374040604,
-0.0043435245752334595,
-0.0019059658516198397,
0.05149976536631584,
-0.016820242628455162,
-0.013918707147240639,
-0.01836482807993889,
0.0018529955996200442,
0.04710501432418823,
-0.011426521465182304,
0.03746536746621132,
0.023790160194039345,
0.03050197660923004,
-0.020566659048199654,
-0.022906741127371788,
0.01605372317135334,
0.020400360226631165,
0.02672288939356804,
-0.010351535864174366,
0.017736852169036865,
-0.05176984518766403,
-0.02188762091100216,
0.024307841435074806,
-0.05241815000772476,
0.027273239567875862,
-0.0003916714049410075,
0.06975492835044861,
-0.017788885161280632,
0.02533910796046257,
0.01449616439640522,
0.02437804453074932,
0.03855748847126961,
0.0036117543932050467,
-0.023936208337545395,
0.02709529921412468,
-0.021364042535424232,
-0.006355329882353544,
-0.03625932335853577,
-0.028927858918905258,
0.0128241628408432,
0.06937221437692642,
-0.005631288047879934,
0.06400124728679657,
0.011367647908627987,
0.033488307148218155,
-0.008898453786969185,
-0.0024706702679395676,
-0.008868656121194363,
0.015966173261404037,
0.009776117280125618,
0.03270743042230606,
-0.0024864349979907274,
-0.012286870740354061,
0.00627971300855279,
0.03561161831021309,
-0.02578756958246231,
-0.013078554533421993,
0.00013020270853303373,
0.027389056980609894,
-0.0015417495742440224,
-0.0105267483741045,
-0.011469000019133091,
0.02512279711663723,
-0.02304708957672119,
0.04363595321774483,
-0.027020160108804703,
-0.046818919479846954,
0.1006682738661766,
0.03163117170333862,
-0.018774138763546944,
0.018127264454960823,
0.006628210656344891,
-0.034731946885585785,
0.028406625613570213,
0.018209313973784447,
-0.009831003844738007,
-0.01015471201390028,
0.013693360611796379,
0.03749079257249832,
-0.010113305412232876,
0.02363051474094391,
-0.020820986479520798,
-0.05111357942223549,
0.0009632076253183186,
-0.03446895629167557,
-0.029096512123942375,
0.06288264691829681,
-0.0034738786052912474,
0.005979279521852732,
0.006940352730453014,
-0.020091205835342407,
0.05054520070552826,
0.02011709474027157,
0.036617957055568695,
-0.029023559764027596,
0.09270258247852325,
-0.027599681168794632,
-0.01404079794883728,
-0.025665869936347008,
0.02425360679626465,
0.09680645912885666,
0.03587063401937485,
0.010076763108372688,
-0.039131421595811844,
-0.0002391614980297163,
-0.02038693055510521,
0.03991727903485298,
-0.008062058128416538,
0.02264997363090515,
-0.017774900421500206,
-0.03367922827601433,
0.014040458016097546,
0.04279499128460884,
0.007994403131306171,
0.03172915428876877,
0.03583948686718941,
-0.06537151336669922,
-0.054898254573345184,
0.01396122481673956,
0.0035381121560931206,
-0.01406904123723507,
0.027436422184109688,
-0.05591220781207085,
0.02694001980125904,
-0.05201546475291252,
-0.0004158775554969907,
-0.07179863750934601,
-0.030151601880788803,
0.019826170057058334,
-0.011079098097980022,
-0.05434473231434822,
0.014694605022668839,
-0.029301220551133156,
-0.010803334414958954,
-0.02993645891547203,
0.02532270736992359,
0.018600914627313614,
-0.010539424605667591,
0.04606907069683075,
0.0065977503545582294,
-0.0004948736750520766,
0.011865751817822456,
0.007856369018554688,
0.013831560499966145,
-0.02057734690606594,
-0.0006661186926066875,
-0.028976239264011383,
0.06463822722434998,
0.008089816197752953,
0.027925284579396248,
-0.013780016452074051,
0.02693105675280094,
-0.005548322107642889,
-0.05890052020549774,
0.01632784493267536,
-0.02658308856189251,
0.03844533488154411,
0.01822700724005699,
0.009004932828247547,
-0.03000127524137497,
0.02928835339844227,
-0.02563825622200966,
-0.006575595587491989,
0.0074247438460588455,
-0.01067251618951559,
0.01888112723827362,
-0.019724160432815552,
0.053520701825618744,
-0.02329932153224945,
-0.006594376172870398,
0.013162024319171906,
-0.03292802348732948,
-0.046268586069345474,
-0.009276939556002617,
0.0318770594894886,
0.02922903560101986,
0.06829634308815002,
-0.008836142718791962,
-0.008305827155709267,
-0.015284466557204723,
-0.10339569300413132,
0.0323583222925663,
0.012923689559102058,
0.0009381145355291665,
-0.01763845421373844,
-0.021875834092497826,
0.029321826994419098,
0.0404878668487072,
-0.010523605160415173,
0.010302748531103134,
-0.006843045353889465,
0.0028743732254952192,
0.009942327626049519,
-0.004953343421220779,
-0.044246941804885864,
-0.002744468627497554,
-0.009586440399289131,
0.0035188868641853333,
-0.0558355338871479,
0.006940462160855532,
0.0031756709795445204,
0.007184442598372698,
-0.0027740008663386106,
0.05959244817495346,
-0.03714137524366379,
0.034306008368730545,
-0.01386395562440157,
-0.012617263942956924,
0.012013302184641361,
0.033035047352313995,
0.0293634831905365,
-0.043875981122255325,
0.00010650702461134642,
-0.03593117743730545,
-0.025359248742461205,
0.00022084075317252427,
0.019442839547991753,
-0.027851564809679985,
0.004513172432780266,
-0.03702641651034355,
0.006134539842605591,
-0.023391228169202805,
-0.0004237702232785523,
-0.04158616438508034,
0.019470296800136566,
0.024807430803775787,
0.003794013289734721,
-0.048104427754879,
0.008740748278796673,
-0.043630462139844894,
0.00633194949477911,
-0.0023468080908060074,
0.002944275736808777,
-0.007010434288531542,
-0.003063842421397567,
-0.005095936823636293,
0.014875723980367184,
0.015514727681875229,
0.012621141038835049,
-0.034269481897354126,
0.025426609441637993,
-0.044609252363443375,
-0.022765424102544785,
0.025089245289564133,
0.02095489762723446,
0.04138888418674469,
0.04466519504785538,
-0.032217323780059814,
-0.023104006424546242,
0.05575835332274437,
0.002143535064533353,
-0.020582538098096848,
-0.009341089054942131,
-0.08397659659385681,
-0.010810642503201962,
-0.01731441169977188,
0.03230053186416626,
0.013079693540930748,
0.03830502927303314,
0.03575056418776512,
0.03565295413136482,
-0.026371516287326813,
-0.010486580431461334,
0.04505326598882675,
0.02654465287923813,
0.039069097489118576,
0.03198252618312836,
-0.022219929844141006,
0.028080502524971962,
0.03655102476477623,
-0.01562630943953991,
-0.0014969512121751904,
-0.01112888753414154,
0.0004461661446839571,
-0.09782394766807556,
0.003201096784323454,
-0.004705796483904123,
0.029680322855710983,
0.03412939980626106,
-0.08819495141506195,
-0.030545854941010475,
0.022143008187413216,
-0.06734105199575424,
0.005583982914686203,
0.010996275581419468,
0.012373849749565125,
-0.030352981761097908,
-0.026848675683140755,
0.00853152945637703,
0.028071163222193718,
0.004857800435274839,
0.03600586578249931,
0.02075488120317459,
0.01883532479405403,
-0.004709858912974596,
-0.0613519549369812,
-0.001513417111709714,
0.04195844754576683,
-0.006928249727934599,
-0.010085058398544788,
0.02447384037077427,
-0.01648758351802826,
-0.001356474356725812,
0.015492623671889305,
0.03011140041053295,
0.02181980200111866,
-0.004279152490198612,
0.02014988474547863,
0.006609261501580477,
0.02886897884309292,
0.013334501534700394,
0.011440936475992203,
0.010373684577643871,
0.02237238921225071,
-0.0011078950483351946,
-0.0020557865500450134,
-0.00748474383726716,
0.024514248594641685,
0.030374675989151,
-0.01573137193918228,
-0.04372267425060272,
0.061303310096263885,
-0.028406638652086258,
0.0032491120509803295,
-0.004666040185838938,
-0.0246337428689003,
0.0423591174185276,
-0.027628209441900253,
-0.008938918821513653,
-0.05742226541042328,
0.03241415321826935,
0.05110376328229904,
-0.02787904441356659,
0.006503820884972811,
0.012488416396081448,
-0.023092109709978104,
-0.032372213900089264,
0.034362852573394775,
-0.012933749705553055,
0.0055927699431777,
-0.08101769536733627,
0.014471720904111862,
0.027437983080744743,
-0.03264226019382477,
0.024924078956246376,
-0.017842425033450127,
-0.011585148051381111,
0.0021101085003465414,
-0.014541856944561005,
0.004397201351821423,
-0.001489725080318749,
-0.02123274840414524,
-0.01676638051867485,
-0.042997486889362335,
0.026414114981889725,
0.014965320006012917,
-0.06812135130167007,
0.03160707280039787,
-0.04719718545675278,
0.029558412730693817,
0.04831830412149429,
0.026303214952349663,
-0.023725135251879692,
-0.02464359626173973,
0.03258911892771721,
-0.02390226535499096,
0.013092131353914738,
-0.0813094973564148,
-0.013877988792955875,
-0.02883247472345829,
0.015135110355913639,
-0.009968923404812813,
0.02066383697092533,
-0.0033974708057940006,
0.0065339007414877415,
-0.00559905543923378,
0.005317902658134699,
0.005396515596657991,
-0.0053152539767324924,
-0.06489047408103943,
0.004366396460682154,
0.02499617263674736,
-0.0078074755147099495,
0.055437374860048294,
0.005356737412512302,
0.011506441980600357,
0.01355745643377304,
-0.01893102377653122,
-0.01065326388925314,
0.007645609322935343,
-0.024531710892915726,
-0.013644182123243809,
-0.00918051041662693,
-0.014984222128987312,
0.026252616196870804,
-0.05293644592165947,
-0.007468934170901775,
0.016119975596666336,
-0.07092781364917755,
-0.00349035719409585,
0.06092209368944168,
0.02702401950955391,
0.03581292927265167,
-0.008779702708125114,
0.024622244760394096,
0.015777364373207092,
-0.03162868320941925,
-0.0012619226472452283,
0.015103072859346867,
0.0011678505688905716,
0.022144293412566185,
0.022399842739105225,
0.09720495343208313,
-0.018918761983513832,
-0.006596921011805534,
0.004273513797670603,
-0.018654799088835716,
-0.023489950224757195,
-0.00029188208281993866,
0.015226436778903008,
-0.026682989671826363,
-0.001782917184755206,
0.03750966861844063,
-0.0144224613904953,
0.07136411219835281,
-0.039788469672203064,
0.038224831223487854,
0.00754405977204442,
0.005300613585859537,
-0.014947017654776573,
0.027729522436857224,
-0.022618310526013374,
0.03778890520334244,
-0.04229000583291054,
-0.017727814614772797,
-0.016311509534716606,
-0.001711009070277214,
0.030449531972408295,
-0.04183942824602127,
0.03190172463655472,
0.002448463113978505,
-0.0012861575232818723,
-0.01832612231373787,
-0.003985702525824308,
-0.019086724147200584,
-0.00889828335493803,
0.0019958955235779285,
0.038026269525289536,
0.016282442957162857,
-0.013619504868984222,
0.020150940865278244,
-0.02736196294426918,
0.04227470979094505,
-0.061207838356494904,
-0.023327477276325226,
-0.00831111054867506,
0.03950168192386627,
0.0005221968749538064,
0.03160043805837631
] |
<p>He is CORRECT. I use $\mathbf{B}=\left(0,0,B_{\perp}\right)$ and he use $\mathbf{B}=\left(0,0,-B_{\perp}\right)$. $B_{\perp}>0$.</p>
<h1>Nov.28.2012</h1>
<p>Basically I got mad with conventions.</p>
<p>1.Here is the link of the book (second edition): </p>
<p><a href="http://books.google.fr/books/about/Quantum_Hall_Effects.html?id=p3JpcdbqBPoC" rel="nofollow">http://books.google.fr/books/about/Quantum_Hall_Effects.html?id=p3JpcdbqBPoC</a></p>
<p>Here is another link for one of his review articles:</p>
<p><a href="http://iopscience.iop.org/0034-4885/72/8/086502" rel="nofollow">http://iopscience.iop.org/0034-4885/72/8/086502</a></p>
<p>2.I am not happy with the negative sign of the commutator $\left[X,Y\right]=-il_{B}^{2}$. Here is my calculation:</p>
<p>$\left[X,Y\right]=\left(\left[x,p_{x}\right]+\left[-p_{y},y\right]\right)/eB+\left[-P_{y},P_{x}\right]/e^{2}B^{2}=il_{B}^{2}$</p>
<p>3.In my calculation, I used some conventions different from Prof.Ezawa's book and article.
Here is my convention:</p>
<p>$X:=x-P_{y}/eB\;;\; Y:=y+P_{x}/eB$</p>
<p><strong>However</strong>, Prof.Ezawa use this convention:</p>
<p>$X:=x+P_{y}/eB\;;\; Y:=y-P_{x}/eB$</p>
<p>To be prepared for being driven mad, please compare them carefully.</p>
<p>4.I think he must be wrong somewhere, for example, in his book (2nd.ed), (10.2.5) and in his article (2.15)</p>
<p>$\left[P_{x},P_{y}\right]=i\hbar^{2}/l_{B}^{2}$</p>
<p>but you know we use minimal coupling $\mathbf{p}\rightarrow\mathbf{p}-\frac{q}{c}\mathbf{A}$ in this problem, $q=-e,e>0,{\mathbf{p}+\frac{e}{c}\mathbf{A}}$ for electrons, as Prof.Ezawa suggested in his book (10.2.3) and his article (2.12). Under this convention, I calculated $\left[P_{x},P_{y}\right]$ as following:</p>
<p>$\left[P_{x},P_{y}\right]=-i\hbar e\left(\left[\partial_{x},A_{y}\right]+\left[A_{x},\partial_{y}\right]\right)/c=-i\hbar eB/c=-i\hbar^{2}/l_{B}^{2}$</p>
<p>Oh my god here is a negative sign.</p>
<p>5.To summarize, I think if we take Prof.Ezawa's convention and apply his result for $\left[P_{x},P_{y}\right]=i\hbar^{2}/l_{B}^{2}$ during the calculation of $\left[X,Y\right]$, we will get his result. But his result for $\left[P_{x},P_{y}\right]=i\hbar^{2}/l_{B}^{2}$ seems not correct.</p>
<p>6.Someone save my day...</p>
<p><img src="http://i.stack.imgur.com/yNnWs.jpg" alt="No!"></p> | 1,471 | [
0.003093076404184103,
-0.032710205763578415,
0.02003542147576809,
-0.0402173176407814,
0.057207535952329636,
-0.004157131537795067,
-0.04273105785250664,
-0.01095584686845541,
0.026391247287392616,
-0.023736348375678062,
0.047529276460409164,
0.02563268132507801,
0.06273868680000305,
0.046502768993377686,
0.008083748631179333,
0.009706735610961914,
-0.023764604702591896,
0.024498101323843002,
-0.012939086183905602,
-0.010161781683564186,
-0.009466356597840786,
0.027056295424699783,
0.010589150711894035,
0.02847154811024666,
-0.021455073729157448,
0.0035044560208916664,
-0.02385096438229084,
-0.007120211608707905,
-0.009482339024543762,
0.08016100525856018,
-0.02748144045472145,
-0.03432758152484894,
0.04835769534111023,
-0.02553391456604004,
-0.018659546971321106,
0.019835883751511574,
0.018694663420319557,
-0.06569825112819672,
0.006021633744239807,
-0.028310654684901237,
-0.03677816689014435,
0.0023503222037106752,
-0.02007123827934265,
0.058144234120845795,
0.005852283909916878,
-0.010479127988219261,
0.014162388630211353,
-0.01828821375966072,
0.030585967004299164,
-0.06838597357273102,
0.06429579108953476,
-0.0063164508901536465,
0.020012756809592247,
-0.004589613061398268,
0.002092804526910186,
-0.04903927817940712,
0.039044808596372604,
0.05799700319766998,
0.002756967209279537,
-0.04821109399199486,
-0.01100213173776865,
-0.0025730326306074858,
0.0021312085445970297,
-0.04578886553645134,
-0.02346111088991165,
-0.000038656995457131416,
0.05044230446219444,
-0.014647569507360458,
0.026309628039598465,
0.0013026960659772158,
0.028234047815203667,
-0.00034275767393410206,
0.012940184213221073,
-0.04035898670554161,
0.07124628126621246,
-0.0111415209248662,
0.016859397292137146,
0.026643794029951096,
-0.01114032045006752,
0.046843934804201126,
-0.035633545368909836,
0.019190283492207527,
0.02042948454618454,
0.01874532923102379,
-0.005864228121936321,
0.00045978068374097347,
0.04790082946419716,
-0.01842694729566574,
0.023974386975169182,
0.018193496391177177,
-0.016194289550185204,
0.004557888023555279,
0.022945985198020935,
-0.027054376900196075,
-0.010280013084411621,
0.05694618448615074,
0.03095238469541073,
0.05430075526237488,
-0.008236486464738846,
-0.024143323302268982,
0.004439575131982565,
-0.027425354346632957,
-0.015394224785268307,
0.08161542564630508,
0.003881230019032955,
-0.009772774763405323,
-0.003095129271969199,
-0.004324264358729124,
-0.006850949488580227,
-0.055057790130376816,
-0.06512914597988129,
0.02983531914651394,
-0.030312728136777878,
-0.0046279653906822205,
-0.01540305931121111,
-0.018640683963894844,
-0.010616888292133808,
0.002963845618069172,
0.016733374446630478,
0.040170568972826004,
0.050077278167009354,
-0.02236102893948555,
0.0033954172395169735,
-0.0235101617872715,
-0.0431625135242939,
0.02652488462626934,
0.06371413171291351,
-0.004130061250180006,
-0.03880727291107178,
0.01831827685236931,
0.06424020975828171,
0.013456933200359344,
0.022762199863791466,
-0.00341251608915627,
0.033481549471616745,
0.01748821698129177,
-0.0699949562549591,
-0.07431292533874512,
0.03755434602499008,
-0.0295633003115654,
0.015641724690794945,
-0.07880844920873642,
-0.025790665298700333,
0.007384926546365023,
0.08996731042861938,
-0.013995392248034477,
0.0076218401081860065,
-0.02884170413017273,
0.023551002144813538,
0.02035789005458355,
-0.0081582460552454,
0.007188013754785061,
-0.003777757054194808,
-0.05278987064957619,
-0.007040841970592737,
-0.03935915231704712,
0.04235344007611275,
0.015435401350259781,
-0.00970348808914423,
-0.004366355016827583,
0.10312186926603317,
0.006097283214330673,
-0.019687708467245102,
-0.008103616535663605,
-0.015816986560821533,
-0.02962779812514782,
0.06824194639921188,
0.009289554320275784,
0.02664736472070217,
0.024464484304189682,
-0.02210029400885105,
0.012000292539596558,
-0.0013506129616871476,
0.0017413435271009803,
0.04394656792283058,
-0.034239090979099274,
-0.006979263387620449,
-0.056262724101543427,
-0.006582899019122124,
-0.01116274669766426,
-0.07400327920913696,
-0.057171884924173355,
-0.03189755976200104,
0.024963555857539177,
-0.031392257660627365,
0.022280754521489143,
-0.008250855840742588,
0.012512066401541233,
0.02522197552025318,
-0.035560715943574905,
-0.024192439392209053,
-0.06966552883386612,
0.0034431936219334602,
0.05739057809114456,
-0.03059614636003971,
0.057667240500450134,
-0.034224193543195724,
0.02182953432202339,
-0.025950677692890167,
-0.03722802922129631,
0.023492300882935524,
0.02905690297484398,
0.014901896938681602,
0.00672272639349103,
0.01935502700507641,
0.02769947052001953,
0.01800505630671978,
0.007054929621517658,
0.05298548564314842,
-0.05006438493728638,
-0.01307563204318285,
0.022541070356965065,
-0.021695125848054886,
0.014942643232643604,
0.04555704444646835,
-0.03941218554973602,
0.02211068756878376,
0.009301537647843361,
-0.014461055397987366,
0.01174034271389246,
-0.05841696262359619,
0.028087755665183067,
0.06170305609703064,
0.023471636697649956,
0.01628153771162033,
0.03655382618308067,
0.003984994720667601,
0.03539023548364639,
0.0053782169707119465,
-0.03454770892858505,
-0.0477459542453289,
0.02280532382428646,
0.0223255455493927,
0.022760143503546715,
-0.026696842163801193,
0.018689734861254692,
-0.0016858386807143688,
-0.007899850606918335,
0.0036221311893314123,
0.015672482550144196,
-0.013433712534606457,
-0.05629124492406845,
0.00300958170555532,
-0.00644170306622982,
-0.015258361585438251,
0.02973235957324505,
0.008331317454576492,
-0.021928030997514725,
0.039721012115478516,
0.00742473267018795,
-0.03449814021587372,
0.004817838780581951,
-0.008848831057548523,
-0.018415670841932297,
-0.011513535864651203,
-0.00939972698688507,
0.03451219201087952,
-0.03464045748114586,
0.03784795477986336,
0.013967740349471569,
-0.03296052664518356,
0.0009230583091266453,
-0.010592191480100155,
-0.04295026883482933,
0.029921794310212135,
-0.03235161677002907,
-0.01044265553355217,
0.014426058158278465,
0.009135528467595577,
-0.04620448872447014,
0.01576198637485504,
-0.00438153138384223,
-0.01655844785273075,
-0.0022723383735865355,
-0.0024429757613688707,
0.002658292418345809,
0.05189100280404091,
0.034053903073072433,
-0.016814082860946655,
-0.016934001818299294,
0.02419026382267475,
-0.001069063087925315,
0.047177158296108246,
-0.013635644689202309,
-0.04801439493894577,
-0.020915070548653603,
-0.07537026703357697,
0.0031109473202377558,
0.024596665054559708,
-0.013799795880913734,
-0.005207203794270754,
0.0009575672447681427,
-0.00924020167440176,
-0.039913762360811234,
-0.03881961852312088,
0.0076889232732355595,
0.022942490875720978,
-0.05684048309922218,
-0.014411896467208862,
0.06142032518982887,
-0.014213223941624165,
-0.037337955087423325,
-0.0030433840584009886,
0.0018884118180721998,
-0.011032731272280216,
0.021058032289147377,
-0.03128604218363762,
-0.00011181557783856988,
-0.007041376084089279,
-0.002865641610696912,
0.01859174482524395,
0.023586399853229523,
-0.019550716504454613,
-0.06899008899927139,
-0.04154403507709503,
-0.001357864122837782,
-0.005684592295438051,
0.020497772842645645,
-0.01966264098882675,
-0.05008473992347717,
0.0981978327035904,
0.02685440517961979,
-0.01107027567923069,
-0.025127142667770386,
-0.01645710878074169,
-0.006567803211510181,
-0.015467698685824871,
-0.008059704676270485,
0.07039259374141693,
-0.012498732656240463,
0.018152104690670967,
-0.012400687672197819,
0.031982988119125366,
0.04855942353606224,
-0.004774695727974176,
-0.03033132292330265,
0.026470208540558815,
-0.03466637432575226,
-0.008926400914788246,
0.079033762216568,
-0.02862432226538658,
0.0011203598696738482,
0.016424108296632767,
0.015525378286838531,
-0.0036515439860522747,
0.013094056397676468,
-0.05059336498379707,
0.03942204266786575,
-0.005112233106046915,
0.023911304771900177,
0.0013788837241008878,
0.029095949605107307,
-0.0014166384935379028,
-0.051388438791036606,
-0.006532157305628061,
-0.0011373793240636587,
0.016653751954436302,
-0.005965313408523798,
0.04415713623166084,
0.061652060598134995,
0.032855838537216187,
0.0009623889345675707,
-0.022784210741519928,
0.016094530001282692,
0.007185391616076231,
0.005810365080833435,
-0.05332278087735176,
-0.01986464112997055,
0.004067684523761272,
0.059286799281835556,
-0.002173655666410923,
-0.01764187403023243,
0.006199284922331572,
-0.023712560534477234,
-0.025572562590241432,
0.013914567418396473,
-0.029639126732945442,
0.05984136462211609,
0.011566152796149254,
0.016712356358766556,
-0.027350429445505142,
-0.01851111836731434,
0.021068546921014786,
-0.014107697643339634,
-0.10068688541650772,
-0.01210835762321949,
-0.022186418995261192,
-0.04339681193232536,
-0.01360368262976408,
-0.01130702719092369,
0.0035561067052185535,
-0.009042649529874325,
-0.026118790730834007,
-0.06628111004829407,
-0.002280320506542921,
-0.04362257570028305,
0.01822931133210659,
-0.02877996489405632,
-0.06506925821304321,
-0.0456644743680954,
0.005489773117005825,
0.0355096310377121,
-0.018122652545571327,
-0.002242427784949541,
0.0042476961389184,
-0.04677198827266693,
0.016298286616802216,
-0.003915372304618359,
0.007668821141123772,
0.03879298269748688,
0.0237160362303257,
-0.013936321251094341,
0.020381299778819084,
-0.009756263345479965,
-0.00006375177326845005,
0.010984902270138264,
0.025720203295350075,
-0.0027125473134219646,
-0.05137322470545769,
-0.024460002779960632,
-0.008668074384331703,
-0.017862871289253235,
-0.018136167898774147,
0.06547178328037262,
0.029354823753237724,
0.012396895326673985,
0.05163557454943657,
0.04911312833428383,
0.009736206382513046,
-0.011808079667389393,
0.04134303703904152,
0.0008457251824438572,
0.02226101979613304,
-0.010361791588366032,
0.000052019720897078514,
0.005351643078029156,
-0.02653316780924797,
0.0137737225741148,
-0.0075713568367064,
-0.040203046053647995,
-0.02426121011376381,
0.0341421440243721,
0.05660666525363922,
0.0018899664282798767,
0.0326230451464653,
0.010648127645254135,
-0.0028999701607972383,
-0.007848365232348442,
0.001935119042173028,
0.012182004749774933,
0.038007382303476334,
0.018080512061715126,
0.0028161536902189255,
0.0020543031860142946,
-0.01897815614938736,
-0.024942629039287567,
0.028164027258753777,
0.0781516432762146,
0.026040416210889816,
0.010237635113298893,
-0.07835857570171356,
-0.03115563467144966,
0.01295100525021553,
-0.0008862984250299633,
0.04347766935825348,
0.020847171545028687,
0.021867996081709862,
-0.033656951040029526,
-0.02458186447620392,
-0.019596299156546593,
0.01552062202244997,
0.013050195761024952,
0.042903728783130646,
-0.05249106511473656,
-0.021711936220526695,
0.0015562959015369415,
-0.0006977347075007856,
0.002994667738676071,
0.06541399657726288,
-0.024756964296102524,
0.024443643167614937,
0.023313745856285095,
0.0325075201690197,
-0.044299110770225525,
-0.09657186269760132,
-0.008939024060964584,
0.003971181809902191,
-0.00002472874621162191,
0.028213897719979286,
0.005751718766987324,
-0.06320541352033615,
0.025435246527194977,
0.024116741493344307,
0.036314841359853745,
0.019296269863843918,
-0.017053229734301567,
0.061900727450847626,
0.02905665710568428,
-0.01596168801188469,
0.08340316265821457,
0.007410811260342598,
-0.05543609336018562,
-0.01522658672183752,
-0.03883595019578934,
0.04023490846157074,
-0.0012302647810429335,
0.04046925902366638,
-0.02747660130262375,
0.018344521522521973,
-0.03473968431353569,
0.034865207970142365,
-0.03956964239478111,
0.01541315671056509,
-0.008139722049236298,
-0.05070344731211662,
0.01125261653214693,
0.0011576879769563675,
-0.012160358019173145,
-0.016033140942454338,
-0.005953976418823004,
0.061437979340553284,
0.00411232141777873,
-0.030061163008213043,
0.03626038506627083,
-0.0006078017759136856,
0.02453388087451458,
0.03309915214776993,
-0.012717323377728462,
0.013252297416329384,
-0.0662631243467331,
-0.008527042344212532,
-0.04659260809421539,
-0.04281030222773552,
0.030463771894574165,
0.006850775331258774,
-0.006887687835842371,
-0.0005149924545548856,
0.004917204845696688,
-0.044371213763952255,
-0.007155366707593203,
0.01930217444896698,
-0.009312812238931656,
-0.03082534298300743,
-0.006077186670154333,
0.021031174808740616,
-0.015528744086623192,
-0.055219195783138275,
-0.049064215272665024,
-0.0019921378698199987,
0.003151986515149474,
-0.00398542545735836,
-0.03578486666083336,
-0.011615992523729801,
-0.007439390290528536,
-0.06715124845504761,
0.025719886645674706,
0.038257598876953125,
-0.04689577594399452,
-0.020884085446596146,
-0.0018697719788178802,
-0.0022612777538597584,
0.03362303599715233,
0.012892205268144608,
-0.03321784734725952,
0.025005662813782692,
-0.01810411736369133,
0.009358750656247139,
0.00596122769638896,
0.04320003464818001,
-0.004601021762937307,
-0.039896659553050995,
-0.00521855428814888,
-0.009685032069683075,
0.028550060465931892,
-0.02026371657848358,
-0.03632931038737297,
0.08378732949495316,
0.03915015980601311,
-0.03502262011170387,
0.003487846115604043,
-0.008230640552937984,
-0.019290128722786903,
0.022780973464250565,
-0.013465452007949352,
-0.03565377742052078,
-0.03183563053607941,
-0.03606988489627838,
-0.0015099986921995878,
-0.01319864671677351,
-0.03881941735744476,
-0.02117769792675972,
0.05098258703947067,
0.03318719193339348,
-0.008481285534799099,
0.04296727478504181,
-0.04398549720644951,
0.039719078689813614,
0.021056361496448517,
0.005892307031899691,
0.01225507166236639,
-0.013302966952323914,
-0.04712420701980591,
-0.02599026821553707,
-0.058048419654369354,
0.027859866619110107,
0.06205775961279869,
0.01766262948513031,
0.03770586848258972,
0.015435498207807541,
0.01199233066290617,
0.009740364737808704,
0.00036056360113434494,
-0.009609339758753777,
0.01036719512194395,
-0.017548400908708572,
0.016663897782564163,
-0.04043002426624298,
-0.0038540083914995193,
0.02568213641643524,
0.055426619946956635,
-0.06856664270162582,
-0.0058557745069265366,
0.060216210782527924,
-0.008943671360611916,
0.020461369305849075,
0.0016462192870676517,
-0.023239102214574814,
0.04498716816306114,
-0.01345931738615036,
0.04091009125113487,
-0.0025365299079567194,
-0.027736997231841087,
0.0591965913772583,
0.032379552721977234,
-0.01657092198729515,
-0.02886216901242733,
-0.04887686297297478,
-0.03438223525881767,
0.008460511453449726,
0.007315219845622778,
0.001703490037471056,
0.016485825181007385,
0.02451166696846485,
0.021715400740504265,
0.01435700710862875,
0.0060037896037101746,
-0.010062364861369133,
-0.03744202107191086,
0.02170022390782833,
-0.019029011949896812,
-0.03306259959936142,
0.03330516442656517,
-0.016783028841018677,
-0.019996007904410362,
0.03192346543073654,
-0.01920420490205288,
0.03657369688153267,
0.03409856557846069,
0.04520011320710182,
-0.015703972429037094,
0.051861923187971115,
-0.04704146832227707,
-0.02006307616829872,
-0.017998360097408295,
-0.004208374302834272,
0.13734686374664307,
0.028539162129163742,
0.03723425418138504,
-0.07899946719408035,
0.0658402293920517,
0.03150865063071251,
0.010428504087030888,
-0.013777674175798893,
0.008177797310054302,
-0.04409719258546829,
0.016080353409051895,
0.002718512900173664,
0.06665409356355667,
0.0073900241404771805,
-0.044181663542985916,
-0.0151395658031106,
-0.027214666828513145,
-0.06334313750267029,
0.050333380699157715,
0.0282167699187994,
-0.009436680935323238,
-0.007928472943603992,
-0.03410666063427925,
0.026254214346408844,
-0.03339128568768501,
0.0018208400579169393,
-0.042538486421108246,
-0.023064760491251945,
0.03346148505806923,
0.0017395539907738566,
-0.020458469167351723,
0.008649659343063831,
0.04130442813038826,
-0.007012624759227037,
-0.006604926194995642,
0.016966354101896286,
0.04108358919620514,
-0.02257958985865116,
0.04693550989031792,
0.009038802236318588,
0.006129002198576927,
0.027784569188952446,
0.03638843446969986,
0.007201869040727615,
-0.03969305381178856,
-0.0010667956667020917,
-0.02676105871796608,
0.09545830637216568,
0.016741693019866943,
-0.004871575627475977,
0.0020716646686196327,
-0.01807383820414543,
0.016141489148139954,
-0.03746041655540466,
-0.017573997378349304,
0.013542860746383667,
0.020327085629105568,
-0.016177678480744362,
0.010432192124426365,
-0.008764718659222126,
0.04352391138672829,
-0.0003110301913693547,
-0.019456418231129646,
0.010877967812120914,
-0.012081109918653965,
0.03305348753929138,
0.01641366258263588,
0.03828366473317146,
0.011382926255464554,
0.008642496541142464,
-0.048507995903491974,
-0.04321608692407608,
-0.033338237553834915,
-0.05946065112948418,
-0.023062173277139664,
0.033609289675951004,
0.028831826522946358,
0.006760672200471163,
-0.03290775418281555,
-0.01218106597661972,
-0.07005318999290466,
0.022524811327457428,
0.026205282658338547,
-0.005666170734912157,
-0.013925418257713318,
0.014578677713871002,
0.0035584447905421257,
0.003999235108494759,
-0.03593980520963669,
-0.02846626751124859,
0.0261959508061409,
0.04307432100176811,
0.013620260171592236,
-0.003115527331829071,
-0.03320656344294548,
-0.01496791560202837,
0.0061554936692118645,
0.00026560810511000454,
-0.011867579072713852,
-0.003045534249395132,
-0.005144751630723476,
0.029337743297219276,
0.02251400239765644,
0.04047257825732231,
-0.009462869726121426,
-0.017030367627739906,
-0.014114821329712868,
-0.0014686990762129426,
0.041223347187042236,
0.03701794147491455,
0.02250972017645836,
-0.006285164505243301,
-0.008383281528949738,
0.015911616384983063,
0.01290527731180191,
0.011583724990487099,
0.011725550517439842,
-0.041213661432266235,
-0.03222866356372833,
-0.0026233128737658262,
-0.011769617907702923,
-0.043848488479852676,
0.008713294751942158,
-0.011759907007217407,
0.04691041260957718,
-0.030126847326755524,
0.03622201830148697,
0.0006231130682863295,
0.02497214265167713,
-0.014539295807480812,
-0.0014010625891387463,
0.07576420903205872,
0.004934651777148247,
-0.03605493903160095,
0.004853487946093082,
0.014658219181001186,
-0.00007353565888479352,
0.016719674691557884,
0.016391050070524216,
-0.023929636925458908,
0.040531057864427567,
-0.03656778112053871,
-0.020975809544324875,
0.02868690900504589,
0.017595425248146057,
0.0014009039150550961,
0.01216903142631054,
-0.017357410863041878,
-0.02802574820816517,
0.044372543692588806,
-0.003926760051399469,
-0.0038951432798057795,
-0.01354625727981329,
-0.031252894550561905,
-0.0130523182451725,
-0.01196421030908823,
0.013768723234534264,
0.006220386363565922,
0.025644835084676743,
0.034914467483758926,
-0.02990102954208851,
-0.045717932283878326,
0.014329802244901657,
-0.016016745939850807,
-0.007013026159256697,
0.021985884755849838,
-0.01278251688927412,
-0.054697711020708084,
-0.002369880210608244,
0.04546518996357918,
-0.017989831045269966,
0.015676429495215416,
-0.012486887164413929,
-0.006442295853048563,
-0.06771329790353775,
-0.057358574122190475,
-0.02143583819270134,
0.01752118021249771,
0.04423920810222626,
-0.06033572182059288,
0.004444233141839504,
0.02673337236046791,
-0.035951487720012665,
0.021597161889076233,
0.013778799213469028,
-0.008752185851335526,
-0.030209222808480263,
0.0028460563626140356,
-0.034897200763225555,
0.00430004857480526,
0.030313460156321526,
0.06781347095966339,
-0.00688199931755662,
0.04256434366106987,
-0.012252142652869225,
-0.0540006086230278,
-0.019703112542629242,
0.0012030298821628094,
0.012431059032678604,
-0.0560678206384182,
0.049263276159763336,
-0.0018820747500285506,
0.004471496678888798,
0.04694833606481552,
-0.012832689099013805,
-0.006563291419297457,
-0.00015903385065030307,
0.027935093268752098,
-0.0037910614628344774,
0.05332391336560249,
0.027033958584070206,
-0.03012820892035961,
0.014436441473662853,
-0.012385064736008644,
0.01818624697625637,
0.026396289467811584,
-0.007979217916727066,
0.055446039885282516,
0.021043242886662483,
0.012129156850278378,
-0.012526270002126694,
0.016915537416934967,
-0.015388539992272854,
-0.007918767631053925,
0.021340392529964447,
-0.0038445070385932922,
0.007628695573657751,
-0.016266662627458572,
0.03641226142644882,
-0.04422643408179283,
-0.0040108077228069305,
0.006441835779696703,
0.00818566419184208,
0.001209575799293816,
0.03715246915817261,
-0.04277778044342995,
-0.04140917956829071,
0.04850994050502777,
-0.004633808974176645,
0.03022049181163311,
-0.05165563151240349,
-0.005256845150142908,
0.012258945032954216,
0.01492217369377613,
0.004206126090139151,
-0.049293484538793564,
-0.06853345036506653,
-0.019784217700362206,
-0.02927723526954651,
0.013738439418375492,
-0.05122417211532593,
-0.012943670153617859,
0.015001032501459122,
-0.036388419568538666,
0.029188670217990875,
0.02545614168047905,
-0.028779201209545135,
-0.035927943885326385,
-0.019729264080524445,
0.011192544363439083,
0.05319514498114586,
0.047872696071863174,
0.01581881195306778,
-0.02230626717209816,
0.018487868830561638,
0.01683851145207882,
0.0459655299782753,
-0.02194986119866371,
0.009168077260255814,
0.029946444556117058,
0.02210107445716858,
0.010316251777112484,
0.007011269684880972,
-0.00737641379237175,
0.04069211706519127,
0.029627207666635513,
0.036412373185157776,
0.012802564539015293,
0.01680886559188366,
-0.057671260088682175,
0.03136448189616203,
-0.010772568173706532,
-0.016386201605200768,
0.07434704899787903,
-0.0012982699554413557,
0.010130858980119228,
0.023449167609214783,
-0.027697116136550903,
-0.058779045939445496,
0.02056426927447319,
-0.04089808464050293,
0.0170491524040699,
0.01706337183713913,
-0.013414934277534485,
0.03622400015592575,
-0.037629272788763046,
0.012798868119716644,
0.02834741771221161,
0.0008851181482896209,
-0.031231028959155083,
0.026000984013080597,
0.003155824262648821,
0.015019161626696587,
0.0016630050959065557,
0.03543972596526146,
-0.0021147250663489103,
0.012722758576273918,
0.020514046773314476,
0.014789438806474209,
0.01758447475731373,
0.027956312522292137,
0.014528232626616955,
0.0530092753469944,
-0.03806295245885849,
0.028437621891498566,
0.035404689610004425,
-0.03517285734415054,
-0.021201826632022858,
-0.004025110509246588,
0.04296223446726799,
-0.013471543788909912,
-0.0006670976872555912,
0.013915009796619415,
-0.0517132394015789,
0.08764027804136276,
-0.036483749747276306,
0.031502701342105865,
0.020416878163814545,
-0.0022415276616811752,
-0.011787809431552887,
0.03207714110612869,
0.0049867224879562855,
0.03844865411520004,
-0.013086918741464615,
-0.0398063063621521,
-0.060584284365177155,
0.0006114458083175123,
-0.03127022460103035,
-0.06173883378505707,
-0.0021054623648524284,
0.022957809269428253,
-0.006331806071102619,
0.021075956523418427,
-0.038088034838438034,
0.0031328806653618813,
-0.03774528577923775,
-0.014293034560978413,
0.04982203617691994,
-0.001449847361072898,
-0.006532423198223114,
0.0007769357180222869,
-0.0035225204192101955,
0.04847489669919014,
-0.040744610130786896,
-0.0017865733243525028,
-0.01112390961498022,
0.008064975030720234,
-0.04150168597698212,
0.006402082275599241
] |
<p>Hi I'm calculating a problem, and I think it ought to be correct - but the result I get isn't.</p>
<p>The problem is described as follow:</p>
<blockquote>
<p>A spacecraft is traveling from Earth to Venus in an elliptical, but
NON-Hohman transfer orbit, starting at the apocentre at 1 AU. The
semi-major axis of this elliptical orbit, a = 0.75 AU. After a few
months the orbit of the spacecraft crosses the orbit of Venus. What
is the “exact” travel time to this crossing point in days?</p>
</blockquote>
<p>With some numbers (which I used for calculations):
$$\mu_s = 1.33 \cdot 10^{11}$$
$$R_{venus} = 0.72 AU$$
$$1 AU = 150 \cdot 10^6 km$$</p>
<p>From the geometrics (elliptical orbit around the sun) the eccentricity can be calculated:
$$a(1+e) = R_{earth} \rightarrow e = \tfrac{1}{3}$$
This then can give the true anomaly in a straight forward manner (from the range equation for an ellips):
$$r = \frac{a(1-e^2)}{1+e\cos(\theta)}$$
$$\cos(\theta) = \frac{a(1-e^2)}{R_{venus}} - 1 = \tfrac{25}{27}$$</p>
<p>Now I'm wondering a bit if I actually take the correct angle for theta... In the rest of my calculations I used this value ($\theta = 22.2 ^{\circ}$) as the angle between the sun-apocenter & sun-orbit crossing vectors. (A schematic drawing on paper did make this "seem correct").</p>
<p>Now from this (and using simple schematic drawing/geometry) the following can be said (to get the eccentric anomaly):
$$R_{venus} \cos(\theta) - ae = a \cos(E)$$
$$E = 0.9818 rad$$
Now the time can be calculated using <a href="http://en.wikipedia.org/wiki/Kepler%27s_Equation" rel="nofollow">kepler's equation</a> as following:
$$E - e\sin(E) = M = n(t - t_p)$$
$$n = \sqrt{\frac{\mu_{sun}}{a^3}} = 3.05 \cdot 10^{-7} s^{-1}$$
That gives
$$t - t_p = t = 2421311 s = 28 d$$</p>
<p>However this is wrong, apparently the correct result is "72 days". What am I doing wrong? Where did I make mistakes?</p> | 1,472 | [
0.004734392743557692,
0.014503618702292442,
-0.008591685444116592,
0.0036077823024243116,
0.06804870814085007,
0.020573601126670837,
-0.0055715832859277725,
0.029239682480692863,
-0.0028218466322869062,
-0.02792580984532833,
0.0431675910949707,
0.05236779525876045,
0.03142476826906204,
-0.003975715022534132,
0.03634559363126755,
-0.0061996313743293285,
-0.03458511829376221,
0.02387596108019352,
0.023650599643588066,
-0.01789490319788456,
0.027761545032262802,
-0.044450558722019196,
-0.0036564976908266544,
-0.03992542624473572,
-0.0015984044875949621,
0.01867000199854374,
0.03783002123236656,
-0.028727954253554344,
-0.02211817353963852,
0.02810944803059101,
-0.017349593341350555,
-0.008793668821454048,
0.04030924290418625,
0.008706401102244854,
-0.007446137256920338,
0.012669398449361324,
0.022191723808646202,
0.013777773827314377,
-0.016533752903342247,
0.03895873576402664,
-0.051170796155929565,
-0.011532180942595005,
-0.004593821242451668,
0.06938290596008301,
-0.0318107008934021,
-0.016912704333662987,
0.009476316161453724,
-0.019038500264286995,
0.06284286826848984,
-0.02080870047211647,
0.06827112287282944,
-0.018200308084487915,
0.03264894708991051,
0.02072984352707863,
0.012229605577886105,
-0.028801336884498596,
0.0692576989531517,
0.037474196404218674,
0.006417444907128811,
-0.0672101303935051,
-0.011514979414641857,
-0.019259938970208168,
-0.020650343969464302,
-0.03051539696753025,
0.007846985012292862,
0.020529627799987793,
-0.03168947994709015,
0.003131163539364934,
0.017610128968954086,
-0.009858972392976284,
0.04692073538899422,
0.02567090280354023,
-0.05112015828490257,
0.007902942597866058,
-0.008663447573781013,
-0.05416540056467056,
0.0036336644552648067,
-0.009200001135468483,
0.04374319314956665,
0.0218510702252388,
-0.03232787922024727,
0.011134039610624313,
0.04933617264032364,
0.04468480870127678,
-0.0018736982019618154,
0.02733328752219677,
0.041674818843603134,
-0.015760019421577454,
0.01548089925199747,
0.010395298711955547,
-0.007621434051543474,
0.04899853840470314,
0.033590417355298996,
-0.01302744634449482,
-0.00866991002112627,
0.06950883567333221,
-0.01708305813372135,
0.029412727802991867,
-0.019156107679009438,
-0.01168588362634182,
-0.01516103558242321,
-0.02961873635649681,
0.0032577156089246273,
0.0650147795677185,
-0.003949901554733515,
-0.01801399327814579,
-0.000868801202159375,
-0.022012611851096153,
-0.0020570862106978893,
-0.03383190184831619,
0.0005769097479060292,
0.034517206251621246,
0.004654355812817812,
0.02849254198372364,
-0.019622493535280228,
0.011401042342185974,
0.012104403227567673,
-0.024371834471821785,
0.03130317106842995,
0.02881845459342003,
0.03298335522413254,
-0.012740976177155972,
0.061990998685359955,
-0.04433697462081909,
-0.03698975592851639,
0.014346446841955185,
0.011663691140711308,
-0.021848075091838837,
-0.05777807906270027,
0.0037871082313358784,
0.026496948674321175,
-0.0324149914085865,
0.0041511994786560535,
-0.00444563664495945,
0.022853821516036987,
-0.01981291174888611,
-0.07578875124454498,
-0.08144961297512054,
-0.007034739945083857,
0.031167563050985336,
-0.011722528375685215,
-0.0792083814740181,
-0.006769681349396706,
0.040573012083768845,
0.08493342995643616,
0.03481666371226311,
0.01957968808710575,
0.021879486739635468,
0.028567258268594742,
-0.00526402797549963,
-0.038220543414354324,
0.041153982281684875,
0.009964427910745144,
-0.08966421335935593,
0.0024372730404138565,
-0.058018527925014496,
-0.006501948460936546,
0.02302475832402706,
0.019352609291672707,
-0.00522265350446105,
0.0655209943652153,
0.009074042551219463,
0.012976795434951782,
0.022681260481476784,
-0.007395849097520113,
-0.026056068018078804,
0.11212953925132751,
0.0412934385240078,
0.005733332596719265,
0.05051672086119652,
0.006063736975193024,
0.027504360303282738,
-0.0044584088027477264,
0.0006859130808152258,
0.06717337667942047,
-0.040485456585884094,
0.0031893167179077864,
-0.06119922548532486,
-0.025124885141849518,
0.011527712456882,
-0.030413618311285973,
-0.05046694353222847,
0.006037749350070953,
-0.01927022449672222,
0.04403912276029587,
0.05044323578476906,
-0.02056415006518364,
0.019344154745340347,
0.03435051068663597,
-0.0352340005338192,
0.007889587432146072,
0.03406853973865509,
0.014889641664922237,
-0.0008014774066396058,
-0.013483610935509205,
0.05888250097632408,
-0.06394299119710922,
0.0041085174307227135,
0.011945436708629131,
0.02323193848133087,
-0.006518632173538208,
0.011816318146884441,
0.046890150755643845,
-0.0346895307302475,
0.05812336876988411,
0.05798571556806564,
0.02122240513563156,
0.030354943126440048,
-0.0002511301718186587,
-0.0010497266193851829,
0.019413305446505547,
-0.02171449363231659,
-0.03463621065020561,
0.03752591833472252,
0.018610410392284393,
0.01778901182115078,
-0.005223905202001333,
0.005761611275374889,
0.0008625327609479427,
0.014533829875290394,
-0.014471516944468021,
0.05859290808439255,
0.042503323405981064,
0.03500674292445183,
0.024331118911504745,
0.03903331980109215,
0.03660350292921066,
0.006742699537426233,
0.016065053641796112,
-0.034715160727500916,
-0.021811025217175484,
-0.0018102882895618677,
0.015094490721821785,
0.03184204548597336,
-0.01278343889862299,
0.015843499451875687,
0.05968557670712471,
0.03743736073374748,
-0.0025308611802756786,
0.00894469115883112,
0.012092547491192818,
-0.020645154640078545,
0.03278291970491409,
0.016609078273177147,
-0.017044154927134514,
0.0355815552175045,
-0.0017837927443906665,
-0.02356654591858387,
-0.01032191887497902,
-0.0040924944914877415,
-0.028231512755155563,
0.01912313513457775,
-0.013664577156305313,
0.014424806460738182,
-0.018032729625701904,
0.052444152534008026,
0.07308568060398102,
-0.0710364356637001,
-0.004779526498168707,
0.035036180168390274,
0.002776645589619875,
-0.0006040371372364461,
-0.005823268089443445,
0.012278764508664608,
-0.0035538985393941402,
0.03569347411394119,
-0.007289071101695299,
0.01599649339914322,
0.02384183742105961,
-0.038394954055547714,
0.01528944168239832,
-0.05497661232948303,
-0.0515165813267231,
-0.00911000557243824,
-0.018894676119089127,
0.015054321847856045,
0.022276941686868668,
-0.057673484086990356,
0.00532122515141964,
-0.0033694528974592686,
-0.018541129305958748,
-0.013314669951796532,
-0.023248732089996338,
0.021121861413121223,
-0.034921012818813324,
0.02581838145852089,
-0.021968994289636612,
0.002353748306632042,
0.025496970862150192,
0.0353035144507885,
0.010442337952554226,
-0.010475126095116138,
0.0016751457005739212,
-0.04120501130819321,
-0.041647497564554214,
-0.03491327911615372,
-0.03346417844295502,
-0.0676853209733963,
-0.02869289740920067,
0.04822991043329239,
0.008559432812035084,
-0.026643414050340652,
0.017556454986333847,
-0.06986051797866821,
-0.022796321660280228,
-0.014689061790704727,
-0.003269534558057785,
0.0055397627875208855,
-0.0452331081032753,
0.08162328600883484,
-0.03217906877398491,
0.028098884969949722,
-0.02688753232359886,
-0.06693311035633087,
-0.04423661530017853,
0.00218870397657156,
-0.018494443967938423,
-0.0027807923033833504,
0.00026687103672884405,
-0.0572308711707592,
0.056808412075042725,
-0.0025926080998033285,
0.012214455753564835,
-0.024082668125629425,
0.04996015131473541,
-0.04043954238295555,
-0.010903986170887947,
0.02042197249829769,
0.02114415168762207,
0.02065972611308098,
0.015320894308388233,
-0.033264532685279846,
0.009476698935031891,
0.027970625087618828,
0.009382483549416065,
-0.0044948020949959755,
0.027669139206409454,
0.012657146900892258,
0.02944042533636093,
0.026704855263233185,
0.00332017638720572,
0.011659949086606503,
0.03950280323624611,
0.013210593722760677,
0.07222216576337814,
0.023279068991541862,
-0.08743081241846085,
0.01154331211000681,
-0.001995341619476676,
0.010069462470710278,
0.04712260141968727,
0.026796581223607063,
0.00480713089928031,
0.019008267670869827,
-0.05376657471060753,
0.028366602957248688,
0.05905505269765854,
-0.022275405004620552,
-0.029572222381830215,
0.07444723695516586,
0.04437302052974701,
-0.015927348285913467,
-0.025056986138224602,
-0.03703466057777405,
0.0046786353923380375,
0.010364534333348274,
-0.02514554187655449,
-0.01625601202249527,
0.03785501793026924,
0.02047777734696865,
-0.007225411478430033,
0.007619088049978018,
-0.031554222106933594,
0.008783719502389431,
-0.047366224229335785,
-0.046712081879377365,
-0.028530018404126167,
-0.005640379618853331,
-0.034180816262960434,
-0.0008083885768428445,
0.01754896715283394,
-0.014429302886128426,
-0.003116896376013756,
0.009020456112921238,
-0.06067546084523201,
0.032865092158317566,
0.012200652621686459,
-0.08415902405977249,
0.005469395779073238,
0.002267461037263274,
-0.005352777894586325,
-0.032810743898153305,
-0.0038912994787096977,
-0.024439474567770958,
0.006146719213575125,
-0.04666808992624283,
0.029599111527204514,
-0.020772861316800117,
0.004746842663735151,
-0.04965754970908165,
0.03991279378533363,
0.014924885705113411,
-0.04340808838605881,
0.0247552040964365,
0.017875611782073975,
-0.018541187047958374,
0.013687546364963055,
-0.026332911103963852,
0.03340918943285942,
0.0019863310735672712,
0.0048679509200155735,
0.0030144338961690664,
-0.0008523334981873631,
-0.0521424263715744,
0.022794820368289948,
-0.028401391580700874,
0.030801817774772644,
0.024004492908716202,
0.012671476230025291,
-0.04156874120235443,
-0.03556313365697861,
-0.02708694338798523,
0.04082789272069931,
0.024149969220161438,
-0.0013255546800792217,
0.013500071130692959,
0.03522385656833649,
-0.030055148527026176,
0.0010130011942237616,
0.003169925883412361,
0.03561950847506523,
0.012131784111261368,
-0.012859088368713856,
-0.04975307360291481,
-0.04144668206572533,
-0.014068099670112133,
0.009509429335594177,
0.014260666444897652,
-0.012443985790014267,
-0.028983337804675102,
-0.03447703272104263,
0.03905902057886124,
-0.01951165311038494,
0.002956098411232233,
0.007673400454223156,
-0.007597006857395172,
0.002453276887536049,
0.008754095993936062,
-0.01589227467775345,
0.0018189908005297184,
-0.0144765330478549,
0.05194048210978508,
-0.00946166180074215,
0.04794637858867645,
-0.07846089452505112,
-0.0256304033100605,
0.04076722264289856,
0.0666610598564148,
-0.006930960807949305,
-0.007887879386544228,
-0.05232943221926689,
-0.0244598388671875,
0.031092803925275803,
-0.013675296679139137,
0.030977241694927216,
-0.04243738576769829,
0.03169742971658707,
-0.01658424735069275,
-0.06040992587804794,
-0.0453098863363266,
0.02658945508301258,
0.005861614365130663,
0.05847777798771858,
-0.036035407334566116,
0.011179428547620773,
0.0263658594340086,
-0.007693266961723566,
0.05503121390938759,
0.04365578293800354,
0.040349334478378296,
-0.014709223061800003,
-0.014383948408067226,
-0.025957584381103516,
0.010667235590517521,
-0.05862107872962952,
-0.021814949810504913,
-0.015556590631604195,
-0.034676287323236465,
0.019485631957650185,
-0.05466184392571449,
-0.0024466707836836576,
0.05548672750592232,
0.022168276831507683,
0.024349234998226166,
-0.017515772953629494,
-0.04716140404343605,
0.034746598452329636,
0.051444198936223984,
-0.005960683338344097,
0.021711891517043114,
0.012113725766539574,
-0.020174046978354454,
0.017908217385411263,
-0.04514935240149498,
-0.014846768230199814,
-0.03250541165471077,
-0.020108355209231377,
-0.0032050437293946743,
0.006171529646962881,
-0.05655582249164581,
0.03350362181663513,
0.0005435585626401007,
0.02103017084300518,
-0.052198056131601334,
-0.004020745866000652,
-0.010256585665047169,
0.03897529095411301,
-0.015360826626420021,
0.04096135124564171,
-0.027300387620925903,
0.0002286260132677853,
-0.011072988621890545,
-0.000528502045199275,
-0.021892854943871498,
-0.02842322178184986,
0.009069221094250679,
0.03392209857702255,
0.019484834745526314,
-0.032784417271614075,
-0.021195147186517715,
0.009766476228833199,
-0.011133480817079544,
-0.05749646574258804,
0.04526401683688164,
-0.04787800833582878,
-0.02144882082939148,
-0.002813964616507292,
-0.05283264443278313,
-0.03985506296157837,
0.03170684725046158,
-0.014688458293676376,
0.025744663551449776,
-0.0005258482997305691,
-0.06465484201908112,
0.022300096228718758,
-0.00877279695123434,
-0.04052804037928581,
-0.037815842777490616,
0.032668329775333405,
-0.009367643855512142,
-0.052933260798454285,
0.01074706669896841,
-0.0206738468259573,
-0.029942667111754417,
-0.023295054212212563,
-0.018195630982518196,
0.04904285818338394,
-0.05523025989532471,
-0.0159476138651371,
-0.012425677850842476,
-0.0010269571794196963,
0.050967589020729065,
-0.032694458961486816,
0.016310004517436028,
0.04362813010811806,
-0.01839207112789154,
-0.0054349456913769245,
-0.0057614087127149105,
0.038325391709804535,
-0.024398179724812508,
-0.033294692635536194,
-0.026077697053551674,
-0.049612097442150116,
0.0008011952158994973,
-0.004632617812603712,
-0.031770970672369,
0.02762478217482567,
-0.0072161476127803326,
0.006170066073536873,
0.011768152005970478,
0.03532455116510391,
0.013156237080693245,
0.0002384579711360857,
-0.03327775374054909,
-0.016513386741280556,
-0.02811911143362522,
-0.033311791718006134,
0.01665494777262211,
-0.027924174442887306,
-0.006999456789344549,
-0.017481930553913116,
0.07571686804294586,
-0.015562357380986214,
-0.0006646579131484032,
0.03548799082636833,
0.029146913439035416,
-0.026027556508779526,
-0.03813479468226433,
-0.011781620793044567,
0.025888806208968163,
0.002773934043943882,
-0.044527024030685425,
-0.0025719923432916403,
-0.0540463887155056,
0.004418085794895887,
0.09596139192581177,
-0.007467776536941528,
0.0002544447488617152,
-0.014143358916044235,
0.019987020641565323,
-0.0017193943494930863,
-0.02588246762752533,
-0.011844792403280735,
-0.03181654214859009,
0.007612792309373617,
0.023276668041944504,
-0.028060799464583397,
-0.012126280926167965,
0.0010641633998602629,
0.0594460554420948,
-0.03541240096092224,
-0.004972646478563547,
-0.004246504977345467,
0.014226273633539677,
0.04662272334098816,
-0.0012719827936962247,
-0.04467621445655823,
0.02234184555709362,
0.02359037473797798,
0.051768090575933456,
0.003995685372501612,
0.007621277589350939,
0.052884478121995926,
0.02925202250480652,
0.029618728905916214,
-0.021398482844233513,
-0.046072524040937424,
-0.02553604170680046,
0.04488194361329079,
0.022630762308835983,
-0.017945080995559692,
0.01482474897056818,
0.007594877853989601,
0.03283364325761795,
-0.025817736983299255,
0.00005595857874141075,
-0.0471380315721035,
-0.08529099822044373,
0.0057153115049004555,
-0.010157023556530476,
-0.059010811150074005,
0.07347548753023148,
-0.017330538481473923,
-0.0033193465787917376,
-0.022817175835371017,
-0.010285516269505024,
0.0010486202081665397,
0.04609888792037964,
0.005834631621837616,
-0.02972573973238468,
0.06506744027137756,
-0.023834040388464928,
0.012962937355041504,
-0.035883933305740356,
0.018952911719679832,
0.1364826112985611,
0.03894846513867378,
-0.014331849291920662,
-0.017393644899129868,
0.024948297068476677,
0.000989214633591473,
-0.0031501054763793945,
-0.047699734568595886,
0.043961599469184875,
-0.011391599662601948,
-0.04443817958235741,
0.026992768049240112,
0.07468396425247192,
-0.027993094176054,
-0.03869776800274849,
0.014669796451926231,
-0.01195521280169487,
-0.03267882019281387,
-0.015896033495664597,
0.026355499401688576,
-0.015076756477355957,
-0.0034182274248450994,
-0.0353902243077755,
0.020879708230495453,
-0.07010077685117722,
0.005872224923223257,
-0.04958345368504524,
-0.02855844609439373,
0.03649178147315979,
0.012643400579690933,
-0.03141411393880844,
0.027626190334558487,
-0.008005800656974316,
-0.0205826535820961,
-0.012620650231838226,
0.047049954533576965,
-0.0024474645033478737,
-0.004685410764068365,
0.02651343122124672,
0.03961168974637985,
0.0076356190256774426,
0.014003661461174488,
0.022872311994433403,
0.021834125742316246,
-0.0642615333199501,
0.02060411125421524,
-0.028268638998270035,
0.08262602984905243,
0.0021020236890763044,
-0.0014044733252376318,
-0.022907080128788948,
0.0006883007008582354,
0.007684857118874788,
-0.05522830784320831,
0.0188856553286314,
-0.029919883236289024,
0.009863498620688915,
0.0017410418950021267,
-0.0407448410987854,
0.028316868469119072,
0.001997371669858694,
0.03566671162843704,
0.046823613345623016,
0.005829959642142057,
-0.002829151228070259,
-0.012114464305341244,
-0.018010005354881287,
0.0442921482026577,
-0.007497432641685009,
-0.040776487439870834,
-0.03324985131621361,
0.0003866624610964209,
-0.022127119824290276,
0.021868610754609108,
0.007802919484674931,
0.04436645284295082,
-0.0033989197108894587,
0.03167136758565903,
-0.040552008897066116,
-0.01299991924315691,
-0.03948383033275604,
0.022599410265684128,
0.03192545101046562,
-0.03716791793704033,
0.0020499704405665398,
-0.034377653151750565,
0.032931137830019,
0.00733277527615428,
0.02795742265880108,
0.0032813879661262035,
-0.007518779952079058,
0.0660916343331337,
0.004199639894068241,
-0.015156409703195095,
-0.043092746287584305,
0.0023650573566555977,
-0.02001327835023403,
-0.011601378209888935,
-0.030074341222643852,
0.026727817952632904,
0.024180922657251358,
0.05399981886148453,
-0.019699715077877045,
0.008869842626154423,
-0.03666117787361145,
-0.007919137366116047,
0.028409773483872414,
-0.015148431994020939,
-0.0018886951729655266,
-0.02279154770076275,
0.009564855135977268,
-0.016214583069086075,
0.007473436184227467,
-0.0008905682479962707,
-0.032847270369529724,
-0.017867818474769592,
0.005347506143152714,
-0.034660547971725464,
0.05806565284729004,
-0.0334932766854763,
0.0028534196317195892,
-0.00451188487932086,
-0.009988428093492985,
-0.024755490943789482,
0.04687057062983513,
-0.026844777166843414,
0.020843729376792908,
-0.014210319146513939,
0.027577035129070282,
0.014434993267059326,
-0.005701511166989803,
0.019222317263484,
0.00917118787765503,
0.012311989441514015,
-0.022975364699959755,
0.008407903835177422,
-0.02245962619781494,
0.04939188063144684,
-0.007565637119114399,
-0.04682838171720505,
-0.011557769030332565,
-0.008415242657065392,
-0.026659689843654633,
0.04414958879351616,
0.005593108478933573,
0.0312579907476902,
0.006260537542402744,
-0.03404449298977852,
0.010019604116678238,
0.07483108341693878,
-0.0056374152190983295,
-0.01549823023378849,
-0.001978063490241766,
0.006245047319680452,
-0.00989161990582943,
0.0090642049908638,
0.029901523143053055,
-0.006857321131974459,
0.03930659592151642,
0.03032056987285614,
0.030175352469086647,
-0.0175824835896492,
-0.019821688532829285,
-0.020398426800966263,
-0.03608715161681175,
-0.0029980253893882036,
-0.01619270071387291,
-0.016506971791386604,
0.032407235354185104,
0.004163764417171478,
-0.020601877942681313,
0.03674373775720596,
0.03127872571349144,
-0.0025124906096607447,
-0.052347514778375626,
0.020038044080138206,
0.059710413217544556,
0.05392961949110031,
0.06523925065994263,
-0.06952757388353348,
0.002706701634451747,
0.04215776175260544,
-0.057997021824121475,
0.0008987787878140807,
-0.04761122539639473,
-0.02615215815603733,
-0.028642524033784866,
-0.03145912289619446,
-0.01756858080625534,
0.020545601844787598,
0.022708535194396973,
0.016654018312692642,
0.0008663655025884509,
0.020590785890817642,
-0.060709770768880844,
-0.06236238777637482,
0.02412617951631546,
0.05248846113681793,
-0.015790358185768127,
0.0043678986839950085,
0.04252079501748085,
0.02028391882777214,
0.0070056430995464325,
0.025180047377943993,
0.010163943283259869,
0.04830087348818779,
0.0021621405612677336,
0.010231103748083115,
0.023268530145287514,
0.018516020849347115,
0.021488601341843605,
-0.028376011177897453,
0.03215445205569267,
-0.027128485962748528,
0.016828889027237892,
0.05270032212138176,
-0.027986254543066025,
-0.020657433196902275,
-0.003934868145734072,
-0.024590181186795235,
-0.02599440887570381,
0.046476930379867554,
-0.009138178080320358,
0.014764057472348213,
0.014506027102470398,
-0.0003001958830282092,
0.0011119024129584432,
-0.03490912914276123,
0.012861727736890316,
-0.03329605236649513,
-0.010821731761097908,
0.026527050882577896,
0.001199206686578691,
-0.025679152458906174,
0.020284196361899376,
-0.009500088170170784,
-0.03816627711057663,
0.022112470120191574,
-0.008755230344831944,
0.028650810942053795,
-0.034810807555913925,
0.037821341305971146,
-0.024356624111533165,
0.007742703426629305,
0.0012163257924839854,
0.04052714258432388,
-0.025663049891591072,
0.02115633711218834,
0.016721181571483612,
-0.013125067576766014,
0.001013633911497891,
-0.00153895013500005,
0.004427539184689522,
-0.0540875680744648,
0.021495699882507324,
-0.023897873237729073,
-0.05358992516994476,
-0.008931024931371212,
-0.03064841218292713,
-0.015274700708687305,
0.029049554839730263,
0.06279487907886505,
0.0195197481662035,
0.014976119622588158,
0.025650426745414734,
0.006511037703603506,
-0.012123366817831993,
-0.05720300227403641,
-0.0015932765090838075,
-0.01592601276934147,
-0.019513359293341637,
0.031141098588705063,
-0.04577253758907318,
-0.02355235256254673,
-0.00925949402153492,
-0.00117237470112741,
-0.02730669267475605,
0.022725606337189674,
0.023158138617873192,
0.007438816595822573,
0.03362779691815376,
-0.008242849260568619,
0.014860834926366806,
0.04609937220811844,
0.04013431444764137,
-0.008273845538496971,
-0.0005272437119856477,
-0.02445981092751026,
-0.03175393119454384,
0.007248855661600828,
-0.07259133458137512,
0.008816258050501347,
-0.01188067626208067,
-0.014838984236121178,
0.037720926105976105,
-0.04491430148482323,
-0.010525563731789589,
0.05111662670969963,
-0.017774667590856552,
-0.01708117127418518,
0.03264209255576134,
-0.05694366991519928,
0.004522155039012432,
-0.0028515479061752558,
0.052710503339767456,
0.006672906223684549,
0.009144331328570843,
0.036640018224716187,
-0.00560820521786809,
0.029938815161585808,
0.004856254905462265,
-0.022039955481886864,
0.004801386501640081,
-0.0025718356482684612,
0.03097570687532425,
0.0027948885690420866,
0.03767521306872368,
0.02868267521262169,
0.010658016428351402,
-0.008107742294669151,
-0.009202313609421253,
-0.008965681307017803,
0.02516026981174946,
-0.01072772778570652,
0.04535409435629845,
0.015893597155809402,
0.03427707403898239,
-0.004624242894351482,
-0.00008746387175051495,
-0.016080966219305992,
-0.02794552966952324,
0.0064713358879089355,
0.0025980377104133368,
0.006293063051998615,
0.00277156219817698,
-0.010464392602443695,
-0.0028924799989908934,
0.03652540221810341,
-0.04836995154619217,
0.016250403597950935,
0.031102800741791725,
0.02440905198454857,
-0.004341907799243927,
-0.05337947607040405,
-0.04559727758169174,
-0.040691956877708435,
0.018032023683190346,
0.039803486317396164,
0.007045338395982981,
-0.00720406835898757,
-0.008800633251667023,
-0.014027044177055359,
0.0458168163895607,
-0.06251056492328644,
-0.026713058352470398,
0.02001132257282734,
0.037833914160728455,
-0.010796395130455494,
0.002532192738726735
] |
<p>I just went through <a href="http://www.nature.com/nature/journal/v505/n7485/full/nature12954.html">Observation of Dirac monopoles in a synthetic magnetic field</a>.</p>
<p>What exactly has been observed?</p>
<p>More importantly, are these monopoles localized inside the apparatus (no stray monopole field lines coming out), or can they be used to create tangible monopoles? (By tangible monopoles I mean an object that is overall a monopole without any external influence. It may contain a condensate or similar inside)</p> | 1,473 | [
-0.012174894101917744,
-0.011469066143035889,
0.02643647976219654,
-0.0572420135140419,
0.041810546070337296,
0.01752004772424698,
-0.03746510669589043,
-0.027859371155500412,
0.016704274341464043,
-0.051329921931028366,
0.017690880224108696,
0.041424524039030075,
0.02932668663561344,
0.0034971407148987055,
-0.017936071380972862,
0.017592865973711014,
-0.025622617453336716,
0.01288745366036892,
0.017072701826691628,
-0.03949737921357155,
0.01587558537721634,
0.020861370489001274,
-0.016407987102866173,
0.005758723244071007,
0.011873398907482624,
-0.010332955047488213,
-0.018038062378764153,
-0.0002419309748802334,
-0.01457903441041708,
0.04249703139066696,
-0.059527695178985596,
-0.019776692613959312,
0.008463922888040543,
-0.0027820863761007786,
0.007747698109596968,
-0.03411378711462021,
-0.03180081769824028,
-0.06454640626907349,
-0.008534213528037071,
0.008192334324121475,
-0.005888951942324638,
-0.049777351319789886,
-0.03786170482635498,
0.04784801974892616,
-0.015830660238862038,
-0.012235607020556927,
-0.00944947823882103,
-0.046108949929475784,
0.07077834010124207,
-0.07489795982837677,
0.03434557095170021,
-0.01114748977124691,
0.028503865003585815,
0.0013035301817581058,
0.0009266600827686489,
-0.0019686406012624502,
0.05078685283660889,
0.0590299628674984,
-0.015785235911607742,
-0.03429856896400452,
-0.03349384292960167,
-0.0068804118782281876,
-0.0061258673667907715,
-0.028334328904747963,
-0.048683490604162216,
0.040196508169174194,
0.00005579828211921267,
0.00026538752717897296,
0.03315617889165878,
-0.034836895763874054,
0.05267135798931122,
0.02977067418396473,
0.023831048980355263,
0.014842045493423939,
0.01262365747243166,
-0.01998012140393257,
0.016136791557073593,
-0.0054724132642149925,
0.03504576534032822,
0.04631951078772545,
-0.01485470961779356,
0.015417558141052723,
0.0012695236364379525,
0.012591800652444363,
-0.007294148206710815,
-0.011040832847356796,
0.040419623255729675,
-0.025617731735110283,
0.020139778032898903,
0.0065031154081225395,
-0.002461352851241827,
-0.009518036618828773,
0.03229722008109093,
0.0005895054782740772,
-0.03496035933494568,
-0.003409609431400895,
-0.009806063026189804,
0.0688561499118805,
-0.03514799103140831,
-0.05182461440563202,
0.00591413676738739,
0.04074259102344513,
0.02959541231393814,
0.09926270693540573,
0.00036476008244790137,
-0.038828641176223755,
-0.02055184170603752,
0.04459570720791817,
-0.009758180007338524,
-0.0058485371991992,
-0.05124562233686447,
0.0009855716489255428,
0.02412179298698902,
-0.027704820036888123,
0.03888840600848198,
-0.04000595211982727,
-0.016551177948713303,
-0.002143214223906398,
0.05572294071316719,
0.09805694222450256,
0.01752331294119358,
-0.037377599626779556,
0.015652772039175034,
-0.03563538193702698,
-0.03725823387503624,
-0.01580379344522953,
0.041041623800992966,
0.037349142134189606,
-0.04392962530255318,
0.019907016307115555,
-0.009968813508749008,
0.003971054684370756,
0.04376599192619324,
0.02664833329617977,
0.020436551421880722,
-0.031105825677514076,
-0.10838040709495544,
-0.054343078285455704,
0.03824179247021675,
-0.008613619022071362,
0.005159948952496052,
-0.05768367648124695,
0.00554275419563055,
0.05644757300615311,
0.09202992916107178,
0.008225171826779842,
-0.03889851272106171,
-0.011820031329989433,
0.048766978085041046,
0.04644768685102463,
-0.024635011330246925,
0.006198321934789419,
-0.006744062528014183,
-0.04724409431219101,
0.00788357388228178,
-0.030930787324905396,
0.045702774077653885,
0.04351940378546715,
0.020194189622998238,
-0.03568057715892792,
0.09005670249462128,
0.012415002100169659,
0.01870230957865715,
0.023251324892044067,
-0.029036933556199074,
-0.027843831107020378,
0.08123818039894104,
-0.011820705607533455,
-0.03277166560292244,
0.0335550531744957,
-0.005688152275979519,
0.02009657397866249,
0.03311330825090408,
0.0312493983656168,
0.021783096715807915,
-0.029397809877991676,
-0.0004524030373431742,
-0.021575111895799637,
0.039951078593730927,
-0.0076612019911408424,
-0.03918682411313057,
-0.005756364203989506,
-0.020122412592172623,
0.017811831086874008,
0.00801475252956152,
0.07260926067829132,
-0.01671285554766655,
-0.05807539075613022,
0.015100381337106228,
-0.07727526128292084,
-0.012264302931725979,
-0.06376881152391434,
-0.0007671383791603148,
-0.018847817555069923,
-0.00906330719590187,
0.049653489142656326,
0.008304160088300705,
0.002513148821890354,
-0.055275581777095795,
-0.056176070123910904,
0.002794824540615082,
0.03468932583928108,
0.0303026270121336,
0.00945453904569149,
0.008921576663851738,
0.02012198232114315,
-0.0022637397050857544,
-0.020566506311297417,
0.030701803043484688,
-0.01993570104241371,
-0.03911140561103821,
-0.004186816047877073,
-0.02967793308198452,
0.008761659264564514,
0.02455189637839794,
0.008663334883749485,
0.0010739635908976197,
-0.021108217537403107,
-0.035122815519571304,
0.029877126216888428,
0.003682025708258152,
0.09376480430364609,
0.01186570804566145,
0.023033712059259415,
0.00012309166777413338,
0.01873353123664856,
0.02911374717950821,
-0.021280562505126,
0.006078002508729696,
-0.0320979580283165,
-0.08571328967809677,
0.008266795426607132,
0.1238054484128952,
0.039868053048849106,
-0.02679191157221794,
0.03742554038763046,
-0.036845963448286057,
0.0457511842250824,
0.04558928683400154,
0.03408142924308777,
-0.04796873778104782,
-0.001599688082933426,
0.0135604003444314,
0.03479982912540436,
0.03183580935001373,
-0.000840028515085578,
0.007668992504477501,
0.01522072684019804,
0.00046579467016272247,
-0.01484097819775343,
0.009574173018336296,
0.01866874098777771,
-0.06396544724702835,
0.004046308342367411,
-0.030560612678527832,
-0.03398000821471214,
0.018724191933870316,
-0.056453637778759,
0.02093435451388359,
-0.004758440423756838,
-0.010874094441533089,
0.01999434269964695,
-0.02578773722052574,
-0.0037543289363384247,
0.04151378199458122,
-0.007604158949106932,
-0.04050125554203987,
-0.014050153084099293,
0.01969391293823719,
-0.056124329566955566,
0.008001205511391163,
-0.02313837967813015,
0.009945028461515903,
-0.006829154212027788,
0.006474440451711416,
0.020582666620612144,
0.002026689937338233,
0.04019780829548836,
-0.020493214949965477,
-0.03876950219273567,
-0.006012706086039543,
-0.052525654435157776,
0.004874889273196459,
0.05304092913866043,
-0.03848733380436897,
0.02243752032518387,
-0.03580848127603531,
-0.012699225917458534,
0.02876889519393444,
-0.0196083951741457,
0.0008284783689305186,
-0.0027186914812773466,
-0.02745671011507511,
-0.060189586132764816,
-0.028873739764094353,
0.0056796264834702015,
0.016972146928310394,
0.0091960234567523,
0.030203549191355705,
0.03851880133152008,
-0.028012309223413467,
0.0015475577674806118,
0.03436338156461716,
0.024668795987963676,
-0.018473351374268532,
-0.021711669862270355,
-0.021527795121073723,
0.04301520437002182,
-0.03548268973827362,
0.047250423580408096,
0.02187664434313774,
-0.06288783252239227,
0.019688475877046585,
-0.062210991978645325,
-0.020874883979558945,
0.00961296632885933,
-0.029335377737879753,
0.00935522373765707,
-0.011088612489402294,
-0.03646707907319069,
0.10415221750736237,
0.0012193479342386127,
-0.05863916501402855,
-0.026612481102347374,
-0.03017614781856537,
-0.029185019433498383,
-0.027989007532596588,
-0.023706914857029915,
0.048552583903074265,
-0.0040800911374390125,
0.03844200447201729,
0.03521322086453438,
0.021704083308577538,
-0.021232783794403076,
0.02111353725194931,
-0.023047804832458496,
0.0040808324702084064,
0.011815791949629784,
-0.009459765627980232,
0.08677937090396881,
0.0032957077492028475,
-0.011723335832357407,
-0.026912858709692955,
0.004301288165152073,
0.04103071242570877,
0.018796734511852264,
-0.043757982552051544,
0.02589736506342888,
0.013304371386766434,
0.0405503511428833,
0.009360266849398613,
0.03913608938455582,
-0.028928318992257118,
-0.013225916773080826,
-0.01039761584252119,
0.005601019598543644,
0.04375943914055824,
-0.0196855366230011,
0.004882133100181818,
0.036142658442258835,
0.044266652315855026,
-0.03215699642896652,
-0.0029975948855280876,
-0.015884920954704285,
-0.008999092504382133,
0.029889428988099098,
-0.03882612660527229,
-0.025191839784383774,
0.053453121334314346,
0.0459752082824707,
0.03770982846617699,
0.004685346037149429,
-0.01655701734125614,
-0.00080906692892313,
-0.03417704626917839,
0.020809736102819443,
-0.025953929871320724,
0.03927423804998398,
0.03174203261733055,
0.022470057010650635,
0.013276099227368832,
0.0030454457737505436,
-0.01615498773753643,
-0.060716286301612854,
-0.08090196549892426,
0.008764136582612991,
-0.039369791746139526,
0.006909278221428394,
-0.01941649056971073,
-0.02279536984860897,
0.002337587997317314,
0.013912035152316093,
-0.016599521040916443,
-0.014392300508916378,
0.004126203712075949,
-0.07453056424856186,
0.006808630656450987,
-0.04033980518579483,
0.0026619834825396538,
-0.04640129208564758,
0.021648868918418884,
0.03385830670595169,
-0.01199621707201004,
0.012710422277450562,
-0.02010294422507286,
-0.038551460951566696,
0.015236874110996723,
-0.020083393901586533,
-0.005281966645270586,
-0.001309507293626666,
0.029202042147517204,
0.04416298866271973,
0.0009136833832599223,
-0.034041497856378555,
0.006295963190495968,
0.03113272227346897,
0.05681493133306503,
-0.014552357606589794,
-0.028561759740114212,
0.0062156845815479755,
-0.055158257484436035,
-0.02444266341626644,
-0.009989873506128788,
0.0385114811360836,
0.00047829141840338707,
0.0030525662004947662,
0.03145905211567879,
0.00497731938958168,
-0.007413811516016722,
0.05051964148879051,
0.03469712659716606,
-0.006397781893610954,
-0.01681865006685257,
-0.0752570852637291,
-0.02979840338230133,
-0.01679295301437378,
-0.002171318279579282,
-0.0003524642961565405,
-0.02185048721730709,
-0.0062635657377541065,
0.016020212322473526,
0.048504073172807693,
0.007913505658507347,
-0.019630108028650284,
0.03611692786216736,
-0.0049216486513614655,
0.019462646916508675,
-0.02230573445558548,
0.039190810173749924,
0.015351271256804466,
0.041015300899744034,
0.059826869517564774,
0.0054796002805233,
-0.025881975889205933,
-0.09948676824569702,
-0.014003810472786427,
0.03346957638859749,
0.01893412321805954,
0.036543380469083786,
-0.011483869515359402,
-0.04681021347641945,
0.006741638761013746,
0.054110754281282425,
-0.03290530666708946,
0.023404506966471672,
-0.022096063941717148,
-0.02532835863530636,
-0.016886109486222267,
0.031055908650159836,
0.008235924877226353,
0.025203797966241837,
-0.02439853735268116,
0.02394956350326538,
-0.051207464188337326,
-0.0232575424015522,
-0.012428498826920986,
0.061177197843790054,
0.02447749301791191,
0.06458229571580887,
0.03971177712082863,
0.03919397294521332,
0.003232357557862997,
-0.026725661009550095,
-0.022188620641827583,
-0.07399197667837143,
0.019430918619036674,
0.028740882873535156,
-0.021007372066378593,
0.06857886165380478,
-0.025630757212638855,
-0.03626709803938866,
-0.03851211443543434,
-0.010276306420564651,
0.029045432806015015,
-0.0026569634210318327,
-0.025155700743198395,
0.022219249978661537,
0.03950078412890434,
0.000649269379209727,
0.03419368341565132,
0.0015937117859721184,
-0.015430735424160957,
-0.0009474304970353842,
0.002459955168887973,
0.057694997638463974,
0.008838453330099583,
-0.002739798044785857,
-0.03376542776823044,
0.002352009527385235,
-0.01960374228656292,
0.05061855539679527,
-0.03659142181277275,
0.007266558241099119,
0.010967808775603771,
-0.043885260820388794,
-0.00804418046027422,
0.02804100140929222,
0.0028892322443425655,
-0.050981707870960236,
-0.009901920333504677,
0.015243621543049812,
0.019779883325099945,
-0.019606301560997963,
-0.016064478084445,
-0.00228317198343575,
0.018382765352725983,
0.04389698803424835,
-0.021518094465136528,
0.005216659978032112,
-0.01610877923667431,
-0.02215503342449665,
0.040175892412662506,
-0.04451790824532509,
0.031721558421850204,
-0.012966983020305634,
-0.02876047044992447,
0.015779899433255196,
-0.07300536334514618,
0.004021540749818087,
-0.0007048316765576601,
-0.013803765177726746,
0.003271599067375064,
-0.07394973933696747,
0.013281043618917465,
0.019216403365135193,
-0.003840526333078742,
-0.038242124021053314,
-0.06150965765118599,
0.02268875204026699,
0.02956395037472248,
0.0057505397126078606,
-0.027559956535696983,
-0.0006350373150780797,
0.002251333324238658,
-0.04764658585190773,
-0.005237802397459745,
0.03057432547211647,
-0.05928092822432518,
-0.006163604091852903,
0.005677300039678812,
0.03341222181916237,
0.05284259095788002,
0.0027622419875115156,
-0.028521861881017685,
0.014612194150686264,
0.013171156868338585,
0.007041472010314465,
0.01737171784043312,
0.02588440477848053,
-0.03547949343919754,
-0.0261533260345459,
-0.014537584967911243,
0.020314708352088928,
0.022949082776904106,
-0.011432022787630558,
-0.01206604577600956,
0.07300616055727005,
0.018721021711826324,
0.021301409229636192,
-0.033143218606710434,
0.004487566649913788,
0.024286214262247086,
0.019269084557890892,
-0.004817814566195011,
0.01662762649357319,
-0.014002436771988869,
-0.017270956188440323,
0.04599286615848541,
0.014061476103961468,
0.012196817435324192,
-0.023186538368463516,
0.042374905198812485,
0.001018414506688714,
0.01475916150957346,
0.009649457409977913,
-0.03257066011428833,
0.011697540059685707,
0.016895964741706848,
0.0224140752106905,
0.009848454967141151,
0.018062105402350426,
-0.04074857011437416,
-0.0324244424700737,
-0.012203602120280266,
-0.011193512938916683,
0.05376559495925903,
0.0007471213466487825,
0.03678752854466438,
0.034644823521375656,
-0.009232932701706886,
-0.039720743894577026,
-0.01355019398033619,
-0.027498558163642883,
0.025216106325387955,
-0.00311215384863317,
0.019669760018587112,
-0.03190439194440842,
0.010123154148459435,
0.02374309115111828,
0.03916217014193535,
-0.02476799301803112,
0.006310054566711187,
0.05133674293756485,
0.038403723388910294,
0.03506359085440636,
-0.016226982697844505,
-0.04183138534426689,
0.05367765948176384,
-0.036039840430021286,
0.04724220931529999,
0.025625115260481834,
0.0027712893206626177,
0.02420923486351967,
0.0071278344839811325,
0.03518145903944969,
-0.010442959144711494,
-0.004783397540450096,
-0.011400904506444931,
0.006264349911361933,
0.003558286465704441,
-0.021444814279675484,
-0.016467969864606857,
-0.015029988251626492,
0.020533613860607147,
0.024629319086670876,
0.03303040564060211,
0.005826551467180252,
-0.0509987510740757,
-0.044432707130908966,
-0.02992570772767067,
-0.005149367731064558,
0.06221434846520424,
0.0025942684151232243,
-0.025658659636974335,
0.029972895979881287,
-0.029568416997790337,
0.03961573913693428,
-0.0025646407157182693,
0.03867986053228378,
-0.032348960638046265,
0.04105433076620102,
-0.02150421403348446,
0.025818370282649994,
-0.004740479402244091,
-0.002200150163844228,
0.11063027381896973,
0.01706639863550663,
-0.01085453201085329,
-0.07959587872028351,
0.013512530364096165,
-0.034348003566265106,
0.026483800262212753,
-0.016832690685987473,
-0.004055065102875233,
-0.022168707102537155,
-0.004092130344361067,
-0.005386721342802048,
0.0637124702334404,
0.0006750908796675503,
0.0442064069211483,
0.04509444907307625,
-0.0054434845224022865,
-0.027680447325110435,
-0.009113049134612083,
0.0332145169377327,
-0.020928990095853806,
-0.0027320832014083862,
-0.05136358365416527,
0.029363537207245827,
-0.01575256511569023,
0.0015477705746889114,
0.002398282755166292,
-0.009168760851025581,
0.022984495386481285,
0.029545696452260017,
-0.03023660182952881,
-0.01683974824845791,
-0.028686780482530594,
-0.015232274308800697,
-0.04046953096985817,
0.011642650701105595,
0.026473872363567352,
0.013660325668752193,
0.0040878960862755775,
0.014999899081885815,
0.010572098195552826,
-0.01740424521267414,
-0.019181516021490097,
0.051578447222709656,
-0.06416788697242737,
-0.008625173009932041,
-0.019398191943764687,
0.029681649059057236,
-0.01518759224563837,
-0.02616479992866516,
-0.02525005117058754,
0.020273879170417786,
0.028362544253468513,
-0.02566031739115715,
-0.02271980606019497,
-0.01719384454190731,
-0.00385744939558208,
-0.005860091652721167,
-0.01895323395729065,
-0.0019382222089916468,
0.04394381493330002,
-0.025766171514987946,
-0.0028282199054956436,
-0.024901168420910835,
-0.0018300157971680164,
0.03983670473098755,
0.009793945588171482,
0.03273512423038483,
0.01758645288646221,
-0.019514193758368492,
-0.06370925158262253,
-0.012541442178189754,
-0.013736166059970856,
0.008012793958187103,
-0.00018382065172772855,
0.007763028610497713,
0.044700268656015396,
-0.0037285955622792244,
-0.0031449119560420513,
0.034121640026569366,
-0.03987598419189453,
0.01502441056072712,
-0.014377917163074017,
-0.04973245784640312,
-0.03671203553676605,
-0.0038094802293926477,
0.01024677511304617,
0.024531805887818336,
-0.04866263270378113,
-0.007783870678395033,
0.0003318293602205813,
0.005181530490517616,
-0.0004131096648052335,
0.003253087168559432,
-0.007775033358484507,
0.01594817265868187,
-0.056296393275260925,
-0.010638651438057423,
-0.004337023012340069,
0.031566403806209564,
0.05086073651909828,
0.001501055434346199,
0.03588247671723366,
0.014863178133964539,
-0.02757376991212368,
0.010992609895765781,
0.05426322668790817,
-0.0497918426990509,
0.003818170167505741,
-0.04796396568417549,
-0.013943911530077457,
-0.04225180298089981,
-0.03573187068104744,
-0.011924343183636665,
-0.016139594838023186,
0.004660384729504585,
0.018441567197442055,
-0.024016544222831726,
-0.003006639890372753,
-0.003664064686745405,
-0.0031864719931036234,
-0.052324067801237106,
-0.01769902929663658,
-0.06573352962732315,
0.005714011378586292,
0.017300141975283623,
0.007833367213606834,
-0.011359059251844883,
0.04061947017908096,
-0.037479083985090256,
0.015512525103986263,
0.03481162711977959,
0.014425757341086864,
-0.030682947486639023,
0.0002815524348989129,
0.048400621861219406,
0.030262764543294907,
0.01709597557783127,
-0.00901589822024107,
-0.03567999228835106,
0.06486444920301437,
-0.033008474856615067,
-0.02112872153520584,
0.023684540763497353,
0.00007445314986398444,
0.002462126314640045,
0.03278113156557083,
-0.025658810511231422,
-0.010172685608267784,
0.05155409500002861,
-0.020348960533738136,
-0.023691590875387192,
0.010001475922763348,
-0.02071862667798996,
0.023092985153198242,
-0.03410444036126137,
0.03145367279648781,
-0.016966108232736588,
0.00026560170226730406,
0.016814276576042175,
0.019569706171751022,
0.026493065059185028,
-0.012144030071794987,
-0.010478483512997627,
-0.0010813508415594697,
0.008516194298863411,
0.017038928344845772,
-0.011752376332879066,
0.0009301517275162041,
0.07027683407068253,
-0.0497782938182354,
0.022265879437327385,
0.03616965562105179,
-0.0015807166928425431,
-0.06947368383407593,
-0.023481708019971848,
-0.016174517571926117,
-0.018342752009630203,
-0.0016518557677045465,
-0.047766659408807755,
0.0045717619359493256,
0.046052999794483185,
-0.07104960829019547,
0.027167676016688347,
-0.04483753442764282,
-0.06401222944259644,
-0.043504681438207626,
-0.02268325164914131,
0.0012061729794368148,
0.04488593339920044,
0.0019009411334991455,
0.04215073212981224,
0.0007471892167814076,
-0.025397062301635742,
-0.029197296127676964,
-0.031206006184220314,
-0.04757941514253616,
0.021761281415820122,
0.012695427052676678,
-0.046789657324552536,
0.07383781671524048,
-0.0011413501342758536,
-0.024375764653086662,
0.02814815379679203,
0.004627942573279142,
-0.015247446484863758,
-0.014547154307365417,
-0.01905122958123684,
-0.0057539199478924274,
0.01940329000353813,
0.029642213135957718,
0.004354729317128658,
-0.008736743591725826,
0.015877429395914078,
0.054341137409210205,
0.007467462681233883,
0.030445381999015808,
0.021564073860645294,
0.009984289295971394,
-0.020121870562434196,
0.04169366508722305,
0.03537527099251747,
-0.024311693385243416,
-0.0015873449156060815,
-0.024962682276964188,
0.010894674807786942,
0.030248943716287613,
-0.03008686937391758,
0.024874195456504822,
-0.02965715155005455,
-0.02737709879875183,
0.020561905577778816,
0.02548103779554367,
-0.0049593192525208,
0.055554941296577454,
-0.01801047846674919,
-0.019003739580512047,
0.020923033356666565,
0.022406958043575287,
0.008244732394814491,
-0.040952350944280624,
-0.01101712416857481,
0.015234163962304592,
0.027064640074968338,
0.042510975152254105,
-0.03172816336154938,
-0.0208596121519804,
0.02493634819984436,
0.008224260061979294,
0.031687431037425995,
-0.016007911413908005,
-0.04513385146856308,
-0.020893806591629982,
-0.04014557600021362,
0.06021037697792053,
-0.01753382198512554,
-0.0074057988822460175,
-0.00700299721211195,
0.005402236245572567,
-0.016993273049592972,
-0.005754808429628611,
0.02660045400261879,
-0.013799578882753849,
0.0050176698714494705,
0.017239568755030632,
0.006099361926317215,
0.008830385282635689,
-0.03176378458738327,
-0.020599365234375,
0.01398651022464037,
-0.025551576167345047,
0.018647266551852226,
-0.0011453063925728202,
-0.01550341211259365,
-0.0029835945460945368,
0.041898466646671295,
0.016723643988370895,
0.020398076623678207,
-0.002209135564044118,
-0.036793358623981476,
0.045176248997449875,
0.001397953717969358,
-0.007957165129482746,
0.06046314164996147,
-0.011336836032569408,
0.027717163786292076,
0.001148064387962222,
-0.00804668478667736,
-0.0034471554681658745,
0.01593170501291752,
-0.029319627210497856,
0.028666792437434196,
-0.02568957209587097,
-0.028770076110959053,
0.034461893141269684,
-0.01733841747045517,
0.02651800960302353,
0.012656948529183865,
-0.03142669424414635,
-0.0060872603207826614,
0.07152242958545685,
0.005722484551370144,
0.018289698287844658,
-0.004201262257993221,
0.0153071703389287,
0.03069673851132393,
0.01175896916538477,
-0.016821283847093582,
0.0905127078294754,
0.017792057245969772,
0.0020359414629638195,
0.01980970986187458,
0.04080817475914955,
-0.037323787808418274,
0.016104836016893387,
0.002262270078063011,
0.05527247115969658,
-0.01055070385336876,
0.007355086039751768,
0.029354529455304146,
-0.02864004671573639,
0.01161941234022379,
-0.005216523539274931,
-0.01987510360777378,
0.10723557323217392,
-0.03158070519566536,
0.006002694368362427,
-0.014773453585803509,
-0.007636304013431072,
0.020883359014987946,
0.012930849567055702,
-0.013036537915468216,
0.05506739765405655,
0.0067667108960449696,
0.004830805119127035,
-0.01628459431231022,
-0.004504162352532148,
0.008380277082324028,
-0.04922693967819214,
0.018952174112200737,
-0.023553933948278427,
0.014855624176561832,
-0.009753067046403885,
-0.029094267636537552,
-0.0029429809655994177,
-0.018824169412255287,
0.012982137501239777,
-0.001536375842988491,
0.023703377693891525,
-0.023505179211497307,
-0.002685755491256714,
-0.022899221628904343,
0.0196924339979887,
-0.03982442989945412,
-0.01041753776371479,
-0.02947288379073143,
0.05524677038192749,
-0.016508903354406357,
0.018549762666225433
] |
<p>I want some explanation of fields and <a href="http://en.wikipedia.org/wiki/Superfield" rel="nofollow">superfields</a> (types and components), and what the relationship between them and representation of a group. </p> | 1,474 | [
-0.03199504688382149,
-0.019327456131577492,
0.009750815108418465,
-0.024069365113973618,
0.05167776718735695,
-0.0005699745379388332,
0.019671032205224037,
-0.043671853840351105,
0.010301007889211178,
-0.0444008931517601,
0.06344537436962128,
-0.019490566104650497,
0.04057313874363899,
0.03168671950697899,
0.013453904539346695,
-0.012899279594421387,
-0.008056633174419403,
-0.014478371478617191,
-0.008169680833816528,
0.0096652926877141,
0.004964971449226141,
0.021834298968315125,
-0.034376613795757294,
-0.0075393859297037125,
0.005545077845454216,
0.04882049188017845,
0.038166847079992294,
0.03163371980190277,
0.032308466732501984,
0.0527813695371151,
-0.013969359919428825,
-0.03949931636452675,
-0.0064435382373631,
0.0122450590133667,
0.011815282516181469,
-0.005638940259814262,
-0.0006053391844034195,
-0.027059154585003853,
-0.004763531498610973,
-0.0043927403166890144,
-0.02680814452469349,
0.004457761999219656,
0.0016929201083257794,
0.02776273339986801,
-0.004581782966852188,
0.024748165160417557,
-0.014350327663123608,
-0.015973426401615143,
0.02489655092358589,
-0.03766796737909317,
0.06328709423542023,
0.01720702275633812,
0.015116432681679726,
0.0013418557355180383,
-0.008827447891235352,
0.01780746877193451,
0.017001593485474586,
0.04449085146188736,
-0.03467413783073425,
-0.05848710611462593,
-0.02521631494164467,
-0.017567718401551247,
0.03637879714369774,
-0.031650327146053314,
-0.016735389828681946,
0.048716943711042404,
-0.007269920781254768,
-0.00960429385304451,
0.030740860849618912,
0.019658036530017853,
0.009876715019345284,
0.01254301518201828,
0.027473565191030502,
-0.02736588567495346,
0.023053230717778206,
-0.056673888117074966,
0.019731126725673676,
-0.03284779191017151,
0.04066227376461029,
0.023575972765684128,
0.0038996378425508738,
0.01770325005054474,
0.00443419860675931,
-0.04731567203998566,
0.01713656820356846,
-0.0177427027374506,
0.053376514464616776,
-0.004209944978356361,
0.021458761766552925,
-0.005567873828113079,
-0.024995319545269012,
-0.017777379602193832,
0.01329547818750143,
0.016307471320033073,
-0.07748652994632721,
0.021529896184802055,
-0.00414935452863574,
0.0320206880569458,
-0.010675998404622078,
0.007656076457351446,
-0.0032711715903133154,
-0.021606775000691414,
0.010115654207766056,
0.071501225233078,
-0.012708362191915512,
-0.011689088307321072,
-0.05539059266448021,
0.007745827082544565,
-0.017146965488791466,
-0.011773820966482162,
0.006186791695654392,
-0.02888689748942852,
-0.006769306026399136,
-0.006945891305804253,
0.029833775013685226,
-0.009586683474481106,
-0.002251214114949107,
0.0002990508801303804,
0.05120081454515457,
0.08484890311956406,
0.07336560636758804,
-0.050524283200502396,
0.007004209794104099,
0.007305243518203497,
-0.09365236014127731,
0.008904854767024517,
0.0032541323453187943,
0.003988597076386213,
-0.045538097620010376,
0.013894516974687576,
0.013438855297863483,
-0.010687632486224174,
-0.021837668493390083,
0.0066877203062176704,
0.015936022624373436,
0.0022083257790654898,
-0.07877951860427856,
-0.07299132645130157,
0.012474210932850838,
-0.017186451703310013,
-0.017690878361463547,
-0.05296120420098305,
0.014342131093144417,
0.01620391383767128,
0.0789058580994606,
0.014596601948142052,
0.0068466756492853165,
0.005365281365811825,
0.043249424546957016,
0.045101944357156754,
-0.009800750762224197,
-0.02326221577823162,
-0.01133270375430584,
-0.018511716276407242,
-0.01684061624109745,
-0.07217232137918472,
0.01667061261832714,
-0.002807482611387968,
-0.008973129093647003,
-0.034965552389621735,
0.07909616827964783,
-0.023146944120526314,
0.0015595856821164489,
0.030698293820023537,
0.001534364535473287,
-0.0010337821440771222,
0.033530838787555695,
-0.011003192514181137,
0.018165649846196175,
0.05193101987242699,
0.00669818464666605,
0.029408376663923264,
0.019267531111836433,
0.059423793107271194,
0.03425382822751999,
-0.0014360978966578841,
-0.00503200339153409,
-0.013559939339756966,
0.021634399890899658,
-0.0288854893296957,
-0.039674438536167145,
-0.04521297290921211,
0.01410551555454731,
0.04845619946718216,
-0.007565881125628948,
-0.0008724985527805984,
0.0018019259441643953,
-0.010367384180426598,
0.022480420768260956,
-0.05370676890015602,
-0.03695032373070717,
-0.062475137412548065,
0.06095915660262108,
-0.02339666336774826,
-0.02655956894159317,
0.03657148778438568,
0.03432320058345795,
-0.032221805304288864,
-0.030408797785639763,
-0.0246826633810997,
-0.03320498391985893,
0.013772809877991676,
0.03055144101381302,
-0.026043543592095375,
-0.004699802491813898,
-0.003117094049230218,
0.009538600221276283,
-0.005430859047919512,
0.047737088054418564,
-0.016909219324588776,
-0.020616434514522552,
0.019581424072384834,
-0.019882747903466225,
0.004926466848701239,
-0.022973524406552315,
-0.007627858314663172,
0.005612993612885475,
0.03812793642282486,
0.0007907548570074141,
0.042623501271009445,
-0.061727963387966156,
0.025540055707097054,
0.020008400082588196,
0.04516895115375519,
0.01767398603260517,
0.038326505571603775,
-0.02265692874789238,
-0.02745666168630123,
-0.008160213939845562,
-0.0004895891761407256,
-0.07004497200250626,
0.006106246262788773,
0.02759740687906742,
0.014882382936775684,
-0.011218919418752193,
-0.018323805183172226,
0.011344402097165585,
0.04436863586306572,
0.0490112267434597,
0.002414153655990958,
-0.017385508865118027,
-0.03712523356080055,
0.001955007901415229,
0.028895651921629906,
0.029664313420653343,
0.009709465317428112,
0.015704050660133362,
0.00780718307942152,
0.034388694912195206,
0.010613362304866314,
-0.03780388832092285,
0.059561748057603836,
-0.005793457385152578,
0.008650251664221287,
0.03347930312156677,
-0.04236055538058281,
0.014525643549859524,
-0.03537897393107414,
0.017443908378481865,
0.019802402704954147,
-0.013063876889646053,
-0.01936078444123268,
-0.04412750154733658,
0.0022519947960972786,
0.004793913569301367,
0.009472029283642769,
-0.051385555416345596,
-0.02227490395307541,
0.009258594363927841,
-0.0012168792309239507,
-0.005029247608035803,
-0.0075756520964205265,
-0.023339780047535896,
-0.07464472204446793,
0.01510654203593731,
0.007074920926243067,
-0.040264662355184555,
0.058241117745637894,
-0.03213849663734436,
-0.027731813490390778,
-0.037756577134132385,
-0.01177607849240303,
0.04472561925649643,
-0.012097516097128391,
-0.06415555626153946,
0.0126707274466753,
-0.04900835081934929,
-0.030375521630048752,
0.031774576753377914,
-0.01673261635005474,
-0.01670008711516857,
-0.021634628996253014,
-0.029967183247208595,
-0.026633713394403458,
0.0013440842740237713,
-0.01675882562994957,
0.037418294697999954,
-0.022550366818904877,
0.007367870770394802,
0.0392768569290638,
-0.011124559678137302,
-0.01035769097507,
-0.0019539138302206993,
-0.0426977202296257,
-0.04566081613302231,
-0.05068187415599823,
0.0004551280289888382,
0.012799852527678013,
-0.04138553515076637,
0.017579834908246994,
0.007305493578314781,
-0.05250407010316849,
-0.0025617906358093023,
-0.030169816687703133,
-0.08930055797100067,
-0.03367073833942413,
0.012558403424918652,
0.03141757845878601,
0.010548158548772335,
-0.01217947993427515,
0.06398944556713104,
0.024270595982670784,
-0.08066865056753159,
-0.024076521396636963,
-0.012369305826723576,
-0.010783577337861061,
-0.0433189831674099,
0.019462881609797478,
0.04094768315553665,
0.011171394027769566,
0.015997903421521187,
0.026883970946073532,
0.028489461168646812,
0.05474329739809036,
0.007519313134253025,
-0.07447624206542969,
0.003473455086350441,
0.00033943020389415324,
0.009081215597689152,
0.046820346266031265,
-0.014299768023192883,
-0.04389691725373268,
0.028387023136019707,
-0.0227118581533432,
0.01652325503528118,
0.023235984146595,
-0.012357141822576523,
-0.004975134506821632,
0.010053661651909351,
0.02520577237010002,
-0.04974706098437309,
0.03539823740720749,
-0.023720746859908104,
-0.01793932355940342,
0.044817566871643066,
0.012812645174562931,
0.012405239045619965,
-0.02798108384013176,
-0.04061590135097504,
0.031164582818746567,
0.03108598291873932,
-0.07000168412923813,
-0.021589456126093864,
0.016197990626096725,
-0.02591150626540184,
0.018553994596004486,
-0.0244123712182045,
-0.026116887107491493,
0.01716739311814308,
0.046223290264606476,
-0.0035967626608908176,
0.03431238979101181,
0.0005226330831646919,
-0.004237925633788109,
-0.058918099850416183,
-0.008436786942183971,
-0.006949268281459808,
0.044040434062480927,
0.021264145150780678,
0.06955026090145111,
0.015496372245252132,
0.010056956671178341,
-0.019603464752435684,
0.01030054036527872,
-0.07833779603242874,
0.005843726452440023,
-0.02181362360715866,
0.04193171486258507,
0.013179530389606953,
-0.011282985098659992,
0.04968680441379547,
-0.005544050130993128,
-0.05287745222449303,
0.011747322976589203,
0.007067338563501835,
-0.04892180114984512,
0.029269356280565262,
-0.020544178783893585,
0.007861150428652763,
-0.030458582565188408,
0.033098455518484116,
0.01379461120814085,
0.01053653284907341,
0.030960042029619217,
0.06826170533895493,
-0.018037568777799606,
-0.013277688063681126,
0.008661053143441677,
-0.017893414944410324,
0.04436028003692627,
0.03584057465195656,
0.053906846791505814,
0.005469414871186018,
-0.03666435182094574,
-0.0036563838366419077,
0.015523973852396011,
0.059043336659669876,
0.043367307633161545,
0.003662198083475232,
0.017949486151337624,
-0.060698501765728,
-0.002899086568504572,
-0.01679958961904049,
0.06000996753573418,
-0.017768394201993942,
-0.0177445150911808,
0.028234558179974556,
0.004141811281442642,
-0.02573721669614315,
0.03775458037853241,
0.04650140926241875,
0.027392731979489326,
-0.038306839764118195,
-0.040554389357566833,
-0.0007479888736270368,
0.005559191107749939,
-0.03660107031464577,
0.018217453733086586,
0.0031200076919049025,
-0.01884499564766884,
-0.006931932643055916,
0.022271690890192986,
-0.04125909134745598,
-0.06417854130268097,
-0.004707245156168938,
-0.013898398727178574,
-0.011310050264000893,
0.009896660223603249,
-0.024193178862333298,
0.015733329579234123,
0.06953614205121994,
0.04786950722336769,
0.0510367825627327,
-0.0027320124208927155,
-0.07726918905973434,
0.016345208510756493,
0.04195474460721016,
0.025961386039853096,
-0.013056552968919277,
0.006348136812448502,
0.00007618871313752607,
-0.01119242887943983,
0.03954846039414406,
-0.028454909101128578,
0.03971097618341446,
-0.023047681897878647,
-0.0025847305078059435,
-0.016399385407567024,
0.018096674233675003,
0.00164476886857301,
0.05498998984694481,
-0.03759019076824188,
0.011627613566815853,
-0.013905158266425133,
0.040487390011548996,
-0.01506290677934885,
0.02396729402244091,
0.00801390502601862,
0.0320490226149559,
-0.0026095386128872633,
0.023779192939400673,
0.001693729660473764,
0.04564742371439934,
-0.04161771014332771,
-0.0486026369035244,
0.00046248783473856747,
0.04288468137383461,
-0.020644661039114,
0.04829362779855728,
-0.03230259567499161,
-0.021760618314146996,
-0.008276283740997314,
0.014809203334152699,
-0.012795373797416687,
-0.010024365969002247,
-0.06672493368387222,
0.04305889084935188,
0.024281568825244904,
-0.005713095888495445,
0.046120233833789825,
0.022394655272364616,
-0.039475809782743454,
-0.014929268509149551,
-0.010897833853960037,
0.002236474771052599,
0.012583681382238865,
0.0619986355304718,
-0.029357634484767914,
-0.007199143525213003,
-0.026402322575449944,
0.06634919345378876,
0.006648775190114975,
-0.01013582106679678,
-0.042865972965955734,
-0.010071838274598122,
-0.0278038140386343,
0.005431287921965122,
-0.015326234512031078,
-0.03080153651535511,
0.001937136985361576,
0.015560275875031948,
0.018687186762690544,
-0.0626802146434784,
0.013733736239373684,
-0.033666543662548065,
0.011385771445930004,
0.006954595446586609,
-0.010712383314967155,
0.031363967806100845,
-0.060577038675546646,
-0.0343007892370224,
0.00017096081865020096,
-0.08659214526414871,
0.03925373777747154,
-0.023088425397872925,
-0.00786580890417099,
0.03356027975678444,
-0.022560587152838707,
-0.025664035230875015,
0.028584588319063187,
-0.03510303050279617,
-0.007162780035287142,
-0.014521853066980839,
0.034965746104717255,
0.05984046310186386,
-0.012487371452152729,
-0.09316660463809967,
-0.055939819663763046,
0.03320060670375824,
0.005740405526012182,
-0.027843544259667397,
-0.011101416312158108,
0.02846096269786358,
-0.0435798242688179,
-0.030218252912163734,
0.024427911266684532,
0.07240524142980576,
-0.04716778174042702,
-0.00788375735282898,
0.031909771263599396,
0.024269627407193184,
0.07451817393302917,
0.024703174829483032,
0.0026589890476316214,
0.003849026747047901,
0.040683239698410034,
0.01855365000665188,
-0.021512961015105247,
-0.002343039494007826,
-0.020672878250479698,
-0.009056600742042065,
-0.03132769092917442,
0.029214249923825264,
0.02452080324292183,
-0.01918979547917843,
0.008588875643908978,
0.008319930173456669,
0.005852268543094397,
-0.024978164583444595,
-0.036237701773643494,
0.00655006617307663,
0.011730455793440342,
0.02288656309247017,
-0.02840239740908146,
0.019512340426445007,
-0.0009658373310230672,
0.002930652117356658,
-0.010044584982097149,
0.0028351026121526957,
0.007018247619271278,
0.046682972460985184,
0.059360895305871964,
-0.024508772417902946,
0.03194990009069443,
0.024577109143137932,
-0.04688810184597969,
-0.00849155057221651,
-0.02231413498520851,
0.009498701430857182,
0.03607172146439552,
0.055919088423252106,
-0.007003106642514467,
0.045476529747247696,
-0.0038101165555417538,
-0.029956240206956863,
0.05181066319346428,
-0.03479467332363129,
0.03005148284137249,
0.05429815500974655,
-0.0019690077751874924,
-0.02612815797328949,
-0.06721269339323044,
-0.008671577088534832,
0.02524474635720253,
-0.0025647019501775503,
0.06182149052619934,
-0.012957070954144001,
0.0037198560312390327,
0.049634501338005066,
0.025827696546912193,
-0.011909782886505127,
0.03158837556838989,
0.026410352438688278,
0.027214305475354195,
-0.004394307732582092,
-0.017736263573169708,
-0.04445439949631691,
0.034188855439424515,
-0.02899467572569847,
0.01181035302579403,
-0.018985707312822342,
0.033250708132982254,
0.017200905829668045,
0.00909397192299366,
0.01740061119198799,
-0.013471507467329502,
-0.03566354140639305,
-0.025650013238191605,
-0.0013402859913185239,
0.04168771207332611,
0.02843756042420864,
-0.005220719613134861,
0.022537020966410637,
0.053500279784202576,
0.002188158920034766,
0.017685549333691597,
0.03304535523056984,
-0.04512902721762657,
-0.03206038102507591,
-0.044342346489429474,
-0.05010354518890381,
0.02818547748029232,
-0.009199937805533409,
-0.0238532442599535,
-0.00257767247967422,
-0.04917503520846367,
0.014269924722611904,
-0.012177321128547192,
0.019667014479637146,
-0.03134626895189285,
0.052497319877147675,
0.022902468219399452,
0.043001290410757065,
0.011955223977565765,
-0.007837388664484024,
0.10767711699008942,
0.06856420636177063,
0.00904863327741623,
-0.03684059530496597,
0.016266023740172386,
0.00608296412974596,
-0.03292249143123627,
-0.04052678123116493,
0.022585205733776093,
-0.02961762435734272,
-0.011056465096771717,
0.03890908136963844,
0.06843293458223343,
0.011040429584681988,
0.017141351476311684,
0.032906778156757355,
-0.01926957070827484,
0.005379450973123312,
-0.021672895178198814,
0.01858348771929741,
-0.028107859194278717,
0.02952142432332039,
-0.05140700563788414,
0.01657050848007202,
0.024393374100327492,
0.012771311216056347,
-0.017618779093027115,
-0.04048110917210579,
0.06461209803819656,
0.022641783580183983,
-0.0008264061762019992,
0.007276931777596474,
0.004458772949874401,
0.0006679644575342536,
-0.07303167134523392,
-0.01092820055782795,
0.02861844189465046,
-0.009379072114825249,
0.011569604277610779,
0.049704015254974365,
0.007097752299159765,
-0.053249143064022064,
0.008191155269742012,
0.045744750648736954,
-0.03842313960194588,
-0.018010761588811874,
-0.04670633375644684,
0.038766101002693176,
-0.01772572286427021,
0.021000251173973083,
-0.0032919482327997684,
0.016190268099308014,
-0.006400164216756821,
-0.022919833660125732,
-0.02450045943260193,
0.0027715666219592094,
0.022945936769247055,
-0.009585895575582981,
-0.024950284510850906,
0.002155324211344123,
0.026295313611626625,
-0.05470840260386467,
0.017837729305028915,
-0.029249567538499832,
-0.010580411180853844,
0.03289619833230972,
-0.04774545133113861,
-0.006956297904253006,
-0.01245641428977251,
0.001193805132061243,
-0.008110619150102139,
-0.012013797648251057,
0.0029224564787000418,
0.056238021701574326,
0.013398692011833191,
0.01301384437829256,
0.005937425885349512,
0.012142356485128403,
0.01424968522042036,
0.003272287780418992,
-0.010540270246565342,
0.01877906545996666,
-0.027631375938653946,
-0.049879830330610275,
0.006071818992495537,
-0.02351430617272854,
0.0209345780313015,
0.01576955057680607,
-0.003714531660079956,
0.045436229556798935,
-0.015433349646627903,
-0.002186811063438654,
-0.011776466853916645,
-0.03867894783616066,
-0.021093564108014107,
0.021173488348722458,
-0.04227291792631149,
-0.012875896878540516,
-0.028756558895111084,
0.006062413100153208,
0.04754326120018959,
-0.01084977388381958,
0.0030412240885198116,
0.06392500549554825,
-0.006096997298300266,
0.023166457191109657,
0.03629489988088608,
-0.031006980687379837,
0.04065234959125519,
0.01061069592833519,
0.029315488412976265,
-0.017232291400432587,
-0.025191066786646843,
0.00917614996433258,
-0.00214607291854918,
0.004484049044549465,
0.003844178281724453,
-0.042433928698301315,
-0.01663241535425186,
-0.011667713522911072,
0.01679382286965847,
-0.022217949852347374,
0.012066847644746304,
-0.07067298144102097,
0.031621046364307404,
0.0031917113810777664,
-0.02870447374880314,
-0.008245830424129963,
0.02139279805123806,
-0.007435749284923077,
0.001438044011592865,
0.026535766199231148,
0.02277250774204731,
-0.01337411254644394,
0.021685654297471046,
0.016324754804372787,
-0.009198836050927639,
0.05401011183857918,
0.004970787558704615,
0.0016039287438616157,
0.007778570521622896,
-0.05068051069974899,
-0.02512594498693943,
0.0468156673014164,
0.011177116073668003,
0.01901816762983799,
0.02220127359032631,
0.01873055100440979,
-0.012318579480051994,
0.019294876605272293,
-0.04454866796731949,
-0.0056722117587924,
-0.006823714356869459,
-0.039550356566905975,
-0.024317726492881775,
-0.02475244551897049,
0.012783775106072426,
0.01924673281610012,
-0.05804818123579025,
0.007393789943307638,
0.013443597592413425,
0.0036443036515265703,
-0.023111162707209587,
0.012972921133041382,
0.023919247090816498,
-0.012202504090964794,
0.011051567271351814,
0.008518395014107227,
0.024028269574046135,
0.026459826156497,
-0.05545381084084511,
0.04318651929497719,
0.011266790330410004,
0.03960632532835007,
-0.04201129451394081,
-0.03825376555323601,
0.03223618492484093,
-0.007949816063046455,
0.05191470682621002,
-0.08615975081920624,
-0.00873225461691618,
0.023367317393422127,
-0.03856544941663742,
0.036516983062028885,
-0.036217667162418365,
-0.043474018573760986,
0.0071826172061264515,
-0.007949859835207462,
-0.028545327484607697,
0.06795711815357208,
0.0014038365334272385,
0.026943080127239227,
-0.00788174383342266,
0.00288440496660769,
0.009223316796123981,
-0.022686967626214027,
-0.06653454154729843,
0.02205868624150753,
-0.015409257262945175,
-0.022437194362282753,
0.06708939373493195,
0.010310170240700245,
-0.01906021498143673,
0.04586753994226456,
-0.026371067389845848,
0.004644537344574928,
0.02053617313504219,
0.012935753911733627,
0.0038025209214538336,
-0.01352941244840622,
0.01869499683380127,
-0.014103570021688938,
-0.046510543674230576,
0.006324060261249542,
0.027951493859291077,
0.0011900775134563446,
0.06329891830682755,
-0.005833283066749573,
-0.008199692703783512,
-0.015953470021486282,
0.02131548710167408,
0.034006986767053604,
-0.03953526169061661,
-0.017599111422896385,
-0.03738688677549362,
-0.004125064704567194,
-0.002728890161961317,
-0.005661726463586092,
0.023190714418888092,
-0.008608134463429451,
-0.012464822269976139,
0.04582643508911133,
-0.017046498134732246,
0.00005390127989812754,
0.06767091155052185,
0.0003467734786681831,
-0.0270832646638155,
0.0001635383378015831,
0.0449102483689785,
0.014200078323483467,
-0.03588200733065605,
0.01661887764930725,
0.021345455199480057,
-0.038063615560531616,
-0.00811926368623972,
-0.028330758213996887,
-0.018759775906801224,
0.023781143128871918,
-0.0009848205372691154,
0.0310041643679142,
-0.06894753873348236,
-0.0518258698284626,
0.049577198922634125,
-0.06898781657218933,
0.046949923038482666,
0.02280387282371521,
-0.010267232544720173,
-0.04593139514327049,
-0.0015386654995381832,
-0.00035933690378442407,
-0.001018189825117588,
0.025365784764289856,
-0.0312481839209795,
0.0034327844623476267,
-0.0008285874500870705,
-0.003539750352501869,
0.03510616719722748,
-0.014673312194645405,
-0.00848503690212965,
0.0011265610810369253,
-0.05448080226778984,
0.002115038223564625,
-0.018978169187903404,
0.010602403432130814,
0.01847267709672451,
0.04283994063735008,
-0.041040778160095215,
0.03645901381969452,
-0.0062987613491714,
-0.02348252572119236,
-0.0032887551933526993,
0.006159615702927113,
0.01526991929858923,
0.06027944013476372,
-0.006826378405094147,
-0.0126019436866045,
0.03541054204106331,
-0.025018248707056046,
-0.005571654066443443,
0.03049316257238388,
-0.027303732931613922,
0.015703711658716202,
-0.0065565044060349464,
-0.01331719197332859,
0.018293552100658417,
-0.08891806751489639,
-0.019831396639347076,
0.07815486192703247,
-0.0488998182117939,
0.007449096534401178,
0.08401019126176834,
0.029133005067706108,
0.018875645473599434,
0.02046753279864788,
-0.01374517660588026,
-0.00819918978959322,
-0.037530411034822464,
0.03280764818191528,
0.04335416108369827,
0.020252568647265434,
0.021003305912017822,
0.004663651809096336,
0.06556888669729233,
0.015061778016388416,
0.02462644688785076,
-0.010033081285655499,
0.023432930931448936,
-0.0657154992222786,
0.020617933943867683,
-0.00020498457888606936,
-0.023325441405177116,
0.05569136515259743,
0.041364990174770355,
0.0011482001282274723,
0.07516638934612274,
-0.04982471466064453,
-0.03209627419710159,
-0.04831898957490921,
0.0155114671215415,
-0.029909182339906693,
-0.01854720525443554,
0.030495060607790947,
0.06196105480194092,
0.009073740802705288,
-0.006353460717946291,
-0.01826944760978222,
-0.028328904882073402,
0.025275802239775658,
-0.029091624543070793,
0.004813038278371096,
0.005659459158778191,
-0.018933085724711418,
-0.008465941995382309,
-0.014552607201039791,
-0.029145488515496254,
0.007311495020985603,
0.04551733285188675,
-0.0013609064044430852,
0.011224213056266308,
0.014417975209653378,
0.018003353849053383,
0.012139568105340004,
0.006211596075445414,
-0.0509457141160965,
-0.009687800891697407,
-0.04698385298252106,
0.005972418002784252,
-0.00762917147949338,
-0.002572404919192195
] |
<p>I am currently studying electrodynamics with all the fields and the like. Now, as I understand it, in a more modern viewpoint there is a duality between electromagnetic fields and photons, with photons being the particles that are exchanged in the process of interaction.</p>
<p>My question is, what is the current explanation to what an electromagnetic field is?
For example, consider a point charge $q_1$. In order for another charge $q_2$ to 'feel' $q_1$, there is an electromagnetic field generated by $q_1$ that allows interaction. However, using the photon picture of view, a charge should then constantly radiate photons in all possible directions to let other charges know that it's here and should be interacted with. This leads to a problem in energy conservation, as each photon carries an energy $h\nu$, and thus even if a charge is at rest it would radiate off its energy and subsequently be gone.</p>
<p>How can this be resolved? What is the real connection between an electromagnetic field and photons?</p> | 21 | [
-0.021382063627243042,
0.00033464221633039415,
0.02401585504412651,
-0.03787238150835037,
0.023790402337908745,
0.04642953351140022,
-0.01422198861837387,
-0.023595113307237625,
0.014812453649938107,
-0.03256469592452049,
0.021815631538629532,
0.041321802884340286,
0.05727560445666313,
0.01089121587574482,
0.03195388987660408,
0.004302092827856541,
0.010888478718698025,
-0.02216339483857155,
-0.016214966773986816,
-0.03373914957046509,
-0.020694276317954063,
0.036215439438819885,
-0.007441785652190447,
0.016066964715719223,
-0.038259100168943405,
0.01820230484008789,
0.003005047095939517,
0.030673088505864143,
0.01814904995262623,
0.06318016350269318,
0.02316465601325035,
-0.050812266767024994,
-0.015932559967041016,
0.01833726465702057,
-0.0042555746622383595,
-0.008615750819444656,
-0.01559685543179512,
-0.041800402104854584,
0.0133417509496212,
0.006497880909591913,
-0.024283617734909058,
-0.015434443019330502,
-0.010489128530025482,
0.04335494711995125,
-0.04004620015621185,
-0.009404024109244347,
-0.0008289169636555016,
-0.003949805628508329,
0.0568055622279644,
-0.07134503126144409,
0.0758020430803299,
-0.00012458348646759987,
0.054143089801073074,
-0.0050349454395473,
-0.013556074351072311,
-0.015954401344060898,
0.07516997307538986,
0.044455815106630325,
0.012854238972067833,
-0.05285646393895149,
-0.03477122262120247,
-0.0020185555331408978,
-0.007288158405572176,
-0.04796302318572998,
-0.041342247277498245,
0.028896797448396683,
-0.01947256177663803,
0.02269352599978447,
0.03940662741661072,
-0.007360151503235102,
0.001684454851783812,
0.014851560816168785,
0.04364362359046936,
0.012898299843072891,
0.006858473177999258,
-0.018116842955350876,
0.028466176241636276,
0.00957517884671688,
0.044738467782735825,
0.000908945279661566,
-0.01933363825082779,
0.004605904221534729,
0.008669571951031685,
0.03304007276892662,
0.015528151765465736,
-0.005530818831175566,
0.055179886519908905,
-0.009987706318497658,
0.005654045380651951,
-0.0020347952377051115,
-0.025186266750097275,
0.0321878083050251,
0.030220700427889824,
-0.0003368329780641943,
-0.024581341072916985,
0.05327633023262024,
0.002855515107512474,
0.027206428349018097,
0.01891995035111904,
-0.04191103205084801,
0.0332750529050827,
0.03916257619857788,
0.01832376793026924,
0.06793840229511261,
-0.004099506419152021,
-0.06577452272176743,
-0.031038040295243263,
0.03125802427530289,
-0.01027651596814394,
-0.005911854561418295,
-0.039697904139757156,
0.023558106273412704,
0.014891408383846283,
0.016112491488456726,
0.03786350414156914,
-0.045205727219581604,
0.01855500601232052,
-0.019034922122955322,
0.06470631062984467,
0.09682755172252655,
0.03448309749364853,
-0.08475944399833679,
0.03467860817909241,
-0.026161734014749527,
-0.07583746314048767,
-0.03306028991937637,
0.03245771676301956,
0.02491803653538227,
-0.036380358040332794,
0.0015784105053171515,
-0.011737496592104435,
-0.02212705835700035,
-0.005114402621984482,
0.017518749460577965,
0.029321448877453804,
-0.049045808613300323,
-0.1019091010093689,
-0.055687885731458664,
0.020063132047653198,
-0.008673330768942833,
-0.042658764868974686,
-0.04980199784040451,
-0.014817426912486553,
0.040706273168325424,
0.09014996141195297,
-0.005955901928246021,
-0.04375297203660011,
0.008524966426193714,
0.045567482709884644,
0.014219198375940323,
-0.008447514846920967,
-0.03225098177790642,
-0.011704126372933388,
-0.01066399086266756,
0.0024079913273453712,
-0.05885976552963257,
0.007918992079794407,
0.03580392152070999,
-0.0036776605993509293,
-0.017847919836640358,
0.09516506642103195,
-0.020340537652373314,
-0.007413158658891916,
0.03397352248430252,
-0.015021830797195435,
-0.021594146266579628,
0.06600429117679596,
0.02336960844695568,
0.028929544612765312,
0.05971438065171242,
0.030391477048397064,
0.019340019673109055,
0.006125669460743666,
0.0557699128985405,
-0.009575000032782555,
-0.036241013556718826,
-0.025554463267326355,
-0.002942432416602969,
0.008261620998382568,
0.008169414475560188,
-0.046327054500579834,
-0.03770367056131363,
-0.016410300508141518,
0.002294681267812848,
-0.004646388813853264,
0.02794228307902813,
-0.013307234272360802,
-0.023961033672094345,
-0.013525363057851791,
-0.030244529247283936,
-0.0011060904944315553,
-0.07058203220367432,
0.026290200650691986,
-0.01781093329191208,
-0.014660896733403206,
-0.001745232380926609,
0.010034723207354546,
-0.010089223273098469,
-0.02729951962828636,
-0.05120106786489487,
0.000018036918845609762,
0.06604845821857452,
-0.007369552738964558,
-0.000016653057173243724,
0.033074792474508286,
0.039687011390924454,
0.0448380745947361,
0.02645714208483696,
0.011334815062582493,
-0.008953501470386982,
-0.05510997772216797,
0.014748911373317242,
-0.04215504974126816,
0.017556188628077507,
0.007351799868047237,
0.007772978860884905,
-0.02725328877568245,
-0.03551141917705536,
-0.022210661321878433,
0.023805176839232445,
-0.008370106108486652,
0.06443612277507782,
-0.004975309129804373,
-0.008532622829079628,
-0.011769140139222145,
0.06346575170755386,
-0.0060065733268857,
-0.004058223683387041,
-0.024431951344013214,
-0.06103447824716568,
-0.032349202781915665,
0.03275638818740845,
0.05871245637536049,
-0.013834718614816666,
-0.029844650998711586,
0.02328282967209816,
-0.004725637845695019,
0.05680733546614647,
0.018936092033982277,
0.024983754381537437,
-0.04984135180711746,
-0.021923640742897987,
0.0369800366461277,
0.03124978579580784,
0.010404491797089577,
0.018612446263432503,
0.0314856581389904,
-0.005224317777901888,
-0.00015524264017585665,
0.01777346059679985,
-0.02008836343884468,
0.04454125463962555,
-0.03461969643831253,
0.014786290004849434,
-0.008305128663778305,
-0.03891238197684288,
0.02712724544107914,
-0.04435224086046219,
0.04733212664723396,
0.001996515318751335,
-0.019952066242694855,
-0.017037957906723022,
-0.009447953663766384,
-0.023792646825313568,
0.0001987654104596004,
0.002152328146621585,
-0.023160841315984726,
-0.015564434230327606,
0.008564991876482964,
-0.01895509846508503,
0.018852176144719124,
0.0021441117860376835,
-0.03298362344503403,
-0.02058565616607666,
-0.026000136509537697,
0.02258785255253315,
0.0291962381452322,
0.028156770393252373,
-0.048613376915454865,
-0.046865738928318024,
-0.009869867004454136,
-0.05826576054096222,
-0.017473945394158363,
0.020251011475920677,
-0.03984799236059189,
-0.005824326537549496,
-0.048885177820920944,
-0.0075326524674892426,
0.04498312249779701,
0.012782816775143147,
0.02447098307311535,
0.004575478378683329,
-0.013337493874132633,
-0.07021452486515045,
-0.021155133843421936,
-0.042046401649713516,
-0.000441448442870751,
0.006329198367893696,
0.00725632393732667,
0.05156581848859787,
-0.04157270863652229,
-0.02577255852520466,
0.024399464949965477,
-0.034300100058317184,
-0.05492590740323067,
-0.030236462131142616,
-0.010569768957793713,
0.023222923278808594,
-0.03244137391448021,
0.04299129918217659,
0.02536279335618019,
-0.06417299807071686,
-0.002179682720452547,
-0.04072320833802223,
-0.046835631132125854,
0.006137211341410875,
-0.03524283692240715,
0.01828775741159916,
0.009507277049124241,
-0.039921846240758896,
0.06426839530467987,
0.031251441687345505,
-0.021357078105211258,
0.027029139921069145,
0.001717585721053183,
-0.010470750741660595,
-0.011363011784851551,
-0.009993613697588444,
0.010652524419128895,
0.014942741952836514,
0.007850582711398602,
0.01630869135260582,
0.0073383101262152195,
-0.013365542516112328,
0.02273951657116413,
-0.014368022792041302,
-0.0012070630909875035,
-0.0026914230547845364,
0.004703607875853777,
0.012573597952723503,
-0.00035907496931031346,
-0.04625803232192993,
0.014417199417948723,
0.0031389647629112005,
-0.0005513309733942151,
0.00040637527126818895,
0.0003197375626768917,
0.0545765683054924,
0.025416389107704163,
0.0381024032831192,
-0.042589712888002396,
0.011583265848457813,
-0.046053461730480194,
-0.01680833473801613,
0.008552948012948036,
0.03686348721385002,
0.01935710199177265,
-0.038596246391534805,
0.004171027336269617,
0.035843003541231155,
0.051346730440855026,
-0.05328666418790817,
-0.04021716117858887,
0.0028762670699507,
0.0031343300361186266,
0.014070799574255943,
-0.010923868045210838,
0.007433139719069004,
0.05192746967077255,
0.031899593770504,
0.04171202704310417,
0.016704361885786057,
-0.030272969976067543,
-0.039871979504823685,
-0.034081049263477325,
0.024052808061242104,
0.035002827644348145,
0.058262426406145096,
0.032965660095214844,
0.05338732525706291,
0.04174889624118805,
0.01768568344414234,
0.015810027718544006,
0.006963849999010563,
-0.08785299956798553,
0.03317004814743996,
-0.038712598383426666,
0.019955269992351532,
-0.05334553122520447,
-0.0016761270817369223,
0.005798639729619026,
-0.016577526926994324,
-0.054580576717853546,
-0.04170142114162445,
-0.037485264241695404,
-0.06002012640237808,
0.014240921474993229,
-0.07585636526346207,
-0.053465764969587326,
-0.03753992170095444,
0.03621770814061165,
0.02861992083489895,
-0.0223226398229599,
-0.0064831990748643875,
0.03594209998846054,
-0.04778388515114784,
-0.004753053188323975,
0.006652037613093853,
0.011742684990167618,
0.0134574668481946,
-0.0037899359595030546,
0.03550400584936142,
-0.000057689980167197064,
-0.011680779978632927,
0.017181962728500366,
0.02225969173014164,
0.06738559156656265,
0.022097475826740265,
-0.022680001333355904,
0.014990340918302536,
-0.04513932019472122,
-0.010650286450982094,
-0.011336236260831356,
0.0735425055027008,
0.007859536446630955,
-0.011261758394539356,
0.01922876387834549,
0.013685833662748337,
-0.020324379205703735,
0.05686507374048233,
0.03448116406798363,
0.004367460496723652,
-0.026283983141183853,
-0.0545114241540432,
0.027379734441637993,
-0.01450189296156168,
0.012570022605359554,
-0.005950427148491144,
-0.02347782626748085,
0.005272592883557081,
-0.028675228357315063,
0.002024812623858452,
-0.011690979823470116,
0.016181178390979767,
-0.007118351757526398,
0.009758819825947285,
0.008136928081512451,
0.0270373597741127,
-0.005619457922875881,
-0.0028255623765289783,
0.06338172405958176,
0.06968624144792557,
0.016708772629499435,
0.004891598131507635,
-0.08391270786523819,
-0.008400560356676579,
0.029721956700086594,
0.03518516570329666,
0.010779794305562973,
-0.02122265286743641,
-0.023006070405244827,
0.008517018519341946,
0.018970059230923653,
-0.022547774016857147,
0.04181328043341637,
-0.008866318501532078,
-0.02970125526189804,
-0.010168245993554592,
-0.017466705292463303,
-0.04074559733271599,
0.03982542082667351,
-0.009665116667747498,
0.016998382285237312,
-0.015181057155132294,
0.00539219006896019,
-0.014003876596689224,
0.042949143797159195,
0.0016641219845041633,
0.04311036318540573,
0.012316789478063583,
-0.007055782712996006,
-0.006247395183891058,
0.015897491946816444,
0.000897933088708669,
-0.0981815904378891,
-0.005059231538325548,
0.014769604429602623,
-0.042742352932691574,
0.04510728269815445,
-0.026093825697898865,
-0.062134094536304474,
-0.019292159005999565,
-0.002462514443323016,
-0.002278696745634079,
0.0040997350588440895,
-0.060138627886772156,
0.024478409439325333,
0.01810196414589882,
0.006238806992769241,
0.05144215747714043,
0.016381537541747093,
-0.029675837606191635,
-0.025851145386695862,
-0.004997239913791418,
0.04690898582339287,
-0.013960438780486584,
-0.0002559635031502694,
-0.02203788422048092,
0.00003466624184511602,
-0.03660200908780098,
0.08878427743911743,
-0.02639058232307434,
-0.017817385494709015,
-0.004313512239605188,
-0.047098878771066666,
-0.03267434611916542,
0.030981063842773438,
-0.024713357910513878,
-0.026694651693105698,
-0.018812531605362892,
0.015055379830300808,
-0.011834298260509968,
-0.010618798434734344,
-0.016404515132308006,
0.004487825091928244,
-0.010348079726099968,
0.018701840192079544,
0.006289280019700527,
0.022910160943865776,
-0.02762843854725361,
-0.00001412063829775434,
-0.0023384515661746264,
-0.026105809956789017,
0.03199320286512375,
-0.01844775304198265,
-0.0038490828592330217,
0.00692688999697566,
-0.07242836058139801,
-0.035577334463596344,
-0.0013407343067228794,
-0.012101107276976109,
0.02857513166964054,
-0.036925308406353,
0.020881982520222664,
0.013991170562803745,
-0.007339859381318092,
-0.08768133074045181,
-0.0650492012500763,
0.011041671968996525,
0.008509603329002857,
-0.010321605019271374,
-0.013354331254959106,
0.027525650337338448,
-0.04352879896759987,
-0.04487265273928642,
0.013377402909100056,
0.0329420380294323,
-0.03826947510242462,
0.016712429001927376,
0.016363931819796562,
0.03405183181166649,
0.0028670087922364473,
-0.023054810240864754,
-0.004338728729635477,
0.024871744215488434,
0.029415588825941086,
-0.004464496858417988,
-0.0008199934381991625,
0.06215425580739975,
-0.0018142815679311752,
-0.0447642058134079,
-0.019963981583714485,
0.006397327408194542,
0.04491475224494934,
-0.01946660503745079,
-0.014828696846961975,
0.03828005492687225,
0.031850069761276245,
-0.02464538998901844,
-0.04109083116054535,
0.03136764466762543,
0.03709902614355087,
0.04160232096910477,
-0.005555635783821344,
0.01334304828196764,
-0.015403795056045055,
-0.04725749045610428,
0.038323089480400085,
-0.017115909606218338,
0.031111376360058784,
0.017422838136553764,
0.02056238055229187,
-0.031461723148822784,
0.007338610477745533,
0.014353915117681026,
0.027098363265395164,
0.00539263105019927,
-0.012491066940128803,
0.014961057342588902,
0.001898587797768414,
-0.010850335471332073,
-0.03515719622373581,
-0.025081809610128403,
-0.03061237558722496,
-0.03495081514120102,
0.07186667621135712,
-0.02106829732656479,
0.05137425661087036,
0.01899680681526661,
0.007036690134555101,
0.008381910622119904,
0.002198100322857499,
-0.018142785876989365,
0.0084378095343709,
0.022095326334238052,
0.020703619346022606,
-0.02426132932305336,
0.011325988918542862,
0.044036202132701874,
0.05183926969766617,
-0.030536703765392303,
0.020366698503494263,
0.018686020746827126,
0.049458298832178116,
0.03044522926211357,
-0.014357473701238632,
-0.06222301721572876,
0.030659154057502747,
-0.04126482456922531,
-0.005254395306110382,
0.031119806692004204,
-0.019868670031428337,
0.045750416815280914,
0.0008554200176149607,
0.01723865419626236,
0.002393832430243492,
-0.0347881056368351,
-0.04041817784309387,
0.01678420789539814,
-0.006996511481702328,
0.03811301290988922,
-0.01636819913983345,
0.00424888776615262,
0.013094360008835793,
-0.01673998311161995,
0.029386626556515694,
0.03632786124944687,
-0.06534219533205032,
-0.04010724648833275,
-0.04743403568863869,
-0.007120179943740368,
0.06968823820352554,
-0.0234087985008955,
-0.01876048743724823,
-0.005146627780050039,
-0.014957928098738194,
0.00830403994768858,
0.004747309256345034,
0.02118827775120735,
-0.03347541764378548,
0.026639433577656746,
-0.02015114575624466,
0.014497256837785244,
-0.024419030174613,
-0.00112519646063447,
0.08636938780546188,
0.03366236388683319,
0.01535235345363617,
-0.048355259001255035,
0.015970546752214432,
-0.039417609572410583,
-0.002962816972285509,
-0.047677673399448395,
0.050516337156295776,
-0.015848839655518532,
0.02310711331665516,
0.0014326508389785886,
0.04478732869029045,
0.021774550899863243,
-0.006463457830250263,
0.06608559191226959,
-0.035954058170318604,
-0.05267874896526337,
0.0011406420962885022,
0.033564090728759766,
-0.0016479381592944264,
0.04598330333828926,
-0.049647681415081024,
0.02291245199739933,
-0.023429887369275093,
-0.015145434997975826,
0.014665081165730953,
-0.035041920840740204,
0.010202879086136818,
-0.010119286365807056,
-0.021336421370506287,
-0.011029757559299469,
0.0016909268451854587,
-0.026381654664874077,
-0.04115772992372513,
0.006658011116087437,
0.027721581980586052,
0.012124953791499138,
0.010975560173392296,
0.00004093482857570052,
0.029552428051829338,
-0.022996988147497177,
0.0336734801530838,
0.03798613324761391,
-0.036693669855594635,
-0.011458183638751507,
-0.004449313040822744,
0.07031629234552383,
-0.01404570136219263,
0.020397450774908066,
0.01416850183159113,
0.009176318533718586,
0.00690847635269165,
-0.026967382058501244,
-0.02004963904619217,
-0.012100385501980782,
0.0324726365506649,
-0.005927929654717445,
0.012031368911266327,
-0.012011305429041386,
0.04547642543911934,
-0.013276376761496067,
0.0255313441157341,
0.001340533490292728,
0.01685953699052334,
-0.007869244553148746,
-0.01596207171678543,
0.048279378563165665,
-0.005089959595352411,
-0.00513787055388093,
-0.009270003996789455,
-0.043170902878046036,
-0.016005180776119232,
-0.029602330178022385,
0.02651236578822136,
0.03726445883512497,
0.01893262006342411,
-0.0010839669266715646,
-0.002838526386767626,
-0.02162226475775242,
-0.07895434647798538,
0.021527143195271492,
-0.013226760551333427,
-0.03951844573020935,
-0.012653287500143051,
0.003460219595581293,
0.006196367088705301,
0.04071865603327751,
-0.0009766651783138514,
0.00792451947927475,
-0.0047643850557506084,
-0.005486397072672844,
0.010124103166162968,
-0.019603192806243896,
-0.009742164984345436,
0.022757800295948982,
-0.012940468266606331,
-0.026335764676332474,
-0.022219544276595116,
0.00530677055940032,
-0.003301970660686493,
0.02176266722381115,
0.015990201383829117,
0.028839459642767906,
-0.02398739941418171,
0.012198556214571,
0.03314125910401344,
-0.005942161660641432,
0.021754642948508263,
-0.012971391901373863,
0.0182033721357584,
-0.041898902505636215,
-0.034555189311504364,
0.010389711707830429,
0.002930393908172846,
-0.0166062880307436,
0.02503073774278164,
-0.03610831871628761,
-0.015519690699875355,
-0.014583943411707878,
0.029579073190689087,
-0.050859007984399796,
-0.04703672230243683,
-0.06596120446920395,
0.018479811027646065,
0.013761281967163086,
-0.03918910399079323,
-0.0068094017915427685,
0.04396214336156845,
-0.019513778388500214,
-0.022011933848261833,
0.016413884237408638,
0.0364348366856575,
-0.015240062959492207,
-0.00003825185922323726,
0.00939854048192501,
0.008022576570510864,
0.0705370232462883,
-0.01516427006572485,
-0.034044358879327774,
0.03450482338666916,
-0.03714046999812126,
-0.05315522849559784,
0.018438365310430527,
0.002521784510463476,
0.034170038998126984,
0.04468375816941261,
-0.01746588945388794,
-0.021664999425411224,
0.028847098350524902,
0.0017209724755957723,
0.007087903097271919,
-0.0011449509765952826,
-0.03894607350230217,
-0.01755828782916069,
-0.02833404205739498,
0.02191101759672165,
0.008932024240493774,
-0.014341740868985653,
0.04022173956036568,
0.00014500621182378381,
0.03094153292477131,
-0.017505500465631485,
-0.004179168492555618,
-0.005997244734317064,
0.020660199224948883,
0.018411247059702873,
0.01674146205186844,
-0.0023267962969839573,
0.04284987598657608,
-0.0392410010099411,
0.01464403048157692,
0.019024750217795372,
0.027379758656024933,
-0.10931042581796646,
-0.020515481010079384,
0.008223816752433777,
0.008256370201706886,
0.040960390120744705,
-0.032700881361961365,
0.01836075447499752,
0.030544979497790337,
-0.06473106145858765,
0.02728859893977642,
-0.012807106599211693,
-0.020213214680552483,
-0.006184208206832409,
0.014299822971224785,
-0.012000225484371185,
0.051390744745731354,
0.027655625715851784,
0.06635525822639465,
0.004211707040667534,
-0.0014979301486164331,
0.01768340915441513,
-0.021191349253058434,
-0.04071154072880745,
0.015931060537695885,
-0.021194688975811005,
0.011396038345992565,
0.0928443893790245,
0.019021375104784966,
-0.013899780809879303,
0.05321989208459854,
-0.018726838752627373,
0.013158385641872883,
0.012074552476406097,
0.007662398740649223,
0.009198654443025589,
0.025410762056708336,
-0.002541367430239916,
-0.02754504233598709,
-0.015854230150580406,
0.0096091628074646,
0.06899655610322952,
0.03916727006435394,
0.0019437584560364485,
0.009199711494147778,
0.014880054630339146,
-0.046719543635845184,
-0.028271296992897987,
0.04501064866781235,
-0.006420090328902006,
-0.01435292512178421,
-0.005669786129146814,
0.031960368156433105,
0.006867375690490007,
-0.014815262518823147,
-0.003640638431534171,
-0.05500316992402077,
-0.04749957099556923,
0.013394868932664394,
0.02075187861919403,
0.01622687466442585,
0.026540115475654602,
0.00003017835842911154,
-0.029824165627360344,
0.02150920033454895,
0.032156042754650116,
0.03904477506875992,
-0.03290046006441116,
0.01341656781733036,
0.04446965456008911,
0.004187185782939196,
0.008507425896823406,
-0.05057170242071152,
-0.044869326055049896,
0.024423053488135338,
-0.002385707339271903,
0.038750261068344116,
-0.01183152012526989,
-0.04754281044006348,
-0.04471276327967644,
-0.058683380484580994,
0.04319402575492859,
-0.008105450309813023,
0.0027491773944348097,
-0.03210650384426117,
-0.03407496586441994,
-0.013200754299759865,
-0.0031864773482084274,
0.06832640618085861,
-0.023770594969391823,
-0.03892792388796806,
0.024062898010015488,
-0.004176646005362272,
0.016309062018990517,
-0.03717983886599541,
-0.023698978126049042,
-0.021018361672759056,
0.0016100737266242504,
-0.02257288247346878,
-0.002796222921460867,
-0.026085125282406807,
0.028000053018331528,
0.02160591632127762,
-0.016173209995031357,
0.034028682857751846,
-0.014814876951277256,
-0.045344576239585876,
0.05368268862366676,
-0.012165676802396774,
-0.011774716898798943,
0.022654002532362938,
-0.017017627134919167,
0.027938256040215492,
0.03939387947320938,
-0.031828779727220535,
-0.0013286626199260354,
0.018332842737436295,
-0.030252644792199135,
-0.022312046959996223,
-0.001470332033932209,
0.01138364803045988,
0.058520279824733734,
-0.04456118121743202,
-0.010968752205371857,
0.0658593475818634,
-0.0434831865131855,
-0.009975203312933445,
0.045376744121313095,
-0.007536780554801226,
0.02567996270954609,
0.034668419510126114,
0.028297292068600655,
-0.00012560421600937843,
0.005693418905138969,
0.015809455886483192,
0.04634878784418106,
0.038822658360004425,
0.0011057173833251,
0.03616867586970329,
0.05152638629078865,
0.00012697020429186523,
0.02376159466803074,
-0.009274887852370739,
0.02489554136991501,
-0.01954084075987339,
0.0008224112098105252,
0.04158075153827667,
0.02282208576798439,
-0.022386031225323677,
0.002585465321317315,
-0.03052370622754097,
0.09191575646400452,
-0.02943621762096882,
0.002883266657590866,
-0.007013469934463501,
0.008684898726642132,
0.002648869762197137,
0.0115569569170475,
0.022849971428513527,
0.06786100566387177,
0.02325713448226452,
0.013654091395437717,
-0.018885817378759384,
-0.0018987719668075442,
0.012469801120460033,
-0.04123571142554283,
0.0351739302277565,
-0.0014374039601534605,
-0.023125996813178062,
-0.019898295402526855,
-0.030462289229035378,
0.012485485523939133,
-0.050060998648405075,
0.034276701509952545,
0.03620745986700058,
0.054748788475990295,
0.016239935532212257,
-0.0008608305361121893,
-0.03538086637854576,
0.05425075814127922,
-0.060648225247859955,
0.02359355241060257,
-0.012759058736264706,
0.011224498972296715,
0.003627535654231906,
0.005148678552359343
] |
<p>In gas metal arc welding, an electric arc forms between the work piece and a consumable wire, heating the work piece and also melting the tip of this consumable wire, which is continually fed into the weld.</p>
<p>I recently found out that it is important to use the correct polarity when welding with direct current. Some electrode (i.e. the consumable wire) materials require that the electrode be positive and others that it be negative. Welding machines come with special mechanisms for reversing the polarity as necessary.</p>
<p>Searching for why this would be the case explains, at best, that this determines whether the work piece or the wire gets the most heat. Having always perceived any such heating as entirely symmetric under polarity reversal, this puzzles me.</p>
<p>Welding tutorials highlight the importance of polarity, as do the instructions on the welding wire and the machines themselves. What are the mechanisms that affect the weld depending on the polarity used?</p> | 1,475 | [
-0.026841294020414352,
-0.0434979684650898,
0.03508777916431427,
-0.017188062891364098,
0.03864579647779465,
0.02366906963288784,
-0.059149120002985,
0.001299377647228539,
0.033810533583164215,
-0.019803928211331367,
0.03537270799279213,
0.013311640359461308,
0.036853522062301636,
0.03775288537144661,
0.04666054621338844,
-0.026214513927698135,
0.04541362449526787,
-0.019616125151515007,
0.004969041328877211,
0.006861010100692511,
0.00016515750030521303,
0.002997345058247447,
-0.006979693192988634,
-0.01417386345565319,
-0.018858138471841812,
0.03912448137998581,
0.008027716539800167,
0.005721224006265402,
0.01576404459774494,
0.01805323362350464,
-0.026093166321516037,
-0.027951370924711227,
-0.01350433100014925,
0.036577124148607254,
0.05350370332598686,
0.0016821104800328612,
-0.006266854703426361,
-0.04526242986321449,
-0.017687615007162094,
0.05635647848248482,
0.02248358726501465,
0.005175445694476366,
-0.022728461772203445,
0.02674289047718048,
-0.007860186509788036,
-0.021766554564237595,
-0.055030789226293564,
0.002412830712273717,
0.03959371894598007,
-0.07452670484781265,
0.029253674671053886,
-0.028224047273397446,
0.046759385615587234,
0.041253700852394104,
-0.007666605059057474,
0.026819903403520584,
0.0709153339266777,
0.04450727999210358,
0.025754470378160477,
-0.055827878415584564,
0.004688791930675507,
-0.009738015942275524,
-0.05730002745985985,
0.003176515456289053,
-0.007988189347088337,
0.02670273184776306,
0.014973859302699566,
-0.05647933483123779,
0.007343486417084932,
0.021416595205664635,
0.02717101387679577,
-0.0024067945778369904,
0.00892067700624466,
0.015392009168863297,
-0.0022493775468319654,
-0.0071807443164289,
0.01803157851099968,
0.031868841499090195,
0.038105882704257965,
0.024656832218170166,
-0.015884552150964737,
-0.00405280664563179,
-0.017384296283125877,
0.05102710425853729,
-0.019016314297914505,
-0.004045458510518074,
0.05950138717889786,
-0.0071350946091115475,
0.023642221465706825,
0.028494160622358322,
0.0007504908135160804,
0.02824668399989605,
-0.0038076811470091343,
-0.006077548488974571,
0.002380626043304801,
0.00321788527071476,
-0.013573063537478447,
0.023489339277148247,
-0.008038366213440895,
-0.01506856083869934,
-0.013042040169239044,
0.011050980538129807,
-0.009926259517669678,
0.07912368327379227,
0.03506159037351608,
-0.03758196905255318,
-0.022936461493372917,
0.008952055126428604,
0.0471271276473999,
-0.024564901366829872,
-0.03875786438584328,
0.006641298066824675,
0.021422361955046654,
0.014642800204455853,
0.020062163472175598,
-0.026202743873000145,
0.006847695913165808,
-0.018311327323317528,
0.03668847680091858,
0.03844810277223587,
0.007146830204874277,
-0.0436113104224205,
0.04131109640002251,
-0.029799072071909904,
-0.03611239045858383,
-0.04926425963640213,
0.04369159787893295,
-0.009374051354825497,
-0.003868158906698227,
0.04174353927373886,
0.03415129706263542,
-0.04338287562131882,
0.0207055676728487,
-0.03022610768675804,
0.012154648080468178,
0.021343888714909554,
-0.07175777852535248,
-0.060698505491018295,
0.0534285344183445,
-0.011907193809747696,
-0.0016459214966744184,
-0.06860960274934769,
-0.05626758188009262,
0.07472874224185944,
0.08768210560083389,
-0.02373700775206089,
-0.0033547438215464354,
-0.054031308740377426,
-0.005708034615963697,
0.014289346523582935,
0.0022733646910637617,
-0.04043254628777504,
0.019176876172423363,
-0.03510338440537453,
-0.03560779616236687,
-0.036510616540908813,
0.02424669824540615,
0.030928203836083412,
0.025645986199378967,
-0.005000434350222349,
0.05243111029267311,
-0.03579047694802284,
-0.016602924093604088,
0.031723275780677795,
-0.025387762114405632,
-0.03450900688767433,
0.0958535447716713,
0.018437637016177177,
-0.00563023891299963,
0.028014766052365303,
0.0012324170675128698,
0.02696193940937519,
0.014844808727502823,
0.020175239071249962,
0.036027293652296066,
-0.059032145887613297,
-0.0037094419822096825,
-0.01960264891386032,
0.0005277228774502873,
0.009156595915555954,
-0.04014161229133606,
-0.02124759554862976,
0.0057813250459730625,
0.026753151789307594,
0.0265276450663805,
0.05139559134840965,
-0.005489687900990248,
0.010900587774813175,
0.032539088279008865,
-0.005722645204514265,
-0.057729098945856094,
-0.05661243572831154,
0.06014776602387428,
-0.027643069624900818,
-0.03276433050632477,
0.0019894083961844444,
0.017931466922163963,
0.004940130282193422,
-0.008809244260191917,
-0.05116446688771248,
0.054056547582149506,
0.041851118206977844,
0.04233558475971222,
-0.019247520714998245,
-0.03704492747783661,
0.0725860744714737,
0.008562230505049229,
-0.018496843054890633,
0.03354358673095703,
-0.036477889865636826,
-0.04111883416771889,
0.012991187162697315,
-0.030163723975419998,
0.02269318513572216,
0.014273948967456818,
-0.05872711166739464,
-0.02229982428252697,
0.026817336678504944,
-0.012191984802484512,
0.06622037291526794,
-0.00443642633035779,
0.04077794775366783,
0.040531858801841736,
0.006239626090973616,
0.0007363123004324734,
0.06310441344976425,
0.01041408535093069,
0.02203180640935898,
0.023769734427332878,
-0.02055840939283371,
-0.05523381382226944,
0.023798372596502304,
0.02924445830285549,
0.017054568976163864,
-0.020104290917515755,
0.014109465293586254,
0.016780709847807884,
0.034522492438554764,
-0.006749127525836229,
-0.0070656235329806805,
0.02896619774401188,
-0.01774938777089119,
0.021067777648568153,
0.010634573176503181,
0.05252637341618538,
0.006992805749177933,
0.015131003223359585,
0.03084125556051731,
0.029797151684761047,
0.010667461901903152,
-0.04614361375570297,
0.06497089564800262,
0.01608307845890522,
-0.0045899818651378155,
0.03942316025495529,
-0.026718826964497566,
0.029476040974259377,
-0.03234999626874924,
0.02839660830795765,
-0.02070486545562744,
0.00615428201854229,
0.01374212559312582,
0.005478914361447096,
-0.009601285681128502,
-0.01254934910684824,
0.023712417110800743,
0.01353961881250143,
0.007672132924199104,
0.023916319012641907,
-0.03749878332018852,
0.01753270998597145,
-0.04375935718417168,
0.00467577064409852,
-0.017038287594914436,
-0.04984604939818382,
-0.006614830810576677,
0.019695309922099113,
0.028646202757954597,
-0.04136750102043152,
-0.02902037464082241,
-0.014339908957481384,
-0.03865087777376175,
0.02986844815313816,
0.0023428259883075953,
-0.031600113958120346,
-0.04627516493201256,
0.00003783505962928757,
0.0034200127702206373,
0.01966666802763939,
0.061188314110040665,
0.023550204932689667,
0.01679820381104946,
-0.0033140727318823338,
-0.051645003259181976,
-0.007863315753638744,
-0.008118515834212303,
0.012520377524197102,
-0.025563281029462814,
-0.021910114213824272,
0.028156880289316177,
0.008297097869217396,
-0.03079059347510338,
0.011747295036911964,
-0.04273513704538345,
-0.048728540539741516,
0.02297842502593994,
-0.024540305137634277,
0.025740958750247955,
0.026640452444553375,
0.03893590718507767,
0.04179168492555618,
-0.05508739501237869,
-0.02282942458987236,
-0.01824824884533882,
-0.005942507181316614,
-0.010652119293808937,
-0.013541209511458874,
-0.006089441012591124,
-0.01207014825195074,
-0.011755063198506832,
0.035029347985982895,
0.02240331843495369,
-0.013939897529780865,
-0.019930632784962654,
-0.026739468798041344,
-0.05130232125520706,
-0.03129305690526962,
0.03114159032702446,
0.04229086637496948,
-0.015414462424814701,
0.018190758302807808,
-0.022999918088316917,
0.06172933056950569,
0.044100649654865265,
0.023965666070580482,
-0.056438300758600235,
0.04277842491865158,
0.012737235985696316,
-0.02890375815331936,
0.02304151840507984,
0.03344765305519104,
-0.026024717837572098,
0.035757798701524734,
0.029027368873357773,
0.0044914125464856625,
0.03777281939983368,
-0.029111064970493317,
0.014835868962109089,
-0.04190535470843315,
0.02830740064382553,
-0.03688761219382286,
0.05290757864713669,
-0.0032811255659908056,
-0.013309323228895664,
-0.006881798151880503,
0.029897404834628105,
0.08569907397031784,
-0.039514899253845215,
-0.022205892950296402,
0.01023454312235117,
0.013060752302408218,
-0.0020463336259126663,
-0.03212262690067291,
-0.013111765496432781,
-0.03113345429301262,
0.01615421287715435,
0.017323045060038567,
-0.0015470498474314809,
0.06499261409044266,
0.044923584908246994,
-0.002289591822773218,
0.024937398731708527,
-0.03431166708469391,
-0.024986883625388145,
-0.07164973020553589,
0.012595897540450096,
0.03047758899629116,
0.04314452037215233,
-0.002400662750005722,
0.04692767560482025,
0.036874882876873016,
0.06107322499155998,
0.003446084214374423,
0.0009838518453761935,
-0.09443290531635284,
0.0336742028594017,
-0.03239697962999344,
0.054341599345207214,
-0.024420058354735374,
-0.017756091430783272,
-0.03577388823032379,
-0.03260480985045433,
-0.02949570305645466,
0.004213235341012478,
-0.00474023399874568,
-0.022180719301104546,
0.03849739581346512,
-0.02412058599293232,
-0.03410528972744942,
-0.028812922537326813,
0.029487360268831253,
0.05800744891166687,
-0.06121556833386421,
0.03992447629570961,
0.00503483647480607,
-0.026925543323159218,
-0.022203478962183,
-0.06759150326251984,
0.017850462347269058,
0.03656358644366264,
0.053113918751478195,
-0.016773071140050888,
0.007667777128517628,
-0.017877519130706787,
0.01728789135813713,
0.034271132200956345,
0.031130880117416382,
-0.006235470063984394,
-0.0126174446195364,
-0.052473727613687515,
-0.01879744976758957,
-0.048118844628334045,
0.00320457830093801,
0.06796316057443619,
0.0009881299920380116,
0.025774454697966576,
0.027030494064092636,
-0.02111888863146305,
-0.014532268047332764,
0.0008249945822171867,
0.015620100311934948,
0.05229052156209946,
-0.02219194732606411,
-0.0534367561340332,
-0.0140147153288126,
-0.016355080530047417,
-0.0003782573330681771,
0.005052286200225353,
-0.002804112620651722,
-0.00919507909566164,
-0.021192947402596474,
0.03193749859929085,
0.011984944343566895,
0.03590535745024681,
0.01363273337483406,
-0.028756115585565567,
0.031215740367770195,
-0.009839840233325958,
-0.005589483305811882,
-0.00027389239403419197,
0.014994759112596512,
0.03375377133488655,
-0.00812406837940216,
-0.029832955449819565,
-0.08969373255968094,
-0.005904793739318848,
0.0732087716460228,
0.05142899230122566,
-0.03322465717792511,
-0.015342919155955315,
-0.028840240091085434,
-0.028785130009055138,
0.03490998595952988,
-0.026933638378977776,
0.06023312732577324,
-0.052252404391765594,
-0.018222695216536522,
-0.03026978299021721,
-0.05322711542248726,
0.002361075021326542,
0.01890423148870468,
0.012110266834497452,
0.018631916493177414,
-0.04854382202029228,
-0.023227278143167496,
-0.007208715192973614,
-0.019565042108297348,
-0.006483003031462431,
-0.010511551052331924,
0.0061426712200045586,
-0.004764267709106207,
-0.006876935251057148,
0.05542765557765961,
0.02206028439104557,
-0.07725702971220016,
-0.007295278366655111,
0.0017979582771658897,
-0.004988374654203653,
0.04183271899819374,
-0.02078726701438427,
-0.027407299727201462,
0.03316386044025421,
-0.027658497914671898,
0.007868550717830658,
-0.040326353162527084,
-0.021295156329870224,
0.03165917843580246,
0.006446229759603739,
-0.014441218227148056,
0.04607103765010834,
0.0014262377517297864,
-0.05998438224196434,
-0.031105605885386467,
-0.0027432567439973354,
0.05470665544271469,
0.005209284368902445,
0.0057572247460484505,
0.0023145959712564945,
-0.007223173044621944,
-0.013655290007591248,
0.03262391686439514,
-0.004241149872541428,
0.023451372981071472,
-0.0005115907406434417,
-0.018445128574967384,
-0.00978193897753954,
0.005865326151251793,
-0.0043831076472997665,
-0.016554197296500206,
0.015348843298852444,
0.037505775690078735,
-0.018125222995877266,
-0.015337243676185608,
0.006954719312489033,
-0.05194474384188652,
0.005957115441560745,
0.007887599989771843,
-0.03581676632165909,
-0.0025628902949392796,
-0.05417440086603165,
-0.004364627879112959,
-0.015287965536117554,
-0.00344347907230258,
0.036408547312021255,
0.005918165668845177,
0.05317220091819763,
0.034466665238142014,
-0.07527638971805573,
-0.006360270548611879,
0.05220332741737366,
0.0009170274715870619,
0.016345646232366562,
-0.05070243403315544,
0.042611051350831985,
-0.01415680255740881,
0.011061138473451138,
-0.04296249896287918,
-0.06755603104829788,
0.02581607736647129,
0.027592429891228676,
-0.030847186222672462,
0.000823336944449693,
-0.0025986756663769484,
0.005670719780027866,
-0.06801524758338928,
0.01440262608230114,
0.05643549561500549,
-0.04370228573679924,
0.012993729673326015,
0.034187860786914825,
0.026800017803907394,
0.07070227712392807,
-0.06231091544032097,
-0.028046930208802223,
0.012456133961677551,
-0.049766652286052704,
0.0052209170535206795,
0.012006710283458233,
0.027863753959536552,
-0.009961358271539211,
-0.07321389019489288,
0.017338110134005547,
0.024084653705358505,
0.03804910555481911,
0.020266305655241013,
-0.013575390912592411,
0.017867261543869972,
-0.01719951257109642,
-0.012563998810946941,
-0.011368228122591972,
0.03321029618382454,
0.014808286912739277,
0.02114541456103325,
0.006830703001469374,
0.02444189414381981,
-0.016814962029457092,
-0.015887299552559853,
-0.004288165830075741,
0.0090925432741642,
0.0027914985548704863,
0.01189722865819931,
0.029056131839752197,
-0.05744011700153351,
0.004266306292265654,
0.03492523357272148,
-0.02619227021932602,
0.06276197731494904,
-0.016144603490829468,
0.040033143013715744,
-0.025087587535381317,
0.001600540359504521,
-0.0255336482077837,
-0.010540183633565903,
0.012928078882396221,
0.0019316188991069794,
0.0381123423576355,
0.01028178445994854,
0.03715667873620987,
-0.027852600440382957,
-0.021075405180454254,
-0.012702200561761856,
-0.0055628493428230286,
0.0027677249163389206,
0.009778637439012527,
0.005519959144294262,
0.03176950663328171,
-0.006721667014062405,
-0.004075474571436644,
0.021853087469935417,
0.042837414890527725,
-0.020575499162077904,
-0.068377785384655,
0.018114235252141953,
0.018271073698997498,
0.029623746871948242,
-0.01513456180691719,
-0.03858482092618942,
0.050547678023576736,
-0.02920375019311905,
0.04324033483862877,
-0.02552034892141819,
0.006289942655712366,
0.04659048467874527,
-0.043659038841724396,
0.0419178381562233,
-0.058547280728816986,
-0.026555059477686882,
-0.015202934853732586,
0.02352825738489628,
0.02218184992671013,
-0.007561632432043552,
-0.02847275882959366,
0.04315479099750519,
0.028240283951163292,
-0.04499790817499161,
0.008475999347865582,
-0.024648593738675117,
-0.04535030946135521,
-0.015364625491201878,
-0.0037768122274428606,
-0.03381825610995293,
0.06915877014398575,
-0.019094286486506462,
0.004567775875329971,
-0.012751905247569084,
-0.020708387717604637,
0.026986297219991684,
0.03604453429579735,
0.04802108556032181,
-0.02167537622153759,
0.06138767674565315,
-0.009194864891469479,
0.028838418424129486,
-0.0180002823472023,
0.01981915719807148,
0.15733107924461365,
0.008660927414894104,
0.022637125104665756,
-0.06485265493392944,
0.0255401823669672,
-0.025298113003373146,
-0.018993323668837547,
-0.00952241476625204,
0.009472323581576347,
-0.026501163840293884,
0.010811454616487026,
0.0298769474029541,
0.00760763231664896,
0.00659782811999321,
-0.007734069135040045,
0.011365393176674843,
-0.0495586171746254,
-0.015322773717343807,
0.011482307687401772,
-0.016013285145163536,
-0.0026983474381268024,
0.03715795278549194,
-0.028773771598935127,
-0.02081841044127941,
-0.0020321037154644728,
-0.01285434141755104,
0.010536689311265945,
-0.04091566428542137,
0.04842444509267807,
-0.034180160611867905,
-0.013864167965948582,
-0.011526495218276978,
0.0011075256625190377,
-0.003315343987196684,
-0.02618696726858616,
0.03255471587181091,
-0.00007978680514497682,
0.0035283418837934732,
0.02597753331065178,
-0.026370607316493988,
-0.007158514112234116,
0.012936613522469997,
0.02546384371817112,
0.03577209264039993,
-0.017040757462382317,
-0.007300971541553736,
0.005478622391819954,
0.004010443575680256,
0.011547793634235859,
-0.017374301329255104,
0.008791289292275906,
-0.003685503266751766,
0.045184724032878876,
-0.02417818084359169,
-0.03541114553809166,
-0.01987634412944317,
-0.004686621483415365,
-0.023504406213760376,
-0.04867559298872948,
-0.027915894985198975,
0.022347621619701385,
-0.007480232045054436,
-0.0006155793671496212,
-0.018486274406313896,
-0.027713999152183533,
0.007068191654980183,
-0.01386452466249466,
0.08072652667760849,
0.018993329256772995,
-0.02207999676465988,
-0.05502360314130783,
0.013242625631392002,
-0.02624533884227276,
-0.00506436824798584,
0.013886447064578533,
0.03592465817928314,
0.029288234189152718,
-0.018737612292170525,
-0.02851080894470215,
-0.01486984733492136,
-0.10250037908554077,
0.03562663495540619,
0.012137345969676971,
0.03772146254777908,
-0.026387516409158707,
0.013116657733917236,
0.02223104238510132,
0.037436697632074356,
-0.028040390461683273,
0.028290610760450363,
0.02987000159919262,
0.001568236155435443,
0.007933201268315315,
-0.013995728455483913,
-0.03180500864982605,
0.024530908092856407,
-0.045905470848083496,
-0.011513683013617992,
0.00209185853600502,
0.046509284526109695,
-0.016494862735271454,
0.010414132848381996,
0.006415139883756638,
0.031544819474220276,
-0.0301253292709589,
-0.022949093952775,
0.013108729384839535,
0.005430982913821936,
-0.011272519826889038,
-0.018968647345900536,
-0.04020609334111214,
-0.06299566477537155,
-0.04746992141008377,
-0.01977003738284111,
0.008844392374157906,
0.018329927697777748,
0.03159245848655701,
0.00987185537815094,
0.029883084818720818,
-0.017819933593273163,
0.0631386786699295,
-0.027578599750995636,
-0.04195571690797806,
-0.03377183899283409,
-0.01582791469991207,
0.008377411402761936,
0.001332780928350985,
-0.008812503889203072,
0.005752377677708864,
0.016905030235648155,
0.020292766392230988,
0.017254652455449104,
0.047159526497125626,
0.011248480528593063,
-0.04693842679262161,
0.02208087034523487,
-0.017568111419677734,
0.03579476475715637,
-0.03146897256374359,
-0.060431428253650665,
0.035242412239313126,
0.004890252836048603,
-0.019519198685884476,
-0.006823820527642965,
-0.024421388283371925,
0.018211299553513527,
0.019758861511945724,
0.002845878480002284,
0.013066787272691727,
0.027461053803563118,
0.014425424858927727,
0.020573657006025314,
0.016169214621186256,
0.029122430831193924,
0.02885766699910164,
0.02361018769443035,
-0.00567952124401927,
-0.006005560513585806,
-0.005144987255334854,
0.013588210567831993,
-0.013415799476206303,
0.011579255573451519,
-0.01862109638750553,
0.009322245605289936,
0.007728819735348225,
-0.0036625757347792387,
0.045486629009246826,
0.02136477269232273,
0.023380791768431664,
0.014202316291630268,
-0.014622393064200878,
0.015047636814415455,
-0.010186721570789814,
-0.017990831285715103,
-0.07483506202697754,
-0.004815395921468735,
0.03187618404626846,
0.0058556366711854935,
0.018598025664687157,
-0.021152155473828316,
0.013451500795781612,
0.015922911465168,
-0.09373722225427628,
0.037692196667194366,
0.00743295531719923,
-0.031550660729408264,
-0.05458011478185654,
-0.008542225696146488,
-0.044320717453956604,
0.04252883046865463,
-0.0016245829174295068,
0.016537001356482506,
0.03206511214375496,
-0.00468827597796917,
-0.01677348092198372,
-0.05995846912264824,
-0.004915507975965738,
0.022406328469514847,
-0.007244409993290901,
-0.01925133541226387,
0.06168438494205475,
-0.01434581633657217,
-0.06452861428260803,
0.03401941433548927,
-0.03777521103620529,
-0.028222911059856415,
-0.009946662001311779,
0.043766289949417114,
-0.04248010739684105,
0.03955279663205147,
0.017792951315641403,
0.014116907492280006,
-0.03149642422795296,
0.00602075457572937,
0.028580177575349808,
0.027130257338285446,
-0.015807120129466057,
0.023219915106892586,
0.01986823044717312,
-0.006050763186067343,
0.004510372411459684,
0.022919125854969025,
-0.05874843895435333,
-0.043390680104494095,
0.020782392472028732,
0.031206300482153893,
0.015652192756533623,
-0.006010457873344421,
0.012790205888450146,
-0.05306810885667801,
-0.0366092324256897,
0.015777455642819405,
0.014108013361692429,
0.051625680178403854,
0.017394013702869415,
-0.030973833054304123,
-0.004876881837844849,
0.03417522832751274,
0.0010960707440972328,
-0.03058442287147045,
-0.013304229825735092,
0.02687457762658596,
0.007900220341980457,
-0.009590966627001762,
-0.006129358895123005,
-0.029158074408769608,
0.01367550902068615,
0.049281228333711624,
-0.01957271248102188,
0.0035174652002751827,
-0.02613263949751854,
-0.023712415248155594,
-0.017497017979621887,
-0.040602318942546844,
0.027602605521678925,
-0.04192904382944107,
-0.030904129147529602,
-0.01782672107219696,
-0.04764802008867264,
-0.012644368223845959,
0.002252629492431879,
0.052659787237644196,
-0.03234664350748062,
-0.010505548678338528,
-0.002110555302351713,
-0.007089121732860804,
0.0036628085654228926,
-0.024541769176721573,
0.03746581822633743,
0.0028379696886986494,
-0.010815713554620743,
0.01853920891880989,
-0.014559420756995678,
-0.03350101038813591,
0.02890031598508358,
-0.011718646623194218,
-0.021484846249222755,
0.023845558986067772,
-0.04196922108530998,
-0.037673525512218475,
0.00972492340952158,
-0.01726270280778408,
0.007600755430757999,
0.06227250024676323,
-0.008445593528449535,
-0.003745243651792407,
-0.02202909253537655,
0.0058898115530610085,
-0.060926198959350586,
-0.012627411633729935,
-0.005926963407546282,
0.009105795994400978,
-0.024511853232979774,
0.046121735125780106,
0.09494733065366745,
-0.028117360547184944,
0.02579881064593792,
-0.037099260836839676,
-0.06804794073104858,
-0.019376827403903008,
0.013162052258849144,
0.03763224184513092,
-0.054980941116809845,
-0.011971862055361271,
-0.017384428530931473,
-0.003849074011668563,
0.06071574613451958,
-0.0006537960143759847,
0.04125163331627846,
0.024657821282744408,
0.022563109174370766,
-0.0065809437073767185,
0.013112290762364864,
-0.01566024124622345,
0.049615856260061264,
-0.0061224838718771935,
-0.004327167756855488,
-0.017588593065738678,
0.005137546453624964,
0.045143235474824905,
0.029436759650707245,
-0.011167241260409355,
-0.00186728045810014,
-0.027364781126379967,
0.04987518489360809,
0.017803849652409554,
-0.012223747558891773,
-0.017180318012833595,
0.0195759367197752,
0.019668957218527794,
-0.003693285631015897,
0.020208189263939857,
0.041553642600774765,
-0.01887461356818676,
-0.013797706924378872,
0.027524873614311218,
0.0077094025909900665,
0.04438217356801033,
-0.022046968340873718,
-0.012457508593797684,
-0.021636055782437325,
0.005708176176995039,
-0.019858798012137413,
-0.029784584417939186,
-0.06003331020474434,
-0.029874110594391823,
0.01086390484124422,
0.043604448437690735,
0.011166918091475964,
0.010670771822333336,
-0.0360536053776741,
-0.011003986932337284,
0.02385856956243515,
-0.03601652756333351,
-0.03182433545589447,
0.013979854993522167,
0.007927183993160725,
-0.007048079743981361,
0.011219847947359085
] |
<p>I wonder if there is a measure of how long a piece of metal takes to reach electrostatic equilibrium. </p>
<p>Does it depend on piece's size? Does it depend on the amount of imbalance?</p>
<p>Lots of websites and textbooks report "after a very short time". But how much short?</p>
<p>Thanks a lot</p> | 1,476 | [
-0.034310292452573776,
-0.011528588831424713,
0.013525720685720444,
-0.031166112050414085,
0.010677099227905273,
0.003910457249730825,
-0.03657156974077225,
-0.010646561160683632,
-0.00784419197589159,
0.0008354752790182829,
0.02474917843937874,
0.05986098200082779,
0.0446418896317482,
0.02908678911626339,
-0.041268330067396164,
0.0034010987728834152,
0.013497250154614449,
-0.02118985913693905,
-0.011282221414148808,
-0.02587125264108181,
0.01394194457679987,
-0.024879666045308113,
0.01967271789908409,
-0.020085832104086876,
-0.04207437112927437,
-0.0077922288328409195,
0.039883002638816833,
-0.03443905711174011,
0.03651861473917961,
0.03398262336850166,
-0.044389624148607254,
-0.038481611758470535,
0.03647297993302345,
-0.0006463617319241166,
0.04580068215727806,
0.00012075629638275132,
0.0151226120069623,
-0.08501522243022919,
-0.04449762403964996,
0.04459265619516373,
-0.008400652557611465,
-0.006717955227941275,
0.011524979956448078,
0.024262597784399986,
-0.0077035329304635525,
-0.01588410511612892,
-0.01860843040049076,
-0.03832167759537697,
0.03943308815360069,
-0.08080226927995682,
0.05858057364821434,
0.01557325478643179,
0.06281524151563644,
-0.012194804847240448,
0.03474876284599304,
-0.016263820230960846,
0.04772607609629631,
0.05766691640019417,
-0.01970331370830536,
-0.014085913076996803,
-0.0056717367842793465,
-0.0076979766599833965,
-0.009751185774803162,
-0.02589970827102661,
-0.01694329082965851,
0.06257414072751999,
-0.016256557777523994,
-0.03646732121706009,
0.04618970677256584,
0.01924603246152401,
-0.0011631702072918415,
0.005055807065218687,
0.03373240679502487,
0.019313765689730644,
0.005450188647955656,
-0.04253993183374405,
0.02974013239145279,
-0.0026764983776956797,
0.006393421906977892,
0.06318854540586472,
-0.05979849398136139,
0.02528386004269123,
0.027872132137417793,
0.029529202729463577,
0.03295100852847099,
-0.035161614418029785,
0.07937638461589813,
-0.033843714743852615,
0.020704682916402817,
0.03727803751826286,
0.006410763133317232,
0.012305524200201035,
0.02573772892355919,
-0.01362407673150301,
-0.010739495046436787,
0.009641267359256744,
0.003614378860220313,
0.05992504209280014,
0.005621080286800861,
0.01627517119050026,
0.048621948808431625,
-0.027416426688432693,
0.02121364325284958,
0.05495590344071388,
0.030455870553851128,
-0.027791520580649376,
-0.048224594444036484,
-0.0109706437215209,
0.021638888865709305,
0.004522762726992369,
-0.03387290984392166,
-0.0016620662063360214,
-0.003823366714641452,
-0.02311178669333458,
-0.008214391767978668,
-0.004094874020665884,
0.003037058748304844,
0.014278526417911053,
0.0535333976149559,
0.018745722249150276,
0.011413263157010078,
-0.04288928210735321,
0.050183773040771484,
-0.01866912469267845,
-0.06521058827638626,
0.013774696737527847,
0.022183969616889954,
0.006093896459788084,
-0.02070852741599083,
0.04497809708118439,
-0.0016512498259544373,
-0.03365971893072128,
0.024770742282271385,
-0.024320097640156746,
0.05130467563867569,
0.019939472898840904,
-0.06020089611411095,
-0.05774034932255745,
0.021884838119149208,
-0.017367057502269745,
-0.010481367819011211,
-0.06292808055877686,
-0.016152629628777504,
0.022353168576955795,
0.024609297513961792,
0.04355553165078163,
0.0011474109487608075,
-0.022959502413868904,
0.03458474576473236,
0.018633289262652397,
-0.05096888169646263,
-0.03282759338617325,
0.0537879578769207,
0.01327431295067072,
0.004086919128894806,
-0.03697533905506134,
0.02879396453499794,
0.053713198751211166,
0.04987535998225212,
-0.004090431146323681,
-0.012558642774820328,
0.005784597247838974,
-0.006782831158488989,
0.02577810175716877,
-0.023869389668107033,
-0.021378513425588608,
0.0761510506272316,
0.0003592969151213765,
-0.01830895058810711,
0.008037162013351917,
0.02747744880616665,
0.02145889587700367,
0.037035372108221054,
0.01998908445239067,
0.052260249853134155,
-0.008090286515653133,
-0.007220866158604622,
-0.019143473356962204,
0.008841616101562977,
-0.0022899049799889326,
-0.0475325845181942,
-0.04277825355529785,
0.007212960161268711,
0.026783253997564316,
-0.006475859321653843,
0.06327255815267563,
-0.02951272577047348,
-0.0064175850711762905,
-0.05307874456048012,
-0.0416736863553524,
-0.04529515653848648,
-0.07757247239351273,
0.02846316248178482,
0.010082542896270752,
-0.05494195222854614,
0.032614439725875854,
0.0004350571834947914,
-0.008617101237177849,
-0.055536940693855286,
-0.05364542454481125,
-0.019326796755194664,
-0.005099062342196703,
-0.004491116851568222,
-0.03581330180168152,
0.014827064238488674,
0.05685354396700859,
0.036390651017427444,
-0.003998607397079468,
0.03321043774485588,
-0.025615179911255836,
-0.0023483664263039827,
-0.0015828332398086786,
-0.030596652999520302,
0.03559241443872452,
0.012868734076619148,
-0.019462086260318756,
0.012707735411822796,
-0.02149631269276142,
0.05531572178006172,
0.03856630623340607,
0.02342459373176098,
0.10192736983299255,
0.03545980900526047,
0.022429509088397026,
0.0035312967374920845,
0.030361494049429893,
-0.001516312942840159,
0.010424189269542694,
0.00023953799973241985,
-0.03421600162982941,
-0.055030468851327896,
0.0021132570691406727,
0.017165344208478928,
0.056768059730529785,
-0.018673954531550407,
0.016467217355966568,
0.01866857148706913,
0.02214060164988041,
0.012466584332287312,
-0.007226084358990192,
-0.021485941484570503,
-0.033381909132003784,
0.012659701518714428,
0.004849456716328859,
-0.019125448539853096,
-0.008556141518056393,
0.028902210295200348,
0.029396647587418556,
0.01245499961078167,
0.004019415937364101,
0.0055068801157176495,
0.003422959242016077,
0.02572416514158249,
0.025004709139466286,
-0.026439320296049118,
-0.06497953832149506,
0.04359188675880432,
-0.016768041998147964,
0.015406429767608643,
-0.019864194095134735,
0.02921147085726261,
0.03563451021909714,
-0.025244833901524544,
0.03302285075187683,
0.024757783859968185,
-0.023739712312817574,
0.022211041301488876,
-0.03586313873529434,
0.025675978511571884,
-0.03766808286309242,
0.026932910084724426,
0.008522730320692062,
0.010702179744839668,
0.0014776760945096612,
-0.01191781461238861,
-0.00250989873893559,
0.0058560725301504135,
0.03226431831717491,
-0.00499670160934329,
-0.023546764627099037,
-0.022635897621512413,
-0.030939364805817604,
0.025957679376006126,
-0.0011672278633341193,
-0.010109854862093925,
-0.015616937540471554,
0.0012947811046615243,
-0.037722475826740265,
0.04333273693919182,
0.013512556441128254,
0.0282607264816761,
0.03183916583657265,
0.010259216651320457,
-0.05173012241721153,
0.018281543627381325,
0.011056400835514069,
-0.025607502087950706,
-0.053802039474248886,
-0.0027380783576518297,
0.0191801767796278,
0.0050930180586874485,
-0.02800200693309307,
0.03985251113772392,
-0.048132628202438354,
-0.025699563324451447,
-0.01279828604310751,
-0.007293506059795618,
0.014541898854076862,
-0.010629464872181416,
0.01426822692155838,
0.01853959448635578,
-0.011811386793851852,
-0.00704586785286665,
-0.045587532222270966,
-0.029464662075042725,
0.041772522032260895,
-0.0323588065803051,
0.04452011361718178,
-0.016459347680211067,
-0.04609902575612068,
0.0859508365392685,
-0.0073807695880532265,
-0.037491634488105774,
0.0028948914259672165,
0.0025196755304932594,
-0.020140230655670166,
0.01797572523355484,
0.007369081024080515,
0.0385730005800724,
0.005551517475396395,
0.00975267868489027,
-0.0008666333742439747,
0.030270598828792572,
0.02171109803020954,
0.00026610790519043803,
0.015107647515833378,
0.035488687455654144,
0.008621093817055225,
0.002598227234557271,
0.021486179903149605,
0.02612018771469593,
-0.048723094165325165,
-0.020957710221409798,
0.012368247844278812,
0.06976806372404099,
0.039034824818372726,
-0.05955950915813446,
0.041499506682157516,
-0.0408029779791832,
-0.008700469508767128,
-0.02194990962743759,
0.03164399415254593,
-0.02802346646785736,
-0.030061256140470505,
-0.014429330825805664,
0.022679820656776428,
0.05727895721793175,
0.006847790442407131,
0.00853896513581276,
0.05631709843873978,
0.056007035076618195,
-0.03276050090789795,
-0.04137982428073883,
0.0004939290229231119,
-0.0032072279136627913,
0.01734277419745922,
-0.056678079068660736,
-0.03616971895098686,
0.03304753080010414,
0.03216762840747833,
0.01748812198638916,
0.01805359125137329,
-0.02441108413040638,
0.010234925895929337,
-0.08124860376119614,
-0.037191007286310196,
0.029434677213430405,
0.04318433627486229,
-0.0038071549497544765,
0.056121986359357834,
0.033135656267404556,
0.012410502880811691,
-0.014049870893359184,
-0.0017592118820175529,
-0.0849096029996872,
0.029802625998854637,
-0.06162961199879646,
-0.0027909905184060335,
0.0019028342794626951,
-0.007361915893852711,
-0.04188361391425133,
-0.023726927116513252,
-0.0165457371622324,
0.007628368213772774,
0.03285055607557297,
-0.05090424790978432,
-0.005194918252527714,
-0.0010912298457697034,
-0.009799941442906857,
-0.0009364811703562737,
0.023215698078274727,
0.017252666875720024,
-0.024071302264928818,
0.013402612879872322,
0.022362399846315384,
-0.01717923954129219,
0.00580366887152195,
-0.016939492896199226,
0.015176620334386826,
-0.005697793792933226,
0.03125987946987152,
0.0058660046197474,
0.008440181612968445,
-0.04504813998937607,
0.013514712452888489,
0.009792734868824482,
0.05963459983468056,
-0.00010603926057228819,
-0.01281196903437376,
-0.049897342920303345,
-0.08178117871284485,
-0.025623926892876625,
-0.0028885260690003633,
0.050341278314590454,
0.006289020646363497,
0.010619007050991058,
-0.02029539830982685,
-0.029437478631734848,
-0.022992372512817383,
0.06667736172676086,
0.05097656324505806,
0.05479371175169945,
-0.02288249507546425,
-0.0592220202088356,
-0.01887698471546173,
-0.035869382321834564,
0.009475222788751125,
0.006809567101299763,
0.002314060227945447,
-0.019558286294341087,
-0.007542901206761599,
0.009267992340028286,
0.016269367188215256,
-0.013528537005186081,
-0.010984750464558601,
-0.0124092111364007,
0.01728076860308647,
-0.0021168463863432407,
0.010380669496953487,
0.06310554593801498,
0.00763089582324028,
0.07377815991640091,
0.015255904756486416,
-0.004472082480788231,
-0.07533691078424454,
0.013462597504258156,
0.06446662545204163,
0.027767261490225792,
-0.03418606519699097,
-0.0093512749299407,
-0.04675061255693436,
0.0012941360473632812,
0.0850411206483841,
-0.008899589069187641,
0.03373422846198082,
-0.05334445461630821,
0.01658560335636139,
-0.049658410251140594,
-0.025165483355522156,
-0.023788873106241226,
-0.00005096512541058473,
0.04347128048539162,
0.014742866158485413,
-0.0204506516456604,
-0.012146295048296452,
0.028144871816039085,
-0.021992245689034462,
0.053363583981990814,
0.04617234691977501,
-0.004339100327342749,
0.02398061193525791,
0.009187847375869751,
-0.028724566102027893,
0.00011279839964117855,
-0.07602766156196594,
-0.00038751569809392095,
-0.01063411682844162,
-0.02101292461156845,
-0.0010306192561984062,
-0.02193583734333515,
-0.04566987603902817,
0.04607051983475685,
0.012316620908677578,
0.028531957417726517,
0.007721221540123224,
-0.030741197988390923,
0.04244065284729004,
0.016910942271351814,
0.0022944726515561342,
0.03319379687309265,
-0.006017943844199181,
-0.01167080644518137,
0.008947119116783142,
0.013967652805149555,
0.04606780409812927,
-0.02777617797255516,
-0.012156345881521702,
-0.015046346001327038,
0.02694450318813324,
-0.028220731765031815,
0.06984059512615204,
0.002188913756981492,
0.009879322722554207,
-0.025728905573487282,
-0.016141759231686592,
0.027240298688411713,
-0.03184124827384949,
0.00922014843672514,
-0.008457491174340248,
0.0047672889195382595,
-0.001819294411689043,
0.020157640799880028,
-0.008163710124790668,
-0.008750712499022484,
-0.0015968347433954477,
0.035883158445358276,
0.02594260685145855,
-0.020129138603806496,
-0.002074343850836158,
-0.059309229254722595,
-0.0240323506295681,
0.013044866733253002,
-0.025562241673469543,
0.06349463015794754,
-0.03165634348988533,
-0.019979361444711685,
0.05632311850786209,
-0.08576084673404694,
-0.00923629105091095,
0.013946757651865482,
0.01586729846894741,
0.059683140367269516,
-0.057837747037410736,
0.032792333513498306,
0.04099900275468826,
0.002080349950119853,
-0.056866202503442764,
-0.06891932338476181,
0.05132867023348808,
0.008873043581843376,
-0.03545427694916725,
-0.014298518188297749,
0.0075725349597632885,
0.026486404240131378,
-0.042782656848430634,
0.03994600847363472,
0.032653406262397766,
-0.024335242807865143,
0.00877593457698822,
0.007643516641110182,
-0.020116012543439865,
0.08186507225036621,
-0.0047487677074968815,
-0.021291067823767662,
-0.022022567689418793,
-0.020680537447333336,
-0.013902338221669197,
-0.0041518365032970905,
0.036200150847435,
-0.017052005976438522,
-0.004068200010806322,
-0.003911721985787153,
-0.0347730852663517,
0.0349864661693573,
0.0008737093885429204,
-0.024008288979530334,
0.013312892988324165,
0.003734633792191744,
-0.010530403815209866,
0.01766432449221611,
0.06136385723948479,
-0.008643064647912979,
0.021040024235844612,
-0.014967428520321846,
-0.00604843208566308,
-0.01978863961994648,
-0.03910287842154503,
0.008265264332294464,
0.04066915810108185,
0.0034594014286994934,
-0.021710755303502083,
0.04347015544772148,
-0.002129372674971819,
-0.024181554093956947,
0.03655600920319557,
-0.014922226779162884,
-0.003547176718711853,
-0.022585393860936165,
-0.022511422634124756,
0.01751178689301014,
0.0013547939015552402,
0.006847287993878126,
-0.0696031004190445,
-0.0007589065935462713,
0.0011605235049501061,
0.030075525864958763,
-0.014434834942221642,
0.046461042016744614,
0.04612315818667412,
0.009549111127853394,
0.0067896475084125996,
-0.022081656381487846,
-0.019537823274731636,
-0.012093632481992245,
0.01351568941026926,
0.03195662051439285,
0.004210263025015593,
0.02181786298751831,
-0.0005044055287726223,
0.027356280013918877,
-0.042218588292598724,
0.0030825010035187006,
0.02731964737176895,
0.017135486006736755,
0.034103721380233765,
-0.011210324242711067,
-0.046936530619859695,
0.011343471705913544,
-0.02339453063905239,
0.05011406168341637,
-0.026766087859869003,
-0.030091090127825737,
-0.008539429865777493,
-0.01266903430223465,
0.025369921699166298,
-0.0662725493311882,
-0.0349845327436924,
-0.02900480106472969,
0.03308691084384918,
0.0011593899689614773,
-0.00689705228433013,
-0.05104667320847511,
0.06513193249702454,
0.006380842067301273,
0.011431491002440453,
0.021096695214509964,
0.018152274191379547,
-0.03799428418278694,
0.004192200023680925,
-0.034464601427316666,
-0.05529481917619705,
0.004027788061648607,
-0.011906604282557964,
-0.03957442566752434,
0.017148690298199654,
-0.015335953794419765,
0.054160214960575104,
0.028856171295046806,
0.0401172898709774,
-0.03110596351325512,
0.061802223324775696,
-0.022245831787586212,
0.03835853189229965,
-0.038661323487758636,
0.03962627798318863,
0.13280785083770752,
0.04218505695462227,
0.00021468200429808348,
-0.0163169763982296,
0.04965349659323692,
-0.018196405842900276,
-0.018218915909528732,
-0.043679576367139816,
-0.01648998260498047,
-0.05616898462176323,
-0.02478807605803013,
0.015160910785198212,
0.037129536271095276,
-0.01583542488515377,
-0.009439964778721333,
0.03111543320119381,
-0.007817267440259457,
-0.00868418999016285,
0.011068626306951046,
0.02991589717566967,
-0.02265627682209015,
0.019750695675611496,
-0.044899262487888336,
0.06193496286869049,
-0.02151760645210743,
-0.02147693745791912,
0.0024780137464404106,
0.011247887276113033,
0.024815276265144348,
0.004074416123330593,
-0.01926332153379917,
0.011951375752687454,
0.008193745277822018,
-0.029426060616970062,
-0.017443668097257614,
0.0364750474691391,
0.03838051110506058,
0.0027131971437484026,
0.011625824496150017,
0.03060907870531082,
0.003862833371385932,
0.0158370528370142,
0.005598447285592556,
0.02476975880563259,
-0.05154570937156677,
0.002379898214712739,
-0.012923508882522583,
-0.0005626080674119294,
-0.02070959098637104,
-0.0022690463811159134,
0.004704820457845926,
-0.0026286509819328785,
0.019089654088020325,
-0.04090767726302147,
-0.06708146631717682,
-0.022007018327713013,
-0.016150102019309998,
0.009020473808050156,
-0.006388178560882807,
-0.031039290130138397,
0.03140365332365036,
-0.02055133879184723,
-0.0286574549973011,
-0.027872363105416298,
-0.0004560686065815389,
0.019496191293001175,
0.019204163923859596,
0.02283516898751259,
-0.0024604015052318573,
-0.018422726541757584,
-0.03028685413300991,
-0.049038201570510864,
-0.03943945840001106,
-0.0025875649880617857,
-0.027886170893907547,
0.05468199402093887,
0.02514657750725746,
-0.017866333946585655,
-0.06177910417318344,
-0.022660033777356148,
-0.06293778121471405,
0.03880845010280609,
0.0070831323973834515,
-0.0052135419100522995,
-0.06236419454216957,
0.010168862529098988,
0.012611041776835918,
0.031208522617816925,
-0.03921688348054886,
0.05657247453927994,
0.0334465429186821,
0.030657298862934113,
-0.005688115488737822,
-0.025806492194533348,
0.0190353374928236,
0.005900919903069735,
-0.03210196644067764,
0.047094278037548065,
-0.010792490094900131,
0.027704861015081406,
0.01378523651510477,
-0.00028656129143200815,
0.05203862115740776,
0.03358291834592819,
-0.031277745962142944,
0.007491184398531914,
0.028022604063153267,
-0.010401732288300991,
-0.00204259785823524,
-0.010529504157602787,
-0.018551910296082497,
-0.042348627001047134,
-0.01602492481470108,
-0.040096938610076904,
-0.0032998870592564344,
0.00885033793747425,
0.008922350592911243,
-0.029990723356604576,
0.04865619167685509,
-0.018808798864483833,
-0.002507483819499612,
-0.024995600804686546,
-0.003664338495582342,
-0.060392361134290695,
-0.014805949293076992,
0.01085321418941021,
0.03892987221479416,
0.01874527335166931,
0.01875140890479088,
-0.01978594996035099,
-0.0012876124819740653,
0.027098480612039566,
0.0091713797301054,
0.01880997233092785,
-0.0007552249589934945,
0.01844191737473011,
0.018067648634314537,
0.046160995960235596,
-0.04778717830777168,
-0.019943874329328537,
0.041094135493040085,
-0.049210235476493835,
-0.01569625921547413,
0.01054361555725336,
-0.002043172949925065,
-0.013553977943956852,
0.04205096885561943,
0.00892954133450985,
0.006893843412399292,
0.06435732543468475,
0.0003069307713303715,
-0.026582807302474976,
-0.005302382167428732,
-0.026863515377044678,
-0.023453444242477417,
0.01926640048623085,
-0.00926743634045124,
-0.031239811331033707,
0.008703626692295074,
0.007282265927642584,
-0.01131931971758604,
-0.0001261680299649015,
-0.020357545465230942,
-0.013103586621582508,
-0.0034382534213364124,
-0.014690553769469261,
0.019169526174664497,
-0.015392741188406944,
0.00954451970756054,
0.08852044492959976,
-0.027112629264593124,
0.01156510878354311,
0.010617912746965885,
-0.038088131695985794,
-0.0852120891213417,
-0.021158920601010323,
0.010940535925328732,
0.00754555594176054,
0.018231185153126717,
-0.03305596858263016,
-0.01265805959701538,
0.01156992930918932,
-0.0855562835931778,
0.02269178256392479,
-0.04451027885079384,
-0.03640525043010712,
-0.023153508082032204,
-0.023099474608898163,
-0.008875090628862381,
0.015098397620022297,
0.003250712063163519,
0.0594048798084259,
0.05276898667216301,
0.05880609154701233,
-0.022470686584711075,
-0.0032430333085358143,
0.005525669548660517,
0.053018718957901,
0.01809864491224289,
-0.03344739228487015,
0.04952182248234749,
-0.04111830145120621,
0.0007478980114683509,
0.02965783327817917,
-0.021558843553066254,
0.01106447633355856,
-0.018750814720988274,
0.046123914420604706,
-0.0325179360806942,
0.008990336209535599,
-0.012289118021726608,
-0.02309156022965908,
-0.003634195076301694,
0.019115043804049492,
-0.018359269946813583,
0.016731727868318558,
-0.015104983933269978,
0.008037352003157139,
0.04329666122794151,
-0.03516320884227753,
-0.004708573222160339,
0.03864717483520508,
-0.03104451857507229,
-0.015245966613292694,
0.0014208258362486959,
0.015607286244630814,
0.009027458727359772,
-0.01865832880139351,
-0.0076763625256717205,
-0.008433444425463676,
-0.006542681250721216,
0.019156906753778458,
0.0060698105953633785,
-0.028964584693312645,
0.04557407647371292,
-0.0026803226210176945,
-0.016793685033917427,
0.013592327944934368,
0.015337317250669003,
-0.0037711539771407843,
-0.04837853088974953,
-0.009384920820593834,
-0.006962702609598637,
-0.004013349302113056,
-0.0016462591011077166,
-0.03192621469497681,
-0.0339985191822052,
0.05195964500308037,
0.013465511612594128,
-0.010012981481850147,
0.03169975057244301,
-0.060095567256212234,
-0.001086261821910739,
-0.06997156888246536,
0.021177807822823524,
-0.030781205743551254,
-0.025305679067969322,
-0.013240540400147438,
-0.06800972670316696,
0.002742165932431817,
0.012072943150997162,
0.04444624483585358,
-0.013120094314217567,
-0.02355467714369297,
-0.0011091240448877215,
-0.04737350717186928,
0.012831506319344044,
-0.03677939623594284,
0.0007292804657481611,
0.004460682161152363,
-0.008700042963027954,
0.0198589488863945,
-0.007537714205682278,
0.048711247742176056,
-0.05118897557258606,
0.01632707379758358,
-0.012621232308447361,
-0.010942668654024601,
-0.052847009152173996,
-0.023867497220635414,
0.05337835103273392,
0.013594275340437889,
0.00550931878387928,
0.0886065810918808,
-0.02019375190138817,
0.029697421938180923,
-0.009842834435403347,
0.011805376037955284,
-0.05901690572500229,
-0.004657288081943989,
-0.026266932487487793,
0.052372947335243225,
-0.02498576231300831,
-0.005094539374113083,
0.0032583503052592278,
-0.043663132935762405,
0.013111429288983345,
0.011797906830906868,
0.009182000532746315,
-0.012215028516948223,
0.04094313830137253,
0.005997398402541876,
0.05862268805503845,
-0.04159348085522652,
-0.004435817711055279,
0.017379503697156906,
-0.003984018228948116,
-0.0009260895312763751,
0.031454842537641525,
0.049005426466464996,
0.01150909997522831,
0.0184735469520092,
-0.007947864942252636,
-0.006216319277882576,
0.024483801797032356,
0.02531774342060089,
-0.0007949999999254942,
0.013669531792402267,
-0.030529214069247246,
0.014223743230104446,
-0.009976891800761223,
0.004461682867258787,
0.034535907208919525,
-0.0468142144382,
0.075129434466362,
-0.015331028029322624,
-0.00886914599686861,
0.008717861957848072,
0.017508117482066154,
-0.022286932915449142,
0.011246740818023682,
0.010228672996163368,
0.0388987734913826,
-0.036569613963365555,
-0.005023535806685686,
-0.019144508987665176,
0.04006274789571762,
0.0011306130327284336,
-0.03518037125468254,
0.0576072596013546,
0.010519828647375107,
0.04599708318710327,
-0.008796734735369682,
0.021318279206752777,
-0.0237937793135643,
-0.010321441106498241,
0.006264094263315201,
0.02661580592393875,
0.03021101839840412,
-0.0019038000609725714,
0.008392355404794216,
0.014503424987196922,
0.026926694437861443,
-0.07801960408687592,
-0.029961714521050453,
-0.054285164922475815,
0.0014171578222885728,
-0.03817123919725418,
0.018120253458619118
] |
<p>Electricity: I was wondering, whether we can pass electricity through air over a distance of 100 meters or so as electricity means the flow of electrons and we have seen the discharge or movement of electrons in a cathode ray tube</p> | 1,477 | [
-0.04861292243003845,
-0.0539802685379982,
0.02652125246822834,
0.002642057603225112,
0.031138911843299866,
-0.010771321132779121,
-0.02149033360183239,
-0.02936118096113205,
0.0328025259077549,
-0.018790055066347122,
0.03595994785428047,
0.05862515792250633,
0.037401385605335236,
0.008012602105736732,
0.0019491794519126415,
-0.004570760764181614,
-0.0199566762894392,
-0.015939410775899887,
-0.0020773119758814573,
-0.00908773671835661,
0.0007097057532519102,
0.013908700086176395,
-0.023061053827404976,
0.03292178735136986,
0.005684933625161648,
0.029514379799365997,
0.04471566528081894,
0.00866530742496252,
0.008734390139579773,
0.03015856444835663,
0.005747146904468536,
-0.0320756621658802,
0.0359523631632328,
0.03643582761287689,
0.028611065819859505,
-0.005480546969920397,
-0.03749314695596695,
-0.03397797793149948,
-0.04871409386396408,
0.011426335200667381,
-0.018163548782467842,
-0.05875068157911301,
0.0289057195186615,
0.030062537640333176,
-0.06070946529507637,
0.03093184530735016,
0.026061994954943657,
-0.03840247169137001,
0.020517023280262947,
-0.07865293323993683,
0.026591220870614052,
-0.005777769722044468,
0.04445713013410568,
0.019303686916828156,
0.015891410410404205,
0.014995536766946316,
0.08431578427553177,
0.04988660663366318,
-0.02687608078122139,
-0.024143319576978683,
0.011722514405846596,
-0.0058080279268324375,
-0.0197143517434597,
-0.04597504064440727,
-0.03246244415640831,
0.012711036950349808,
-0.0283941850066185,
-0.022295821458101273,
0.005591459106653929,
-0.012277290225028992,
0.021722080186009407,
0.034068427979946136,
0.012604440562427044,
0.02074725553393364,
0.02966049686074257,
-0.007900268770754337,
0.015422656200826168,
-0.00549188582226634,
0.047220613807439804,
0.08037765324115753,
-0.023392178118228912,
-0.025526661425828934,
0.02668668143451214,
0.002030901610851288,
0.007270046975463629,
-0.03267272189259529,
0.08592641353607178,
-0.0021134810522198677,
0.019212085753679276,
-0.0066712601110339165,
0.0050646099261939526,
-0.025688622146844864,
0.014319679699838161,
0.005931356456130743,
-0.011664447374641895,
0.02138836309313774,
-0.023751018568873405,
0.04317111521959305,
0.0092784333974123,
-0.01721232570707798,
0.04493808001279831,
0.040173497051000595,
0.07204987853765488,
0.05522311478853226,
0.025641921907663345,
-0.032347820699214935,
-0.014131552539765835,
-0.008070340380072594,
0.019447507336735725,
0.012032253667712212,
-0.04453964903950691,
0.013728084042668343,
-0.011612813919782639,
-0.008610010147094727,
0.007392886094748974,
-0.008611875586211681,
0.008588945493102074,
-0.035973627120256424,
0.03556949272751808,
0.08875107020139694,
0.034681499004364014,
-0.03945491835474968,
0.05638056620955467,
-0.008869415149092674,
-0.06685483455657959,
0.01731543056666851,
0.0063610076904296875,
0.0025869072414934635,
-0.03364516422152519,
0.03592284396290779,
-0.027632998302578926,
0.012301111593842506,
0.002435117494314909,
-0.004534817300736904,
0.06967215985059738,
0.004299100022763014,
-0.09978537261486053,
-0.06327366828918457,
0.006718879099935293,
0.023440418764948845,
-0.006688838358968496,
-0.08778107166290283,
0.04652424529194832,
0.004961698781698942,
0.05955846980214119,
0.013331957161426544,
-0.009255406446754932,
-0.023483743891119957,
0.018903007730841637,
0.00039537210250273347,
-0.03947072848677635,
0.00018300516239833087,
0.043711453676223755,
-0.018332595005631447,
0.04274749010801315,
-0.04008188471198082,
0.0010976474732160568,
0.04804378002882004,
0.016706038266420364,
-0.0421457402408123,
0.03369765356183052,
-0.02497703768312931,
0.002934814663603902,
-0.008412383496761322,
-0.010503958910703659,
-0.03373014181852341,
0.06401377171278,
0.017465533688664436,
0.02865104004740715,
0.03602191060781479,
0.040080565959215164,
0.04441177845001221,
0.0019085011444985867,
-0.02597111649811268,
0.04400761052966118,
-0.03521491214632988,
-0.015131469815969467,
-0.03774842247366905,
0.009962508454918861,
0.01985221914947033,
-0.04369741678237915,
-0.017823224887251854,
0.03868052363395691,
0.03845683112740517,
0.013207472860813141,
0.06460202485322952,
-0.011320838704705238,
-0.023311855271458626,
0.016770465299487114,
-0.03288685530424118,
-0.029177777469158173,
-0.023740354925394058,
0.05216551944613457,
-0.02515004202723503,
0.021742915734648705,
-0.004917307756841183,
-0.027640147134661674,
0.005838377866894007,
-0.07265609502792358,
-0.0291569996625185,
-0.009744998067617416,
0.050201691687107086,
0.009758122265338898,
-0.02235516905784607,
0.007027049083262682,
0.07629856467247009,
0.01880231313407421,
0.020642252638936043,
0.01716756261885166,
-0.0015462531009688973,
-0.013701348565518856,
-0.011050072498619556,
-0.04899271950125694,
0.0334143191576004,
0.037209708243608475,
0.004149103071540594,
0.036363158375024796,
0.01432407833635807,
-0.009721118025481701,
0.02496967650949955,
-0.011192642152309418,
0.10300560295581818,
0.040965352207422256,
0.027824295684695244,
0.0054477788507938385,
0.053409088402986526,
0.028317883610725403,
-0.01668427139520645,
0.006634035147726536,
-0.03510856255888939,
-0.08196812123060226,
-0.011454467661678791,
0.03832443431019783,
-0.014590628445148468,
-0.021020835265517235,
0.017914649099111557,
0.005211460869759321,
0.03149260953068733,
0.03968269005417824,
0.03580332547426224,
0.004061377607285976,
-0.037769533693790436,
-0.020291997119784355,
0.010842595249414444,
-0.009976653382182121,
0.017562616616487503,
0.04312874376773834,
0.026720618829131126,
0.02535834163427353,
-0.001964021474123001,
-0.016215570271015167,
0.0330335795879364,
-0.028083063662052155,
0.03132759779691696,
-0.0176706463098526,
-0.005622255615890026,
0.04127577692270279,
-0.06661645323038101,
0.0023740536998957396,
-0.01490769349038601,
0.0042909602634608746,
0.019457831978797913,
-0.005072471685707569,
0.0038578028324991465,
0.011330793611705303,
0.02852742001414299,
-0.008850177749991417,
-0.00020001381926704198,
0.02425072342157364,
-0.07562385499477386,
-0.007643215358257294,
-0.028367456048727036,
0.02824115939438343,
-0.03252513334155083,
0.0028091936837881804,
0.06610874831676483,
0.046716008335351944,
0.05350575968623161,
-0.020853931084275246,
-0.06580045074224472,
-0.037303775548934937,
-0.06135635823011398,
0.004864687565714121,
0.014175795949995518,
0.001842751051299274,
0.03493360057473183,
-0.019571520388126373,
-0.029534397646784782,
0.05048597604036331,
-0.027138881385326385,
0.009065099991858006,
0.032604388892650604,
-0.028481902554631233,
-0.03348333761096001,
0.03397323936223984,
-0.01846597157418728,
0.018701812252402306,
0.00988057442009449,
-0.01939593069255352,
0.059634845703840256,
-0.010558349080383778,
0.00037445477209985256,
0.027199646458029747,
-0.04091225191950798,
-0.04743707925081253,
-0.02513504959642887,
0.014422516338527203,
0.024328896775841713,
-0.045828238129615784,
0.02389260195195675,
0.0003072130202781409,
-0.05395166575908661,
-0.0007071275031194091,
-0.023205876350402832,
-0.021447673439979553,
0.03360600769519806,
0.012973474338650703,
0.02742776647210121,
-0.01501905545592308,
-0.027971409261226654,
0.032892290502786636,
0.005829385947436094,
-0.053453054279088974,
0.0022025438956916332,
-0.04233928769826889,
-0.029761891812086105,
-0.002076147822663188,
-0.033775269985198975,
0.03146074712276459,
-0.006816220469772816,
0.0018398610409349203,
0.05175161734223366,
0.031084241345524788,
0.0008590143988840282,
-0.004171718843281269,
-0.01512556616216898,
-0.016530735418200493,
0.02037539705634117,
-0.013744553551077843,
0.07311488687992096,
0.005746765527874231,
-0.02823576331138611,
0.01955198310315609,
-0.028519487008452415,
0.013858401216566563,
0.039454080164432526,
-0.021213220432400703,
0.048131801187992096,
-0.008639848791062832,
0.015136473812162876,
-0.024769699200987816,
0.039515841752290726,
0.00432709651067853,
0.00524848373606801,
-0.0026341229677200317,
0.00892749335616827,
0.07013991475105286,
-0.018346255645155907,
-0.0230634193867445,
0.02422274835407734,
0.1254604458808899,
-0.022618800401687622,
-0.030983906239271164,
0.023424169048666954,
0.028990251943469048,
0.027708884328603745,
0.016647610813379288,
-0.030169110745191574,
0.0044146026484668255,
0.03953973576426506,
0.01806604117155075,
0.022758005186915398,
-0.019671481102705002,
0.002034292556345463,
-0.06432579457759857,
-0.013257740996778011,
-0.03093716874718666,
0.030701830983161926,
-0.00007146275311242789,
0.04722297936677933,
0.05773652717471123,
0.02539798989892006,
0.022116614505648613,
0.012001781724393368,
-0.06282930821180344,
-0.014659290201961994,
-0.02950667403638363,
-0.024505650624632835,
-0.0211725402623415,
0.00317842373624444,
-0.027223680168390274,
0.01971825584769249,
-0.004324077162891626,
-0.026631951332092285,
-0.033966463059186935,
-0.05133052542805672,
-0.001823220169171691,
-0.04511973261833191,
-0.04470747709274292,
-0.047988515347242355,
0.01628902554512024,
0.00555841252207756,
0.003762907348573208,
0.025838160887360573,
0.01659417524933815,
0.002060215687379241,
-0.018282176926732063,
0.0055730608291924,
-0.008559571579098701,
-0.010473983362317085,
0.024623267352581024,
0.017492957413196564,
-0.027536438778042793,
-0.0458536222577095,
0.010505249723792076,
-0.010030729696154594,
0.035554446280002594,
-0.032157912850379944,
0.0023703002370893955,
-0.044672057032585144,
-0.02840939350426197,
-0.019166989251971245,
-0.029366347938776016,
0.00448628282174468,
0.009876602329313755,
0.021258044987916946,
0.008751464076340199,
-0.024513736367225647,
-0.03850094601511955,
0.03574642911553383,
0.024108830839395523,
0.018252750858664513,
-0.023904506117105484,
-0.037029750645160675,
-0.006525557022541761,
-0.021535726264119148,
-0.02111745998263359,
0.030117174610495567,
0.01198431197553873,
-0.01651492528617382,
0.0006577839958481491,
0.030610989779233932,
0.00821262039244175,
-0.03936517611145973,
0.016069816425442696,
0.016104836016893387,
-0.008985590189695358,
-0.004764189012348652,
-0.02101731114089489,
-0.017387887462973595,
-0.013465783558785915,
0.017103826627135277,
0.004197925794869661,
-0.028890196233987808,
-0.08559439331293106,
0.011558831669390202,
0.04184336960315704,
0.05727531388401985,
-0.04657857120037079,
-0.016378046944737434,
-0.042490050196647644,
0.007702384144067764,
0.011769003234803677,
0.003615566762164235,
-0.0008530562627129257,
-0.08974616974592209,
-0.02380061149597168,
-0.04457445442676544,
-0.07254314422607422,
0.0058230264112353325,
0.032017067074775696,
0.028211167082190514,
-0.012461159378290176,
0.011799866333603859,
-0.009899833239614964,
0.014395512640476227,
0.028186311945319176,
0.04557210952043533,
0.06729986518621445,
0.05079909414052963,
0.009504357352852821,
-0.021942202001810074,
-0.006006913725286722,
-0.02162276767194271,
-0.055976297706365585,
-0.0055625466629862785,
0.020376402884721756,
-0.04273270443081856,
0.016077296808362007,
-0.01434664148837328,
-0.024006042629480362,
0.03136935085058212,
-0.006466432474553585,
0.010228199884295464,
-0.015463804826140404,
-0.016702840104699135,
0.01665523648262024,
0.03915974870324135,
-0.0010250948835164309,
0.0717935711145401,
0.020080018788576126,
-0.052500590682029724,
0.011041647754609585,
0.026061048731207848,
0.05448708310723305,
-0.01258778478950262,
-0.03283405676484108,
-0.006642715074121952,
0.012699797749519348,
-0.011511839926242828,
0.03827022388577461,
-0.01134581584483385,
0.017776641994714737,
-0.013944955542683601,
-0.055503252893686295,
-0.020066983997821808,
0.02207350730895996,
0.030099576339125633,
-0.008700716309249401,
-0.030796384438872337,
0.030621536076068878,
-0.020492957904934883,
-0.06480167806148529,
-0.004859712906181812,
0.009755967184901237,
0.03166399151086807,
0.034283772110939026,
-0.019040631130337715,
-0.016694458201527596,
-0.05204761400818825,
0.02063640020787716,
0.010392148047685623,
-0.05625408887863159,
0.06044694781303406,
-0.007082738447934389,
-0.03846287354826927,
0.0181452427059412,
-0.059987153857946396,
-0.05609414353966713,
0.027318382635712624,
0.00005581636287388392,
0.03851497545838356,
-0.04871515557169914,
0.05159038305282593,
-0.016340354457497597,
0.008664127439260483,
-0.054018035531044006,
-0.05295699089765549,
0.04374265670776367,
0.06491078436374664,
-0.0010899988701567054,
-0.03698107972741127,
-0.011269801296293736,
-0.056655365973711014,
-0.02599094621837139,
-0.01292460411787033,
0.03186214715242386,
-0.027763789519667625,
0.034348856657743454,
-0.0020115594379603863,
-0.0013340121367946267,
0.04737569019198418,
0.01755141280591488,
-0.022985311225056648,
0.014495516195893288,
-0.0022163954563438892,
0.013547173701226711,
-0.018982240930199623,
0.03708432987332344,
-0.03237174451351166,
-0.020810099318623543,
0.01500619761645794,
-0.017992421984672546,
-0.0025173132307827473,
-0.049357131123542786,
-0.014340239576995373,
0.03167317062616348,
-0.024864571169018745,
-0.013058282434940338,
0.024012064561247826,
0.06114485114812851,
-0.013840309344232082,
0.024473518133163452,
-0.036194249987602234,
0.02208862081170082,
-0.04751758277416229,
-0.034615419805049896,
0.02014762908220291,
0.018586670979857445,
0.016654785722494125,
-0.0062584890983998775,
0.029072297737002373,
-0.02613016590476036,
0.0008729946566745639,
0.017847875133156776,
0.012271445244550705,
0.041924476623535156,
-0.02407580241560936,
0.004618842154741287,
0.021566035225987434,
0.01206078939139843,
0.021659934893250465,
-0.024637063965201378,
0.0016198891680687666,
-0.03891536593437195,
0.03500045835971832,
-0.003065986093133688,
0.0595584399998188,
-0.013745076954364777,
0.011499660089612007,
0.023541178554296494,
-0.00004509870268520899,
-0.02281266637146473,
0.03600672632455826,
-0.0034758017864078283,
0.006115166004747152,
0.021105218678712845,
0.052296288311481476,
0.013278665021061897,
0.054640039801597595,
0.028635170310735703,
-0.02424970082938671,
0.012204097583889961,
0.04035941883921623,
0.035314179956912994,
-0.017146650701761246,
-0.04713864624500275,
0.020067967474460602,
-0.0648401603102684,
0.016799042001366615,
-0.0027674792800098658,
-0.011536638252437115,
0.018171420320868492,
-0.008314179256558418,
-0.007851487025618553,
-0.04494071751832962,
-0.004261536058038473,
-0.05973410978913307,
-0.0007222655694931746,
-0.004492678213864565,
0.03603176772594452,
-0.02162211760878563,
-0.01494696643203497,
0.015776364132761955,
-0.005334340035915375,
0.007994763553142548,
0.029352551326155663,
-0.05517435073852539,
-0.036343056708574295,
-0.010327085852622986,
-0.031431250274181366,
0.055671434849500656,
-0.0020973377395421267,
-0.005041839554905891,
-0.005022036377340555,
-0.01793007366359234,
0.06332635879516602,
0.012072799727320671,
0.02083156630396843,
-0.019213970750570297,
0.07982417196035385,
0.0016234138747677207,
0.03324722871184349,
0.0019450810505077243,
0.044348448514938354,
0.10080979764461517,
0.020620644092559814,
0.008613644167780876,
-0.043488454073667526,
-0.022270645946264267,
-0.035868071019649506,
0.007061247248202562,
-0.04492230713367462,
-0.0060963439755141735,
-0.02530207671225071,
0.02929016761481762,
0.027494579553604126,
0.04778629168868065,
0.013564550317823887,
0.033380262553691864,
0.06158323213458061,
-0.03916303068399429,
-0.02166655845940113,
0.011224258691072464,
0.0014912850456312299,
-0.014970531687140465,
0.03305813670158386,
-0.03877877816557884,
0.038462698459625244,
-0.06678038835525513,
0.00963470246642828,
0.00834865216165781,
-0.06362410634756088,
0.051874175667762756,
-0.016242682933807373,
-0.05037211254239082,
-0.027748199179768562,
0.02807372435927391,
-0.021338356658816338,
-0.045747678726911545,
0.005100159905850887,
0.041858453303575516,
0.006024835631251335,
-0.01476447656750679,
0.03516419604420662,
0.004144362173974514,
0.008682280778884888,
-0.00244641350582242,
0.0322987325489521,
-0.05868249386548996,
-0.031088612973690033,
-0.009973172098398209,
-0.009639725089073181,
-0.009175902232527733,
0.02705124020576477,
0.008252153173089027,
0.04409532994031906,
0.015374096110463142,
-0.03120652213692665,
-0.021458309143781662,
-0.028598856180906296,
0.021191159263253212,
-0.010766863822937012,
-0.017404107376933098,
-0.06737692654132843,
0.02891700342297554,
-0.013830035924911499,
0.018627259880304337,
-0.017089953646063805,
0.011937441304326057,
0.016229839995503426,
0.03929920867085457,
0.02700529620051384,
-0.04575740173459053,
-0.049673981964588165,
-0.00820915400981903,
-0.0029684994369745255,
-0.03585968166589737,
0.004491550847887993,
0.031144550070166588,
0.061064548790454865,
0.021340325474739075,
0.002844166476279497,
-0.01608191803097725,
0.009573654271662235,
-0.03250590339303017,
0.017410211265087128,
0.022469861432909966,
0.015453004278242588,
-0.006722174119204283,
-0.014421866275370121,
-0.011855688877403736,
0.012789168395102024,
-0.014244306832551956,
-0.005872377194464207,
-0.012136762961745262,
0.027562931180000305,
0.01834583841264248,
-0.03658444806933403,
-0.0324084497988224,
0.0013700859853997827,
-0.048089783638715744,
0.0199006088078022,
-0.016724783927202225,
0.05597493797540665,
0.033863719552755356,
-0.006552277598530054,
-0.006029854528605938,
-0.015320554375648499,
-0.02139933779835701,
0.008855486288666725,
0.027277423068881035,
-0.055161040276288986,
-0.012435940094292164,
0.00215122546069324,
0.008960929699242115,
-0.009022952988743782,
-0.023344554007053375,
-0.04072462394833565,
0.011719114147126675,
-0.0018433466320857406,
0.014788403175771236,
0.005956845823675394,
0.03284430503845215,
-0.013943113386631012,
0.012701917439699173,
-0.032367825508117676,
0.01495581679046154,
-0.04713526368141174,
0.01785566657781601,
-0.002749898936599493,
-0.03295118734240532,
0.0014242613688111305,
0.007179110310971737,
-0.04451223835349083,
0.02186395600438118,
0.017431484535336494,
0.03502647578716278,
0.012695161625742912,
-0.01832726038992405,
0.008805930614471436,
0.005836856085807085,
0.021145930513739586,
-0.026220260187983513,
-0.03086976893246174,
0.05083651468157768,
-0.02648063190281391,
-0.04185117781162262,
0.04156023636460304,
-0.0031413377728313208,
0.03798161819577217,
0.029012531042099,
-0.04395350441336632,
-0.0014756995951756835,
0.07942494750022888,
0.01970289647579193,
-0.0003638402558863163,
-0.006926138885319233,
-0.03798116743564606,
-0.0049232360906898975,
-0.005597075913101435,
0.01428527757525444,
-0.054462090134620667,
-0.006579370237886906,
0.02755107171833515,
0.034320756793022156,
0.004405486397445202,
0.02011723630130291,
0.0038386874366551638,
-0.039520226418972015,
0.005816183518618345,
0.03687560185790062,
0.00015548495866823941,
0.021104643121361732,
0.05181324481964111,
-0.004580426961183548,
0.025053540244698524,
0.005669532809406519,
-0.010805000551044941,
-0.08397403359413147,
0.008956522680819035,
0.02223937213420868,
-0.016091404482722282,
0.016042858362197876,
-0.0514339953660965,
0.026017652824521065,
0.018126225098967552,
-0.088371142745018,
0.009325061924755573,
-0.01741562783718109,
0.000486782199004665,
-0.019511576741933823,
0.026919271796941757,
0.0007786456262692809,
0.014417878352105618,
0.02607690915465355,
0.0490042008459568,
-0.004530276171863079,
0.020341064780950546,
0.028445061296224594,
-0.014158056117594242,
-0.049897342920303345,
0.029736757278442383,
-0.004821552895009518,
-0.019554555416107178,
0.057894282042980194,
-0.03418203070759773,
0.0043935710564255714,
0.01649048551917076,
0.013117806054651737,
0.03480317443609238,
-0.010710312984883785,
0.0032013875897973776,
0.008459862321615219,
0.01882099360227585,
-0.01680791936814785,
0.012075847014784813,
-0.03474538400769234,
0.027296343818306923,
-0.003570239758118987,
0.012443073093891144,
-0.028661079704761505,
-0.008884342387318611,
0.011970051564276218,
-0.030899079516530037,
-0.046322327107191086,
0.005175828468054533,
-0.04170212894678116,
-0.04909701272845268,
0.011964789591729641,
0.026791224256157875,
0.00942918285727501,
-0.004753067623823881,
-0.019884897395968437,
-0.03425638750195503,
-0.018162038177251816,
0.01280131284147501,
-0.04079551622271538,
-0.003264394588768482,
0.0171856377273798,
-0.02485397830605507,
-0.016262348741292953,
0.019398685544729233,
-0.014365934766829014,
-0.005324698053300381,
-0.010958236642181873,
-0.014435259625315666,
0.0035888722632080317,
0.03097664937376976,
0.009801920503377914,
-0.04024200141429901,
-0.019941242411732674,
-0.004590757191181183,
0.012460741214454174,
0.025904709473252296,
0.044377878308296204,
-0.008165949024260044,
0.0009994495194405317,
-0.035558316856622696,
0.01655217632651329,
-0.023342546075582504,
-0.013569909147918224,
-0.040305882692337036,
-0.02820468693971634,
0.001322577241808176,
0.01399211399257183,
0.08990165591239929,
-0.025503413751721382,
-0.030748527497053146,
0.011696734465658665,
0.02010602131485939,
0.039741985499858856,
-0.0211088377982378,
0.013153781183063984,
-0.020355848595499992,
-0.06637986749410629,
-0.02044529654085636,
-0.008023403584957123,
-0.030591977760195732,
0.019804760813713074,
0.01169194933027029,
-0.0024420274421572685,
0.030707374215126038,
-0.03579319268465042,
-0.025448594242334366,
0.005380819085985422,
0.0578158013522625,
-0.03786072880029678,
0.018999595195055008,
0.005190270021557808,
-0.01277871336787939,
-0.006354693789035082,
-0.013146486133337021,
-0.020006058737635612,
0.03251867741346359,
-0.02023807168006897,
0.022565675899386406,
-0.025611024349927902,
-0.0025564744137227535,
0.015098156407475471,
-0.06198796629905701,
0.0026878113858401775,
0.024029430001974106,
-0.032310325652360916,
0.021388117223978043,
0.07105762511491776,
0.008656671270728111,
0.01883842796087265,
-0.015050193294882774,
-0.0028378369752317667,
0.0011353937443345785,
-0.003669549711048603,
-0.058434151113033295,
0.03371461480855942,
0.04908579960465431,
-0.04103059694170952,
0.007374880835413933,
0.0038369137328118086,
0.03400641679763794,
0.0002761200303211808,
0.013375403359532356,
0.03928011283278465,
-0.020913071930408478,
-0.01785333640873432,
-0.004868714138865471,
0.002307840157300234,
-0.037272363901138306,
0.03967086970806122,
-0.04277603700757027,
0.08889805525541306,
-0.017155427485704422,
0.023852964863181114,
-0.0005614245892502367,
0.017379503697156906,
-0.020754650235176086,
0.011216551996767521,
0.005031553562730551,
0.03259264677762985,
0.011930747888982296,
0.00592684606090188,
-0.03254946693778038,
-0.0017658573342487216,
0.0008297645836137235,
-0.052504707127809525,
0.013935171999037266,
-0.04632003977894783,
-0.005539858713746071,
-0.041231539100408554,
-0.012297791428864002,
-0.0028400137089192867,
0.006242615636438131,
0.036294613033533096,
0.015182874165475368,
0.03160201385617256,
0.011383824050426483,
-0.012327640317380428,
-0.00823303870856762,
0.06308595091104507,
-0.07152928411960602,
0.0010636602528393269,
-0.018650485202670097,
0.012007616460323334,
0.005880184005945921,
0.001672859420068562
] |
<p>In Griffiths's <em>Introduction to Quantum Mechanics</em>, he says that the time dependence of an expectation value is
$$\frac{d\langle Q\rangle}{dt}=\frac{i}{\hbar}\langle [H,Q]\rangle+\langle \frac{\partial Q}{\partial t}\rangle$$
And I also saw a lecture note saying that time dependence of an expectation value is:
$$\frac{\partial}{\partial t}\langle \hat{Q}(t)\rangle=-\frac{i}{h}\langle [\hat{Q}, \hat{H}]\rangle$$</p>
<p>I know they are saying the same thing. For me the second one is quite easy to understand. But how can I understand the first one? </p> | 1,478 | [
0.030756695196032524,
-0.058837298303842545,
0.034264206886291504,
-0.03754948079586029,
0.03548075258731842,
0.030943075194954872,
-0.023212775588035583,
0.04588787630200386,
0.03549571707844734,
-0.01955624483525753,
0.03510073572397232,
0.05032416060566902,
0.07085656374692917,
-0.03577283024787903,
0.02407165989279747,
0.03789227083325386,
0.01694513112306595,
-0.027041858062148094,
-0.040314365178346634,
-0.004669736605137587,
0.023681219667196274,
0.05327537655830383,
0.019989434629678726,
0.0029294616542756557,
-0.011927814222872257,
0.023917706683278084,
0.02882334589958191,
-0.0021924502216279507,
0.026972023770213127,
0.08307702839374542,
-0.016247833147644997,
-0.026870964094996452,
-0.022637315094470978,
0.030597979202866554,
-0.015457553789019585,
-0.008635369129478931,
-0.024957865476608276,
-0.05133781582117081,
-0.009525161236524582,
0.02075445093214512,
-0.05960606411099434,
-0.013182633556425571,
0.0017356054158881307,
0.04011664539575577,
-0.030879592522978783,
0.012811943888664246,
0.044568512588739395,
-0.04169370234012604,
0.02362189069390297,
-0.06835838407278061,
0.07929034531116486,
-0.0030999404843896627,
0.04471792280673981,
0.032541655004024506,
-0.042167965322732925,
0.0038643996231257915,
0.04076763242483139,
0.07291018217802048,
-0.00597456144168973,
-0.08229333907365799,
-0.032020069658756256,
-0.03055933304131031,
-0.018052639439702034,
-0.01827184483408928,
-0.003008689032867551,
0.003593653440475464,
0.01718265563249588,
-0.005911926738917828,
0.01567879319190979,
-0.02155967988073826,
0.015628429129719734,
0.02749161422252655,
0.07449710369110107,
-0.02564326860010624,
0.028410479426383972,
-0.008483869023621082,
0.038793228566646576,
0.02705768309533596,
0.045202456414699554,
0.004453191068023443,
0.014711662195622921,
0.01777440868318081,
0.04110247269272804,
0.035452164709568024,
-0.015984928235411644,
-0.010388985276222229,
0.07804352790117264,
0.0059166825376451015,
0.01707635633647442,
0.03383631631731987,
-0.03046410158276558,
0.05597484111785889,
0.022074652835726738,
-0.01906725950539112,
-0.01191861554980278,
0.03090684302151203,
0.022117070853710175,
0.051409486681222916,
-0.007165816146880388,
-0.02098526805639267,
-0.005962829105556011,
-0.04669186845421791,
0.011951464228332043,
0.05112261697649956,
-0.006576594430953264,
-0.012058956548571587,
-0.03696261718869209,
0.030011113733053207,
-0.020142314955592155,
-0.021327871829271317,
-0.024363169446587563,
0.040258873254060745,
-0.0019735731184482574,
0.0230976901948452,
-0.027599168941378593,
-0.01653883047401905,
0.015207653865218163,
0.0047963401302695274,
0.05603015422821045,
0.05157902091741562,
0.0012577493907883763,
-0.02636132761836052,
0.025173643603920937,
-0.0042547499760985374,
-0.07891460508108139,
0.029408473521471024,
0.05309690162539482,
-0.005304940510541201,
-0.02381729893386364,
0.03707962483167648,
0.007507840637117624,
-0.0021778387017548084,
0.01319095678627491,
0.0378120020031929,
0.021853169426321983,
-0.02994704432785511,
-0.09435729682445526,
-0.051670704036951065,
0.009401766583323479,
-0.007554659154266119,
-0.00007212012133095413,
-0.06990513205528259,
-0.005732215475291014,
0.061900749802589417,
0.04155158996582031,
0.017877444624900818,
0.037247516214847565,
0.003243438433855772,
0.02423487976193428,
0.0031323565635830164,
-0.03175836428999901,
-0.046331413090229034,
0.00003747998925973661,
0.00299995020031929,
0.01481983345001936,
-0.0555013045668602,
0.01024577021598816,
0.039304737001657486,
-0.002141968347132206,
-0.027320658788084984,
0.06317904591560364,
-0.03647138178348541,
-0.04094485938549042,
0.03982602432370186,
-0.014780045486986637,
-0.0328175388276577,
0.07366964221000671,
0.015696896240115166,
0.0006695393240079284,
0.036023352295160294,
0.03650816157460213,
0.006718218792229891,
-0.017100108787417412,
0.037691425532102585,
0.00590071827173233,
-0.04040290415287018,
-0.011945478618144989,
-0.01663588359951973,
0.013943216763436794,
0.008170903660356998,
-0.02049676887691021,
-0.028624480590224266,
-0.017352676019072533,
0.011415394023060799,
-0.018194502219557762,
-0.0007124338881112635,
0.028344642370939255,
0.003503119107335806,
-0.03376245126128197,
-0.030011314898729324,
-0.034302886575460434,
-0.06638677418231964,
0.03257341682910919,
-0.0071303085424005985,
0.00752932159230113,
0.021751701831817627,
0.015730146318674088,
-0.00041665794560685754,
-0.012520985677838326,
-0.061162255704402924,
0.015858130529522896,
-0.024690983816981316,
0.00031161733204498887,
-0.05000925436615944,
0.03885789215564728,
0.05262205749750137,
0.022334806621074677,
0.007235766388475895,
0.04603740572929382,
-0.03899778798222542,
-0.010967900976538658,
0.029498402029275894,
-0.03046344220638275,
0.05654524266719818,
0.03378923237323761,
-0.04049539193511009,
0.011688093654811382,
-0.03782063350081444,
0.00009944380872184411,
-0.0056587038561701775,
-0.008445297367870808,
0.04348716139793396,
0.04570852592587471,
-0.003359314287081361,
-0.020296143367886543,
0.029431525617837906,
0.022430049255490303,
0.0016301637515425682,
-0.004007074050605297,
-0.03502502292394638,
-0.020939592272043228,
0.013539032079279423,
0.04492466524243355,
0.022194907069206238,
-0.019772831350564957,
0.030342958867549896,
0.032200537621974945,
0.023015648126602173,
0.017806969583034515,
0.0258332509547472,
-0.020063158124685287,
-0.003254928858950734,
0.024382391944527626,
0.014003857038915157,
-0.016614895313978195,
0.0019579732324928045,
0.04109319671988487,
-0.01694140024483204,
0.03661918640136719,
-0.007933469489216805,
-0.03205510601401329,
0.05662053823471069,
-0.023809874430298805,
0.01336701586842537,
0.009485725313425064,
-0.04651661962270737,
0.03863057866692543,
-0.03941060230135918,
-0.0026833952870219946,
0.019432485103607178,
-0.024124234914779663,
-0.012012758292257786,
-0.020608073100447655,
-0.03630777820944786,
0.0094836987555027,
-0.010330735705792904,
-0.02372371405363083,
0.0024185297079384327,
0.014442073181271553,
-0.005345781333744526,
0.034340936690568924,
-0.010436591692268848,
-0.028125423938035965,
-0.028987180441617966,
-0.052147768437862396,
0.017990771681070328,
0.030422596260905266,
0.0020338408648967743,
-0.022145787253975868,
-0.03594176471233368,
0.002591978758573532,
-0.03834952041506767,
0.025715623050928116,
0.03493781387805939,
-0.05077965185046196,
0.012955522164702415,
-0.04851531982421875,
-0.050103072077035904,
0.08499706536531448,
-0.008556646294891834,
0.016600366681814194,
-0.004065696615725756,
-0.03616112843155861,
-0.03758533298969269,
-0.04072952643036842,
-0.01084164995700121,
0.01641778275370598,
-0.030322253704071045,
0.01202403660863638,
0.05803634971380234,
-0.04190748557448387,
-0.0012704059481620789,
0.036822609603405,
-0.010985663160681725,
-0.025512516498565674,
-0.029832854866981506,
-0.02425093948841095,
0.012066402472555637,
-0.01078088115900755,
0.012971597723662853,
0.03739539161324501,
-0.04492662847042084,
-0.043702736496925354,
-0.06349768489599228,
-0.05996432527899742,
0.046169742941856384,
0.023954417556524277,
0.01928316056728363,
-0.002133674453943968,
-0.022398173809051514,
0.07039429247379303,
-0.0013717516558244824,
-0.006096730940043926,
0.006537734530866146,
0.007668382953852415,
-0.014410505071282387,
-0.003985900431871414,
0.019052842631936073,
0.02778371423482895,
0.003816707991063595,
0.023727692663669586,
0.004562379326671362,
0.026930486783385277,
0.0367034450173378,
0.004969427827745676,
-0.02077171579003334,
0.01865956373512745,
0.02196701243519783,
-0.0008580572321079671,
0.02907971292734146,
0.015139213763177395,
-0.02564837597310543,
-0.010513273999094963,
-0.0012453242670744658,
0.045856326818466187,
0.010504995472729206,
-0.0035071945749223232,
0.07778216898441315,
-0.0343298614025116,
-0.03705593943595886,
-0.03659144416451454,
0.0636848583817482,
-0.04577340930700302,
-0.015484686009585857,
0.009350883774459362,
-0.00004259230991010554,
0.017129486426711082,
-0.049970537424087524,
0.014767572283744812,
0.033641453832387924,
-0.0023445512633770704,
-0.03465524688363075,
-0.03537886589765549,
-0.0016688586911186576,
-0.02762775495648384,
0.04655509814620018,
-0.049097690731287,
-0.03454800322651863,
0.03210833668708801,
0.015167857520282269,
-0.008264048025012016,
-0.006639578379690647,
-0.05067916959524155,
-0.03757144510746002,
-0.0661386027932167,
0.026823917403817177,
0.04340768977999687,
0.059736158698797226,
0.05774308741092682,
0.06725895404815674,
0.021802010014653206,
0.01925312727689743,
0.04109002277255058,
-0.032110363245010376,
-0.04195297881960869,
0.01722809486091137,
-0.011572515591979027,
-0.020274950191378593,
-0.027214759960770607,
-0.0022494462318718433,
0.04839588701725006,
-0.04034166783094406,
-0.04358378052711487,
-0.014414533041417599,
-0.03042561560869217,
-0.03207399323582649,
0.014048932120203972,
-0.05638723447918892,
-0.03441080451011658,
-0.0368889644742012,
0.030300837010145187,
0.04716681316494942,
0.0009802557760849595,
0.00875145010650158,
0.051157496869564056,
-0.020891161635518074,
-0.023064669221639633,
-0.008160711266100407,
-0.011958112008869648,
0.027660327032208443,
-0.005479960702359676,
0.05529305338859558,
0.015472969971597195,
-0.0031073668505996466,
0.019801456481218338,
-0.008352335542440414,
0.09115394204854965,
0.007106516510248184,
-0.04468068853020668,
0.026023268699645996,
-0.0427161380648613,
0.009048014879226685,
-0.0030951150692999363,
0.04257345572113991,
0.0076831732876598835,
0.008712046779692173,
0.02710767835378647,
0.007717514410614967,
-0.017198285087943077,
0.041187021881341934,
0.022254396229982376,
-0.018082797527313232,
-0.007476013619452715,
-0.04711208865046501,
0.031419623643159866,
-0.017480041831731796,
-0.004961783066391945,
0.006084805820137262,
0.001128736650571227,
-0.017893033102154732,
0.02644880674779415,
0.010522815398871899,
0.010200301185250282,
0.024977579712867737,
-0.00674090813845396,
0.031991519033908844,
0.0010657006641849875,
0.012860921211540699,
-0.02811134047806263,
0.01715330220758915,
0.01605730503797531,
0.03686266764998436,
0.0012052280362695456,
0.02400515042245388,
-0.0784289687871933,
-0.02153792791068554,
0.02213171310722828,
0.03294450417160988,
-0.045617155730724335,
-0.020580505952239037,
-0.0288128312677145,
-0.019464343786239624,
0.03251916542649269,
-0.005609050393104553,
0.016796473413705826,
0.0022236492950469255,
-0.04725848138332367,
-0.03821234405040741,
-0.018390847370028496,
-0.013703597709536552,
0.0296955369412899,
0.002465869067236781,
0.04813390225172043,
-0.024859629571437836,
-0.026597974821925163,
-0.0257884431630373,
0.002388282446190715,
0.031881969422101974,
0.0792866051197052,
0.012625576928257942,
-0.0006639606435783207,
0.005535757169127464,
0.05117849260568619,
-0.022456301376223564,
-0.07460030913352966,
0.0019917995668947697,
-0.01155045721679926,
0.01578938402235508,
0.0534428134560585,
-0.05383678898215294,
-0.03177652135491371,
-0.014932768419384956,
0.02702953666448593,
-0.015534883365035057,
0.01837916485965252,
-0.014444398693740368,
0.034498587250709534,
0.00029191470821388066,
-0.0239877849817276,
0.05928739160299301,
0.012328637763857841,
0.0014812203589826822,
-0.004044096916913986,
-0.026441480964422226,
0.05425172671675682,
-0.03305063769221306,
0.039970800280570984,
-0.05045228824019432,
-0.007461280561983585,
-0.02376718819141388,
0.03191763907670975,
0.005553922615945339,
0.01261345949023962,
-0.012568363919854164,
-0.027825456112623215,
-0.000225095558562316,
0.02556745894253254,
0.03346012532711029,
-0.03279250115156174,
-0.02528223767876625,
0.02910967916250229,
0.004304917063564062,
-0.022989360615611076,
-0.0053716991096735,
-0.024175412952899933,
-0.0041435654275119305,
0.019314486533403397,
-0.014912701211869717,
0.04659910500049591,
-0.03329411894083023,
-0.04998677968978882,
0.015577549114823341,
-0.03133870288729668,
-0.004253529477864504,
-0.011192087084054947,
-0.01024466473609209,
0.013410280458629131,
0.0069158561527729034,
-0.038360487669706345,
0.005439919885247946,
-0.016528639942407608,
0.030536074191331863,
-0.07593418657779694,
0.03647635877132416,
0.02877945825457573,
0.005301295313984156,
-0.0907941609621048,
-0.044155433773994446,
0.031999263912439346,
0.0061698658391833305,
-0.03737300634384155,
-0.0004350862873252481,
-0.0020392623264342546,
-0.0039250049740076065,
-0.023033706471323967,
-0.008832658641040325,
0.05086245387792587,
0.021598827093839645,
0.00843901839107275,
0.0056809326633811,
0.03768780082464218,
0.05556856095790863,
-0.00787381362169981,
0.015590880997478962,
0.0131445387378335,
-0.0035807641688734293,
-0.04378744587302208,
-0.016177160665392876,
0.03932655230164528,
-0.0176545437425375,
0.01578020490705967,
-0.029601987451314926,
0.022642504423856735,
0.00009932656394084916,
-0.02529885806143284,
-0.03867950662970543,
0.020108694210648537,
0.03994369134306908,
0.015613086521625519,
-0.0385260283946991,
-0.019164683297276497,
0.013179903849959373,
0.01181037537753582,
-0.005894099362194538,
-0.029753107577562332,
-0.014453666284680367,
-0.03523446246981621,
0.004454376641660929,
-0.0033435598015785217,
0.019497839733958244,
0.004594390280544758,
0.0483422689139843,
-0.005301740951836109,
-0.005399078596383333,
0.047193821519613266,
-0.022182151675224304,
-0.004483006428927183,
-0.0007076430483721197,
-0.018763097003102303,
0.02057017758488655,
-0.0230843685567379,
-0.036992352455854416,
-0.04140893369913101,
-0.05520034581422806,
0.03372741863131523,
0.050638627260923386,
-0.023092584684491158,
0.07749000191688538,
0.011212167330086231,
0.02276311255991459,
-0.023619269952178,
-0.021387647837400436,
-0.04509389400482178,
0.010342894122004509,
-0.013058016076683998,
0.022134875878691673,
-0.0303838811814785,
0.008809075690805912,
0.024949172511696815,
0.046196967363357544,
-0.033787112683057785,
0.02790188230574131,
0.012276307679712772,
0.027585890144109726,
0.018976572901010513,
0.0071148560382425785,
-0.04891331493854523,
0.03487063944339752,
-0.02669433131814003,
0.019558168947696686,
-0.04424363747239113,
0.004635236691683531,
0.018851548433303833,
0.03809753805398941,
-0.017972905188798904,
-0.04251113533973694,
-0.0037221587263047695,
-0.03347101807594299,
0.02229023352265358,
0.021530168130993843,
0.018509885296225548,
0.010662587359547615,
0.043773822486400604,
0.023125650361180305,
0.021342579275369644,
0.026182888075709343,
0.021842798218131065,
-0.047956064343452454,
-0.005750732496380806,
-0.040971461683511734,
-0.029017824679613113,
0.019017258659005165,
-0.030640406534075737,
-0.02361467108130455,
0.0011705461656674743,
-0.014928791671991348,
0.017345895990729332,
-0.01113799773156643,
0.017991358414292336,
-0.0341012179851532,
0.090451680123806,
0.007567781955003738,
-0.004476186819374561,
-0.02324438840150833,
0.002391044981777668,
0.10119616240262985,
0.05608966574072838,
0.03276219218969345,
-0.06233426555991173,
0.008404983207583427,
0.02139010839164257,
0.006789457052946091,
-0.03079822286963463,
0.012563599273562431,
0.025383029133081436,
0.025901470333337784,
0.02896687015891075,
0.007927917875349522,
0.017264602705836296,
-0.00843734946101904,
0.024121666327118874,
-0.034244779497385025,
-0.023685095831751823,
-0.011295844800770283,
0.04804641380906105,
0.008647452108561993,
0.03619024530053139,
-0.07986722886562347,
0.020512526854872704,
-0.041848260909318924,
0.038244329392910004,
0.000847574498038739,
-0.05325310304760933,
0.01201601605862379,
0.007598508149385452,
-0.03564605116844177,
0.013197611086070538,
0.007856116630136967,
0.000937324482947588,
-0.048185646533966064,
0.046987250447273254,
-0.019441520795226097,
0.009639267809689045,
0.019761350005865097,
0.010494701564311981,
0.03292377293109894,
-0.02219226211309433,
-0.0026485573034733534,
0.021136723458766937,
-0.025174064561724663,
-0.025123870000243187,
-0.018527206033468246,
0.06610265374183655,
0.0007307167979888618,
-0.027187315747141838,
-0.007329788524657488,
-0.02053847722709179,
-0.0023894617334008217,
-0.04941234365105629,
0.0072846184484660625,
-0.009949990548193455,
0.031986743211746216,
-0.03603263944387436,
0.044057708233594894,
-0.03379480168223381,
0.007830340415239334,
-0.019237108528614044,
0.03156723827123642,
-0.0020189485512673855,
-0.01160399243235588,
0.014312462881207466,
-0.029379162937402725,
0.019153373315930367,
-0.03191746026277542,
-0.036056146025657654,
-0.001533989328891039,
-0.01094106212258339,
-0.04705727845430374,
-0.0454416386783123,
0.005967249162495136,
0.003540807170793414,
0.05242156609892845,
-0.01920289173722267,
-0.009893693961203098,
-0.0267155934125185,
-0.04362661764025688,
0.03370022028684616,
-0.02116815373301506,
-0.03809431940317154,
0.005156363360583782,
0.015875862911343575,
0.0026985639706254005,
0.0292800385504961,
-0.021758057177066803,
0.03468335047364235,
0.010012787766754627,
0.004031953401863575,
0.04420061782002449,
-0.030699189752340317,
-0.006424360908567905,
0.02656008116900921,
0.0046627516858279705,
-0.01923636719584465,
-0.022373199462890625,
0.009721262380480766,
0.008177630603313446,
-0.016233695670962334,
-0.045886099338531494,
0.012738470919430256,
0.013037584722042084,
0.010940744541585445,
0.001637506764382124,
-0.02235347032546997,
0.0030085486359894276,
0.03041819855570793,
0.02221909537911415,
-0.058896295726299286,
-0.0267647635191679,
-0.039177682250738144,
0.013936610892415047,
0.016141526401042938,
0.002236459869891405,
-0.0020274019334465265,
-0.002363119274377823,
-0.01652142032980919,
0.05428353697061539,
0.017016008496284485,
-0.0019356503617018461,
-0.08102908730506897,
0.03387629985809326,
-0.010620263405144215,
-0.0032806331291794777,
-0.00047013768926262856,
0.018299467861652374,
-0.007577326614409685,
-0.04481842368841171,
0.05325913429260254,
0.05216285586357117,
0.00606049969792366,
-0.008142117410898209,
0.009872747585177422,
-0.011845813132822514,
0.01884995773434639,
-0.012479713186621666,
-0.027663664892315865,
0.03053092025220394,
-0.02979772351682186,
-0.016826555132865906,
0.03884221240878105,
0.04855814203619957,
0.015050169080495834,
0.045041631907224655,
-0.012803173623979092,
-0.03391391783952713,
0.045517440885305405,
-0.0394301563501358,
-0.034339405596256256,
0.016518285498023033,
-0.05732205510139465,
-0.0169738307595253,
-0.036153536289930344,
-0.003643742995336652,
0.028132585808634758,
0.013985068537294865,
0.02696152776479721,
0.009668690152466297,
-0.0017083018319681287,
-0.0053767431527376175,
0.015003854408860207,
0.016420509666204453,
0.028321485966444016,
0.04347711056470871,
-0.016644755378365517,
0.029556164517998695,
0.08624594658613205,
-0.04409543424844742,
0.02132478915154934,
-0.019300060346722603,
0.028213810175657272,
-0.06813912838697433,
-0.011387485079467297,
0.017465483397245407,
-0.03200649842619896,
0.05121348053216934,
-0.04061715677380562,
-0.025303170084953308,
0.021114934235811234,
-0.04290341958403587,
0.04611542820930481,
-0.02916707471013069,
-0.0020045286510139704,
0.006178996525704861,
0.0035514074843376875,
0.0025005685165524483,
0.06673146784305573,
0.04047341272234917,
0.03599681705236435,
0.011745098978281021,
0.02088150568306446,
0.009641685523092747,
-0.03150550648570061,
-0.019614405930042267,
0.01786276139318943,
0.008201362565159798,
-0.042520344257354736,
0.04021735116839409,
-0.030556589365005493,
-0.03925997391343117,
0.044261857867240906,
-0.017409058287739754,
-0.023869311437010765,
-0.016338225454092026,
0.0017980459379032254,
0.03217219188809395,
0.012827669270336628,
0.0019484399817883968,
-0.04682102054357529,
-0.00007765745249344036,
0.027122564613819122,
0.03713670372962952,
-0.021451547741889954,
0.01676017791032791,
-0.010675282217562199,
-0.02303367666900158,
-0.02951785735785961,
-0.02449163980782032,
0.03304538130760193,
0.015622355975210667,
-0.023403938859701157,
0.03224499896168709,
-0.006523347459733486,
0.02242416888475418,
-0.005206150468438864,
0.04754764959216118,
-0.004762191325426102,
-0.02663200907409191,
0.018841542303562164,
-0.0029165372252464294,
0.018196143209934235,
0.0010200749384239316,
-0.04260589927434921,
-0.041151996701955795,
0.05494534596800804,
0.019955266267061234,
-0.040778473019599915,
-0.0705965906381607,
-0.02349849045276642,
-0.009009999223053455,
-0.021867388859391212,
0.01647818647325039,
-0.030290592461824417,
-0.062312621623277664,
0.006947759073227644,
-0.008089683949947357,
0.008877131156623363,
-0.042634058743715286,
-0.026888033375144005,
-0.0275278203189373,
-0.06699705868959427,
0.05305904150009155,
0.008782239630818367,
-0.031185347586870193,
-0.06544076651334763,
0.00031728509929962456,
-0.025950275361537933,
-0.0018013549270108342,
0.048248764127492905,
0.01746559515595436,
-0.024931158870458603,
0.01577087491750717,
-0.029323210939764977,
0.018265651538968086,
-0.0453452430665493,
-0.01105219591408968,
-0.019737448543310165,
0.017057497054338455,
0.005519322119653225,
0.008933895267546177,
-0.01136965025216341,
0.024247318506240845,
-0.0022213722113519907,
-0.020912395790219307,
0.05414370447397232,
0.004141833633184433,
-0.004318350926041603,
0.039529357105493546,
0.02976602502167225,
-0.009822051972150803,
0.07030715048313141,
-0.01429795753210783,
0.021165084093809128,
0.014398057945072651,
-0.04448392614722252,
-0.05094098299741745,
0.04796413332223892,
-0.024350779131054878,
-0.009559320285916328,
0.013476459309458733,
0.0010620919056236744,
0.017408529296517372,
-0.019879156723618507,
-0.05437444895505905,
0.01907319389283657,
-0.016192182898521423,
0.013348895125091076,
0.05353204160928726,
0.013492584228515625,
0.05350501090288162,
-0.010918842628598213,
-0.0030808867886662483,
0.020778806880116463,
0.007563428021967411,
0.007056033704429865,
0.02901405654847622,
0.042451877146959305,
0.00723972637206316,
0.02483063004910946,
0.030890395864844322,
-0.019908301532268524,
0.008610446937382221,
0.026527827605605125,
0.01921859383583069,
-0.03551865741610527,
-0.03240664675831795,
-0.014483090490102768,
-0.009986648336052895,
-0.02006903849542141,
0.02751372940838337,
-0.03437903895974159,
0.05423440784215927,
-0.01970778964459896,
0.006725761573761702,
0.0007779184961691499,
0.0032107734587043524,
-0.03903813660144806,
-0.009682086296379566,
0.028733406215906143,
0.05502140149474144,
0.006550121121108532,
-0.03957938402891159,
-0.022441091015934944,
-0.012837333604693413,
-0.015388431027531624,
-0.030081668868660927,
0.01616613380610943,
0.02421332709491253,
-0.021374478936195374,
-0.04573187604546547,
-0.024496812373399734,
-0.012767661362886429,
-0.027818558737635612,
0.018776308745145798,
0.030831553041934967,
0.03184175491333008,
-0.0022037960588932037,
-0.003760423744097352,
-0.014135546050965786,
0.045680705457925797,
-0.10283226519823074,
-0.001750156981870532,
-0.03373296931385994,
0.015870682895183563,
0.013676904141902924,
-0.004299543797969818
] |
<p>Note 1: This is probably as much a maths question as physics.
Note 2: I am not sure if my use of the the term conductance is correct.</p>
<p>I want to make a kiln. The walls will be thick. I can come to two figures for the conductivity of a kiln of given dimensions, between which the actual conductivity will lie. For example:</p>
<p>Assume:
Kiln inner dimensions: 1m x 1m x 1m
Kiln outer dimensions: 2m x 2m x 2m
Kiln lining material conductivity: 0.5 W/mK</p>
<p>Lower bound kiln wall conductance
= MaterialConductivity * Area / depth
= 0.5 * 1*1*1*6 / 0.5
= 6 W/K</p>
<p>Upper bound kiln wall conductance
= MaterialConductivity * Area / depth
= 0.5 * 2*2*2*6 / 0.5
= 48 W/K</p>
<p><strong>My question</strong>: in the context of a thick-walled cuboid with consistent wall thickness, how do I calculate thermal conductance? Or more generically:</p>
<ol>
<li>Can I split this up into calculations for 6x 3d trapezoids?</li>
<li>How would thermal conductance of the trapezoid be calculated?</li>
</ol>
<p>Thanks</p> | 1,479 | [
-0.024980271235108376,
-0.023542948067188263,
-0.007836038246750832,
-0.007544776890426874,
0.05818323418498039,
0.016240853816270828,
-0.008628711104393005,
-0.02702447399497032,
-0.0013856651494279504,
-0.018681397661566734,
0.044421013444662094,
0.013074050657451153,
0.04557869955897331,
0.03017161227762699,
0.02829703874886036,
-0.012768423184752464,
-0.006033297628164291,
0.006948524154722691,
0.007672514300793409,
-0.06343243271112442,
0.020057562738656998,
0.001465476001612842,
-0.001844898913986981,
-0.01199064776301384,
-0.03163986653089523,
0.0704682469367981,
0.0038585951551795006,
-0.01438992004841566,
0.004669783171266317,
0.04568850249052048,
0.005875792354345322,
-0.025731481611728668,
0.02704543247818947,
0.020846836268901825,
0.03990931808948517,
-0.004502379335463047,
-0.051560740917921066,
-0.02155347913503647,
-0.05416348576545715,
0.013371121138334274,
-0.026952438056468964,
-0.015226256102323532,
0.008578808978199959,
-0.008815701119601727,
0.02278297208249569,
-0.01470146980136633,
0.022441893815994263,
-0.05786672234535217,
-0.004828646779060364,
-0.07730797678232193,
0.03335268795490265,
-0.035524722188711166,
0.08027665317058563,
0.04726313054561615,
0.0011593676172196865,
-0.042139261960983276,
0.06852959096431732,
0.06248936429619789,
0.009699061512947083,
-0.023904576897621155,
-0.003682004287838936,
0.02000308595597744,
0.013339350931346416,
-0.01424852479249239,
-0.03271016851067543,
0.04889962822198868,
-0.022141464054584503,
-0.0463324636220932,
0.007446759380400181,
-0.015484672039747238,
0.033142197877168655,
-0.01924189366400242,
0.01390891894698143,
-0.029944155365228653,
0.014710555784404278,
0.013324224390089512,
0.003796270349994302,
0.0349658764898777,
0.056861162185668945,
-0.011591796763241291,
-0.0717516541481018,
0.020027069374918938,
0.046589478850364685,
0.01772173121571541,
0.013565342873334885,
-0.002359946258366108,
0.05365534499287605,
-0.019051311537623405,
0.005271458066999912,
0.010162228718400002,
0.0165760088711977,
0.020140448585152626,
0.07374826818704605,
0.0073803868144750595,
-0.015854395925998688,
-0.003063386073336005,
0.01865146867930889,
0.05894405394792557,
-0.03018166311085224,
-0.018041454255580902,
-0.010520165786147118,
-0.010082748718559742,
-0.0028907121159136295,
0.08810539543628693,
0.023220406845211983,
-0.014859288930892944,
0.0006277821958065033,
0.023198015987873077,
0.00450586061924696,
-0.0316748172044754,
-0.02332833595573902,
0.004992861766368151,
-0.00006090314855100587,
-0.014806494116783142,
-0.0014694184064865112,
-0.0686500072479248,
-0.026564085856080055,
-0.025695687159895897,
-0.02129490301012993,
0.014925428666174412,
0.0539703294634819,
-0.011396747082471848,
0.041424598544836044,
-0.01193296816200018,
-0.1313675343990326,
0.036028556525707245,
0.016937537118792534,
-0.01392377633601427,
-0.04106483235955238,
0.024493327364325523,
0.05036047101020813,
-0.026642579585313797,
0.01602434366941452,
-0.020715566352009773,
0.03382517024874687,
0.014483336359262466,
-0.036889802664518356,
-0.07368427515029907,
0.0065123410895466805,
-0.008130514062941074,
-0.024721838533878326,
-0.040143340826034546,
0.00837141927331686,
0.03061646595597267,
0.07275978475809097,
0.002510285470634699,
-0.008343132212758064,
-0.017706291750073433,
-0.009247115813195705,
-0.002171681961044669,
-0.07022581994533539,
-0.027386406436562538,
0.0017205232288688421,
-0.004117094911634922,
0.03059788979589939,
-0.04018788784742355,
0.033795397728681564,
0.03023936040699482,
-0.02136807143688202,
-0.028872167691588402,
0.05713436380028725,
0.008629236370325089,
-0.016202880069613457,
0.015141294337809086,
-0.027460213750600815,
-0.02165209874510765,
0.08281309902667999,
-0.0018908270867541432,
0.023049229755997658,
-0.013043110258877277,
0.009507822804152966,
-0.009917084127664566,
-0.01683824695646763,
0.004681320860981941,
0.04965413361787796,
0.011753102764487267,
0.015649568289518356,
-0.008096096105873585,
-0.02023843489587307,
0.045463092625141144,
-0.06859101355075836,
-0.030356477946043015,
-0.005306527949869633,
-0.004188742488622665,
-0.009404846467077732,
0.05954413115978241,
-0.02391081675887108,
-0.024476341903209686,
0.018309498205780983,
-0.019966069608926773,
-0.04829477146267891,
-0.0873139277100563,
0.027561724185943604,
-0.010463537648320198,
-0.03082858771085739,
-0.006634073331952095,
-0.035313211381435394,
-0.006655532866716385,
-0.014531450346112251,
-0.0020912878680974245,
0.008171097375452518,
-0.0031248722225427628,
0.030945580452680588,
-0.010872975923120975,
0.004073591437190771,
0.027078624814748764,
0.024858038872480392,
-0.018573293462395668,
0.03305543214082718,
-0.03563088923692703,
0.01366480067372322,
-0.02897792123258114,
-0.041830096393823624,
0.001927272416651249,
-0.017498182132840157,
-0.03733573108911514,
0.023560555651783943,
-0.020890600979328156,
-0.026531517505645752,
0.04361002892255783,
-0.029444165527820587,
0.07712911069393158,
0.050545237958431244,
0.030058370903134346,
-0.01917223259806633,
0.03656851127743721,
-0.037671271711587906,
0.043631915003061295,
0.00444360077381134,
-0.03534965589642525,
-0.05236835405230522,
0.01335007045418024,
0.00027276109904050827,
0.012937371619045734,
-0.0531742200255394,
0.0009981384500861168,
0.03840602561831474,
0.022034350782632828,
0.012143746018409729,
0.011753367260098457,
-0.0008633501129224896,
0.00528856972232461,
0.0012762440601363778,
-0.012239123694598675,
0.0208464153110981,
-0.0007126857526600361,
-0.02899654395878315,
0.0021225314121693373,
0.015139230526983738,
-0.026173414662480354,
-0.02543691173195839,
0.0478491485118866,
-0.005161310080438852,
-0.024181710556149483,
-0.011077072471380234,
-0.0005730066332034767,
0.02781878411769867,
-0.028929078951478004,
-0.00480300560593605,
0.02200416289269924,
0.041180986911058426,
0.01920420117676258,
-0.011629801243543625,
-0.0016940904315561056,
0.032105859369039536,
0.017613034695386887,
0.012285224162042141,
-0.018729327246546745,
0.018461711704730988,
-0.0313592404127121,
0.00967556145042181,
-0.010682987980544567,
0.008345884270966053,
-0.009247084148228168,
-0.031744904816150665,
0.027830200269818306,
0.02203596569597721,
0.003141268389299512,
-0.02825370989739895,
-0.029179643839597702,
-0.04430381953716278,
0.0059024496003985405,
0.014667081646621227,
0.028848545625805855,
-0.05577694624662399,
-0.005000882316380739,
-0.028640786185860634,
-0.025938840582966805,
0.03727507218718529,
0.014436116442084312,
-0.04665882885456085,
0.038910482078790665,
-0.009311766363680363,
-0.037374868988990784,
0.012768383137881756,
0.011742232367396355,
0.04192975535988808,
-0.027477623894810677,
0.04727042838931084,
0.06744177639484406,
-0.01002857182174921,
-0.006192649714648724,
-0.0032448694109916687,
-0.023494219407439232,
-0.04445726051926613,
-0.015763845294713974,
-0.014594947919249535,
0.005319864489138126,
0.019458260387182236,
0.05377496778964996,
0.03514368459582329,
-0.024891989305615425,
0.005084820557385683,
-0.035656195133924484,
-0.010249508544802666,
0.01847960241138935,
-0.03374605253338814,
0.004558546934276819,
-0.01218368485569954,
-0.014612148515880108,
0.0955866202712059,
-0.0042809294536709785,
-0.03277551755309105,
-0.0026510206516832113,
-0.02649892494082451,
-0.019825410097837448,
-0.015145423822104931,
0.0011683908523991704,
0.00014551807544194162,
-0.05710908770561218,
0.0192743968218565,
-0.006665700115263462,
0.05971992760896683,
0.05956399813294411,
-0.00023353943834081292,
0.01699608936905861,
-0.01467713713645935,
0.014555194415152073,
-0.02413749508559704,
0.04826062545180321,
0.045043446123600006,
-0.011405746452510357,
0.05845210701227188,
-0.02484007366001606,
0.004549204371869564,
0.07088009268045425,
-0.05356330797076225,
0.007178119383752346,
-0.002711108885705471,
0.03908022493124008,
-0.028833286836743355,
0.03088543377816677,
-0.0216897651553154,
-0.030168475583195686,
0.0077322921715676785,
0.05009124055504799,
0.03962983191013336,
0.006326718721538782,
0.007325006648898125,
0.02453305944800377,
0.03927363455295563,
0.022158773615956306,
0.024269958958029747,
0.0012814641231670976,
0.0036760454531759024,
-0.010816148482263088,
0.007525013294070959,
-0.030475452542304993,
0.008720578625798225,
0.0403885692358017,
0.04547277092933655,
0.022053508087992668,
0.02240408957004547,
0.014910316094756126,
-0.06345681846141815,
-0.03768323361873627,
-0.03511391580104828,
0.0618087537586689,
-0.018938707187771797,
0.021604131907224655,
-0.0009982878109440207,
-0.013760648667812347,
0.04242262616753578,
-0.0011583411833271384,
-0.0824505016207695,
0.01268359087407589,
-0.008543445728719234,
-0.02138862945139408,
0.006534474901854992,
0.014584829099476337,
-0.02831684611737728,
-0.01696261577308178,
-0.01790708489716053,
0.039170581847429276,
-0.005124676041305065,
-0.0490727573633194,
0.025267722085118294,
0.005122103728353977,
-0.040947455912828445,
-0.01638145186007023,
0.032234326004981995,
0.04892265424132347,
-0.04966450110077858,
0.01586286723613739,
0.008959970436990261,
-0.004636484198272228,
0.014601519331336021,
-0.004418766126036644,
0.011744705028831959,
0.012776341289281845,
0.06793877482414246,
-0.026094604283571243,
0.025441469624638557,
-0.013509322889149189,
0.03667955845594406,
0.03268558904528618,
0.04656180366873741,
-0.03248625621199608,
-0.010163689032196999,
-0.013752587139606476,
-0.035880278795957565,
-0.016007933765649796,
0.029898302629590034,
0.06924200803041458,
-0.021528728306293488,
0.0030041285790503025,
0.017790883779525757,
-0.007802693173289299,
-0.021391142159700394,
-0.018003832548856735,
0.041530076414346695,
0.0063093965873122215,
-0.009707260876893997,
-0.004430698696523905,
-0.07548240572214127,
-0.009212418459355831,
-0.0023471300955861807,
0.032961804419755936,
0.004174089524894953,
-0.019964389503002167,
0.039231445640325546,
0.009391289204359055,
0.000016794283510535024,
-0.03336721286177635,
0.0559760257601738,
0.029425811022520065,
0.014231368899345398,
-0.0373607762157917,
-0.033345747739076614,
0.017669353634119034,
0.039245348423719406,
0.014547239989042282,
-0.021241936832666397,
-0.026869969442486763,
-0.06364089250564575,
-0.02120707929134369,
0.05031317099928856,
0.05936808884143829,
-0.028541846200823784,
0.0006046572234481573,
-0.025458909571170807,
-0.011770982295274734,
0.06521502137184143,
-0.022014733403921127,
0.039477355778217316,
-0.03064066730439663,
0.02056146413087845,
-0.01681557670235634,
-0.0027095789555460215,
-0.030236544087529182,
0.019003156572580338,
0.02722991816699505,
0.03526845574378967,
-0.028581729158759117,
0.008837452158331871,
0.02595086395740509,
0.03994935750961304,
0.010081326588988304,
0.02442106418311596,
-0.0006355614750646055,
0.038926862180233,
-0.019649894908070564,
0.003566224593669176,
0.007848571985960007,
-0.04741782695055008,
-0.009844074957072735,
-0.008767790161073208,
-0.015152659267187119,
0.0301690474152565,
-0.04614609107375145,
-0.009900339879095554,
0.04275888204574585,
0.02112007327377796,
0.02617848850786686,
0.005168416537344456,
-0.006802297197282314,
0.06694875657558441,
0.023424463346600533,
0.009587420150637627,
0.02935449592769146,
0.00938832014799118,
0.008918586187064648,
0.006319779437035322,
-0.009402427822351456,
-0.019017092883586884,
-0.016624948009848595,
-0.01587522216141224,
-0.01731867901980877,
-0.007716766558587551,
-0.0076562887988984585,
0.05422019585967064,
0.006235545966774225,
0.04426516592502594,
-0.006540617439895868,
-0.031737640500068665,
0.022579671815037727,
0.0423940047621727,
-0.014640632085502148,
-0.01067271176725626,
0.004046423826366663,
0.040191564708948135,
-0.0019486064556986094,
-0.049561262130737305,
0.012251193635165691,
0.005035076756030321,
0.03592105209827423,
0.012090759351849556,
-0.0046020871959626675,
0.003590121166780591,
-0.0574558861553669,
0.011798105202615261,
0.009556298144161701,
-0.02809695154428482,
0.07124549895524979,
-0.018944622948765755,
0.040381453931331635,
0.026218973100185394,
-0.06129908561706543,
0.01580135151743889,
0.0036108437925577164,
0.0005557701806537807,
0.023072943091392517,
-0.007958607748150826,
0.021052230149507523,
0.004755772650241852,
0.028538143262267113,
-0.06632262468338013,
-0.02486523427069187,
0.015182358212769032,
0.014501272700726986,
-0.0058547016233205795,
-0.0483778640627861,
-0.04572156444191933,
0.0019689027685672045,
-0.05840372294187546,
0.01158500649034977,
0.11016999930143356,
-0.023606926202774048,
-0.017430918291211128,
0.01964743062853813,
0.033501408994197845,
0.07376880198717117,
0.016718098893761635,
0.0119247455149889,
-0.013139450922608376,
-0.023330291733145714,
-0.002672544214874506,
0.015708327293395996,
0.041689757257699966,
-0.03535299375653267,
-0.013015899807214737,
0.023679537698626518,
0.010508616454899311,
0.05938190594315529,
0.009423496201634407,
0.021009674295783043,
0.017474336549639702,
0.008957709185779095,
-0.03252875432372093,
-0.01262851431965828,
0.045953765511512756,
-0.00288398121483624,
0.02125580981373787,
-0.0452594980597496,
-0.007935505360364914,
-0.06325561553239822,
-0.01692562736570835,
-0.007016254123300314,
0.026773303747177124,
-0.018472708761692047,
-0.023922493681311607,
0.06418228149414062,
-0.016238972544670105,
-0.02551862969994545,
-0.002402280457317829,
-0.020604176446795464,
-0.016739435493946075,
-0.025671707466244698,
-0.02045559138059616,
-0.0010039099724963307,
-0.015652664005756378,
0.0036322164814919233,
-0.02783759869635105,
-0.049215685576200485,
0.021289430558681488,
0.05911288410425186,
-0.014724832028150558,
0.01829717680811882,
0.0015491500962525606,
-0.02027607150375843,
0.008942502550780773,
-0.0022683097049593925,
-0.0026442280504852533,
0.019120946526527405,
0.008960165083408356,
0.03848140686750412,
-0.003267560852691531,
-0.01061707828193903,
0.032848112285137177,
0.022399762645363808,
-0.008240316063165665,
0.004852890968322754,
-0.015676727518439293,
0.03373117372393608,
-0.008042936213314533,
-0.019973238930106163,
-0.027608392760157585,
0.05726710334420204,
-0.031406596302986145,
0.029126541689038277,
0.0048662396147847176,
-0.014975515194237232,
0.06556125730276108,
0.04509124159812927,
-0.03879281133413315,
-0.05115475505590439,
-0.03212001919746399,
-0.05480305850505829,
0.01017784420400858,
0.04313782602548599,
0.00048381646047346294,
-0.02038528025150299,
0.027021685615181923,
0.05273982509970665,
-0.008289502002298832,
-0.014845865778625011,
-0.004126221407204866,
-0.04472872614860535,
0.009144880808889866,
-0.0006441316800191998,
-0.047715697437524796,
-0.005996569525450468,
0.0473315492272377,
-0.0048558032140135765,
0.06508789956569672,
-0.0092271463945508,
0.022501427680253983,
0.015364433638751507,
0.06811534613370895,
0.010316279716789722,
0.056834328919649124,
-0.015296201221644878,
0.021523507311940193,
-0.014538398943841457,
0.04258095845580101,
0.13356924057006836,
0.01745958998799324,
-0.005150846671313047,
-0.05291937664151192,
0.03612241894006729,
-0.028735879808664322,
-0.04875790327787399,
-0.046702321618795395,
-0.002988868160173297,
-0.022071033716201782,
-0.024836547672748566,
0.03344161435961723,
0.06380317360162735,
-0.00607968820258975,
0.010875415988266468,
0.04223351553082466,
-0.03915509581565857,
-0.02416362799704075,
0.011284686625003815,
0.02729230746626854,
-0.000657681142911315,
0.006493097171187401,
-0.036339156329631805,
0.0158905778080225,
-0.01830480247735977,
-0.024132568389177322,
-0.002689576707780361,
-0.01895388774573803,
0.0619223453104496,
0.0005874134367331862,
-0.06651579588651657,
0.020591214299201965,
0.01695733331143856,
-0.04410445690155029,
-0.02831464633345604,
0.04366730898618698,
0.04821021109819412,
-0.019571863114833832,
0.04528263211250305,
0.04345983266830444,
0.011883558705449104,
0.016500212252140045,
-0.0008492728229612112,
0.03942151367664337,
0.011113838292658329,
0.00801883451640606,
-0.02824382856488228,
0.008183293044567108,
0.01404430903494358,
-0.03893578425049782,
0.021251581609249115,
0.020071104168891907,
0.05851118266582489,
-0.07245345413684845,
-0.003495605196803808,
0.013831251300871372,
0.023374337702989578,
-0.04938477650284767,
-0.0018856946844607592,
-0.007409851532429457,
0.020213525742292404,
0.012455386109650135,
-0.0067108310759067535,
-0.0028485392685979605,
-0.012274283915758133,
0.016085943207144737,
-0.045668572187423706,
0.07996822893619537,
0.017984328791499138,
-0.0015531179960817099,
-0.05113404616713524,
-0.018442099913954735,
-0.020274093374609947,
-0.02720022387802601,
-0.0029860720969736576,
0.03598193824291229,
0.02716469205915928,
-0.01586240530014038,
-0.024859685450792313,
0.0061571476981043816,
-0.055183637887239456,
0.012019616551697254,
-0.01521962322294712,
0.033554807305336,
-0.03773287683725357,
-0.04778093472123146,
0.012082599103450775,
0.05210627242922783,
-0.007144682575017214,
-0.039274539798498154,
-0.042545102536678314,
0.017237555235624313,
0.02774658054113388,
-0.051812656223773956,
-0.00380792492069304,
-0.012197498232126236,
-0.06298695504665375,
0.0018338898662477732,
-0.0004318974679335952,
0.05704782158136368,
0.026006635278463364,
0.025413161143660545,
-0.032050494104623795,
0.02191317453980446,
-0.03729015588760376,
-0.010564783588051796,
0.03279538080096245,
-0.04311973229050636,
-0.00869134534150362,
0.0023927984293550253,
0.004549174103885889,
-0.014711289666593075,
-0.05177215486764908,
-0.03629159927368164,
-0.04424947500228882,
0.009490594267845154,
-0.005224848166108131,
-0.042896728962659836,
-0.0020746879745274782,
-0.027565427124500275,
-0.025641337037086487,
-0.015227580443024635,
-0.00830989982932806,
-0.010586289688944817,
-0.04898013174533844,
0.018485724925994873,
-0.02432820200920105,
0.0022224695421755314,
-0.021675217896699905,
-0.021920813247561455,
0.016349872574210167,
-0.004726449493318796,
-0.02322591282427311,
-0.015568661503493786,
-0.04440600425004959,
0.004102454520761967,
-0.0037840905133634806,
0.03717510402202606,
-0.05628182366490364,
-0.055520277470350266,
-0.0034308736212551594,
-0.019329681992530823,
-0.05296671390533447,
0.007674827240407467,
-0.041956596076488495,
0.03508301451802254,
0.01733098365366459,
-0.016963694244623184,
-0.0023535664658993483,
0.05104834586381912,
-0.017554976046085358,
-0.0010921136708930135,
-0.010770205408334732,
-0.012315301224589348,
0.03948269784450531,
-0.026046253740787506,
0.0028115762397646904,
-0.03532300144433975,
0.012960189022123814,
0.0337388813495636,
0.027816040441393852,
0.021914906799793243,
-0.021974513307213783,
0.0016107844421640038,
-0.00940608885139227,
-0.019672812893986702,
0.0010874762665480375,
0.00299282418563962,
0.012805519625544548,
0.03467177599668503,
-0.04769241064786911,
-0.004317824728786945,
0.033439524471759796,
0.012846743687987328,
-0.08486008644104004,
-0.009778081439435482,
0.011379734613001347,
-0.009783930145204067,
0.026623671874403954,
-0.10282842814922333,
0.039165299385786057,
-0.003915444947779179,
-0.06575798243284225,
0.03154097869992256,
-0.010139771737158298,
-0.021829189732670784,
-0.06138528883457184,
-0.019796473905444145,
0.010509556159377098,
0.008378482423722744,
0.01901809498667717,
0.02168864943087101,
-0.009692879393696785,
0.01129424199461937,
0.021242769435048103,
-0.03741498291492462,
-0.01084478572010994,
0.022437872365117073,
-0.03028780221939087,
-0.01201925240457058,
0.01953992247581482,
0.0031300983391702175,
0.010090905241668224,
-0.002742188982665539,
-0.0393383651971817,
0.01035443227738142,
0.0006547347875311971,
0.025178106501698494,
0.00038164888974279165,
0.005725322291254997,
0.04330004006624222,
0.001256049843505025,
0.03332570940256119,
0.010732083581387997,
0.04024476930499077,
-0.02150484174489975,
-0.0258890800178051,
0.01968686282634735,
0.030357811599969864,
-0.008382432162761688,
0.015520034357905388,
0.023804130032658577,
-0.022073669359087944,
0.009844353422522545,
-0.018956728279590607,
0.01203532237559557,
0.06436381489038467,
-0.028926333412528038,
-0.015475604683160782,
-0.03986038267612457,
-0.012971080839633942,
0.03281698748469353,
0.023157350718975067,
-0.023738756775856018,
-0.03765397146344185,
-0.012170754373073578,
-0.022090671584010124,
-0.01290320698171854,
0.003364776959642768,
-0.01490605715662241,
-0.029475055634975433,
-0.054813969880342484,
0.03928361088037491,
0.0035799844190478325,
-0.011943535879254341,
-0.03266821429133415,
-0.018611710518598557,
0.03779305890202522,
0.010645009577274323,
0.03933392092585564,
0.020551012828946114,
-0.03596479073166847,
-0.005421319976449013,
-0.036916255950927734,
0.04776642844080925,
-0.00833110511302948,
-0.03414686769247055,
-0.021988866850733757,
-0.04911455512046814,
0.001965722069144249,
0.0006628647679463029,
0.09072177857160568,
-0.014907868579030037,
-0.008001075126230717,
0.006022271700203419,
-0.01053603831678629,
0.008612802252173424,
-0.060139868408441544,
-0.0038706641644239426,
-0.0010532852029427886,
-0.008964777924120426,
-0.02339654043316841,
-0.01982949674129486,
-0.026743587106466293,
0.014234650880098343,
0.047853950411081314,
0.010603789240121841,
0.02310081198811531,
0.01374003291130066,
-0.02157762087881565,
0.0176073145121336,
0.015700869262218475,
-0.0051385448314249516,
0.08692526817321777,
0.0016472171992063522,
-0.02672366239130497,
0.025889862328767776,
-0.01586819998919964,
-0.014002550393342972,
0.011592542752623558,
-0.02418510802090168,
0.00496858824044466,
-0.035884689539670944,
-0.021894017234444618,
0.027232468128204346,
-0.05314548686146736,
-0.01968260481953621,
0.01959296502172947,
-0.040141597390174866,
-0.025802014395594597,
0.04581880569458008,
0.026573503389954567,
0.040879979729652405,
-0.05547579377889633,
0.0011651813983917236,
0.01959288865327835,
-0.012624965980648994,
-0.0034440658055245876,
0.006917858961969614,
0.02863389067351818,
0.01938723586499691,
-0.027675529941916466,
0.03283435478806496,
-0.00979657843708992,
0.0015290131559595466,
-0.00932928267866373,
0.04147249832749367,
0.005704611539840698,
-0.03639187663793564,
0.030782824382185936,
-0.013261276297271252,
-0.021877454593777657,
-0.021936705335974693,
-0.040544647723436356,
0.06131492927670479,
-0.005409710109233856,
-0.005343954544514418,
-0.035668302327394485,
-0.02047029137611389,
0.010816095396876335,
0.05004486069083214,
0.032225918024778366,
0.03660766780376434,
-0.008669580332934856,
0.02410208433866501,
-0.01313845906406641,
-0.013970687054097652,
0.04693927243351936,
-0.03788598254323006,
0.010406699031591415,
-0.02228783629834652,
0.00871292594820261,
0.004205651115626097,
-0.024672189727425575,
0.02451368235051632,
0.010954273864626884,
0.046304456889629364,
0.06394477933645248,
0.01923798955976963,
-0.009142130613327026,
0.0037197587080299854,
0.012741324491798878,
0.0727415457367897,
-0.027881938964128494,
-0.018070416525006294,
-0.01850058324635029,
0.029337646439671516,
0.015466264449059963,
0.015031307935714722
] |
<p>Consider general state of a system with spin-$1/2$</p>
<p>$$ \psi = \frac{1}{\sqrt{2}}\left[\phi_{+1/2}(x) \left( \begin{array}{cc} 1 \\ 0 \\ \end{array} \right) + \phi_{-1/2}(x) \left( \begin{array}{cc} 0 \\ 1 \\ \end{array} \right)\right]. $$</p>
<p>If I created an apparatus which measures <em>only spin</em> would that imply that the $x$-dependence of $\psi$ remains uncertain after measurement? E.g. if the system appeared to be in $+1/2$ state then the coordinate part of wave function (w.f.) didn't undergo collapse</p>
<p>$$ \psi' = \phi_{+1/2}(x) \left( \begin{array}{cc} 1 \\ 0 \\ \end{array} \right) .$$</p>
<p>Maybe such an apparatus cannot be created (why?) or if one "part" of w.f. is measured then all other "parts" necessarily collapse too, but their values go by unnoticed?</p>
<p><strong>UPD</strong></p>
<p>In a more general way: I have a set of "uncoupled" observables $\alpha$, $\beta$ (say spin and isospin). If I measure $\alpha$ does that mean that $\beta$ will also take a definite value (will be measured indirectly).</p> | 1,480 | [
0.019420748576521873,
0.005286724306643009,
-0.004802888259291649,
-0.03630124777555466,
0.018670106306672096,
-0.00011025895219063386,
-0.07329531759023666,
-0.02213658206164837,
0.037364259362220764,
-0.029133787378668785,
0.03624456003308296,
-0.005049200728535652,
0.0325651653110981,
0.02593846805393696,
0.000032742536859586835,
0.011062996461987495,
-0.0026940421666949987,
0.011906428262591362,
-0.024905189871788025,
-0.047885145992040634,
0.01913106068968773,
0.04187694564461708,
0.019946614280343056,
0.006929236464202404,
-0.013233695179224014,
0.03716123476624489,
-0.036663979291915894,
-0.015811551362276077,
-0.002491924213245511,
0.07769536972045898,
-0.05505122244358063,
-0.04258805513381958,
0.0032986693549901247,
0.021094541996717453,
0.044212017208337784,
-0.013293708674609661,
-0.009845544584095478,
-0.05470587685704231,
0.018658747896552086,
0.009150735102593899,
-0.0636630728840828,
-0.014963831752538681,
-0.035800039768218994,
0.004786808043718338,
-0.04435644671320915,
-0.037435706704854965,
-0.0009024241007864475,
-0.016218218952417374,
0.06323306262493134,
-0.048950035125017166,
0.0319284163415432,
0.01766352728009224,
0.0370117723941803,
-0.005672489758580923,
-0.006825606804341078,
-0.004464295227080584,
0.04838813096284866,
0.06768275052309036,
-0.0050388602539896965,
-0.03448622301220894,
-0.038429856300354004,
-0.00717717781662941,
0.01930469460785389,
-0.01944499835371971,
-0.022744880989193916,
0.038640331476926804,
-0.00034246270661242306,
-0.013267694972455502,
0.032414861023426056,
-0.031181706115603447,
0.01968546025454998,
0.018974699079990387,
0.03592338785529137,
0.004979074466973543,
0.005696799140423536,
0.01751529425382614,
0.027054468169808388,
0.015697462484240532,
0.023661551997065544,
0.03317366912961006,
0.015086529776453972,
0.03640759736299515,
0.048026878386735916,
0.004828792065382004,
-0.012213013134896755,
-0.01950962096452713,
0.06058920547366142,
-0.017359167337417603,
0.039205942302942276,
0.03170867636799812,
0.024828322231769562,
-0.0179300457239151,
0.020968804135918617,
-0.04262705519795418,
-0.026363475248217583,
0.029986418783664703,
-0.0004367798683233559,
0.052963245660066605,
-0.007877632044255733,
-0.02749600075185299,
-0.016394179314374924,
-0.013576294295489788,
0.024757612496614456,
0.055221058428287506,
0.01122377347201109,
-0.006267399527132511,
-0.015458747744560242,
0.01779892109334469,
-0.010019121691584587,
-0.04090244323015213,
0.011556150391697884,
0.02160833589732647,
-0.0068519627675414085,
0.015691427513957024,
0.026371480897068977,
0.0037953283172100782,
-0.0225317794829607,
-0.02813696302473545,
0.054711174219846725,
0.0617326982319355,
0.022261809557676315,
-0.0018065216718241572,
-0.007401788607239723,
-0.04307796433568001,
-0.09096702188253403,
0.033758264034986496,
0.032608747482299805,
-0.0018175420118495822,
-0.07157915830612183,
0.026535145938396454,
0.02787463739514351,
0.0010625575669109821,
0.04082890972495079,
0.0077789234928786755,
0.01804942451417446,
-0.007625891361385584,
-0.09461085498332977,
-0.050457365810871124,
0.013544909656047821,
-0.006082102656364441,
-0.005408570170402527,
-0.019933389499783516,
-0.0032846874091774225,
0.06085485219955444,
0.09327193349599838,
-0.034027665853500366,
0.01785033382475376,
0.020505525171756744,
0.027847422286868095,
0.015023479238152504,
-0.022773901000618935,
-0.03677913919091225,
-0.017911503091454506,
-0.04978659376502037,
-0.035154785960912704,
-0.02496519312262535,
0.05279766023159027,
0.054710641503334045,
-0.0076133497059345245,
0.004398052580654621,
0.015682388097047806,
-0.02180648408830166,
0.013400656171143055,
0.021443773061037064,
-0.005897761322557926,
-0.031633149832487106,
0.07302363961935043,
-0.0034618848003447056,
0.014322029426693916,
0.02269507572054863,
-0.010332410223782063,
0.003709038021042943,
-0.019747890532016754,
0.021665770560503006,
0.04917985200881958,
0.0018153081182390451,
-0.08096778392791748,
-0.030263224616646767,
0.008650610223412514,
-0.010836814530193806,
-0.03484489768743515,
-0.014486902393400669,
-0.07339999824762344,
0.04002012684941292,
0.03340280428528786,
0.04059362784028053,
0.02660568617284298,
-0.005033002234995365,
0.00992621760815382,
-0.04047396779060364,
-0.021459074690937996,
-0.03233782947063446,
-0.0005559389828704298,
0.03121696598827839,
-0.01308488193899393,
0.06523047387599945,
-0.004499606788158417,
-0.00887398049235344,
-0.00018938013818114996,
-0.03523941710591316,
-0.0023687260691076517,
0.007508025970309973,
0.015267756767570972,
-0.023715632036328316,
0.004490673076361418,
0.013995816931128502,
0.029182814061641693,
-0.004865811672061682,
0.049991361796855927,
-0.03175114467740059,
-0.046707406640052795,
0.009372086264193058,
-0.030244925990700722,
0.0060463654808700085,
0.024053869768977165,
-0.005125605501234531,
0.01403115876019001,
-0.02346167527139187,
-0.017046578228473663,
0.005543746519833803,
-0.0507119819521904,
0.04443217068910599,
0.053101327270269394,
-0.045532215386629105,
0.00013553188182413578,
0.041888415813446045,
0.044929079711437225,
0.0016110361320897937,
-0.02320803515613079,
-0.01705971732735634,
-0.036450523883104324,
-0.017706692218780518,
0.018172428011894226,
0.05352276191115379,
-0.03093884140253067,
0.029546918347477913,
0.023045718669891357,
0.004690576810389757,
0.015979966148734093,
0.01386096328496933,
0.003096651751548052,
-0.01829189620912075,
-0.014913132414221764,
-0.004369768314063549,
0.02153870277106762,
0.02251112088561058,
0.0070521896705031395,
0.01410633884370327,
0.0029139574617147446,
-0.0028007091023027897,
-0.009980108588933945,
-0.00530601991340518,
-0.010036109946668148,
-0.00688916677609086,
0.000662187288980931,
-0.034403275698423386,
0.018688149750232697,
0.004922151565551758,
0.02354501001536846,
0.005019397474825382,
-0.031005216762423515,
0.008233482949435711,
-0.020773211494088173,
-0.0357922688126564,
0.010536865331232548,
0.004509203601628542,
-0.04606161266565323,
-0.04987344890832901,
0.015198110602796078,
-0.0318109393119812,
-0.02043803595006466,
-0.024083876982331276,
0.0024259265046566725,
0.014486238360404968,
-0.0051599713042378426,
0.09084635227918625,
-0.010422173887491226,
0.013755121268332005,
-0.06993447989225388,
-0.043717168271541595,
-0.014949703589081764,
-0.01810399815440178,
0.04246329888701439,
0.04139013588428497,
-0.05051156505942345,
-0.013078512623906136,
-0.05374062433838844,
-0.024889584630727768,
0.00930362194776535,
-0.016831273213028908,
0.010662930086255074,
0.0009634646121412516,
-0.01037618052214384,
-0.07608213275671005,
-0.03528044745326042,
-0.014473541639745235,
-0.03427506983280182,
-0.03963948041200638,
-0.006700937170535326,
0.05758335813879967,
0.011757854372262955,
-0.010392071679234505,
-0.008624543435871601,
-0.010932328179478645,
-0.01897360198199749,
-0.015070213936269283,
-0.017838211730122566,
0.036054953932762146,
-0.033570852130651474,
-0.004653635434806347,
0.026697073131799698,
-0.02104877308011055,
-0.03457263484597206,
-0.06836321204900742,
-0.07337813079357147,
0.0076014818623661995,
0.01899133063852787,
-0.0008517251699231565,
0.012571088038384914,
0.003904634853824973,
0.11776989698410034,
0.014591624028980732,
-0.03587473928928375,
-0.025609824806451797,
0.03753285855054855,
-0.00017167067562695593,
-0.047050148248672485,
-0.05030515044927597,
-0.01469948049634695,
0.037861499935388565,
0.07481058686971664,
0.021330464631319046,
0.035113342106342316,
0.0061944820918142796,
0.03966553881764412,
0.00654235016554594,
0.047026585787534714,
0.04681386798620224,
-0.01837279088795185,
0.04296578839421272,
0.0357278473675251,
-0.001122802495956421,
-0.01767861098051071,
0.010754871182143688,
0.02030956745147705,
0.03430422395467758,
-0.04861653968691826,
0.0562991201877594,
0.013348681852221489,
0.02034967765212059,
0.010635079815983772,
0.04695562273263931,
0.01187426969408989,
-0.02042507566511631,
-0.017491426318883896,
-0.0015171418199315667,
0.04547640308737755,
-0.006099153775721788,
0.008252336643636227,
0.06549279391765594,
0.013820911757647991,
-0.02859676256775856,
-0.05469980090856552,
-0.014932830817997456,
0.00992575567215681,
0.042800676077604294,
-0.008235512301325798,
-0.03841934725642204,
0.05780794471502304,
0.056197021156549454,
0.030602669343352318,
-0.03343692049384117,
-0.01605367287993431,
-0.018656132742762566,
-0.054112616926431656,
-0.010824020951986313,
-0.02605876326560974,
0.03052608296275139,
0.0355808287858963,
0.0428447425365448,
0.05587146803736687,
-0.003250907873734832,
-0.036209963262081146,
-0.007405764888972044,
-0.0960051417350769,
-0.00192813400644809,
0.00894040334969759,
0.014280092902481556,
0.0016667499439790845,
0.02704838290810585,
0.023745562881231308,
-0.01197205763310194,
-0.019292229786515236,
-0.0447048582136631,
0.003912363667041063,
-0.061387550085783005,
0.01161831896752119,
-0.011493965983390808,
-0.03357445076107979,
-0.04801663011312485,
0.06177854165434837,
0.03721797838807106,
-0.020637821406126022,
0.012210181914269924,
0.0028672185726463795,
-0.020995374768972397,
0.03131887689232826,
-0.04842783883213997,
0.00810152292251587,
0.017662422731518745,
0.02603769302368164,
0.0735294297337532,
0.016081474721431732,
0.014185575768351555,
-0.0054441187530756,
0.052548106759786606,
0.0752139538526535,
-0.02184605598449707,
-0.01992453634738922,
0.015129811130464077,
0.024620696902275085,
-0.002154909074306488,
-0.0022545354440808296,
0.03446785360574722,
0.04117169603705406,
0.02393632009625435,
0.009890617802739143,
0.0016859181923791766,
-0.002779185539111495,
0.02264443226158619,
0.03150369971990585,
0.007892976514995098,
0.00015814192011021078,
-0.021925782784819603,
-0.015438350848853588,
-0.006071353796869516,
-0.007748366333544254,
-0.04896791651844978,
-0.003169082570821047,
0.010371771641075611,
-0.01580852083861828,
0.011893751099705696,
0.017363185063004494,
-0.0066929468885064125,
0.026368090882897377,
0.006825657095760107,
-0.012802873738110065,
0.0076188030652701855,
0.00018865990568883717,
0.03138439357280731,
0.02161666937172413,
0.025584297254681587,
0.018374809995293617,
-0.011232584714889526,
-0.05680033192038536,
0.002776205074042082,
0.015405352227389812,
0.024208853021264076,
0.0049276938661932945,
-0.0027755387127399445,
-0.010308784432709217,
-0.04050981253385544,
0.0327061265707016,
-0.007094814907759428,
0.013413714244961739,
-0.022010060027241707,
-0.03221624344587326,
-0.023439008742570877,
-0.05324004590511322,
-0.043222419917583466,
0.014757378958165646,
0.00527960853651166,
0.019548505544662476,
-0.01694357767701149,
-0.016735069453716278,
0.003993717022240162,
-0.0057098157703876495,
-0.002904977183789015,
0.023642821237444878,
0.003872751956805587,
0.0008111207280308008,
-0.013854749500751495,
0.0186415184289217,
-0.0077939871698617935,
-0.0924062430858612,
0.017963340505957603,
0.000004552633072307799,
-0.022765478119254112,
0.048919614404439926,
-0.020911922678351402,
-0.07999751716852188,
0.021452581509947777,
-0.0020270829554647207,
-0.02715340442955494,
0.05689273029565811,
-0.03684563189744949,
0.07158723473548889,
0.03487240523099899,
-0.004806595388799906,
0.06047600507736206,
0.03445242717862129,
0.02557501010596752,
-0.003770790994167328,
-0.0065809437073767185,
-0.009477385319769382,
-0.03711583837866783,
0.03813730552792549,
-0.05458329617977142,
0.026670603081583977,
-0.023271052166819572,
0.05151749774813652,
-0.0005523792351596057,
0.02046319469809532,
0.01538335345685482,
-0.022628992795944214,
0.00018577047740109265,
0.01019753236323595,
-0.0034716760274022818,
0.015692483633756638,
-0.04694204032421112,
0.018121734261512756,
-0.0056254686787724495,
-0.03466639295220375,
-0.031564921140670776,
0.03196316584944725,
0.005022453144192696,
0.06158899515867233,
-0.012644520029425621,
0.021437842398881912,
-0.021650338545441628,
0.00242494884878397,
0.017627350986003876,
-0.03404463082551956,
0.007685363292694092,
-0.0032487406861037016,
-0.003112089354544878,
0.022867197170853615,
-0.016594216227531433,
-0.029327020049095154,
0.028032878413796425,
0.00025716592790558934,
-0.02202196605503559,
-0.043191175907850266,
-0.011514042504131794,
0.017763247713446617,
-0.0042096031829714775,
-0.08139704912900925,
-0.030151812359690666,
0.0072217704728245735,
0.016305362805724144,
0.019934918731451035,
0.013840959407389164,
0.018983734771609306,
-0.0008372689480893314,
-0.0006975748692639172,
-0.019847502931952477,
0.001916038803756237,
-0.010812406428158283,
0.0034532640129327774,
0.0045961011201143265,
0.008245854638516903,
0.02713417075574398,
-0.027904419228434563,
0.00078547652810812,
0.010978251695632935,
0.002345113083720207,
-0.013658294454216957,
0.026754116639494896,
-0.002803534036502242,
-0.03487810865044594,
-0.0712977796792984,
-0.003747564973309636,
-0.008535304106771946,
0.0017381546786054969,
0.0016177339712157845,
-0.004254668485373259,
0.010026006028056145,
0.004552584607154131,
0.01183070708066225,
0.02551458217203617,
-0.040229879319667816,
0.0023737074807286263,
0.004918185528367758,
0.05649859085679054,
-0.011707939207553864,
-0.029050305485725403,
-0.03724765405058861,
0.016741424798965454,
-0.005028108134865761,
-0.03394516184926033,
0.0052520208992064,
0.039316512644290924,
0.010335912927985191,
-0.018538545817136765,
0.02887653559446335,
-0.01250411942601204,
0.01785499043762684,
0.027301859110593796,
0.007161238696426153,
0.01492287963628769,
0.023402534425258636,
-0.03232302516698837,
-0.003269131062552333,
-0.03459397330880165,
-0.0018220891943201423,
0.0387040413916111,
0.015876611694693565,
0.01200894359499216,
0.010554056614637375,
-0.014607175253331661,
-0.021913355216383934,
-0.02325884997844696,
-0.0094007458537817,
0.0023069141898304224,
0.007602110505104065,
0.05383892357349396,
-0.047018181532621384,
-0.00906682014465332,
0.02971271239221096,
0.011472675018012524,
-0.005374946165829897,
-0.0035456891637295485,
0.028304988518357277,
0.02974797412753105,
0.03236117959022522,
-0.04745166376233101,
-0.03448748588562012,
0.04232307896018028,
-0.01987644098699093,
-0.009599534794688225,
-0.0029331643600016832,
-0.02568023093044758,
0.016351832076907158,
0.010145527310669422,
0.05785746872425079,
-0.03657903894782066,
-0.01860804483294487,
-0.06133710592985153,
0.008449668064713478,
0.005948780570179224,
0.002895783632993698,
-0.005259884987026453,
0.010034305974841118,
0.044116679579019547,
0.006108637899160385,
0.02894473634660244,
-0.008990616537630558,
-0.07692937552928925,
-0.031572841107845306,
-0.02208486571907997,
-0.0506778322160244,
0.06111175939440727,
-0.016495583578944206,
-0.009185243397951126,
0.014292195439338684,
-0.04451138526201248,
0.04635649174451828,
0.005965250078588724,
0.04963620752096176,
-0.03209483250975609,
0.03481077775359154,
0.00902154203504324,
0.052556440234184265,
0.0022641478572040796,
-0.006100846454501152,
0.13037554919719696,
0.03661563992500305,
0.03961637616157532,
-0.04187542200088501,
-0.031904228031635284,
-0.006829303689301014,
0.0502232164144516,
-0.007019690703600645,
0.01892194151878357,
0.03397339954972267,
-0.005117539782077074,
-0.008150343783199787,
0.07395265996456146,
0.012815244495868683,
0.0007518722559325397,
0.029995759949088097,
-0.04810767248272896,
-0.011398144997656345,
-0.016808243468403816,
0.034094974398612976,
-0.004464189521968365,
-0.005321941804140806,
-0.011114419437944889,
0.018380790948867798,
-0.005111244507133961,
0.021176228299736977,
0.016207778826355934,
-0.041173819452524185,
-0.017546964809298515,
-0.012549162842333317,
-0.021882886067032814,
0.015207655727863312,
-0.007252268958836794,
0.006579797714948654,
-0.013728721998631954,
0.020761463791131973,
0.0291755311191082,
-0.02926056832075119,
0.016000699251890182,
0.033873289823532104,
-0.016015565022826195,
0.004065657965838909,
0.008535250090062618,
0.015250332653522491,
-0.062364235520362854,
-0.0008423965773545206,
-0.007460632361471653,
0.06544697284698486,
-0.0092000812292099,
-0.021543601527810097,
-0.017670828849077225,
-0.034519534558057785,
0.014850146137177944,
-0.024654287844896317,
-0.04258715733885765,
0.0107184499502182,
-0.002528996439650655,
-0.03449321910738945,
0.0003600922937039286,
0.006365080364048481,
-0.005567926913499832,
-0.0017741905758157372,
0.014410399831831455,
0.00033688335679471493,
-0.03251736983656883,
-0.027009494602680206,
0.015233398415148258,
0.0509006530046463,
0.040007080882787704,
0.007999151013791561,
-0.0269320011138916,
-0.014588841237127781,
-0.025779232382774353,
-0.015199165791273117,
0.03132049739360809,
-0.007791909854859114,
0.02179975062608719,
-0.011354881338775158,
0.025390731170773506,
0.00043646208359859884,
-0.029595401138067245,
0.024073803797364235,
-0.05478912591934204,
-0.0042331586591899395,
-0.011695615015923977,
0.010753503069281578,
-0.012721914798021317,
0.027225635945796967,
-0.05266793072223663,
-0.06814652681350708,
-0.0013444827636703849,
0.07283960282802582,
0.025417275726795197,
-0.017140991985797882,
-0.024928929284214973,
0.007706453558057547,
-0.035214390605688095,
0.015788352116942406,
0.010022313334047794,
0.006693228613585234,
0.0168596338480711,
-0.004089804366230965,
-0.010865149088203907,
0.008476311340928078,
-0.010356402955949306,
-0.02109195664525032,
0.026828670874238014,
-0.04921475797891617,
-0.005513433832675219,
0.023313773795962334,
0.02999359928071499,
-0.0219617560505867,
-0.022918859496712685,
-0.014702223241329193,
-0.006926754955202341,
0.0033626225776970387,
0.03017175756394863,
-0.0391373373568058,
-0.009954056702554226,
-0.0005291334236972034,
0.03766993433237076,
0.006658569443970919,
-0.0009796172380447388,
-0.044487278908491135,
-0.014783342368900776,
-0.006854000501334667,
-0.03164709731936455,
0.025110509246587753,
0.014215542003512383,
0.024327555671334267,
-0.04628068581223488,
-0.00020891653548460454,
0.03570690378546715,
-0.05856074020266533,
0.009656651876866817,
0.02602658048272133,
0.03411733731627464,
0.020259380340576172,
-0.02038010023534298,
-0.030635729432106018,
0.006673998199403286,
-0.058622341603040695,
-0.03203956410288811,
0.08224517107009888,
-0.0006725015118718147,
0.03361418470740318,
0.02727017179131508,
-0.0019020525505766273,
-0.022402191534638405,
-0.0013684452278539538,
-0.05483615770936012,
-0.019038911908864975,
0.017478859052062035,
-0.012235761620104313,
-0.031094031408429146,
-0.0002553070953581482,
0.0355331189930439,
0.007981236092746258,
-0.011932269670069218,
0.04494307190179825,
0.02097320184111595,
0.028663823381066322,
0.038889411836862564,
0.02511591464281082,
0.006338018458336592,
0.04128721356391907,
0.024203704670071602,
-0.03947722166776657,
0.014908285811543465,
0.07899000495672226,
-0.06482749432325363,
0.023423928767442703,
0.024675853550434113,
0.013976379297673702,
-0.09629081934690475,
-0.02446657046675682,
-0.011100893840193748,
0.016509270295500755,
0.016693096607923508,
-0.010378476232290268,
0.023781921714544296,
0.044549424201250076,
-0.10139408707618713,
0.0321619026362896,
-0.031578339636325836,
-0.00378618692047894,
-0.01216570008546114,
-0.0112150264903903,
-0.06809001415967941,
0.056196533143520355,
0.017865220084786415,
0.035615261644124985,
-0.0026574397925287485,
0.04771743342280388,
-0.03551296144723892,
-0.035308998078107834,
-0.03797603398561478,
-0.012942751869559288,
-0.01987536996603012,
-0.04103377088904381,
0.07096606492996216,
-0.03559895604848862,
-0.010597923770546913,
-0.01239185780286789,
-0.026296965777873993,
0.009354596957564354,
-0.030382927507162094,
-0.005890973843634129,
0.0017061089165508747,
0.01356068067252636,
-0.002952694660052657,
0.009073627181351185,
0.008974025025963783,
-0.008333228528499603,
0.027561185881495476,
0.03197948634624481,
0.013532447628676891,
0.013430961407721043,
0.014037417247891426,
-0.028778228908777237,
-0.02299504354596138,
0.008110414259135723,
0.003992090001702309,
-0.013557303696870804,
0.0035084683913737535,
0.042899638414382935,
0.0013744570314884186,
-0.02768946997821331,
0.014680641703307629,
-0.023157835006713867,
-0.022331995889544487,
0.019168345257639885,
0.05180537328124046,
0.0027109042275696993,
-0.007010472938418388,
-0.01987413875758648,
-0.02892799861729145,
0.05233397334814072,
0.0071943411603569984,
-0.036050211638212204,
-0.0449727438390255,
-0.02841752953827381,
-0.009743385948240757,
0.017307842150330544,
0.04547058045864105,
-0.006495303474366665,
-0.04223757982254028,
0.014219929464161396,
-0.007560328580439091,
0.0025543842930346727,
-0.019241265952587128,
-0.03216657042503357,
-0.026910513639450073,
-0.09994399547576904,
0.02388426661491394,
0.02130923420190811,
0.013588636182248592,
-0.015100257471203804,
-0.0011056142393499613,
-0.022014286369085312,
-0.01550198346376419,
0.057545069605112076,
0.028280647471547127,
-0.004476489033550024,
0.033526018261909485,
0.019884558394551277,
-0.00660576019436121,
-0.005148486699908972,
0.028041159734129906,
-0.04168150573968887,
0.008746478706598282,
0.002693301299586892,
-0.027568720281124115,
-0.006278222892433405,
0.025032591074705124,
0.035884592682123184,
0.01981266401708126,
0.003136806422844529,
-0.0040176426991820335,
-0.021654518321156502,
0.06160770356655121,
-0.02148369513452053,
0.0006015410763211548,
0.054457150399684906,
0.0026192190125584602,
0.050608742982149124,
0.04504112899303436,
-0.04670153558254242,
-0.07956410944461823,
0.03233044967055321,
-0.015156494453549385,
-0.04870298132300377,
-0.017795240506529808,
-0.0023597613908350468,
0.017360202968120575,
-0.029849227517843246,
-0.026078971102833748,
0.018353622406721115,
-0.03521805256605148,
-0.017373228445649147,
0.030569586902856827,
0.01637103408575058,
0.053323857486248016,
0.013784999027848244,
-0.002904658205807209,
0.03710201382637024,
-0.006794283632189035,
0.03941554203629494,
0.06880757957696915,
0.03758452832698822,
0.03604188933968544,
0.018341409042477608,
0.028426768258213997,
-0.029861142858862877,
0.0135255241766572,
0.016613958403468132,
0.05727522075176239,
-0.007308024913072586,
0.0036365515552461147,
0.037139955908060074,
0.0074416217394173145,
-0.010573669336736202,
-0.018986985087394714,
-0.03599582612514496,
0.07868452370166779,
-0.03458181768655777,
0.013452460058033466,
-0.05623279884457588,
-0.00006921859312569723,
-0.013018982484936714,
0.007443360984325409,
0.042925409972667694,
0.0579114705324173,
-0.008351922035217285,
-0.001857762224972248,
-0.05851137265563011,
0.014280392788350582,
0.02660343423485756,
-0.038969092071056366,
0.006590007338672876,
-0.019098777323961258,
0.002876362996175885,
0.024651503190398216,
-0.04741751402616501,
-0.03217382729053497,
-0.04716026037931442,
0.021780934184789658,
0.014798492193222046,
0.014658628031611443,
-0.020075876265764236,
-0.010275157168507576,
-0.0707874596118927,
0.07984249293804169,
-0.04413861781358719,
-0.016978371888399124,
0.0018229030538350344,
0.04478835687041283,
-0.012279083020985126,
-0.02294895425438881
] |
<p>Are there any hamiltonian systems without a periodic orbit? Can anyone give me an example?</p>
<p>If such a system exists, does this fact have any implication on its quantum version?</p> | 1,481 | [
-0.03043862245976925,
-0.009489615447819233,
0.0013808459043502808,
-0.006594033446162939,
0.040697574615478516,
-0.002004876034334302,
-0.027970217168331146,
-0.033551644533872604,
0.0028140887152403593,
-0.055760707706213,
0.014026333577930927,
0.011008958332240582,
0.021016985177993774,
0.00674614030867815,
-0.009584206156432629,
-0.004553135018795729,
-0.020108256489038467,
-0.017114801332354546,
-0.017807340249419212,
0.011344858445227146,
0.009505780413746834,
0.036834683269262314,
0.03978560492396355,
0.0076646627858281136,
0.005927212070673704,
0.024108940735459328,
0.020503822714090347,
0.0022459544707089663,
0.04813957214355469,
0.0742403119802475,
-0.02104584313929081,
-0.01155538484454155,
-0.008433694019913673,
0.045739635825157166,
0.03184325620532036,
0.016003673896193504,
-0.047790978103876114,
-0.027447208762168884,
0.02130476012825966,
-0.02608976885676384,
-0.02502797171473503,
-0.01571521908044815,
-0.02625439129769802,
0.03966990113258362,
-0.002006721682846546,
0.01476840116083622,
0.023157257586717606,
-0.001241935882717371,
0.07497365772724152,
-0.05904524028301239,
0.050580091774463654,
0.0040850769728422165,
0.0022862902842462063,
0.006817047018557787,
0.01640787534415722,
-0.014355686493217945,
0.06844688206911087,
0.08862883597612381,
-0.03476196527481079,
-0.03743609040975571,
-0.04571086913347244,
-0.03921014443039894,
0.008167088963091373,
-0.036299820989370346,
-0.05089360848069191,
0.03563963621854782,
0.019976459443569183,
-0.06639000028371811,
0.006357939448207617,
0.029347114264965057,
-0.02247653529047966,
-0.010113084688782692,
0.025094730779528618,
-0.0424359105527401,
0.0033141165040433407,
-0.04004335403442383,
0.01849011331796646,
-0.0036992074456065893,
0.02000434882938862,
0.04735599085688591,
-0.015371531248092651,
-0.004699881188571453,
0.0024735929910093546,
0.00851296167820692,
-0.004156617913395166,
-0.0064470707438886166,
0.03032093495130539,
0.0039221495389938354,
-0.02719706855714321,
0.03400326892733574,
-0.024604929611086845,
0.0005304334335960448,
0.03436257690191269,
-0.014897658489644527,
-0.020600715652108192,
0.008363056927919388,
0.036236975342035294,
0.05447213351726532,
-0.0031121261417865753,
-0.019817037507891655,
0.020988313481211662,
-0.04126076400279999,
0.003070308594033122,
0.10349683463573456,
0.02650672197341919,
-0.00457637058570981,
-0.00171544193290174,
0.029139211401343346,
-0.026090769097208977,
0.028096238151192665,
-0.005435382016003132,
0.003742724657058716,
0.02338608354330063,
-0.017702650278806686,
0.001639724476262927,
0.0047862292267382145,
-0.012286379002034664,
-0.017378387972712517,
0.026838159188628197,
0.11321231722831726,
0.008549420163035393,
-0.023117953911423683,
0.0020003467798233032,
-0.06298526376485825,
-0.03327915072441101,
0.02101019024848938,
0.05886391922831535,
0.012646765448153019,
-0.043646715581417084,
-0.008326329290866852,
0.023352982476353645,
-0.01294961478561163,
0.047811318188905716,
-0.016422230750322342,
0.05589507147669792,
-0.037261273711919785,
-0.10578504204750061,
-0.03557934612035751,
0.033665724098682404,
-0.005199030973017216,
-0.024275733157992363,
-0.0661359503865242,
0.03754337504506111,
0.031777795404195786,
0.07155308127403259,
0.006802708841860294,
-0.034644633531570435,
0.033201515674591064,
0.03826863318681717,
0.02911500446498394,
0.007576838601380587,
0.0009169055265374482,
0.0063177673146128654,
-0.07586333155632019,
-0.00611546216532588,
-0.057200878858566284,
0.03376775607466698,
0.03030357137322426,
0.04061727598309517,
-0.010465536266565323,
0.04907479137182236,
-0.028405094519257545,
0.020404277369379997,
0.02601258084177971,
0.017276152968406677,
-0.03211263194680214,
0.05953134596347809,
-0.0012634053127840161,
0.029438341036438942,
0.016529306769371033,
0.019651146605610847,
0.04213717579841614,
0.0060854721814394,
0.054290056228637695,
0.03420436009764671,
-0.030390840023756027,
-0.038595400750637054,
-0.006708860397338867,
0.008633499033749104,
-0.008538486436009407,
-0.020046338438987732,
-0.019710659980773926,
0.001439798274077475,
0.011347784660756588,
-0.01422550342977047,
0.04643194004893303,
0.009737703949213028,
0.04216450825333595,
0.026008063927292824,
-0.04443943127989769,
0.0035480703227221966,
-0.03904392197728157,
0.030695529654622078,
0.020269572734832764,
-0.0334431454539299,
0.041589993983507156,
0.04319906234741211,
-0.02559310756623745,
-0.02124343253672123,
-0.04489699751138687,
0.016735313460230827,
0.008429831825196743,
-0.01935272105038166,
-0.052762698382139206,
0.026308288797736168,
0.040182556957006454,
0.0367303341627121,
0.0222624521702528,
0.03640884533524513,
-0.025998815894126892,
-0.030182955786585808,
-0.012428559362888336,
0.00044371880358085036,
0.03330458328127861,
-0.02115144394338131,
0.006550039630383253,
0.023512985557317734,
-0.029125168919563293,
-0.03366638347506523,
0.032374124974012375,
-0.05776373669505119,
0.04768642783164978,
0.032623667269945145,
0.0003500276361592114,
0.02491309680044651,
0.06345423310995102,
0.027364300563931465,
0.01025362592190504,
-0.0011308949906378984,
-0.033682018518447876,
-0.04813100025057793,
0.01827068254351616,
0.019861361011862755,
0.031456172466278076,
-0.04344015568494797,
0.03880167752504349,
0.02313433215022087,
0.07085945457220078,
0.022381851449608803,
0.014399121515452862,
-0.010110489092767239,
-0.020892847329378128,
0.047110579907894135,
0.006507393904030323,
0.023632382974028587,
0.005644208285957575,
0.04781515151262283,
-0.016009025275707245,
0.003108941251412034,
0.023076297715306282,
-0.05855041742324829,
0.039299752563238144,
-0.00407301913946867,
0.010545140132308006,
0.01761719211935997,
-0.035336364060640335,
0.05815340206027031,
-0.02434605173766613,
0.034806691110134125,
0.005612100008875132,
-0.04250552877783775,
-0.00005351024083211087,
-0.008778175339102745,
-0.020773807540535927,
-0.02478971891105175,
-0.012393801473081112,
-0.05259428173303604,
-0.04236004874110222,
0.04198477789759636,
-0.00477154366672039,
0.009629417210817337,
-0.03891316056251526,
0.00990479439496994,
-0.018162624910473824,
0.007890410721302032,
0.039873458445072174,
0.01745256967842579,
0.009852500632405281,
-0.030744457617402077,
-0.010072396136820316,
0.012102042324841022,
-0.04000864177942276,
-0.00142923672683537,
0.0362643264234066,
-0.034166499972343445,
0.024844355881214142,
-0.02902127057313919,
-0.03162726014852524,
0.060879625380039215,
-0.0067574819549918175,
0.024136625230312347,
0.016883812844753265,
-0.02917557768523693,
-0.04080226272344589,
-0.024325575679540634,
-0.029258057475090027,
-0.023370295763015747,
-0.08354060351848602,
0.01065334677696228,
0.03928646817803383,
-0.006038688123226166,
-0.033563412725925446,
-0.02480279840528965,
-0.030548926442861557,
-0.016123810783028603,
0.007781698368489742,
-0.016098137944936752,
0.04746539518237114,
-0.04403584823012352,
0.018825437873601913,
0.034573331475257874,
-0.04739903658628464,
0.018476778641343117,
-0.0696980282664299,
-0.04197760671377182,
0.008167789317667484,
-0.02736763469874859,
0.002854598220437765,
-0.010905822739005089,
-0.021502990275621414,
0.06405709683895111,
0.02533101476728916,
-0.0023522682022303343,
-0.02218986116349697,
-0.023480214178562164,
0.005278906784951687,
-0.03937053307890892,
0.013955406844615936,
0.01264408603310585,
0.008748598396778107,
0.007838934659957886,
0.033365052193403244,
0.005665631033480167,
0.008311477489769459,
0.02702530473470688,
-0.019954081624746323,
0.009668105281889439,
0.03292424976825714,
0.03170399367809296,
0.038880519568920135,
0.011360999196767807,
-0.03286211937665939,
0.01259306538850069,
-0.004677257966250181,
0.02485811524093151,
0.0040383231826126575,
-0.05609392002224922,
0.06571370363235474,
-0.010735749267041683,
0.02035604789853096,
0.02608403004705906,
0.04548739269375801,
-0.002983923302963376,
0.007329014129936695,
-0.038493745028972626,
0.0738782286643982,
0.029641669243574142,
0.017340179532766342,
0.02210226096212864,
0.03251204639673233,
0.0007735680555924773,
-0.03433408588171005,
0.024723121896386147,
0.024946581572294235,
-0.002649056725203991,
0.027829453349113464,
-0.013680540025234222,
-0.03359128162264824,
0.024623116478323936,
0.0001761722087394446,
0.04176619276404381,
0.01161854900419712,
-0.029526157304644585,
-0.01143418624997139,
-0.0503053218126297,
-0.016859957948327065,
-0.023006943985819817,
0.03099326230585575,
0.008210413157939911,
0.025005949661135674,
-0.031759317964315414,
0.0350918285548687,
-0.00926982332020998,
0.004987812601029873,
-0.04720519483089447,
0.01061782706528902,
-0.03237910941243172,
-0.027946460992097855,
0.016215670853853226,
0.029439175501465797,
-0.010983391664922237,
-0.014707537367939949,
-0.04753868654370308,
-0.025877146050333977,
0.0022585636470466852,
-0.05834043771028519,
-0.015995606780052185,
-0.020894011482596397,
-0.03965757414698601,
0.005128121469169855,
-0.025150241330266,
0.001423972425982356,
-0.04047079384326935,
0.030699098482728004,
0.012383415363729,
-0.022321226075291634,
0.015695922076702118,
0.002306994516402483,
0.012801150791347027,
0.0035197664983570576,
-0.0007249644841067493,
0.01665089651942253,
0.03873505815863609,
-0.014805154874920845,
-0.019623029977083206,
0.00025973733863793314,
0.06799812614917755,
0.01873617060482502,
0.0018281469820067286,
0.03215118870139122,
-0.04505930840969086,
-0.01695229858160019,
0.022892914712429047,
0.0605759434401989,
-0.010054501704871655,
0.022573262453079224,
0.017994312569499016,
-0.015831688418984413,
0.005573521833866835,
0.022914249449968338,
0.02272624894976616,
0.040326863527297974,
-0.012521570548415184,
-0.027413731440901756,
0.0022227384615689516,
-0.021867040544748306,
0.0077252318151295185,
0.017787644639611244,
-0.02811037190258503,
-0.004476973321288824,
0.022937320172786713,
0.0011040422832593322,
0.036500561982393265,
-0.0066546848975121975,
-0.026521457359194756,
-0.006529755424708128,
0.045744992792606354,
-0.02603849396109581,
0.029632914811372757,
0.029519466683268547,
0.022768398746848106,
0.0178038589656353,
0.00665799668058753,
0.011204815469682217,
-0.09609808772802353,
-0.014410671778023243,
0.05259612575173378,
-0.006532403640449047,
-0.0007497865008190274,
-0.009075455367565155,
-0.03596672788262367,
-0.03644830733537674,
0.04068399593234062,
-0.008896702900528908,
0.045995503664016724,
-0.029963867738842964,
-0.025081316009163857,
-0.030404306948184967,
-0.04091121256351471,
0.05048558488488197,
0.02770918235182762,
-0.013223294168710709,
0.0077296094968914986,
-0.0023628873750567436,
-0.002797979861497879,
-0.020889276638627052,
0.00217846198938787,
0.03342215716838837,
0.05852275714278221,
0.022515641525387764,
-0.012811471708118916,
0.004430205095559359,
0.01633707620203495,
-0.03638917952775955,
-0.1054660752415657,
-0.00627159234136343,
0.021854441612958908,
0.0118710333481431,
0.03434055298566818,
-0.05060170590877533,
-0.05190133675932884,
-0.018190667033195496,
-0.011988871730864048,
0.00875772349536419,
0.03988746926188469,
-0.03620662912726402,
0.017923176288604736,
0.010129647329449654,
0.011036256328225136,
0.03340563923120499,
0.04577973112463951,
0.001423293724656105,
-0.03353625908493996,
-0.004623666871339083,
0.04087303951382637,
-0.0628667101264,
0.00810521561652422,
-0.03812476992607117,
0.020105352625250816,
-0.033603064715862274,
0.032807499170303345,
-0.01807328686118126,
-0.018157832324504852,
0.03927057608962059,
-0.027931079268455505,
-0.014673283323645592,
0.018917350098490715,
0.010664084926247597,
0.0010143262334167957,
-0.03247828036546707,
0.03268654644489288,
-0.010592826642096043,
-0.0218378696590662,
0.007789370603859425,
-0.0086674178019166,
-0.01667523756623268,
0.03361954912543297,
-0.021135997027158737,
0.027982838451862335,
-0.04741746932268143,
-0.024840330705046654,
-0.010975584387779236,
-0.039947930723428726,
0.053879763931035995,
-0.01619994267821312,
-0.026536617428064346,
0.054624561220407486,
-0.04564701020717621,
-0.02607862465083599,
0.01909095048904419,
-0.037196263670921326,
-0.010722660459578037,
-0.03696398809552193,
0.039929069578647614,
0.012900086119771004,
-0.005790038499981165,
-0.08094712346792221,
-0.05919380113482475,
0.03002554178237915,
0.0036799393128603697,
-0.03087272308766842,
0.0046836077235639095,
0.0389607772231102,
-0.03426546975970268,
0.005412941332906485,
0.014045163057744503,
0.011387904174625874,
-0.046651408076286316,
0.002943270606920123,
0.02780652977526188,
0.014197497628629208,
0.030671007931232452,
0.011574167758226395,
-0.027925793081521988,
0.007608034182339907,
-0.032536230981349945,
-0.0010767735075205564,
-0.04760539159178734,
0.060184042900800705,
-0.01070756558328867,
-0.014476805925369263,
-0.0347558818757534,
-0.02776457369327545,
0.006258697714656591,
-0.010142956860363483,
-0.01269204169511795,
0.05212521180510521,
0.00031483024940826,
0.014221319928765297,
-0.00911895465105772,
-0.006610619369894266,
-0.00938531756401062,
0.014714590273797512,
-0.0008077311795204878,
0.02022922784090042,
-0.000012536824215203524,
-0.07019329816102982,
0.017969707027077675,
-0.004966270178556442,
-0.036680735647678375,
0.003980681765824556,
0.07512170076370239,
0.03492331504821777,
-0.01032413449138403,
0.026387332007288933,
-0.01176527515053749,
-0.019575191661715508,
-0.010580037720501423,
0.017125684767961502,
-0.01397908478975296,
-0.03629022464156151,
-0.021740484982728958,
-0.0710935890674591,
-0.028722915798425674,
0.023095380514860153,
0.05656670406460762,
-0.002004689071327448,
0.021790223196148872,
-0.01766889914870262,
0.009385253302752972,
-0.008870070800185204,
0.018129048869013786,
-0.010215148329734802,
0.011012120172381401,
0.00876948144286871,
0.030023539438843727,
-0.030213041231036186,
0.024955645203590393,
0.02823951654136181,
0.06314128637313843,
-0.02975262515246868,
0.028471969068050385,
0.0478917695581913,
0.011446038261055946,
0.016282860189676285,
0.019543517380952835,
-0.057477694004774094,
0.03754575550556183,
-0.025178909301757812,
0.05984479933977127,
0.01828543096780777,
-0.04954387992620468,
0.029095370322465897,
0.013085845857858658,
0.01431717537343502,
-0.023990517482161522,
0.004886388313025236,
-0.01559115294367075,
0.06811171770095825,
0.0042774127796292305,
0.04581940546631813,
0.00930651742964983,
-0.010494583286345005,
0.01998567394912243,
0.01697656884789467,
0.003766955342143774,
-0.0021778098307549953,
-0.04542529955506325,
-0.010340611450374126,
-0.0256577767431736,
-0.06576916575431824,
0.03609007969498634,
0.005326545797288418,
0.005211291369050741,
-0.017379624769091606,
-0.0041404967196285725,
0.006377506069839001,
0.023487141355872154,
0.031902264803647995,
-0.02320202812552452,
0.03763411566615105,
0.002595352241769433,
0.02241526171565056,
-0.01306901965290308,
0.05059899017214775,
0.11117918789386749,
0.03595919907093048,
0.02136140875518322,
-0.06423154473304749,
0.005806404631584883,
-0.0050315759144723415,
0.015919357538223267,
-0.0410897471010685,
0.0476689413189888,
0.010264611802995205,
-0.019566545262932777,
-0.03577446565032005,
0.03753603249788284,
-0.011532752774655819,
-0.009356433525681496,
0.05207756534218788,
-0.023433195427060127,
-0.020478975027799606,
-0.023913294076919556,
-0.014966797083616257,
0.016366444528102875,
0.005945684388279915,
-0.01753820665180683,
0.01482150424271822,
-0.04451167583465576,
0.003890765830874443,
-0.05521524325013161,
-0.037126168608665466,
0.027234183624386787,
0.036551520228385925,
-0.026189811527729034,
-0.007203221321105957,
0.020299848169088364,
-0.023652788251638412,
-0.0451538972556591,
0.018650222569704056,
0.017920073121786118,
0.002861684188246727,
0.041263408958911896,
0.06473369896411896,
0.010723406448960304,
0.0036882194690406322,
0.016562841832637787,
-0.011375590227544308,
-0.06001173332333565,
0.012923088856041431,
-0.019343992695212364,
0.02909795753657818,
-0.0416644886136055,
0.025615185499191284,
-0.014995505101978779,
-0.019516561180353165,
-0.038682326674461365,
-0.05631290376186371,
-0.0050131576135754585,
-0.02777010388672352,
0.014166117645800114,
-0.01805100217461586,
-0.06422880291938782,
-0.01684868521988392,
-0.013926628045737743,
-0.01358283031731844,
-0.002980031305924058,
-0.01893530786037445,
-0.01094834040850401,
0.00769699877128005,
0.03530847281217575,
0.03718676418066025,
-0.012845487333834171,
-0.02026153728365898,
-0.0066123283468186855,
-0.014190738089382648,
-0.060872867703437805,
-0.03242598474025726,
-0.0013653377536684275,
0.019963987171649933,
0.051513802260160446,
0.011248515918850899,
-0.026749439537525177,
-0.008293441496789455,
-0.03708362206816673,
-0.0010497310431674123,
0.011678197421133518,
-0.022529860958456993,
0.005766726098954678,
0.00036500615533441305,
0.04384947195649147,
0.023525254800915718,
-0.06242220103740692,
0.010999629274010658,
0.000534282298758626,
-0.002654468175023794,
0.030408494174480438,
-0.010648471303284168,
-0.0004329050425440073,
-0.009929471649229527,
-0.01999729685485363,
0.012154607102274895,
-0.032705482095479965,
0.0010234174551442266,
0.03074384666979313,
0.010639233514666557,
-0.009130807593464851,
0.045019496232271194,
-0.01780889555811882,
-0.004233933053910732,
0.02727821096777916,
-0.03549015522003174,
0.009535747580230236,
0.006312382407486439,
0.05296967551112175,
-0.07067759335041046,
-0.07111722230911255,
-0.027979359030723572,
0.016372334212064743,
-0.013730796054005623,
0.012365915812551975,
-0.028223885223269463,
0.0014322905335575342,
-0.002691206755116582,
0.061184369027614594,
-0.055751025676727295,
0.01639113575220108,
-0.06296970695257187,
0.006724899634718895,
0.03647409752011299,
0.0202565286308527,
-0.023525826632976532,
0.028461746871471405,
0.0031041183974593878,
-0.035622961819171906,
0.05055905878543854,
0.05463942140340805,
-0.016334131360054016,
0.025540122762322426,
0.017387986183166504,
0.0012665764661505818,
0.0241238996386528,
-0.009532016701996326,
-0.046188224107027054,
0.03593486547470093,
-0.045099738985300064,
-0.020154155790805817,
0.023291558027267456,
-0.06109112128615379,
0.018361615017056465,
0.032994337379932404,
-0.03135345131158829,
-0.007007816806435585,
0.008033119142055511,
0.0022450473625212908,
0.0012534121051430702,
0.03558191657066345,
-0.0046156831085681915,
-0.04018690437078476,
-0.0015989356907084584,
0.00016366096679121256,
-0.02897937409579754,
-0.0019334350945428014,
0.027376992627978325,
0.06445583701133728,
0.02595026046037674,
-0.030472440645098686,
-0.02673186920583248,
-0.007924759760499,
0.038751374930143356,
0.004993602633476257,
0.014893380925059319,
-0.0005190459196455777,
-0.008710852824151516,
-0.02936655282974243,
0.05261979624629021,
0.02026379108428955,
-0.008360621519386768,
-0.07657883316278458,
-0.013056733645498753,
-0.015355550684034824,
0.005070541985332966,
0.04400041699409485,
-0.01528074685484171,
-0.023754611611366272,
0.042158301919698715,
-0.11702187359333038,
0.045238837599754333,
-0.02017633058130741,
-0.02042638696730137,
-0.006048706825822592,
-0.006592826917767525,
-0.05113529413938522,
0.04473071172833443,
0.04696255177259445,
0.0008395471377298236,
0.023784594610333443,
0.02740098536014557,
-0.009520621038973331,
-0.00024065010074991733,
-0.005780847277492285,
0.0049389079213142395,
-0.018790753558278084,
-0.01125864777714014,
0.03329683467745781,
-0.03621397912502289,
-0.006226522848010063,
0.022453101351857185,
-0.001894135493785143,
0.02195027284324169,
-0.046193256974220276,
0.0062761371955275536,
-0.012436592020094395,
0.05788448825478554,
0.031096745282411575,
-0.0017580138519406319,
-0.042707785964012146,
0.0014115137746557593,
-0.0020938972011208534,
0.05498489737510681,
-0.035033807158470154,
0.01209211628884077,
0.02913600020110607,
-0.026446545496582985,
-0.025495480746030807,
0.021191507577896118,
-0.011406448669731617,
0.032828085124492645,
-0.0033516555558890104,
-0.009095555171370506,
0.003489208407700062,
-0.008700890466570854,
0.001810787245631218,
-0.012418613769114017,
-0.003948379307985306,
-0.003241306636482477,
-0.0025695960503071547,
-0.005136593710631132,
0.033167555928230286,
-0.005037568509578705,
-0.04253220930695534,
0.04248790070414543,
0.019107969477772713,
-0.016927404329180717,
-0.08226493746042252,
0.0043346816673874855,
-0.011533292941749096,
-0.003339971648529172,
-0.02114727534353733,
-0.05515018850564957,
-0.02042369171977043,
0.0598829910159111,
-0.012561826035380363,
0.0010912911966443062,
-0.03669679909944534,
-0.020944643765687943,
-0.011657709255814552,
-0.04271401837468147,
0.04528949409723282,
0.013050013221800327,
0.02139299362897873,
-0.011820552870631218,
-0.03187045082449913,
-0.016171853989362717,
-0.01581106148660183,
0.033720601350069046,
-0.0024677126202732325,
-0.002056676894426346,
0.02877391315996647,
0.017519323155283928,
0.025402147322893143,
-0.007214623037725687,
0.01921168528497219,
-0.025563770905137062,
0.01798410899937153,
0.016348473727703094,
-0.030774326995015144,
-0.04031553864479065,
0.037973444908857346,
0.05517468973994255,
-0.017264671623706818,
0.011051113717257977,
0.00846819207072258,
-0.029649240896105766,
0.07748191803693771,
0.0353502593934536,
0.010853483341634274,
0.0681418851017952,
0.003717635991051793,
0.04200674593448639,
0.013391717337071896,
-0.03819502890110016,
-0.027044957503676414,
-0.0006018975400365889,
-0.06951261311769485,
0.007425628136843443,
-0.03214375302195549,
-0.042547110468149185,
-0.00022832205286249518,
-0.005356893874704838,
0.02092936262488365,
0.030266346409916878,
-0.020806198939681053,
-0.03791603446006775,
0.03390023112297058,
-0.006511611398309469,
0.029777856543660164,
0.003642449853941798,
0.014969222247600555,
0.0459749735891819,
0.04207305237650871,
-0.0034898726735264063,
0.06637804210186005,
0.016781842336058617,
-0.000974617141764611,
0.011733435094356537,
0.012079527601599693,
-0.01458191592246294,
0.0055002556182444096,
0.027544548735022545,
0.05383366718888283,
-0.013225719332695007,
-0.010738657787442207,
0.04991970583796501,
0.0033442305866628885,
0.0007767506176605821,
0.0008088927716016769,
-0.03869051858782768,
0.07289139926433563,
-0.007902373559772968,
-0.010272826068103313,
-0.03423751890659332,
0.013393447734415531,
-0.010097866877913475,
-0.0033534178510308266,
-0.0060418955981731415,
0.03277341276407242,
-0.044977735728025436,
-0.009656133130192757,
-0.03024011291563511,
0.03035084530711174,
0.00002355114702368155,
-0.06656152009963989,
0.014817948453128338,
0.010440250858664513,
0.007914711721241474,
-0.022300755605101585,
0.005439562723040581,
-0.03718457370996475,
-0.017298612743616104,
0.011547301895916462,
0.023787453770637512,
0.03293396905064583,
-0.02426065504550934,
0.009280593134462833,
-0.07233878970146179,
0.040670957416296005,
-0.056275054812431335,
0.0002427301078569144,
-0.026308979839086533,
0.01845560036599636,
-0.035601306706666946,
0.01643744856119156
] |
<p>Suppose a body is moving in a circle about a fixed point. In the frame of reference of the body, is the centripetal force felt or is only the centrifugal force felt? </p>
<p>More generally, does a body only feel the effect of pseudo forces in an accelerated reference frame?</p> | 1,482 | [
-0.010868704877793789,
-0.03955027833580971,
-0.03498771786689758,
-0.04036131501197815,
0.031689029186964035,
0.011318066157400608,
-0.028903763741254807,
-0.020924938842654228,
-0.01752864569425583,
-0.005001407582312822,
0.01154506765305996,
0.05361349508166313,
0.031081147491931915,
-0.006519723683595657,
-0.00029480847297236323,
-0.018403111025691032,
-0.0015322634717449546,
-0.0025403660256415606,
-0.01086876168847084,
-0.04137123003602028,
0.0062358141876757145,
0.005057468544691801,
0.010921499691903591,
-0.02970130369067192,
-0.04130616411566734,
-0.013200473040342331,
0.0458085797727108,
-0.038800064474344254,
0.0032306828070431948,
0.03235473483800888,
-0.007141211535781622,
-0.012513646855950356,
-0.043752994388341904,
-0.004716289695352316,
0.02250068634748459,
0.0225142203271389,
-0.05343244597315788,
-0.01257339771836996,
-0.003565144259482622,
0.043191999197006226,
-0.07203762978315353,
-0.005831254180520773,
0.0006034672260284424,
0.09022997319698334,
-0.0356784462928772,
0.040181126445531845,
-0.017467467114329338,
0.04055320844054222,
0.0830787643790245,
-0.04360411316156387,
0.07407502830028534,
-0.006202469114214182,
0.01919594593346119,
-0.008505481295287609,
-0.008095664903521538,
-0.009594629518687725,
0.06635106354951859,
0.03674107417464256,
-0.0378500372171402,
-0.04129691421985626,
-0.03252477943897247,
-0.012405374087393284,
-0.03733595088124275,
-0.03379035368561745,
-0.004280690103769302,
0.02849453128874302,
-0.016288479790091515,
-0.028221726417541504,
0.024670323356986046,
-0.010920940898358822,
-0.00729548092931509,
0.004277602303773165,
-0.012645155191421509,
0.015543592162430286,
0.00917469896376133,
-0.043145447969436646,
0.03752843290567398,
0.021748865023255348,
0.03538840264081955,
0.038297828286886215,
-0.02692253887653351,
0.006710608024150133,
0.018625397235155106,
0.06189023330807686,
0.030817676335573196,
-0.03370461240410805,
0.020343583077192307,
-0.00020090957696083933,
-0.0009730609599500895,
0.05232223495841026,
0.012623508460819721,
0.010993403382599354,
0.02302040345966816,
-0.02821025438606739,
-0.039663009345531464,
0.02629603073000908,
-0.004189932253211737,
0.05294362083077431,
0.020535320043563843,
0.011832335963845253,
0.012850767001509666,
-0.02317912131547928,
0.024855611845850945,
0.08123421669006348,
0.01414501667022705,
-0.003219400066882372,
-0.015955321490764618,
-0.00629291171208024,
-0.030826596543192863,
-0.016481969505548477,
-0.02603326551616192,
0.0157160684466362,
-0.014111784286797047,
0.016048459336161613,
0.03560706228017807,
0.006443186197429895,
-0.023046176880598068,
-0.016385236755013466,
0.053114570677280426,
0.016542190685868263,
0.065016970038414,
-0.01610018126666546,
-0.024325938895344734,
-0.016695117577910423,
0.00446323212236166,
0.008884984068572521,
0.03312879428267479,
-0.02276141569018364,
-0.013181840069591999,
-0.023090628907084465,
0.006872159894555807,
-0.05321309715509415,
-0.03392764553427696,
0.014907391741871834,
0.022462859749794006,
-0.00583517225459218,
-0.09991629421710968,
-0.08154114335775375,
0.05453032627701759,
0.015563507564365864,
-0.003906973637640476,
-0.06426344811916351,
0.060313716530799866,
0.00575844245031476,
0.07697513699531555,
0.00023155237431637943,
-0.020503612235188484,
0.03261742368340492,
0.03335921838879585,
0.020171411335468292,
-0.0016450077528133988,
-0.02636132761836052,
-0.02033490315079689,
-0.06352703273296356,
-0.05537842959165573,
-0.037768907845020294,
0.03200926631689072,
0.03805992752313614,
0.008298791013658047,
-0.0059539745561778545,
0.039633363485336304,
-0.0208588857203722,
0.025394147261977196,
0.007415729109197855,
0.0018827257445082068,
-0.018045421689748764,
0.04843239113688469,
0.010552294552326202,
-0.01919594034552574,
0.055906135588884354,
0.020744502544403076,
0.0479213185608387,
0.010620761662721634,
0.024532705545425415,
0.0583527646958828,
-0.03460763022303581,
0.012464044615626335,
0.005105350632220507,
-0.0012234986061230302,
0.001883928314782679,
-0.05164482071995735,
-0.041340336203575134,
0.024002859368920326,
-0.032139506191015244,
0.008343929424881935,
0.07402914017438889,
0.03857896104454994,
0.010378246195614338,
0.020044192671775818,
-0.023259462788701057,
0.024113664403557777,
-0.07414093613624573,
0.016128331422805786,
-0.009743008762598038,
-0.0043023196049034595,
0.011644880287349224,
0.055325910449028015,
0.023175397887825966,
-0.04653995856642723,
0.0022123127710074186,
-0.0034377670381218195,
0.029842106625437737,
-0.015530358999967575,
-0.016831589862704277,
0.019714143127202988,
0.015207437798380852,
0.02622973546385765,
-0.0006150504923425615,
-0.009963656775653362,
-0.0016305232420563698,
-0.01749204657971859,
-0.003423096379265189,
-0.023494239896535873,
0.025660986080765724,
0.028536569327116013,
0.04534514620900154,
-0.008327788673341274,
0.0016424988862127066,
-0.014522256329655647,
0.061467546969652176,
-0.03595413267612457,
0.08818791061639786,
0.057443924248218536,
-0.017636951059103012,
0.052020363509655,
0.04571736603975296,
0.009658688679337502,
-0.012173343449831009,
0.013035112991929054,
-0.0329892635345459,
-0.03972620889544487,
-0.023794982582330704,
0.03285151720046997,
0.025717834010720253,
-0.043207619339227676,
0.021608799695968628,
0.046221669763326645,
0.048307646065950394,
0.010292498394846916,
0.009653069078922272,
-0.02240520715713501,
-0.06851807236671448,
0.03355836868286133,
0.027827121317386627,
0.007662882562726736,
-0.023757057264447212,
0.038350582122802734,
0.04705745354294777,
-0.010373231023550034,
-0.00040869813528843224,
-0.00487262150272727,
0.02555890940129757,
-0.02286813221871853,
0.008662168867886066,
-0.017303254455327988,
-0.04192935675382614,
0.04976523667573929,
0.0056540388613939285,
0.006299740634858608,
-0.008267569355666637,
-0.038564346730709076,
0.002700026845559478,
-0.017686277627944946,
-0.01064025703817606,
0.01587897352874279,
-0.00399980740621686,
-0.041781410574913025,
-0.04660763591527939,
0.03878681734204292,
-0.008577958680689335,
-0.0068034278228878975,
-0.04306909814476967,
0.0014755328884348273,
0.0045691924169659615,
-0.0055488054640591145,
0.011646031402051449,
0.017049357295036316,
0.0616915225982666,
-0.019082708284258842,
-0.006028953939676285,
-0.05090722814202309,
-0.04543431103229523,
0.008211134001612663,
0.03560865297913551,
-0.02848515659570694,
0.052875977009534836,
-0.06808304041624069,
-0.015330360271036625,
0.029450014233589172,
-0.002893861848860979,
0.0005315066082403064,
0.018106022849678993,
-0.01240753848105669,
-0.05145750939846039,
0.03159942477941513,
-0.03736826032400131,
-0.017615491524338722,
-0.040030308067798615,
-0.005084571428596973,
0.05600583180785179,
-0.007412539795041084,
-0.00947206374257803,
0.010840542614459991,
-0.056787144392728806,
-0.04212189093232155,
0.011016776785254478,
0.019634433090686798,
0.024488374590873718,
-0.05408705025911331,
0.024477003142237663,
0.01982925832271576,
-0.03409808501601219,
0.00007924714009277523,
-0.027470720931887627,
-0.031192533671855927,
0.03613660857081413,
-0.018382087349891663,
0.039699066430330276,
0.01536417193710804,
-0.006771256681531668,
0.08545762300491333,
0.020490974187850952,
-0.0342622771859169,
-0.03414255380630493,
-0.012385409325361252,
-0.017005931586027145,
-0.0007774065597914159,
-0.014637867920100689,
0.03574172407388687,
-0.030143678188323975,
-0.01287344191223383,
0.06538908183574677,
-0.012075263075530529,
0.020149707794189453,
0.03695834428071976,
-0.019030269235372543,
-0.02696811594069004,
0.04706098139286041,
-0.014108779840171337,
0.03358609229326248,
0.034288324415683746,
-0.012445504777133465,
-0.030427832156419754,
-0.008204017765820026,
0.030015718191862106,
0.0456358902156353,
-0.04057193174958229,
0.05151916295289993,
0.038333114236593246,
0.02039976790547371,
0.03401406109333038,
0.06456685811281204,
0.0015942433383315802,
0.001393521437421441,
-0.016456713899970055,
0.03099953569471836,
0.033671099692583084,
-0.039086442440748215,
-0.024257885292172432,
0.04911747947335243,
0.048050057142972946,
-0.02552984468638897,
-0.03534362465143204,
0.017910419031977654,
-0.008627810515463352,
0.06238391995429993,
-0.07739300280809402,
-0.056833233684301376,
0.007442510221153498,
0.011342192068696022,
0.01955866999924183,
0.07290522009134293,
-0.024067500606179237,
0.012429913505911827,
-0.05977363511919975,
-0.02098420448601246,
-0.006360986735671759,
0.037874333560466766,
-0.001019794843159616,
0.03580034151673317,
0.007818179205060005,
0.008253579959273338,
0.00452017318457365,
0.03514844551682472,
-0.0653848871588707,
0.0468151718378067,
-0.031592730432748795,
-0.013539881445467472,
-0.008179053664207458,
0.018897200003266335,
0.017389453947544098,
-0.02772984467446804,
-0.0015765841817483306,
-0.0297127403318882,
-0.026947807520627975,
-0.031132565811276436,
0.007375266402959824,
0.010307429358363152,
-0.03952983394265175,
-0.029091164469718933,
0.010538189671933651,
0.04791449010372162,
-0.0320640467107296,
0.06675972789525986,
0.004786093253642321,
-0.0584445595741272,
0.00839532446116209,
-0.01946103200316429,
0.01649555191397667,
-0.009621743112802505,
0.014967438764870167,
0.021328875795006752,
0.013929623179137707,
-0.019722381606698036,
0.0031738814432173967,
0.01721224933862686,
0.01670939102768898,
0.05001640319824219,
-0.019012844190001488,
-0.027941260486841202,
-0.10331585258245468,
0.0006522787734866142,
0.006734265014529228,
0.026469385251402855,
0.0060964422300457954,
-0.014733810909092426,
0.030719423666596413,
0.004585313145071268,
-0.0035423729568719864,
0.03527430444955826,
0.03174549341201782,
0.024242809042334557,
-0.02520669251680374,
-0.04646339267492294,
0.01959056593477726,
-0.01878858543932438,
0.034962669014930725,
0.024122444912791252,
-0.02997068129479885,
-0.046377602964639664,
0.005345299374312162,
0.0035621868446469307,
0.04368928447365761,
-0.016005564481019974,
0.03753271326422691,
-0.026179324835538864,
0.021466098725795746,
-0.0064071910455822945,
0.013497327454388142,
0.023032527416944504,
0.025576548650860786,
0.08643350750207901,
0.006082178559154272,
-0.032080747187137604,
-0.04778473451733589,
-0.0063192956149578094,
0.0662282258272171,
0.015917252749204636,
0.00022845347120892256,
-0.04041776806116104,
-0.05376923456788063,
-0.035637859255075455,
0.05762223154306412,
-0.035381194204092026,
-0.002340164966881275,
-0.040785182267427444,
0.006676096003502607,
-0.04886820912361145,
-0.06368761509656906,
-0.034597788006067276,
-0.00797994714230299,
-0.034419622272253036,
-0.019240133464336395,
-0.055904366075992584,
-0.0011324742808938026,
0.01162489503622055,
0.0010325175244361162,
0.03149176761507988,
0.03377895802259445,
0.07568764686584473,
-0.018705321475863457,
-0.039468925446271896,
0.026638507843017578,
-0.028396064415574074,
-0.04281914606690407,
-0.028319023549556732,
0.05294828489422798,
0.006128611508756876,
0.037252429872751236,
-0.03663719445466995,
-0.008425590582191944,
0.01019131951034069,
-0.05741927772760391,
-0.006145873572677374,
0.012210145592689514,
-0.04278900474309921,
0.02239294908940792,
0.022761961445212364,
-0.0012298707151785493,
0.03703269362449646,
0.020910583436489105,
-0.021640682592988014,
-0.007534557022154331,
-0.00943957082927227,
0.009806251153349876,
-0.016404422000050545,
0.018838826566934586,
-0.022279338911175728,
-0.01365748606622219,
-0.03763151168823242,
0.029442111030220985,
-0.019154461100697517,
0.019252661615610123,
-0.026093430817127228,
-0.0345689058303833,
-0.020926836878061295,
0.052374739199876785,
0.03774779662489891,
0.014506368897855282,
-0.010331228375434875,
-0.023535726591944695,
-0.01795572228729725,
0.015667404979467392,
-0.0019083539955317974,
-0.0008045940776355565,
-0.005698282737284899,
0.06408306211233139,
-0.001570069114677608,
0.010415169410407543,
-0.015884529799222946,
-0.013498849235475063,
0.007990201935172081,
-0.08042524755001068,
0.03333785757422447,
-0.009395631030201912,
-0.011548620648682117,
0.03766009211540222,
-0.006332024931907654,
0.020023489370942116,
0.010205953381955624,
-0.025014808401465416,
0.024694358929991722,
-0.02624349482357502,
0.012861772440373898,
0.028198571875691414,
0.01930677518248558,
-0.05519871041178703,
-0.03478950634598732,
0.036780454218387604,
0.0170008335262537,
0.015598681755363941,
-0.006999477278441191,
0.009543186984956264,
-0.04427233338356018,
-0.022481009364128113,
-0.0019542588852345943,
0.05077289417386055,
-0.007528277114033699,
-0.012779192067682743,
-0.0017446206184104085,
-0.02639327570796013,
0.024666840210556984,
-0.02941162884235382,
-0.029354559257626534,
0.013328805565834045,
0.021503519266843796,
-0.02764238230884075,
-0.0066342707723379135,
0.08117394149303436,
-0.037881482392549515,
-0.028077803552150726,
-0.023111198097467422,
-0.005536079406738281,
0.020244989544153214,
0.017696136608719826,
0.01899578794836998,
0.027892719954252243,
-0.02400815114378929,
-0.03542407602071762,
-0.027337530627846718,
0.013802998699247837,
-0.011340412311255932,
0.032969482243061066,
0.01676330342888832,
0.002504281932488084,
-0.03345830366015434,
-0.018581055104732513,
0.005254948977380991,
0.028453145176172256,
-0.005299448501318693,
0.004105264786630869,
0.05663036182522774,
0.007956510409712791,
0.017412830144166946,
0.007391039282083511,
-0.010674301534891129,
0.04373304173350334,
-0.037695515900850296,
-0.01283770427107811,
0.013202235102653503,
-0.00286494311876595,
-0.0115512041375041,
0.013709179125726223,
0.004381820093840361,
-0.017394453287124634,
0.06284481287002563,
-0.007758716121315956,
0.05775696784257889,
0.02111845649778843,
0.022229431197047234,
-0.007453798782080412,
-0.003988992422819138,
0.003967188764363527,
-0.033494967967271805,
-0.019039057195186615,
0.03024837002158165,
-0.02933025173842907,
0.014657367020845413,
0.016703171655535698,
0.04331709444522858,
-0.02440710924565792,
-0.00553330359980464,
0.03814399242401123,
0.027280695736408234,
0.01913900300860405,
-0.035145848989486694,
-0.006829935126006603,
0.016765663400292397,
-0.027649639174342155,
0.0568091943860054,
-0.0014299286995083094,
-0.03254120424389839,
0.07212462276220322,
0.011290676891803741,
0.03731005638837814,
-0.013535727746784687,
-0.0016764502506703138,
-0.001175635028630495,
-0.0035954751074314117,
0.003401984926313162,
0.03837635740637779,
-0.05063702538609505,
-0.02444124035537243,
0.029448360204696655,
-0.015903301537036896,
0.02347954362630844,
-0.007374804466962814,
-0.043055083602666855,
-0.015809951350092888,
-0.04436236619949341,
-0.03346780315041542,
-0.0031327628530561924,
0.030076730996370316,
-0.025961311534047127,
0.026303093880414963,
-0.021258777007460594,
0.035695288330316544,
0.005819256417453289,
0.013677997514605522,
-0.006642099004238844,
0.049513548612594604,
-0.021864574402570724,
0.0031709976028651,
-0.0070020221173763275,
-0.017352502793073654,
0.11373785138130188,
0.0042043388821184635,
-0.013868623413145542,
-0.04562593251466751,
0.01719963550567627,
-0.01817696914076805,
0.03857607766985893,
-0.02476625144481659,
-0.01024522352963686,
-0.0183150302618742,
0.0002478760725352913,
0.035197313874959946,
0.06776663661003113,
-0.011592498049139977,
-0.0278302188962698,
0.03725243732333183,
-0.04173831641674042,
-0.0010848838137462735,
-0.018892347812652588,
-0.014068164862692356,
-0.008272426202893257,
0.00442496920004487,
0.00019584826077334583,
0.03604259714484215,
-0.026727667078375816,
0.02535122260451317,
-0.056620001792907715,
-0.029929885640740395,
-0.003729512682184577,
0.0041282749734818935,
-0.04622461274266243,
0.010281623341143131,
-0.01012058649212122,
-0.027761276811361313,
-0.04760739579796791,
0.030203472822904587,
0.00895270612090826,
-0.02203872986137867,
0.05714262276887894,
0.019683558493852615,
0.00360311777330935,
0.022880923002958298,
-0.012394491583108902,
0.025018416345119476,
-0.04868195950984955,
0.03582659363746643,
-0.022239889949560165,
0.04700368642807007,
0.0039017319213598967,
-0.020620539784431458,
0.03434421494603157,
-0.0034951430279761553,
-0.0007348089711740613,
-0.05800316482782364,
-0.0024086704943329096,
-0.006964314728975296,
-0.009661679156124592,
-0.006259319372475147,
-0.061904773116111755,
-0.04508797824382782,
0.052037313580513,
0.0115812998265028,
-0.0054001472890377045,
-0.026067722588777542,
0.029089193791151047,
0.007084849290549755,
0.01916034147143364,
0.01850437931716442,
-0.039073243737220764,
-0.017554888501763344,
0.005752048920840025,
0.002188186626881361,
-0.04821944236755371,
0.00841843243688345,
0.014952145516872406,
-0.003929320257157087,
0.044865503907203674,
-0.027212996035814285,
-0.006638695485889912,
-0.05311214178800583,
-0.0320986807346344,
0.017875000834465027,
-0.004017243627458811,
-0.0024246457032859325,
0.0015660886419937015,
0.005955985747277737,
0.0222346018999815,
0.008701721206307411,
0.0002417825162410736,
0.005839658435434103,
-0.010986226610839367,
0.023381195962429047,
0.03182290866971016,
0.0015113489935174584,
0.0027448683977127075,
0.00493931258097291,
0.0358121357858181,
0.012106469832360744,
-0.043365877121686935,
0.02564210817217827,
0.02433812990784645,
0.015695564448833466,
-0.02371605485677719,
0.03138565272092819,
0.003289254382252693,
0.009764066897332668,
0.04740570858120918,
-0.02678065374493599,
-0.020558934658765793,
0.012024618685245514,
0.026886755600571632,
-0.06950227916240692,
-0.008541097864508629,
-0.060014866292476654,
-0.014866791665554047,
-0.026336774230003357,
0.04400114715099335,
-0.019631946459412575,
0.023262185975909233,
0.0024455373641103506,
-0.003944616299122572,
-0.05971383675932884,
0.01218882855027914,
-0.032839156687259674,
0.013792810961604118,
0.029177580028772354,
-0.014851021580398083,
0.005048807710409164,
0.018147306516766548,
-0.033930033445358276,
-0.025038031861186028,
-0.004882758017629385,
-0.01388203538954258,
-0.028739793226122856,
0.00035665338509716094,
0.029901746660470963,
-0.03138049319386482,
0.044266585260629654,
-0.00952614564448595,
0.005910271778702736,
0.003424178110435605,
-0.04477248713374138,
-0.022935714572668076,
0.040760818868875504,
-0.02737322263419628,
0.041522786021232605,
-0.007752740290015936,
-0.018456080928444862,
0.02942267246544361,
0.051680732518434525,
0.013676871545612812,
-0.012644889764487743,
0.012735924683511257,
-0.020798049867153168,
-0.005904802121222019,
0.012568628415465355,
0.03231491521000862,
-0.03965519368648529,
-0.012864428572356701,
0.0583859384059906,
0.012945561669766903,
-0.02199624292552471,
0.0043660178780555725,
-0.02113879844546318,
-0.01121038943529129,
-0.029742343351244926,
0.028760090470314026,
0.010939360596239567,
0.03815477713942528,
0.024357343092560768,
-0.01730448007583618,
-0.005056549329310656,
0.015758123248815536,
0.018986867740750313,
-0.08986812084913254,
-0.04186994209885597,
0.005857438780367374,
0.02425394579768181,
-0.008131303824484348,
-0.03642292320728302,
0.014084807597100735,
0.04493110999464989,
-0.0845174789428711,
0.009392550215125084,
-0.02394556999206543,
-0.01622564159333706,
0.002699493430554867,
0.017993247136473656,
0.007077561691403389,
0.03705954551696777,
0.031227415427565575,
0.029153643175959587,
0.004959133919328451,
0.009310365654528141,
-0.013843321241438389,
-0.044900454580783844,
0.005452207289636135,
0.028961695730686188,
-0.004127675201743841,
-0.002712951973080635,
0.06740976125001907,
-0.014906293712556362,
-0.02752561867237091,
0.04537751525640488,
0.026218578219413757,
0.007528067100793123,
-0.026991255581378937,
-0.006350445561110973,
0.010630456730723381,
0.022997668012976646,
-0.00145861622877419,
-0.0406917966902256,
-0.03859390690922737,
0.04971588775515556,
-0.02445404604077339,
0.05105263367295265,
-0.04270467534661293,
-0.0035307148937135935,
0.022434893995523453,
-0.016003860160708427,
-0.04147816076874733,
0.019598033279180527,
0.012770646251738071,
-0.014813756570219994,
-0.02717725746333599,
0.013030416332185268,
0.004488952923566103,
-0.001021091127768159,
0.010760150849819183,
-0.05264309048652649,
0.03811320662498474,
0.01722261868417263,
-0.04196865111589432,
-0.010915654711425304,
0.03327581658959389,
-0.008726045489311218,
0.016582924872636795,
-0.03926687687635422,
-0.02702372707426548,
0.00255300453864038,
-0.052339907735586166,
-0.012002729810774326,
0.005801064893603325,
0.0044197337701916695,
-0.03706149011850357,
-0.04186277464032173,
0.0035069668665528297,
0.025018714368343353,
0.05323577672243118,
-0.031138770282268524,
-0.0031783967278897762,
-0.017118284478783607,
-0.05550803244113922,
-0.07696632295846939,
0.01353581715375185,
0.0071721854619681835,
-0.032709479331970215,
-0.02727409638464451,
-0.02400178834795952,
-0.035291887819767,
0.021435154601931572,
0.034181904047727585,
0.005793355405330658,
-0.008377705700695515,
0.04055749624967575,
-0.02613990381360054,
-0.01396863255649805,
-0.04747847840189934,
-0.006362990476191044,
-0.024659644812345505,
-0.02673262357711792,
-0.04468419402837753,
-0.014776731841266155,
-0.06163632497191429,
0.009802560321986675,
0.021035000681877136,
0.016045821830630302,
0.06259909272193909,
-0.02706001326441765,
-0.036557190120220184,
0.08058538287878036,
0.07034865766763687,
0.01947087049484253,
0.07113724201917648,
0.00993726123124361,
0.031788576394319534,
0.05354698747396469,
-0.054370805621147156,
-0.0183181781321764,
0.02085159346461296,
-0.010775492526590824,
-0.012294992804527283,
-0.020837709307670593,
-0.0015772496117278934,
-0.010337956249713898,
-0.02850058488547802,
0.009512530639767647,
0.05127556249499321,
-0.02786860801279545,
-0.005018359981477261,
0.002716813236474991,
0.04421140253543854,
0.03238174319267273,
-0.015899721533060074,
0.03309720754623413,
0.01794290542602539,
-0.017742345109581947,
0.0030557813588529825,
0.022033987566828728,
0.018331825733184814,
0.007089986000210047,
-0.02344340831041336,
0.026479553431272507,
-0.025787554681301117,
0.003411869052797556,
0.0017629214562475681,
0.05781840160489082,
-0.05234747752547264,
-0.0036281589418649673,
0.004575755912810564,
-0.01512303575873375,
0.029206523671746254,
0.03304975479841232,
-0.01684241183102131,
0.05312765762209892,
-0.05270523205399513,
0.02926422841846943,
-0.025236349552869797,
-0.01674751006066799,
-0.018933486193418503,
0.015593738295137882,
0.0026881960220634937,
0.043159425258636475,
0.004889253061264753,
-0.008998431265354156,
-0.006986294873058796,
-0.027616271749138832,
0.03255167230963707,
0.008932949975132942,
-0.0028256818186491728,
-0.004188540857285261,
0.009230761788785458,
0.020240668207406998,
0.00380246271379292,
-0.02606753259897232,
0.014827889390289783,
0.04557930305600166,
0.03176083415746689,
0.06098020449280739,
-0.014986627735197544,
0.004727356135845184,
-0.005700402427464724,
0.024076253175735474,
-0.08574289828538895,
0.004807957448065281,
0.017645256593823433,
0.03651569411158562,
0.003353723557665944,
-0.017810145393013954
] |
<p>Let's suppose I have a point charge moving arbitrarily in space. As far I know, Maxwell's equations don't determine a unique electric and magnetic field, they only determine a family of electric and magnetic fields. What other information do I need in order to know uniquely the electric and magnetic field produced by a moving (the particle is moving arbitrarily) point charge?</p>
<p>I'm not asking for a method for solving it, I just want to know what other information (apart from Maxwell equations) do I need.</p> | 1,483 | [
-0.03189326822757721,
0.01711282506585121,
-0.01219133473932743,
-0.0314578078687191,
0.024766918271780014,
0.0008250439423136413,
-0.012515210546553135,
-0.017227595672011375,
-0.006108160130679607,
-0.018381567671895027,
0.03763508424162865,
0.04290851205587387,
0.06020195037126541,
0.03540521115064621,
0.01922101341187954,
-0.00856420211493969,
-0.010640389285981655,
0.0005161099252291024,
0.003985924646258354,
-0.049158673733472824,
-0.014580033719539642,
0.007910101674497128,
0.02170727774500847,
0.009798453189432621,
-0.0281824953854084,
0.014221643097698689,
0.029413893818855286,
0.019122062250971794,
0.01881171017885208,
0.04397342726588249,
-0.010644079186022282,
-0.04789131134748459,
0.008992049843072891,
0.04694363474845886,
0.009623258374631405,
-0.010554961860179901,
-0.03888193890452385,
-0.03688139095902443,
-0.020259270444512367,
0.005562198348343372,
-0.03769619017839432,
-0.007417663931846619,
0.010007515549659729,
0.05719321221113205,
-0.038106586784124374,
0.023598773404955864,
-0.003519538789987564,
-0.01050119660794735,
0.07292497158050537,
-0.06724496930837631,
0.09473927319049835,
0.024947963654994965,
0.042192570865154266,
0.027210351079702377,
-0.012605897150933743,
0.011188306845724583,
0.092500239610672,
0.06366772949695587,
-0.013552564196288586,
-0.03565290570259094,
-0.03883429616689682,
-0.024957606568932533,
0.0007738056592643261,
-0.06582380831241608,
-0.03509986773133278,
0.05570944771170616,
-0.00249349232763052,
-0.02151942253112793,
0.031924862414598465,
-0.008352300152182579,
0.034857504069805145,
0.008185189217329025,
0.02418283000588417,
-0.00931709073483944,
0.0105771254748106,
-0.018871115520596504,
0.01692180708050728,
0.0063430918380618095,
0.05908620357513428,
-0.001740246545523405,
-0.04613093286752701,
-0.0023771850392222404,
0.012494852766394615,
0.05039939284324646,
0.0005836993805132806,
-0.02030893974006176,
0.023505326360464096,
-0.019313452765345573,
0.01085052452981472,
0.0073552681133151054,
-0.024979542940855026,
0.021703196689486504,
0.024351684376597404,
-0.019789356738328934,
-0.020063800737261772,
0.030362017452716827,
-0.01892036199569702,
0.043280210345983505,
0.013140867464244366,
-0.020923204720020294,
0.03582802414894104,
-0.009691936895251274,
-0.020943528041243553,
0.046246521174907684,
0.0033351569436490536,
-0.0048243142664432526,
-0.015892302617430687,
-0.001418233965523541,
-0.021815480664372444,
0.021539941430091858,
-0.004886829759925604,
0.040460094809532166,
0.00958035234361887,
-0.0009984519565477967,
0.04442526772618294,
-0.01628759503364563,
0.03580731526017189,
-0.01620675064623356,
0.027171600610017776,
0.07704050838947296,
0.031203901395201683,
-0.06185642257332802,
0.018716569989919662,
-0.010429139249026775,
-0.07622215896844864,
-0.040348876267671585,
0.012995148077607155,
0.01582057774066925,
-0.013506259769201279,
0.005581246223300695,
-0.00639738654717803,
-0.01715068519115448,
0.00672589847818017,
-0.020299367606639862,
0.02832362800836563,
-0.0032318870071321726,
-0.10685006529092789,
-0.040978845208883286,
-0.0062763444148004055,
-0.013590626418590546,
-0.020844101905822754,
-0.07914413511753082,
-0.007388054393231869,
0.011138959787786007,
0.05663800984621048,
-0.01079869456589222,
-0.003972712904214859,
0.010273627936840057,
0.058026012033224106,
-0.00768325524404645,
-0.024308502674102783,
-0.025819838047027588,
-0.02041519433259964,
-0.0333041213452816,
-0.004935719538480043,
-0.05092115327715874,
-0.00833860132843256,
0.011971716769039631,
-0.02229001745581627,
-0.020697755739092827,
0.0661647692322731,
-0.013631847687065601,
-0.003029594896361232,
0.0070220413617789745,
-0.009966244921088219,
0.01633618399500847,
0.06420525908470154,
0.01664145477116108,
0.002267303643748164,
0.050703007727861404,
0.007850497029721737,
0.035180289298295975,
0.020696299150586128,
0.01465099398046732,
0.06904803216457367,
-0.04423854872584343,
-0.03744494915008545,
0.010968925431370735,
0.03292215242981911,
0.019906016066670418,
-0.02465248480439186,
-0.04897509887814522,
0.020445896312594414,
-0.005357023328542709,
0.005407620221376419,
0.04085296764969826,
-0.017976321280002594,
-0.0017792409053072333,
-0.014816459268331528,
-0.040200941264629364,
-0.012963107787072659,
-0.039819687604904175,
0.02764502726495266,
-0.014604437164962292,
-0.020645231008529663,
0.04706357419490814,
-0.009331456385552883,
0.024107683449983597,
-0.05601898208260536,
-0.06145600229501724,
0.008925084955990314,
0.03684891760349274,
-0.028111306950449944,
-0.04283042252063751,
0.013662205077707767,
0.012136408127844334,
0.059085361659526825,
0.030740641057491302,
0.01710904762148857,
-0.007067444268614054,
-0.03712227940559387,
0.0002299837360624224,
-0.04650735855102539,
0.006762358359992504,
0.010396378114819527,
0.012786492705345154,
-0.007513688877224922,
0.012449593283236027,
0.002792968647554517,
0.03758321329951286,
0.0002186392666772008,
0.08034909516572952,
0.04610701650381088,
0.024020064622163773,
-0.006163557060062885,
0.04122336581349373,
0.0017234955448657274,
-0.019076695665717125,
-0.0047642504796385765,
-0.03875690698623657,
-0.048122189939022064,
-0.0009464506874792278,
0.05118107795715332,
-0.0025620677042752504,
-0.062319111078977585,
0.01981191523373127,
0.008998529985547066,
0.02833470329642296,
0.032008714973926544,
0.042243439704179764,
-0.04495732858777046,
-0.037149980664253235,
0.041796308010816574,
0.01611296460032463,
-0.035095106810331345,
0.006416503805667162,
0.0629957765340805,
0.017664559185504913,
0.0013068380067124963,
-0.010777083225548267,
-0.0404437817633152,
0.051067810505628586,
-0.031357504427433014,
0.0009019096032716334,
0.009741717018187046,
-0.03646427020430565,
0.038928717374801636,
-0.01931191049516201,
0.06700271368026733,
0.008788034319877625,
-0.02515650913119316,
-0.01978304609656334,
-0.007025319617241621,
0.005421270150691271,
0.02986767515540123,
-0.02243850566446781,
-0.03469502180814743,
0.01776800863444805,
0.018427468836307526,
-0.05889134481549263,
0.011642777360975742,
0.022359175607562065,
-0.022922400385141373,
-0.01665797270834446,
0.001525657600723207,
0.019467562437057495,
0.008516646921634674,
0.02197960764169693,
-0.0013522885274142027,
-0.022104350849986076,
-0.010628340765833855,
-0.03999907895922661,
0.0004970466834492981,
0.03787548094987869,
-0.05772598087787628,
0.027894051745533943,
-0.049233876168727875,
-0.041755303740501404,
0.05547359585762024,
-0.009794307872653008,
-0.010733873583376408,
0.025527991354465485,
-0.013467762619256973,
-0.06618668884038925,
0.0138986986130476,
-0.04617039114236832,
0.03381960466504097,
-0.02753460220992565,
0.007799228187650442,
0.03298582881689072,
0.0006734102498739958,
-0.037275731563568115,
-0.0013767320197075605,
-0.06625038385391235,
-0.01325869932770729,
-0.003951153252273798,
-0.0016526622930541635,
0.03682852163910866,
-0.03800220414996147,
0.051081582903862,
0.03581736981868744,
-0.04738374799489975,
-0.0038067272398620844,
-0.004111758898943663,
-0.04405613988637924,
0.018997443839907646,
-0.004154309630393982,
0.032264918088912964,
-0.03751100227236748,
-0.0689995065331459,
0.06130148842930794,
0.017909200862050056,
-0.04649442806839943,
-0.006246103905141354,
-0.008988595567643642,
-0.016492672264575958,
-0.024515919387340546,
-0.0217610951513052,
0.012331103906035423,
-0.0021028188057243824,
-0.002706357976421714,
0.055044449865818024,
0.004192359745502472,
0.009206854738295078,
0.022994166240096092,
-0.00352167384698987,
0.0004958336357958615,
0.005992966704070568,
0.01154360268265009,
0.04666329175233841,
0.011578455567359924,
-0.05098111182451248,
0.008861132897436619,
0.012023895978927612,
0.01487551536411047,
0.019267668947577477,
-0.029651634395122528,
0.03369442746043205,
-0.001053554704412818,
0.0034391407389193773,
-0.04103818163275719,
0.013305645436048508,
-0.022295182570815086,
-0.012871949002146721,
-0.011540035717189312,
0.011211303062736988,
0.016081225126981735,
-0.017640411853790283,
-0.003252902766689658,
0.054182298481464386,
0.030917612835764885,
-0.036456361413002014,
-0.023416932672262192,
-0.011587810702621937,
-0.00769661134108901,
0.01975896768271923,
-0.004549067933112383,
-0.026863234117627144,
0.02384871058166027,
0.008166982792317867,
0.02703838236629963,
0.022010138258337975,
-0.014552175998687744,
-0.009235653094947338,
-0.02816174551844597,
0.012700348161160946,
0.01264853123575449,
0.04707267880439758,
0.009921371936798096,
0.06788899749517441,
0.02425423264503479,
-0.0015116374706849456,
0.032901473343372345,
0.042764194309711456,
-0.06233387067914009,
0.051664456725120544,
-0.02356957644224167,
-0.03704481199383736,
-0.040925513952970505,
-0.02598482370376587,
0.00910656712949276,
-0.019871093332767487,
-0.016805941238999367,
0.0031063868664205074,
-0.010918826796114445,
-0.07842037826776505,
0.020405316725373268,
-0.04137890785932541,
-0.03505874052643776,
-0.051727376878261566,
0.06190593168139458,
0.028285086154937744,
-0.038456011563539505,
0.008006162010133266,
0.03768225014209747,
-0.024682244285941124,
-0.020199166610836983,
-0.022344302386045456,
0.0008363665547221899,
0.008357730694115162,
0.003738269442692399,
-0.0022682189010083675,
0.007007278501987457,
-0.018939180299639702,
-0.01088531594723463,
-0.012478353455662727,
0.053713586181402206,
0.007887199521064758,
0.0008738160249777138,
-0.05196134001016617,
-0.04683864489197731,
0.0028362367302179337,
-0.017741765826940536,
0.07266886532306671,
-0.011456568725407124,
-0.007307093124836683,
0.03225182741880417,
0.03792119398713112,
-0.003914195112884045,
0.00752492668107152,
0.050471026450395584,
0.026289481669664383,
-0.033132199198007584,
-0.027205919846892357,
0.03543880209326744,
-0.019498677924275398,
-0.01555959414690733,
0.01394673716276884,
-0.013536200858652592,
0.00014804860984440893,
-0.010034634731709957,
0.003804248059168458,
0.009541617706418037,
0.010030275210738182,
0.014151858165860176,
-0.016898028552532196,
0.015282198786735535,
-0.005265597254037857,
-0.0032175860833376646,
-0.006834925152361393,
0.04150691255927086,
0.042964912950992584,
0.002089193556457758,
-0.03375786915421486,
-0.09045922756195068,
-0.0027230186387896538,
0.033598486334085464,
-0.00048166437773033977,
0.002266518771648407,
-0.027435939759016037,
-0.06522426754236221,
0.022095395252108574,
0.05860331654548645,
-0.02300429716706276,
0.02781621553003788,
0.03420408442616463,
-0.0048581319861114025,
0.0034464430063962936,
-0.007462799083441496,
-0.07029595226049423,
0.05194804072380066,
-0.007736668456345797,
0.02125283144414425,
-0.049110375344753265,
0.020856956019997597,
-0.005609697196632624,
0.047284457832574844,
0.01628829911351204,
0.07470748573541641,
0.03177671879529953,
0.007561018690466881,
-0.01255305577069521,
0.0031889956444501877,
0.0027195028960704803,
-0.06016579270362854,
-0.002063262742012739,
0.0027175182476639748,
0.003836940275505185,
0.039663154631853104,
-0.03615415468811989,
-0.05978701636195183,
-0.0007985860574990511,
-0.032761018723249435,
0.015624059364199638,
0.015068303793668747,
-0.045897532254457474,
0.027290867641568184,
-0.0013931079301983118,
0.030989307910203934,
0.06327635049819946,
-0.0060675619170069695,
-0.004585022106766701,
-0.030759260058403015,
-0.007187077309936285,
0.01876344531774521,
-0.028125038370490074,
-0.01080213114619255,
0.011689330451190472,
0.043352339416742325,
-0.042328961193561554,
0.08606807142496109,
-0.04820186272263527,
0.0023218169808387756,
0.004128653556108475,
-0.025807717815041542,
-0.038076251745224,
0.04542677477002144,
-0.004226030316203833,
-0.004297235980629921,
-0.025145534425973892,
0.024816522374749184,
-0.026076165959239006,
-0.027688277885317802,
0.006064308807253838,
0.02608511969447136,
-0.0050005256198346615,
0.014349083416163921,
-0.00915975496172905,
0.02293785661458969,
-0.011577509343624115,
0.009841540828347206,
0.016905374825000763,
-0.03602415323257446,
0.040746718645095825,
0.004011915065348148,
-0.004247238393872976,
0.027192143723368645,
-0.10645309090614319,
-0.0525268130004406,
0.03817204385995865,
0.004588764626532793,
0.05443660169839859,
-0.060121048241853714,
0.0028107385151088238,
-0.019652720540761948,
0.01360462885349989,
-0.062021005898714066,
-0.06802595406770706,
0.014099572785198689,
0.032976794987916946,
0.003647888544946909,
-0.043431296944618225,
0.02400064468383789,
-0.025652948766946793,
-0.038662638515233994,
0.018920795992016792,
0.04834720119833946,
-0.003947282209992409,
-0.023887280374765396,
-0.003788680536672473,
0.026180710643529892,
0.01959388330578804,
-0.0023749149404466152,
-0.00311084883287549,
0.05972890555858612,
-0.025266630575060844,
0.03477802127599716,
0.019407514482736588,
0.03073175437748432,
0.006080434657633305,
-0.028948361054062843,
-0.03451722860336304,
0.025739528238773346,
0.029700102284550667,
-0.04777642339468002,
0.006649964023381472,
0.026022188365459442,
0.03207958862185478,
-0.018018752336502075,
-0.03161739557981491,
0.023866327479481697,
-0.022483084350824356,
0.0020803457591682673,
-0.015008197166025639,
0.022488031536340714,
-0.0415511317551136,
-0.00501641072332859,
0.022983666509389877,
-0.004537368658930063,
0.03547888249158859,
-0.01814834401011467,
0.015857426449656487,
-0.01995192840695381,
-0.007707945071160793,
0.046656228601932526,
0.02523854188621044,
0.031585391610860825,
-0.013527062721550465,
0.015909861773252487,
0.005576495546847582,
0.025894807651638985,
-0.034375716000795364,
0.0011416447814553976,
-0.003467497881501913,
-0.003343206364661455,
0.06869173049926758,
-0.008939949795603752,
0.08182000368833542,
0.028068026527762413,
0.029179874807596207,
-0.02471095323562622,
0.04010789096355438,
-0.0033940726425498724,
0.012691279873251915,
-0.0036819702945649624,
0.03721337020397186,
0.007094885688275099,
0.006941495928913355,
-0.000004890045147476485,
0.04980621114373207,
-0.026636367663741112,
-0.007529726717621088,
0.007267802953720093,
0.027045149356126785,
0.04232072830200195,
-0.0025148626882582903,
-0.06347240507602692,
0.039546430110931396,
-0.02369525097310543,
0.016648607328534126,
0.023120084777474403,
-0.012195653282105923,
0.06243787705898285,
-0.00273406645283103,
0.01118798553943634,
0.006186532787978649,
-0.03397068753838539,
-0.019102806225419044,
0.027966180816292763,
0.0411008782684803,
0.009059569798409939,
-0.005979128181934357,
0.05577092990279198,
-0.012654107064008713,
0.0007978808134794235,
-0.009304700419306755,
0.012348110787570477,
-0.06757651269435883,
-0.030807584524154663,
-0.05356791615486145,
-0.04175545275211334,
0.06913129985332489,
0.03621263429522514,
-0.00514594279229641,
0.0099370451644063,
-0.006974372081458569,
0.040467116981744766,
0.03306351602077484,
0.03791480138897896,
-0.0413968451321125,
0.059641871601343155,
-0.02259881980717182,
0.00785317737609148,
-0.03543343022465706,
0.024669496342539787,
0.10472527891397476,
0.03562600910663605,
0.050255026668310165,
-0.05100853368639946,
-0.008000616915524006,
-0.04091643542051315,
0.016512557864189148,
-0.03888414055109024,
0.05372225493192673,
-0.027628213167190552,
0.021737556904554367,
0.007150424178689718,
0.03131072223186493,
-0.018024390563368797,
0.019027717411518097,
0.06554228812456131,
-0.04493166506290436,
-0.02419975772500038,
0.008413771167397499,
0.031257957220077515,
0.017140183597803116,
0.013964598998427391,
-0.03489876538515091,
0.04217856377363205,
-0.0549735464155674,
-0.0029299689922481775,
-0.027847135439515114,
-0.0446426160633564,
0.023079995065927505,
0.002765113487839699,
-0.0578434020280838,
-0.0021116421557962894,
0.01867055706679821,
-0.006915637757629156,
-0.07238032668828964,
0.00877302698791027,
0.050067659467458725,
-0.0019685819279402494,
0.010108250193297863,
-0.00275196461006999,
0.0346466489136219,
0.00006046851922292262,
0.013978979550302029,
0.025990908965468407,
-0.027925029397010803,
0.000004723374331661034,
-0.03603573516011238,
0.047480929642915726,
-0.010335426777601242,
0.006587967276573181,
0.01747114770114422,
0.026080356910824776,
0.0011982041178271174,
-0.04468914121389389,
-0.03495199233293533,
-0.042707376182079315,
-0.0018769924063235521,
-0.031278062611818314,
0.009033464826643467,
-0.036576323211193085,
0.05697251111268997,
-0.0012672373559325933,
-0.010497155599296093,
-0.02511107362806797,
0.028385523706674576,
-0.015501557849347591,
-0.00009644452802604064,
0.035916417837142944,
0.005669151898473501,
-0.0408744178712368,
-0.015646640211343765,
-0.08029273897409439,
-0.028647951781749725,
0.009191165678203106,
0.026579611003398895,
0.030020922422409058,
0.012076768092811108,
-0.015734322369098663,
-0.019506875425577164,
0.028107773512601852,
-0.06993763148784637,
0.007232240401208401,
0.003078318201005459,
-0.014708730392158031,
-0.009562977589666843,
0.02974225953221321,
0.01648004539310932,
0.07571045309305191,
0.0034949891269207,
0.03996682167053223,
-0.0002394963667029515,
0.005079786293208599,
0.006334088277071714,
-0.014617395587265491,
0.018728548660874367,
-0.0008312512654811144,
-0.026991790160536766,
0.01690046302974224,
-0.014859285205602646,
0.009536918252706528,
0.03787557780742645,
0.02560318261384964,
0.015329843387007713,
0.03312940150499344,
-0.03469257056713104,
0.030772868543863297,
0.013337205164134502,
-0.012180555611848831,
0.0008255844586528838,
-0.007218002341687679,
-0.0010949234711006284,
-0.019614819437265396,
0.01416242029517889,
0.0026591962669044733,
0.01068587601184845,
0.007325283717364073,
0.004636083729565144,
-0.015962695702910423,
-0.016584109514951706,
0.004146031104028225,
0.013123247772455215,
-0.03939617797732353,
0.013738017529249191,
-0.023210501298308372,
0.03078298456966877,
-0.017091665416955948,
-0.019836880266666412,
-0.019713159650564194,
0.015366503968834877,
-0.025558732450008392,
-0.020079197362065315,
0.022961176931858063,
0.006004462018609047,
-0.008882526308298111,
0.007314917165786028,
-0.006863748654723167,
-0.0006126702064648271,
0.07187332212924957,
-0.013724948279559612,
-0.02335197851061821,
0.009259602054953575,
-0.03663911670446396,
-0.04785161837935448,
0.019900085404515266,
-0.014845927245914936,
0.033485036343336105,
0.05429068207740784,
-0.01586870476603508,
-0.007415415719151497,
0.07030908018350601,
0.007899319753050804,
-0.000967028783634305,
-0.010694652795791626,
-0.030152710154652596,
-0.0071134185418486595,
-0.02672688663005829,
0.028503529727458954,
-0.015565264970064163,
-0.025717638432979584,
0.03337627649307251,
-0.009142511524260044,
-0.0018970572855323553,
-0.03673482686281204,
0.0227518267929554,
0.027007441967725754,
-0.01896914653480053,
0.06761941313743591,
0.010029640980064869,
0.04712808132171631,
0.052968453615903854,
-0.009989832527935505,
-0.009378073737025261,
0.01384031679481268,
0.01991991698741913,
-0.1069193035364151,
-0.022731054574251175,
0.014209005050361156,
-0.0021233430597931147,
0.032310228794813156,
-0.049407076090574265,
0.017368875443935394,
0.0546991340816021,
-0.08856089413166046,
-0.01658165082335472,
-0.005604300182312727,
0.019755080342292786,
-0.0007043256773613393,
-0.03437019884586334,
-0.0030315725598484278,
0.046399593353271484,
0.055301036685705185,
0.05519618093967438,
-0.006169621832668781,
0.008388717658817768,
-0.004712546244263649,
-0.02462051622569561,
-0.042275335639715195,
0.02493472956120968,
0.024767974391579628,
-0.021163389086723328,
0.03836273401975632,
0.00923215039074421,
-0.018587704747915268,
0.008685557171702385,
-0.01515872497111559,
-0.01438677217811346,
-0.01861952245235443,
0.035516683012247086,
0.020764319226145744,
0.023100880905985832,
-0.028218012303113937,
-0.031926073133945465,
-0.012376762926578522,
-0.00552511028945446,
0.002734944922849536,
0.022333670407533646,
-0.018658429384231567,
-0.014382782392203808,
0.017059775069355965,
-0.019129248335957527,
-0.03126571699976921,
0.032452236860990524,
-0.044542670249938965,
-0.0170020442456007,
-0.010157494805753231,
0.04056588187813759,
0.0026065402198582888,
-0.004321535583585501,
-0.005341378040611744,
-0.05295024812221527,
0.006697036791592836,
0.025360800325870514,
0.006637089885771275,
-0.010404044762253761,
0.027484798803925514,
-0.0456538200378418,
-0.050266820937395096,
0.040260810405015945,
0.00776968477293849,
0.02269563637673855,
-0.07779346406459808,
-0.003078065114095807,
0.05015596002340317,
-0.006723124533891678,
-0.006255926564335823,
-0.055965356528759,
-0.03732961416244507,
0.0006810533232055604,
0.045055948197841644,
0.013693626970052719,
-0.00593689875677228,
-0.012298538349568844,
-0.0032525567803531885,
-0.04690057784318924,
0.040237072855234146,
0.0034029728267341852,
-0.02968498505651951,
-0.018955543637275696,
-0.05016123130917549,
-0.022354856133461,
0.04685627296566963,
0.05634922534227371,
-0.04151969030499458,
-0.043533988296985626,
0.03141466900706291,
-0.014671193435788155,
-0.00002685541403479874,
-0.07456645369529724,
-0.02079777605831623,
0.01420572865754366,
-0.0051645319908857346,
-0.01217960100620985,
-0.013996860943734646,
-0.006474141497164965,
0.02770249731838703,
0.003798859193921089,
0.009175052866339684,
0.012843189761042595,
-0.023353910073637962,
-0.038987088948488235,
0.013328921049833298,
0.012909543700516224,
-0.009722663089632988,
0.023735154420137405,
-0.006209262181073427,
-0.005617661401629448,
0.023571403697133064,
-0.02732750028371811,
-0.00877727847546339,
0.016024377197027206,
-0.06307774037122726,
-0.014173144474625587,
-0.007715469226241112,
0.006424461957067251,
0.04170612618327141,
-0.0375869944691658,
0.01438970398157835,
0.03733212873339653,
-0.026895109564065933,
-0.011881226673722267,
0.05534568428993225,
0.00472730677574873,
0.0025352120865136385,
-0.006989909801632166,
0.016649670898914337,
0.021366577595472336,
-0.008103557862341404,
-0.022158296778798103,
0.027658792212605476,
0.03773118183016777,
-0.012031489983201027,
0.022937951609492302,
0.029101068153977394,
0.003329422092065215,
0.017580687999725342,
-0.0010359114967286587,
0.02561541460454464,
-0.033900536596775055,
0.018098121508955956,
0.005797498393803835,
-0.030857009813189507,
0.04278881102800369,
-0.010617532767355442,
-0.042401134967803955,
0.08378705382347107,
-0.01394626684486866,
0.0019509706180542707,
-0.013637730851769447,
0.022631941363215446,
-0.005723465234041214,
0.014660968445241451,
-0.0067442720755934715,
0.058972932398319244,
0.017422573640942574,
0.004915109369903803,
-0.005288772284984589,
-0.03033330850303173,
0.013512258417904377,
-0.028504885733127594,
0.017350271344184875,
0.011989835649728775,
0.0062239631079137325,
-0.03530767187476158,
0.0034511759877204895,
-0.05151869356632233,
-0.011260357685387135,
0.026630625128746033,
0.034448880702257156,
0.018300216645002365,
-0.002802779898047447,
-0.024463698267936707,
-0.05067719146609306,
0.016714170575141907,
-0.07202213257551193,
-0.020412925630807877,
-0.025683850049972534,
-0.006369615439325571,
-0.006044241599738598,
-0.00678782956674695
] |
<p>I'm supposed to use law of cosines on $S_1S_2P$ in the following diagram that relates to a lens:</p>
<p><img src="http://puu.sh/5zDtv.jpg" alt="triangle diagram"></p>
<p>To arrive at the following equation:</p>
<p>$$
\frac{r_2}{r_1} = [1 - 2(\frac{a}{r_1})sin(\theta) + (\frac{a}{r_1})^2]^\frac{1}{2}
$$</p>
<p>I decided to work backwards from this equation, and got to:</p>
<p>$$
r_2^2 = r_1^2 + a^2 - 2ar_1cos(\theta)
$$</p>
<p>But I'm not sure how to proceed, or if I'm even on the right track, as I have no idea how to turn the sin into a cos.</p>
<p>Can anyone help point me in the right direction?</p>
<p>Thanks.</p> | 1,484 | [
0.0039107343181967735,
-0.0037121714558452368,
-0.014435973018407822,
-0.0009343671845272183,
0.009046081453561783,
0.0033969362266361713,
-0.02196398749947548,
-0.022746125236153603,
-0.011846412904560566,
-0.02223782055079937,
0.037423744797706604,
0.029215244576334953,
0.043732766062021255,
0.028616679832339287,
0.03404667228460312,
0.006715007126331329,
-0.04797133803367615,
-0.025062736123800278,
-0.0013531576842069626,
0.014205564744770527,
-0.008458588272333145,
-0.0051278844475746155,
-0.010627072304487228,
-0.012157429940998554,
-0.0019289988558739424,
0.014036508277058601,
0.04356146603822708,
-0.014633423648774624,
-0.01844053715467453,
0.04423951730132103,
-0.01845748908817768,
-0.03856736421585083,
0.014030824415385723,
0.031946100294589996,
-0.003401992842555046,
-0.003951719030737877,
-0.024283384904265404,
-0.007544998545199633,
-0.02064618095755577,
0.034037522971630096,
0.004145728424191475,
0.025634711608290672,
-0.002887279260903597,
0.034002210944890976,
-0.006021423265337944,
0.0033481065183877945,
-0.01741182431578636,
-0.004887663759291172,
0.04417052119970322,
-0.07398504763841629,
0.11118271946907043,
0.007717271335422993,
0.012619627639651299,
0.04803541675209999,
0.024609031155705452,
-0.0032187476754188538,
0.06530366837978363,
0.0205739326775074,
-0.015439899638295174,
-0.04530595615506172,
-0.02616308443248272,
-0.004457870963960886,
-0.03102140501141548,
-0.012409992516040802,
-0.005107174161821604,
-0.007346867583692074,
-0.00820695236325264,
0.005373271182179451,
0.04585099220275879,
-0.012771638110280037,
0.021393608301877975,
0.01905142329633236,
0.018851161003112793,
-0.018091188743710518,
-0.011408569291234016,
-0.04314572364091873,
-0.001625776058062911,
0.04129761829972267,
0.003536214819177985,
0.025686264038085938,
-0.0035935817286372185,
0.028528237715363503,
0.0007409766549244523,
0.05300239473581314,
0.017389900982379913,
-0.01671012118458748,
0.04736390337347984,
0.007588015403598547,
0.006157437805086374,
-0.0034785589668899775,
-0.008876504376530647,
0.005014619790017605,
0.018476372584700584,
-0.030268259346485138,
-0.023936040699481964,
0.030837571248412132,
-0.017739122733473778,
0.05862187221646309,
0.001710624317638576,
-0.04194377362728119,
-0.01912684552371502,
-0.03616455942392349,
0.017437627539038658,
0.08550595492124557,
-0.020725389942526817,
-0.010273784399032593,
-0.005285243503749371,
0.012180065736174583,
-0.0017817195039242506,
-0.01659928634762764,
-0.06090380996465683,
0.04617995023727417,
0.0003931235405616462,
0.024707956239581108,
-0.0041888016276061535,
-0.028209161013364792,
-0.005043437238782644,
0.01692846417427063,
0.06074267625808716,
0.051427777856588364,
0.08901861310005188,
-0.021325256675481796,
0.026983018964529037,
-0.04890251159667969,
-0.05228741839528084,
0.015019765123724937,
0.00946385320276022,
-0.009032079018652439,
-0.0013203922426328063,
0.010660126805305481,
0.04299324005842209,
0.004107617773115635,
0.00366956926882267,
-0.005763842258602381,
-0.0019832197576761246,
-0.03475058451294899,
-0.07287565618753433,
-0.07649502903223038,
0.011794528923928738,
0.002388586988672614,
0.030783681198954582,
-0.08697199821472168,
0.048647936433553696,
0.021968742832541466,
0.10717275738716125,
0.005595230031758547,
-0.0009663835517130792,
0.010777306742966175,
0.06477873027324677,
-0.02111632004380226,
-0.016416611149907112,
-0.0040177539922297,
0.0024532938841730356,
-0.028684042394161224,
0.0073005701415240765,
-0.0582091249525547,
0.037028562277555466,
0.0033725963439792395,
0.011207535862922668,
0.003905726131051779,
0.06100629270076752,
-0.01859772391617298,
0.007308914326131344,
0.008272361010313034,
-0.02756430208683014,
-0.032417360693216324,
0.08775784820318222,
0.01809188723564148,
-0.024356501176953316,
0.047820284962654114,
-0.018924400210380554,
0.021531056612730026,
-0.010459845885634422,
0.0233633890748024,
0.04631127417087555,
0.014380915090441704,
0.008569720201194286,
-0.022776590660214424,
-0.00015100020391400903,
0.021008828654885292,
-0.015410851687192917,
-0.041063714772462845,
-0.0025554585736244917,
0.030772468075156212,
0.010239681228995323,
0.04117872565984726,
-0.02556881494820118,
-0.026207655668258667,
-0.0008877877262420952,
-0.035049572587013245,
0.021203279495239258,
-0.01125500351190567,
0.009029362350702286,
-0.0178260188549757,
0.0020412395242601633,
0.020449042320251465,
0.022295817732810974,
0.02957417070865631,
0.00988259632140398,
-0.015652360394597054,
-0.017952634021639824,
0.019696231931447983,
0.03870519995689392,
0.0008251569233834743,
0.05954418331384659,
0.05109897255897522,
0.05114494636654854,
0.024894312024116516,
0.030666492879390717,
-0.0205079335719347,
0.040485311299562454,
-0.027590222656726837,
-0.024298785254359245,
0.023112988099455833,
0.0012535282876342535,
0.010255808010697365,
-0.007328092120587826,
0.03909265995025635,
-0.00366306328214705,
0.027546225115656853,
-0.016147254034876823,
0.0494263581931591,
0.052635371685028076,
0.05536404252052307,
0.006642460823059082,
0.02724107727408409,
0.018115948885679245,
0.040802087634801865,
-0.006965228356420994,
-0.021146392449736595,
-0.018758499994874,
0.020324332639575005,
0.03945164754986763,
0.025690585374832153,
-0.038537874817848206,
-0.02555106021463871,
0.05549120530486107,
0.03367719054222107,
0.03982559219002724,
0.033561788499355316,
-0.016333039849996567,
-0.04640563949942589,
0.0029091639444231987,
0.035222288221120834,
0.001106417621485889,
0.006634461227804422,
-0.024867219850420952,
-0.018281059339642525,
0.0022260346449911594,
0.01958049088716507,
-0.02399693988263607,
0.020547013729810715,
-0.059767816215753555,
0.021571235731244087,
0.013865616172552109,
0.03265192732214928,
0.04249222204089165,
-0.007879363372921944,
-0.0049012890085577965,
0.03853078559041023,
0.020828882232308388,
-0.029337208718061447,
-0.030154675245285034,
0.012273859232664108,
0.022746548056602478,
-0.004883235786110163,
-0.011320247314870358,
-0.004454957786947489,
0.024337459355592728,
-0.04829507693648338,
-0.027636384591460228,
-0.01090817991644144,
-0.04844559356570244,
-0.056461676955223083,
-0.001366589218378067,
-0.00745187234133482,
0.016662735491991043,
0.015005028806626797,
-0.0074394759722054005,
-0.03923182189464569,
0.010935923084616661,
-0.007943586446344852,
0.024797473102808,
-0.004697960801422596,
-0.03485215827822685,
0.004182309843599796,
-0.005174909718334675,
-0.0006733405753038824,
0.036511581391096115,
0.03505731746554375,
0.008045599795877934,
-0.012316854670643806,
-0.011191083118319511,
-0.04388876631855965,
-0.01194460503757,
-0.03901250287890434,
0.03993690386414528,
-0.04241811856627464,
-0.021888041868805885,
0.022211039438843727,
0.021268285810947418,
-0.039407167583703995,
0.008952786214649677,
-0.04493945091962814,
-0.03325355798006058,
-0.01938432827591896,
0.03004619851708412,
0.024074586108326912,
-0.030392132699489594,
0.015010601840913296,
0.005832581780850887,
0.006534033454954624,
0.03501846641302109,
-0.05219121277332306,
-0.053574997931718826,
0.012660288251936436,
0.03150605410337448,
0.017037400975823402,
-0.023939749225974083,
-0.0380537323653698,
0.08222217857837677,
0.011362028308212757,
-0.009942629374563694,
0.005947261583060026,
0.011274865828454494,
-0.004433221649378538,
-0.04414163902401924,
-0.02177547663450241,
0.029280178248882294,
-0.03596261143684387,
0.03538395091891289,
-0.018442004919052124,
-0.007645368110388517,
0.06868894398212433,
0.0015542582841590047,
0.007739902473986149,
0.0071855830028653145,
-0.009854943491518497,
-0.003005266422405839,
0.05332469567656517,
0.016151878982782364,
0.013847414404153824,
0.03150937333703041,
-0.01653600111603737,
0.06627744436264038,
0.009022517129778862,
-0.0461813285946846,
-0.015067541971802711,
-0.016764041036367416,
0.009134041145443916,
0.007034140173345804,
0.05498571693897247,
0.029597559943795204,
0.016449036076664925,
-0.0024393119383603334,
0.013666028156876564,
0.07416847348213196,
-0.033946532756090164,
-0.0029221216682344675,
0.04063546657562256,
0.005635801237076521,
-0.012821764685213566,
-0.02498096227645874,
-0.04758293554186821,
0.003368551144376397,
0.02287532016634941,
-0.012708961963653564,
-0.04475846886634827,
0.03841526806354523,
0.020329549908638,
0.01946423389017582,
-0.0030354640912264585,
-0.030124465003609657,
0.04675030708312988,
-0.04247428849339485,
-0.02400382049381733,
-0.03797180578112602,
0.041671622544527054,
-0.017733482643961906,
0.06556657701730728,
0.0621759407222271,
-0.0035538088995963335,
0.046211060136556625,
0.024820547550916672,
-0.08042565733194351,
0.05404520779848099,
-0.012270175851881504,
-0.017003249377012253,
-0.026235509663820267,
-0.011765370145440102,
0.026427263393998146,
-0.015679843723773956,
0.012727612629532814,
-0.011371796950697899,
-0.025762341916561127,
-0.0016006393125280738,
0.012475484050810337,
-0.02237350307404995,
-0.02605474926531315,
-0.03244485333561897,
0.0497208833694458,
0.011424200609326363,
-0.0607168972492218,
0.01206956710666418,
0.04090883582830429,
-0.006791289430111647,
0.03580410033464432,
-0.049691569060087204,
0.022055398672819138,
0.010379508137702942,
0.015205222181975842,
0.03109177015721798,
0.02673317678272724,
0.015979742631316185,
0.018586205318570137,
0.0017595887184143066,
0.04627386853098869,
0.018690118566155434,
0.005968286190181971,
-0.03324969485402107,
-0.04671232029795647,
-0.02784688025712967,
-0.0038251150399446487,
0.0750964879989624,
-0.017097651958465576,
-0.053003281354904175,
0.02902497537434101,
-0.027280209586024284,
-0.006696243304759264,
0.033032290637493134,
0.06946253031492233,
-0.0021325198467820883,
-0.034360650926828384,
-0.043640319257974625,
-0.022758159786462784,
-0.01637372374534607,
-0.0020245681516826153,
0.050729624927043915,
0.008751226589083672,
-0.022565755993127823,
-0.016204092651605606,
0.03755246847867966,
0.00020947503799106926,
0.001763776526786387,
0.06013481318950653,
-0.031464047729969025,
0.04049914702773094,
0.035741325467824936,
-0.022503560408949852,
0.01748766005039215,
0.04216265305876732,
0.037180207669734955,
0.005545964930206537,
0.01755966991186142,
-0.06597691029310226,
-0.023713979870080948,
0.030401337891817093,
0.016365960240364075,
-0.01535024307668209,
-0.022430771961808205,
-0.04581274092197418,
-0.05365925654768944,
0.04629243165254593,
-0.022280290722846985,
0.056932806968688965,
-0.003982487600296736,
-0.012296771630644798,
-0.006521835457533598,
0.01602637954056263,
-0.06507326662540436,
0.018306897953152657,
-0.005218029022216797,
0.028587037697434425,
-0.015286477282643318,
-0.01708018220961094,
-0.013691817410290241,
-0.020165886729955673,
0.008199213072657585,
0.06445947289466858,
0.013940544798970222,
-0.040012676268815994,
0.011369970627129078,
0.019601425155997276,
0.0002938870165962726,
-0.030403412878513336,
0.04764633998274803,
-0.015145114623010159,
-0.0337325856089592,
0.0019796837586909533,
-0.03402399644255638,
-0.013908689841628075,
0.04074280709028244,
-0.011599035002291203,
0.020937258377671242,
0.010773192159831524,
-0.024794064462184906,
-0.018384354189038277,
0.05735883489251137,
-0.03620970621705055,
0.014789607375860214,
0.031184380874037743,
-0.018626665696501732,
-0.008908916264772415,
-0.023377923294901848,
0.01748901791870594,
0.0026714724954217672,
-0.033936116844415665,
-0.018876204267144203,
0.005015797447413206,
-0.04281539469957352,
0.021618464961647987,
0.000911389128305018,
0.03658771142363548,
-0.03651127219200134,
-0.003394111292436719,
0.012556674890220165,
0.047709494829177856,
-0.020473437383770943,
0.012721161358058453,
0.013334132730960846,
0.020522013306617737,
0.006817671936005354,
-0.020041098818182945,
0.0018231397261843085,
-0.02391343005001545,
0.015269097872078419,
0.012747625820338726,
-0.004425723571330309,
0.030322030186653137,
-0.05554209277033806,
-0.003491407260298729,
-0.018611891195178032,
-0.06655517220497131,
0.0782506987452507,
-0.044457726180553436,
0.008825922384858131,
0.022227155044674873,
-0.07164618372917175,
-0.030110858380794525,
0.030753403902053833,
-0.008002026006579399,
0.012811269611120224,
-0.08403102308511734,
-0.012215537950396538,
0.03183075413107872,
-0.012144878506660461,
-0.03404875099658966,
-0.05241531506180763,
0.018851222470402718,
-0.004301372915506363,
-0.022559724748134613,
0.0016529206186532974,
-0.014775499701499939,
0.006371673662215471,
-0.04027596488595009,
0.004246638622134924,
0.02582627907395363,
-0.062445834279060364,
-0.012637670151889324,
0.00017654348630458117,
0.021727800369262695,
0.06664324551820755,
-0.001138770137913525,
-0.019070202484726906,
0.04157391935586929,
-0.012878772802650928,
0.0013915705494582653,
0.013585474342107773,
0.04011807590723038,
-0.03906207159161568,
-0.019351890310645103,
-0.040968697518110275,
-0.026293093338608742,
0.04109073057770729,
-0.03880392014980316,
0.016536518931388855,
-0.03670603781938553,
0.029067102819681168,
0.02933044359087944,
-0.03753674402832985,
0.003080781316384673,
0.00015929978690110147,
0.017688395455479622,
-0.044371213763952255,
0.0005092680803500116,
-0.03549821302294731,
-0.026232510805130005,
0.010717751458287239,
-0.0013363787438720465,
0.05224275588989258,
0.0007547078421339393,
0.07033993303775787,
-0.01767369918525219,
0.003210643073543906,
0.002453576773405075,
-0.0018277378985658288,
0.006998543627560139,
0.01303170993924141,
0.04294736310839653,
0.03550027310848236,
0.01950354315340519,
-0.056964341551065445,
0.023755908012390137,
-0.04737578704953194,
-0.021576376631855965,
0.1304793655872345,
-0.027394747361540794,
0.049950774759054184,
0.020598387345671654,
0.014945306815207005,
0.02145238406956196,
-0.0030441624112427235,
-0.0010253601940348744,
-0.01796296052634716,
0.018514078110456467,
0.03556730970740318,
-0.05196535959839821,
-0.0017386957770213485,
-0.012463637627661228,
0.028247127309441566,
0.03215587139129639,
0.02251722849905491,
0.008505904115736485,
0.048316940665245056,
0.0022800129372626543,
0.0015145782381296158,
-0.059339527040719986,
0.028699181973934174,
0.012866872362792492,
0.009425736963748932,
-0.018452947959303856,
-0.01959475688636303,
0.04740529507398605,
-0.003744350280612707,
0.05119256302714348,
-0.03197510540485382,
-0.031248973682522774,
-0.032268036156892776,
0.011410324834287167,
0.010502776131033897,
0.005016333889216185,
-0.02295466884970665,
0.007509191986173391,
0.017875541001558304,
0.026310617104172707,
0.03559238091111183,
-0.05202990397810936,
-0.04870116338133812,
-0.03112752176821232,
-0.05909256637096405,
-0.053262121975421906,
0.0686267763376236,
0.013160036876797676,
0.01587359420955181,
0.027040623128414154,
-0.013293878175318241,
-0.003921565134078264,
0.04625248536467552,
0.005882962606847286,
-0.040650710463523865,
0.05800819396972656,
-0.010379472747445107,
0.027287347242236137,
-0.003245110157877207,
-0.03374860808253288,
0.10070734471082687,
0.01794777251780033,
-0.02643619291484356,
-0.04545155167579651,
0.011294165626168251,
-0.04139620065689087,
0.0011259564198553562,
-0.06715023517608643,
0.050927627831697464,
-0.0282116811722517,
-0.020404629409313202,
0.02613186463713646,
0.03871775045990944,
-0.02399786002933979,
-0.009704384952783585,
0.03443162515759468,
-0.035206522792577744,
-0.03797302767634392,
-0.017331918701529503,
-0.028294313699007034,
-0.02853701449930668,
0.03589090332388878,
-0.024729307740926743,
0.04708438366651535,
-0.06507664918899536,
-0.0425012931227684,
-0.025344843044877052,
-0.011534389108419418,
-0.008179237134754658,
0.00375134265050292,
-0.015129857696592808,
0.029521863907575607,
-0.007736871484667063,
-0.009404969401657581,
-0.01933193951845169,
0.06007545813918114,
0.02826002612709999,
-0.02834414876997471,
0.014746704138815403,
0.005600741598755121,
-0.0029905554838478565,
0.0032319962047040462,
0.044006649404764175,
-0.01314491592347622,
-0.05129116028547287,
-0.0018856633687391877,
-0.0036005061119794846,
0.05700325965881348,
0.008381130173802376,
0.0016680390108376741,
-0.01740925945341587,
-0.004571815952658653,
0.026493143290281296,
-0.052290383726358414,
-0.005371655337512493,
0.020991768687963486,
-0.0036357392091304064,
-0.015786834061145782,
-0.03750183805823326,
0.0027980818413197994,
0.013730433769524097,
0.017412370070815086,
0.014641346409916878,
-0.010006571188569069,
0.012054653838276863,
-0.016527190804481506,
0.0041962587274611,
0.03762603551149368,
-0.004872229881584644,
-0.04010478034615517,
-0.010352247394621372,
0.009662143886089325,
-0.02026386559009552,
-0.006561243440955877,
0.032468318939208984,
0.028615592047572136,
-0.003487038193270564,
0.014969578944146633,
-0.02329280786216259,
-0.04003836214542389,
-0.06661161780357361,
0.015171734616160393,
-0.01657906360924244,
-0.013069935142993927,
-0.025102831423282623,
-0.0336097776889801,
0.047665003687143326,
0.0424148365855217,
-0.047606371343135834,
-0.0030721789225935936,
0.017376016825437546,
0.050623685121536255,
0.0686950758099556,
-0.048834387212991714,
-0.0321149118244648,
0.020812181755900383,
-0.005584139376878738,
-0.031165331602096558,
-0.023835590109229088,
0.012281804345548153,
0.0452752523124218,
0.03234673663973808,
-0.02557838335633278,
-0.0012466288171708584,
-0.032972078770399094,
0.010872730053961277,
0.007970243692398071,
-0.02081221714615822,
0.05069539695978165,
-0.03428857773542404,
0.038954220712184906,
-0.005800317972898483,
-0.0048467800952494144,
0.018167050555348396,
-0.0175393708050251,
0.019911618903279305,
-0.013316827826201916,
-0.021658746525645256,
-0.020368507131934166,
-0.02420441247522831,
-0.017650658264756203,
-0.04625155031681061,
-0.020199591293931007,
0.0014374811435118318,
0.015057159587740898,
-0.005703907459974289,
0.029945746064186096,
-0.0028093140572309494,
0.06601515412330627,
-0.0016807341016829014,
-0.03576774522662163,
0.01404162310063839,
0.004834501538425684,
0.006532987579703331,
-0.004919958766549826,
0.012106678448617458,
-0.051140256226062775,
0.05376603081822395,
-0.057219795882701874,
-0.02239980362355709,
0.017112458124756813,
-0.021449925377964973,
-0.007107430137693882,
0.004198542796075344,
0.009889950975775719,
0.03939814865589142,
0.004866588860750198,
-0.05221845209598541,
0.006475541740655899,
0.03607621043920517,
0.014866736717522144,
-0.02158336713910103,
-0.00237740995362401,
-0.04279153048992157,
0.02718588151037693,
-0.013943352736532688,
0.0010666778543964028,
-0.025766968727111816,
0.007619389332830906,
0.017384450882673264,
0.00783057976514101,
-0.021022727712988853,
-0.02681388147175312,
0.00964951142668724,
-0.027325473725795746,
-0.008663518354296684,
-0.010731888934969902,
-0.017526229843497276,
0.054430313408374786,
-0.01086440309882164,
-0.019176630303263664,
0.01282932423055172,
0.013103198260068893,
0.012912166304886341,
-0.062022484838962555,
-0.007574793417006731,
-0.008512008003890514,
0.007085055112838745,
0.03125566616654396,
-0.0784754529595375,
0.007521198131144047,
0.015128225088119507,
-0.07424471527338028,
-0.019670112058520317,
-0.015649214386940002,
-0.05597879737615585,
-0.03546959161758423,
0.003762640058994293,
-0.005530799273401499,
0.03647951781749725,
-0.018418479710817337,
0.06674380600452423,
0.013444792479276657,
-0.008156494237482548,
-0.005762495566159487,
-0.023970987647771835,
0.026873378083109856,
0.011946500279009342,
0.006047605071216822,
-0.03465646132826805,
0.029523976147174835,
-0.02511751651763916,
-0.014632356353104115,
0.01593642309308052,
-0.016636740416288376,
0.013350443914532661,
0.025909924879670143,
0.04550951346755028,
-0.02700461633503437,
0.025765474885702133,
0.006733638700097799,
-0.008368904702365398,
-0.012701631523668766,
-0.022678866982460022,
0.017666954547166824,
0.018137045204639435,
-0.014387600123882294,
-0.005443678703159094,
0.03660184144973755,
-0.039254650473594666,
-0.045730188488960266,
0.006283033639192581,
-0.023398960009217262,
-0.006045884918421507,
0.0046364073641598225,
-0.03505365550518036,
0.029797418043017387,
-0.04548487812280655,
0.007675367873162031,
-0.047135159373283386,
-0.016121014952659607,
0.03899949789047241,
-0.028470778837800026,
-0.002827286720275879,
0.01886310614645481,
-0.026791781187057495,
-0.050536178052425385,
0.009472968056797981,
0.016181934624910355,
-0.023372162133455276,
-0.049429282546043396,
0.00421281298622489,
0.007290487643331289,
0.000016606294593657367,
0.01422068104147911,
-0.01126107294112444,
-0.001689653960056603,
0.04621994495391846,
0.007137876935303211,
0.014338315464556217,
0.054928380995988846,
-0.02048356644809246,
-0.022018734365701675,
-0.08677985519170761,
0.03158389404416084,
-0.007584898266941309,
-0.04067632928490639,
-0.010690641589462757,
-0.020119745284318924,
-0.010131524875760078,
0.03907983750104904,
0.0590064711868763,
-0.0005083711002953351,
0.037093956023454666,
-0.0018282554810866714,
0.02304912358522415,
0.03192991763353348,
-0.04458615183830261,
0.02430330216884613,
0.023517832159996033,
0.0076244487427175045,
-0.014292002655565739,
-0.008462212979793549,
-0.04310588166117668,
0.01674528233706951,
-0.0016083570662885904,
-0.0011842412641271949,
0.03862634673714638,
0.0022138585336506367,
-0.06707870960235596,
-0.016114141792058945,
-0.03926590457558632,
0.008993047289550304,
0.10582248866558075,
-0.0053716180846095085,
-0.033508624881505966,
0.029186585918068886,
-0.03717220574617386,
-0.03387223929166794,
0.03420695289969444,
-0.05987654998898506,
-0.023092102259397507,
-0.023450978100299835,
-0.002079530619084835,
0.05431610718369484,
-0.07080737501382828,
-0.0065425243228673935,
-0.010517919436097145,
-0.04693697765469551,
-0.033091746270656586,
0.05016130208969116,
-0.01828704960644245,
0.004306572489440441,
-0.013029636815190315,
0.027674619108438492,
0.005165641661733389,
-0.019192438572645187,
0.05416324734687805,
0.030044924467802048,
0.029488112777471542,
0.005385684780776501,
-0.000877267390023917,
0.06495446711778641,
0.020647956058382988,
0.005444795824587345,
-0.02239457331597805,
0.035312309861183167,
-0.008243018761277199,
-0.011674962006509304,
-0.00453327689319849,
-0.03135707229375839,
0.0037959567271173,
0.014511417597532272,
-0.024656301364302635,
0.03991086781024933,
-0.03137899190187454,
0.021888166666030884,
-0.033614203333854675,
0.0209418423473835,
-0.04004094377160072,
0.028071630746126175,
0.0497107207775116,
-0.0034128129482269287,
-0.0005130124627612531,
-0.031304288655519485,
-0.0139140784740448,
-0.02212189882993698,
-0.01576261967420578,
-0.008598433807492256,
0.03295160084962845,
0.04863746464252472,
0.0075761545449495316,
-0.017756160348653793,
-0.04346994310617447,
-0.010676541365683079,
-0.03210956230759621,
0.003877566894516349,
0.03843741863965988,
0.0030086010228842497,
0.00895808357745409,
0.023457303643226624,
-0.0002378708013566211,
0.02697872929275036,
-0.07570721209049225,
-0.041656237095594406,
0.0480278916656971,
0.012331339530646801,
-0.00668925978243351,
-0.017723554745316505
] |
<p>It's been a while, and I'm trying to verify my understanding. I remember reasoning (but never being taught) that the sum of the (normalized) electric and magnetic waves in a single electromagnetic wave at any single point in time is always one. Like so:</p>
<pre><code>Given A of em-wave is normalized (max = 1, min = -1)
abs(sum(A of m-wave, A of e-wave)) = 1
</code></pre>
<p>I haven't been able to find anywhere that says this specifically (I probably suck at searching, or am wrong). Am I correct in my understanding?</p> | 1,485 | [
-0.019234631210565567,
-0.02641633339226246,
-0.018776699900627136,
-0.007351039908826351,
0.05207621678709984,
0.023158032447099686,
-0.010450122877955437,
-0.017191944643855095,
0.00046517321607097983,
0.000751613057218492,
0.05275227874517441,
0.0363728292286396,
0.06629319489002228,
0.012469053268432617,
0.0525168739259243,
0.008838977664709091,
-0.00448363134637475,
0.01365301851183176,
0.0014839463401585817,
-0.03929343819618225,
-0.013037028722465038,
0.017285048961639404,
0.03118712641298771,
-0.0069763208739459515,
0.015212411992251873,
0.022049477323889732,
0.01657283492386341,
-0.01062232255935669,
0.028791658580303192,
0.04523115232586861,
0.0008354921592399478,
-0.033050961792469025,
-0.0006974622374400496,
0.046317268162965775,
0.04405353218317032,
-0.009412090294063091,
-0.021366208791732788,
-0.030708864331245422,
-0.029616545885801315,
0.03338923677802086,
0.06129639595746994,
-0.03180722892284393,
-0.024889109656214714,
0.02778860740363598,
-0.06812290847301483,
0.009098262526094913,
0.0009617540054023266,
0.0074495235458016396,
0.022021332755684853,
-0.06791946291923523,
0.08613074570894241,
-0.03388042002916336,
0.07294686883687973,
0.012039035558700562,
-0.013669909909367561,
0.0024608245585113764,
0.08830659836530685,
0.00774969020858407,
0.032430365681648254,
-0.06877324730157852,
-0.021128494292497635,
-0.02246120013296604,
0.0027890887577086687,
0.023943789303302765,
-0.028894351795315742,
0.02655686065554619,
-0.016953090205788612,
-0.02204585075378418,
0.027122650295495987,
-0.03050505369901657,
-0.007814779877662659,
0.03350955992937088,
0.02701725624501705,
-0.03747427091002464,
0.017205018550157547,
-0.01258211862295866,
0.03094184212386608,
0.0038023090455681086,
0.04262568801641464,
0.03203374892473221,
-0.024739524349570274,
0.014785617589950562,
0.03275357559323311,
0.049882303923368454,
0.03002980537712574,
-0.013857772573828697,
0.08203378319740295,
-0.02605103701353073,
-0.002971892710775137,
0.012065712362527847,
-0.01639637164771557,
0.03274082392454147,
0.01862885244190693,
-0.007676369976252317,
-0.0455329455435276,
0.058813221752643585,
0.010391359217464924,
0.01682237908244133,
0.028349725529551506,
-0.038759417831897736,
0.008579454384744167,
-0.01076813880354166,
0.02659507654607296,
0.03808391094207764,
0.00011269326932961121,
0.006749284453690052,
-0.044220875948667526,
0.05591336637735367,
-0.028517859056591988,
-0.0008039963431656361,
-0.033888641744852066,
0.005258334334939718,
-0.014132407493889332,
-0.002458282047882676,
0.00484514469280839,
-0.015657130628824234,
0.03568653389811516,
0.011481061577796936,
0.03805694729089737,
0.0664367526769638,
0.04824269935488701,
-0.025874877348542213,
0.02765275165438652,
-0.01472031231969595,
-0.09647401422262192,
0.0008948952308855951,
-0.01720137521624565,
0.0321798175573349,
-0.049631524831056595,
0.06714608520269394,
-0.03004434145987034,
-0.02117551676928997,
-0.00034435829729773104,
-0.020146992057561874,
0.04324156790971756,
-0.021099461242556572,
-0.10036612302064896,
-0.04874927178025246,
-0.010041046887636185,
-0.03082229197025299,
-0.031130483373999596,
-0.05379358306527138,
0.013536578044295311,
0.008336523547768593,
0.07111351937055588,
0.02759525552392006,
0.027029545977711678,
-0.01039680652320385,
0.027289606630802155,
0.03003651835024357,
-0.004764039535075426,
-0.024070700630545616,
0.003775540739297867,
-0.020218275487422943,
-0.0023037311621010303,
-0.07127097994089127,
-0.0051982952281832695,
0.03024730272591114,
-0.003394148778170347,
0.020027339458465576,
0.0572030134499073,
-0.0059090848080813885,
0.0005072253406979144,
0.02644878439605236,
-0.02059318870306015,
-0.045782413333654404,
0.09463407844305038,
0.03639630600810051,
0.005199634935706854,
0.03784320876002312,
0.0045363642275333405,
-0.00761708477512002,
-0.007021437399089336,
0.034453559666872025,
0.012570101767778397,
-0.05351322516798973,
-0.008435352705419064,
-0.02631295844912529,
0.03443208709359169,
0.034999363124370575,
-0.02255103923380375,
-0.054076045751571655,
0.013011932373046875,
0.035426829010248184,
0.010880985297262669,
0.05972107872366905,
-0.044390592724084854,
-0.03853728249669075,
-0.002241651527583599,
-0.0605817586183548,
0.018409550189971924,
-0.04208626225590706,
0.006418124306946993,
-0.0015255229081958532,
-0.02153678610920906,
-0.007782961707562208,
-0.009571080096065998,
0.02930455654859543,
-0.052418775856494904,
-0.060732390731573105,
-0.013693766668438911,
0.007658421993255615,
0.04286467283964157,
-0.04319605603814125,
0.02586938627064228,
0.04630446061491966,
0.038522638380527496,
0.017653733491897583,
0.016313469037413597,
-0.036458175629377365,
-0.023149315267801285,
-0.0011528714094311,
-0.040088966488838196,
0.036466676741838455,
0.04960772395133972,
0.01436819788068533,
-0.005625959485769272,
0.010554319247603416,
0.014172852039337158,
0.0022193663753569126,
-0.0340212844312191,
0.03070317767560482,
0.021673398092389107,
-0.008397755213081837,
-0.02630225010216236,
0.017199520021677017,
0.044950008392333984,
0.005093003623187542,
0.010929682292044163,
-0.01943153701722622,
-0.01249375008046627,
0.033434946089982986,
0.02763996459543705,
0.022983133792877197,
-0.02683715708553791,
-0.01043987087905407,
0.030925922095775604,
0.06464207172393799,
0.042522843927145004,
0.041444361209869385,
-0.014620807021856308,
-0.024717485532164574,
-0.004549907986074686,
0.016591016203165054,
0.020642831921577454,
0.024323370307683945,
0.04421928897500038,
-0.005443120840936899,
-0.020117664709687233,
0.03590742498636246,
-0.0014354269951581955,
0.0047869933769106865,
-0.0005466101574711502,
0.02873835153877735,
-0.019886530935764313,
-0.04522347077727318,
0.013542207889258862,
-0.040807537734508514,
0.049462608993053436,
-0.0019375513074919581,
-0.01674012467265129,
-0.05639348924160004,
-0.0385991595685482,
-0.00507556926459074,
-0.015156637877225876,
-0.004880249500274658,
-0.021023249253630638,
-0.011494021862745285,
0.02191498503088951,
-0.021438144147396088,
0.008103758096694946,
-0.03286246955394745,
-0.04496442899107933,
-0.050719864666461945,
-0.018797772005200386,
0.029647085815668106,
0.02229941450059414,
0.05014139041304588,
-0.062176745384931564,
-0.05483830347657204,
-0.037930168211460114,
-0.023667560890316963,
0.021592218428850174,
0.013872811570763588,
-0.02804526686668396,
0.0058281999081373215,
-0.01986125484108925,
-0.04235994070768356,
0.09396392107009888,
-0.019328681752085686,
-0.03197164461016655,
0.016617655754089355,
-0.009975869208574295,
-0.05029871687293053,
-0.03349984437227249,
-0.050423234701156616,
0.008973601274192333,
-0.017082789912819862,
0.0014486887957900763,
0.06062823161482811,
0.012744449079036713,
-0.059412579983472824,
0.020397545769810677,
-0.029538342729210854,
-0.025553492829203606,
-0.03861845284700394,
-0.06385339796543121,
-0.011445742100477219,
-0.05079801753163338,
-0.0043503656052052975,
0.016103146597743034,
-0.05709155276417732,
0.006123451050370932,
-0.03240286931395531,
-0.07514090836048126,
0.04145602881908417,
-0.012193409726023674,
0.060502007603645325,
0.0005473732016980648,
-0.045652564615011215,
0.08215545862913132,
0.013096509501338005,
-0.015227830037474632,
-0.02217639796435833,
0.03598276153206825,
0.022480890154838562,
0.007905305363237858,
0.017817365005612373,
0.05649670585989952,
-0.0006840747082605958,
0.012659684754908085,
0.0019200900569558144,
0.031725335866212845,
0.05115471035242081,
0.012030777521431446,
0.02522406354546547,
0.0242268368601799,
-0.01997905597090721,
0.018644610419869423,
0.044820722192525864,
0.07377323508262634,
-0.0027982969768345356,
0.02380869723856449,
0.029793670400977135,
0.03586617484688759,
0.0022770061623305082,
-0.029633117839694023,
0.04282126575708389,
-0.014554488472640514,
0.025818606838583946,
-0.0568309910595417,
0.042020440101623535,
-0.019787954166531563,
-0.008151398971676826,
-0.00838395394384861,
0.028218260034918785,
0.010673237964510918,
-0.02718578465282917,
-0.010367538779973984,
0.025657057762145996,
0.019194036722183228,
-0.043393731117248535,
-0.005145046394318342,
0.006981394719332457,
-0.007572172675281763,
0.041787274181842804,
-0.05988755449652672,
-0.009386789985001087,
0.05014845356345177,
0.019708117470145226,
0.03404342010617256,
0.019652802497148514,
-0.06770391762256622,
0.007224670611321926,
-0.07072187960147858,
-0.005561078432947397,
0.029321720823645592,
0.03130964934825897,
-0.0026836602482944727,
0.061068616807460785,
0.019275179132819176,
0.020906945690512657,
0.026371780782938004,
0.005812068469822407,
-0.07749206572771072,
-0.00047640089178457856,
-0.018374532461166382,
-0.036463651806116104,
-0.015878895297646523,
-0.018520284444093704,
-0.01083702128380537,
-0.02371997945010662,
-0.014009801670908928,
0.009413668885827065,
-0.018423017114400864,
-0.0669335201382637,
0.03150397539138794,
-0.0234360508620739,
0.003645806573331356,
-0.04403143748641014,
0.028826318681240082,
0.027852846309542656,
0.008584204129874706,
-0.009035159833729267,
0.034723956137895584,
-0.03977954015135765,
-0.0032583160791546106,
-0.00695775356143713,
-0.0011254148557782173,
0.03628561273217201,
-0.00022130945581011474,
0.04716644063591957,
0.029985662549734116,
-0.03452778235077858,
0.011362973600625992,
0.0188321303576231,
0.06943808495998383,
0.011080866679549217,
-0.03902916610240936,
-0.009325133636593819,
-0.008224422112107277,
-0.03414461761713028,
-0.0057146609760820866,
0.035775817930698395,
0.04611098766326904,
0.009059861302375793,
-0.0018456259276717901,
0.035965774208307266,
-0.0022972319275140762,
0.041368767619132996,
0.13169719278812408,
-0.024702874943614006,
-0.015254084020853043,
-0.08233090490102768,
0.014501268044114113,
-0.04077597334980965,
0.016323212534189224,
0.01660859026014805,
0.012569662183523178,
-0.0016236911760643125,
-0.015801716595888138,
-0.00040385412285104394,
-0.0002585027541499585,
0.03807932883501053,
-0.007720282766968012,
0.0062995669431984425,
-0.0024948841892182827,
0.005201265215873718,
-0.00844742450863123,
0.03570556640625,
0.0385739840567112,
0.03789066895842552,
0.022008392959833145,
-0.04531994089484215,
-0.08113497495651245,
0.005101795308291912,
-0.0014184934552758932,
0.02567172609269619,
0.023809298872947693,
-0.0020393417216837406,
-0.02273193933069706,
-0.010982107371091843,
0.04112459346652031,
-0.02038378082215786,
0.05249859392642975,
0.039385564625263214,
0.012607471086084843,
-0.02704518660902977,
-0.025738641619682312,
0.004123677033931017,
0.02762012928724289,
0.0002857719373423606,
0.03477852791547775,
0.0005167071940377355,
0.018807152286171913,
-0.022204669192433357,
0.002071915427222848,
0.02537933737039566,
0.038513921201229095,
-0.027864068746566772,
-0.005278505850583315,
-0.027687329798936844,
0.010577005334198475,
-0.02537013776600361,
-0.0829116478562355,
0.015867728739976883,
0.010807952843606472,
-0.008093656972050667,
0.06093155965209007,
-0.0004991191672161222,
-0.011832457967102528,
0.05876912921667099,
0.03171288222074509,
-0.0012980501633137465,
-0.0072878096252679825,
-0.03006635792553425,
0.03911060839891434,
0.024342067539691925,
-0.01649712212383747,
0.010493158362805843,
-0.006084901746362448,
-0.011182747781276703,
0.006558694411069155,
-0.04239534214138985,
0.020404532551765442,
0.000026540585167822428,
-0.00867606233805418,
-0.006433650851249695,
0.019998392090201378,
-0.018988078460097313,
0.03630021959543228,
-0.026316676288843155,
-0.004042196087539196,
-0.0010216665687039495,
-0.012757066637277603,
-0.03778218850493431,
0.03273436427116394,
-0.032976482063531876,
-0.030901584774255753,
0.007248621433973312,
0.011442411690950394,
-0.03157152235507965,
-0.03984774276614189,
0.01825033314526081,
-0.05525844171643257,
0.01391252689063549,
0.023610079661011696,
0.00590806407853961,
0.0077461665496230125,
-0.013948280364274979,
-0.006639408878982067,
0.011631356552243233,
-0.030706634745001793,
0.01536329835653305,
-0.03834342956542969,
0.024966463446617126,
0.01710081659257412,
-0.05024006590247154,
-0.05034743621945381,
0.014072761870920658,
0.01213522907346487,
0.026154931634664536,
-0.07315962761640549,
0.013567190617322922,
0.005945500917732716,
0.008493217639625072,
-0.0297707486897707,
-0.043142013251781464,
0.03660225868225098,
0.024401424452662468,
-0.02126505970954895,
-0.03162161260843277,
-0.013575266115367413,
-0.029193194583058357,
-0.014206652529537678,
-0.00729856314137578,
0.03850696235895157,
-0.04327043518424034,
-0.020503360778093338,
0.02071356028318405,
0.011706954799592495,
0.054021283984184265,
0.019156480208039284,
-0.022366000339388847,
0.0420725978910923,
-0.031945668160915375,
0.00735987676307559,
-0.0011621088488027453,
0.04741765558719635,
-0.031755417585372925,
-0.006765815429389477,
-0.04720595106482506,
-0.015458358451724052,
0.034774795174598694,
-0.02257409133017063,
-0.04391218349337578,
0.011469216085970402,
0.011021851561963558,
0.011313377879559994,
-0.0347345806658268,
0.015657540410757065,
-0.03637227788567543,
0.010635670274496078,
0.010592465288937092,
-0.010755715891718864,
-0.04708586260676384,
-0.03389986604452133,
0.013693389482796192,
0.014556342735886574,
0.00799929816275835,
0.023184413090348244,
0.0702468529343605,
0.017722683027386665,
0.010688901878893375,
-0.0007859710021875799,
-0.019314303994178772,
-0.005371423438191414,
0.0227931197732687,
0.00385227776132524,
0.01800881139934063,
0.012163314037024975,
0.01695578545331955,
-0.00970606878399849,
-0.02546164020895958,
0.02142365463078022,
0.05676046013832092,
-0.029453720897436142,
0.06945597380399704,
0.05099167302250862,
0.013702795840799809,
-0.027554070577025414,
-0.029899464920163155,
-0.009433466009795666,
0.019102374091744423,
-0.012593241408467293,
0.03935231640934944,
-0.03371531516313553,
-0.016575587913393974,
0.020939918234944344,
0.040583837777376175,
-0.007056157570332289,
-0.02038636803627014,
0.008033199235796928,
0.027714625000953674,
-0.00927234161645174,
0.028557084500789642,
-0.043825726956129074,
0.046861257404088974,
-0.061911776661872864,
0.002845889888703823,
0.027154359966516495,
-0.015877986326813698,
0.011936856433749199,
-0.016149982810020447,
0.010559618473052979,
-0.06197914853692055,
-0.037205133587121964,
-0.0016802683239802718,
0.029907463118433952,
0.02760014869272709,
-0.01688394509255886,
0.01504134014248848,
-0.0028416782151907682,
0.05335136875510216,
0.004720910917967558,
0.012624095194041729,
0.0019932733848690987,
-0.052593763917684555,
-0.03294133394956589,
-0.03829358518123627,
-0.021278053522109985,
0.03697376325726509,
0.006167471408843994,
-0.007627516519278288,
-0.016780542209744453,
-0.03670724108815193,
0.043420322239398956,
0.024223482236266136,
0.02468264475464821,
0.004054817836731672,
0.03728562220931053,
0.03758587688207626,
0.012903481721878052,
-0.03696833550930023,
-0.024860018864274025,
0.12417423725128174,
0.07273959368467331,
0.026356546208262444,
-0.036903608590364456,
0.010738808661699295,
-0.024737026542425156,
0.012072454206645489,
-0.03199312463402748,
0.013831451535224915,
-0.03871211037039757,
0.0355435386300087,
0.03796575590968132,
0.029078878462314606,
0.015998389571905136,
-0.0241488516330719,
0.013485460542142391,
-0.03642171993851662,
-0.03533654659986496,
0.030653083696961403,
0.051646266132593155,
0.005888334475457668,
0.0010798197472468019,
-0.07956574857234955,
0.019636062905192375,
-0.037783633917570114,
-0.022850094363093376,
-0.010975446552038193,
0.00508797587826848,
0.027383554726839066,
-0.004101613536477089,
-0.013207915239036083,
0.02285050041973591,
0.01951294019818306,
-0.03128251060843468,
-0.045465923845767975,
0.0008155928226187825,
0.05032607913017273,
0.024376964196562767,
-0.007582682650536299,
0.017231203615665436,
0.044576436281204224,
-0.005632805172353983,
0.021813206374645233,
0.027602003887295723,
-0.04276970401406288,
0.025747306644916534,
-0.014747667126357555,
0.04223015531897545,
-0.035713594406843185,
0.030531909316778183,
-0.0019503375515341759,
0.0005722976638935506,
-0.02001972496509552,
-0.047907013446092606,
-0.01150464452803135,
0.001090501551516354,
0.032466985285282135,
-0.016204556450247765,
0.05062739923596382,
0.005763100925832987,
0.009645725600421429,
0.005588918924331665,
0.009823634289205074,
-0.016939489170908928,
0.017570646479725838,
0.03978175297379494,
-0.0383288599550724,
0.042259618639945984,
-0.03883613646030426,
-0.03336109593510628,
-0.0033510648645460606,
-0.04466183856129646,
-0.014683402143418789,
-0.013647210784256458,
0.022836579009890556,
0.003779244376346469,
0.02601022645831108,
-0.0010990219889208674,
-0.005477269180119038,
-0.025931276381015778,
-0.05953969061374664,
0.004780493211001158,
-0.01230604387819767,
-0.03229658305644989,
0.003082125447690487,
-0.01128636859357357,
0.022931456565856934,
0.04722510278224945,
-0.038090672343969345,
0.02113996259868145,
0.003999758046120405,
0.02459307387471199,
0.009482217021286488,
-0.022472167387604713,
-0.028060054406523705,
0.009384576231241226,
-0.021525956690311432,
0.015442692674696445,
-0.03755250200629234,
0.01550198718905449,
0.025871649384498596,
0.031679943203926086,
0.000919158395845443,
0.03162185475230217,
-0.02039886824786663,
-0.015820013359189034,
-0.0092180036008358,
-0.02688811719417572,
0.03116321749985218,
0.02225542441010475,
0.0007978291832841933,
-0.02110975608229637,
0.0055241878144443035,
0.0019044510554522276,
-0.006571945268660784,
0.004786595236510038,
0.02101818285882473,
-0.032135967165231705,
0.016886349767446518,
0.011979904025793076,
-0.009650377556681633,
-0.01911325193941593,
-0.019427431747317314,
-0.03851405158638954,
0.016028447076678276,
-0.005940699949860573,
-0.03436353802680969,
-0.012852258048951626,
0.0011456417851150036,
-0.028335075825452805,
-0.038889992982149124,
0.03163525089621544,
0.018439726904034615,
0.006334269419312477,
0.014690930023789406,
-0.02098536677658558,
-0.011223642155528069,
0.060153257101774216,
-0.01778983324766159,
-0.03496663272380829,
0.00795790832489729,
-0.041424110531806946,
-0.015173893421888351,
0.044160448014736176,
0.025038201361894608,
0.019549669697880745,
0.04120286926627159,
-0.0006558952736668289,
-0.017423061653971672,
0.04766351357102394,
0.010868722572922707,
-0.01470453292131424,
0.0071117025800049305,
-0.017748376354575157,
0.021600697189569473,
0.000636870798189193,
-0.005844391882419586,
0.00456980662420392,
-0.012424711138010025,
-0.008725620806217194,
0.024036897346377373,
0.0007126180571503937,
-0.031472381204366684,
-0.010347950272262096,
0.027732471004128456,
-0.006078846286982298,
0.047638971358537674,
-0.017983172088861465,
0.011156699620187283,
0.0389564074575901,
-0.02406788058578968,
0.013204747810959816,
-0.017236070707440376,
0.00946315098553896,
-0.07779345661401749,
-0.0226628128439188,
0.03205070272088051,
0.01557473000138998,
0.032849494367837906,
-0.02035689726471901,
0.009219536557793617,
0.006975480355322361,
-0.08835428953170776,
-0.00820750743150711,
-0.012573000974953175,
-0.018475200980901718,
-0.03142423555254936,
-0.012527749873697758,
-0.0010471026180312037,
0.035664673894643784,
0.009408350102603436,
0.045050304383039474,
-0.012108688242733479,
0.001175195793621242,
-0.021068276837468147,
-0.016328157857060432,
-0.04335691034793854,
0.027821950614452362,
0.018866442143917084,
-0.01484955195337534,
0.008559847250580788,
-0.026707354933023453,
-0.006966329179704189,
0.03813374042510986,
-0.05934831127524376,
-0.0209208931773901,
0.0136204082518816,
0.0643746554851532,
0.0424734391272068,
0.019697757437825203,
0.003860953962430358,
-0.02255942113697529,
-0.011311371810734272,
0.01763947121798992,
0.03504473343491554,
0.026593562215566635,
-0.018462952226400375,
0.002726706676185131,
0.024162964895367622,
-0.04890704154968262,
-0.07565872371196747,
0.030256373807787895,
-0.003525610314682126,
-0.003436378203332424,
0.003100453643128276,
-0.001962608890607953,
-0.011319117620587349,
-0.018441898748278618,
-0.02355288527905941,
-0.03520027920603752,
-0.006756354123353958,
0.0489494614303112,
0.010851569473743439,
0.002372107934206724,
-0.01227289903908968,
-0.001414791215211153,
-0.0484897717833519,
0.0291508287191391,
0.025551585480570793,
0.01153659075498581,
-0.0252580177038908,
0.010851938277482986,
0.029743695631623268,
0.019196318462491035,
0.018786035478115082,
-0.04536838456988335,
-0.013636256568133831,
-0.012591410428285599,
0.012747623957693577,
-0.0046745408326387405,
0.005659535061568022,
-0.051941268146038055,
-0.005460214801132679,
-0.06570009142160416,
0.04742735996842384,
-0.024571493268013,
0.011539789848029613,
-0.02257247269153595,
-0.01700657419860363,
-0.02869424596428871,
0.030573884025216103,
0.05129107087850571,
-0.0032016297336667776,
0.0033380298409610987,
-0.0073616402223706245,
-0.022884542122483253,
0.0297533106058836,
-0.02096754126250744,
0.01744689792394638,
0.019455887377262115,
-0.034715354442596436,
-0.010490366257727146,
-0.0046334341168403625,
-0.0014854575274512172,
-0.03993212431669235,
-0.007801486644893885,
-0.0001847307285061106,
0.013266620226204395,
-0.06671565026044846,
-0.02630322426557541,
0.025334356352686882,
0.03302215784788132,
-0.04153701290488243,
0.035505399107933044,
-0.022851578891277313,
-0.01111773680895567,
0.014062492176890373,
-0.018928149715065956,
-0.05911817401647568,
0.01857282593846321,
-0.03496727719902992,
0.02663726732134819,
0.004846459720283747,
0.03700653463602066,
0.05108318105340004,
-0.049470432102680206,
-0.022447073832154274,
0.02909596636891365,
-0.02850913815200329,
-0.04901736229658127,
0.059427544474601746,
-0.00824082549661398,
0.031452324241399765,
-0.03554011881351471,
0.009887092746794224,
0.008892519399523735,
-0.04284851998090744,
0.02134844847023487,
0.05224350094795227,
0.03575340285897255,
0.007267137989401817,
0.00929405726492405,
0.020036350935697556,
-0.0071428208611905575,
0.02266635186970234,
-0.016292264685034752,
0.015833446756005287,
-0.003030484076589346,
-0.02718823403120041,
0.02937941439449787,
-0.02444029599428177,
-0.010802035219967365,
0.03148374333977699,
0.010220857337117195,
0.04308512434363365,
-0.046860549598932266,
0.01653313636779785,
-0.002131831832230091,
-0.013525282964110374,
-0.013060437515377998,
0.017190666869282722,
0.0013997263740748167,
0.03550214320421219,
-0.022885333746671677,
-0.05353233218193054,
-0.037854328751564026,
-0.010468808002769947,
0.045786142349243164,
-0.0344485379755497,
0.06704416126012802,
-0.008066889829933643,
-0.017803851515054703,
0.00933643989264965,
0.0008837345521897078,
-0.08116206526756287,
-0.011283563449978828,
-0.008823554031550884,
0.006752799265086651,
-0.009153909049928188,
-0.014835229143500328,
-0.015102130360901356,
-0.019478680565953255,
0.02360386587679386,
-0.03110518306493759,
-0.01101883314549923,
-0.048878420144319534,
0.04190736636519432,
0.008179782889783382,
0.019826414063572884
] |
<p>Many years ego, Earth was hot. Over time, it has lost energy and has become colder. Is it now in equilibrium or is its total energy changing?</p> | 1,486 | [
-0.028764476999640465,
-0.02835889160633087,
-0.018287016078829765,
0.007910429500043392,
0.035118091851472855,
0.031003441661596298,
-0.03194384649395943,
-0.02374451979994774,
-0.02125231735408306,
-0.05329541862010956,
0.025853756815195084,
0.011259849183261395,
0.0037381674628704786,
0.028096575289964676,
0.039907731115818024,
-0.011753544211387634,
0.03155980259180069,
0.00896240584552288,
0.006856680382043123,
-0.009489360265433788,
-0.012404643930494785,
-0.006921929307281971,
-0.0037611101288348436,
0.01614748127758503,
-0.04812170937657356,
0.026693321764469147,
0.01621926575899124,
-0.004240848124027252,
0.0342545323073864,
0.08872868865728378,
-0.013833632692694664,
-0.016020892187952995,
-0.0017362145008519292,
0.03258807212114334,
0.02853463403880596,
0.005565819330513477,
-0.0006425100145861506,
-0.027836555615067482,
0.0037777817342430353,
0.08178462088108063,
-0.031120680272579193,
-0.026055017486214638,
-0.016347402706742287,
0.03171270713210106,
-0.037331268191337585,
0.0005478270468302071,
0.004551513586193323,
0.008494793437421322,
0.04823983460664749,
-0.041026465594768524,
0.06618262082338333,
-0.02396521531045437,
0.04390835762023926,
0.029336100444197655,
-0.017964128404855728,
-0.00743861123919487,
0.05128426104784012,
0.04947659373283386,
0.009779166430234909,
-0.04781508073210716,
-0.013117393478751183,
-0.017880380153656006,
-0.001224108156748116,
-0.009205823764204979,
-0.011456267908215523,
0.025208307430148125,
-0.0017338048201054335,
-0.023174887523055077,
0.040489476174116135,
0.03403922915458679,
0.00887496117502451,
0.020000606775283813,
0.011714066378772259,
0.008409361355006695,
0.01955345645546913,
-0.05092787370085716,
0.0016566152917221189,
0.027600368484854698,
0.024584688246250153,
0.044691551476716995,
0.0009771630866453052,
0.01749102957546711,
0.03853737562894821,
0.0379495769739151,
0.03603431209921837,
0.01967542991042137,
0.06838591396808624,
-0.0005722992937080562,
-0.005712583661079407,
0.053156036883592606,
0.03700840473175049,
0.028523197397589684,
0.011748692020773888,
-0.054176539182662964,
-0.04667501524090767,
0.023142492398619652,
0.00016385508934035897,
0.045700836926698685,
-0.0012181788915768266,
-0.006124619394540787,
0.06134571507573128,
0.023731667548418045,
0.03058980032801628,
0.032975759357213974,
0.02749805524945259,
0.0009546894580125809,
-0.079103484749794,
-0.02507271245121956,
0.001276808325201273,
-0.03667331114411354,
-0.04674287140369415,
-0.018486792221665382,
-0.02592204511165619,
-0.0026780597399920225,
0.035301677882671356,
-0.014053217135369778,
-0.014946267008781433,
-0.03495784103870392,
0.04038233309984207,
0.029576437547802925,
0.03365202248096466,
-0.001462658867239952,
0.02767542004585266,
0.005429766606539488,
-0.06402210146188736,
0.014649463817477226,
0.028874116018414497,
-0.026156270876526833,
-0.055019501596689224,
0.0697222426533699,
-0.02250562235713005,
-0.047831594944000244,
-0.03631841018795967,
-0.03227156400680542,
0.025131147354841232,
-0.006228849291801453,
-0.09589461237192154,
-0.041211944073438644,
0.0477004274725914,
-0.03787178173661232,
-0.027566757053136826,
-0.06754018366336823,
-0.012026630342006683,
0.0170331671833992,
0.07409670203924179,
-0.003561889985576272,
0.0026425006799399853,
0.0329001359641552,
0.07122240215539932,
-0.012920479290187359,
-0.014803714118897915,
-0.02468266524374485,
0.023036843165755272,
-0.030850624665617943,
-0.011075562797486782,
-0.07277439534664154,
0.004429905209690332,
0.057477593421936035,
-0.012592853046953678,
0.0315006747841835,
0.010027904994785786,
-0.022618770599365234,
-0.03515992686152458,
0.019689157605171204,
-0.018638065084815025,
-0.02644026279449463,
0.08600829541683197,
-0.01817130669951439,
0.013038703240454197,
0.014478322118520737,
0.045507658272981644,
0.0590207464993,
0.030593693256378174,
0.03587637469172478,
0.02497994899749756,
-0.014869590289890766,
0.044515691697597504,
-0.03285964950919151,
-0.01951630786061287,
0.02600223757326603,
-0.07123616337776184,
-0.03186984360218048,
0.030865605920553207,
-0.01897754706442356,
0.03250199556350708,
0.0843275859951973,
-0.02947455644607544,
-0.01994027942419052,
0.018266428261995316,
-0.05543176084756851,
-0.05112029239535332,
-0.0799342468380928,
0.005530719645321369,
0.007287346292287111,
0.0180717371404171,
-0.02974572777748108,
0.06378208845853806,
0.038659509271383286,
-0.037584297358989716,
-0.02044893242418766,
0.03499899432063103,
0.05028741806745529,
0.017790591344237328,
-0.011162691749632359,
0.024363361299037933,
0.08196767419576645,
0.051320865750312805,
0.02038118988275528,
-0.021903151646256447,
-0.020807230845093727,
-0.039932504296302795,
-0.007635337300598621,
-0.013115468434989452,
0.01664728671312332,
-0.00487191416323185,
-0.03430876508355141,
-0.025185663253068924,
0.009324713610112667,
0.022581253200769424,
-0.0023535778746008873,
0.005964018404483795,
0.0404975488781929,
0.009152504615485668,
-0.006654794327914715,
-0.0011072878260165453,
0.032146189361810684,
0.0024746637791395187,
0.008461328223347664,
-0.024170128628611565,
0.002732390770688653,
-0.05042389780282974,
0.013131828047335148,
0.03372516110539436,
0.04579184204339981,
-0.029366567730903625,
0.02108941785991192,
0.043415527790784836,
0.04457598552107811,
0.008877535350620747,
-0.011776383966207504,
0.007868720218539238,
-0.013359971344470978,
0.03810732066631317,
-0.023021316155791283,
0.037300772964954376,
0.03952747583389282,
0.030103150755167007,
0.01787310093641281,
-0.017321325838565826,
0.014127998612821102,
-0.020171821117401123,
0.04151305556297302,
0.01111739780753851,
0.01714279130101204,
-0.001366039039567113,
-0.0287251565605402,
-0.017153508961200714,
-0.04394877329468727,
0.023238150402903557,
-0.0037188807036727667,
0.010741847567260265,
0.015363971702754498,
-0.03280426189303398,
-0.012685167603194714,
0.007195395417511463,
0.008525636978447437,
0.004859960172325373,
-0.014963679946959019,
0.05843468755483627,
0.00249497895129025,
0.019681353121995926,
-0.024304719641804695,
-0.0033385129645466805,
-0.018407754600048065,
-0.029840324074029922,
0.01911240816116333,
-0.006308306008577347,
-0.00932470615953207,
-0.04397287964820862,
-0.016761912032961845,
-0.02899915911257267,
-0.025780729949474335,
-0.014804163947701454,
0.01705005206167698,
-0.04822022095322609,
0.015100419521331787,
0.0032962181139737368,
-0.030462883412837982,
0.044210709631443024,
0.03449877351522446,
0.027994429692626,
0.07302621006965637,
0.008501303382217884,
-0.07221943885087967,
-0.012808474712073803,
-0.005212078802287579,
-0.017279300838708878,
-0.006738430354744196,
0.015429064631462097,
0.06055392697453499,
-0.06686598062515259,
-0.00030589994275942445,
-0.006137819495052099,
-0.056738901883363724,
-0.043043844401836395,
-0.0333840548992157,
-0.03253103420138359,
0.003457308979704976,
-0.00048509659245610237,
0.041230637580156326,
0.03893004730343819,
-0.052635837346315384,
0.004254213999956846,
-0.04516706243157387,
-0.05348781496286392,
0.016049789264798164,
-0.042123258113861084,
0.033766746520996094,
-0.02600672096014023,
-0.05325720086693764,
0.042465582489967346,
0.006419824436306953,
-0.010578048415482044,
-0.01103975810110569,
-0.004154734313488007,
-0.010149406269192696,
-0.014076734893023968,
0.003085762495175004,
-0.011823947541415691,
0.023053590208292007,
-0.005548545625060797,
-0.012002444826066494,
0.023755857720971107,
0.011475668288767338,
0.02151213213801384,
-0.031551294028759,
0.042818229645490646,
-0.011074045673012733,
0.021045764908194542,
0.02427787147462368,
-0.004035027697682381,
-0.0018843471771106124,
0.016168247908353806,
-0.0014378192136064172,
0.03611432760953903,
0.021562451496720314,
-0.045956868678331375,
0.07587282359600067,
-0.024706551805138588,
-0.00591679522767663,
-0.044207070022821426,
0.07032348960638046,
-0.002485111355781555,
0.007904483936727047,
-0.01088318508118391,
0.008164324797689915,
0.04522758722305298,
0.021601220592856407,
-0.02384479157626629,
0.02842479944229126,
0.04419690743088722,
-0.027929741889238358,
-0.03511912375688553,
0.025127796456217766,
-0.008036982268095016,
0.027025509625673294,
0.006036795675754547,
-0.024757081642746925,
0.060212671756744385,
0.018029218539595604,
0.027733812108635902,
0.024855908006429672,
-0.03794834390282631,
0.018342284485697746,
-0.0659092366695404,
-0.006053151562809944,
-0.002477790927514434,
0.055455826222896576,
-0.018472149968147278,
0.0335506796836853,
0.013174280524253845,
0.02836017869412899,
0.033271949738264084,
0.006347078364342451,
-0.06887013465166092,
0.03785029053688049,
-0.04705992713570595,
0.02177976258099079,
0.002184994285926223,
0.04532048478722572,
0.00472260732203722,
-0.039710044860839844,
0.012606291100382805,
-0.0420251190662384,
-0.021199021488428116,
-0.03289096802473068,
-0.015263380482792854,
-0.021571213379502296,
-0.021149421110749245,
-0.011698377318680286,
-0.000005472603334055748,
0.052560433745384216,
-0.034990448504686356,
0.04451907426118851,
0.056439001113176346,
-0.009534885175526142,
-0.00958635751157999,
-0.01625056192278862,
-0.00912536308169365,
0.0009698775829747319,
-0.002002464374527335,
0.007997007109224796,
0.025048289448022842,
-0.020188605412840843,
0.01629786565899849,
0.008638828061521053,
0.030102532356977463,
-0.018757319077849388,
-0.0020234405528753996,
-0.016242757439613342,
-0.03562742471694946,
-0.028744900599122047,
0.03126135468482971,
0.017213791608810425,
0.004131762310862541,
0.026871448382735252,
0.012674504891037941,
0.019016429781913757,
-0.028921285644173622,
0.06318102031946182,
0.03676547855138779,
-0.02899244613945484,
-0.00851714052259922,
-0.030522393062710762,
-0.004225801210850477,
-0.03745723143219948,
0.0022998861968517303,
0.038208071142435074,
-0.008951902389526367,
-0.009748593904078007,
-0.032394204288721085,
0.018486855551600456,
0.021908584982156754,
0.004407122731208801,
-0.002494356594979763,
0.02218523807823658,
0.04907292127609253,
0.03225811570882797,
-0.018866417929530144,
0.025965647771954536,
0.026371022686362267,
0.041782181710004807,
-0.00807917583733797,
-0.02167586050927639,
-0.0727536752820015,
0.010995118878781796,
0.027799183502793312,
0.027033211663365364,
-0.021729493513703346,
-0.005951260216534138,
-0.08931341767311096,
-0.015557609498500824,
0.03157864511013031,
-0.022300494834780693,
0.027446141466498375,
-0.025168677791953087,
-0.008097078651189804,
0.002478496404364705,
-0.04001173377037048,
-0.007246911991387606,
0.0091957226395607,
-0.027013467624783516,
0.03167647495865822,
-0.01281061116605997,
-0.02177157998085022,
-0.012407680042088032,
0.016337066888809204,
0.025347890332341194,
0.014372386038303375,
0.012211070396006107,
0.03129071742296219,
-0.014767564833164215,
0.025427058339118958,
-0.03316985443234444,
-0.07728900015354156,
-0.02587759681046009,
-0.0038085749838501215,
-0.043333593755960464,
0.013940032571554184,
0.0032978050876408815,
-0.06551835685968399,
0.00834824051707983,
-0.006024037953466177,
-0.03735706955194473,
-0.03363689035177231,
-0.06167371943593025,
0.021730685606598854,
0.010308682918548584,
-0.017602190375328064,
0.05976244807243347,
0.021062364801764488,
-0.04423512518405914,
0.006874302867799997,
-0.014746066182851791,
0.01857519894838333,
-0.04728349670767784,
0.027762455865740776,
0.010927128605544567,
-0.022067276760935783,
-0.010674885474145412,
0.014643397182226181,
0.017856987193226814,
0.026813309639692307,
0.0010907910764217377,
-0.032482195645570755,
0.00199696677736938,
-0.011189647018909454,
0.0077289738692343235,
0.013131850399076939,
0.006677944678813219,
0.017359238117933273,
-0.03393185883760452,
-0.028173798695206642,
0.026947373524308205,
0.011936729773879051,
0.002163295168429613,
0.006377653684467077,
-0.03314198553562164,
0.04430587217211723,
-0.03642939776182175,
-0.030187608674168587,
-0.023730017244815826,
-0.03709184750914574,
0.06553295254707336,
-0.01062335167080164,
0.01529600378125906,
0.05340193957090378,
-0.07739385962486267,
-0.007014350965619087,
-0.018278049305081367,
0.02165978029370308,
-0.005198224913328886,
-0.01733633317053318,
0.05874359980225563,
0.03446466848254204,
0.04148177430033684,
-0.06643420457839966,
-0.04590964689850807,
0.0003880548174493015,
0.014410942792892456,
-0.02876676432788372,
-0.036321740597486496,
-0.006986462045460939,
-0.031232211738824844,
-0.04751487448811531,
-0.008611305616796017,
0.036079298704862595,
-0.015541678294539452,
0.030262183398008347,
-0.01138034276664257,
0.01772855594754219,
0.04088257625699043,
-0.05477432534098625,
-0.004709838889539242,
0.018392937257885933,
-0.028462860733270645,
-0.035993438214063644,
-0.0702977105975151,
0.06785303354263306,
-0.01684493012726307,
-0.0031069666147232056,
0.02181711234152317,
0.001849522814154625,
0.031022652983665466,
0.03259154036641121,
-0.02743302658200264,
0.025335213169455528,
-0.028126375749707222,
-0.03541442006826401,
-0.006795341614633799,
0.056825973093509674,
-0.01793556660413742,
0.05097974091768265,
-0.017606070265173912,
-0.007941842079162598,
0.02764255553483963,
-0.05824067443609238,
-0.00016338579007424414,
-0.0011710054241120815,
-0.012656116858124733,
0.02810886688530445,
0.10335633903741837,
0.0001680745044723153,
-0.00238397135399282,
0.004023960791528225,
-0.01631433516740799,
0.01347789354622364,
0.013398350216448307,
0.004713980481028557,
-0.021887322887778282,
-0.04517557844519615,
-0.04021164029836655,
-0.0246583241969347,
0.0005885152495466173,
-0.009681601077318192,
0.05882388353347778,
-0.010167037136852741,
0.06163357198238373,
0.04396427422761917,
0.009763839654624462,
0.058678027242422104,
-0.027423996478319168,
0.011639689095318317,
-0.0036161041352897882,
-0.013312680646777153,
0.014827977865934372,
-0.025889981538057327,
0.0009535044082440436,
0.0575995147228241,
0.042274147272109985,
-0.03446211293339729,
0.06176948547363281,
-0.004548223689198494,
0.0195525661110878,
0.028869520872831345,
-0.017664117738604546,
-0.06100231781601906,
0.005439967382699251,
-0.056502167135477066,
0.049102164804935455,
0.0158739872276783,
0.008376049809157848,
0.026564378291368484,
-0.01524573564529419,
-0.008442587219178677,
-0.03604426607489586,
-0.01726444438099861,
-0.06683330982923508,
0.005997246131300926,
-0.004306751303374767,
0.02908412739634514,
-0.011006850749254227,
0.036861851811409,
0.01408759132027626,
-0.014048713259398937,
-0.010503996163606644,
0.00199832022190094,
-0.07349643111228943,
-0.021340161561965942,
0.010324518196284771,
-0.04435111582279205,
0.02181600034236908,
-0.01715816929936409,
-0.012150991708040237,
0.0016647394513711333,
-0.001561659388244152,
-0.015696996822953224,
0.03042341023683548,
0.03266087546944618,
-0.017961855977773666,
0.06246121972799301,
-0.020368093624711037,
0.006276278290897608,
-0.03249283879995346,
0.027383597567677498,
0.1245322898030281,
0.06417305767536163,
-0.001793581759557128,
-0.06979858130216599,
0.04467067867517471,
-0.04649671912193298,
-0.020704027265310287,
-0.02031862735748291,
-0.02318681590259075,
-0.011555024422705173,
0.030832849442958832,
0.01779167167842388,
0.049361638724803925,
-0.002900282619521022,
-0.042501579970121384,
0.043942924588918686,
-0.011122632771730423,
0.0025436661671847105,
0.006003521382808685,
0.012727215886116028,
-0.03614505007863045,
0.03229285776615143,
-0.05064305290579796,
0.0012819527182728052,
-0.026342343538999557,
-0.016270030289888382,
-0.04434629902243614,
-0.06520229578018188,
0.01972460001707077,
0.03064306266605854,
-0.06126260757446289,
0.020747076719999313,
0.001325457589700818,
0.007205320056527853,
-0.03544365242123604,
0.026667922735214233,
0.017147749662399292,
-0.00281326612457633,
0.0035216636024415493,
0.016530225053429604,
0.035214558243751526,
0.001609652186743915,
0.02265719696879387,
0.0028761348221451044,
-0.0032233435194939375,
-0.02191684953868389,
-0.027605049312114716,
0.04076414927840233,
-0.00516384094953537,
0.02554933913052082,
-0.012399635277688503,
0.0069030760787427425,
-0.03328993543982506,
-0.018123148009181023,
-0.008741801604628563,
0.017052404582500458,
0.02048913761973381,
-0.012279290705919266,
-0.048761192709207535,
-0.02960745431482792,
0.004338645841926336,
-0.013428857550024986,
0.030568426474928856,
0.021199192851781845,
-0.00011161604197695851,
0.010497860610485077,
-0.014558861032128334,
0.04031093791127205,
-0.0332159698009491,
-0.011409715749323368,
-0.00478486530482769,
-0.026152310892939568,
-0.03963889926671982,
-0.0369003564119339,
0.014641270972788334,
-0.005546468775719404,
0.02439836598932743,
0.026404039934277534,
-0.01438865065574646,
-0.04997280240058899,
-0.056512363255023956,
0.029184119775891304,
-0.026675736531615257,
-0.006462654564529657,
-0.014965975657105446,
0.002714012051001191,
0.007369615137577057,
-0.0030529890209436417,
-0.022980086505413055,
0.014284653589129448,
0.015363345853984356,
-0.008667097426950932,
0.02764880657196045,
-0.028863362967967987,
-0.015045934356749058,
0.0010210963664576411,
-0.028603138402104378,
-0.012600929476320744,
-0.036441802978515625,
0.06162894889712334,
0.006637450307607651,
-0.007147832773625851,
0.005552622489631176,
0.02625986561179161,
-0.018297730013728142,
0.036594487726688385,
0.019352445378899574,
-0.0037111782003194094,
-0.03687712177634239,
0.030538521707057953,
-0.022154880687594414,
-0.020622124895453453,
-0.02244221605360508,
-0.04301820695400238,
0.004609195049852133,
0.007273838855326176,
0.038531992584466934,
-0.045940790325403214,
0.05628384277224541,
-0.034992922097444534,
0.06238434091210365,
-0.0553797148168087,
-0.03326687961816788,
-0.07274357229471207,
-0.03776509314775467,
0.028318367898464203,
-0.0067240651696920395,
0.013231867924332619,
0.021703410893678665,
-0.026720354333519936,
-0.023226259276270866,
0.04823984578251839,
0.0014621398877352476,
0.01995636709034443,
0.005031646229326725,
0.029466403648257256,
-0.023460691794753075,
0.05462702736258507,
-0.045119110494852066,
-0.061356231570243835,
0.026822933927178383,
-0.02733015827834606,
-0.011185498908162117,
0.0350358784198761,
0.011151758022606373,
0.04159348085522652,
0.01998838596045971,
-0.013940034434199333,
0.001227934961207211,
0.053434181958436966,
-0.00236475165002048,
0.012412589974701405,
0.0031585802789777517,
-0.015455305576324463,
0.006500730291008949,
0.039775602519512177,
0.013328531756997108,
-0.01914123073220253,
-0.03004235215485096,
0.048746027052402496,
0.036931030452251434,
-0.010797209106385708,
-0.01908584125339985,
-0.013232622295618057,
-0.04615512862801552,
0.007072469685226679,
0.021434251219034195,
0.02699882909655571,
0.048673100769519806,
0.04433458670973778,
-0.04117179289460182,
-0.002017719903960824,
0.01247293222695589,
-0.019836287945508957,
-0.051799096167087555,
-0.0030277797486633062,
-0.0002573577221482992,
-0.021608304232358932,
0.012687730602920055,
-0.046482983976602554,
0.038316141813993454,
0.048810508102178574,
-0.04054849594831467,
0.0066528297029435635,
-0.009691569022834301,
-0.015526017174124718,
-0.008657029829919338,
-0.000637090124655515,
-0.013460421934723854,
0.04142291098833084,
0.0577395036816597,
0.06180501729249954,
-0.004259227309376001,
0.02376573160290718,
-0.01792137511074543,
-0.017651332542300224,
-0.020581837743520737,
-0.0018880997085943818,
-0.005648029036819935,
-0.003355717286467552,
0.0002013984340010211,
-0.004381997510790825,
-0.026088334619998932,
0.029909376055002213,
-0.03388052061200142,
0.06682288646697998,
0.022532092407345772,
0.009640819393098354,
-0.011514810845255852,
0.012101955711841583,
0.0001424675720045343,
-0.045969314873218536,
-0.004149538930505514,
0.021998096257448196,
0.002041819039732218,
0.04422900825738907,
0.014450662769377232,
-0.0008612483507022262,
0.002365869702771306,
-0.04930165782570839,
-0.013516086153686047,
0.03899300470948219,
-0.00566001096740365,
0.0025426973588764668,
0.02184656448662281,
0.005411518272012472,
0.002918824553489685,
0.0011762866051867604,
-0.024509718641638756,
-0.04084918275475502,
-0.01900930143892765,
0.019593369215726852,
-0.0025917361490428448,
0.012463487684726715,
0.0013419585302472115,
0.019152700901031494,
0.009039629250764847,
-0.0017457217909395695,
-0.012525521218776703,
-0.005458855535835028,
-0.047607678920030594,
0.009697365574538708,
0.005159727763384581,
-0.03477661311626434,
-0.04388110712170601,
-0.044112399220466614,
-0.05353445187211037,
0.02499094046652317,
0.03810388594865799,
0.022942302748560905,
-0.01937771774828434,
-0.0810917392373085,
-0.03587334603071213,
-0.03152395784854889,
0.02053154818713665,
-0.03655006363987923,
-0.013737962581217289,
-0.018385739997029305,
-0.016105594113469124,
-0.031707871705293655,
-0.005463560111820698,
0.041078489273786545,
-0.006581738591194153,
0.0038546554278582335,
0.00168760831002146,
-0.0006255593616515398,
0.044228099286556244,
-0.05500330403447151,
0.031013812869787216,
0.009155103005468845,
-0.017428085207939148,
0.034409742802381516,
-0.02228284627199173,
0.00997464545071125,
0.005882956087589264,
0.03475566208362579,
-0.02025921456515789,
0.05258847028017044,
0.00272721191868186,
-0.005640352610498667,
0.05090275779366493,
0.00031653750920668244,
-0.029641268774867058,
0.058900851756334305,
-0.04209102690219879,
0.031137648969888687,
0.023919861763715744,
-0.005781440529972315,
-0.03158114105463028,
0.01815906912088394,
-0.021092191338539124,
-0.0003576372691895813,
0.02875816822052002,
-0.025698717683553696,
0.040916722267866135,
-0.04743489250540733,
0.00451187277212739,
0.03233054280281067,
-0.02485436387360096,
0.014394758269190788,
0.009847941808402538,
-0.012941287830471992,
0.03937489539384842,
-0.002512335544452071,
0.025352222844958305,
-0.016108853742480278,
0.026718534529209137,
0.015295800752937794,
0.04173523932695389,
0.037299782037734985,
-0.004269050434231758,
0.033541783690452576,
0.00167887716088444,
-0.011563424952328205,
0.017216309905052185,
-0.004428783431649208,
0.011495912447571754,
-0.03968289867043495,
-0.04902461916208267,
0.028752628713846207,
0.008852411061525345,
-0.013826953247189522,
0.03171009197831154,
0.012162590399384499,
0.04920995235443115,
-0.03577323257923126,
-0.009898679330945015,
-0.007030253764241934,
-0.022153163328766823,
-0.03278797119855881,
0.007202691398561001,
0.006960252765566111,
0.019682276993989944,
0.01068534329533577,
-0.017682772129774094,
-0.005842799320816994,
0.04071590676903725,
0.018630824983119965,
-0.021944791078567505,
0.02336171269416809,
-0.01586788333952427,
-0.014261441305279732,
-0.007675631437450647,
0.01567712426185608,
-0.04174283891916275,
-0.028569182381033897,
0.02563268318772316,
0.03799023851752281,
0.051562413573265076,
0.013690064661204815,
-0.012690715491771698,
-0.030016431584954262,
0.02860500104725361,
-0.04336236044764519,
0.0005891557666473091,
-0.00862019695341587,
0.035949986428022385,
-0.008085057139396667,
-0.026868607848882675
] |
<p>From my limited experience with ham radio when I was a kid, I expect transmitting and receiving antennas to have lengths that are on the same order of magnitude as the wavelength, and in fact I recall having to mess around to compensate for the fact that a given antenna wouldn't be properly resonant over an entire frequency band. This also seems to match up with what we see with musical instruments, where, e.g., a saxophone's tube is half a wavelength and a clarinet's is a quarter.</p>
<p>For commercial FM radio with a frequency of 100 MHz, the wavelength is about 3 m, so I can believe that some of the receiving antennas I've seen are a half-wave or quarter wave. But for AM radio at 1000 kHz, the wavelength is 300 m, which is obviously not a practical length for a receiving antenna.</p>
<p>Can anyone explain this in physics terms, hopefully without making me break out my copy of Jackson and wade through pages of spherical harmonics? Does AM reception suffer from the length mismatch, e.g., by being less efficient? Does it benefit from it because it's so far off resonance that the frequency response is even across the whole band? Is there a dipole approximation that's valid for AM only? For both AM and FM? If the sensitivity is suppressed for the too-short antenna, is there some simple way to estimate the suppression factor, e.g., by assuming a Breit-Wigner shape for a resonance?</p>
<p><a href="http://physics.stackexchange.com/questions/21266/some-questions-about-car-radio-and-cellphone-antennas">This question</a> touched on this issue, but only tangentially, and the answers actually seem inconsistent with the observed facts about AM. Also related but not identical: <a href="http://physics.stackexchange.com/questions/43422/radio-communication-and-antennas">Radio communication and antennas</a></p> | 1,487 | [
-0.04841107875108719,
-0.04057281091809273,
0.009340878576040268,
-0.0226610004901886,
0.05864061415195465,
0.01409294456243515,
-0.02924029342830181,
-0.044639598578214645,
0.047062087804079056,
-0.014219612814486027,
0.009941840544342995,
0.04384137690067291,
0.04782243072986603,
-0.0014362151268869638,
0.04463351517915726,
-0.026121364906430244,
-0.0035524526610970497,
-0.011447752825915813,
-0.00920279510319233,
-0.05775398761034012,
-0.003663875861093402,
0.03742338716983795,
-0.007614688482135534,
-0.039214856922626495,
-0.0208623968064785,
0.0414251983165741,
0.06711211800575256,
0.020881937816739082,
0.0076852901838719845,
0.03289425000548363,
-0.006149563007056713,
0.011890116147696972,
0.01962965354323387,
0.02022085338830948,
0.011069629341363907,
-0.0003052668762393296,
-0.018776288256049156,
-0.04008537158370018,
0.009965348057448864,
0.02746054157614708,
-0.02261001616716385,
0.01724470593035221,
0.0011637801071628928,
0.006171077955514193,
-0.06728726625442505,
0.003512841649353504,
0.0017210791120305657,
-0.04996800422668457,
0.04232289642095566,
-0.031554628163576126,
0.05664655566215515,
0.023252107203006744,
0.019678322598338127,
0.007044695317745209,
-0.0017575541278347373,
0.001924585783854127,
0.08256807923316956,
0.04336893558502197,
-0.02220243588089943,
-0.08814209699630737,
0.008660657331347466,
-0.026067379862070084,
-0.06543079763650894,
0.01333568524569273,
-0.015458906069397926,
0.03841448947787285,
-0.016382476314902306,
-0.0213940292596817,
0.04759512469172478,
0.017226452007889748,
0.01101150643080473,
-0.00569962989538908,
0.04217763990163803,
0.0189532283693552,
0.011175541207194328,
-0.02228759415447712,
0.00021783840202260762,
0.015973158180713654,
0.06502965092658997,
0.00999377854168415,
-0.030110569670796394,
0.004845082759857178,
-0.010112429037690163,
0.055417969822883606,
0.025009730830788612,
-0.0012534413253888488,
0.04516749829053879,
-0.04042069613933563,
0.01274803839623928,
0.05071324482560158,
0.0033829757012426853,
0.023936323821544647,
0.06664418429136276,
-0.02821888029575348,
-0.01798379234969616,
0.044942088425159454,
-0.007638417184352875,
0.03909255936741829,
0.02734343148767948,
-0.01653471030294895,
0.009822992607951164,
-0.012585829012095928,
0.03005027398467064,
0.05140050873160362,
0.015294957906007767,
-0.00471443310379982,
-0.03184797987341881,
0.0038821811322122812,
-0.05518685653805733,
0.009689689613878727,
-0.013264219276607037,
0.02320936694741249,
0.0035421280190348625,
0.0014355218736454844,
0.01753399893641472,
-0.028008507564663887,
0.02486327849328518,
0.0020994332153350115,
0.05875103920698166,
0.07959207892417908,
0.0053671859204769135,
-0.03243036940693855,
0.020785469561815262,
-0.041938990354537964,
-0.08595120161771774,
-0.032823797315359116,
-0.012073235586285591,
0.006002095993608236,
-0.07314543426036835,
0.01203934010118246,
0.020430760458111763,
-0.01661398634314537,
0.049108054488897324,
-0.004992452450096607,
0.028278138488531113,
-0.01385621540248394,
-0.06134255230426788,
-0.07902753353118896,
-0.01604353077709675,
0.00012852047802880406,
0.011029169894754887,
-0.08406125754117966,
0.011262438260018826,
0.02443113923072815,
0.09277472645044327,
0.02605372481048107,
0.010600225999951363,
-0.01745460368692875,
0.04207731410861015,
0.014145351015031338,
-0.02184462919831276,
-0.025376714766025543,
-0.008992372080683708,
-0.023810213431715965,
-0.009334787726402283,
-0.02488570101559162,
0.027387186884880066,
0.026085253804922104,
0.01921667344868183,
-0.011453019455075264,
0.07978837937116623,
0.022576432675123215,
-0.0343753956258297,
-0.010840884409844875,
-0.03880457952618599,
-0.027130143716931343,
0.08005477488040924,
-0.0005817935452796519,
-0.01162327453494072,
0.017141710966825485,
-0.02190152183175087,
0.010175401344895363,
0.013260120525956154,
-0.015361248515546322,
0.007548229303210974,
-0.047220371663570404,
0.019210515543818474,
-0.02075854502618313,
0.015215311199426651,
0.011694320477545261,
-0.018245205283164978,
-0.008528517559170723,
-0.0072027212008833885,
0.025709593668580055,
0.02825460024178028,
0.041015446186065674,
-0.011298345401883125,
0.0057186223566532135,
0.024894438683986664,
0.010484644211828709,
-0.023773983120918274,
-0.013477646745741367,
0.022238699719309807,
0.02604631520807743,
-0.004835442639887333,
0.03229762613773346,
-0.00631306879222393,
-0.04166264086961746,
-0.02546352706849575,
-0.029437750577926636,
0.016654521226882935,
0.02607121132314205,
0.03310685232281685,
-0.007813597097992897,
0.016100849956274033,
0.061986442655324936,
0.013112607412040234,
-0.009648150764405727,
0.03679510951042175,
-0.021356873214244843,
-0.09135288000106812,
-0.024733416736125946,
-0.03626411035656929,
0.05287979915738106,
0.040732719004154205,
0.025894269347190857,
-0.022730175405740738,
-0.05130962282419205,
-0.003557940013706684,
0.03432604670524597,
-0.031179914250969887,
0.055808648467063904,
0.028539981693029404,
0.017774993553757668,
0.041291411966085434,
0.0653226226568222,
0.0358722098171711,
-0.008065594360232353,
-0.0039003610145300627,
-0.011716856621205807,
-0.06667983531951904,
0.011910506524145603,
0.0694790631532669,
0.0060442411340773106,
-0.030873719602823257,
0.0228761937469244,
0.005123096518218517,
0.03695717453956604,
0.04633145406842232,
0.03727448359131813,
-0.02892039343714714,
-0.04947527498006821,
-0.019736921414732933,
0.025108592584729195,
-0.008482996374368668,
0.004200925584882498,
0.00797311868518591,
-0.013615693897008896,
-0.007404422387480736,
-0.006512605585157871,
0.019547104835510254,
0.02327137440443039,
0.02357914298772812,
0.02122189849615097,
-0.007690266240388155,
-0.018411122262477875,
0.037056077271699905,
-0.04710874333977699,
-0.010421131737530231,
0.01276039145886898,
-0.01753617264330387,
-0.002656963188201189,
-0.012556757777929306,
0.03352873772382736,
-0.0071930428966879845,
-0.03160836547613144,
-0.01548705156892538,
0.01072409562766552,
0.017168588936328888,
-0.04676274582743645,
0.006907833740115166,
-0.05769259110093117,
-0.0026344710495322943,
-0.03581090644001961,
-0.01847742311656475,
0.03964633122086525,
0.01976471208035946,
0.04185842350125313,
-0.02308223582804203,
-0.017683275043964386,
-0.014610903337597847,
-0.02345246635377407,
-0.005924366880208254,
-0.014247825369238853,
-0.0031638103537261486,
-0.0026884281542152166,
-0.084922194480896,
0.006037740036845207,
0.02286655828356743,
0.0040442985482513905,
0.01537240669131279,
-0.026384100317955017,
-0.023995796218514442,
-0.07411940395832062,
-0.045809630304574966,
-0.002854586811736226,
0.019380679354071617,
0.0013671760680153966,
-0.01864141784608364,
0.04465992748737335,
0.029646867886185646,
-0.016012229025363922,
0.006799614056944847,
-0.02506629377603531,
-0.008226469159126282,
-0.016179287806153297,
-0.019395612180233,
0.0026220669969916344,
-0.025676483288407326,
0.009624998085200787,
0.0019476544111967087,
-0.034547045826911926,
-0.019946735352277756,
-0.04626799002289772,
-0.05380954593420029,
0.004096184857189655,
-0.018254728987812996,
0.10159829258918762,
0.03861752152442932,
0.0019810416270047426,
0.04815797135233879,
0.025528600439429283,
-0.00035726005444303155,
-0.011043381877243519,
0.02417215146124363,
-0.0009574288269504905,
-0.04336520656943321,
0.014060565270483494,
0.07872365415096283,
0.0005355249159038067,
0.027357231825590134,
0.02552345022559166,
-0.005473667755723,
0.009570405818521976,
0.05998007580637932,
-0.02172199822962284,
-0.005386900622397661,
-0.012851675972342491,
-0.004791373386979103,
0.06815581768751144,
0.04183841124176979,
-0.006929632741957903,
0.031184513121843338,
0.008494487032294273,
0.03905640169978142,
0.027455657720565796,
-0.05794527009129524,
0.009834866970777512,
-0.016215184703469276,
0.02522996813058853,
-0.01845129020512104,
0.036638353019952774,
-0.0068787140771746635,
0.012334137223660946,
-0.01120248343795538,
0.0042768786661326885,
0.051374975591897964,
-0.017937621101737022,
0.005494806915521622,
0.03219498693943024,
0.029284505173563957,
-0.01195485144853592,
-0.0007241166313178837,
-0.0005097624380141497,
-0.018595587462186813,
-0.006035098806023598,
-0.053883299231529236,
-0.02859077788889408,
0.03576653450727463,
0.025065384805202484,
0.01269999798387289,
0.00358697515912354,
-0.03931159898638725,
-0.02318909578025341,
-0.05770908668637276,
0.015183407813310623,
-0.04079078882932663,
0.05537843704223633,
-0.017675990238785744,
0.009560413658618927,
0.005702858325093985,
0.0152119230479002,
-0.010607589967548847,
-0.004838855937123299,
-0.05364406108856201,
0.01969592086970806,
-0.06809427589178085,
-0.013743375428020954,
-0.0017128800973296165,
-0.007655934896320105,
-0.005726892035454512,
-0.008238428272306919,
-0.007335455156862736,
-0.015627630054950714,
0.017790745943784714,
-0.028424005955457687,
0.002288130344823003,
-0.010192451998591423,
-0.03773185610771179,
-0.04536817967891693,
0.029774116352200508,
0.004744777921587229,
0.0033849661704152822,
0.03721272572875023,
0.03693277761340141,
-0.028975000604987144,
-0.024379728361964226,
-0.01736471801996231,
0.014059706591069698,
-0.022136062383651733,
0.029633570462465286,
0.02768351137638092,
0.003444696543738246,
-0.033724572509527206,
-0.01535247452557087,
0.04610766842961311,
0.06768643856048584,
0.009693906642496586,
0.010648367926478386,
-0.0005860076053068042,
-0.06357228755950928,
-0.03324319049715996,
-0.029017465189099312,
0.026624899357557297,
-0.01965561881661415,
-0.004361465107649565,
0.037530314177274704,
-0.02439434640109539,
-0.037976279854774475,
0.04414283484220505,
0.004422630183398724,
-0.0026050980668514967,
0.0011227871291339397,
-0.04213431850075722,
-0.0015888747293502092,
-0.00970336701720953,
0.025632651522755623,
-0.0022347010672092438,
-0.006028763484209776,
0.006362502928823233,
-0.029489021748304367,
0.0467521958053112,
0.005329817533493042,
-0.006961483508348465,
0.02420485019683838,
-0.0004891418502666056,
-0.009789149276912212,
-0.010547458194196224,
-0.018403302878141403,
0.007619358599185944,
0.04248795285820961,
0.059972167015075684,
0.024157270789146423,
-0.028463121503591537,
-0.09119392186403275,
0.007050782907754183,
0.023815207183361053,
0.045696619898080826,
0.0035486756823956966,
0.012857671827077866,
-0.047723185271024704,
-0.02504948526620865,
-0.01562546193599701,
0.010275780223309994,
0.04460012912750244,
-0.04844933748245239,
0.009152792394161224,
-0.01943272165954113,
-0.005414437502622604,
-0.024888193234801292,
-0.015467842109501362,
0.015897482633590698,
0.009063417091965675,
-0.044448330998420715,
-0.006363279186189175,
-0.022260136902332306,
0.016737893223762512,
0.05726822838187218,
0.008752640336751938,
0.04165926203131676,
-0.00022326532052829862,
0.010960924439132214,
-0.002766253659501672,
-0.012418593280017376,
-0.05722472071647644,
-0.02636224590241909,
0.019920116290450096,
-0.031780142337083817,
0.05485418066382408,
-0.023265304043889046,
-0.019911514595150948,
0.07771515846252441,
0.05959240347146988,
-0.01260607223957777,
-0.009678501635789871,
-0.02330036833882332,
0.06192531809210777,
-0.0027502579614520073,
0.004171809647232294,
0.07613677531480789,
0.006619733292609453,
-0.003093603765591979,
0.02382996678352356,
0.016591550782322884,
0.016459086909890175,
-0.001393539598211646,
-0.0059541380032896996,
-0.014980429783463478,
0.0020225453190505505,
-0.026873715221881866,
0.07283821702003479,
0.00030716057517565787,
-0.011575505137443542,
0.0029440002981573343,
-0.04989299550652504,
-0.02263321727514267,
0.01073531061410904,
-0.04808208718895912,
0.004723343998193741,
0.0327666811645031,
0.002436037641018629,
-0.008987151086330414,
0.0055216834880411625,
0.013425814919173717,
-0.01951264590024948,
0.0015452068764716387,
0.03394773229956627,
-0.022015206515789032,
-0.006318376399576664,
-0.03375927731394768,
0.0049124653451144695,
-0.013902240432798862,
-0.04036635160446167,
0.058958690613508224,
-0.051325488835573196,
-0.023353086784482002,
0.023763926699757576,
-0.03605577349662781,
-0.027496391907334328,
0.007923913188278675,
-0.024090124294161797,
0.05350291728973389,
-0.006611926015466452,
0.01646280661225319,
0.019829856231808662,
-0.01389405783265829,
-0.0435062050819397,
0.012391142547130585,
0.03864387050271034,
0.04845516011118889,
-0.016797801479697227,
-0.031756121665239334,
-0.018934767693281174,
-0.02526903711259365,
-0.03584546595811844,
0.007617337163537741,
0.02508588321506977,
-0.06931371241807938,
0.010092083364725113,
0.0016805529594421387,
0.01150735467672348,
0.06827031821012497,
-0.02035895735025406,
0.0056681158021092415,
0.020287755876779556,
-0.0428350530564785,
0.014540516771376133,
-0.01400801632553339,
0.04496728628873825,
-0.030871178954839706,
-0.05634688213467598,
0.0029194122180342674,
-0.04830661416053772,
0.00957315880805254,
0.019910592585802078,
-0.04424985498189926,
0.033480286598205566,
-0.022840308025479317,
0.0172612015157938,
0.0038412651047110558,
0.01086338795721531,
0.006071626208722591,
0.026653112843632698,
-0.019520431756973267,
-0.023940250277519226,
-0.05955108255147934,
-0.007388055324554443,
0.016412312164902687,
0.032400280237197876,
0.022660402581095695,
-0.018825311213731766,
0.05507032200694084,
-0.00894473772495985,
-0.02592022716999054,
0.005728514865040779,
0.000272012606728822,
0.03038569912314415,
-0.03026481531560421,
-0.009194079786539078,
0.020669301971793175,
0.05311967432498932,
-0.008069570176303387,
-0.0645892396569252,
-0.049143534153699875,
0.00912483874708414,
0.05115044116973877,
-0.00321552949026227,
0.03115377388894558,
0.050973087549209595,
-0.0028791583608835936,
-0.0405336432158947,
-0.024963362142443657,
-0.01320695225149393,
0.014416981488466263,
-0.009654778987169266,
0.015113607980310917,
-0.024203380569815636,
0.017161661759018898,
0.007279674056917429,
0.029491130262613297,
-0.0016307454789057374,
0.007491396274417639,
0.025558173656463623,
0.059838131070137024,
0.01820334792137146,
-0.013739796355366707,
-0.03651455417275429,
0.042439498007297516,
-0.04756283015012741,
-0.0025438095908612013,
0.03922409564256668,
0.0021333019249141216,
0.018657227978110313,
0.05346107482910156,
0.027385029941797256,
-0.03655533865094185,
-0.00004340239320299588,
-0.04479743167757988,
-0.0034272782504558563,
0.025485126301646233,
-0.00806459505110979,
-0.01296996045857668,
-0.03556806221604347,
0.04187973588705063,
-0.02174600400030613,
0.011099174618721008,
0.015963900834321976,
-0.04577859491109848,
-0.02338346838951111,
-0.010181835852563381,
-0.06974918395280838,
0.05517423897981644,
0.022359544411301613,
-0.03291087970137596,
0.0594765767455101,
-0.08551213145256042,
0.04700643941760063,
0.005431181285530329,
0.030088873580098152,
-0.01619877479970455,
0.03084607422351837,
0.00022652902407571673,
-0.009274301119148731,
-0.01634806953370571,
0.008517404086887836,
0.1354345679283142,
0.02813982218503952,
0.008843732997775078,
-0.0204585213214159,
0.012778175063431263,
-0.0216608177870512,
0.001934961648657918,
-0.042269788682460785,
-0.0030333036556839943,
-0.024261919781565666,
0.01979558728635311,
0.033803436905145645,
0.059268273413181305,
-0.0038403733633458614,
-0.010951424948871136,
0.01861846074461937,
-0.019625717774033546,
-0.013705715537071228,
-0.0002290617412654683,
0.008608226664364338,
0.03658653423190117,
0.015155245549976826,
-0.0445253849029541,
0.02159702591598034,
-0.012482819147408009,
0.0011794171296060085,
0.002314535668119788,
-0.015800612047314644,
0.009001468308269978,
-0.0465347096323967,
-0.030645962804555893,
0.015043145976960659,
-0.006446139421314001,
-0.02166682481765747,
-0.031011207029223442,
0.06558116525411606,
0.03304393216967583,
0.0026249573566019535,
-0.03766874969005585,
0.029330134391784668,
0.016565177589654922,
-0.011196091771125793,
0.025913970544934273,
0.01945360004901886,
-0.04405951499938965,
0.014640492387115955,
-0.017567213624715805,
0.04027099907398224,
-0.0000026720551886683097,
-0.02376924827694893,
0.0025091725401580334,
-0.001911494298838079,
0.014161376282572746,
-0.05865306779742241,
0.022676702588796616,
-0.008571549318730831,
0.0017494121566414833,
-0.03277144208550453,
-0.0019403407350182533,
-0.03108920343220234,
0.04952153563499451,
0.008309399709105492,
-0.004241523798555136,
0.01200488954782486,
0.014336216263473034,
-0.01685631461441517,
-0.016722427681088448,
0.02604849822819233,
0.01620844379067421,
-0.06715678423643112,
-0.03290707990527153,
-0.014072063378989697,
-0.06600279361009598,
-0.0018942562164738774,
0.010906744748353958,
0.032473426312208176,
0.061487819999456406,
0.020629413425922394,
-0.008150751702487469,
-0.023884005844593048,
-0.07644587010145187,
0.04415307939052582,
-0.0012253597378730774,
0.006526440382003784,
-0.003204736625775695,
-0.032944206148386,
0.004407593514770269,
0.02533690817654133,
-0.00914363656193018,
0.037622202187776566,
-0.04642969369888306,
0.030241968110203743,
0.018170645460486412,
-0.02308672107756138,
-0.03047346882522106,
0.007266472093760967,
-0.03868355229496956,
-0.010965587571263313,
0.01742502860724926,
0.045564763247966766,
0.031324923038482666,
0.035555824637413025,
0.006593906786292791,
0.019641444087028503,
-0.047965120524168015,
-0.04274916648864746,
-0.02796226181089878,
-0.04185369983315468,
0.005484763998538256,
-0.013447047211229801,
0.017585815861821175,
-0.029311800375580788,
-0.03844138979911804,
-0.03484794497489929,
-0.015158136375248432,
0.00030269930721260607,
-0.006881700363010168,
0.01703491620719433,
0.04181666299700737,
-0.027225589379668236,
-0.03498588502407074,
-0.04450717568397522,
0.03563070297241211,
-0.02115854248404503,
-0.006563413888216019,
-0.017488358542323112,
-0.009134925901889801,
-0.000842127192299813,
-0.009601039811968803,
-0.05728236958384514,
-0.013332693837583065,
-0.0003794993390329182,
-0.0027352063916623592,
-0.009799974970519543,
0.020462224259972572,
-0.002796625019982457,
0.0450056716799736,
0.06621017307043076,
-0.02697202004492283,
-0.005731377750635147,
0.06596163660287857,
-0.02424103021621704,
-0.04654090479016304,
0.02506084367632866,
-0.03825807571411133,
0.034909892827272415,
-0.010346509516239166,
-0.015189840458333492,
-0.0079840999096632,
0.061678458005189896,
0.010757271200418472,
-0.015552069991827011,
-0.0015265534166246653,
0.03648225590586662,
0.04796825349330902,
-0.03001672402024269,
0.010114843025803566,
-0.037161700427532196,
0.0025188769213855267,
-0.016987411305308342,
0.019251158460974693,
0.006868802011013031,
0.00941481813788414,
-0.006623521912842989,
-0.02827206626534462,
-0.03456598520278931,
0.015994088724255562,
0.009473354555666447,
0.0011887268628925085,
0.02695326879620552,
0.005929287988692522,
0.04976167157292366,
0.009684140793979168,
0.03469995781779289,
-0.10234744101762772,
-0.020020876079797745,
0.013991654850542545,
0.033613670617341995,
0.029461082071065903,
-0.045000478625297546,
0.0006793104112148285,
0.009594486095011234,
-0.08806776255369186,
0.0033043939620256424,
0.005802247207611799,
-0.019287729635834694,
-0.029042979702353477,
0.00277200760319829,
-0.03817237541079521,
-0.004308909643441439,
-0.009128417819738388,
0.0554627887904644,
-0.008326204493641853,
-0.0023695409763604403,
-0.027764515951275826,
-0.06504296511411667,
-0.021818310022354126,
0.035810988396406174,
-0.0024463720619678497,
-0.010609119199216366,
0.05387291684746742,
-0.033854998648166656,
0.02234991453588009,
0.0551772378385067,
-0.04054994881153107,
0.013309501111507416,
-0.04709367826581001,
-0.0317431278526783,
0.02495860494673252,
0.03561178594827652,
0.03269924223423004,
-0.03319019451737404,
-0.005978793371468782,
0.01946737803518772,
-0.009504932910203934,
-0.008301567286252975,
-0.022198695689439774,
-0.002060998696833849,
0.032695382833480835,
-0.017800206318497658,
-0.007971654646098614,
0.004814909305423498,
-0.023937372490763664,
-0.007567055989056826,
0.016577433794736862,
0.015337553806602955,
0.005312624853104353,
-0.020352711901068687,
0.037873197346925735,
-0.04713665321469307,
-0.03335244208574295,
0.0066108619794249535,
0.022937916219234467,
-0.02594776079058647,
0.017523400485515594,
0.015612868592143059,
-0.002555249026045203,
0.012715225107967854,
0.006627420894801617,
-0.010653257369995117,
-0.021253133192658424,
0.00374623597599566,
-0.0055550928227603436,
0.05380513146519661,
0.015343423932790756,
-0.004952156450599432,
-0.044960666447877884,
0.017878618091344833,
0.01191221084445715,
0.010633382946252823,
-0.00998636707663536,
-0.03334733843803406,
-0.0027420285623520613,
-0.07715114206075668,
0.015716828405857086,
0.01842886209487915,
0.0040077148005366325,
-0.02906990982592106,
-0.06549040973186493,
-0.0004782682517543435,
0.02917558141052723,
0.055507924407720566,
-0.005076069850474596,
-0.034908100962638855,
0.017834555357694626,
-0.025242339819669724,
-0.000057048167946049944,
-0.04276205599308014,
0.004148094914853573,
0.051823731511831284,
0.002182064112275839,
-0.008000443689525127,
-0.002747500780969858,
-0.010936693288385868,
-0.025581838563084602,
-0.0019794413819909096,
0.020880432799458504,
-0.00017920637037605047,
-0.0033164992928504944,
-0.032591428607702255,
0.08031129091978073,
0.04469287022948265,
0.009434505365788937,
0.029205063357949257,
0.03684427589178085,
-0.001726857153698802,
0.024082019925117493,
-0.019898410886526108,
-0.04636520519852638,
0.03664405643939972,
-0.015613675117492676,
0.014067599549889565,
-0.03172849491238594,
0.07219623029232025,
0.03248950466513634,
-0.023552928119897842,
0.0035737096332013607,
0.044372886419296265,
-0.0171202402561903,
-0.042908985167741776,
0.04701753333210945,
0.009134064428508282,
0.013013510964810848,
0.007690518628805876,
0.009934195317327976,
0.010111307725310326,
-0.02959541790187359,
-0.024653945118188858,
0.004313264507800341,
0.0033935941755771637,
0.017977813258767128,
0.026756804436445236,
0.04103706032037735,
-0.004809931386262178,
0.02568908780813217,
0.03054835833609104,
0.04450691491365433,
-0.020865732803940773,
-0.014307281002402306,
0.04622526466846466,
-0.00060892483452335,
-0.05148168280720711,
0.04958794265985489,
-0.012142657302320004,
0.06359466165304184,
0.023282691836357117,
-0.003978369291871786,
0.006451769266277552,
-0.01811882108449936,
0.01709716208279133,
0.022154029458761215,
0.008218763396143913,
0.0008458591182716191,
-0.015153901651501656,
0.004385804757475853,
-0.011546600610017776,
-0.02882874198257923,
0.05345412716269493,
-0.0445815771818161,
0.0030738653149455786,
-0.014313061721622944,
-0.012494014576077461,
-0.024400316178798676,
-0.021956562995910645,
0.01863080821931362,
-0.0016317757545039058,
0.04018165543675423,
0.051252856850624084,
-0.013132003135979176,
-0.0303825531154871,
0.029715703800320625,
0.014223539270460606,
0.027395501732826233,
-0.08009687811136246,
0.004541539121419191,
-0.02048785425722599,
0.008133760653436184,
-0.00273515610024333,
-0.015979759395122528
] |
<p>When quantizing a system, what is the more (physically) fundamental commutation relation, $[q,p]$ or $[a,a^\dagger]$? (or are they completely equivalent?)</p>
<p>For instance, in Peskin & Schroeder's QFT, section 3.5, when trying to quantize the Dirac field, they first say what commutation relation they <em>expect</em> to get for $[\Psi(\vec{x}),\Psi^\dagger(\vec{y})]$ (where $i\Psi^\dagger$ is the conjugate momentum to $\Psi$), in analogy to the Klein-Gordon field, then they <em>postulate</em> a commutation relation between $[a^r_{\vec{p}},a^{s\dagger}_{\vec{q}}]$ etc., and then verify that they indeed get what they expected for $[\Psi(\vec{x}),\Psi^\dagger(\vec{y})]$.</p>
<p>Why did we need to postulate the value of $[a^r_{\vec{p}},a^{s\dagger}_{\vec{q}}]$? Couldn't we have just computed it off of $[\Psi(\vec{x}),\Psi^\dagger(\vec{y})]$? (which, by expecting to get it, we could have just as well already <em>postulated</em> it).</p>
<p>I suppose that would entail explicitly writing something like:
$$ a_{\vec{p}}^r = \frac{1}{\sqrt{2E_{\vec{p}}}} u^{r\dagger}(\vec{p})\int_{\mathbb{R}^3}d^3\vec{x}\,e^{-i\vec{p}\cdot\vec{x}}\Psi(\vec{x})$$
and a similar expression for $b$.</p> | 1,488 | [
0.007630296517163515,
0.02375251241028309,
0.008081615902483463,
-0.027654757723212242,
0.0201096273958683,
-0.0024828906171023846,
-0.0634925439953804,
-0.04111321642994881,
-0.006925451569259167,
-0.0017903551924973726,
-0.013624760322272778,
0.01625501736998558,
0.04012921079993248,
0.03328089788556099,
0.0025120896752923727,
0.033365000039339066,
0.005807556677609682,
-0.0401373989880085,
0.012199345044791698,
-0.03323382884263992,
-0.020393075421452522,
0.03748335316777229,
-0.008886345662176609,
-0.0039721024222671986,
0.0024722632952034473,
0.021579086780548096,
-0.013955097645521164,
-0.0010681728599593043,
-0.0012385736918076873,
0.0575031116604805,
-0.008678564801812172,
-0.014902768656611443,
0.016014331951737404,
-0.00121365359518677,
0.04374897480010986,
0.03284510597586632,
-0.021564923226833344,
-0.028587469831109047,
0.005165984388440847,
0.027689732611179352,
-0.06259290128946304,
0.00014709291281178594,
-0.03425232693552971,
0.025077536702156067,
-0.007406048011034727,
0.014775386080145836,
0.008342976681888103,
-0.007679180707782507,
0.023772703483700752,
-0.045661259442567825,
0.06041755899786949,
0.04013274237513542,
0.0021160903852432966,
0.03302248194813728,
-0.014674379490315914,
-0.008756302297115326,
0.07892876863479614,
0.03515346348285675,
0.005188037641346455,
-0.05413885414600372,
-0.029443256556987762,
0.002850848250091076,
-0.0325249619781971,
-0.05138126388192177,
0.009255261160433292,
-0.019792605191469193,
0.040339529514312744,
-0.026053084060549736,
0.01623566634953022,
-0.037958692759275436,
0.01393601018935442,
0.03312879428267479,
0.031719669699668884,
-0.022003110498189926,
0.020610468462109566,
0.010127169080078602,
-0.01617578975856304,
0.003869374981150031,
0.033751603215932846,
0.005665885284543037,
0.0018022870644927025,
0.03167346492409706,
0.005757129285484552,
0.01809554174542427,
0.015372573398053646,
0.015558538027107716,
0.04948566481471062,
0.01625443436205387,
-0.041066817939281464,
0.024998003616929054,
-0.02526472881436348,
0.0065699913538992405,
0.040530070662498474,
-0.04599006474018097,
-0.0020461445674300194,
0.03717655688524246,
0.011001271195709705,
0.03353613615036011,
-0.006150550674647093,
-0.029673423618078232,
-0.023515734821558,
-0.03363037109375,
-0.005034218076616526,
0.08387725055217743,
0.01822533644735813,
0.002794122789055109,
0.0020079524256289005,
0.03325651213526726,
-0.020600195974111557,
-0.040093496441841125,
-0.03564077615737915,
0.03586410731077194,
-0.05709543079137802,
0.03273163363337517,
-0.0403132289648056,
-0.004607899580150843,
0.03248649835586548,
0.0047375597059726715,
0.02816551737487316,
0.08052384108304977,
0.013092177920043468,
-0.03263094276189804,
-0.008996710181236267,
-0.040419720113277435,
-0.06919999420642853,
-0.0029598555993288755,
0.03868906572461128,
0.007806392386555672,
-0.056616347283124924,
0.00885066483169794,
0.010720751248300076,
0.014677063561975956,
-0.0274136234074831,
-0.008485129103064537,
-0.002793836873024702,
-0.024005340412259102,
-0.12811531126499176,
-0.06488244980573654,
0.018037056550383568,
-0.00911104679107666,
-0.03098147362470627,
-0.05806918814778328,
-0.003364689415320754,
0.034582119435071945,
0.10559134185314178,
-0.01955510675907135,
-0.02392171137034893,
0.01098393090069294,
0.010351130738854408,
0.013124773278832436,
0.0029783518984913826,
-0.04589535668492317,
-0.005485009867697954,
-0.029246089980006218,
-0.02455301582813263,
-0.006701554637402296,
0.05992412194609642,
0.0531904436647892,
0.0025454754941165447,
0.01686040125787258,
0.07558020949363708,
-0.03614126145839691,
-0.00734145799651742,
0.012636917643249035,
-0.010276920162141323,
-0.0350852906703949,
0.04123097285628319,
0.02677062898874283,
0.021011073142290115,
0.041600681841373444,
-0.04554504528641701,
0.009064299054443836,
-0.0004493420128710568,
0.046806879341602325,
0.01459826622158289,
-0.03300159052014351,
-0.03301744535565376,
-0.049240611493587494,
-0.010268901474773884,
-0.013295666314661503,
-0.010076597332954407,
-0.05768231302499771,
-0.009056175127625465,
-0.0004280513967387378,
-0.005700637586414814,
0.029393091797828674,
0.005718911997973919,
0.008847163990139961,
0.0019562009256333113,
-0.04239014908671379,
-0.029593929648399353,
-0.06439756602048874,
0.0011386699043214321,
0.00904325395822525,
-0.05015171691775322,
0.044112008064985275,
-0.01676078885793686,
0.012902728281915188,
0.012992328964173794,
-0.057389114052057266,
0.045337479561567307,
0.049111977219581604,
0.0199038814753294,
0.011475677601993084,
0.049525823444128036,
0.0311464574187994,
0.032888177782297134,
0.00834392849355936,
0.013524452224373817,
-0.011746946722269058,
-0.02568223513662815,
0.01065819337964058,
0.004400188103318214,
0.023763833567500114,
0.0037944482173770666,
-0.013418484479188919,
0.018812555819749832,
-0.010586238466203213,
-0.04241444543004036,
0.024522650986909866,
-0.044850561767816544,
0.04005207121372223,
0.044728703796863556,
-0.017456483095884323,
-0.007259460166096687,
0.06233064457774162,
0.016162153333425522,
0.06786356121301651,
0.008972776122391224,
-0.029496075585484505,
-0.05407598987221718,
0.004788897931575775,
0.03369549289345741,
0.039275895804166794,
-0.04381261393427849,
0.015049617737531662,
0.006548858247697353,
0.0424671396613121,
0.029043085873126984,
0.008573849685490131,
-0.01257365569472313,
-0.04578967019915581,
0.004937297198921442,
-0.014740511775016785,
-0.002291169250383973,
-0.01907510496675968,
0.0014631503727287054,
-0.016099857166409492,
0.0011713970452547073,
0.0025840268936008215,
-0.024322839453816414,
0.010331053286790848,
-0.03463815525174141,
0.013055860996246338,
0.017643703147768974,
-0.04495009407401085,
0.02365708537399769,
-0.01661047898232937,
0.041264813393354416,
0.015125024132430553,
-0.012961733154952526,
0.0014603360323235393,
-0.0258629210293293,
-0.019607163965702057,
0.01605052687227726,
-0.021548708900809288,
-0.036906033754348755,
-0.011419480666518211,
-0.009968635626137257,
-0.009509519673883915,
0.008697345852851868,
-0.018713293597102165,
-0.023173436522483826,
-0.016337404027581215,
-0.017742009833455086,
0.036777324974536896,
0.0033847796730697155,
0.038171421736478806,
-0.0526776984333992,
0.0034879883751273155,
0.0636921375989914,
-0.008901815861463547,
0.01889651268720627,
0.03628767654299736,
-0.03354170173406601,
0.0007301137666217983,
-0.05477732792496681,
-0.025498662143945694,
0.03438197821378708,
-0.022353211417794228,
0.016177229583263397,
0.0011081529082730412,
-0.007685982622206211,
-0.017828242853283882,
-0.012522640638053417,
-0.009076742455363274,
0.0008863582625053823,
-0.018108218908309937,
-0.009746035560965538,
0.022099561989307404,
-0.013440263457596302,
-0.061166100203990936,
-0.011219636537134647,
0.013221357017755508,
-0.03675493225455284,
0.004952825605869293,
0.002376655349507928,
-0.015913596376776695,
-0.037357330322265625,
0.028679629787802696,
0.05204419046640396,
-0.03469705954194069,
-0.033130668103694916,
-0.05020672455430031,
-0.009009339846670628,
0.02195810340344906,
0.0035329197999089956,
0.03414327651262283,
-0.0055577936582267284,
-0.029583444818854332,
0.08967625349760056,
0.002813806524500251,
-0.034700557589530945,
0.012567081488668919,
0.017981216311454773,
0.0128529267385602,
-0.009559979662299156,
-0.0095071317628026,
0.02039189077913761,
0.014251329004764557,
0.05177658423781395,
0.004814471583813429,
0.02647976018488407,
0.01313797477632761,
-0.02695930190384388,
0.0005686930962838233,
0.0438782162964344,
0.004865587223321199,
0.0371708869934082,
0.035663653165102005,
-0.014881746843457222,
0.017292598262429237,
-0.012715295888483524,
-0.002930182497948408,
-0.007510276045650244,
0.014238337986171246,
-0.053318895399570465,
0.07732796669006348,
0.032447632402181625,
0.014061194844543934,
0.015525927767157555,
0.022614337503910065,
-0.007777781691402197,
-0.05818229541182518,
-0.014702492393553257,
0.018431181088089943,
-0.005224586930125952,
0.007647435646504164,
0.014786957763135433,
0.04016396775841713,
0.039093390107154846,
-0.03551185876131058,
-0.02889234386384487,
-0.010499568656086922,
-0.02247222512960434,
0.03808699548244476,
-0.01599196530878544,
-0.03602570667862892,
0.04818040877580643,
0.019537126645445824,
-0.005012706853449345,
-0.017219247296452522,
-0.019649231806397438,
-0.032586172223091125,
-0.05636642500758171,
-0.0031559020280838013,
-0.01804708130657673,
0.04513451084494591,
0.025615761056542397,
0.05739068612456322,
0.04116591066122055,
0.02241692505776882,
-0.034689199179410934,
0.011029344983398914,
-0.08382630348205566,
-0.009637952782213688,
-0.005103384144604206,
-0.0037526742089539766,
-0.038922253996133804,
-0.0401507243514061,
0.029507089406251907,
-0.022297648712992668,
-0.04431415721774101,
-0.024285869672894478,
-0.031481653451919556,
-0.06539054960012436,
0.04500488564372063,
-0.04818863049149513,
-0.05922296643257141,
-0.031025653705000877,
0.026631472632288933,
0.0598176009953022,
-0.02026735618710518,
-0.019209440797567368,
0.02683488465845585,
-0.047470226883888245,
-0.01098884642124176,
-0.011094880290329456,
0.021678363904356956,
0.026671191677451134,
0.011406796984374523,
0.02798386476933956,
-0.004856196232140064,
-0.006754514295607805,
-0.029864555224776268,
0.023522302508354187,
0.0676378384232521,
0.0050202724523842335,
-0.07669412344694138,
-0.01727818325161934,
-0.048016469925642014,
0.008398132398724556,
0.018663935363292694,
0.0970710963010788,
-0.017961541190743446,
-0.01088090892881155,
0.030804162845015526,
-0.004791596904397011,
0.009041492827236652,
0.013118271715939045,
0.04389622434973717,
-0.0061563546769320965,
-0.03398400545120239,
-0.047116104513406754,
0.04903852194547653,
0.020598387345671654,
-0.017895232886075974,
-0.008820661343634129,
0.02604241669178009,
-0.010030290111899376,
-0.0011382566299289465,
0.026273196563124657,
0.02446148544549942,
-0.03855695202946663,
0.004675065632909536,
0.011529040522873402,
-0.007931671105325222,
0.022641470655798912,
-0.02148548699915409,
0.010108535178005695,
0.04462772235274315,
0.006422776263207197,
0.01511302124708891,
0.005433149170130491,
-0.030537450686097145,
-0.014391511678695679,
0.04050814360380173,
0.046147461980581284,
0.009870409034192562,
0.0007947837002575397,
-0.028574315831065178,
-0.026629135012626648,
0.03017132543027401,
-0.0006229265127331018,
0.03070605918765068,
-0.023857207968831062,
-0.00008423341932939366,
-0.026166249066591263,
-0.05620549991726875,
-0.056119855493307114,
0.04241432249546051,
0.0026311322581022978,
0.0023706986103206873,
-0.05357230454683304,
-0.0019407386425882578,
-0.04683183133602142,
0.017990710213780403,
0.006975898519158363,
0.028297191485762596,
-0.00043776677921414375,
0.011203862726688385,
-0.010659235529601574,
0.004454062320291996,
-0.010061899200081825,
-0.08571116626262665,
-0.0072263008914887905,
0.01966625265777111,
0.005133627448230982,
0.03719983622431755,
-0.007725005969405174,
-0.0316016711294651,
0.027868961915373802,
0.0020748302340507507,
-0.02069951593875885,
0.05304739624261856,
-0.06434037536382675,
0.07446916401386261,
0.020610569044947624,
0.0005041731055825949,
0.03651353344321251,
0.016872307285666466,
-0.01436799019575119,
-0.019127847626805305,
-0.028221027925610542,
0.02066974900662899,
-0.004983087070286274,
-0.002844391856342554,
-0.032368917018175125,
-0.019571783021092415,
-0.020265070721507072,
0.030292697250843048,
-0.03134928643703461,
0.014614983461797237,
-0.0021822506096214056,
-0.043826255947351456,
-0.022293061017990112,
-0.013568642549216747,
-0.023709258064627647,
0.003028095932677388,
-0.01327093318104744,
0.008960995823144913,
0.029455894604325294,
-0.012989758513867855,
0.0097494563087821,
0.023989204317331314,
0.0015942526515573263,
0.06151813268661499,
-0.005949046928435564,
0.0023341840133070946,
-0.005070724058896303,
-0.02637760154902935,
0.00884935911744833,
-0.024226244539022446,
0.02517283335328102,
-0.002970258705317974,
-0.005291453097015619,
-0.013281339779496193,
-0.023880740627646446,
-0.060921188443899155,
-0.004622556734830141,
-0.00013527808187063783,
-0.0020681587047874928,
-0.05070600286126137,
-0.020671743899583817,
0.01562386192381382,
0.02123456448316574,
-0.07295036315917969,
-0.010601239278912544,
0.0066316681914031506,
0.010543611831963062,
-0.04202592372894287,
-0.009680846706032753,
0.013157264329493046,
-0.005463860463351011,
-0.020298294723033905,
-0.01099158264696598,
0.039018530398607254,
-0.04135895520448685,
0.02303755283355713,
-0.021011073142290115,
0.0084335096180439,
0.0070317406207323074,
-0.042792923748493195,
0.0273255817592144,
0.04202786833047867,
0.0061269053258001804,
0.030311763286590576,
0.014386981725692749,
0.035478927195072174,
-0.0020558226387947798,
-0.0519820898771286,
-0.005986322648823261,
-0.02576593868434429,
0.03694098815321922,
-0.01998853124678135,
0.0010716948891058564,
0.017417384311556816,
0.0209774412214756,
0.019673606380820274,
-0.004080096259713173,
0.002658768091350794,
0.01655477285385132,
0.027376443147659302,
-0.0031043244525790215,
-0.011108781211078167,
-0.038881566375494,
-0.027189169079065323,
0.019629288464784622,
-0.027429085224866867,
-0.008074488490819931,
-0.002281530061736703,
0.04423033446073532,
-0.01707572117447853,
0.01047288067638874,
0.009607111103832722,
0.010262038558721542,
0.00442860834300518,
-0.009191892109811306,
0.04022190719842911,
0.011849799193441868,
0.0029665075708180666,
0.010009114630520344,
-0.02604277804493904,
-0.0920996218919754,
0.021506033837795258,
0.0862923115491867,
0.012589211575686932,
0.06819536536931992,
0.04208499193191528,
-0.031130248680710793,
-0.020355042070150375,
-0.0008687813533470035,
-0.025542564690113068,
0.01047396007925272,
0.0007456835592165589,
0.034179382026195526,
-0.056361716240644455,
-0.012306283228099346,
0.02047710120677948,
0.037414565682411194,
-0.0397450290620327,
0.0014402478700503707,
0.009440791793167591,
0.034639954566955566,
0.007720996625721455,
-0.053011704236269,
-0.07430070638656616,
0.060581766068935394,
-0.023596253246068954,
0.03610936924815178,
0.015234281308948994,
0.01709345355629921,
0.0268055759370327,
0.030966825783252716,
-0.011922253295779228,
-0.027297936379909515,
-0.017483053728938103,
-0.044004667550325394,
0.004917596932500601,
0.037286773324012756,
0.006153914146125317,
-0.001822948339395225,
0.009170669130980968,
0.021468041464686394,
0.006211208179593086,
0.020562123507261276,
0.04306125268340111,
-0.0274090263992548,
0.02547522448003292,
-0.0470578633248806,
-0.049578532576560974,
0.03755786269903183,
-0.007423838600516319,
-0.019000064581632614,
-0.01729641854763031,
-0.017816441133618355,
0.05841091647744179,
0.003520264755934477,
0.02068408951163292,
-0.03808123245835304,
0.0639554038643837,
-0.0071561154909431934,
0.023615684360265732,
-0.01063401810824871,
0.01762913353741169,
0.14104855060577393,
0.027120664715766907,
0.020443685352802277,
-0.059819385409355164,
-0.00596430990844965,
0.005554542411118746,
0.015664471313357353,
0.009707421995699406,
0.00598884979262948,
-0.003919314593076706,
-0.013986071571707726,
-0.01839585229754448,
0.0768023133277893,
-0.01081534568220377,
-0.02903246134519577,
0.008732667192816734,
-0.05812963843345642,
-0.04328083619475365,
0.014390543103218079,
0.03774288296699524,
-0.000364450563210994,
0.016480127349495888,
-0.034799911081790924,
-0.005502816755324602,
-0.010319276712834835,
0.027394289150834084,
-0.018381154164671898,
-0.0008083943394012749,
0.03230936825275421,
-0.0022193575277924538,
-0.032362647354602814,
-0.03366745635867119,
0.002342949388548732,
-0.0162946954369545,
-0.02784682810306549,
-0.006232780404388905,
0.04621283710002899,
-0.02540460042655468,
0.036991044878959656,
0.02030923031270504,
-0.02232629805803299,
0.011141892522573471,
-0.0032752742990851402,
0.013662964105606079,
-0.05189632624387741,
-0.023505788296461105,
-0.019429657608270645,
0.07720617949962616,
-0.0160248763859272,
0.006865635979920626,
0.004197108093649149,
-0.03900609537959099,
0.018753845244646072,
-0.026519883424043655,
-0.010497224517166615,
-0.019215211272239685,
0.005811545066535473,
-0.0370972603559494,
0.014927917160093784,
-0.026404602453112602,
0.018430491909384727,
0.001019315212033689,
0.04044990986585617,
-0.03425493463873863,
-0.02249964326620102,
-0.009866165928542614,
0.006155813578516245,
0.019268160685896873,
0.012264596298336983,
0.005744981113821268,
0.0050103808753192425,
-0.026810787618160248,
-0.04295819625258446,
-0.05407862737774849,
0.026686618104577065,
0.025338290259242058,
0.05861179158091545,
0.014955944381654263,
0.007717410568147898,
-0.0434374064207077,
-0.05405431613326073,
0.02497589774429798,
-0.02020316570997238,
-0.014077844098210335,
-0.033379584550857544,
0.0007699376437813044,
0.022672777995467186,
0.06169939413666725,
-0.03114940971136093,
0.0001457873295294121,
0.014986601658165455,
0.025004329159855843,
0.05015876889228821,
0.018796663731336594,
0.004848353564739227,
0.0258106030523777,
-0.038083914667367935,
0.028882090002298355,
-0.011988557875156403,
-0.03634997829794884,
0.028938982635736465,
0.011095714755356312,
-0.004755532834678888,
0.048938557505607605,
-0.002650648355484009,
-0.00017440384544897825,
0.009251496754586697,
-0.023075416684150696,
0.0024285083636641502,
0.02318894863128662,
0.0058898054994642735,
-0.02786836586892605,
-0.016261622309684753,
0.014953567646443844,
-0.0005381322116591036,
-0.024036940187215805,
-0.004302343353629112,
-0.01820533722639084,
-0.03927641734480858,
-0.029589954763650894,
0.027341723442077637,
-0.04307056963443756,
0.009212198667228222,
-0.04031968489289284,
0.04509824886918068,
-0.023998379707336426,
-0.01732032187283039,
-0.0424983985722065,
0.04165918752551079,
-0.006292691454291344,
-0.005760489031672478,
-0.002254738472402096,
-0.001383843133226037,
-0.05705798789858818,
-0.006442209705710411,
0.01083780825138092,
-0.013500077649950981,
0.006007170770317316,
0.045713432133197784,
-0.02700062282383442,
0.017025457695126534,
-0.03480841964483261,
-0.023464584723114967,
0.054955579340457916,
0.016646964475512505,
0.007698443252593279,
0.04750986397266388,
-0.017704902216792107,
-0.02879008837044239,
0.025570427998900414,
-0.016673214733600616,
-0.02461724542081356,
-0.022375771775841713,
-0.049061618745326996,
-0.019972121343016624,
-0.006948390044271946,
0.045942649245262146,
-0.008066100999712944,
-0.0078026591800153255,
0.029855653643608093,
-0.009656228125095367,
-0.03075767681002617,
0.001834968221373856,
0.013725150376558304,
-0.006537948735058308,
0.06610271334648132,
0.03849758580327034,
-0.011745885945856571,
0.01437031663954258,
0.023933392018079758,
-0.027167128399014473,
0.018626177683472633,
0.06907842308282852,
0.007138768211007118,
-0.09714020043611526,
-0.024688227102160454,
-0.0032419199123978615,
0.05228514224290848,
0.03343783691525459,
-0.06633194535970688,
0.018594913184642792,
0.03641867637634277,
-0.07318641990423203,
0.0355563648045063,
0.0016066021053120494,
-0.0049641309306025505,
-0.01677773892879486,
0.02132202312350273,
-0.03061801940202713,
0.07533641904592514,
-0.004053168464452028,
0.028443846851587296,
-0.019045360386371613,
0.018523644655942917,
-0.0029279664158821106,
-0.00478012440726161,
-0.06340917199850082,
0.006230004597455263,
-0.0068586417473852634,
-0.01865241676568985,
0.08188988268375397,
-0.028235984966158867,
-0.002048817230388522,
0.022084424272179604,
0.017583582550287247,
0.011307780630886555,
-0.015485133975744247,
0.0417524054646492,
0.022831130772829056,
-0.0023353626020252705,
0.015019485726952553,
-0.012358935549855232,
-0.009100377559661865,
-0.04905754700303078,
0.02953913062810898,
0.03500155732035637,
-0.006882937159389257,
0.005569839850068092,
0.023962950333952904,
-0.01732100546360016,
-0.01545322872698307,
0.039526812732219696,
-0.023012381047010422,
-0.018307439982891083,
0.011742240749299526,
-0.0010385565692558885,
-0.017999468371272087,
0.007055078633129597,
0.04556788131594658,
-0.04091930761933327,
-0.004252928774803877,
0.020815424621105194,
0.014981994405388832,
-0.015280653722584248,
0.048592377454042435,
-0.03311393782496452,
-0.027064234018325806,
0.0456177219748497,
0.004378716927021742,
0.04077526181936264,
-0.07160044461488724,
-0.029010560363531113,
0.010233890265226364,
0.0246768519282341,
0.022147612646222115,
-0.04225028306245804,
-0.04083289951086044,
-0.00570062268525362,
0.008000705391168594,
0.020814459770917892,
-0.04331864044070244,
-0.005082244519144297,
0.0026518204249441624,
-0.05233770236372948,
0.02497045136988163,
0.04512006416916847,
-0.01896905153989792,
-0.0332319475710392,
-0.006624976638704538,
0.03581712767481804,
0.00025780577561818063,
0.05265853926539421,
-0.006468858569860458,
-0.026249121874570847,
0.05051357299089432,
0.010119467973709106,
0.02127244509756565,
-0.033014822751283646,
-0.010661733336746693,
-0.017712285742163658,
0.030371295288205147,
0.009005503728985786,
-0.006192166358232498,
-0.020386600866913795,
0.04071316495537758,
-0.011594429612159729,
0.0033763940446078777,
-0.022929420694708824,
0.01596740446984768,
-0.040085360407829285,
0.08287506550550461,
-0.011187328957021236,
0.019755404442548752,
0.05570597946643829,
0.01508767157793045,
0.024125592783093452,
0.04480550065636635,
-0.06712733209133148,
0.007074103225022554,
-0.0035153573844581842,
-0.03076791763305664,
0.005297146737575531,
0.03215751051902771,
-0.039538245648145676,
0.03292049840092659,
-0.04265206679701805,
0.00528910243883729,
0.04635140672326088,
-0.04466415196657181,
-0.02735009230673313,
0.07898348569869995,
0.0029334863647818565,
0.04083843529224396,
0.040610626339912415,
0.030359957367181778,
0.038558121770620346,
0.012961195781826973,
0.02310393750667572,
0.01448900531977415,
0.03663816303014755,
0.012462634593248367,
0.0073285955004394054,
0.055674806237220764,
-0.034273456782102585,
0.027132613584399223,
0.028195613995194435,
0.011131618171930313,
-0.048272497951984406,
0.02887684851884842,
0.04150332883000374,
-0.03054228611290455,
-0.0015762406401336193,
0.03298840671777725,
-0.0532398521900177,
0.12594102323055267,
-0.017961347475647926,
-0.002725765574723482,
-0.004002508241683245,
0.01869426667690277,
-0.0012288229772821069,
0.015241825021803379,
0.015251862816512585,
0.03910522162914276,
0.0015772650949656963,
-0.0021875612437725067,
-0.05929897353053093,
0.00561115937307477,
-0.0014713759301230311,
-0.026014382019639015,
-0.012111338786780834,
0.02096548117697239,
-0.026615403592586517,
0.0059413062408566475,
-0.02052253484725952,
-0.003859471995383501,
0.012672294862568378,
0.041467029601335526,
0.012759272940456867,
0.023501474410295486,
0.016209324821829796,
0.019373560324311256,
-0.02467498928308487,
0.03537385165691376,
-0.04137882962822914,
0.019732829183340073,
-0.00942159816622734,
0.023028027266263962,
0.014214787632226944,
-0.01642736978828907
] |
<p>If we imagine ourselves to be a civilization capable of manipulating very heavy masses in arbitrary spatial and momentum configurations (because we have access to large amounts of motive force, for example), then we can imagine building ponderous rings such that light, pointed in a particular direction, will be gravitationally bent around it and will arrive back precisely where it began. This mimics the behaviour of light at the event horizon of a black hole - there is no escape. To what extent can models like this simulate a real black hole and yield real physical insight as to what lies inside?</p> | 1,489 | [
-0.02417946420609951,
-0.044842127710580826,
-0.000336228113155812,
-0.05883615463972092,
0.06136409938335419,
0.0038021171931177378,
-0.05168884992599487,
-0.031254783272743225,
-0.013607552275061607,
-0.0058715613558888435,
0.005348514299839735,
0.02104269713163376,
0.04104992747306824,
0.009518465958535671,
-0.024977892637252808,
0.030659126117825508,
-0.02058158442378044,
0.014276329427957535,
-0.0202444139868021,
-0.04565676674246788,
0.0033854611683636904,
0.022022884339094162,
-0.007269051857292652,
0.003194002900272608,
-0.0648040622472763,
-0.00046305256546474993,
0.0237555094063282,
-0.04022078216075897,
0.017794225364923477,
0.03583039715886116,
-0.005762613378465176,
0.018650732934474945,
-0.025127731263637543,
0.04801419377326965,
0.014503540471196175,
-0.024980105459690094,
-0.027475478127598763,
-0.04150761291384697,
-0.0046431515365839005,
0.003180441679432988,
-0.025552112609148026,
-0.01943754218518734,
-0.002111652633175254,
0.05101974308490753,
0.008718486875295639,
0.000016365915143978782,
-0.023485597223043442,
-0.02709328383207321,
0.04056244343519211,
-0.06337911635637283,
0.03697909042239189,
-0.011010012589395046,
0.0037906726356595755,
0.02044609934091568,
-0.0016595604829490185,
-0.01764494739472866,
0.07906098663806915,
0.07590807229280472,
-0.03388969972729683,
-0.028957368806004524,
-0.02989555522799492,
0.029379142448306084,
-0.018168698996305466,
-0.01970846764743328,
-0.012023020535707474,
0.02040930464863777,
-0.008550073020160198,
0.0012666493421420455,
0.04427495226264,
0.0034449708182364702,
0.025309428572654724,
0.019471390172839165,
-0.0014458904042840004,
0.02365216799080372,
-0.020695162937045097,
-0.03426174074411392,
-0.007189431693404913,
-0.018232034519314766,
0.030571427196264267,
0.047626227140426636,
-0.009563502855598927,
-0.014958929270505905,
0.036373719573020935,
0.044894877821207047,
0.02093208022415638,
0.01806521601974964,
0.06191640347242355,
-0.03690951690077782,
0.01731746457517147,
0.011494871228933334,
-0.028071556240320206,
0.004303068853914738,
0.011208114214241505,
-0.01217625755816698,
-0.03222084045410156,
0.002773106098175049,
-0.003399711800739169,
0.06450151652097702,
-0.021837683394551277,
-0.007360544055700302,
-0.02819356881082058,
0.025030892342329025,
-0.008829304948449135,
0.0435061976313591,
-0.0016350856749340892,
-0.04171651974320412,
-0.026297196745872498,
0.04952438175678253,
-0.017201507464051247,
-0.025507120415568352,
-0.05917201563715935,
0.02518739365041256,
0.0010179104283452034,
-0.026695868000388145,
0.04531392455101013,
-0.052596475929021835,
-0.007930327206850052,
-0.04034794867038727,
0.058302752673625946,
0.05937888100743294,
0.036136824637651443,
-0.017885388806462288,
0.04081396386027336,
-0.05874459072947502,
-0.04242043197154999,
-0.005874705966562033,
0.06457000970840454,
-0.020533647388219833,
-0.04737095534801483,
-0.007121111266314983,
0.022917523980140686,
-0.013672711327672005,
-0.0008581336005590856,
-0.004475404042750597,
0.05203516036272049,
-0.042783673852682114,
-0.09600646048784256,
-0.06282880157232285,
0.013008671812713146,
-0.001665871706791222,
-0.014929207041859627,
-0.04457258805632591,
-0.003900840412825346,
0.04564126953482628,
0.10181503742933273,
0.003194002201780677,
-0.0011861722450703382,
0.028296006843447685,
0.039088789373636246,
-0.0027997693978250027,
-0.009396659210324287,
0.014045488089323044,
-0.0100614745169878,
-0.012362864799797535,
0.0044702403247356415,
-0.09801030904054642,
0.015216054394841194,
0.0337214320898056,
-0.009990677237510681,
-0.043368469923734665,
0.05024966597557068,
-0.021797187626361847,
0.0272434800863266,
0.013995185494422913,
-0.031970832496881485,
0.015745112672448158,
0.09246136248111725,
0.014293326064944267,
-0.006329194642603397,
0.02610008791089058,
-0.0017621195875108242,
0.0357004776597023,
0.05353506654500961,
0.021073559299111366,
-0.006102460436522961,
-0.05925102159380913,
0.021627357229590416,
0.016132766380906105,
0.029719384387135506,
-0.0029941231478005648,
0.0038162388373166323,
-0.05923834815621376,
0.006469023413956165,
-0.014566645957529545,
-0.01050290185958147,
0.030551331117749214,
-0.01602383702993393,
-0.0537753663957119,
0.004316993057727814,
-0.049393754452466965,
0.003949151840060949,
-0.06371419876813889,
0.0315689817070961,
0.016526512801647186,
0.04227329045534134,
0.03482416272163391,
0.01658531278371811,
0.05323011055588722,
-0.032242655754089355,
-0.015218603424727917,
-0.006003221496939659,
0.030861524865031242,
-0.007773715071380138,
0.017539754509925842,
0.0061327689327299595,
0.025064855813980103,
0.00788816623389721,
-0.03509395197033882,
-0.005439698696136475,
0.004035810474306345,
-0.02983204647898674,
-0.02277412638068199,
-0.0030798939988017082,
0.0380549356341362,
-0.018413906916975975,
0.007958835922181606,
0.0134245865046978,
0.007473915349692106,
0.03644980117678642,
0.019191691651940346,
-0.015516380779445171,
0.08911313116550446,
0.030582623556256294,
0.037137340754270554,
-0.012972014024853706,
0.04097621887922287,
0.0046250480227172375,
-0.005690404679626226,
0.010955167934298515,
-0.03203672543168068,
-0.03649413585662842,
0.008768902160227299,
0.044273559004068375,
0.05210096761584282,
-0.047908931970596313,
0.03630536049604416,
0.054222073405981064,
0.07159867882728577,
0.028258752077817917,
0.021366683766245842,
-0.04983626306056976,
0.02532760053873062,
0.03465479612350464,
0.026252325624227524,
0.020509090274572372,
0.021318107843399048,
0.03935684636235237,
0.008031484670937061,
-0.03984006866812706,
-0.02228226326406002,
-0.022364739328622818,
0.0225202739238739,
-0.008454392664134502,
0.00200304901227355,
-0.028510861098766327,
-0.029973788186907768,
0.0051066200248897076,
-0.012890110723674297,
-0.01450697798281908,
0.02673100121319294,
0.0014784279046580195,
-0.001909999642521143,
-0.06807839125394821,
0.012626216746866703,
0.0013705975143238902,
0.02136395312845707,
0.012042584829032421,
-0.037747304886579514,
0.03674890846014023,
-0.050392646342515945,
0.05059981718659401,
-0.03519511967897415,
-0.008271188475191593,
-0.05142626166343689,
0.030924180522561073,
-0.00301517266780138,
0.021445823833346367,
0.009386655874550343,
-0.0071737198159098625,
-0.05543471500277519,
0.01223649363964796,
-0.00635672640055418,
-0.019424615427851677,
0.02581852115690708,
-0.06540238112211227,
0.023469112813472748,
-0.014267688617110252,
-0.010212956927716732,
0.03924233838915825,
-0.01012064702808857,
0.012010372243821621,
0.021249476820230484,
-0.025089550763368607,
-0.01804838888347149,
0.003814384574070573,
-0.01235082559287548,
-0.01656942442059517,
-0.005893409717828035,
0.01748819276690483,
0.014943954534828663,
-0.0038031165022403,
-0.022180482745170593,
0.040041569620370865,
0.001502464059740305,
-0.040668874979019165,
0.006394608877599239,
0.014091693796217442,
-0.001438120729289949,
-0.02690422721207142,
0.06233694404363632,
0.008236601948738098,
-0.0622263140976429,
0.013593626208603382,
-0.032410722225904465,
-0.03177027031779289,
0.026119744405150414,
-0.00676208920776844,
0.017191946506500244,
0.01068577729165554,
0.006159077398478985,
0.07353394478559494,
0.009080693125724792,
-0.007400142028927803,
-0.029020724818110466,
-0.029148340225219727,
-0.015521330758929253,
-0.007455745711922646,
0.01745857670903206,
0.02997872605919838,
-0.0167721938341856,
0.0013890749542042613,
0.03541898727416992,
-0.011426245793700218,
0.008501928299665451,
0.0007807769579812884,
-0.02126777544617653,
0.012683567591011524,
-0.029217097908258438,
-0.004359168000519276,
0.005526799708604813,
-0.019532689824700356,
-0.027897458523511887,
0.018023669719696045,
-0.006214635446667671,
0.028732039034366608,
0.03810625150799751,
-0.0483398400247097,
0.03378670662641525,
0.024056753143668175,
0.011393836699426174,
0.03587201237678528,
0.020220011472702026,
-0.036521535366773605,
-0.02824549376964569,
0.002999648917466402,
0.024658288806676865,
0.06521747261285782,
0.019853860139846802,
-0.020271554589271545,
0.01911255531013012,
0.06543762236833572,
-0.025898834690451622,
-0.010140601545572281,
-0.004152698442339897,
-0.02506410889327526,
0.014332075603306293,
-0.01900075376033783,
-0.01048118807375431,
0.0438823476433754,
0.024981750175356865,
0.030222265049815178,
0.010681094601750374,
-0.00014902018301654607,
-0.013835590332746506,
-0.05715277045965195,
0.005372142419219017,
-0.017335640266537666,
0.014670509845018387,
-0.010167235508561134,
0.017470087856054306,
0.023453135043382645,
0.004876208491623402,
-0.005606384947896004,
-0.01872911863029003,
-0.07847894728183746,
0.0009091779356822371,
-0.03404337540268898,
0.00705689424648881,
-0.009861298836767673,
0.0008930773474276066,
-0.0180580522865057,
-0.02471340261399746,
-0.02252368815243244,
-0.002166050486266613,
-0.022833019495010376,
-0.09378975629806519,
0.011467973701655865,
-0.04795684292912483,
-0.06302255392074585,
0.022834131494164467,
0.04205649718642235,
0.04550045728683472,
0.04474823549389839,
0.013163818046450615,
0.01017251517623663,
-0.030062265694141388,
-0.0025166566483676434,
-0.005793989170342684,
0.016836540773510933,
0.006390562281012535,
0.057886138558387756,
0.0724041610956192,
0.011942433193325996,
-0.059328120201826096,
0.0043167113326489925,
0.04529483616352081,
0.014815261587500572,
0.007972738705575466,
-0.014614665880799294,
-0.01771903783082962,
-0.03449171781539917,
-0.01774265617132187,
0.011399797163903713,
0.07179813086986542,
-0.02008000947535038,
-0.005597468465566635,
0.02110040932893753,
-0.0034875122364610434,
-0.0008270217222161591,
-0.0017693976406008005,
0.04950664937496185,
0.027860550209879875,
-0.04996377229690552,
-0.04883904382586479,
-0.04046593979001045,
-0.011314155533909798,
0.030295701697468758,
0.015197155065834522,
-0.039871908724308014,
-0.0197612252086401,
0.03400406986474991,
0.018037086352705956,
0.00018223616643808782,
-0.021238811314105988,
0.015409381128847599,
-0.017026729881763458,
0.016766827553510666,
-0.016874218359589577,
0.06532968580722809,
0.02462458424270153,
0.03810577094554901,
0.04179496318101883,
0.04069483280181885,
0.00642775883898139,
-0.0831814557313919,
-0.02713858336210251,
0.046492043882608414,
0.023822980001568794,
0.021434299647808075,
-0.01502134557813406,
-0.05018553137779236,
-0.010550047270953655,
0.06331952661275864,
-0.013872127048671246,
0.04467031732201576,
-0.0049142055213451385,
0.0006878914427943528,
0.001954484498128295,
0.0164213664829731,
0.008422547951340675,
0.048266056925058365,
-0.04003900662064552,
-0.021616509184241295,
-0.034101396799087524,
0.03383802995085716,
0.01315539050847292,
0.032830335199832916,
0.0245658028870821,
0.02915945276618004,
0.005656786262989044,
-0.002619617385789752,
-0.002193712629377842,
0.0016963309608399868,
-0.024210432544350624,
-0.08237624168395996,
0.0049959393218159676,
0.02175809256732464,
-0.07977935671806335,
0.029459504410624504,
-0.04488969221711159,
-0.0205756314098835,
0.018082162365317345,
-0.0008045706781558692,
-0.0009481101878918707,
0.0058526694774627686,
-0.04227873682975769,
-0.02134842425584793,
0.008301706984639168,
-0.008499746210873127,
0.04868197813630104,
0.016801699995994568,
0.0012784581631422043,
-0.007080826908349991,
-0.0026017220225185156,
0.06372781842947006,
-0.02449760213494301,
-0.011889693327248096,
-0.009920692071318626,
-0.010678179562091827,
-0.005506711546331644,
0.05929270386695862,
0.03421869874000549,
-0.000011600996913330164,
0.03904718533158302,
-0.025105005130171776,
-0.03355729207396507,
0.04905087873339653,
0.014254281297326088,
0.004814203828573227,
-0.0262735728174448,
0.02723531983792782,
0.013524936512112617,
-0.04336097091436386,
0.00493954261764884,
-0.00008391508890781552,
0.022189345210790634,
0.04515037313103676,
0.009347387589514256,
0.03390536084771156,
-0.021407708525657654,
0.006150080356746912,
0.04777582734823227,
-0.034837689250707626,
0.07221593707799911,
-0.01213219203054905,
0.03291076794266701,
0.061856459826231,
-0.05830787867307663,
0.003870479529723525,
-0.023702295497059822,
-0.0012260240036994219,
0.0348493866622448,
-0.04143775999546051,
-0.00637270649895072,
0.036292366683483124,
0.02118454873561859,
-0.061037831008434296,
-0.0439513698220253,
0.03385268524289131,
0.005883601028472185,
-0.0026761856861412525,
-0.027262993156909943,
0.038640715181827545,
-0.0299154631793499,
-0.037353064864873886,
-0.06338275969028473,
0.028365496546030045,
-0.028651997447013855,
0.02270815707743168,
-0.031187640503048897,
-0.00715803075581789,
0.03208387643098831,
0.01891186460852623,
-0.05894746631383896,
0.02104136534035206,
0.037763457745313644,
0.013817248865962029,
-0.017176633700728416,
0.07020991295576096,
-0.01602151244878769,
-0.043936844915151596,
-0.04801664128899574,
0.008537323214113712,
0.04521389678120613,
-0.010195768438279629,
0.0502554252743721,
0.04495076835155487,
0.020558446645736694,
0.03937012702226639,
-0.01515938714146614,
0.018285755068063736,
-0.0030027113389223814,
0.04380042105913162,
0.003315923735499382,
-0.0043289209716022015,
0.023197822272777557,
-0.054674599319696426,
0.09544381499290466,
0.0056770239025354385,
-0.014007991179823875,
-0.0234602689743042,
0.03998041898012161,
0.020899925380945206,
-0.017534175887703896,
-0.0020750712137669325,
-0.02222021110355854,
0.01930379681289196,
-0.02244918793439865,
0.022727256640791893,
0.03903784602880478,
0.021052047610282898,
-0.011503172107040882,
-0.07190275937318802,
-0.03585917502641678,
-0.01803699880838394,
0.10056782513856888,
0.006049280520528555,
0.019764885306358337,
0.03943036496639252,
0.004459661431610584,
-0.025832366198301315,
-0.027618421241641045,
0.005780892912298441,
0.00042255737935192883,
-0.0074698589742183685,
0.0213893111795187,
-0.016877008602023125,
0.015459963120520115,
0.01654871366918087,
0.03313479572534561,
-0.009298844262957573,
0.031810663640499115,
0.027063710615038872,
0.02931208908557892,
-0.00039664527866989374,
0.010696821846067905,
-0.05008859559893608,
0.028923481702804565,
-0.06693069636821747,
0.04988826438784599,
-0.008657330647110939,
0.027192188426852226,
0.02308838628232479,
-0.015606963075697422,
0.03104342706501484,
-0.0015201662899926305,
-0.0340823270380497,
-0.03412702679634094,
0.009289037436246872,
0.008377926424145699,
0.03171566501259804,
-0.028797294944524765,
0.026071561500430107,
0.004908849485218525,
0.008451882749795914,
0.013817566446959972,
-0.003802327439188957,
-0.08005135506391525,
-0.06513340026140213,
-0.037724751979112625,
-0.04699451103806496,
0.0474805049598217,
0.018976574763655663,
-0.004583731293678284,
0.04387178272008896,
-0.06852227449417114,
-0.019590990617871284,
0.01291477307677269,
0.035428982228040695,
-0.008441158570349216,
0.039010293781757355,
-0.019812075421214104,
0.017276233062148094,
-0.05100969225168228,
-0.009706396609544754,
0.0891360193490982,
0.028707213699817657,
0.005906884092837572,
-0.07096974551677704,
-0.00036862021079286933,
-0.033088259398937225,
0.01560076791793108,
-0.04529796540737152,
0.041531000286340714,
-0.032749149948358536,
0.006476967129856348,
0.001472752308472991,
0.03498804569244385,
0.0009748685406520963,
-0.010930746793746948,
0.018672360107302666,
-0.014794624410569668,
-0.0349859781563282,
0.0023087819572538137,
0.002649617614224553,
-0.021882031112909317,
0.04131760448217392,
-0.04034661874175072,
0.015287486836314201,
-0.00807313621044159,
-0.0013850968098267913,
0.0072039104998111725,
-0.011444917879998684,
0.008883303962647915,
-0.011134634725749493,
-0.039255838841199875,
-0.011627353727817535,
-0.00627500656992197,
-0.04147982597351074,
-0.024507468566298485,
0.03286903724074364,
0.014218381606042385,
-0.0053879558108747005,
0.0265301875770092,
0.004714843351393938,
0.007899371907114983,
0.00487155094742775,
-0.012885669246315956,
0.005437817424535751,
-0.045342348515987396,
0.01781381294131279,
0.0018044083844870329,
0.03332529962062836,
-0.03866212069988251,
0.0050099091604352,
0.018029935657978058,
-0.014077113941311836,
-0.0009601369965821505,
-0.02216801978647709,
-0.03628244623541832,
-0.01698976382613182,
-0.010602128691971302,
0.006167669780552387,
-0.040525417774915695,
0.01837128959596157,
0.02622959017753601,
0.012682533822953701,
0.03849019855260849,
-0.021356459707021713,
0.0055105495266616344,
0.010895309038460255,
-0.023841556161642075,
0.0468430295586586,
0.00004786468343809247,
0.0006346596637740731,
-0.03988198935985565,
-0.004569726064801216,
-0.057656291872262955,
0.018768349662423134,
0.030477410182356834,
0.045579563826322556,
0.00018096058920491487,
0.011542636901140213,
0.009755920618772507,
0.020204339176416397,
-0.036531224846839905,
-0.0008198381401598454,
-0.03899156302213669,
-0.06254004687070847,
-0.04333668574690819,
-0.002114125993102789,
0.05026058852672577,
0.02470061369240284,
0.00703435530886054,
-0.022664781659841537,
-0.0035960953682661057,
0.010688509792089462,
0.011788989417254925,
-0.04008041322231293,
-0.01646658405661583,
0.010279233567416668,
-0.023782143369317055,
0.0031313735526055098,
-0.01547720655798912,
0.0012081542517989874,
0.010424374602735043,
-0.022920072078704834,
0.01456791628152132,
0.031119659543037415,
-0.02188117802143097,
0.024198120459914207,
0.021164916455745697,
-0.02528659999370575,
-0.01272480096668005,
-0.01073378324508667,
0.03705956041812897,
-0.043710578233003616,
-0.0361781008541584,
-0.039168234914541245,
-0.06528423726558685,
-0.026748159900307655,
0.027126118540763855,
-0.008251748979091644,
0.03108532913029194,
-0.0076303337700665,
0.0015366410370916128,
-0.07151620090007782,
0.009172631427645683,
-0.0379360131919384,
0.02342526987195015,
0.016871090978384018,
-0.024660464376211166,
0.005770531948655844,
0.029047854244709015,
-0.004072721116244793,
-0.00746007589623332,
0.026197874918580055,
0.000560748390853405,
-0.03336576372385025,
0.005159400869160891,
0.028459491208195686,
-0.016016963869333267,
0.022932732477784157,
0.012952109798789024,
-0.04361414164304733,
0.03374115005135536,
-0.015546631067991257,
-0.02855471521615982,
0.05021289736032486,
-0.014964938163757324,
0.0455995537340641,
0.016040481626987457,
-0.0314466618001461,
0.019816525280475616,
0.02923392504453659,
-0.006914424244314432,
-0.03223498538136482,
0.026495089754462242,
-0.015676802024245262,
-0.008433997631072998,
0.015079917386174202,
0.04766099154949188,
-0.05037888512015343,
-0.032146092504262924,
0.0505986362695694,
0.009577742777764797,
-0.003395170671865344,
-0.00036211308906786144,
-0.012256092391908169,
-0.014067656360566616,
0.00990617647767067,
-0.010629719123244286,
-0.001890213810838759,
0.02367136999964714,
0.03855210170149803,
-0.032363176345825195,
0.04041776433587074,
0.06324350088834763,
0.00486279372125864,
-0.10271214693784714,
-0.052419837564229965,
0.00956717412918806,
0.011396816931664944,
0.02333436906337738,
-0.0400121845304966,
0.04175856336951256,
-0.010329226031899452,
-0.09447294473648071,
0.0046709091402590275,
-0.025510091334581375,
-0.03740965947508812,
-0.018248019739985466,
0.0028764852322638035,
-0.009667208418250084,
0.031444016844034195,
0.02335590124130249,
0.024758230894804,
0.00030147554934956133,
-0.015608936548233032,
-0.01615092158317566,
-0.0020182314328849316,
0.0003544168430380523,
0.008688767440617085,
-0.025621578097343445,
0.023018186911940575,
0.07604112476110458,
0.0034545143134891987,
-0.026101965457201004,
0.017632953822612762,
0.03806707262992859,
0.017256787046790123,
-0.0013557998463511467,
0.0048891277983784676,
0.014453967101871967,
0.022592617198824883,
0.004149250220507383,
-0.017072878777980804,
-0.05200400948524475,
-0.015381306409835815,
0.007099511567503214,
0.032374363392591476,
-0.03846149891614914,
-0.01290945615619421,
-0.010484788566827774,
-0.033671241253614426,
-0.009899330325424671,
0.005628529470413923,
-0.004445514176040888,
-0.029164299368858337,
-0.010347296483814716,
0.010371225886046886,
-0.013545840978622437,
-0.027721812948584557,
0.01263564545661211,
-0.07747378945350647,
0.002950445981696248,
-0.0025071974378079176,
0.031736359000205994,
-0.00853284914046526,
0.039455171674489975,
-0.017665142193436623,
-0.028678931295871735,
-0.009973190724849701,
-0.02209336683154106,
0.01228315569460392,
-0.025767214596271515,
-0.0005189448711462319,
-0.0007260747952386737,
-0.00621775072067976,
0.027897024527192116,
-0.04761233180761337,
0.0020753606222569942,
0.05785474181175232,
-0.010948898270726204,
0.02339871972799301,
0.006376227363944054,
-0.0584857203066349,
-0.03737717866897583,
-0.05306020751595497,
0.026962367817759514,
-0.04120834916830063,
0.018158456310629845,
-0.022089816629886627,
-0.007556828670203686,
0.003398875007405877,
0.007254099473357201,
0.03618977218866348,
-0.031608399003744125,
-0.016892945393919945,
0.031230149790644646,
-0.0005733075668103993,
-0.0016640166286379099,
-0.01591494120657444,
-0.004436139017343521,
-0.002196746412664652,
-0.05102139338850975,
-0.01899924874305725,
-0.008357648737728596,
-0.015549694187939167,
0.01200114842504263,
0.029163742437958717,
0.002868912648409605,
0.0035297696013003588,
-0.00908750481903553,
-0.030341031029820442,
0.06339746713638306,
0.0015302731189876795,
0.022488554939627647,
0.06783859431743622,
0.006032595410943031,
0.027702195569872856,
0.030696045607328415,
-0.02848421223461628,
0.007651494350284338,
0.04069049283862114,
-0.025047030299901962,
-0.007536876015365124,
0.00406015757471323,
0.0006654115277342498,
0.007348341401666403,
-0.04240470752120018,
0.01670142449438572,
0.0286976657807827,
-0.03202040493488312,
0.012370153330266476,
0.06374698132276535,
-0.013516679406166077,
0.02103384956717491,
-0.027026761323213577,
0.01258761901408434,
-0.006449915003031492,
0.021111981943249702,
-0.014482290484011173,
0.03602898493409157,
0.025758778676390648,
0.009550091810524464,
0.01895553059875965,
0.03243742883205414,
-0.02937432937324047,
0.02996637672185898,
-0.012955524027347565,
0.05245831608772278,
-0.053342245519161224,
-0.0025207665748894215,
0.023772725835442543,
-0.02652078866958618,
0.007422682363539934,
0.012236470356583595,
-0.01237949263304472,
0.11257486045360565,
0.01155327819287777,
-0.0004988787695765495,
0.015670493245124817,
-0.01424277201294899,
-0.005895111244171858,
0.04482327401638031,
0.018697122111916542,
0.044007185846567154,
0.026781143620610237,
-0.006403204053640366,
-0.03192916139960289,
-0.0053183576092123985,
0.040402110666036606,
0.0023009199649095535,
-0.028609683737158775,
-0.02179679088294506,
-0.0211478378623724,
0.0073710293509066105,
-0.020334910601377487,
-0.03123581036925316,
-0.03778532147407532,
0.012969225645065308,
0.027693508192896843,
0.027992036193609238,
0.027192311361432076,
-0.0024614615831524134,
-0.0039051121566444635,
0.04956149309873581,
-0.06978748738765717,
0.00911477580666542,
-0.022965511307120323,
0.031638003885746,
-0.0087699880823493,
-0.029016803950071335
] |
<p>When we shoot a single photon out into space, the chance that it will eventually return to our vicinity from a different direction is vanishingly small, even though spatial curvature exists due to the gravitational influence of the distribution of mass energy throughout the universe. It is hard to imagine any regularity of motion for all possible photon directions in this quasi-random mass-energy structure. So lets flip this around, and, assuming a strictly random mass-energy distribution, the question can be asked as to whether any discernable common patterns exist for all possible photon trips? Such patterns need not necessarily exist in 3D space, but may exist in something like lattice k-space, or in Fourier space, or indeed any conceptual space, given the assumption of randomness of the mass-energy distribution throughout the cosmos. Another way to ask this question is to enquire as to what kind of distribution (in any space of our choosing) is to be expected?</p> | 1,490 | [
-0.009704673662781715,
-0.024947233498096466,
0.024951238185167313,
-0.045470960438251495,
0.036900635808706284,
0.0342177115380764,
-0.0036790291778743267,
-0.011246643960475922,
0.01796025037765503,
-0.04931238666176796,
0.011447533965110779,
0.032502420246601105,
0.044136423617601395,
0.003327546175569296,
0.03610503673553467,
0.013047248125076294,
-0.02446075901389122,
-0.01321912370622158,
-0.03270074352622032,
-0.06563062965869904,
0.04660477861762047,
0.02354803867638111,
0.01330862008035183,
0.01675032265484333,
-0.05156456306576729,
0.0017372401198372245,
-0.015417455695569515,
0.006075435783714056,
0.018370725214481354,
0.04472273960709572,
-0.01475430279970169,
0.0034133740700781345,
-0.01063986774533987,
0.06826505064964294,
0.018004003912210464,
-0.018679842352867126,
-0.04074603319168091,
-0.03119293972849846,
0.006435706280171871,
0.009285303764045238,
-0.05441690608859062,
-0.028109127655625343,
-0.04063915088772774,
0.04817330837249756,
-0.025586765259504318,
0.0011967921163886786,
-0.007952050305902958,
-0.02062583714723587,
0.0761636272072792,
-0.05375583842396736,
0.0923464447259903,
-0.009008929133415222,
0.01184472069144249,
0.029215583577752113,
-0.020284682512283325,
-0.014721892774105072,
0.06363120675086975,
0.05395239591598511,
-0.0033734499011188745,
-0.016661575064063072,
-0.03674021735787392,
0.005686840508133173,
0.02470005862414837,
-0.012982589192688465,
-0.0203924011439085,
0.03950587287545204,
-0.03857054561376572,
-0.024611718952655792,
0.016474783420562744,
-0.013182517141103745,
0.009561940096318722,
0.045234162360429764,
0.08563632518053055,
0.009171385318040848,
-0.0004750954103656113,
0.024951938539743423,
0.03009529411792755,
-0.0036831293255090714,
0.04587215557694435,
0.00029669623472727835,
-0.013790114782750607,
-0.029106412082910538,
-0.023084469139575958,
0.02304791286587715,
0.003759924788028002,
0.019793761894106865,
0.03569450601935387,
-0.05753481760621071,
-0.0003295139176771045,
0.03303796052932739,
0.016630031168460846,
0.016847068443894386,
0.03446381911635399,
0.03654364496469498,
-0.04864654317498207,
0.04044115170836449,
0.022204509004950523,
0.0020811764989048243,
0.011609126813709736,
-0.005832988768815994,
0.01766332983970642,
-0.019144603982567787,
-0.015471622347831726,
0.05710429698228836,
-0.011787519790232182,
-0.011605765670537949,
-0.05658066272735596,
0.05135703459382057,
-0.03159158304333687,
0.015603171661496162,
-0.024189218878746033,
0.05979905650019646,
0.013952129520475864,
0.01568036712706089,
0.020022956654429436,
-0.00606003450229764,
-0.005861608777195215,
-0.0674738734960556,
0.049961864948272705,
0.08635454624891281,
0.04838421195745468,
-0.037357356399297714,
0.04048210754990578,
-0.05411459133028984,
-0.04555761069059372,
-0.0058106062933802605,
0.06600464135408401,
0.013896883465349674,
-0.039581019431352615,
0.004759080708026886,
-0.015680348500609398,
-0.019762421026825905,
0.023073045536875725,
-0.0020759140606969595,
0.03190315514802933,
-0.04096685349941254,
-0.1108909323811531,
-0.0440690703690052,
0.006577986758202314,
-0.0008962403517216444,
-0.021391185000538826,
-0.04487442597746849,
-0.00961116049438715,
0.041939329355955124,
0.059113647788763046,
-0.026132898405194283,
-0.0017680228920653462,
-0.03439510241150856,
0.03299489617347717,
0.01640382781624794,
-0.04359240084886551,
0.004739002790302038,
-0.014906429685652256,
-0.04958166927099228,
0.005229976959526539,
-0.0683114156126976,
0.030493922531604767,
0.03489798307418823,
0.044302698224782944,
-0.027955833822488785,
0.038084473460912704,
-0.016141358762979507,
0.0190361849963665,
-0.011944754049181938,
0.016469143331050873,
-0.02788410894572735,
0.08308571577072144,
0.055945880711078644,
0.0019086510874330997,
0.015864189714193344,
0.0029813377186656,
0.017867356538772583,
-0.011321534402668476,
0.02469468116760254,
0.01637604646384716,
-0.0409373976290226,
0.008305180817842484,
0.023883681744337082,
0.031032346189022064,
-0.004685092717409134,
-0.016404476016759872,
-0.021914536133408546,
-0.013189946301281452,
-0.024815352633595467,
-0.011742381379008293,
0.026330456137657166,
-0.0031870580278337,
-0.026062870398163795,
0.03219559043645859,
-0.013925326056778431,
0.013738767243921757,
-0.010987472720444202,
0.003986122086644173,
-0.02102263644337654,
-0.03232252970337868,
0.024265410378575325,
0.011894294992089272,
0.011662831529974937,
-0.015948381274938583,
-0.040740903466939926,
0.0012213874142616987,
0.009192035533487797,
-0.01710270531475544,
-0.012921635992825031,
-0.007926584221422672,
0.045225922018289566,
-0.001386782736517489,
-0.013529744930565357,
0.0015223762020468712,
-0.005144056398421526,
-0.03175046667456627,
-0.008295444771647453,
-0.04743274673819542,
0.03931036219000816,
0.0022028342355042696,
0.03538912534713745,
0.004495036788284779,
0.021190987899899483,
-0.021122772246599197,
0.0056723677553236485,
-0.04975849390029907,
0.03061320260167122,
0.05445154011249542,
0.01575545035302639,
-0.03614112362265587,
0.02899388037621975,
-0.01292930543422699,
-0.006886858493089676,
-0.015726923942565918,
-0.09136354178190231,
-0.027897018939256668,
0.0010379221057519317,
0.02939886599779129,
0.02189335785806179,
-0.020364543423056602,
0.04407808557152748,
0.05524318292737007,
0.04999522492289543,
0.001399455708451569,
0.027922406792640686,
-0.03910134360194206,
-0.00436315406113863,
0.012206150218844414,
0.0197310708463192,
0.017545178532600403,
0.0001806711807148531,
-0.000506509211845696,
-0.001249703811481595,
-0.03899094834923744,
-0.0041543287225067616,
-0.03832583874464035,
-0.004147781990468502,
-0.021792059764266014,
0.018976718187332153,
-0.0100075863301754,
-0.031761977821588516,
0.04264933615922928,
-0.031590864062309265,
0.012935743667185307,
0.04875541105866432,
-0.01777634024620056,
-0.014640126377344131,
-0.026663392782211304,
-0.025112850591540337,
-0.0009435722604393959,
0.03577763959765434,
-0.033241234719753265,
-0.01160826813429594,
0.02484477497637272,
-0.007269200403243303,
0.040261708199977875,
-0.03362278267741203,
-0.00047216209350153804,
-0.00294781313277781,
0.003455383935943246,
0.04008856415748596,
0.006921652238816023,
0.012371554039418697,
-0.02353370375931263,
-0.038785096257925034,
0.009892082773149014,
0.008851462975144386,
-0.00819817278534174,
-0.010472058318555355,
-0.04190782457590103,
0.013666152022778988,
-0.020433027297258377,
-0.03939028084278107,
0.023999013006687164,
-0.022435417398810387,
0.04423443228006363,
0.03683401271700859,
-0.032397303730249405,
-0.04186069965362549,
0.004774284083396196,
-0.012255369685590267,
-0.015833402052521706,
0.0034903562627732754,
0.014133213087916374,
0.039152465760707855,
-0.02698523737490177,
-0.081296406686306,
0.012366115115582943,
-0.021994447335600853,
-0.06144951283931732,
-0.0386856272816658,
0.00967840850353241,
0.031710006296634674,
-0.0696108341217041,
0.053786661475896835,
0.02345643937587738,
-0.026849422603845596,
-0.01705828122794628,
-0.06619230657815933,
-0.03139638528227806,
0.013854495249688625,
-0.0006173687870614231,
0.04997096583247185,
-0.023475689813494682,
0.001920049311593175,
0.04648818075656891,
0.05844264477491379,
-0.02672899141907692,
0.010274290107190609,
0.005850563291460276,
-0.020295465365052223,
-0.015202303417026997,
0.011295891366899014,
-0.012956212274730206,
0.015291797928512096,
0.04465170577168465,
0.03921807184815407,
0.0452277809381485,
0.009848911315202713,
-0.02051837183535099,
-0.009711910970509052,
0.01840350776910782,
0.03343413025140762,
-0.008786958642303944,
0.0013915786985307932,
0.028650877997279167,
-0.01942501775920391,
0.0041815610602498055,
0.023812754079699516,
-0.01431947760283947,
0.016593676060438156,
-0.04123277962207794,
0.042829208076000214,
-0.01536357868462801,
0.016024576500058174,
-0.040066011250019073,
-0.006842700764536858,
0.005335613619536161,
-0.02109459415078163,
-0.008192431181669235,
0.04403006657958031,
0.04938022047281265,
0.003511248156428337,
0.00960535928606987,
0.010327563621103764,
0.06374040246009827,
-0.020951569080352783,
-0.020118193700909615,
0.0059359995648264885,
0.007288122083991766,
-0.006011460442095995,
-0.011410924606025219,
-0.026183098554611206,
0.03249932453036308,
0.035434842109680176,
0.05828826129436493,
-0.0016513691516593099,
-0.020970111712813377,
-0.012192578986287117,
-0.030987858772277832,
-0.010741027072072029,
-0.016253238543868065,
0.05361636355519295,
-0.008022133260965347,
0.03623951971530914,
0.038680583238601685,
-0.011421943083405495,
-0.02504546195268631,
0.011889750137925148,
-0.06538932025432587,
-0.003698481945320964,
-0.025840697810053825,
0.02571003884077072,
-0.024731943383812904,
-0.02653079852461815,
-0.010947017930448055,
-0.02703421749174595,
-0.013424338772892952,
0.02889874391257763,
0.00490975845605135,
-0.07808618247509003,
-0.01473377738147974,
-0.04954053834080696,
-0.06680077314376831,
-0.0016297880792990327,
0.023026151582598686,
0.04557473212480545,
0.009110404178500175,
0.01918470300734043,
-0.006245770025998354,
-0.023139366880059242,
-0.021682240068912506,
0.006730364169925451,
0.03576014190912247,
-0.009425315074622631,
0.005287317559123039,
0.021495429798960686,
-0.015444036573171616,
-0.0033099185675382614,
0.014493337832391262,
-0.011965721845626831,
0.041944362223148346,
0.016137130558490753,
-0.023556821048259735,
0.02347196452319622,
-0.02222132869064808,
0.01038104947656393,
0.02544461563229561,
0.033769041299819946,
0.025051534175872803,
0.01798722892999649,
0.05359683558344841,
0.025212999433279037,
-0.02366538532078266,
0.02987917885184288,
0.058437902480363846,
-0.027659930288791656,
-0.023394182324409485,
-0.047886621206998825,
-0.003912807907909155,
0.02995745837688446,
-0.0218986663967371,
0.026090506464242935,
-0.013113850727677345,
-0.009212415665388107,
0.004098479636013508,
0.006345121189951897,
0.04477731138467789,
-0.009964200668036938,
0.007287111133337021,
-0.03460632637143135,
0.00854792632162571,
-0.030186094343662262,
0.01639474928379059,
-0.015834424644708633,
-0.0359962172806263,
0.07187104970216751,
0.049760013818740845,
-0.026116738095879555,
-0.05155813694000244,
0.020041415467858315,
0.0418696403503418,
0.019040202721953392,
-0.0037901499308645725,
-0.001699170214124024,
-0.05052681639790535,
-0.018790675327181816,
0.010176564566791058,
-0.020538531243801117,
-0.006182920187711716,
0.001270109205506742,
-0.023083101958036423,
0.011330154724419117,
-0.04363677650690079,
-0.005655743181705475,
0.019484559074044228,
0.023377591744065285,
-0.002597504062578082,
-0.020742351189255714,
0.0011186461197212338,
-0.03165145218372345,
0.03997059538960457,
0.038181133568286896,
0.033719275146722794,
0.02646038308739662,
-0.010710600763559341,
-0.04761088266968727,
0.00822654739022255,
0.023668108507990837,
-0.08636702597141266,
0.020987462252378464,
0.008467541076242924,
-0.026537269353866577,
0.07304377108812332,
-0.02242492511868477,
-0.03616950288414955,
0.011244293302297592,
-0.020839275792241096,
0.00010194422793574631,
0.00020961702102795243,
-0.019104519858956337,
0.0036912206560373306,
0.027224920690059662,
0.04746845364570618,
0.04388011246919632,
0.031423889100551605,
0.007482160814106464,
-0.03274616599082947,
0.007455070968717337,
0.058072056621313095,
-0.0005650782259181142,
-0.0033879813272506,
-0.045050203800201416,
-0.036693934351205826,
-0.012259041890501976,
0.049743443727493286,
-0.008028131909668446,
-0.04665515199303627,
0.018290380015969276,
-0.043245088309049606,
-0.027569862082600594,
0.0431496761739254,
-0.0007017675670795143,
0.015165654011070728,
-0.02904708869755268,
0.03927263244986534,
-0.016601258888840675,
-0.011766730807721615,
0.008089935407042503,
0.008273134008049965,
0.004545186180621386,
0.04536747187376022,
0.02501342073082924,
0.010369374416768551,
-0.025489436462521553,
0.04151788353919983,
-0.0005125351599417627,
-0.02729303017258644,
0.04921836778521538,
0.025900688022375107,
0.012977827340364456,
0.03915201872587204,
-0.047576650977134705,
-0.021432168781757355,
-0.022148355841636658,
-0.020846562460064888,
0.03494170680642128,
-0.018269581720232964,
0.016190169379115105,
-0.03141195699572563,
0.027758091688156128,
-0.11893782764673233,
-0.04040970653295517,
0.00455480208620429,
0.05172291025519371,
0.00444667087867856,
-0.04006033018231392,
0.01451382227241993,
-0.05654359236359596,
-0.008684508502483368,
-0.008761369623243809,
0.07466362416744232,
-0.017905881628394127,
-0.004578591790050268,
-0.03082237020134926,
0.022691892459988594,
0.05075444281101227,
-0.0034697242081165314,
-0.03583265841007233,
0.06393840909004211,
0.028353959321975708,
-0.014097066596150398,
-0.027355024591088295,
0.05357867479324341,
-0.023103144019842148,
-0.05559413135051727,
-0.043059464544057846,
0.005766947753727436,
0.016295455396175385,
-0.07403700053691864,
-0.042284511029720306,
0.02199261263012886,
0.022566763684153557,
0.017918715253472328,
-0.02186119742691517,
0.0004367172659840435,
-0.006874678190797567,
0.007289335131645203,
-0.0026182059664279222,
-0.004627348855137825,
0.009896351955831051,
-0.0412491112947464,
0.050995394587516785,
0.00019274618534836918,
0.020583661273121834,
0.027648726478219032,
0.016438549384474754,
0.008455755189061165,
-0.05589207634329796,
0.013309668749570847,
0.00271094823256135,
0.01555324625223875,
-0.03155961632728577,
-0.002608669688925147,
0.03489375114440918,
-0.0015496705891564488,
-0.01328123826533556,
-0.04790055379271507,
-0.04381324350833893,
0.01349288783967495,
0.08374103903770447,
-0.014502745121717453,
0.03304881229996681,
0.016856946051120758,
-0.02371339499950409,
-0.002604859881103039,
0.012674723751842976,
0.013869189657270908,
-0.00621866574510932,
0.014561948366463184,
0.02535713091492653,
-0.025919893756508827,
0.026398804038763046,
0.032587774097919464,
0.06118165701627731,
-0.03649429231882095,
0.04830554500222206,
0.013987395912408829,
0.024655809625983238,
0.05166143551468849,
-0.00924572441726923,
-0.04664423689246178,
0.03280597925186157,
-0.05867192521691322,
0.03861376643180847,
0.024143682792782784,
-0.03406257554888725,
0.021399881690740585,
0.03958182409405708,
0.002410644432529807,
-0.01025390625,
-0.029530048370361328,
-0.0323968380689621,
0.020390696823596954,
0.02627750299870968,
0.050088975578546524,
-0.0008434971678070724,
0.002728331834077835,
0.017405884340405464,
0.03151653707027435,
-0.016576535999774933,
0.0325009822845459,
-0.06448633968830109,
-0.04617181792855263,
-0.043639376759529114,
-0.04034338891506195,
0.06133783236145973,
0.00727399718016386,
-0.01799461804330349,
-0.015882045030593872,
-0.031671084463596344,
0.020711716264486313,
0.03213344141840935,
0.044337768107652664,
0.02273678593337536,
0.06083449348807335,
-0.01587458699941635,
0.034751228988170624,
-0.0489751361310482,
-0.007872319780290127,
0.1131557747721672,
0.06993769109249115,
0.016332361847162247,
-0.052729081362485886,
0.002419655444100499,
-0.06034310534596443,
0.006063869688659906,
-0.02481999434530735,
0.03817891702055931,
0.015443176962435246,
0.006804371252655983,
0.017950575798749924,
0.06781493872404099,
-0.013949180021882057,
-0.013326260261237621,
0.04508579149842262,
-0.041605591773986816,
-0.036058299243450165,
0.021249091252684593,
0.001632567378692329,
0.0309284720569849,
0.01966433972120285,
-0.025898359715938568,
0.00926763005554676,
-0.009665881283581257,
0.013823325745761395,
0.0263501089066267,
-0.02633572742342949,
0.010210689157247543,
0.030739039182662964,
-0.013171621598303318,
-0.018087834119796753,
0.019833633676171303,
-0.022329965606331825,
-0.015688398852944374,
-0.013699227944016457,
0.028911549597978592,
-0.039425626397132874,
0.009322459809482098,
0.007491871248930693,
0.019641311839222908,
0.020478874444961548,
0.0012337056687101722,
-0.0062766531482338905,
-0.016427544876933098,
-0.00813357438892126,
-0.015728838741779327,
0.03182147443294525,
-0.01764136180281639,
0.0038189480546861887,
-0.011641304939985275,
-0.012862707488238811,
0.01385494414716959,
-0.055950820446014404,
0.007954065687954426,
-0.04085094854235649,
0.058698620647192,
-0.025399580597877502,
-0.013997109606862068,
0.011861170642077923,
-0.007304327096790075,
-0.014326915144920349,
0.03011038899421692,
-0.023716675117611885,
0.010148533619940281,
-0.00610803347080946,
-0.012898273766040802,
0.06584646552801132,
-0.01808970607817173,
-0.019167575985193253,
-0.047329723834991455,
-0.029882030561566353,
-0.03695186972618103,
-0.01879090815782547,
0.006916179787367582,
0.023073382675647736,
0.020463993772864342,
0.0035602508578449488,
-0.01809491589665413,
0.01269796397536993,
-0.021330654621124268,
0.0035045426338911057,
-0.043576523661613464,
-0.03836682438850403,
0.0044390191324055195,
0.005511227063834667,
0.03118734247982502,
0.029079928994178772,
0.019252656027674675,
-0.013596009463071823,
-0.00007597063813591376,
0.039618443697690964,
0.02461344748735428,
-0.035360585898160934,
0.009109425358474255,
-0.0046667177230119705,
-0.016740117222070694,
-0.012698599137365818,
-0.007410721387714148,
0.0027084127068519592,
-0.021773144602775574,
0.01657145656645298,
0.018253834918141365,
0.0204471368342638,
-0.017063017934560776,
-0.006639997474849224,
0.0031085729133337736,
-0.03753717988729477,
-0.0190619807690382,
0.021837592124938965,
-0.038496650755405426,
-0.040864571928977966,
-0.05430470407009125,
-0.00580268818885088,
0.023264644667506218,
-0.009775843471288681,
0.010514091700315475,
-0.04463501647114754,
-0.0032942367251962423,
-0.012402473017573357,
0.008765908889472485,
-0.03204699605703354,
-0.018965132534503937,
-0.033900268375873566,
0.011590867303311825,
0.008892001584172249,
-0.01761811412870884,
-0.019213121384382248,
0.006536068394780159,
-0.023539545014500618,
-0.03247315436601639,
-0.019515903666615486,
0.05028499290347099,
-0.011755994521081448,
0.0025874245911836624,
0.0281742662191391,
-0.02822621911764145,
0.041786037385463715,
-0.04091533645987511,
-0.015855994075536728,
0.012855282053351402,
-0.052534423768520355,
-0.05452839657664299,
0.014039178378880024,
-0.03582129254937172,
0.011368034407496452,
0.03636565059423447,
-0.003975267522037029,
0.010628581047058105,
0.04675810784101486,
-0.005535840056836605,
-0.0023343549109995365,
0.026321424171328545,
0.007352745626121759,
-0.013533445075154305,
-0.03095031902194023,
0.0470077209174633,
-0.03531317040324211,
-0.05076766014099121,
0.008140706457197666,
0.025828327983617783,
0.000029509441446862184,
-0.0025673757772892714,
-0.008315377868711948,
-0.060727912932634354,
0.014663445763289928,
-0.0012593879364430904,
0.027310319244861603,
0.015694938600063324,
0.04794171452522278,
-0.04779118299484253,
0.014445740729570389,
0.028534462675452232,
0.003787251655012369,
-0.09234865009784698,
-0.02797773666679859,
0.029972640797495842,
-0.008927401155233383,
0.004106414038687944,
-0.03471508249640465,
-0.01196545921266079,
0.03409813717007637,
-0.08311611413955688,
0.07072503119707108,
0.009658950380980968,
-0.008154790848493576,
-0.03428632766008377,
0.03134257346391678,
-0.0007182562840171158,
0.04154719039797783,
0.04038233682513237,
0.042259905487298965,
0.007268296554684639,
0.005807304754853249,
-0.006406630389392376,
-0.0019544598180800676,
0.014301474206149578,
-0.0039016094524413347,
-0.006293782498687506,
0.02481864020228386,
0.059776727110147476,
0.0002173966495320201,
-0.029657207429409027,
0.030474046245217323,
0.02635227143764496,
-0.0030509454663842916,
-0.011221801862120628,
-0.003491678973659873,
-0.005191088188439608,
0.03509580343961716,
0.019377989694476128,
0.00121198536362499,
-0.022111423313617706,
-0.02923342026770115,
0.04581388458609581,
0.028438644483685493,
-0.02019272744655609,
0.029890436679124832,
0.01254208292812109,
-0.022106146439909935,
-0.02866315096616745,
0.04445541277527809,
0.02766210027039051,
-0.029411043971776962,
-0.010759434662759304,
0.008337816223502159,
0.038225769996643066,
-0.009244103915989399,
0.02424381859600544,
-0.08412348479032516,
0.007536775432527065,
-0.010142365470528603,
0.006575793959200382,
0.009833204559981823,
0.01451143715530634,
-0.012721927836537361,
-0.038442645221948624,
-0.003642716910690069,
-0.001983076799660921,
-0.007988912053406239,
-0.0362120196223259,
-0.022769203409552574,
-0.014735549688339233,
0.023053688928484917,
0.026594161987304688,
-0.06577588617801666,
-0.015918102115392685,
0.03647197410464287,
0.00442048953846097,
0.030966095626354218,
0.03493879735469818,
-0.0072084940038621426,
-0.03502650186419487,
-0.06342338025569916,
0.01079936046153307,
-0.033621884882450104,
0.04606981202960014,
-0.03810470923781395,
0.0045458655804395676,
0.014058168977499008,
-0.0011907161679118872,
0.023052185773849487,
-0.03128350153565407,
0.01625347137451172,
0.0014529587933793664,
0.012846000492572784,
0.03421131893992424,
-0.06727590411901474,
-0.01137523166835308,
-0.055246397852897644,
-0.01628771424293518,
-0.0507613942027092,
-0.0011658216826617718,
-0.008206157945096493,
-0.02079727314412594,
0.0020518440287560225,
-0.015506363473832607,
0.021366242319345474,
-0.0034163573291152716,
0.006199526600539684,
0.050896789878606796,
0.03553509712219238,
0.0010869817342609167,
-0.0036963841412216425,
0.012458966113626957,
0.0038079514633864164,
0.019249334931373596,
-0.02527964673936367,
-0.039208754897117615,
0.02374986559152603,
-0.003942230250686407,
-0.0810651034116745,
-0.010814373381435871,
0.050985705107450485,
0.038675274699926376,
-0.029780812561511993,
-0.027703439816832542,
0.02135404385626316,
-0.04268398508429527,
-0.016001271083950996,
0.04502495378255844,
-0.019606372341513634,
0.03820759430527687,
0.012986804358661175,
0.015380694530904293,
0.02059401571750641,
0.009136990644037724,
0.016667809337377548,
0.04149162024259567,
0.03434174135327339,
-0.029280705377459526,
0.013425842858850956,
-0.025561729446053505,
-0.01449078880250454,
0.018917029723525047,
-0.006253461819142103,
0.06740056723356247,
-0.0309744980186224,
0.036434803158044815,
0.054381102323532104,
0.04554149508476257,
-0.019785260781645775,
0.0035012143198400736,
-0.0030584733467549086,
0.06972406804561615,
0.006798145826905966,
0.009918027557432652,
-0.01956157572567463,
-0.003441177075728774,
0.0162239708006382,
0.03910500183701515,
-0.014451220631599426,
0.040215540677309036,
0.036958999931812286,
0.004437537398189306,
-0.017707224935293198,
0.02644728682935238,
0.05845479667186737,
-0.029721727594733238,
0.0024024273734539747,
-0.0065093315206468105,
-0.04962298274040222,
0.0068502891808748245,
0.01324193924665451,
-0.029061948880553246,
-0.044439930468797684,
0.0015830035554245114,
0.027978597208857536,
0.05526840314269066,
0.007608945015817881,
0.018564797937870026,
-0.05649951845407486,
0.06086287274956703,
-0.061794787645339966,
0.009491454809904099,
-0.04249270632863045,
0.03913593664765358,
0.003599146381020546,
-0.018551098182797432
] |
<p>Regarding the Bremsstrahlung Radiation emitted when a charged particle curves inside a uniform magnetic field; Is there a way of calculating the angle through which the charged particle will precess before emitting the first quantum of radiation? Also, is there a way of determining the angle through which the charged particle will precess between the first and second emissions of radiation? </p>
<p>My investigations revealed only what I think are the angles of emission relative to the tangent of the curve <a href="http://en.wikipedia.org/wiki/Bremsstrahlung#Angular_distribution" rel="nofollow">here</a>. </p> | 1,491 | [
-0.03541690483689308,
-0.03519130498170853,
0.0136262821033597,
-0.03754549100995064,
0.05567207932472229,
0.03149578720331192,
-0.0327611118555069,
-0.0009901471203193069,
0.0011893485207110643,
-0.03875118866562843,
0.019279781728982925,
0.031075356528162956,
0.04786479100584984,
0.04499387368559837,
0.045129187405109406,
-0.020572762936353683,
0.0012235490139573812,
0.017765266820788383,
0.021890757605433464,
-0.05925421416759491,
0.02080208994448185,
0.030310802161693573,
-0.03659374266862869,
0.000144939825986512,
-0.01954742521047592,
0.011164279654622078,
0.0341334268450737,
0.04412880167365074,
0.03182724118232727,
0.041539013385772705,
-0.01081003900617361,
0.0009647448896430433,
0.030102407559752464,
0.015649352222681046,
0.029540762305259705,
-0.014186138287186623,
-0.002956764306873083,
-0.050356339663267136,
-0.03930941969156265,
0.03196369856595993,
-0.021793266758322716,
0.0034726187586784363,
-0.025560839101672173,
0.04816105216741562,
-0.027870824560523033,
-0.03306238725781441,
-0.0376950241625309,
-0.027484320104122162,
0.06569784134626389,
-0.047341976314783096,
0.07194649428129196,
-0.03152558580040932,
0.0015533616533502936,
-0.01647135242819786,
-0.01093373354524374,
-0.0018398166866973042,
0.05476236343383789,
0.04598866030573845,
0.0038917665369808674,
-0.055977869778871536,
-0.011964156292378902,
-0.04021437466144562,
-0.015703745186328888,
0.002399280434474349,
-0.026353169232606888,
0.019222985953092575,
-0.015140513889491558,
-0.021695492789149284,
0.03957794979214668,
0.007186143659055233,
0.018252046778798103,
0.020505817607045174,
0.05750684440135956,
-0.02131042629480362,
0.01523385476320982,
0.003725635353475809,
0.026267532259225845,
0.011647246778011322,
0.040643710643053055,
0.027165822684764862,
-0.02868536114692688,
0.013067679479718208,
0.046523161232471466,
0.035334065556526184,
0.012953219003975391,
-0.0014288033125922084,
0.045278314501047134,
-0.0003801543789450079,
0.031607259064912796,
0.043381936848163605,
0.013266080990433693,
0.04669348523020744,
0.02602163702249527,
-0.0075639523565769196,
-0.03706638887524605,
0.032948970794677734,
-0.0011513994541019201,
0.08772806078195572,
0.011512708850204945,
-0.05887303128838539,
0.059099260717630386,
-0.015077706426382065,
-0.01566952094435692,
0.07601545751094818,
0.022855130955576897,
-0.009621264412999153,
-0.021052313968539238,
0.034782107919454575,
-0.05005263909697533,
-0.03353297337889671,
-0.00918450579047203,
-0.005370092112571001,
0.01589146815240383,
-0.023077476769685745,
-0.00679140305146575,
0.006100263446569443,
0.011136808432638645,
0.0013365627964958549,
0.06166166812181473,
0.05115833133459091,
0.024736721068620682,
-0.024118073284626007,
0.0409606397151947,
-0.027449481189250946,
-0.0385739766061306,
-0.034925397485494614,
0.05829470604658127,
0.0008866919670253992,
-0.05976200848817825,
0.02724616788327694,
-0.010998815298080444,
-0.024124721065163612,
0.038965631276369095,
-0.019387202337384224,
-0.002690217923372984,
-0.013543877750635147,
-0.08588501811027527,
-0.07531694322824478,
0.01629003696143627,
-0.009782107546925545,
0.012110667303204536,
-0.0640367642045021,
0.03478914871811867,
0.06347062438726425,
0.08309511095285416,
0.0004542098904494196,
-0.004044326022267342,
-0.0347345769405365,
0.04698985069990158,
-0.017619330435991287,
-0.017882926389575005,
0.025436604395508766,
0.004829139448702335,
-0.010812388733029366,
-0.02616661600768566,
-0.021167073398828506,
0.03577928990125656,
0.026865599676966667,
0.004302119370549917,
-0.029547367244958878,
0.051581140607595444,
0.00841179583221674,
0.009670768864452839,
-0.0025071031413972378,
-0.009990463964641094,
-0.01892727240920067,
0.10783742368221283,
0.05937761440873146,
-0.020988157019019127,
0.013440176844596863,
0.020951591432094574,
0.028413746505975723,
0.0037161146756261587,
-0.011567619629204273,
0.03965208679437637,
-0.06114208325743675,
-0.036602385342121124,
-0.02346249483525753,
0.035646624863147736,
-0.0005058637470938265,
-0.04283635690808296,
-0.023203827440738678,
-0.007388085126876831,
0.02677289769053459,
-0.003974453080445528,
0.02286187931895256,
0.013640530407428741,
0.007022957317531109,
-0.0174108874052763,
-0.037240974605083466,
0.014671857468783855,
-0.0389125719666481,
0.02722802944481373,
0.0001635845983400941,
-0.03703552857041359,
-0.01411566510796547,
0.010155546478927135,
0.026940466836094856,
-0.016200480982661247,
-0.046444959938526154,
-0.025418782606720924,
0.03551483899354935,
0.005037134047597647,
-0.01572614163160324,
0.005271213594824076,
0.07295466214418411,
0.010048320516943932,
0.029071975499391556,
0.02575918473303318,
-0.009435185231268406,
-0.0049092029221355915,
-0.02319524437189102,
-0.038901448249816895,
0.02138952910900116,
0.03618356212973595,
0.023332657292485237,
-0.006327080074697733,
-0.003256943542510271,
-0.01133203599601984,
0.002856371458619833,
-0.012013637460768223,
0.07728295028209686,
0.04615363851189613,
0.023434272035956383,
0.01090211234986782,
0.025278549641370773,
0.02521868608891964,
-0.005325489677488804,
0.004600708372890949,
-0.051652729511260986,
-0.041125863790512085,
-0.002699409844353795,
0.026974087581038475,
0.0038909795694053173,
-0.06752105802297592,
-0.006714921910315752,
0.03863324224948883,
0.05253264307975769,
0.0011347896652296185,
0.045006465166807175,
-0.05077759549021721,
-0.03151636943221092,
-0.027747146785259247,
0.004978122189640999,
-0.02278381958603859,
-0.01012537069618702,
0.03961274027824402,
0.007022049743682146,
-0.008274229243397713,
0.024884872138500214,
-0.028059469535946846,
0.006042585242539644,
-0.04582265019416809,
0.007441760040819645,
0.000013336273696040735,
-0.05816217139363289,
0.060050930827856064,
-0.02478908561170101,
0.026323722675442696,
-0.021727722138166428,
-0.026742687448859215,
-0.014249797910451889,
0.027029836550354958,
-0.003811578033491969,
0.005769720301032066,
-0.03267836570739746,
-0.039389144629240036,
0.0025935813318938017,
0.03965407609939575,
-0.04761431738734245,
0.011166932992637157,
-0.015686679631471634,
-0.023273443803191185,
-0.0026038805954158306,
0.02448766864836216,
0.009684416465461254,
0.050916485488414764,
-0.0065151397138834,
-0.007373934146016836,
-0.039058323949575424,
-0.00786910392343998,
-0.012523205950856209,
0.013507611118257046,
0.030426597222685814,
-0.04509218409657478,
0.023880308493971825,
-0.027010422199964523,
-0.031726986169815063,
0.035746295005083084,
-0.025254562497138977,
0.007552504073828459,
0.0414271242916584,
-0.012087822891771793,
-0.06472352147102356,
-0.03281676024198532,
0.006043889559805393,
-0.003922905772924423,
-0.0474967360496521,
-0.007043071556836367,
0.04106353968381882,
-0.010205941274762154,
-0.009946697391569614,
0.04204045236110687,
-0.04482464864850044,
-0.013037623837590218,
-0.021800896152853966,
0.012141542509198189,
0.005268588662147522,
0.01699039712548256,
0.030744031071662903,
0.0077474419958889484,
-0.054890282452106476,
-0.025576243177056313,
-0.03590108081698418,
-0.04327705129981041,
0.039277803152799606,
-0.007243947125971317,
0.02128560096025467,
-0.015331574715673923,
-0.04407849907875061,
0.05592544004321098,
0.023931188508868217,
-0.03437068313360214,
-0.03201648220419884,
-0.004080282524228096,
-0.007553522475063801,
-0.011446853168308735,
-0.014089667238295078,
0.004040034953504801,
0.01773885264992714,
-0.005667193792760372,
-0.006253005005419254,
0.010530748404562473,
0.0224077720195055,
0.02521313913166523,
0.020801585167646408,
0.026571182534098625,
0.004681364167481661,
0.024012502282857895,
0.022551722824573517,
0.018707500770688057,
-0.011462313123047352,
0.012888344936072826,
0.025688813999295235,
0.028117585927248,
0.007200238294899464,
-0.04897494241595268,
0.04773695394396782,
0.014993554912507534,
0.03863856941461563,
-0.002140906173735857,
0.01486673578619957,
-0.020746607333421707,
0.013169636949896812,
-0.0048653301782906055,
0.033520374447107315,
0.0358060784637928,
0.0059464056976139545,
0.029634008184075356,
0.029014509171247482,
0.027819065377116203,
-0.02337195910513401,
-0.007734884507954121,
-0.014699215069413185,
0.0006703250110149384,
0.03329339623451233,
-0.03668076545000076,
-0.03827184811234474,
0.033804066479206085,
0.043560076504945755,
0.0474700890481472,
0.030715087428689003,
-0.02290324494242668,
-0.00129387725610286,
-0.04205165430903435,
0.0017089077737182379,
0.021624887362122536,
0.0312349796295166,
0.04279410466551781,
0.028175005689263344,
0.027737610042095184,
0.02696523256599903,
0.009453867562115192,
-0.004550247918814421,
-0.10882096737623215,
0.03373785689473152,
-0.025764955207705498,
-0.005382309667766094,
0.009863562881946564,
-0.015555511228740215,
-0.030656957998871803,
-0.03641898185014725,
-0.029395103454589844,
-0.01734469272196293,
-0.025351744145154953,
-0.020633846521377563,
0.05424870550632477,
-0.01671307347714901,
-0.03323505073785782,
-0.019181063398718834,
0.06434518843889236,
0.028031446039676666,
-0.014262938871979713,
0.05039702355861664,
0.0175776407122612,
-0.05651833489537239,
0.02606157772243023,
0.0054185036569833755,
0.023205850273370743,
-0.029492389410734177,
0.031475406140089035,
0.03677040711045265,
-0.010328384116292,
-0.03940132260322571,
-0.0142427459359169,
-0.0034479901660233736,
0.06057557463645935,
0.047917481511831284,
-0.04019935429096222,
-0.019756823778152466,
-0.05432594567537308,
0.008167292922735214,
-0.017545774579048157,
0.07451178133487701,
-0.008067327551543713,
0.04492354765534401,
0.023593194782733917,
-0.02843593619763851,
0.001138361869379878,
0.008800636045634747,
0.05467153340578079,
0.021887313574552536,
-0.008935239166021347,
-0.02954789064824581,
-0.004699213895946741,
0.013080449774861336,
0.011789621785283089,
-0.032839078456163406,
-0.016882654279470444,
-0.030094798654317856,
-0.01036909595131874,
0.03491229563951492,
0.04528595507144928,
0.011672696098685265,
0.019142067059874535,
-0.008292172104120255,
0.028715208172798157,
0.0196615569293499,
-0.0037182422820478678,
0.023695487529039383,
0.0054941787384450436,
0.02826257236301899,
0.0008681983454152942,
-0.017844771966338158,
-0.0771435871720314,
-0.0266557689756155,
0.03265581279993057,
0.046558305621147156,
-0.0053747789934277534,
-0.009385442361235619,
-0.03426268324255943,
0.003207660047337413,
0.0641939789056778,
0.0029134994838386774,
0.04405913129448891,
-0.0205647274851799,
0.0023755792062729597,
-0.024720480665564537,
-0.018615644425153732,
-0.05721287429332733,
0.05146710202097893,
0.006030561868101358,
0.0030393251217901707,
-0.07197866588830948,
-0.012254921719431877,
0.0023978296667337418,
0.004486300051212311,
0.05589444562792778,
0.043420977890491486,
0.037326615303754807,
0.0037908947560936213,
-0.00916797760874033,
0.03287637606263161,
0.010921083390712738,
-0.06984863430261612,
0.02162724733352661,
0.016215050593018532,
-0.02662689983844757,
0.05055766552686691,
-0.029901230707764626,
-0.03866112604737282,
0.01481396984308958,
-0.003739458043128252,
0.028844716027379036,
0.01164907868951559,
-0.058822933584451675,
0.04396723583340645,
0.01943855918943882,
0.02132350206375122,
0.060230955481529236,
0.01938595622777939,
-0.03255096822977066,
0.01355820707976818,
-0.018663330003619194,
0.033708881586790085,
0.013358727097511292,
-0.022360267117619514,
-0.03392671048641205,
0.049266062676906586,
-0.009662514552474022,
0.07115824520587921,
-0.04637039825320244,
-0.009139830246567726,
0.009531809948384762,
0.005190185736864805,
-0.006230717059224844,
0.05844835191965103,
-0.020152298733592033,
-0.000319028680678457,
-0.0402168445289135,
0.021883845329284668,
-0.025839464738965034,
-0.02020290680229664,
0.023840628564357758,
-0.04862348362803459,
0.022312013432383537,
0.048028312623500824,
-0.021803004667162895,
-0.004552171565592289,
-0.031043751165270805,
0.0014475439675152302,
0.008820170536637306,
-0.04846999794244766,
0.03471190854907036,
-0.011296989396214485,
-0.019709384068846703,
0.03801380842924118,
-0.033390551805496216,
-0.028799664229154587,
-0.005003088619560003,
-0.0024020394776016474,
0.0522715263068676,
-0.050595514476299286,
0.01176402997225523,
-0.010092994198203087,
0.0025897843297570944,
-0.06735049188137054,
-0.04264187440276146,
-0.0032138084061443806,
-0.0045733144506812096,
-0.03333247825503349,
-0.02356371469795704,
-0.008709239773452282,
-0.027771010994911194,
-0.01332221832126379,
0.017924312502145767,
0.02408595010638237,
-0.038224782794713974,
0.008548974990844727,
0.01846526935696602,
-0.005139281507581472,
0.036170121282339096,
-0.0015848680632188916,
-0.04270253702998161,
0.01126773003488779,
-0.02714639902114868,
-0.009514440782368183,
0.015343103557825089,
0.03706825524568558,
-0.012837395071983337,
-0.03202303126454353,
-0.025895874947309494,
0.009983470663428307,
0.040654607117176056,
0.009603513404726982,
-0.04762440174818039,
0.0277432668954134,
0.05403633415699005,
-0.022418757900595665,
-0.005644432734698057,
-0.002147080609574914,
0.004382139537483454,
0.008624864742159843,
-0.028198478743433952,
-0.009840031154453754,
-0.04642316326498985,
-0.0447118878364563,
0.016967741772532463,
-0.004493224434554577,
0.02959142066538334,
-0.008187888190150261,
0.04864463955163956,
-0.020476827397942543,
-0.030962398275732994,
-0.0078008281998336315,
-0.0017496820073574781,
0.009681809693574905,
-0.03523910790681839,
0.02488228678703308,
0.005107030738145113,
0.013619134202599525,
-0.014869236387312412,
-0.03667781874537468,
-0.015641575679183006,
-0.03307744860649109,
0.07190033048391342,
0.015076857060194016,
0.07824268937110901,
0.015821659937500954,
0.03689994290471077,
-0.04438594728708267,
-0.004096486605703831,
0.0008374977624043822,
-0.045754604041576385,
0.024963557720184326,
0.023946067318320274,
-0.03255562484264374,
0.00400721887126565,
-0.009232373908162117,
0.04272964969277382,
-0.026834476739168167,
0.02479707822203636,
-0.009876823052763939,
0.022851716727018356,
0.03185988590121269,
0.01574605144560337,
-0.04525626078248024,
0.04047450050711632,
-0.025831034407019615,
0.04837697371840477,
-0.012398749589920044,
-0.029563773423433304,
0.031508952379226685,
-0.0033168985974043608,
0.005640733055770397,
-0.03160734102129936,
0.000560979766305536,
-0.02729032002389431,
0.02722281403839588,
-0.005695066414773464,
0.006974485702812672,
-0.039000362157821655,
-0.006619045976549387,
0.03470320254564285,
-0.011096639558672905,
0.018510129302740097,
-0.006055016536265612,
-0.041571520268917084,
-0.0248219333589077,
-0.052642129361629486,
-0.05652659758925438,
0.05473756045103073,
-0.019597534090280533,
-0.002123217796906829,
0.016584498807787895,
-0.01420745998620987,
0.034440651535987854,
0.021057507023215294,
0.03586313873529434,
-0.00429877731949091,
0.06184367090463638,
-0.049206335097551346,
-0.006340767722576857,
-0.02275850623846054,
0.01621786318719387,
0.11188140511512756,
0.049262356013059616,
-0.009788664057850838,
-0.060731470584869385,
0.011133148334920406,
-0.01518516056239605,
0.02992253378033638,
-0.025950554758310318,
0.0170502457767725,
-0.04356345534324646,
-0.015234099701046944,
0.014600262977182865,
0.01792317070066929,
-0.021817516535520554,
0.016995539888739586,
0.03526746854186058,
-0.0347159281373024,
-0.03542715311050415,
0.0005627243081107736,
0.04573788493871689,
0.02949812449514866,
0.0286246407777071,
-0.03576027601957321,
0.010893866419792175,
-0.04387042671442032,
0.011911813169717789,
-0.0356643907725811,
-0.01580350287258625,
0.01158963330090046,
-0.04505956172943115,
-0.045976269990205765,
0.010659623891115189,
0.009901839308440685,
-0.028932977467775345,
-0.05529771372675896,
0.024742266163229942,
0.03896036744117737,
-0.008995221927762032,
0.03646575286984444,
0.025504527613520622,
0.02033178135752678,
0.00019462939235381782,
0.029677046462893486,
0.05145789682865143,
-0.027939539402723312,
0.004479165188968182,
-0.005497491452842951,
0.027565814554691315,
-0.02226373925805092,
-0.025963295251131058,
-0.029671674594283104,
-0.011756451800465584,
0.03993646055459976,
-0.05173511430621147,
0.006012129597365856,
-0.017953738570213318,
-0.0025161695666611195,
-0.015526521019637585,
0.005064979661256075,
-0.0026314526330679655,
0.027608215808868408,
0.04627581313252449,
-0.015598321333527565,
-0.0026727744843810797,
-0.0025197637733072042,
0.025523647665977478,
0.01158055942505598,
0.07623273134231567,
-0.007215229794383049,
-0.04174526408314705,
-0.03446374088525772,
-0.042722806334495544,
-0.057872239500284195,
-0.006406470667570829,
0.03358861431479454,
-0.005599561147391796,
0.05590876191854477,
0.01374161709100008,
-0.06597390025854111,
0.005559305194765329,
-0.03764953836798668,
0.0189433041960001,
0.01822267845273018,
-0.006290351040661335,
-0.006142129190266132,
0.037526778876781464,
0.03346019238233566,
0.051165103912353516,
-0.032925933599472046,
0.02669036202132702,
0.018280550837516785,
0.008724077604711056,
0.016196539625525475,
-0.018845705315470695,
0.0026271918322890997,
0.010271823965013027,
0.014594243839383125,
-0.009152214974164963,
-0.0641825720667839,
0.04713193699717522,
-0.003695318941026926,
0.013582287356257439,
0.0071289329789578915,
0.012648804113268852,
-0.029433755204081535,
-0.005503712687641382,
-0.02645944617688656,
-0.018003586679697037,
0.008801554329693317,
0.006505010183900595,
-0.007559291552752256,
-0.07060038298368454,
0.009865515865385532,
-0.00991091039031744,
0.019028596580028534,
0.003635542932897806,
0.032701510936021805,
-0.02118910290300846,
0.025090321898460388,
0.0012260049115866423,
0.017111986875534058,
0.0031185701955109835,
-0.00878383032977581,
0.021145600825548172,
0.02416909858584404,
-0.009979626163840294,
-0.01126509066671133,
-0.04334809631109238,
0.03572211414575577,
0.02572205662727356,
-0.03006449155509472,
-0.0021008311305195093,
0.02537122741341591,
-0.015633495524525642,
0.004620935767889023,
0.05199894309043884,
0.013444013893604279,
0.031096842139959335,
0.005917375907301903,
-0.008545069955289364,
-0.0014636663254350424,
-0.0666012093424797,
-0.057258762419223785,
0.02627669833600521,
-0.016247985884547234,
0.0034930864349007607,
0.027541903778910637,
0.02370794489979744,
0.01111376192420721,
0.058622196316719055,
0.005693094339221716,
-0.018806571140885353,
-0.006611715070903301,
-0.010108950547873974,
0.0027799331583082676,
-0.01967090182006359,
0.016501471400260925,
-0.009545058943331242,
-0.0048814089968800545,
0.03483881428837776,
0.016426196321845055,
-0.02512022666633129,
-0.011928492225706577,
0.0027133487164974213,
-0.02393193356692791,
-0.007997579872608185,
0.017592012882232666,
-0.0007195368525572121,
0.04857376217842102,
0.05288014933466911,
-0.034873031079769135,
0.030726734548807144,
-0.013612281531095505,
0.003855191869661212,
-0.09803035110235214,
-0.033519864082336426,
-0.013755522668361664,
-0.008496063761413097,
0.02047990821301937,
-0.06111741438508034,
-0.012098697014153004,
0.04007253795862198,
-0.0620669424533844,
0.004011054057627916,
-0.0016127295093610883,
-0.01985541731119156,
-0.05049033835530281,
-0.012952636927366257,
-0.05556275323033333,
0.050711896270513535,
0.02829948253929615,
0.08752341568470001,
0.037035293877124786,
-0.027571460232138634,
-0.024595389142632484,
-0.05752284824848175,
-0.024439986795186996,
0.004889205098152161,
0.02153594046831131,
-0.014650619588792324,
0.08509622514247894,
-0.05267753079533577,
0.010179494507610798,
0.035331785678863525,
-0.04948706924915314,
0.010163815692067146,
-0.027180034667253494,
0.008310502395033836,
0.007183554582297802,
0.03145145997405052,
0.0046985941007733345,
-0.009222305379807949,
0.006804522126913071,
-0.008032376877963543,
0.024325285106897354,
0.011879420839250088,
-0.01781339943408966,
0.023048294708132744,
0.05255555734038353,
-0.00002172009408241138,
-0.030027443543076515,
0.04309716820716858,
-0.0010783432517200708,
-0.023746337741613388,
-0.005379389505833387,
0.03391130268573761,
-0.016513606533408165,
-0.009269557893276215,
0.006770831532776356,
-0.04770850017666817,
0.03289404138922691,
-0.007132003083825111,
-0.007412848528474569,
-0.005010370630770922,
0.0036688034888356924,
-0.014758043922483921,
-0.04774967208504677,
0.011987905018031597,
-0.040740903466939926,
-0.013220054097473621,
-0.04413409158587456,
0.02292547933757305,
0.006675878539681435,
0.02517632208764553,
0.03717520460486412,
-0.06557954102754593,
-0.039435975253582,
0.029987182468175888,
0.012004056014120579,
0.015599329955875874,
0.02823662757873535,
-0.0008683191845193505,
-0.023801134899258614,
-0.041040726006031036,
0.06173349544405937,
-0.03342660889029503,
-0.018547307699918747,
-0.03226223960518837,
-0.052505604922771454,
-0.014753851108253002,
0.018452387303113937,
0.049413058906793594,
0.002008273033425212,
-0.0125289810821414,
0.0004321046872064471,
-0.006550113670527935,
0.015554919838905334,
-0.037342432886362076,
0.0018767347792163491,
-0.0016341580776497722,
-0.03620870038866997,
-0.016228973865509033,
-0.007663619704544544,
-0.038329049944877625,
0.023131532594561577,
0.015342065133154392,
0.0061883945018053055,
0.026613274589180946,
-0.06309107691049576,
-0.027195554226636887,
0.024553563445806503,
-0.01418799813836813,
-0.013408469036221504,
0.03050006553530693,
0.00958943646401167,
0.0033957583364099264,
0.030582567676901817,
-0.013720391318202019,
-0.060688335448503494,
-0.021308232098817825,
-0.03132535144686699,
-0.0006406730972230434,
-0.03764048591256142,
-0.01623919978737831,
0.039964910596609116,
-0.04912577196955681,
0.006712949834764004,
0.023909443989396095,
-0.06457380205392838,
-0.01320294477045536,
0.024583911523222923,
-0.020221557468175888,
0.010894685983657837,
0.0005959465634077787,
0.020913492888212204,
0.047287777066230774,
-0.016652116551995277,
-0.009775150567293167,
0.06226545199751854,
0.037184085696935654,
0.021235845983028412,
0.02379631996154785,
0.031254712492227554,
-0.0024915304966270924,
-0.009906074032187462,
0.007202304434031248,
0.03392144665122032,
-0.040413230657577515,
-0.02383647859096527,
0.04664229601621628,
-0.001234790193848312,
-0.022555548697710037,
0.023326687514781952,
-0.04280721768736839,
0.034539949148893356,
-0.024363793432712555,
-0.008413110859692097,
-0.023254405707120895,
-0.01504142489284277,
-0.005520479753613472,
0.017001623287796974,
0.01840050332248211,
0.05703994259238243,
-0.020970111712813377,
-0.02193460799753666,
0.013301234692335129,
0.0037530965637415648,
0.04324905574321747,
-0.0286564864218235,
0.0003251884481869638,
-0.022358320653438568,
-0.006424341816455126,
-0.0031617083586752415,
-0.03565329685807228,
-0.025379082188010216,
-0.034004032611846924,
0.007134942337870598,
0.019051218405365944,
0.0453660823404789,
-0.03335743397474289,
0.025613555684685707,
-0.039159584790468216,
0.033883895725011826,
-0.05873708799481392,
-0.03529171645641327,
-0.004685910884290934,
0.043606024235486984,
-0.03544209152460098,
0.0021801013499498367
] |
<p>Let's say two objects are sitting adjacent (in contact) to each other. If we start pushing one of them, we know that both the objects move, remaining in contact to each other. But let's now consider imparting an impulse to one of the objects, instead of a steady force. I expect the two objects to start moving, but this time with different velocities, and thus developing a separation between them.</p>
<p>As a test case, let's say that we push the object which has mass $M$, and the other object has mass $m$; where $M > m$.</p>
<p>I expect the smaller mass to move off with a higher velocity.</p>
<p>But I can't find a mathematical description for it.</p>
<p>Assuming that the force is large enough, we have $F dt$ as the impulse on the combination. On the mass $M$, the impulse is $(F-N) dt$, where $N$ is the contact force between the two masses. Also, $N dt$ is the impulse on the object of mass $m$.</p>
<p>How can I calculate the velocities of the two masses, knowing that both the masses were at rest before the impulse.</p> | 1,492 | [
-0.016235949471592903,
-0.0005378176574595273,
-0.03345492482185364,
-0.006051269825547934,
-0.004211043938994408,
-0.02734524942934513,
-0.025355758145451546,
0.008747342973947525,
0.03249295428395271,
-0.02134142629802227,
0.004103279206901789,
0.04409470781683922,
0.051648639142513275,
0.007473267614841461,
0.03225792199373245,
-0.0035961144603788853,
-0.019018005579710007,
-0.014603420160710812,
0.04277556389570236,
-0.03018908202648163,
0.0016506400424987078,
0.0032175134401768446,
0.052427325397729874,
-0.0073467823676764965,
-0.021334834396839142,
0.012854180298745632,
0.008049349300563335,
-0.03615821525454521,
-0.008708848617970943,
0.02967197075486183,
-0.0013681427808478475,
-0.03660120815038681,
-0.024499593302607536,
0.00035877240588888526,
-0.004896815866231918,
0.017221489921212196,
-0.04628367722034454,
-0.022530971094965935,
-0.004133368376642466,
0.006812036037445068,
-0.060516923666000366,
-0.016958927735686302,
-0.01265030074864626,
0.058834586292505264,
-0.013769645243883133,
0.013396166265010834,
0.05046702176332474,
-0.022538311779499054,
0.05735890939831734,
-0.03909272328019142,
0.08673649281263351,
-0.00662234565243125,
0.07726308703422546,
0.02967325784265995,
-0.0003849311324302107,
0.0000017474401374784065,
0.05315432697534561,
0.08966593444347382,
-0.012246917933225632,
-0.020020317286252975,
-0.02532457746565342,
-0.05292635038495064,
-0.027855560183525085,
-0.02794588729739189,
-0.00265938276425004,
0.03292926400899887,
-0.04200854152441025,
-0.013932127505540848,
0.005332717671990395,
-0.008156228810548782,
0.014892916195094585,
-0.011936381459236145,
0.06075041741132736,
-0.034026969224214554,
0.0029773074202239513,
-0.009135599248111248,
0.036484748125076294,
0.013066179119050503,
0.024101298302412033,
0.026680393144488335,
-0.030709262937307358,
0.014437330886721611,
0.04627486318349838,
0.044077761471271515,
0.019409481436014175,
-0.049853600561618805,
0.04810734838247299,
-0.012088860385119915,
0.004653907846659422,
0.0155962398275733,
-0.039563290774822235,
0.0005927245947532356,
0.027374718338251114,
-0.004070247523486614,
0.0073556676506996155,
0.02988538146018982,
0.02343061938881874,
0.021489422768354416,
0.002409891691058874,
-0.03678572177886963,
-0.01967495121061802,
-0.032422930002212524,
0.011295241303741932,
0.08396919071674347,
-0.000833730970043689,
-0.009957633912563324,
-0.03010035678744316,
0.024359015747904778,
-0.008698312565684319,
-0.006081799045205116,
-0.027623817324638367,
0.025417670607566833,
0.0009500269661657512,
0.000729478255379945,
0.00521591491997242,
0.007809826638549566,
-0.023003406822681427,
-0.01976233348250389,
0.03919168934226036,
0.04080275073647499,
0.07285203784704208,
-0.033843666315078735,
0.022573605179786682,
-0.04995520040392876,
-0.03773666173219681,
-0.01453384105116129,
0.03515882045030594,
0.006401700899004936,
-0.002705500926822424,
0.023780396208167076,
0.0070747872814536095,
-0.06551865488290787,
0.0006677773199044168,
0.00935233011841774,
0.016739504411816597,
-0.0030965281184762716,
-0.07300849258899689,
-0.04999130219221115,
0.04660550877451897,
-0.04397711530327797,
-0.008767143823206425,
-0.09983470290899277,
0.005616269074380398,
0.04165137931704521,
0.0564471073448658,
0.04378122836351395,
-0.019049543887376785,
-0.004647776484489441,
0.06316647678613663,
0.015364741906523705,
0.008029102347791195,
-0.047078851610422134,
-0.016974514350295067,
-0.017619647085666656,
0.016761604696512222,
-0.05132476985454559,
0.0226590558886528,
0.03289550170302391,
-0.008117347955703735,
-0.00023292034165933728,
0.04651598632335663,
-0.010976974852383137,
-0.02865825779736042,
0.01859559863805771,
0.05172530189156532,
0.010037519969046116,
0.061530862003564835,
0.024899829179048538,
-0.012264272198081017,
0.0591118298470974,
0.0654737651348114,
0.03243909403681755,
0.041032202541828156,
0.04873894155025482,
0.009015044197440147,
-0.031650569289922714,
-0.042288266122341156,
0.01299232617020607,
-0.01151143666356802,
-0.03235766664147377,
-0.008221718482673168,
-0.07711677253246307,
-0.03351851925253868,
-0.019222570583224297,
0.010890762321650982,
0.01906583271920681,
0.033813267946243286,
0.01877249963581562,
-0.019482342526316643,
-0.02841082215309143,
-0.022249169647693634,
-0.08829408138990402,
0.02483637072145939,
-0.005593505688011646,
0.012541667558252811,
0.015327297151088715,
0.018000705167651176,
0.018965382128953934,
-0.011905035004019737,
-0.008003860712051392,
-0.00958096794784069,
0.008299201726913452,
-0.016160935163497925,
-0.015620645135641098,
0.005542485974729061,
0.053238797932863235,
0.031869616359472275,
0.0109592005610466,
-0.0063352882862091064,
0.008338142186403275,
-0.012018530629575253,
0.024580245837569237,
-0.02599702589213848,
-0.004248784389346838,
0.005993685685098171,
0.023677177727222443,
0.010426037013530731,
-0.03832664340734482,
0.028433965519070625,
0.03927174583077431,
-0.01130008976906538,
0.08838596194982529,
0.07434016466140747,
0.04614454135298729,
-0.015835745260119438,
0.04668519273400307,
0.010241962969303131,
0.006153488531708717,
0.006805554963648319,
-0.056785013526678085,
-0.02746828831732273,
-0.030602991580963135,
0.004476888570934534,
0.02559792436659336,
-0.024490198120474815,
0.028269188478589058,
0.05404426530003548,
0.01783706806600094,
0.02569008059799671,
0.03286844491958618,
-0.02065911702811718,
-0.014502509497106075,
0.04137280955910683,
0.017658518627285957,
0.0026590018533170223,
-0.010812523774802685,
0.005816484801471233,
0.029538339003920555,
0.02108648233115673,
-0.006635767407715321,
-0.015102619305253029,
0.014603568241000175,
-0.009616131894290447,
0.03443877771496773,
-0.012030073441565037,
-0.04631204903125763,
0.020089125260710716,
0.016814934089779854,
0.02378258854150772,
0.028947889804840088,
-0.0014148715417832136,
-0.012264073826372623,
-0.05377449095249176,
0.007965787313878536,
0.025981172919273376,
-0.030032560229301453,
-0.015003527514636517,
-0.00786626897752285,
0.010799048468470573,
-0.05887990817427635,
0.016981547698378563,
0.0030528991483151913,
-0.03456776589155197,
-0.023158114403486252,
-0.026712708175182343,
0.012111435644328594,
0.029077783226966858,
0.025066372007131577,
-0.017966723069548607,
-0.01499145571142435,
-0.005741117522120476,
-0.03109893389046192,
0.0053758337162435055,
-0.0075953034684062,
-0.03464898839592934,
0.03604992851614952,
-0.06195599213242531,
-0.04333259165287018,
0.05032917484641075,
0.028072085231542587,
-0.014763114973902702,
0.003464014967903495,
0.00046559443580918014,
-0.07970740646123886,
-0.009800302796065807,
-0.01684228703379631,
-0.014984664507210255,
-0.017261013388633728,
0.011971543543040752,
0.05639668181538582,
0.015825113281607628,
-0.03870705887675285,
0.006178407464176416,
-0.03995728865265846,
-0.046072352677583694,
-0.03615178167819977,
-0.01159189734607935,
0.010308382101356983,
-0.024469271302223206,
0.021819891408085823,
0.013771976344287395,
0.007963362149894238,
-0.006807807367295027,
-0.05917731299996376,
-0.03748246282339096,
-0.0006647689151577652,
-0.0038775084540247917,
0.07111606001853943,
0.011808386072516441,
-0.043336719274520874,
0.07209663093090057,
-0.0020399726927280426,
-0.007374570704996586,
-0.01300137396901846,
0.0040764776058495045,
0.009781325235962868,
0.003967142663896084,
0.019173605367541313,
0.03335297480225563,
-0.004508371464908123,
0.0038844342343509197,
0.08143854886293411,
-0.011514014564454556,
0.028576930984854698,
-0.008808011189103127,
0.006749120075255632,
-0.008101736195385456,
0.019695080816745758,
0.007205233909189701,
0.016593020409345627,
0.003960177302360535,
-0.026506207883358,
0.03996289521455765,
-0.01929977908730507,
0.045069530606269836,
0.0015446855686604977,
-0.04279110208153725,
0.0390518382191658,
0.01331502478569746,
-0.034409988671541214,
-0.003465455723926425,
0.03334531933069229,
0.019589990377426147,
-0.0073263682425022125,
0.004595219157636166,
0.039470259100198746,
0.04725848510861397,
-0.03814946860074997,
0.015610157512128353,
0.05285583809018135,
0.01652676798403263,
-0.03146664425730705,
-0.02264881320297718,
0.0009057316347025335,
-0.00332736037671566,
0.03423942252993584,
-0.016724178567528725,
0.016282852739095688,
0.0014740834012627602,
-0.007109023630619049,
0.03481022268533707,
-0.004965788684785366,
-0.009902210906147957,
0.032129038125276566,
-0.057905543595552444,
-0.0076684728264808655,
0.03879233077168465,
0.03538314998149872,
-0.006089244969189167,
0.06850097328424454,
0.022115008905529976,
0.02260279282927513,
0.03090202622115612,
-0.009624829515814781,
-0.08159305155277252,
0.016273926943540573,
-0.03068503737449646,
-0.05490051582455635,
-0.020671464502811432,
0.0029612688813358545,
-0.052763160318136215,
0.012432800605893135,
-0.01581644080579281,
-0.019866090267896652,
-0.011209772899746895,
-0.06954599171876907,
0.00184147828258574,
-0.07848601788282394,
-0.059457164257764816,
0.013294252566993237,
-0.004091275855898857,
0.036443714052438736,
-0.03418981283903122,
0.02665354125201702,
0.03571047633886337,
0.0031839823350310326,
-0.0004262686416041106,
-0.04576653987169266,
-0.004608598072081804,
0.00002364835745538585,
0.020133931189775467,
0.00010463401849847287,
0.048474643379449844,
-0.006276661530137062,
0.015575086697936058,
-0.023419279605150223,
0.04076153784990311,
0.03607539087533951,
-0.0368097722530365,
-0.04192766919732094,
-0.062070053070783615,
0.017894357442855835,
-0.011089459992945194,
0.05475626885890961,
0.002508023986592889,
-0.008960324339568615,
0.03754352405667305,
-0.0034300119150429964,
0.007260560058057308,
0.03368478640913963,
0.04644366353750229,
0.01217983104288578,
-0.010534409433603287,
-0.06542956084012985,
0.00640138192102313,
-0.01584641821682453,
-0.008890606462955475,
0.03487556800246239,
-0.011936888098716736,
0.0028666751459240913,
0.031285420060157776,
0.010060509666800499,
0.05006377398967743,
0.005534409079700708,
0.0028337333351373672,
-0.019472697749733925,
0.009398690424859524,
-0.03424340859055519,
-0.02146637998521328,
-0.016599658876657486,
0.029886573553085327,
0.03775288164615631,
0.0003257196513004601,
0.006115123629570007,
-0.08533384650945663,
-0.01560041680932045,
0.01255076564848423,
-0.02272353135049343,
-0.03376716375350952,
0.011969140730798244,
-0.040129486471414566,
-0.025531552731990814,
0.053064148873090744,
-0.02720009535551071,
0.01520141027867794,
-0.02223159745335579,
0.009122716262936592,
0.007475802209228277,
0.016229143366217613,
-0.028607817366719246,
0.02036416530609131,
0.01019182987511158,
-0.010419132187962532,
-0.01509108580648899,
-0.010013232938945293,
-0.00435568718239665,
0.008284476585686207,
0.04025217890739441,
0.06194121018052101,
0.01644141972064972,
-0.013116635382175446,
-0.02609621360898018,
-0.0006510439561679959,
-0.015766579657793045,
-0.05934011936187744,
0.021905306726694107,
-0.008543021976947784,
-0.004437254276126623,
0.006244101095944643,
-0.06963025033473969,
-0.04287193715572357,
0.04600511118769646,
-0.01420619897544384,
-0.006283028516918421,
0.0019053852884098887,
-0.020827464759349823,
0.03020014427602291,
0.02117466926574707,
0.0056589930318295956,
0.04233929142355919,
0.032718442380428314,
-0.0031946906819939613,
-0.03738652169704437,
0.00783807784318924,
0.03279201686382294,
-0.01917663961648941,
-0.012200124561786652,
-0.03395060822367668,
0.03419511020183563,
-0.04373275116086006,
0.07387455552816391,
-0.00925831962376833,
0.03586633503437042,
-0.003252812661230564,
-0.03107006847858429,
-0.01899285800755024,
0.06957626342773438,
0.006791999097913504,
0.024822315201163292,
0.01691269502043724,
0.009446284733712673,
0.014556732028722763,
0.02031106874346733,
0.014894089661538601,
-0.005308033432811499,
0.04567556828260422,
0.019216706976294518,
-0.040539130568504333,
0.045215073972940445,
-0.027640243992209435,
-0.0069943806156516075,
0.018897661939263344,
-0.04272786155343056,
0.04539789259433746,
0.002562051173299551,
0.012625397183001041,
0.03670436516404152,
-0.03855438157916069,
-0.039103008806705475,
0.018493587151169777,
-0.007061384152621031,
0.03261493146419525,
-0.07744886726140976,
0.0027979055885225534,
0.027970461174845695,
0.019230805337429047,
-0.053310882300138474,
-0.051212724298238754,
0.03925107792019844,
-0.012017619796097279,
0.003188330912962556,
-0.057864006608724594,
0.002169232815504074,
-0.008573428727686405,
-0.010949917137622833,
0.01627863198518753,
0.09389819949865341,
0.01968272589147091,
-0.007909493520855904,
0.0010321575682610273,
0.030953584238886833,
0.025878997519612312,
0.017776427790522575,
0.013213337399065495,
-0.014040222391486168,
-0.012961212545633316,
-0.040097177028656006,
0.03858821839094162,
0.04773489013314247,
-0.03945853188633919,
-0.020862683653831482,
-0.017423665151000023,
-0.022306960076093674,
0.016409270465373993,
-0.047316111624240875,
0.03170280158519745,
0.03476926311850548,
0.051268212497234344,
0.014400837011635303,
-0.026130681857466698,
0.04570719227194786,
0.011141532100737095,
-0.01052315253764391,
0.006288070697337389,
0.0033301475923508406,
-0.012677634134888649,
-0.06659277528524399,
0.025780782103538513,
-0.019181974232196808,
-0.010934404097497463,
-0.0334891676902771,
0.04927150532603264,
-0.012042347341775894,
0.022795245051383972,
0.03253161162137985,
0.0230031106621027,
0.04874749854207039,
-0.021845154464244843,
-0.04486241564154625,
0.015619779005646706,
-0.021856503561139107,
-0.040229372680187225,
-0.0169548150151968,
-0.036454640328884125,
-0.01744922250509262,
0.07261738181114197,
-0.064316526055336,
0.0819668173789978,
0.02254149504005909,
-0.01272089034318924,
-0.02087663859128952,
0.0110630439594388,
0.012900229543447495,
-0.013833587989211082,
-0.02147994190454483,
0.0253713708370924,
-0.054655298590660095,
0.020942138507962227,
0.02913711965084076,
0.03540116548538208,
-0.016821907833218575,
-0.008923403918743134,
-0.014104313217103481,
0.013674722984433174,
0.024979442358016968,
-0.02623969316482544,
0.004204967524856329,
0.010846571065485477,
-0.019216803833842278,
0.009001142345368862,
-0.01962488517165184,
-0.026484763249754906,
0.05150236561894417,
0.02329864352941513,
-0.009833903051912785,
-0.03514315187931061,
0.0036516098771244287,
-0.027502065524458885,
0.015329493209719658,
0.01542273722589016,
0.03038693778216839,
0.045531414449214935,
0.03293529152870178,
0.012493242509663105,
0.01779029704630375,
0.024949265643954277,
-0.005210685543715954,
-0.027490952983498573,
-0.04796227440237999,
-0.07074678689241409,
-0.04844849929213524,
0.02087036892771721,
-0.022294171154499054,
-0.026677729561924934,
0.03800390288233757,
-0.021954908967018127,
-0.000957017473410815,
0.020240047946572304,
0.02042342536151409,
-0.033426836133003235,
0.12019190192222595,
-0.0014571024803444743,
-0.008643439039587975,
-0.02476481720805168,
0.02761339396238327,
0.11735883355140686,
0.03478202968835831,
0.021918267011642456,
-0.019442761316895485,
-0.009844244457781315,
0.001593494787812233,
-0.0333460308611393,
-0.045418817549943924,
0.02418450452387333,
0.033556099981069565,
-0.005375090520828962,
0.00012492733367253095,
0.05545400083065033,
0.004963099956512451,
-0.028875429183244705,
0.043133560568094254,
-0.006426140666007996,
-0.015238489024341106,
-0.021769624203443527,
0.00813652016222477,
-0.008467614650726318,
-0.01428566686809063,
-0.01097848266363144,
0.032600075006484985,
0.030781032517552376,
0.005826962646096945,
-0.01671651378273964,
-0.017253335565328598,
0.0361018106341362,
0.0023568752221763134,
-0.02276349812746048,
0.045776162296533585,
0.026771320030093193,
-0.05003565177321434,
-0.010365229099988937,
0.05677511915564537,
0.018420357257127762,
-0.030474500730633736,
0.027531620115041733,
0.017779389396309853,
0.014003230258822441,
0.0281598512083292,
0.015154535882174969,
0.007262108381837606,
-0.05303944647312164,
-0.001640973729081452,
-0.02694593369960785,
0.041091736406087875,
-0.00662422738969326,
0.008801461197435856,
0.00844230130314827,
-0.004379237070679665,
0.005080342758446932,
-0.048525985330343246,
-0.010130191221833229,
0.001456802012398839,
0.024120919406414032,
0.007156602572649717,
0.01294319424778223,
0.004370001144707203,
0.024546870961785316,
0.009123235940933228,
0.003119627246633172,
-0.01985674351453781,
-0.006341060157865286,
0.01637587882578373,
0.01998325064778328,
0.026231423020362854,
0.0025412659160792828,
-0.01769118197262287,
-0.01138799637556076,
-0.03345431759953499,
-0.03941141813993454,
-0.0054784128442406654,
-0.0005378493224270642,
0.0538780651986599,
0.0033048493787646294,
-0.020996568724513054,
-0.026915641501545906,
-0.047151412814855576,
-0.07228711247444153,
0.040902234613895416,
-0.013896208256483078,
-0.05696801841259003,
-0.021295880898833275,
-0.014764227904379368,
0.009590458124876022,
0.04895421862602234,
-0.037042662501335144,
0.014370003715157509,
-0.026537016034126282,
0.037780966609716415,
0.03090054541826248,
0.004629197530448437,
-0.01665559597313404,
0.011337300762534142,
-0.0025804101023823023,
0.015461494214832783,
-0.03337768465280533,
0.03641480579972267,
0.022911321371793747,
-0.010809654369950294,
0.014389334246516228,
0.016891496255993843,
-0.020397597923874855,
0.017510714009404182,
0.02999178133904934,
-0.020063750445842743,
-0.019469672814011574,
0.011916449293494225,
-0.015104183927178383,
-0.028588229790329933,
-0.014881119132041931,
-0.01752483658492565,
-0.015686796978116035,
-0.01945638284087181,
0.02707829885184765,
-0.032323937863111496,
-0.00966687873005867,
-0.044694576412439346,
0.029246214777231216,
-0.031927961856126785,
-0.002230236306786537,
-0.02973838523030281,
-0.0019046610686928034,
-0.015644416213035583,
-0.009188897907733917,
-0.04561339318752289,
0.05158310756087303,
-0.035985350608825684,
0.0034542428329586983,
-0.0064195794984698296,
0.0023008857388049364,
-0.009914043359458447,
0.008915044367313385,
0.04076625034213066,
-0.04230167716741562,
0.029326556250452995,
0.01807234436273575,
-0.019178714603185654,
0.016578126698732376,
-0.04294444993138313,
-0.06619826704263687,
-0.0025973075535148382,
0.0023897893261164427,
0.044313762336969376,
0.018096642568707466,
-0.018148353323340416,
-0.027006253600120544,
0.09865697473287582,
-0.036235056817531586,
-0.03505532816052437,
0.013333548791706562,
-0.030832530930638313,
-0.056436460465192795,
-0.0069046723656356335,
-0.006810201797634363,
-0.0179697684943676,
-0.012461060658097267,
-0.007807087153196335,
-0.0036964057944715023,
-0.0022425223141908646,
-0.020132476463913918,
0.03522666171193123,
0.0161339920014143,
0.04905923828482628,
0.022101594135165215,
-0.002863877220079303,
0.03725991025567055,
0.046099260449409485,
0.00825883261859417,
-0.023161524906754494,
0.03523208573460579,
0.015658346936106682,
-0.106168732047081,
-0.00846402533352375,
-0.008004991337656975,
0.02858830988407135,
0.053852442651987076,
-0.06311406195163727,
0.006702038459479809,
0.014876572415232658,
-0.04073198139667511,
0.028579987585544586,
-0.05748087540268898,
-0.007530651520937681,
0.0022606179118156433,
-0.011776222847402096,
-0.006708143278956413,
0.040207311511039734,
0.023728957399725914,
0.046658072620630264,
0.007072877138853073,
0.0028513255529105663,
-0.03241724148392677,
0.005076891276985407,
-0.00744676124304533,
0.008476904593408108,
0.011893508024513721,
0.029094304889440536,
0.09548856317996979,
0.005640675779432058,
-0.044066186994314194,
0.04018382728099823,
-0.008533556945621967,
-0.020378831773996353,
-0.0010004527866840363,
0.019660357385873795,
-0.005131285171955824,
0.008507753722369671,
-0.004671039991080761,
0.013111794367432594,
-0.0059661236591637135,
0.040823448449373245,
-0.0015634476440027356,
0.005143491085618734,
-0.035852331668138504,
-0.015569927170872688,
0.04916778951883316,
-0.0487205870449543,
-0.02548820711672306,
0.0009801663691177964,
0.003773775650188327,
-0.02305123768746853,
0.01128681842237711,
-0.010453133843839169,
0.035530056804418564,
-0.013021000660955906,
-0.020630331709980965,
-0.01960057206451893,
-0.01612158492207527,
0.04930318892002106,
-0.0312480628490448,
-0.004937469959259033,
0.038861263543367386,
-0.019816303625702858,
0.0030429523903876543,
-0.0074411965906620026,
0.0069805048406124115,
-0.006967305671423674,
-0.09824419766664505,
-0.022918425500392914,
0.01726565510034561,
-0.025452235713601112,
-0.04432728514075279,
-0.04710320383310318,
-0.008676966652274132,
0.04648084565997124,
-0.01548184547573328,
0.01084950566291809,
-0.001219816505908966,
-0.013288340531289577,
-0.014952720142900944,
-0.06022503972053528,
0.015358556061983109,
0.011296475306153297,
-0.041734036058187485,
-0.04064758121967316,
0.0040500229224562645,
0.00470790034160018,
-0.010179526172578335,
0.0663435235619545,
0.010754911229014397,
-0.021682752296328545,
0.014157833531498909,
-0.01103406585752964,
0.022637194022536278,
-0.035094305872917175,
-0.03410191833972931,
-0.006121826358139515,
0.017997732385993004,
0.009877233766019344,
0.004807742778211832,
-0.026011820882558823,
0.034919917583465576,
-0.022908633574843407,
0.0009198545012623072,
-0.01179653499275446,
0.008014940656721592,
-0.04273408651351929,
0.038062985986471176,
0.0166282057762146,
0.01966734044253826,
0.05457897484302521,
-0.017636680975556374,
0.026146743446588516,
-0.010175399482250214,
-0.03138496354222298,
-0.07982607930898666,
0.01739732176065445,
-0.042798206210136414,
-0.03440724313259125,
-0.029405608773231506,
-0.009715123102068901,
-0.019250912591814995,
-0.06661318987607956,
-0.016136931255459785,
0.016027098521590233,
-0.029118357226252556,
0.010760541073977947,
0.008159084245562553,
0.03896629810333252,
0.04895046725869179,
0.011212460696697235,
0.004975269082933664,
0.02280210517346859,
-0.03494184836745262,
0.022726768627762794,
0.01919161155819893,
0.006788518745452166,
-0.013244425877928734,
-0.018303772434592247,
0.04182904213666916,
0.00888892449438572,
0.002001578686758876,
0.0329211987555027,
0.023481864482164383,
0.007113990373909473,
0.0004758775467053056,
-0.02014293149113655,
-0.018082140013575554,
0.003333252388983965,
0.03593204542994499,
-0.035761915147304535,
0.06352052837610245,
-0.0071684615686535835,
0.03126420080661774,
-0.013057498261332512,
0.02077350579202175,
-0.007257010787725449,
0.005566637963056564,
-0.03564788028597832,
0.018800241872668266,
-0.05354311317205429,
-0.0003377164248377085,
-0.004067674744874239,
-0.03925743326544762,
0.01958264410495758,
0.007114829961210489,
0.03109116666018963,
0.001428408082574606,
0.00568119203671813,
-0.008414654061198235,
-0.02431214228272438,
-0.026627948507666588,
-0.020933756604790688,
0.04794366657733917,
0.06668921560049057,
0.02915337309241295,
-0.010132483206689358,
0.01290131825953722,
-0.03409462422132492,
0.04453960061073303,
-0.06619071215391159,
-0.026355041190981865,
-0.018814444541931152,
0.011256774887442589,
0.007532935123890638,
0.0008528020698577166
] |
<p>Apparently (first paragraph of <a href="http://en.wikipedia.org/wiki/Second_harmonic_generation">this article</a>) the lack of <em>inversion symmetry</em> is some crystals allows all sort of nonlinear optic phenomena. </p>
<p>Now. Does anyone know of an intuitive or just physical explanation as to <em>why</em> this is the case?</p>
<p>What does <em>inversion symmetry</em> mean and what is so special about it?</p> | 1,493 | [
-0.05991169437766075,
-0.028315076604485512,
0.02731977589428425,
-0.03934195637702942,
0.048474978655576706,
0.01919255591928959,
-0.03346938267350197,
0.00952826626598835,
-0.016917193308472633,
-0.03151935338973999,
0.04382907599210739,
-0.007776763755828142,
0.054064974188804626,
0.026621825993061066,
0.00693591870367527,
0.016096001490950584,
-0.02985581010580063,
0.004948407877236605,
-0.029144756495952606,
0.0005082304123789072,
-0.03876405581831932,
0.02136538177728653,
-0.03160553425550461,
0.008231532759964466,
-0.0423462837934494,
0.01493937335908413,
0.018210818991065025,
0.02740151807665825,
0.05358121544122696,
0.04116073623299599,
0.008732762187719345,
-0.0016235358780249953,
0.007555300369858742,
0.027157850563526154,
0.017083995044231415,
0.018229838460683823,
-0.010924647562205791,
-0.03980530798435211,
0.02837425470352173,
0.03252788633108139,
0.004708442371338606,
0.014223397709429264,
-0.011995694600045681,
0.03433728590607643,
-0.02227018028497696,
0.023473916575312614,
-0.020579397678375244,
0.01072768960148096,
0.033437494188547134,
-0.07728611677885056,
0.08110605925321579,
0.013261335901916027,
0.0033833335619419813,
0.01721568964421749,
0.00883542187511921,
0.0192802082747221,
0.04287276044487953,
0.06954748928546906,
0.0016447072848677635,
-0.06869915872812271,
-0.012741568498313427,
-0.020996280014514923,
-0.031759489327669144,
-0.02569025754928589,
-0.02878807857632637,
0.03253459557890892,
0.030957723036408424,
-0.013288433663547039,
0.04578448832035065,
0.006284061353653669,
-0.012468497268855572,
-0.003246600041165948,
0.02907460555434227,
-0.01711105741560459,
0.017367403954267502,
-0.02230304293334484,
0.02669561840593815,
0.005070519633591175,
0.005288598593324423,
-0.02574893645942211,
0.018369480967521667,
-0.004544323310256004,
-0.011983105912804604,
0.038764987140893936,
-0.02214820124208927,
-0.008988437242805958,
0.06236543878912926,
-0.012612218037247658,
0.023752007633447647,
0.03101091831922531,
0.005409548059105873,
0.02655312418937683,
0.03223197162151337,
0.012142670340836048,
-0.04951774328947067,
-0.009626194834709167,
0.0012974231503903866,
0.06287737935781479,
-0.0032999191898852587,
-0.00453795725479722,
0.013567909598350525,
-0.016118351370096207,
0.03735422343015671,
0.0749354138970375,
-0.01686144806444645,
-0.05178345367312431,
-0.016225390136241913,
0.03923880681395531,
0.016064433380961418,
0.024951625615358353,
-0.0066728428937494755,
-0.012899458408355713,
0.018536413088440895,
0.013560634106397629,
0.018595250323414803,
0.01300229225307703,
0.007623602636158466,
-0.0024087599013000727,
0.03148718178272247,
0.06864739209413528,
0.0076467255130410194,
-0.014798247255384922,
0.04666627570986748,
-0.033201999962329865,
-0.08689779788255692,
-0.012226232327520847,
0.02253660559654236,
-0.009896405041217804,
-0.01827826350927353,
0.005045619793236256,
0.018812287598848343,
-0.027837704867124557,
-0.003407502779737115,
-0.027001623064279556,
0.034121301025152206,
-0.021207798272371292,
-0.1065642386674881,
-0.07613733410835266,
0.01607443578541279,
0.015021654777228832,
-0.011302819475531578,
-0.0968736857175827,
0.014333298429846764,
0.06710390001535416,
0.09006884694099426,
-0.012626844458281994,
0.03823494911193848,
0.006966114044189453,
0.07935231178998947,
0.03975776210427284,
0.0015933322720229626,
-0.01230478473007679,
0.017015108838677406,
-0.043769147247076035,
0.020061619579792023,
-0.08277308195829391,
0.026652883738279343,
-0.0049311271868646145,
-0.012124109081923962,
-0.03167211636900902,
0.039188235998153687,
-0.009786130860447884,
-0.002143380232155323,
0.014639826491475105,
-0.04176914319396019,
0.0015930323861539364,
0.07345028221607208,
-0.012757423333823681,
-0.0052899871952831745,
0.0367286242544651,
-0.0400388166308403,
0.04595226049423218,
-0.006211736239492893,
0.04664059355854988,
0.0183967687189579,
-0.025093410164117813,
-0.004935166332870722,
-0.00009415055683348328,
-0.004058511462062597,
-0.0029427504632622004,
-0.024067439138889313,
-0.017441853880882263,
0.02428588643670082,
0.028780395165085793,
-0.0003859681310132146,
0.01347985677421093,
-0.029208220541477203,
-0.01995137892663479,
0.03302093967795372,
-0.08450309932231903,
-0.016029486432671547,
-0.0403435193002224,
0.02637985721230507,
0.024887938052415848,
-0.04840636998414993,
0.011931647546589375,
0.04741090163588524,
0.0007277227123267949,
-0.014095570892095566,
0.00035497898352332413,
-0.01169808954000473,
0.012701609171926975,
0.01983948051929474,
-0.01694541797041893,
0.049607373774051666,
0.05137353017926216,
0.012328173965215683,
0.0033372631296515465,
0.02005000412464142,
-0.012950615026056767,
-0.029158225283026695,
0.01412669662386179,
-0.003151704790070653,
0.027364632114768028,
-0.012368896044790745,
-0.01304863952100277,
-0.02022785320878029,
0.026293419301509857,
-0.01082129031419754,
0.04707152768969536,
-0.033610954880714417,
0.03740973025560379,
0.05555213615298271,
0.017366064712405205,
-0.010161133483052254,
0.048727720975875854,
0.013234617188572884,
0.017718316987156868,
0.03489683195948601,
-0.013011432252824306,
-0.05430943891406059,
0.016615005210042,
0.05005991458892822,
0.03676960617303848,
-0.050082918256521225,
0.023315543308854103,
0.005522402469068766,
0.05159760266542435,
0.01984282024204731,
0.026166660711169243,
-0.05250665545463562,
-0.03673873841762543,
0.024327492341399193,
-0.0005695390864275396,
0.023756280541419983,
0.0522841140627861,
0.03445780649781227,
-0.022209715098142624,
-0.005513419397175312,
-0.025443634018301964,
-0.011342358775436878,
0.03037400171160698,
-0.01881137676537037,
0.010145073756575584,
-0.019408583641052246,
-0.01619544066488743,
0.02412242814898491,
-0.011949649080634117,
0.02977566234767437,
0.03420557826757431,
-0.0032329761888831854,
0.005240441765636206,
-0.021360158920288086,
0.007991497404873371,
0.0010404267814010382,
-0.018947623670101166,
-0.031979236751794815,
-0.02437739074230194,
0.030275126919150352,
-0.043118853121995926,
-0.013749731704592705,
-0.01015025656670332,
0.01613122597336769,
-0.05163529887795448,
-0.037421345710754395,
0.022988278418779373,
0.022192418575286865,
0.053106889128685,
-0.02700677514076233,
-0.021807556971907616,
0.004707480315119028,
-0.024381227791309357,
0.0221997182816267,
0.012663115747272968,
-0.033298738300800323,
-0.0017567344475537539,
-0.03363003581762314,
-0.01663893647491932,
0.04084443300962448,
-0.014181410893797874,
0.01138842198997736,
-0.026868188753724098,
-0.016383392736315727,
-0.052408672869205475,
-0.02109052799642086,
-0.02450859546661377,
0.034955162554979324,
-0.0082451356574893,
-0.0015937861753627658,
0.004629122093319893,
-0.031018409878015518,
-0.053367700427770615,
0.008981621824204922,
-0.03038863092660904,
-0.021671684458851814,
-0.004892964847385883,
0.007614951580762863,
0.0032337764278054237,
-0.04098279029130936,
0.0016558676725253463,
0.01542248297482729,
-0.03565167263150215,
0.014757485128939152,
-0.049181804060935974,
-0.03961789980530739,
0.0024719680659472942,
0.01985323429107666,
0.04945511370897293,
-0.006120376288890839,
-0.032985903322696686,
0.09293653070926666,
0.05344998463988304,
-0.016187751665711403,
-0.04096259921789169,
-0.013454378582537174,
0.009960625320672989,
-0.061681799590587616,
0.0370849147439003,
0.04787579923868179,
0.018980475142598152,
0.05264107510447502,
0.0013915124582126737,
0.05033920705318451,
0.03859492391347885,
-0.004990893881767988,
-0.03461962938308716,
-0.007611092645674944,
0.004962544422596693,
0.007406095042824745,
0.005171935074031353,
0.019331475719809532,
-0.03702123463153839,
0.0006042562890797853,
0.00827945675700903,
-0.0042607225477695465,
0.009010165929794312,
-0.046614840626716614,
0.05517461895942688,
-0.010994818061590195,
-0.01188806351274252,
-0.03871404752135277,
0.051192719489336014,
0.0025925389491021633,
0.03845736384391785,
0.0012038913555443287,
0.026751942932605743,
0.0496337004005909,
-0.020082468166947365,
0.0066376943141222,
0.002314880955964327,
0.026838481426239014,
-0.025358207523822784,
0.00030924950260668993,
0.008551524952054024,
-0.00808714795857668,
0.02748025767505169,
0.005380377173423767,
0.0006782901473343372,
0.06960718333721161,
0.02797085978090763,
0.014153423719108105,
0.010746325366199017,
-0.015258253552019596,
-0.011577341705560684,
-0.009773099794983864,
0.04668857902288437,
-0.04973297938704491,
0.054968226701021194,
-0.00984608568251133,
0.06289670616388321,
0.028477290645241737,
0.052399635314941406,
-0.015140559524297714,
0.0009455537656322122,
-0.09429758042097092,
0.0338398776948452,
-0.029619064182043076,
0.01233223732560873,
-0.041295554488897324,
-0.008613753132522106,
-0.014878409914672375,
-0.020067304372787476,
-0.04843401163816452,
-0.03143176808953285,
0.010357224382460117,
-0.04152308404445648,
-0.016726016998291016,
-0.0038617050740867853,
0.002123407553881407,
-0.006462707184255123,
0.010829958133399487,
-0.017033403739333153,
-0.041678719222545624,
-0.013864293694496155,
0.022941354662179947,
-0.038243383169174194,
0.004623462446033955,
-0.005443928763270378,
0.024371465668082237,
0.035428486764431,
0.023315928876399994,
0.0048692128621041775,
0.0445939302444458,
-0.016485165804624557,
-0.025809744372963905,
-0.007386023178696632,
0.05611364170908928,
0.002484273398295045,
0.03107774816453457,
-0.01538905594497919,
-0.01605755276978016,
-0.02038896083831787,
-0.004494653549045324,
0.06599783897399902,
0.0005762109067291021,
0.01690036617219448,
0.017705002799630165,
0.019713938236236572,
-0.03789568319916725,
0.030344892293214798,
-0.01398403849452734,
0.03276722505688667,
-0.021267496049404144,
-0.056683726608753204,
-0.02630256861448288,
-0.04869263246655464,
-0.022706078365445137,
0.027416381984949112,
-0.009896515868604183,
-0.015178290195763111,
0.006052177865058184,
0.024342147633433342,
-0.0016186076682060957,
0.01469104178249836,
-0.00006515247514471412,
-0.0006103389896452427,
0.013983250595629215,
0.0214121975004673,
0.019960619509220123,
-0.024061735719442368,
0.04982423037290573,
0.07490913569927216,
0.029207149520516396,
0.0027361372485756874,
-0.07969162613153458,
0.021187013015151024,
0.04395907372236252,
-0.013001709245145321,
-0.010803892277181149,
-0.006703998427838087,
-0.05823379382491112,
-0.03422711044549942,
-0.007478888612240553,
0.0025701099075376987,
0.0631934329867363,
-0.0211145281791687,
-0.015317440964281559,
-0.028436794877052307,
-0.008515344932675362,
0.013364189304411411,
0.007189587689936161,
0.02597382292151451,
0.021940594539046288,
-0.026773087680339813,
0.0038005465175956488,
-0.010683994740247726,
0.024544401094317436,
0.006510527338832617,
0.04616684094071388,
-0.026669062674045563,
0.01480480283498764,
-0.0005756712635047734,
0.03426714241504669,
-0.03728727251291275,
-0.055488165467977524,
-0.006643134634941816,
0.0026068680454045534,
-0.0014566100435331464,
0.06175084039568901,
-0.038493454456329346,
-0.064635269343853,
-0.0004527876735664904,
0.037774089723825455,
0.01732274703681469,
-0.015213116072118282,
-0.00026091496692970395,
0.002529704477638006,
0.033944014459848404,
0.00866776704788208,
0.04602479562163353,
0.011292879469692707,
-0.05257086828351021,
-0.009196637198328972,
-0.01568383164703846,
0.036404140293598175,
-0.04140105098485947,
-0.001488125417381525,
-0.018369242548942566,
0.01135431881994009,
-0.052369385957717896,
0.08250807225704193,
-0.013049013912677765,
0.023375460878014565,
0.030204396694898605,
-0.020791489630937576,
0.0021691909059882164,
0.03688083589076996,
0.010465887375175953,
-0.01447275374084711,
-0.022955432534217834,
0.05121378228068352,
0.014230824075639248,
-0.02386164292693138,
0.04398571327328682,
0.0037826497573405504,
-0.009365372359752655,
0.06060614809393883,
0.025984972715377808,
0.02560550346970558,
-0.040297240018844604,
-0.033734507858753204,
0.0035925181582570076,
-0.03285614028573036,
0.0393453985452652,
-0.018470261245965958,
0.004835112951695919,
0.04238583892583847,
-0.06034465506672859,
-0.009901734068989754,
0.02015550062060356,
-0.030393218621611595,
0.009123831056058407,
-0.041504282504320145,
0.05373527854681015,
0.03045952506363392,
0.009325781837105751,
-0.07636597752571106,
-0.07081376016139984,
0.010076062753796577,
-0.012388169765472412,
-0.06085379421710968,
-0.0104969572275877,
-0.009473727084696293,
0.01610514521598816,
-0.04705768823623657,
0.0392022542655468,
0.034234076738357544,
-0.010920433327555656,
-0.004835077561438084,
0.008597726002335548,
0.0024840771220624447,
0.0297385361045599,
-0.02039664424955845,
-0.06447573006153107,
0.02624499425292015,
-0.031036391854286194,
0.02577645145356655,
0.012283122166991234,
0.048088617622852325,
-0.01068462897092104,
-0.020684631541371346,
-0.03340306878089905,
0.014293511398136616,
0.013406086713075638,
0.0007131377351470292,
-0.01601557992398739,
0.01366046629846096,
0.014981565065681934,
-0.004557318054139614,
-0.042607422918081284,
-0.0053194141946733,
-0.02339688502252102,
0.03658183291554451,
-0.022532837465405464,
-0.012076658196747303,
-0.028933342546224594,
-0.018098756670951843,
0.011742067523300648,
0.02410571090877056,
0.005123117472976446,
0.00520526897162199,
0.09938018023967743,
-0.01977895386517048,
-0.0012295185588300228,
0.0030493519734591246,
-0.024959683418273926,
0.009503944776952267,
0.013670925050973892,
0.011881403625011444,
-0.014896070584654808,
0.0342128612101078,
-0.0368795283138752,
-0.03132908046245575,
-0.002524555427953601,
0.029127206653356552,
0.0871828943490982,
-0.041771747171878815,
0.0646139532327652,
0.037184249609708786,
-0.00686267577111721,
-0.011638343334197998,
-0.025683332234621048,
0.02792842872440815,
0.005963672883808613,
0.016753651201725006,
0.02246532216668129,
-0.02465331181883812,
-0.007562878541648388,
0.023000426590442657,
0.05936838686466217,
-0.005510939285159111,
0.022093383595347404,
0.042455900460481644,
0.050529081374406815,
-0.012584002688527107,
-0.025730473920702934,
-0.062233101576566696,
0.06058928743004799,
-0.06279896944761276,
0.05293305218219757,
0.036770422011613846,
-0.004584276583045721,
0.012932675890624523,
-0.04755239933729172,
0.02762657403945923,
-0.03449137508869171,
-0.020382951945066452,
-0.017456579953432083,
-0.0019869774114340544,
-0.010206218808889389,
0.014812717214226723,
-0.016263145953416824,
-0.013385103084146976,
0.00916720274835825,
0.011006292887032032,
0.017108526080846786,
0.006896976847201586,
-0.08133482933044434,
-0.041227519512176514,
-0.006892521865665913,
-0.03821338340640068,
0.012645430862903595,
0.0007653430220670998,
-0.008873133920133114,
0.006809118203818798,
-0.04393545538187027,
0.024061257019639015,
0.003517142264172435,
0.03690377250313759,
-0.008462483994662762,
0.03920600935816765,
0.016582874581217766,
0.06397870182991028,
0.0021159471943974495,
-0.01137395016849041,
0.10522007197141647,
0.036862023174762726,
-0.0008763939840719104,
-0.06740356236696243,
0.054881975054740906,
-0.023609019815921783,
0.027403004467487335,
-0.010977840051054955,
0.02089245244860649,
-0.02558748424053192,
0.03806105628609657,
-0.005367814097553492,
0.06643741577863693,
-0.006856643129140139,
-0.008528049103915691,
0.026938647031784058,
-0.05684966593980789,
-0.02030569314956665,
0.019983984529972076,
0.00434080371633172,
-0.011744002811610699,
-0.009656542912125587,
-0.01946371980011463,
0.006811538711190224,
-0.02482832781970501,
-0.030467920005321503,
-0.02631094679236412,
-0.05658211186528206,
-0.0027055456303060055,
0.020184287801384926,
-0.013928606174886227,
-0.0002176318084821105,
0.027661528438329697,
-0.01748153194785118,
-0.062081385403871536,
0.00744064524769783,
-0.020056849345564842,
-0.01959387958049774,
0.013163518160581589,
0.011806471273303032,
0.012073968537151814,
-0.007815026678144932,
0.03492928668856621,
0.022280151024460793,
-0.04033972695469856,
0.012192838825285435,
-0.0004611861950252205,
0.01549600437283516,
-0.03239991143345833,
-0.019653353840112686,
-0.028400249779224396,
-0.026225417852401733,
-0.0016024743672460318,
-0.0569748654961586,
-0.03437894210219383,
-0.0032314287964254618,
0.004294423386454582,
-0.0026469931472092867,
-0.02239062264561653,
-0.011589638888835907,
-0.01910429634153843,
0.0035953884944319725,
0.013792078010737896,
-0.04357179254293442,
-0.01564582623541355,
-0.010606570169329643,
0.012182317674160004,
0.005332676228135824,
-0.009810478426516056,
-0.034954581409692764,
-0.04675547778606415,
-0.00805296003818512,
-0.037937890738248825,
-0.026062428951263428,
0.0036060072015970945,
0.016225004568696022,
0.03994081914424896,
0.0014619899448007345,
-0.061845384538173676,
-0.013503559865057468,
-0.053155265748500824,
0.00873198639601469,
0.002453011926263571,
-0.0138626117259264,
-0.01180628128349781,
0.02439533919095993,
0.04433561488986015,
0.019014665856957436,
-0.03922789916396141,
0.0360284298658371,
0.003938422072678804,
-0.019013099372386932,
0.009496569633483887,
-0.014866042882204056,
-0.04466529190540314,
0.019974077120423317,
0.014020692557096481,
0.004134124144911766,
0.015979360789060593,
-0.01523137092590332,
0.025810634717345238,
0.008513178676366806,
0.0353906974196434,
0.0262136273086071,
-0.033084332942962646,
-0.007414978463202715,
0.018470391631126404,
-0.021011661738157272,
0.041157275438308716,
0.016966326162219048,
0.0059095388278365135,
-0.02391495183110237,
-0.058901455253362656,
-0.011653656139969826,
-0.010361937806010246,
0.03946534916758537,
0.0360734760761261,
0.010376141406595707,
-0.02390637807548046,
-0.016495417803525925,
0.02971961535513401,
-0.02557186409831047,
-0.03429300710558891,
-0.0214640274643898,
0.0007257310207933187,
-0.033145517110824585,
0.009160904213786125,
-0.014001546427607536,
0.02127186581492424,
-0.007026616018265486,
-0.024358198046684265,
0.037415679544210434,
0.05927995964884758,
0.004019557032734156,
0.03207667917013168,
0.025420255959033966,
-0.004498718772083521,
0.014685150235891342,
-0.012195904739201069,
-0.04280415549874306,
0.019054841250181198,
-0.047712087631225586,
-0.04018029943108559,
0.02096930705010891,
0.002553253434598446,
-0.013154157437384129,
-0.00007738896238151938,
0.003422851674258709,
-0.03338708356022835,
0.046111878007650375,
-0.016741594299674034,
-0.007048281375318766,
-0.005089884623885155,
-0.010370450094342232,
0.01072964258491993,
-0.03683893755078316,
-0.04079289361834526,
-0.049382615834474564,
-0.006918391678482294,
0.029175633564591408,
0.013007678091526031,
0.0005876771174371243,
-0.05383630469441414,
0.01320906076580286,
-0.011794268153607845,
0.019219553098082542,
0.01009973045438528,
0.018500085920095444,
0.035854365676641464,
0.03372824192047119,
-0.011844792403280735,
0.059989310801029205,
0.009610168635845184,
0.0014886363642290235,
-0.09932871907949448,
-0.0016417333390563726,
0.019083183258771896,
-0.005443574395030737,
0.04279978200793266,
-0.0654166117310524,
0.046884339302778244,
0.009008143097162247,
-0.08899922668933868,
0.029330167919397354,
-0.012925773859024048,
-0.04485881328582764,
-0.0317758172750473,
0.00035205372842028737,
-0.02314678579568863,
0.03268961235880852,
0.023057693615555763,
0.032482318580150604,
0.038950007408857346,
0.00008570367936044931,
-0.02441534213721752,
0.01632937230169773,
-0.013895093463361263,
0.03092353604733944,
0.014166653156280518,
0.008871274068951607,
0.0508171021938324,
0.012313670478761196,
-0.033835530281066895,
0.005232473369687796,
-0.031493548303842545,
0.004434810485690832,
0.035479702055454254,
0.019252022728323936,
-0.025366023182868958,
0.04938522353768349,
-0.009110591374337673,
-0.02239777334034443,
-0.05155835300683975,
0.018690261989831924,
0.04819506034255028,
0.02782714180648327,
0.026420770213007927,
-0.01880100928246975,
0.010038644075393677,
-0.03250979259610176,
0.018906239420175552,
0.016212711110711098,
-0.023444460704922676,
0.010001245886087418,
0.011414851061999798,
0.004664657171815634,
0.035756759345531464,
-0.014498481526970863,
0.023987343534827232,
-0.06861729174852371,
-0.039407577365636826,
-0.024261102080345154,
0.020921867340803146,
0.012453826144337654,
0.049339327961206436,
-0.031204402446746826,
-0.057560503482818604,
0.04703449830412865,
0.010343864560127258,
-0.016811534762382507,
-0.06127988174557686,
-0.012144175358116627,
0.02032484859228134,
-0.02657250501215458,
0.032203782349824905,
-0.020874986425042152,
-0.05182310938835144,
0.06395137310028076,
0.01908782683312893,
0.04101387783885002,
-0.003879181109368801,
-0.08107789605855942,
-0.02008686773478985,
-0.05839516595005989,
0.03669409826397896,
0.0040818084962666035,
-0.009014359675347805,
-0.01109491940587759,
0.002821392612531781,
0.000019572202290873975,
0.02205592393875122,
0.034539844840765,
-0.02417374588549137,
-0.007888050749897957,
0.003830790752544999,
0.00553250964730978,
0.025735681876540184,
-0.011135216802358627,
-0.020291758701205254,
0.010897841304540634,
-0.014950495213270187,
-0.017619146034121513,
-0.019836729392409325,
-0.05351842939853668,
0.013967224396765232,
0.005684495437890291,
-0.0336730070412159,
0.03561489284038544,
0.009116069413721561,
-0.03254813328385353,
0.0702158510684967,
-0.01452395785599947,
-0.056874047964811325,
0.0572710819542408,
-0.00958931539207697,
-0.025056639686226845,
0.019303441047668457,
-0.00867443811148405,
-0.06049912050366402,
0.019080117344856262,
-0.030851885676383972,
-0.0013586056884378195,
-0.017726076766848564,
-0.018678994849324226,
0.061242882162332535,
-0.002270955592393875,
0.006457690615206957,
0.01927691511809826,
-0.020762020722031593,
-0.006932158954441547,
0.03633926063776016,
0.00045499057159759104,
0.02513968199491501,
-0.008572316728532314,
0.01340657938271761,
-0.011611148715019226,
0.009246179834008217,
0.003233247669413686,
0.047752317041158676,
-0.022037098184227943,
0.028460539877414703,
0.023744994774460793,
0.027852537110447884,
0.01349675003439188,
0.0026625983882695436,
0.021168077364563942,
0.03116983361542225,
-0.058421745896339417,
-0.004032977856695652,
0.035741496831178665,
-0.007242580410093069,
0.03586626425385475,
0.02741367369890213,
-0.016195205971598625,
0.06422562152147293,
-0.022266807034611702,
0.021442892029881477,
-0.02681684121489525,
0.031204387545585632,
-0.021954726427793503,
-0.030501162633299828,
0.03432656452059746,
0.03288915008306503,
0.009249001741409302,
-0.004941262770444155,
-0.02016538381576538,
0.01671309396624565,
0.025567198172211647,
-0.055619824677705765,
0.01953897997736931,
0.0036415064241737127,
-0.03240473195910454,
0.018246393650770187,
-0.015818703919649124,
-0.02350357361137867,
-0.006611870601773262,
0.011607038788497448,
0.022037938237190247,
0.004244263283908367,
0.0316753126680851,
-0.006454345304518938,
-0.0301830917596817,
0.02754591405391693,
-0.062003206461668015,
-0.024413377046585083,
-0.015595367178320885,
-0.008731040172278881,
-0.06328051537275314,
-0.02303076721727848
] |
<p>How do <a href="http://simple.wikipedia.org/wiki/String_theory" rel="nofollow">strings</a> present in particles give mass to them? Is it only by vibrating? I have been trying to find the answer but could not find it anywhere, can this question be answered?</p> | 1,494 | [
-0.001132671139203012,
-0.02902989834547043,
-0.005148628260940313,
-0.07456153631210327,
-0.004781775642186403,
0.03183765709400177,
-0.0415494330227375,
-0.01807641051709652,
0.008152936585247517,
-0.03375346586108208,
0.0029646814800798893,
0.02483603172004223,
0.025076409801840782,
0.01345096342265606,
0.009147107601165771,
0.02448183484375477,
-0.0001405501097906381,
-0.019818708300590515,
-0.025059984996914864,
-0.01694345474243164,
-0.018144557252526283,
0.011320481076836586,
0.005592765286564827,
0.006226377096027136,
-0.006464925594627857,
0.00857299193739891,
0.04168145731091499,
0.03507561609148979,
0.021508704870939255,
0.041219595819711685,
0.010198925621807575,
-0.01109297201037407,
0.01013022381812334,
0.012710589915513992,
0.009064361453056335,
-0.02306186594069004,
-0.026932040229439735,
0.0011367442784830928,
0.011334314942359924,
0.014966154471039772,
-0.032009247690439224,
-0.014437430538237095,
-0.015062026679515839,
0.042377885431051254,
-0.017815886065363884,
0.0032183194998651743,
-0.0005882462719455361,
0.0022356172557920218,
0.06773103028535843,
-0.08628048747777939,
0.08027514815330505,
0.00969238206744194,
0.016971593722701073,
0.015079507604241371,
-0.006722616031765938,
-0.0164193008095026,
0.0695226639509201,
0.04702037200331688,
-0.037222154438495636,
-0.06678378582000732,
-0.022923126816749573,
0.00941459834575653,
0.0005058174720034003,
-0.05103306472301483,
-0.023591764271259308,
0.0443267822265625,
-0.021501027047634125,
0.01926952786743641,
0.06397691369056702,
0.022976955398917198,
-0.004078633617609739,
0.0004603797278832644,
0.05206918716430664,
0.007020560558885336,
-0.0008927882881835103,
-0.019719744101166725,
0.05018951743841171,
0.0011864211410284042,
0.04033936560153961,
0.056132324039936066,
-0.013753318227827549,
0.0010354070691391826,
0.031911700963974,
0.03552746772766113,
0.003994301427155733,
-0.039698582142591476,
0.08685813844203949,
-0.007420399226248264,
0.014212382957339287,
0.057154566049575806,
-0.009859077632427216,
-0.01915978640317917,
0.03929034620523453,
-0.00722460076212883,
0.007208886090666056,
0.019638247787952423,
0.00906659197062254,
0.04893653467297554,
0.023929951712489128,
-0.017909813672304153,
0.028603598475456238,
-0.004532999824732542,
0.06014454737305641,
0.06726768612861633,
-0.014826459810137749,
-0.027032965794205666,
-0.019441571086645126,
0.01982530951499939,
-0.04883178323507309,
-0.0048326291143894196,
-0.0500197671353817,
0.009089497849345207,
-0.011048979125916958,
-0.04223861172795296,
0.03713153302669525,
-0.02049051597714424,
0.012073442339897156,
-0.01161262672394514,
0.049121834337711334,
0.056571729481220245,
0.03292418643832207,
-0.0567593090236187,
0.014318102039396763,
-0.02030208148062229,
-0.027439836412668228,
-0.012079472653567791,
0.010617095045745373,
-0.00014043883129488677,
-0.021896984428167343,
0.045451417565345764,
-0.00695990351960063,
-0.032815270125865936,
0.027383815497159958,
0.0013313745148479939,
0.04907122999429703,
-0.0005726636154577136,
-0.11159609258174896,
-0.038978759199380875,
0.07721006870269775,
-0.01902424730360508,
-0.013889250345528126,
-0.06896892935037613,
-0.009589903987944126,
0.03551480174064636,
0.06221869960427284,
0.02310962602496147,
0.0001922954252222553,
0.02832387201488018,
0.037183571606874466,
0.01169451791793108,
0.00036865912261419,
-0.046897612512111664,
0.008429338224232197,
-0.027945250272750854,
0.018082020804286003,
-0.03410571813583374,
0.03050881251692772,
0.03191479668021202,
-0.012858206406235695,
-0.020659536123275757,
0.06749623268842697,
-0.018572386354207993,
0.007854340597987175,
0.03134949132800102,
-0.005058514419943094,
-0.03969186171889305,
0.03638947755098343,
0.031837910413742065,
-0.04666342958807945,
0.034767474979162216,
-0.013168124482035637,
0.0053374129347503185,
0.033503029495477676,
0.030778640881180763,
-0.006780443247407675,
-0.03685535490512848,
-0.06529426574707031,
-0.016363579779863358,
0.028698083013296127,
-0.0023673782125115395,
-0.047109633684158325,
-0.03358554095029831,
-0.012769554741680622,
0.021213822066783905,
-0.012161670252680779,
0.030636336654424667,
-0.003976076375693083,
-0.01245795376598835,
-0.03690599277615547,
-0.035112857818603516,
-0.010188386775553226,
-0.05895819887518883,
0.028114521875977516,
-0.028383761644363403,
-0.011035316623747349,
-0.0002327577822143212,
0.021251758560538292,
-0.01575002446770668,
-0.04461833834648132,
-0.004760848358273506,
-0.017765602096915245,
0.040826816111803055,
-0.014079653657972813,
-0.010364674031734467,
-0.0029440121725201607,
0.05878986418247223,
0.05029386281967163,
-0.006559598259627819,
0.016638990491628647,
-0.003500749124214053,
-0.013172135688364506,
0.007194047328084707,
-0.011292124167084694,
0.006785457022488117,
-0.030239954590797424,
-0.0191941037774086,
0.015748074278235435,
-0.046771351248025894,
-0.019269051030278206,
0.067130908370018,
-0.014665915630757809,
0.10359383374452591,
0.0384267121553421,
-0.004808575380593538,
0.009423444978892803,
0.03003733418881893,
-0.004861559718847275,
0.02650662139058113,
-0.015868913382291794,
-0.0520012341439724,
-0.06961522996425629,
-0.015404910780489445,
0.03505712002515793,
0.027044175192713737,
-0.02902277000248432,
0.022326886653900146,
0.017710160464048386,
0.024574531242251396,
0.009428356774151325,
0.0245206356048584,
-0.0406656414270401,
-0.029976999387145042,
0.013976874761283398,
0.022006385028362274,
-0.009326493367552757,
0.02508019283413887,
0.023260463029146194,
0.027612904086709023,
0.010424231179058552,
-0.0009602619102224708,
-0.007974998094141483,
0.040375396609306335,
-0.009478566236793995,
0.014239338226616383,
0.018757089972496033,
-0.05221187323331833,
0.03919510915875435,
-0.027869250625371933,
0.029593516141176224,
0.002216263208538294,
0.00045730266720056534,
-0.002467934973537922,
0.007306452374905348,
-0.009061974473297596,
-0.004324078094214201,
0.001350525300949812,
-0.004627489484846592,
-0.009098839946091175,
0.0015566234942525625,
-0.0553039014339447,
0.01419178955256939,
0.0013156688073650002,
-0.014036502689123154,
-0.0018909428035840392,
0.018383510410785675,
0.03792053461074829,
0.022279998287558556,
0.0440821535885334,
-0.04945923388004303,
-0.03684554994106293,
0.01721687987446785,
-0.06817015260457993,
-0.024962030351161957,
0.015831582248210907,
-0.03242528438568115,
0.03547540307044983,
-0.0491388775408268,
-0.028115645051002502,
0.03315596282482147,
-0.021415404975414276,
0.029902154579758644,
0.002876091515645385,
-0.004177689552307129,
-0.01865897700190544,
-0.012230676598846912,
-0.028449269011616707,
0.01665283925831318,
-0.019106155261397362,
0.05562465265393257,
0.02299404889345169,
0.022414986044168472,
-0.01922256126999855,
0.007921240292489529,
-0.04835275560617447,
-0.05228601023554802,
0.004338557366281748,
-0.0057215457782149315,
0.01619245857000351,
-0.03540082648396492,
0.03704937547445297,
0.010158111341297626,
-0.04002794995903969,
0.022546865046024323,
-0.03234654664993286,
-0.01978992484509945,
0.0415746346116066,
-0.016525212675333023,
0.03458099067211151,
0.01795021817088127,
-0.07984106242656708,
0.07059968262910843,
0.016385504975914955,
-0.06467726826667786,
0.0004762155294883996,
-0.03065773844718933,
-0.008994217030704021,
-0.028668122366070747,
0.03691722825169563,
0.04138362780213356,
-0.011642182245850563,
0.011111369356513023,
0.10470833629369736,
0.014673935249447823,
0.025046387687325478,
0.002680636942386627,
-0.024184390902519226,
-0.02994939312338829,
-0.003296398790553212,
-0.012511496432125568,
0.03318600729107857,
-0.008037986233830452,
-0.030189480632543564,
0.001544855535030365,
0.01887219212949276,
0.03363567590713501,
-0.019248057156801224,
-0.021878084167838097,
0.054537974298000336,
0.041027989238500595,
0.009982354007661343,
-0.024090705439448357,
0.028405094519257545,
-0.008430315181612968,
-0.017369389533996582,
0.027118781581521034,
-0.014448699541389942,
0.02592642232775688,
-0.0020237260032445192,
-0.006586677394807339,
-0.0009507037466391921,
0.05635913088917732,
-0.01931813172996044,
-0.024301627650856972,
-0.005608406849205494,
-0.0059110368601977825,
0.018313312903046608,
-0.025391800329089165,
-0.0379415787756443,
0.03454631194472313,
0.0521710179746151,
0.04955587908625603,
-0.009919261559844017,
-0.05383467674255371,
0.0010408806847408414,
-0.050213612616062164,
0.01013625506311655,
-0.010833966545760632,
0.0267366673797369,
-0.008501301519572735,
0.08303127437829971,
0.013136274181306362,
0.030940204858779907,
0.01793295331299305,
-0.03037603572010994,
-0.08987454324960709,
0.03210272267460823,
-0.06071342155337334,
-0.004080064594745636,
-0.017583979293704033,
-0.013640547171235085,
-0.03606652095913887,
-0.002811610698699951,
-0.022033290937542915,
-0.036407459527254105,
-0.023829221725463867,
-0.06518969684839249,
-0.01637468859553337,
-0.06013843044638634,
-0.032328151166439056,
-0.018324507400393486,
0.01164514385163784,
0.03710899502038956,
-0.0315607488155365,
0.011635406874120235,
0.03829024359583855,
-0.02850971184670925,
0.021625563502311707,
-0.026266878470778465,
0.0006977226585149765,
0.007053290493786335,
-0.004287055227905512,
0.049065522849559784,
0.017548467963933945,
-0.028081752359867096,
0.019630085676908493,
-0.003939769230782986,
0.04499586671590805,
0.022077666595578194,
-0.02812979370355606,
-0.011280970647931099,
-0.03369365632534027,
0.010538977570831776,
-0.009550115093588829,
0.03623495250940323,
-0.014985022135078907,
-0.006782029755413532,
0.047440432012081146,
-0.02068432606756687,
-0.01798948086798191,
0.07608065754175186,
0.033787794411182404,
0.030305931344628334,
-0.017934828996658325,
-0.05463006719946861,
0.009445308707654476,
-0.0227865818887949,
-0.01580844633281231,
0.026387838646769524,
0.0036598604638129473,
-0.022273436188697815,
0.02151516079902649,
0.016562890261411667,
0.01310593169182539,
-0.002830187091603875,
-0.018811272457242012,
-0.015747560188174248,
0.028889205306768417,
-0.03899629786610603,
-0.0021556622814387083,
0.006130221299827099,
0.022839203476905823,
0.027732983231544495,
-0.0016358745051547885,
-0.03163567930459976,
-0.07497294247150421,
-0.015200112015008926,
0.006724063772708178,
0.03261275216937065,
-0.025516364723443985,
0.00486283004283905,
-0.03181334212422371,
-0.011000740341842175,
0.029638631269335747,
-0.034366004168987274,
0.012976398691534996,
-0.024860886856913567,
0.02598145790398121,
-0.016825461760163307,
0.014773024246096611,
0.01779336854815483,
0.03238466754555702,
-0.02299528755247593,
0.01651838980615139,
-0.018062693998217583,
-0.02110891416668892,
-0.0367228128015995,
0.046916913241147995,
0.01354913879185915,
0.03356506675481796,
0.016114328056573868,
0.023928958922624588,
0.019665654748678207,
0.0216346587985754,
-0.029346389696002007,
-0.08712572604417801,
0.008102179504930973,
0.0050260452553629875,
-0.017263110727071762,
0.007858023047447205,
-0.026113756000995636,
-0.06171902269124985,
-0.005671657156199217,
0.011837534606456757,
-0.018354689702391624,
-0.023470323532819748,
-0.046969223767519,
-0.004951806738972664,
0.028056051582098007,
-0.002056616125628352,
0.04604310169816017,
0.0407906249165535,
-0.045423369854688644,
-0.03491649404168129,
-0.011982724070549011,
0.03666987270116806,
-0.039325207471847534,
-0.004950488917529583,
-0.012623845599591732,
0.005691522266715765,
-0.04192717745900154,
0.029142089188098907,
0.02954740822315216,
-0.014172578230500221,
-0.02076132409274578,
-0.04284309223294258,
-0.0360429547727108,
0.020664429292082787,
0.008968673646450043,
-0.004547207150608301,
-0.021868392825126648,
0.03847506642341614,
0.005897395312786102,
-0.030626466497778893,
0.023885514587163925,
0.02470375783741474,
-0.004268461838364601,
0.00798937026411295,
0.0019965902902185917,
0.03994683548808098,
-0.017426202073693275,
-0.016125736758112907,
0.036453407257795334,
-0.05833466723561287,
0.07078705728054047,
-0.015405585989356041,
-0.014109933748841286,
0.008256856352090836,
-0.08684396743774414,
-0.062399640679359436,
-0.037705861032009125,
-0.004863300826400518,
0.028011474758386612,
-0.03464294970035553,
0.050542883574962616,
0.008569955825805664,
0.009110820479691029,
-0.03768351674079895,
-0.057573989033699036,
0.0286027193069458,
0.017917450517416,
0.001438066945411265,
-0.0017414288595318794,
0.03437225520610809,
-0.025820530951023102,
-0.020465416833758354,
-0.002334961900487542,
0.016106700524687767,
-0.04500814527273178,
0.00854252278804779,
0.026931416243314743,
0.0048681297339499,
0.05063921585679054,
0.01981365866959095,
-0.05114137753844261,
0.010796410962939262,
-0.00564955361187458,
0.00101250980515033,
-0.014159675687551498,
0.06194476783275604,
-0.008283133618533611,
-0.052743855863809586,
0.00417517963796854,
0.005204026587307453,
0.04423168674111366,
-0.011989975348114967,
0.01726345531642437,
0.038359664380550385,
0.07087749987840652,
0.0008900358807295561,
-0.02924771048128605,
0.03752783313393593,
0.0040719532407820225,
0.030113261193037033,
-0.0037423374596983194,
0.02215120568871498,
-0.029721682891249657,
-0.009869839064776897,
0.0441448800265789,
-0.008907144889235497,
0.027266105636954308,
0.00763470446690917,
0.04347245395183563,
0.003254394745454192,
-0.021271880716085434,
0.016890257596969604,
-0.015475098975002766,
0.008605827577412128,
0.004055280704051256,
-0.0018711178563535213,
-0.013347181491553783,
0.008067332208156586,
0.007461243774741888,
-0.03206819295883179,
-0.021144529804587364,
0.007951957173645496,
0.05265484377741814,
0.000577586586587131,
0.06538113951683044,
0.029975662007927895,
-0.024564780294895172,
0.005139918532222509,
-0.006761041469871998,
-0.020899241790175438,
-0.024780884385108948,
0.009974728338420391,
-0.00019338626589160413,
-0.05352834239602089,
0.002547368174418807,
0.03997110202908516,
0.04003481566905975,
-0.04541192203760147,
0.016779305413365364,
0.05947235971689224,
0.013380547054111958,
-0.002785860560834408,
-0.0010666034650057554,
-0.023437635973095894,
0.01018490456044674,
0.012242579832673073,
0.05129803344607353,
-0.0006278604851104319,
-0.007598480675369501,
0.021004436537623405,
0.008901700377464294,
0.021499449387192726,
0.013980619609355927,
0.0013141407398507,
-0.030204905197024345,
0.0442768856883049,
0.0011775428429245949,
0.014609131030738354,
0.013452508486807346,
0.019125400111079216,
0.005010609980672598,
0.01717786304652691,
0.040005285292863846,
0.002891033887863159,
-0.06137313321232796,
-0.020041365176439285,
-0.03199814632534981,
-0.0586913637816906,
0.048604752868413925,
-0.009355646558105946,
-0.0597328282892704,
0.05247688665986061,
-0.023789508268237114,
0.036393046379089355,
0.02389482595026493,
0.04640845209360123,
-0.04347508028149605,
0.06884738057851791,
-0.014691464602947235,
0.008798268623650074,
0.0020433273166418076,
0.017168698832392693,
0.10260532796382904,
0.03033357299864292,
0.007010604254901409,
-0.07462464272975922,
0.0051478855311870575,
0.0035266070626676083,
0.012735002674162388,
-0.0388723760843277,
0.022519268095493317,
0.003948439843952656,
0.02735498733818531,
-0.012887734919786453,
0.06609980762004852,
-0.03638271614909172,
-0.010099980980157852,
0.07151815295219421,
-0.02426338568329811,
-0.06571029126644135,
-0.03313685953617096,
0.014532030560076237,
-0.007682876195758581,
0.025682568550109863,
-0.059872038662433624,
0.037362560629844666,
-0.028500597923994064,
-0.027331672608852386,
-0.02455173432826996,
-0.04265790060162544,
0.014156259596347809,
-0.009793613106012344,
-0.020701102912425995,
-0.00242722500115633,
0.04052826017141342,
-0.028247730806469917,
-0.06485395133495331,
0.024236364290118217,
0.027524348348379135,
0.0005258219316601753,
-0.0017819511704146862,
-0.00059905817033723,
-0.010854354128241539,
0.017562618479132652,
-0.009218275547027588,
0.04137055203318596,
-0.06619766354560852,
-0.012630107812583447,
-0.015789037570357323,
0.011827358044683933,
0.008558705449104309,
0.0013269750634208322,
0.012225535698235035,
0.012883246876299381,
0.0017291989643126726,
-0.04298768937587738,
-0.0004719097923953086,
0.0059648239985108376,
0.02375977858901024,
-0.03888625651597977,
-0.017127715051174164,
-0.009320405311882496,
0.007298900280147791,
-0.013298951089382172,
0.025831161066889763,
-0.0015066089108586311,
0.018467552959918976,
0.007085795979946852,
-0.015679271891713142,
-0.021500030532479286,
-0.039583779871463776,
0.0025811195373535156,
-0.02463647350668907,
-0.03571723774075508,
-0.04269499331712723,
-0.00625563645735383,
0.017356138676404953,
0.04334673658013344,
0.03221657872200012,
0.01909433864057064,
0.011359445750713348,
0.016947461292147636,
-0.03350366652011871,
0.02492225170135498,
0.0005699248285964131,
-0.029236456379294395,
-0.03132113814353943,
-0.005873302463442087,
0.008688876405358315,
0.04642154276371002,
-0.019946858286857605,
0.027821103110909462,
-0.01464677695184946,
-0.01378759928047657,
0.0026534227654337883,
-0.04564395919442177,
-0.0009111296385526657,
0.027019798755645752,
-0.00005516277815331705,
-0.00181001634337008,
0.005594111513346434,
0.01847023516893387,
0.024640511721372604,
0.0047929552383720875,
-0.01770208589732647,
0.06827239692211151,
-0.03818977624177933,
0.0014564309967681766,
0.011633320711553097,
-0.015086826868355274,
0.028303900733590126,
0.03620254248380661,
0.004280381370335817,
-0.04461154714226723,
-0.03383893519639969,
0.01445792242884636,
-0.0004176566726528108,
0.028917396441102028,
0.05939089134335518,
-0.03989587351679802,
0.05398161709308624,
-0.05161314457654953,
0.020389031618833542,
-0.06607778370380402,
0.0069491141475737095,
-0.09428631514310837,
0.0011084950529038906,
0.003206010442227125,
-0.0013655750080943108,
-0.03618280962109566,
0.01449594646692276,
-0.03627606853842735,
-0.02702910080552101,
0.038104623556137085,
0.007092291954904795,
0.0005568877677433193,
-0.01039896346628666,
0.0421333946287632,
-0.02249009534716606,
0.026733621954917908,
0.01961834728717804,
-0.03759952634572983,
0.036656949669122696,
-0.06423622369766235,
-0.030461570248007774,
-0.0032068155705928802,
-0.04208098351955414,
0.01612594723701477,
0.024476507678627968,
-0.029353808611631393,
-0.011430745013058186,
0.05356423929333687,
-0.017158880829811096,
0.0007378833834081888,
0.00696429843083024,
-0.04993165284395218,
-0.004412097856402397,
0.02497551590204239,
-0.012305991724133492,
0.0068236044608056545,
-0.013024398125708103,
0.05139949917793274,
0.021263645961880684,
-0.009807337075471878,
-0.006902939639985561,
0.009346717037260532,
-0.012371625751256943,
0.04058434069156647,
0.028094274923205376,
0.038466669619083405,
-0.015038819052278996,
0.040058016777038574,
-0.021179474890232086,
0.005073535721749067,
-0.02481471560895443,
-0.0016668945318087935,
-0.07188011705875397,
-0.015083562582731247,
-0.016586720943450928,
-0.020485108718276024,
0.032626863569021225,
0.00603486830368638,
0.017513306811451912,
0.012261664494872093,
-0.03555505722761154,
0.03692960366606712,
-0.04492846876382828,
-0.019758909940719604,
-0.006636722479015589,
-0.020841285586357117,
-0.017154857516288757,
0.04140402749180794,
0.029376206919550896,
0.08025084435939789,
-0.01404473278671503,
0.015538319945335388,
0.002756365342065692,
-0.0019921776838600636,
-0.01580093801021576,
0.04349932074546814,
0.0020681177265942097,
-0.00026752360281534493,
0.08278561383485794,
-0.016946805641055107,
-0.01009251456707716,
0.04276210069656372,
0.012153751216828823,
-0.006405842490494251,
0.013886754401028156,
-0.0008971065399236977,
0.02068517729640007,
0.02446845732629299,
0.0032945536077022552,
-0.006747548468410969,
0.00429665669798851,
0.026244554668664932,
0.010037938132882118,
0.002611426869407296,
-0.029667118564248085,
0.0017811711877584457,
0.0010498827323317528,
-0.04519641026854515,
-0.007298143580555916,
0.003966872580349445,
-0.0384223572909832,
0.0023541904520243406,
-0.016008766368031502,
-0.003585238941013813,
-0.00013764861796516925,
-0.018840167671442032,
-0.029488205909729004,
-0.04562961682677269,
0.0039036362431943417,
0.033178772777318954,
0.008993140421807766,
-0.02328473888337612,
0.04124269634485245,
0.04336569085717201,
0.0024130993988364935,
0.009916413575410843,
0.01754191517829895,
-0.020497018471360207,
-0.02410789206624031,
0.0004641605482902378,
0.05072900280356407,
0.04735702648758888,
-0.004836278967559338,
-0.05558359622955322,
-0.016549667343497276,
0.06159307435154915,
0.017816884443163872,
0.002537255175411701,
-0.03702803701162338,
-0.04085618257522583,
-0.0011465073330327868,
-0.07166092842817307,
0.026365723460912704,
0.026522813364863396,
-0.00784895196557045,
-0.05450921878218651,
-0.019609330222010612,
0.022653385996818542,
0.04500202089548111,
0.04219954088330269,
-0.01282862015068531,
-0.004517838824540377,
0.019234290346503258,
-0.005646668374538422,
0.010413998737931252,
-0.022311775013804436,
0.00417315261438489,
-0.010736304335296154,
-0.04319386929273605,
-0.02158653549849987,
-0.006490384694188833,
-0.02426569163799286,
0.04251609370112419,
0.04228353127837181,
-0.013430921360850334,
0.03142937645316124,
-0.04526541754603386,
-0.04388311505317688,
0.05944296717643738,
0.007943437434732914,
0.012588701210916042,
0.063789002597332,
-0.030940141528844833,
0.022608768194913864,
0.03649582341313362,
-0.019645284861326218,
-0.01103326678276062,
0.04642708599567413,
-0.05480830371379852,
0.021840952336788177,
0.0019836751744151115,
-0.005932206753641367,
0.005567779764533043,
-0.022020289674401283,
-0.006447191350162029,
0.050848837941884995,
0.0028809444047510624,
-0.03992814943194389,
0.05721720680594444,
0.0028486838564276695,
0.022514235228300095,
0.04742595925927162,
0.01119034830480814,
0.02877851016819477,
-0.029704499989748,
0.01160248089581728,
0.06312549859285355,
0.022506916895508766,
0.006969133857637644,
-0.01657172664999962,
0.015158534049987793,
0.00011126894969493151,
0.006554542109370232,
-0.003333762288093567,
0.01602935418486595,
-0.05947088450193405,
-0.051642075181007385,
-0.010531790554523468,
-0.046094860881567,
0.015177215449512005,
0.05046597123146057,
-0.021971125155687332,
0.10083702951669693,
-0.015212374739348888,
0.031013958156108856,
0.03329465538263321,
-0.0004414703871589154,
-0.006967468187212944,
-0.007060735020786524,
-0.032925400882959366,
0.025850731879472733,
-0.005581818521022797,
-0.01839354820549488,
-0.02468084543943405,
-0.016431182622909546,
0.01174695510417223,
-0.030226705595850945,
-0.0032443434465676546,
0.02146056294441223,
-0.00013912294525653124,
-0.008695281110703945,
-0.013982943259179592,
-0.0038025977555662394,
-0.01626477763056755,
0.050231993198394775,
0.030678818002343178,
-0.005439657252281904,
-0.027021894231438637,
0.006474034860730171,
-0.04444914311170578,
0.046495940536260605,
-0.04795874282717705,
0.008929703384637833,
-0.02973814122378826,
0.0026562665589153767,
-0.048912011086940765,
-0.021594803780317307
] |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.